Leibniz's Correspondence in Science, Technology and Medicine (1676 -1701): Core Themes and Core Texts 9004354905, 9789004354906

Citation preview

MEDIE VA L A ND E A RLY MODER N PHIL O S OPH Y A ND S C IENCE

Leibniz’s Correspondence in Science, Technology and Medicine (1676–1701) Core Themes and Core Texts JAMES G. O’HAR A

SERIES EDI TOR C .H. L Ü T H Y

Leibniz’s Correspondence in Science, Technology and Medicine (1676–1701)

Medieval and Early Modern Philosophy and Science Editors C.H. Lüthy (Radboud University) Editorial Consultants Joël Biard (University of Tours) Jürgen Renn (Max-Planck-Institute for the History of Science) Theo Verbeek (University of Utrecht)

volume 39

The titles published in this series are listed at brill.com/memps

Leibniz’s Correspondence in Science, Technology and Medicine (1676–1701) Core Themes and Core Texts By

James G. O’Hara

LEIDEN | BOSTON

Cover illustration: Papin’s submersible vessel (1691). Source: Denis Papin to Christiaan Huygens, August 26, 1691 (Huygens, Oeuvres Complètes, vol. 10, p. 120). Library of Congress Cataloging-in-Publication Data Names: O’Hara, J. G. (James G.), 1948- author. Title: Leibniz’s correspondence in science, technology and medicine  (1676-1701) : core themes and core texts / by James G. O’Hara. Description: Leiden ; Boston : Brill, [2024] | Series: Medieval and early  modern philosophy and science, 2468-6808 ; volume 39 | Includes  bibliographical references and index. Identifiers: LCCN 2023045943 (print) | LCCN 2023045944 (ebook) |  ISBN 9789004354906 (hardback) | ISBN 9789004687363 (ebook) Subjects: LCSH: Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. |  Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716—Correspondence. |  Philosophers—Germany—Correspondence. |  Mathematicians—Germany—Correspondence. Classification: LCC B2598 .O43 2024 (print) | LCC B2598 (ebook) |  DDC 193—dc23/eng/20231101 LC record available at https://lccn.loc.gov/2023045943 LC ebook record available at https://lccn.loc.gov/2023045944

Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/brill-typeface. issn 2468-6808 isbn 978-90-04-35490-6 (hardback) isbn 978-90-04-68736-3 (e-book) DOI 10.1163/9789004687363 Copyright 2024 by Koninklijke Brill BV, Leiden, The Netherlands. Koninklijke Brill BV incorporates the imprints Brill, Brill Nijhoff, Brill Schöningh, Brill Fink, Brill mentis, Brill Wageningen Academic, Vandenhoeck & Ruprecht, Böhlau and V&R unipress. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Requests for re-use and/or translations must be addressed to Koninklijke Brill BV via brill.com or copyright.com. This book is printed on acid-free paper and produced in a sustainable manner.

Contents Preface ix Acknowledgements xvii List of Illustrations xviii Introduction: The Core Themes 1 1 Biographical Background (1676–1701) 4 2 Mathematics 15 3 Natural Philosophy 50 4 Physics 87 5 Energy Conversion, Transmission, Storage and Power Technology 133 6 Engineering 151 7 Projects 167 8 Alchemy and Chemistry 208 9 Earth Sciences: Geology, Mineralogy, Paleontology and Ethnography, Etymology 225 10 Biology and Life Sciences 232 11 Medicine 241

The Correspondence: Core Texts 1 1676–June 1683 271 1 Biographical Background (1676–June 1683) 271 2 Mathematics 279 3 Natural Philosophy and Physics 287 4 Technology: Mining in the Harz District 307 5 Projects: Calculating Machines 312 6 Techno-Economic Projects 314 7 Projects: The Organization of Science 324 8 Alchemy and Chemistry 328 9 Geology, Mineralogy and Paleontology 342 10 Medicine 345 2 July 1683–1690 356 1 Biographical Background (1683–1690) 356 2 Mathematics: Infinitesimal Calculus and Other Issues 358

vi

Contents

3 4 5 6 7 8 9 10 11

Natural Philosophy 362 Physics: Celestial Mechanics, Mechanics, Acoustics, Optics and Sundry Topics 365 Technology: Mining and Power Technology 384 Ballistae – Military Engines and Engineering 399 Engineering Science 402 Projects: Economics and Administration 406 Alchemy and Chemistry 410 Geology, Mineralogy and Paleontology 419 Biology and Medicine 421

3 1691–1693 427 1 Biographical Background (1691–1693) 427 2 Infinitesimal Calculus and Other Mathematics 431 3 Natural Philosophy and Dynamics 450 4 Physics: Celestial and Terrestrial Mechanics 462 5 Physics: Optics 467 6 Engineering Science: Hydromechanics and Mechanics of Fluids 474 7 Projects: Calculating Machines and Cryptography 483 8 Projects: Experiments with Submersible Vessels 487 9 Techno-Economic Projects 496 10 Projects: The Organization of Science 499 11 Medicine 500 4 1694–June 1696 507 1 Biographical Background (1694–June 1696) 507 2 Infinitesimal Calculus and Other Mathematics 509 3 Dynamics and Natural Philosophy 525 4 Physics: Celestial Mechanics, Gravitation 540 5 Physics: Optics 553 6 Power Technology and Mining 566 7 Engineering 572 8 Engineering: Ballistae, Military Engines 575 9 Projects: Mathematical Instruments and Calculating Machines 578 10 Projects: Submersibles, Diving Vessels and Navigation 585 11 Projects: Economics and Trade 591 12 Projects: The Organization of Science and Education 597 13 Medicine and Res Medica 601

Contents

vii

5 July 1696–1698 617 1 Biographical Background (July 1696–1698) 617 2 Mathematics: The Brachistochrone and Isoperimetric Problems 619 3 Mathematics: The Priority Dispute 632 4 Mathematics: Criticism of the Differential Calculus 639 5 Mathematics: Mathematical Textbooks and Sundry Topics 644 6 Natural Philosophy: The Controversy with Papin about “Vis Viva” and “Actio” 646 7 Physics: Optics 682 8 Power Technology 685 9 Civil Engineering, Garden Design and Architecture 698 10 Other Engineering Enterprises 703 11 Process or Chemical Engineering 709 12 Projects: Cryptography 713 13 Projects: Brandy Distillation 716 14 Alchemy and Chemistry 721 15 Paleontology and Earth History 723 16 Biology 726 17 Medicine 733 6 1699–1701 744 1 Biographical Background (1699–1701) 744 2 Mathematics 746 3 Natural Philosophy 757 4 Physics 775 5 Astronomy and Calendar Reform 782 6 Power Technology 800 7 Engineering: Manufactories 804 8 Projects: Calculating Machines 814 9 Projects: the Berlin Society of Sciences and the Organization of Science 818 10 Alchemy 829 11 Geology, Mineralogy, Paleontology, Ethnography and Etymology 840 12 Biology 844 13 Medicine 850

viii Epilogue: Core Theses and Conclusion 861 1 The Ten Theses 861 2 Conclusion and Concluding Thesis 897 Bibliography 901 Index of Names 958 Index of Subjects 968

Contents

Preface Leibniz’s correspondence in mathematics, science and technology is being edited and published in Series III of the German Academy Edition of all of his writings and letters.1 The first volume of the third series covering the period of Leibniz’s sojourn in Paris (1672–1676) was edited by Joseph Ehrenfried Hofmann (1900–1973) and published posthumously in 1976, and in a revised form in 1988.2 Hofmann was a scholar  – whose specialist interest was the development of Leibniz’s infinitesimal calculus during the Paris period – and the author of Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672–1676), published in 1949,3 and of Leibniz in Paris 1672–1676 – his growth to mathematical maturity, published in 1974 and reprinted in 2008.4 The overriding interest in mathematics in the first volume of the series meant that the systematic presentation of Leibniz’s correspondence in science, technology – a term that was used for the first time in the modern sense more than 60 years after Leibniz’s death – and medicine only began with the publication of the second volume in 1987, which covered Leibniz’s first years in Hanover from 1676 to 1679.5 Subsequent volumes of the series then appeared in 1991, 1995, 2003, 2004, 2011 and 2015, covering Leibniz’s life to the year 1701.6 The present work aims to present in English central themes, and central texts, from Leibniz’s correspondence in science, technology and medicine derived mainly from the first eight volumes of Series III of the Academy Edition. Chapter 1 presents key texts published (for the most part) in the first three volumes of the series. Each one of the following five chapters (Chapters 2 to 6) then presents texts published (again for the most part) in a specific volume of the series (volumes 4 to 8). The author of the present work (writing here in the third person) has coedited the texts of (and coauthored the introductions to) the latter five volumes. However, the ideas and interpretations presented 1 The Academy Edition of all of Leibniz’s writings and letters (A) = G. W. Leibniz, Sämtliche Schriften und Briefe, published by the Prussian, later German, and most recently BerlinBrandenburg Academy of Sciences, together with the Academy of Sciences in Göttingen, Darmstadt (later Leipzig, most recently Berlin), 1923–; to date (end of 2022) 64 volumes in 7 series (I–IV, VI–VIII) have been published. 2 A III,1 = Academy Edition, ser. III, vol. 1. 3 J. E. Hofmann, Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672–1676), Munich, 1949. 4 J. E. Hofmann, Leibniz in Paris 1672–1676 – his growth to mathematical maturity, London and New York, 1974 and 2008 (reprint). 5 A III,2. 6 A III,3–8.

x

Preface

here in the introduction, and in the text presentations, are the outcome of the joint editorial ‘spadework’ undertaken in cooperation with a range of former colleagues over a period of twenty six years spent at the ‘Leibniz-Archiv’, the editorial and research center at the ‘Gottfried Wilhelm Leibniz Bibliothek’, the State Library of the German federal state of Lower Saxony, in Hanover. A play on words, a pun around the German word ‘Band’ (meaning volume), gave rise within the editorial team to the designation ‘Bandleader’ (bandleader or band leader) for the most senior colleague working on a particular volume. In this vein then, mention must be made here of the ‘band leaders’ whose ideas and interpretations find expression in the present work (albeit in translation by the author), namely Herbert Breger (Volume 3), Heinz-Jürgen Heß (Volumes 2, 4, 5 and 6), and Charlotte Wahl (Volume 8). The author of the present work then had the honor to act as a ‘big band leader’ for Volume 7 (with more than 1000 printed pages), covering the period of the greatest density of Leibniz’s correspondence in mathematics, science and technology, namely from July 1696 to December 1698. Besides the ideas and interpretations of the ‘band leaders’ referred to here, those of other former colleagues who worked on the volumes of Series III may possibly also be found in the present work, namely Ralf Krömer and Heike Sefrin-Weis (Volume 7) and Uwe Mayer (Volume 8). If the play on words, or pun, around the German word ‘Band’ be applied to the present volume, then the author must surely be seen in his role as a ‘broad band leader’ and architect of a volume in which there is a shift away from a predominance of mathematics, with scientific subject areas now becoming more prevalent. While mathematics retains its pivotal (or pole) position in many respects, nine other scientific or scholarly subject areas have been identified and included alongside mathematics. The present ‘broad band’ represents, as it were, a decathlon of the history of science and technology at the end of the seventeenth century, with the ‘broad band leader’ assuming the role here of an editorial decathlete. The author’s penchant for a ‘broad-band’ approach is attributable, on the one hand, to a scholarly background in engineering, engineering science and the history of science and technology (rather than mathematics and history of mathematics, or philosophy and history of philosophy) and, on the other hand, to a latitudinal early academic career development (spent for the most part in western Europe along or near the 53rd parallel north, or circle of latitude), specifically at the National University of Ireland, the former University of Manchester Institute of Science and Technology (UMIST), the former ‘Technische Hogeschool Delft’, and the former ‘Institut für Socialund Wirtschaftsgeschichte’, the then center for social and economic history, and history of technology, at the University of Hamburg. Although not primarily concerned with Leibniz or his correspondents, the works of a number

Preface

xi

of former mentors, influencers and colleagues are cited in the footnotes, and listed in the Bibliography. These include James Dooge (history of fluid mechanics after Galileo), Donald Cardwell (thermodynamics in the early industrial age), Richard Hills (history of power technology), Alan Williams (medieval and early-modern arms and armor), Emrys Evans (Celtic studies), Olaf Pedersen and Maureen Farrell (early physics and astronomy, and the historical interaction between science and religion), Volker Bialas (Kepler Edition), specialists in Christiaan Huygens studies from the years between the Huygens anniversary celebrations in 1979 and 1995 (including Henk Bos, Joella Yoder, Jan van Maanen), and Ulrich Troitzsch (technological thought in the late seventeenth and eighteenth centuries). Although not intended as a biography of Leibniz, the Introduction and the six chapters present factual and chronological biographical information, which is intended to serve as a frame of reference for his interaction with his correspondents and which in turn may serve as a basis for Leibniz biographical and chronological studies in the future.7 The work Leibniz: A biography of the historian of mathematics and physics, Eric J. Aiton (1920–1991), was for the author of the present work the first real introduction to Leibniz studies.8 Having first encountered the biographer at the University of Manchester in the mid-1970s, it was a pleasure to have discussions with him in Germany at the end of the following decade. However, Aiton’s biography was published at the time when only the first volume of Leibniz’s correspondence in mathematics, science and technology had been published. A further issue is the fact that the sum total of Leibniz’s correspondence covers many more scholarly fields than those scientific areas treated in the present work, as for example the fields of logic, metaphysics, ethics, jurisprudence, political and social philosophy, and history (to name just those alluded to by a peer reviewer of the present work) and which of course are central aspects for biographers of Leibniz like, for example, Maria Rosa Antognazza.9 At all events, the author of the present work would argue that Leibniz, following studies and academic qualification in philosophy and jurisprudence, first became a scientist – an alchemist or chemist,10

7

Cf., for example, K. Müller, G. Krönert (eds.), Leben und Werk von G. W. Leibniz: Eine Chronik, Frankfurt am Main, 1969. 8 E. J. Aiton, Leibniz: A biography, Bristol and Boston, 1985 and Gottfried Wilhelm Leibniz: Eine Biographie, Frankfurt am Main, 1991. 9 M. R. Antognazza, Leibniz: An intellectual biography, New York, 2008. 10 That is, prior to the denigration of alchemy, an attitude that first began to take hold in the eighteenth century; cf. p. 105 in: N. Guicciardini, Isaac Newton and natural philosophy, London (and Chicago), 2018.

xii

Preface

who in 1667 was secretary of an alchemical society in Nuremberg,11 and who contemplated at that time editing the works of renowned alchemists – before becoming a jurist, mathematician, engineer, scientist and philosopher. If the years 1672–1676 marked (in the words of Hofmann) Leibniz’s growth to mathematical maturity, the years 1676–1701 surely marked his growth to maturity in a range of scientific disciplines. The raison d’être then of the present work is accordingly – following in the footsteps of Eric Aiton – to lay on the foundation of Leibniz’s correspondence the groundwork for a more pronounced scientific dimension in future Leibniz biographical studies. In this sense too, the ten ‘theses’ presented in the epilogue – each arising within one of the ten subject areas considered, and each epitomized by a leading quotation, reflecting Leibniz’s ambitions and intentions in that field – should be seen. Leibniz’s correspondence reveals his fundamental standpoint that, although mathematics and the sciences are rooted in metaphysics, or (to use the formulation of the author’s former colleague at the Leibniz edition, Hartmut Hecht) are within the paradigm of metaphysics,12 one cannot use metaphysics to explain the physical world (or universe) and its laws. In view of the traditional proximity of paradigms and scientific revolutions,13 in the history of science and mathematics,14 the author of the present work suggests an alternative paradigm, or framework, which might be formulated as ‘Gottfried Wilhelm Leibniz’s Correspondence: Science, Technology and Medicine within the paradigm of the Scientific Revolution’. Leibniz’s correspondence reveals him not just as a philosopher, but also as a scientist in the tradition of major figures of the Scientific Revolution of the seventeenth century, which saw the replacement of qualitative scholastic Aristotelian natural philosophy by quantitative mechanistic Newtonian mathematical physics and the evolution of ‘Classical

11 Cf. G. MacDonald Ross, “Leibniz and the Nuremberg alchemical society”, Studia Leibnitiana, vol. 6(2), (1974), pp. 222–248. 12 Cf. H. Hecht, Gottfried Wilhelm Leibniz: Mathematik und Naturwissenschaften im Paradigma der Metaphysik, Stuttgart, Leipzig, 1992. In the context of this ‘paradigm of metaphysics’, see also for example: R. T. W. Arthur, Classic thinkers: Leibniz, Cambridge, UK, and Malden, MA, 2014. 13 Cf. T. S. Kuhn, The structure of scientific revolutions, Chicago, 1962, 1970, 1996, and 2012; see chap. V (The priority of paradigms); T. S. Kuhn, The Copernican revolution: Planetary astronomy in the development of western thought, Cambridge, MA, 1957 and 1992. 14 In this context, cf. R. C. Brown, The tangled origins of the Leibnizian calculus: A case study of a mathematical revolution, Singapore, New Jersey, London, 2012; see in particular chap. 1, pp. 1–14 (Evolution or revolution in mathematics: The case of Leibniz), and chap. 11, pp. 231–244 (Some concluding remarks on mathematical change).

Preface

xiii

Science’.15 The Scientific Revolution likewise saw the appearance of a group of outstanding scientists and mathematicians, which included Johannes Kepler, Galileo Galilei, René Descartes, Pierre de Fermat, Christiaan Huygens, Isaac Newton,16 and of course Leibniz himself, and which pursued an envisioned goal – that followed from Galileo’s new conception of the task of science and that was in accordance with the explicit statement by Newton of the mathematical principles of natural philosophy (in the title of his magnum opus) – of discovering the mathematical relations that hold for the physical world (or universe).17 As regards philosophy, Leibniz appears at times to be at odds not just with Cartesian philosophy, but with metaphysics as such. Specifically he appears to follow in the footsteps of Galileo as an engineer and proponent of rational thought and experimental science.18 Leibniz even expressed his standpoint (in a letter to Friedrich Hoffmann on November 1, 1701) that, in higher education, a single lesson (or lecture hour) in experimental science had a greater value for him than a hundred corresponding lessons in metaphysics, logic, or ethics. Drawing inspiration from the book Christianity not mysterious (1696) of the Irish “heretic” John Toland,19 one who, having fallen out with the Catholic Church, subsequently fell foul of the Irish Protestant Ascendancy, before going on to become a “persona non grata” in Hanover,20 and with the perception that 15 Cf. E. J. Dijksterhuis. De mechanisering van het wereldbeeld, Amsterdam, 1950, 1983, 1998, and 2006: E. J. Dijksterhuis (C. Dikshoorn, trans.), The mechanization of the world picture, Oxford, London, New York, 1961, 1969, and Princeton, 1986; see Part IV (The evolution of classical science). 16 Cf. for example: I. Bernard Cohen, The Newtonian revolution with illustrations of the transformation of scientific ideas, Cambridge and New York, 1980 and 1983; H. F. Cohen, The scientific revolution: A historiographical inquiry, Chicago, 1994; J. Henry, The scientific revolution and the origins of modern science, Basingstoke, New York, 1997; J. C. Boudri (S. McGlinn, trans.), What was mechanical about mechanics: The concept of force between metaphysics and mechanics from Newton to Lagrange, Dordrecht, 2002; see chap. 1, pp. 5–8 (The horizon of the scientific revolution). 17 Cf. M. Kline, Mathematics in western culture, Oxford, London, New York, 1953 and 1964; see chap. 16 (The Newtonian influence: Science and philosophy), in particular p. 237. 18 Cf. M. Valleriani, Galileo engineer (Boston Studies in the Philosophy of Science, vol. 269), Dordrecht, Heidelberg, London, New York, 2010. 19 Cf. J. G. Simms, “John Toland (1670–1722), Donegal heretic”, Irish Historical Studies, vol. 16, no. 63, (March 1969), pp. 304–320; M. Brown, A political biography of John Toland, Oxford, New York, 2012, and in particular chap. 1 (Ireland, 1670–1697), chap. 2 (London, 1697–1700), and chap. 3 (Hanover, 1701–1707). 20 Cf. N. Gädeke, “Matières d’esprit et de curiosité oder: Warum wurde John Toland in Hannover zur persona non grata?”, pp. 145–166, in: W. Li, S. Noreik (eds.), G.W. Leibniz und der Gelehrtenhabitus: Anonymität, Pseudonymität, Camouflage, Cologne, Weimar, Vienna, 2016.

xiv

Preface

Leibniz’s standpoint (namely that, although mathematics and the sciences are rooted in metaphysics, one cannot use metaphysics to explain the physical world) mirrors Toland’s deistic, rationalistic, and controversial standpoint (namely that, although God created the world, there was no subsequent divine interaction with, or direct intervention in, that created world),21 the author of the present work coined the title ‘Science not metaphysical’ for an earlier publication on Galileo’s influence on Leibniz, which was also intended as a plea for a research and editorial approach to the edition of Leibniz’s correspondence in mathematics, science and technology, within the framework of the academic field of history of science and technology, and embracing the paradigm of the scientific revolution, rather than that of metaphysics.22 In the history of science and religion, following the triumph of CopernicanGalilean heliocentrism,23 geological, geomorphological, cosmological, and cosmogenic theorizing then served – in the time of Newton and Leibniz – to greatly undermine the strict historical veracity of Biblical narrative.24 And so the interaction between science and religion in the early-modern period led ultimately, in the words of Olaf Pedersen, to a “divorce of science and

21 Cf. J. Toland, Christianity not mysterious, or a treatise shewing, that there is nothing in the Gospel contrary to reason, nor above it, and that no Christian doctrine can properly be call’d a mystery, London, 1696; P. Mc Guinness, A. Harrison, R. Kearney (eds.), John Toland’s Christianity not mysterious: Text, associated works and critical essays, Dublin, 1997. Regarding Leibniz’s thought on divine creation, see for example N. G. Robertson, “The doctrine of creation and the enlightenment”, pp. 425–439, in: R. D. Crouse, W. Otten, W. Hannam, M. Treschow (eds.), Divine creation in ancient, medieval, and early modern thought, Leiden, Boston, 2007. 22 Cf. J. G. O’Hara, “Science not metaphysical: Leibniz als Naturwissenschaftler in der Nachfolge von Galilei”, pp. [33]–56 in: M. Kempe (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung, vol. 1, 2013. 23 Cf., for example, O. Pedersen, Early physics and astronomy: A historical introduction, Cambridge, 1974 and 1993, chap. 20 (The reform of astronomy), and in particular pp. 263–282 (Nicolaus Copernicus, and after Copernicus); F. Krafft, “Die Copernicanische Revolution”, Antike und Abendland, vol. 40, (1994), pp. 1–30 (Reprinted as pp. 181–214 in: H. Kuester (ed.), Das sechzehnte Jahrhundert: Europäische Renaissance, Regensburg, 1995); M. A. Finocchiaro, Defending Copernicus and Galileo: Critical reasoning in the two affairs (Boston Studies in the Philosophy of Science, vol. 280), Dordrecht, Heidelberg, London, New York, 2010; J. L. Heilbron, Galileo, Oxford, 2010. 24 Cf. I. Leask, “Constant process: The science of Toland’s pantheisticon”, Eighteenth-Century Ireland/ Iris an dá chultúr [Ireland of the two cultures], vol. 34, (2019): pp. 11–27, in particular p. 16.

Preface

xv

religion”.25 Pedersen has, for example, likewise described Leibniz’s meeting with the Danish physician, geologist, and Catholic theologian Nicola(u)s Steno (Niels Stensen) in Hanover, on December 7, 1677,26 as the meeting of a “Scientist and [a] Saint”, of a “Rationalist” and a “Faithful Observer”, and which was the overture perhaps to their extensive scientific, philosophical, and theological exchanges.27 In the light of this divorce of science and religion, Leibniz chose, in treating the physical world, to take the low road, as it were, of enlightenment, and of rational thought and scientific rationalism,28 rather than the high road, so to speak, of mysticism, religion and theology.29 In this sense then Leibniz stands apart from contemporaries like Robert Boyle, Isaac Newton, William Whiston, and others, who have been broadly characterized as ‘scientist-theologians’, or as advocates of a physico-theology, and who were inspired by a sense of compatibility of science and religion.30 Accordingly, following the concluding thesis of this work – which underlines Leibniz’s role both in the development of rational scientific thought in the last quarter of 25 Cf. O. Pedersen, “The divorce of science and religion: Historical interaction between science and religion”, pp. 139–160, in: J. Fennema, I. Paul (eds.), Science and religion: One world – Changing perspectives on reality, Dordrecht, Boston, London, 1990. 26 Cf. K. Müller, G. Krönert, 1969 (note 7), p. 50. 27 Cf. A. Vibeke Vad, “Polidore and Théophile: The rationalist and the faithful observer”, pp. 39–47 (in particular p. 39) in: K. Ascani, H. Kermit, G. Skytte (eds.), Niccolo Stenone (1638–1686): Anatomista, geologo, vescovo, Atti del seminario organizzato da Universitetsbiblioteket i Tromsø e l’Accademia di Danimarca lunedi 23 ottobre 2000 [Proceedings of a Conference on October 23, 2000], (Analecta Romana Instituti Danici, Suppl. XXXI), Rome, 2002; H. Kermit, M. Drake (trans.), Niels Stensen 1638–1686: The scientist who was beatified, Leominster, Herefordshire, UK, 2003; R. Andrault, M. Lærke (eds.), “Leibniz and Steno, 1675–1680”, chap. 3 (pp. 63–84), in: R. Andrault,  M. Lærke (eds.), Steno and the philosophers (Studies in Intellectual History, vol. 276), Leiden, 2018. 28 Cf. M. Dascal (ed.), Leibniz: What kind of rationalist? Logic, epistemology, and the unity of science, vol. 13, Dordrecht, 2009; see in particular pp. 1–13 (Introduction) and pp. [83]–152 (Part II: Natural sciences and mathematics). 29 Cf., for example, G. MacDonald Ross, “Leibniz and the origin of things”, Part III (Theology and mysticism), chap. 17 (pp. [241]–257) in: M. Dascal, E. Yakira (eds.), Leibniz and Adam, Tel Aviv, 1993; A. P. Coudert, R. H. Popkin, G. M. Weiner (eds.), Leibniz, mysticism and religion (International archives of the history of ideas, no. 158), Dordrecht, Boston, London, 1998; L. Strickland (ed.), Leibniz on God and religion: A reader, London, 2016. 30 Cf. R. Jakapi, “Early modern natural philosophy allied with revealed religion: Boyle and Whiston”, part IV, chap. 19 (pp. 233–244), in: M. Fuller, D. Evers, A. Runehov, K.-W. Sæther, B. Michollet (eds.), Issues in science and theology: nature and beyond: Transcendence and immanence in science and theology, Cham, Switzerland, 2020; A. Wragge-Morley, Aesthetic science: Representing nature in the Royal Society of London, 1650–1720, Chicago, 2020, in particular Sect.1 (Physico-theology, natural philosophy, and sensory experience).

xvi

Preface

the seventeenth century, and in an adherence to the principle of the separation of science and religion  – and considering also his autobiographical self-characterization of his tiger-like vivacity and sprightly manners (in his letter to Rudolf Christian von Bodenhausen on December 30, 1693), the last line of the Epilogue may be seen as the unofficial title of this book.

Acknowledgements I wish to thank my former colleagues and the present staff of the ‘Leibniz-Archiv’, the Leibniz editorial and research center, at the ‘Gottfried Wilhelm Leibniz Bibliothek’ in Hanover for their assistance and support in the preparation of this book. I am grateful to the ‘Gottfried Wilhelm Leibniz Bibliothek’, the main repository of the literary estate of Leibniz, and in particular of the manuscript letters cited, paraphrased, quoted and translated in this work, for access to its historical rare book and manuscript collections over more than three decades. All of the letter texts cited, quoted, and translated have been previously published (or cited) in the volumes of the Leibniz Academy Edition. I am grateful to the ‘Gottfried Wilhelm Leibniz Bibliothek’, and to the Leibniz Edition, for permission to cite, quote and translate the texts presented here. I am particularly grateful to Michael Kempe, the present head of the ‘Leibniz Archiv’, for his encouragement and practical support in the preparation of this volume. Among other things, I am grateful for access to the retro-digitized versions of older volumes of the Leibniz Edition. An earlier version of this work was circulated among the present staff members of the series III (Leibniz’s correspondence in mathematics, science and technology) and series VII (Leibniz’s mathematical writings) of the editorial project. I am grateful for the comments, corrections and improvement suggestions received in return, particularly from Siegmund Probst and Hartmut Hecht, the present and former heads of the series VII and VIII (Leibniz’s scientific writings), respectively. Other feedback from former colleagues and visitors in Hannover, such as the doctoral student Arthur Caillé (Rennes 1 University in France), was much appreciated. I am also grateful for the encouraging and constructive comments, and suggestions, of the three anonymous peer reviewers, as well as those of the Editorial team at Brill in Leiden, and in particular for the editorial assistance provided by Rosanna Woensdregt, and by her colleagues Simona Casadio, Alessandra Giliberto and Theo Joppe. James Gabriel O’Hara Hameln, December 2022

Illustrations All of the items in the following list of illustrations (with the exception of the first and the last) have been drawn by the author following the figures in the original manuscripts using the Adobe Illustrator graphics design and drawing program. All these drawings have previously been published in the volumes of the Leibniz Academy Edition. The first and last items are facsimile copies taken from the Oeuvres Complètes de Christiaan Huygens and the Leibniz Academy Edition, respectively. 1 Papin’s submersible vessel (1691) 492 2 Papin’s mechanical thought experiment 529 3 Leibniz’s engineering thought experiment 531 4 Leibniz’s sketch of a damaged rod-engine transmission line 568 5 Leibniz’s drawing illustrating Johannes Teyler’s method of calculating the quantity of fire power in a fortification array 575 6 Sketch of Papin’s thought experiment regarding the substitution or replacement of a body by a surrogate body during a two-body collision 652 7 Another sketch of Papin’s thought experiment regarding the substitution or replacement of a body by a surrogate body during a two-body collision 654 8 Yet another sketch of Papin’s thought experiment regarding the substitution or replacement of a body by a surrogate body during a two-body collision 655 9 Sketch of Papin’s thought experiment to demonstrate the equivalence of separate collisions of a body with two other bodies 657 10 Sketch of Leibniz’s thought experiment regarding the collision of a body moving along the diameter of a square with two other bodies resting at a corner 665 11 Sketch of Leibniz’s design for sealing, or making airtight, the contact between a piston and a pump cylinder 691 12 Papin’s drawing of his new blast furnace 706 13 Sketch of Leibniz’s thought experiment regarding the collision of a body moving along the diameter of a square with two other bodies resting at a corner 759 14 Papin’s sketch of the thought experiment regarding the collision of three spheres at a corner of a square 760 15 Sketch of Leibniz’s physical thought experiment regarding the operating principle of the barometer 777 16 Drawing of Francesco Maria Levanto’s reverberation furnace 805 17 Drawing of Jobst Heinrich Voigt’s threshing-machine 810

Introduction: The Core Themes Scripsi innumera, et de innumeris, sed edidi pauca et de paucis.1 Leibniz to Jacob Bernoulli, Early April 1697

∵ Leibniz’s correspondence in science, technology and medicine in the twenty five year period from 1676 to 1701, which consists of more than 2000 letters to, from or between more than 200 correspondents, has been edited and published in the Leibniz Academy Edition, providing a total of more than 5000 printed or digitized pages. These letters from the period between 1676 and 1701 represent less than a fifth of Leibniz’s total correspondence and but a fraction of his total extant manuscript collection.2 Leibniz’s remark (quoted above) to Jacob Bernoulli in early April 1697 to the effect that, while he had written countless texts on countless topics, he had published but sparsely on a sparsity of such topics, epitomizes the nature of his literary estate. More than ninety per cent of the letters considered here have appeared in the volumes of the third series (Correspondence in Mathematics, Science and Technology) whereas less than ten per cent have been published either in the volumes of the first series (General Political and Scholarly Correspondence) like, for example, much of Leibniz’s correspondence relating to mining in the Harz mountains, or of the second series (Philosophical Correspondence) like, for example, his correspondence in 1671–1672 with Otto von Guericke. Among Leibniz’s correspondents in the area of science, technology and medicine, besides the mathematician Johann Bernoulli, four individuals stand out in terms of the volume and significance of their correspondence with him, namely Johann Daniel Crafft, Christiaan Huygens, Denis Papin and Ehrenfried Walter von Tschirnhaus. The twenty-five year period of Leibniz’s life under consideration (1676 to 1701) consists of two periods of eleven and a half years separated by that of his 1 Translation: I have written countless texts on countless topics, but I have published but sparsely on a sparsity of such topics. Source: A III,7 N. 88, p. 364 = G. W. Leibniz, Academy Edition (A), ser. III, vol. 7, item (letter) no. 88, p. 364. 2 Cf. J. G. O’Hara, “‘A chaos of jottings that I do not have the leisure to arrange and mark with headings’. Leibniz’s manuscript papers and their repository”, chap. 10 (pp. 159–170) in: M. Hunter (ed.), Archives of the Scientific Revolution: The formation and exchange of ideas in seventeenth-century Europe, Woodbridge, UK & Rochester, NY, 1998.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_002

2

Introduction: The Core Themes

grand tour of Germany, Austria and Italy (from November 1687 to June 1690). This Introduction (which presents the core themes of the correspondence) is followed by six chapters (which present core texts from the letters) and an Epilogue (which presents ten theses from ten subject areas, based on formulations by Leibniz himself, and the main conclusions). Chapter 1 covers almost seven years in Leibniz’s life, starting in 1676 with the conclusion (in early October) of his four-year stay in Paris, his second London sojourn (arrival there on October 18), his onward sea journey to Holland and his arrival in Amsterdam on November 13 (where he met Jan Swammerdam and Jan Hudde), his tour to Haarlem, Leiden, Delft (where he met Antoni van Leeuwenhoek) and the Hague (where he met Baruch de Spinoza), his onward journey to Germany and arrival in Hanover in the last days of 1676.3 The year 1676 also saw the commencement of Leibniz’s indirect correspondence with Isaac Newton through an intermediary, namely the secretary of the Royal Society Heinrich (or Henry) Oldenburg. This took the form of a consignment sent by Oldenburg to Leibniz from London, on August 5, 1676,4 and Newton’s letter from Cambridge to Oldenburg for Leibniz of November 3, 1676.5 Chapter 2 covers Leibniz’s correspondence over a period of seven and a half years from mid-year 1683 until the end of 1690. The chapters 3 through 6 cover the eleven years with the greatest density of Leibniz’s correspondence in science, technology and medicine, from 1691 to 1701. Chapter 3 encompasses a thirty-six month period (1691–1693) whereas chapters 4 and 5 each cover periods of just thirty months, January 1694 to June 1696 and July 1696 to December 1698, respectively. Chapter 6 covers the final thirty-six month period (1699–1701). Leibniz’s correspondence is multilingual. He himself wrote letters and texts in Latin, French or German; his correspondents wrote in these languages but sometimes also in Italian (like the Swedish physician Magnus Gabriel Block), in Dutch (like the Danish mathematician Jørgen or Georg Mohr) or in English (as in the case the physician and chemist Friedrich Slare who refrained from writing Latin following Leibniz’s request for him to do so). The core texts presented in chapters 1 through 6 are introduced, translated or paraphrased in English and quoted in the original language in the footnotes. Sometimes Leibniz and his correspondents provided dates for their communications according to the Julian Calendar (old style, stilo veteri, s. v.) while, on other occasions, the Gregorian Calendar (new style, stilo novo, s. n.) was followed or, sometimes, 3 Cf. E. J. Aiton, Leibniz: A biography, Bristol and Boston, 1985; Gottfried Wilhelm Leibniz: Eine Biographie, Frankfurt am Main, 1991, in particular pp. 66–70 (English edition). 4 A III,1 N. 88, pp. 430–558. 5 A III,2 N. 38, pp. 83–116.

Introduction: The Core Themes

3

double dates were provided. Throughout the present work all dates are quoted or arranged chronologically according to the Gregorian Calendar following the practice of the Leibniz Academy Edition. Thus, the chronology of events presented in this Introduction, and the texts presented in chapters 1 through 6, all follow the Gregorian Calendar. The form of the dates given or quoted in the present work follows that used by a number of Leibniz’s correspondents living in England in the late seventeenth century. Thus, Isaac Newton in his letter sent to Heinrich (or Henry) Oldenburg for Leibniz provided the address and date in the form “Cantabr. Octob. 24 1676”; on another occasion another English correspondent, John Wallis, provided this information in the form “Oxoniae, Jan. 16 1698/9 stilo Angliae”; a third correspondent, Hans Sloane, for example, chose the form “London Apr. 27. 1700. s. v.”. In the present work then (as in the Leibniz Academy Edition), these addresses and dates are given or quoted as “Cambridge, November 3, 1676”, “Oxford, January 26, 1699”, and “London, May 8, 1700” (viz. ‘stilo Americae’). Each of the ten subject headings in this introduction, and each of the following six chapters, is provided in the heading with a pertinent quotation from Leibniz. These quotations are the basis for the ‘theses’ presented in the Epilogue; each represents a main idea, opinion, or theory of Leibniz. These quotations, and all the core texts presented in chapters 1 through 6, as well as the primary and secondary printed sources cited have been verified and are provided with references in the footnotes. The themes in Leibniz’s correspondence in science, technology and medicine are introduced here under the following eleven headings: 1. Biographical Background (1676–1701) 2. Mathematics (Calculus, Special Problems, Number Systems) 3. Natural Philosophy (Dynamica, the “Vis Viva” Controversy) 4. Physics (Abstract and Concrete; Theoretical and Applied); Influence of Galileo, Boyle, Mariotte; Laws of Motion; Astronomy; Celestial and Terrestrial (Newtonian) Mechanics; Terrestrial Magnetism; Meteorology; Theory of Matter; Elasticity; Sound and Acoustics; Strength of Materials; Motion in Resisting Media; Optics, Theories of Light, Catoptrics, Dioptrics, Optical Instruments, Microscopy 5. Energy Conversion, Transmission, Storage and Power Technology; Mining and Transportation 6. Engineering: Ballistae or Military Engines; Civil Engineering; Engineering Manufactories; Process Engineering; Engineering Science (Mechanics of Fluids) 7. Projects: Calculating Machines and Cryptography; Military-related Projects like the development of submarine vessels; Economic Projects; Organization of Science and Education

4

Introduction: The Core Themes

8. 9.

Alchemy and Chemistry Geological and Earth Sciences: Geology, Mineralogy, Paleontology; Ethnography and Etymology 10. Biology and the Life Sciences 11. Medicine: Anatomy, Physiology, Pathology; Therapeutics, Pharmacology, Epidemiology, Demography; the Medical Profession, Mathematization and Rationalization. 1

Biographical Background (1676–1701) Mir gehet es wie dem tiegerthier, von dem man sagt, was es nicht im ersten andern oder dritten sprung erreiche, das laße es lauffen.6 Leibniz to Rudolf Christian von Bodenhausen, December 30, 1693

1.1 The Period from 1676 to Mid-1683 Leibniz’s correspondence in mathematics, science and technology between November 1676 and December 1679 – with almost fifty individuals including Johann Daniel Crafft, Christiaan Huygens, Jean Paul de La Roque, Edme Mariotte, Heinrich or Henry Oldenburg and Ehrenfried Walther von Tschirnhaus – documents a phase of development of his thought and action which, following four years of rich intellectual creativity and of independence in Paris, was directed towards the exact sciences and shaped by the circumstances at the ducal residence in Hanover. His correspondence in mathematics, science and technology in the subsequent three and a half years, between 1680 and June 1683, then increased to encompass more than sixty individuals and included the continuing correspondences with Crafft, Mariotte, and Tschirnhaus. Important aspects of Leibniz’s biography in the early 1680s included his continuing duties in the service of the Hanoverian court. However, the beginning of the year 1680 marked an important change in this respect. With the death of duke Johann Friedrich (on December 28, 1679) he had lost a prince with scholarly interests and an open-minded conversation partner and a supporter of his fervidly pursued windmill project for the improvement of the efficiency of the ore mines in the Harz mountains. He was however soon able to count on the continuation of his standing at court and his appointment as court counselor and librarian under the new duke Ernst August but he was

6 A III,5 N. 201, p. 672. Translation: I am like the tiger, of which it is said, that it will let its prey escape if it does not catch it in one, two or three leaps.

Introduction: The Core Themes

5

never able to establish a similar bond of trust with Ernst August as had previously existed with Johann Friedrich. In contrast to his predecessor, Ernst August was in the main interested in political rather than in scholarly matters. A striking example for this is seen in the contentious discussions about the Douceur cast-iron process. Leibniz had purchased during the reign of Johann Friedrich, and with his mandate, a process for the ostensible production of malleable cast iron from the French engineer Noel Douceur, a process that was considered to have particular value in the production of canons. However – not least due to the lack of qualified technical personnel in Hanover – it proved not to be possible to appropriately verify the process within a reasonable period of time. Douceur received half of the purchase price of 1000 livres at once and the other half was entrusted to Mariotte in order to be paid out once the process had been successfully tested. A difficult situation then ensued for Leibniz when Ernst August refused to sanction the payment of the outstanding sum. Leibniz was accused of having induced the deceased predecessor into superfluous expenditure, since, it was claimed, Prince Rupert of the Rhine (1619–1682) was already in possession of a similar or even better process for tempering iron. The somewhat inept Douceur had the good fortune to have the backing of a powerful advocate in the guise of the trustee Mariotte who vigorously pressed his claim. Following Leibniz’s request Mariotte reappraised the process and arrived at a (for Douceur) positive result which in turn put Leibniz in a very difficult situation. A number of compromise suggestions were to be of no avail and Mariotte refused to act as a broker or creditor for the impoverished Douceur and continued to refer to his own verification of the process. In the end, Leibniz conceded and a further installment of 400 livres was paid out – unbeknown to the Hanoverian court – to Douceur on March 17, 1682. The outstanding dues of 100 livres were only paid out in 1685. In the first year of the reign of Ernst August, Leibniz also undertook two attempts to persuade his new master to cover expenditure for scientific purposes. Firstly, Leibniz was interested in a fuming liquid – which was discussed in correspondence with Günther Christoph Schelhammer – and, secondly, he wished to purchase an exemplar of Denis Papin’s steam digester, the precursor of the modern pressure cooker and he corresponded with Frederick Slare about the matter. In both cases the purchase did not materialize and the duke appears to have reacted, if at all, with skepticism or disapproval. In addition, the continuing lack of success of his windmill project in the Harz mountains surely proved all the more bitter for him. Leibniz was unusually often away from Hanover in the early 1680s and besides his regular journeys to the Harz mountains in connection with the

6

Introduction: The Core Themes

windmill project, other destinations included Brunswick, Celle and places even further afield in Westphalia and Saxony. There he met up with the mining official Benjamin Olitsch and carried out chemical experiments in Dresden together with Johann Daniel Crafft. In Hanover too Leibniz found new conversation partners like the personal physician of the duke, Christof Pratisius, Martin Elers, Friedrich Schrader, Tschirnhaus and an extended stay by the Dutch mathematician Johann Jakob Ferguson provided opportunities for discussion. In the summer of 1680 Leibniz made an effort to obtain a court appointment in Vienna where the position of librarian at the imperial court had become vacant. Crafft encouraged him to make every effort to secure this position since direct access to the emperor would have greatly benefited their planned joint economic projects. Leibniz himself pursued a prospective appointment as librarian and privy counsellor at the imperial court with the argument that through such economic projects the house of Austria might once again find itself in the ascendant. Leibniz, however, soon learned from Crafft that another candidate had been appointed imperial librarian and that their deliberations had been to no avail. Leibniz’s efforts to become a member of the French Académie des Sciences proved likewise to be in vain. Following a first unsuccessful attempt while still in Paris, he once again turned to Christiaan Huygens in September 1679 in this matter. Huygens reported at the beginning of 1680 about a consultation concerning the matter with Jean Gallois who was well disposed to such an appointment. The correspondence with Huygens was however interrupted before the initiative could be further pursued. Huygens departed from Paris in 1681 and Leibniz’s prospects of an appointment then dwindled accordingly. Notwithstanding this personal setback, Leibniz subsequently supported with remarkable altruism the candidacy of Tschirnhaus for appointment to the Académie des Sciences in the following year. In correspondence with Gallois he lauded Tschirnhaus’ scholarly achievements and he generously made available for communication to the Académie des Sciences the process for the production of phosphorus which, at that juncture, was known to only a few persons. The communication of the phosphorus process in particular had been for Tschirnhaus an act of exceptional generosity on Leibniz’s part and to which expressions of friendship and gratitude in Tschirnhaus’ letters in the spring and summer of 1682 testify. In the course of events Tschirnhaus was successful in being accepted as a member of the Académie des Sciences. Leibniz, encouraged by the success of his compatriot, then drafted a letter to the founder of the Académie Jean Baptiste Colbert, in October 1682, but dispatched instead a letter to Gallois of whose continuing esteem he had

Introduction: The Core Themes

7

been informed by Tschirnhaus. In this letter Leibniz expressed his desire to be admitted to the Académie as a foreign member entrusted with duties in the field of geological research in the Harz mountains. Alas, the admission of Tschirnhaus to the Académie had in fact worsened the prospects for Leibniz himself. Gallois appeared unwilling to advocate the admission of a further foreign member not resident in Paris. These setbacks do not reflect Leibniz’s public standing at this juncture, however, and he continued to receive expressions of reverence and respect in the letters from correspondents such as Friedrich Schrader and the fellow of the Royal Society, Detlev Clüver; and Leibniz’s mathematical article on the arithmetic quadrature of the circle,7 in the Acta Eruditorum of February 1682, was translated into English and appeared in the Philosophical Collections. Leibniz was also informed by correspondents such as Christoph Pfautz and Sebastian Scheffer that extracts and quotations from his letters concerning questions of meteorology and terrestrial magnetism had been printed in Albert Meyer’s Dissertatio mathematica de observationibus aerometricis (1681) and in Johann Christoph Sturm’s Epistola invitatoria ad observationes magneticae variationis  … instituendas (1682), respectively. Notwithstanding such recognition, Leibniz also had to stomach the satirical remarks about him in Johann Joachim Becher’s Närrische Weißheit und weise Narrheit (foolish wisdom or wise foolery/ folly’ish wisdom or wise folly) of 1682 in which the author made fun of him as the inventor of a stagecoach with which one might travel from Hanover to Amsterdam in six hours. 1.2 The Period from Mid-1683 to 1690 Leibniz’s correspondence in mathematics, science and technology between July 1683 and December 1690 consists of almost 300 epistolary exchanges involving about sixty individuals including Huygens, Crafft, and Tschirnhaus. Leibniz’s life and career development between 1683 and 1690 was markedly shaped by a number of important developments. Firstly, following a ducal decree, his efforts for the improvement of the efficiency of the ore mines in the Harz mountains had to be wound up. Secondly, his acceptance of a commission to write a dynastic history of the House of Welf (Guelf or Guelph) involved extensive travel in different regions of Germany, Austria and Italy. Subsequently, towards the end of 1690, his promotion to the position of director of the Ducal Library in Wolfenbüttel was in the offing, an appointment that 7 Cf. D. Crippa, The impossibility of squaring the circle in the 17th century: A debate among Gregory, Huygens and Leibniz (Frontiers in the history of science), Cham (Switzerland), 2019; see in particular chap. 3, pp. 93–156 (Leibniz’s arithmetical quadrature of the circle).

8

Introduction: The Core Themes

was to make him into a commuter between the neighboring towns of Hanover and Wolfenbüttel within the principality of Brunswick-Wolfenbüttel. Leibniz’s efforts in the Harz Mountains for the testing of engineering techniques, processes and procedures with the goal of improving the revenue from the mines can be traced back to the year 1679. By the middle of 1683 these activities had incurred costs amounting to about five times his annual salary without a successful conclusion being in sight. Accordingly, at the end of 1683, duke Ernst August ordered the discontinuation of treasury payments for these trials. Since Leibniz was still very convinced of the technical feasibility of his proposals for improvement of ore production, he ordered the continuation of the work for a further year at his own personal expense. However, by the spring of 1685 the point had arrived for him to concede and comply with the desires of the duke for the conclusion of the test series. Leibniz’s disappointment in this matter was offset by the circumstance that his sovereign managed to awaken his interest in a project of a very different nature, namely to research and write the dynastic history. As regards the historiographical assignment Leibniz then quickly immersed himself in the work surrounding the planned history and, in particular, that of obtaining new and reliable sources. In this context he undertook exploratory journeys to the archives of the ruling branches of the House of Welf. However, it quickly became apparent that in addition sources in libraries and archives in Bavaria needed to be consulted and there in turn he found references to Italian sources. Thus, from originally smaller journeys in his own region, there developed a great, almost three-year long expedition whose main stations were Munich, Augsburg, Vienna, Venice, Rome, Florence, Bologna, Modena and Ferrara.8 Leibniz’s grand tour through Germany, Austria and Italy is documented, firstly, in his correspondence with his friend and associate Johann Daniel Crafft, with whom he met up in January 1688 in Graupen (now Krupka) in northern Bohemia for detailed discussions, secondly, in the proposals he laid before the emperor in Vienna towards the end of the same year and, thirdly, in a series of communications sent during his stay in Rome from April to November 1689. His writings and correspondence concerning China with Claudio Filippo Grimaldi – superior of the Jesuit mission and president of the ‘Tribunale Mathematicum’ in Peking – deserve particular mention here as do the exchanges with mathematics professors like Vitale Giordani and Domenico Quarteroni as well as with the French numismatist Nicolas Toinard and with the French expatriate in Rome Adrien Auzout. During his (presumably second) 8 Cf. A. Robinet, G. W. Leibniz: Iter Italicum (Mars 1689–Mars 1690), Florence, 1988.

Introduction: The Core Themes

9

sojourn in Vienna, Leibniz conducted extensive discussions with Christian Holeysen, the son of a moneyer of Augsburg and a chemist who employed ores from the Hungarian mines. It had been Leibniz’s intention to visit those mines himself but in the end he had to abandon the idea. Among his multifarious duties and occupations during the 1680s was the search for suitable assistants and travel companions. In this context, his correspondences with the apothecary Johann Christian Wachsmuth and with the mining engineer Friedrich Heyn deserve particular mention; the latter reported about his experience in the mines of Cornwall and he accompanied Leibniz on the first leg of the Italian journey. 1.3 The Period from 1691 to 1693 Leibniz’s correspondences in mathematics, science and technology for the years 1691–1693 involved a total of about 30 individuals including the continuing exchanges with Crafft, and Huygens and that now initiated with Denis Papin. Particularly important for Leibniz at this juncture – even though the number of letters exchanged was not great – were his correspondences with Johann Bernoulli, Domenico Guglielmini, Guillaume François de L’Hospital, Newton, Christoph Pfautz, Bernardino Ramazzini, Tschirnhaus and Johann Georg Volckamer. The most important biographical events for Leibniz in the early 1690s were his appointment as director of the library in Wolfenbüttel on January 14, 1691, the appearance in May 1693 of his monumental work on sources for international law, the coming into being and the taking shape of his history of the Welfs, the Hanoverian dynasty’s procurement of electoral status in 1692, his efforts to bring about a reunion of the Christian churches and the revival of his interest in the ore mines in the Harz mountains. The completion of Leibniz’s Codex juris gentium diplomaticus (published in 1693) which contained records and charters relating to treaties and records of agreements in international law from the twelfth to the fifteenth centuries, as well as efforts to find documents for a planned follow-up volume, are reflected in his correspondence from 1693. Leibniz hoped for support in obtaining material from among his circle of acquaintances which included diplomats, librarians and scholars. Thus, his antennal senses reached out to Holland, England and Italy in the quest for interesting documents for the Codex and the planned supplementary volume, or Mantissa. Leibniz’s involvement in writing the history of the Welf dynasty led, in addition to his duties as librarian, to numerous local journeys, for example to Hildesheim, Celle and Brunswick. Economic projects, conceived together with Crafft, made a journey to Hamburg necessary in the second half of

10

Introduction: The Core Themes

September 1693 and, at the end of the same year, there followed a new phase of regular visits to the Harz district. On March 20, 1693, Leibniz sent a printed copy of the title page with an announcement of the Codex to Huygens who, although impressed by Leibniz’s project, was not prepared to collaborate in the undertaking and – in his reply on September 17 – he even expressed his dismay that Leibniz should be sacrificing his time for it. Notwithstanding Huygens’ skepticism, Leibniz did not abandon the hope of obtaining material from Dutch and English sources through his mediation. He hoped that with the help of Huygens’ brother Constantijn  – secretary to ‘stadholder-king’ William III  – to achieve the cooperation of English scholars in locating relevant documents from English archival sources. Although Huygens wrote to his brother on Leibniz’s behalf the initiative proved to be of no avail. Through the intermediation of Henri Justel, the Royal Librarian in London, Leibniz eventually made contact with the English scholar Thomas Smith who was to give him intensive support in his historical research. In Italy, Leibniz hoped to avail of the multifarious contacts of Antonio Magliabechi – the custodian of the grand ducal library in Florence – in order to obtain material for the continuation of his Codex and here Rudolf Christian von Bodenhausen acted as intermediary. In Germany, Leibniz approached, among others, Johann Dolaeus and the librarian in Kassel, Johann Sebastian Haes, in an effort to obtain material for the supplementary volume of his Codex. Much of what was discussed in Leibniz’s correspondence in the years 1691–1693 was connected with his planned ‘opus historicum’. In this connection, the natural-historical development of the earth became a central theme of an extensive correspondence with the French scientist, traveler, cartographer and orientalist Melchisédech Thévenot until his death in 1692. Here the groundwork was done for the first part of the history of the Welf dynasty viz. his posthumously published Protogaea (1749). Thereafter, Leibniz worked on the following part that was to be concerned with the barbarian migrations. In this context, the idea of protolanguage on which all later languages were based, and the origin of human beings were central research topics for him. He used comparative linguistics here as a means to shed light on the interrelationship of languages and thus the relatedness and origin of peoples. In this context then, the subject areas of geology, mineralogy, paleontology, ethnography and etymology came together. 1.4 The Period from 1694 to Mid-1696 Leibniz’s correspondence in mathematics, science and technology in the thirty month period between January 1694 and June 1696, involved a total of about

Introduction: The Core Themes

11

30 individuals of which a dozen were newcomers. The period in question also witnessed the death of one Leibniz’s most prolific correspondents, namely of Christian Huygens in July 1695. Nonetheless, Huygens’ correspondence was one of the most voluminous in this period alongside those with Johann Bernoulli, Bodenhausen, Guillaume François de L’Hospital, and Denis Papin. Particularly important for Leibniz were his correspondences with, besides Huygens, Jacob and Johann Bernoulli, L’Hospital, Newton and John Wallis, even though only a single letter was exchanged with each of the latter two in this period. Three very different events cast a characteristic light on the circumstances of Leibniz’s life at this juncture. The first, in chronological order, was Leibniz’s attempt to move to the Berlin court by obtaining the position left vacant there by the death of Samuel von Pufendorf, jurist and renovator of natural law, on October 24, 1694. The second event was the appearance of the first volume of Wallis’ Opera Mathematica, in the preface to which the impression was given that Leibniz already had had access to the Newtonian fluxional calculus in 1676. The third event was his (long aspired to) privy-council appointment as minister of justice on July 12, 1696. The first event reflected Leibniz’s discontent with his personal and professional situation in Hanover and in particular his being overburdened with the dynastic history project. The second event documented the growing inclination of the English mathematicians to claim Newton’s priority in the development of the infinitesimal calculus and to repress the influence of the Leibnizian form of the calculus. Finally, his promotion at the Hanoverian court indicates that Leibniz’s commitment to promoting the interests of the (now) elector Ernst August had to a certain degree found recognition at court. However, with the death of the sovereign early in 1698 Leibniz’s situation was destined to change once again. Leibniz continued to live the life of a traveler and commuter in the early and mid-1690s. He made more than two dozen journeys out of Hanover to Wolfenbüttel  – sometimes combined with visits to the nearby town of Brunswick and to the Harz mountains  – in the thirty month period under consideration. These visits to Wolfenbüttel were undertaken not just in his capacity as director of the ducal library there, and in connection with the dynastic history he had been commissioned to write, but also in the context of his fostering relations with the princes at the two Brunswick-Lüneburg courts in Wolfenbüttel and Celle. On the other hand, his journey to Holland in November 1694 – with a stopover in Münster on the outward leg and a detour to Arnstein and Kassel on the return stage – was without the knowledge of his superiors and out of the ordinary. The main purpose of that journey was the support of his long-time collaborator, and one-time friend, Johann Daniel Crafft in the context of perhaps the most important economic project at this

12

Introduction: The Core Themes

juncture, namely the formation of a company for the production and marketing of brandy conceived by the two “projectors”,9 as part of a trade war with France. Leibniz’s primary obligation in the service of the house of BrunswickLüneburg was, however, the authoring of a history of the dynasty from its origins in the middle ages to his own day. In addition, as historian and jurist, he was entrusted with a range of further administrative tasks such as the defense in print of the recently attained electoral status within the Holy Roman Empire, the consolidation of the claim of the electress of Hanover to the English throne, the directorship and reorganization of the library in Wolfenbüttel, in addition to a range of demands on his legal expertise. Accompanying these official duties, a range of further activities arose through his own initiative such as the promotion of academies and learned societies or the pursuit of church reunion. Of particular significance was the extensive acquisition of archival material for the planned dynastic history which went hand in hand with the preparation of a supplementary volume, or Mantissa, to his Codex juris gentium diplomaticus (1693). In his correspondence with Bodenhausen, Leibniz sought support in motivating the dilatory Magliabechi to expedite the dispatch of desired manuscripts from Tuscan sources. Queries in connection with Leibniz’s research on the early representatives of the house of Este were duly sent through Bodenhausen to the Tuscan historian Cosimo Della Rena. These probably remained unanswered and so Leibniz could – on the occasion of the transmission of his Lettera su la connessione delle serme case di Brunsvic e D’Este (1695) to Bernardino Ramazzini on December 16, 1695  – hardly desist from complaining about the lack of support from the Italians for his research on the line of Este which was of central importance for his dynastic history project. 1.5 The Period from Mid-1696 to 1698 Sixty per cent of Leibniz’s correspondence in mathematics, science and technology, in the thirty-month period between July 1696 and December 1698, represented the continuation of existing correspondences. However, in the wake of the death of Christiaan Huygens in July 1695, this period also witnessed the passing of two other of his most prolific correspondents, namely Rudolf Christian von Bodenhausen and Johann Daniel Crafft. The correspondences with Johann Bernoulli and Denis Papin then became the most voluminous and 9 Cf. D. Defoe, An essay upon projects, London, 1697, in particular “Of projectors” (pp. 31ff.). Although not referred to by Leibniz, Daniel Defoe’s terminology will be followed in the present work.

Introduction: The Core Themes

13

together they amount to more than half of the total of Leibniz’s correspondence in mathematics, science and technology in this period. From 1696 Leibniz’s duties at court, as well as his own historical, political and philosophical undertakings, increasingly commanded his attention. Two dates were of particular significance. On August 13, 1696, he was informed about his appointment as privy counselor of justice and, on February 2, 1698, his sovereign, the elector Ernst August of Hanover died following a partial transfer of governmental business to his successor Georg Ludwig in the previous year. The new sovereign – no doubt with his own ambitions to the English crown in mind – increasingly put pressure on Leibniz to conclude his principal commission, namely to write a history of the Welf dynasty. Leibniz’s promotion in the summer of 1696 already implied an increased commitment to more rapid progress on the dynastic history project. And so, at this juncture, Leibniz became increasingly involved in questions of dynastic succession and of ecclesiastical policy. In the summer of 1697 Tsar Peter of Russia travelled though Brandenburg, an event that induced Leibniz to prepare a memorandum. Further fruits of this period of activity were the publication of his Novissima Sinica (1697), and of the editions Accessiones historicae (1698) and Mantissa Codicis juris gentium diplomatici (1700). This range of activities was sometimes also reflected in his mathematical and scientific correspondences, as for example in letters to John Wallis where he advocated a reconciliation of the Protestant churches and a Protestant mission to China. The broad spectrum and the burden of Leibniz’s activities also had implications for his health and ability to cope. For assistance with his inchoate or contemplated projects he continually sought research assistants or associates. Thus he longed for the support of talented mathematicians for the realization of his planned opus ‘Scientia infiniti’ or for the advancement of his ‘Analysis situs’. The quest for a younger collaborator finally did bear fruit and resulted in the initiation in the summer of 1697 of one of Leibniz’s most voluminous correspondences  – both before and after the year 1701  – namely that with Rudolf Christian Wagner. 1.6 The Period from 1699 to 1701 Leibniz’s correspondence in mathematics, science and technology in the three-year period between January 1699 and December 1701, involved a total of some 34 correspondents of which the half were newcomers. Among those newcomers, Friedrich Hoffmann, Ole Christensen Rømer, Hans Sloane, Pierre Varignon, and Francesco Bianchini – with whom correspondence was resumed after an interruption of ten years – deserve particular mention. The

14

Introduction: The Core Themes

frequency and volume of the correspondence with Johann Bernoulli ebbed in the triennium in question while those with L’Hospital, Magnus Gabriel Block, Johann Andreas Stisser and John Wallis were concluded. In addition, in the spring of 1700, the extended discussion with Denis Papin concerning “vis viva” and the correct measure of force came to an end. The densest correspondence in the period under consideration was that with Rudolf Christian Wagner, the aspirant mathematics professor in Helmstedt, who acted as Leibniz’s assistant and organized for him a variety of technical matters, such as those relating to his calculating machines. Wagner’s correspondence with Leibniz reveals also the important role his mentor had in his academic advancement. With the support of the Helmstedt professor Johann Andreas Schmidt and through Leibniz’s political influence at the court in Wolfenbüttel, Wagner was preferred to a rival candidate and was able to commence his duties as professor in November 1701. Two important events, namely the foundation of the Berlin Society of Sciences (“Berliner Sozietät der Wissenschaften”) and the Protestant calendar reform, were to be major influences on Leibniz’s correspondence in the period under consideration. For the scholar and scientist Leibniz, a long-held desire was fulfilled in February 1699 when L’Hospital informed him about his appointment as a foreign member of the lately-reformed Académie des Science. The circumstance that Johann and Jacob Bernoulli, who had distinguished themselves in the further development of the differential calculus, had received the same honor was tantamount to an additional tribute to Leibniz. His joy over this development is reflected in his correspondence with Johann Bernoulli who, through his correspondent Pierre Varignon, had even closer contact with the Académie than Leibniz did. Through Bernoulli he learned the names of the other members. From another source he obtained information about the financing of the Académie and he learned in particular that he could expect no remuneration from his appointment. Even more important for Leibniz, however, was the foundation in July 1700 of the Berlin Society of Sciences and his appointment as its first president. It led to extended stays in Berlin from May to August 1700 and again between October 1701 and January 1702. Of significance also were two secretive journeys (in the last months of 1700 and in May–June 1701) to Vienna in connection with his efforts for a reunification of the Christian churches and his admittance to the Court Council of the Empire and the Aulic Council. These activities and further secretive activities in the forefront of the War of the Spanish Succession also found expression in Leibniz’s correspondence in mathematics, science and technology in the years 1700 and 1701.

Introduction: The Core Themes

15

2 Mathematics Tout ce que nous trouvons par nos methods est justifié encor par les experiences autant que le reste de la Geometrie.10 Leibniz to Detlev Clüver, End of June or first half of July, 1696

In comparison with the outstanding importance of mathematics during Leibniz’s years in Paris (1672–1676) and his first three years in Hanover (1677– 1679), the subject had a somewhat reduced importance in his correspondence during the early 1680s. This is attributable to the fact that his correspondence with Huygens and Tschirnhaus was less voluminous and, furthermore, to the circumstance that, following the death of Oldenburg, the mathematically relevant correspondence with the Royal Society of London was interrupted. To his sole letter to Huygens in this period, on February 5, 1680, Leibniz attached his “Specimem Methodi meae de Maximis et Minimis” which in the dispatched letter had the heading “Exemplum ex Nova mea Tangentium Methodo ductum”. In effect, this example, which Leibniz would once again include in the first publication of his differential calculus, namely in his article “Nova methodus pro maximis et minimis” of 1684, was to prove particularly suitable for demonstrating the superiority of the new calculus.11 10 A III,6 N. 247, p. 810; Translation: All that which we find by our methods [in calculus] is justified also by [practical] experience or experiment, just like for the rest of mathematics. Regarding the Leibnizian Principle of the unity of theory and practice, and the consequences for mathematics, science and technology, cf., for example, E. Knobloch, “Theoria cum praxi: Leibniz und die Folgen für Wissenschaft und Technik”, Studia Leibnitiana, vol. 19(2), (1987), pp. 129–147; B.-W. Schulze, Erlebnisse an Grenzen – Grenzerlebnisse mit der Mathematik, Basel 2013, in particular pp. 101–106 (“Theoria cum praxi”). 11 Regarding the Leibnizian calculus and its development, cf. for example: H. J. M. Bos, “Differentials, higher-order differentials and the derivative in the Leibnizian calculus”, Archive for History of Exact Sciences, vol. 14 (1), (1974), pp. 1–90; H. J. M. Bos, “L’Élaboration du calcul infinitesimal: Huygens entre Pascal et Leibniz”, pp. 115–122 in: R. Taton (intro.), Huygens et la France: Table ronde du C.N.R.S. Paris, 27–29 mars 1979, Paris, 1982; H. Loeffel, Blaise Pascal 1623–1662, (Vita Mathematica, vol. 2), Basel. Boston, 1987, in particular chap. 6 (Der Weg zur Infinitesimalrechnung); H.-J. Heß, F. Nagel (eds.), Der Ausbau des Calculus durch Leibniz und die Brüder Bernoulli: Symposion der Gottfried-Wilhelm-Leibniz-Gesellschaft und der Bernoulli-Edition der Naturforschenden Gesellschaft in Basel, 15. bis 17. Juni 1987, (Studia Leibnitiana, Special issue no. 17), Stuttgart, 1989; H.-J. Heß, “Mathematics: Invention of infinitesimal calculus”, pp. 44–55 in: K. Popp, E. Stein (eds.), Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000; C. S. Roero, “Gottfried Wilhelm Leibniz’ first three papers on the calculus (1684, 1686, 1693)”, chap. 4 (pp. 46–58) in: I. Grattan-Guinness (ed.), Landmark writings in western mathematics 1640–1940, Amsterdam, Boston, 2005; S. Probst,

16

Introduction: The Core Themes

Already in February 1682, in the second monthly installment of the Acta Eruditorum, the new journal of Leipzig under the editorship of Otto Mencke,12 Leibniz published the article “De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus expressa”, in which the so-called ‘Leibniz series’, the technical term ‘transcendent’ and an equation with the unknown in the exponent (viz. xx, or x to the power of x) appeared in print for the first time. Subsequently, Leibniz prepared another article, this time on simple interest and discount calculation, which was intensely discussed in his correspondence with the mathematics professor and co-editor of the new journal, Christoph Pfautz, and which duly appeared in October 1683. Consideration of the expressions, referred to here, in which the unknown or the variable appears in the exponent had, as in the years prior to this, particularly engaged Leibniz’s mathematical mind. He saw here to a certain extent the hitherto missing keystone to the completion of his infinitesimal calculus. The introduction of expressions in which the unknown or variable appeared in the exponent also attracted the interest of Johann Jakob Ferguson and Tschirnhaus and provided occasion for discussion between the latter and Leibniz as to whether such expressions or curvilinear coordinates are better suited for describing transcendental curves. Regarding other questions relating to the theory of curves and the infinitesimal calculus, Leibniz’s correspondence with Tschirnhaus likewise proved to be particularly fruitful. On May 31, 1682, for example, this correspondent referred to a procedure for the determination of points of inflexion having explained a few days earlier his method of tangents to Leibniz, which would be applicable also for certain transcendental curves and which was published then in the Acta Eruditorum in December 1682. Considerable attention was likewise given – in letters exchanged between May and August 1682  – to a detailed discussion of Tschirnhaus’ problem of the catacaustic curve, as well as related problems like the diacaustic curve, these being curves which arise in connection with the reflection and refraction of light. Leibniz found opportunity for a summarizing representation of his most important mathematical accomplishments in two separate letters, of April–May and July–August 1680, respectively, to the Jesuits François de la Chaise, the confessor to Louis XIV, and to Adam Adamandy Kochański, the

“The calculus”, chap. 11 (pp. 211–224), in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. 12 Cf. A. H. Laeven, L. Richards (trans.), The »Acta Eruditorum« under the editorship of Otto Mencke (1644–1707): The history of an international learned journal between 1682 and 1707, Amsterdam, 1990.

Introduction: The Core Themes

17

Polish mathematician and polymath.13 In the letter to La Chaise, he referred for example to a “characteristica geometrica”, a geometric characteristic which included his analysis situs,14 or ‘geometria situs’, the geometry of location.15 Leibniz’s extensive exchange of ideas in the early 1680s with Ferguson,16 who was the author of a much appreciated book entitled Labyrinthus Algebrae (1667), included questions of number theory, the calculation of annuities, the solution of equations, the quadrature of the circle by means of a curve studied and constructed by Pierre de Fermat, James Gregory and Guido Grandi, and later to be known as the ‘Witch of Agnesi’ curve (called after Maria Gaetana Agnesi 1718–1799),17 the summation of the series of the reciprocal triangular numbers, an extreme value problem, the Huygens’ cycloidal pendulum, and a curve problem similar to the example of the Leibniz’s tangent method communicated to Huygens, an inverse tangent problem, the real sum of two imaginary expressions, the extension of binomial development to broken exponents, and the solution of non-homogeneous equation systems, a matter which was related to Leibniz’s studies of the theory of determinants,18 and which in turn 13 Cf. A. Heinekamp, “Kochanski als Leibniz-Korrespondent”, Organon Warszawa, vol. 14, (1978), pp. 73–106; B. Lisiak, “Leibniz’s scientific collaboration with Adam Kochański, S.J.”, Roczniki Filozoficzne / Annales de Philosophie / Annals of Philosophy, vol. 65(2), (2017), pp. 205–222. 14 Cf. V. De Risi, “Analysis Situs, the foundations of mathematics and a geometry of space”, chap. 13 (pp. 247–258), in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. 15 Cf. L. E. Loemker (ed., trans.), Gottfried Wilhelm Leibniz: Philosophical papers and letters (The new synthese historical library book series, vol. 2), Chicago, 1956, and Dordrecht, 1969 and 1989, in particular “Studies in a geometry of situation, 1679”, chap. 27 (pp. 248–258); M. Kline, Mathematical thought from ancient to modern times, vol. 3, New York, Oxford, 1972, in particular p. 1158 and p. 1163 in chap. 50 (The beginnings of topology). 16 Cf. J. A. van Maanen, “Johan Jacob Ferguson. geb. um 1630 im Haag (?), gest. vor dem 24. November 1706, vermutlich am 6. Oktober 1691, in Amsterdam”, Studia Leibnitiana, vol. 22, (1990), pp. 203–216. 17 Cf. G. Bernardi, The unforgotten sisters: Female astronomers and scientists before Caroline Herschel, Cham, Heidelberg, New York, Dordrecht, London, 2016, in particular chap. 18, pp. 115–120; C. Martini, and G. Wolfschmidt (ed.), Zwei Frauenleben für die Wissenschaft im 18. Jahrhundert: Eine vergleichende Fallstudie zu Émilie du Châtelet und Maria Gaetana Agnesi, (Nuncius Hamburgensis  – Beiträge zur Geschichte der Naturwissenschaften, vol. 43), Hamburg, 2017. 18 Cf. E. Knobloch, Der Beginn der Determinantentheorie. Leibnizens nachgelassene Studien zum Determinantenkalkül, Hildesheim, 1980; E. Knobloch, “First European theory of determinants”, pp. 56–64 in: K. Popp, and E. Stein (eds.): Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000; E. Knobloch, “Determinant theory, symmetric functions and dyadic”, chap. 12 (pp. 225–246), in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

18

Introduction: The Core Themes

represented an application example of his thought concerning his ‘universal characteristic’.19 The basic idea, which involved the use of numbers instead of letters, was also explained by Leibniz in a letter to Detlev Clüver, on May 28, 1680, in which he insisted on the superiority of his combinatorial characteristic in comparison with normal algebra. Leibniz’s considerations of number systems other than the decimal system also stood in connection with the combinatorial characteristic. In discussions in Hanover with Ferguson in the spring of 1680, Leibniz had apparently elaborated number systems to the base 2, 11 and 12. The dyadic or binary number system also found the interest of Tschirnhaus in a letter of May 27, 1682. Leibniz, writing to him at the end of June 1682, expressed his expectation that many “harmoniae” would be found in the binary system which were not so evident in other number systems. In his reply of July 26, 1680, to a letter Leibniz wrote to Clüver on May 28, 1680, the correspondent referred to the binary system but warned however that anyone wanting to bring about the general introduction of the system could expect to face considerable difficulties. Leibniz, in his reply on September 10 of that year, expressed his surprise at Clüver’s congenial understanding in relation to this and related questions but he clarified his standpoint however, stressing namely that he did not conceive the binary system for general use but merely for theoretical purposes. Just as one might consider the period of Leibniz’s Paris sojourn (1672–1676) to be the foundational phase of Leibnizian mathematics, one may also treat the first seven years in Hanover that followed as an expansion phase.20 In this period the newly created infinitesimal calculus developed into a widely diversified discipline with multifarious – in particular physical – applications. This development took place in the stillness of Leibniz’s study. In the year 1684 the mature phase of the Leibnizian calculus began. At the beginning of this development came the fundamental publications on differential and integral calculus. There followed in rapid succession a series of journal articles in which physical themes were treated mathematically and quantitatively and the public controversy about the true measure of force brought Leibniz to prominence in learned circles. Also in connection with this dispute, and in particular that 19 Cf. D. E. Mungello, Curious land: Jesuit accommodation and the origins of Sinology, Honolulu, 1985 (and 1989), in particular “Proto-Sinology and the seventeenth-century European Search for a universal language”, chap. VI (pp. 174–207), and specifically “Leibniz’ search for a universal characteristic” (pp. 191–197). 20 Cf. H.-J. Hess, “Maturing in retirement: The unknown period of the Leibnizian calculus between Paris and publication (1676–1684)”, pp. 247–288 in: M. Galuzzi (ed.), Giornate di Storia della Matematica, Commenda di Rende (Italy), 1991, and 2nd extended version, 1993.

Introduction: The Core Themes

19

with François Abbé de Catelan, stood the first mathematical competition initiated by Leibniz, namely the challenge to solve the isochrone problem which called for the determination of the curve along which a body descending under the influence of terrestrial gravity reaches the datum or base line in the same period of time regardless of the point on the curve from which the descent began. The publication of Leibniz’s solution of the problem – the isochrone curve or semi-cubic parabola – in April 1689 represented a landmark in the prolonged dispute with the Cartesians (in particular with the Abbé Catelan) which at that point had been going on for several years. During his years in Paris Leibniz had already provided friends and correspondents with a more or less far-reaching insight into his new methods in the areas of tangent determination and quadratures. Among his friends, or associates, Huygens and Tschirnhaus in particular should be mentioned in this context and, among his correspondents, men like Henry Oldenburg and Jean-Paul de La Roque stand out. Leibniz’s willingness to communicate had the objective of obtaining critical suggestions and of making his results known, and thus securing his priority claims. This policy of keeping a limited public informed about his results proved difficult after 1676 at the remote and secluded ducal residence in Hanover and it proved difficult to maintain friendships and scholarly correspondence from there. It also became clear to Leibniz that long-term reticence in relation to his most important discoveries would inevitably lead to priority disputes. The fact that the first such dispute arose with one of his last remaining Parisian associates, who was both a Saxon compatriot and a friend, must have come as a shock to both of them.21 In the article “Methodus  … quadraturam, aut impossibilitatem ejusdem  … determinandi”, published in the Acta Eruditorum in October 1683, Tschirnhaus made public insufficiently understood parts of the Leibnizian quadrature method. Since Tschirnhaus failed to answer a (no longer extant) dispatch of February 1684 from Leibniz, seeking clarification, the latter decided to publish the article “De dimensionibus figurarum inveniendis” in the Acta Eruditorum in May 1684 in order to assert his priority claims and to correct a flawed assertion of Tschirnhaus. The latter, for his part, claimed in a letter of August 31, 1684, that he had been completely misunderstood by Leibniz and he believed that he had done nothing wrong in his altruistic efforts for the advancement of the common good, an exercise in which he had previously experienced Leibniz as fellow advocate. Tschirnhaus’ “Responsio ad objectionem”  – in which he tried to refute the allegations of 21 Cf. U. Mayer, Zwischen Brennpunkt und Peripherie  – Der sächsische Mathematiker, Techniker und Philosoph Ehrenfried Walther von Tschirnhaus (1651–1708), Doctoral dissertation, Halle-Wittenberg (Martin-Luther-Universität), 2001.

20

Introduction: The Core Themes

Leibniz – was first intended as an article for publication in the Acta Eruditorum but it was eventually forwarded directly to Leibniz as an attachment to the letter of August 31, 1684. At this juncture Leibniz finally decided to publish an account of the first part of his infinitesimal calculus, namely the differential calculus, in the epoch-making contribution entitled “Nova methodus de maximis et minimis”, which appeared in the Acta Eruditorum in October 1684. Notwithstanding subsequent conciliatory efforts on Leibniz’s part, his correspondence with Tschirnhaus was interrupted for almost a decade in the wake of this dispute. The second part of Leibniz’s analysis, namely his recondite geometry or integral calculus, duly appeared with the title “De geometria recondita” in the Acta Eruditorum in June 1686. Leibniz’s continuing efforts to make his infinitesimal calculus known among colleagues can be seen in his correspondence with figures like the mathematician and scientist Christiaan Huygens.22 As Leibniz’s senior, and mentor in mathematics during their years together in Paris, Huygens had been informed about his discoveries in analysis. Up to his return to the Netherlands in 1681 – which resulted in an interruption of their correspondence – Huygens remained skeptical about the necessity and power of the Leibniz’s methods in comparison with his own geometrical methods. On January 11, 1680, he had expressed the desire to see a sample showing the power of Leibniz’s infinitesimal calculus. Leibniz had complied by sending, on February 5, a “Specimen methodi meae de maximis et minimis” with a problem calling for the determination of the tangent to a curve having a constant sum of the reciprocal distances from four given points on the axis. Huygens did not tackle this problem at once but, when (in March 1687) he came across the task again, he immediately found a suitable geometrical method to solve it and so he continued to be skeptical about Leibniz’s methods. After Leibniz had enunciated the isochrone problem in the Nouvelles de la République des Lettres in September 1687, the correspondence with Huygens was revived in January 1688 with a letter Leibniz wrote on seeing Huygens’ solution of the problem in the October number of the same journal. Having established agreement between Huygens’ and his own solution, Leibniz sketched his own method for the determination of the curve.

22 Cf. H. J. M. Bos, “Huygens and mathematics”, pp. 126–146 in: H. J. M. Bos et. al (eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979, Lisse, 1980; J. G. Yoder, Unrolling time: Christiaan Huygens and the mathematization of nature, Cambridge, 1988, 1990 and 2004. Regarding Huygens as a scientist (astronomer and physicist), cf., for example, H. Aldersey-Williams, Dutch light: Christiaan Huygens and the making of science in Europe, London, 2020, and Het leven van Christiaan Huygens, Amsterdam, 2020.

Introduction: The Core Themes

21

He also used the occasion of providing a letter of recommendation for another correspondent, namely Johann Jakob Spener, to present Huygens, on July 25, 1690, with the main features of his infinitesimal calculus and to indicate the relevant articles in the Acta Eruditorum. Replying a month later (on August 24), Huygens alluded to a certain obscurity he sensed in Leibniz’s calculus and he claimed to be in possession himself of an equivalent method; he accordingly presented another challenge for Leibniz’s calculus in the form of two problems involving the inverse tangent method, essentially the task of determining two curves having been given their respective subtangents. Leibniz’s efforts to solve the inverse tangent problems presented by Huygens, as well as the latter’s reaction, are revealed in their continuing correspondence in the last quarter of the year 1690. Huygens could not, however, be convinced at this stage of the superiority of the Leibnizian calculus and in addition misunderstanding and confusion about the respective solution curves employed, as well as Huygens’ aversion to the exponential equations used by Leibniz, only reinforced the correspondent’s skepticism. The triennium that followed (viz. 1691–1693) was to be one of the most productive phases for Leibniz’s mathematics in all of his years in Hanover. Whereas, in the wake of his discovery of the infinitesimal calculus in Paris between 1672 and 1676, he had remained irresolute over years about when and how to best inform the public about his new mathematical methods, there followed on the first series of articles in the Acta Eruditorum on the differential and integral calculus – in October 1684 and June 1686, respectively – a period of reticence lasting a number of years, primarily a consequence of his research tour through Germany, Austria and Italy. The few journal articles that did appear arose not so much from the spontaneity of mathematical creativity but rather from a sense of necessity not to publish results too late. Thus, Leibniz’s articles about movement in a resisting medium of January 1689 and about the foundation of celestial motions of February 1689 have to be seen in connection with the appearance of Newton’s Philosophiae naturalis principia mathematica in 1687, whereas the publication of his isochrone solution in April 1689 represented a temporary conclusion of the smouldering dispute with the Cartesians (in particular with the Abbé Catelan). The curve in question (the isochrone or semi-cubic parabola) was the desired solution to the first mathematical contest or challenge question conceived to demonstrate the superiority of his infinitesimal calculus. Leibniz had challenged Catelan to determine the curve along which a body under the influence of terrestrial gravity approaches the earth’s surface at a constant speed. A related question was the problem of finding the paracentric isochrone, or the curve along which a body under the influence of terrestrial gravity veers away from a given point at a constant speed.

22

Introduction: The Core Themes

This problem, although enunciated by Leibniz himself, was however not seriously tackled at this juncture. Further mathematical contests were to follow. Jacob Bernoulli, who, besides Leibniz and Huygens, had solved the isochrone problem, combined his solution in May 1690 with a retaliation challenge question addressed to the creator of the differential calculus, namely to mathematically determine the form of the catenary, that is to find the curve described by a non-extensile catena or chain suspended at its extremities from two points having the same elevation and under the influence of terrestrial gravity. In July 1690, Leibniz, who immediately solved the hanging chain problem for himself, set the turn of the year 1690–1691 as a deadline for all mathematicians wanting to join the contest to submit their solutions. In early December 1690, Jacob Bernoulli’s younger (but estranged) brother Johann,23 sent (as first) his solution to the editors of the Acta Eruditorum, as Leibniz learned from a letter sent by Christoph Pfautz on February 14, 1691. Huygens, after some hesitation, forwarded his solution through Leibniz to the journal editors in Leipzig.24 From Leibniz’s circle, Tschirnhaus alone – although he had been explicitly approached by Leibniz in the matter – failed to respond to the challenge. And so, Leibniz was only able to present two solutions (in addition to his own) of the catenary problem in the June 1691 number of the Acta Eruditorum. The initiator of the competition, Jacob Bernoulli, published his solution in an article that immediately followed Leibniz’s solution.25 Leibniz’s correspondence with Rudolf Christian von Bodenhausen and Huygens provides interesting background information about this contest, as for example about Leibniz’s sense of pride regarding his own solution, about his attempts to make this solution comprehensible for Bodenhausen, about his ambition to make the contest known in Italy, the homeland of Galileo Galilei – who had been one of the first to tackle this problem,26 albeit without success – and about Huygens’ suspicions that Leibniz might have been prematurely 23 Cf. J. A. van Maanen, “Johann Bernoulli, man of contrasts”, Nieuw Archief voor Wiskunde, ser. 4, part 11, no. 3, (Nov. 1993), pp. 241–246; R. Thiele, “Das Zerwürfnis Johann Bernoullis mit seinem Bruder Jakob”, Acta Historica Leopoldina, vol. 27, (1997), pp. 257–276. 24 Cf. J. Bukowski, “Christiaan Huygens and the problem of the hanging chain”, The College Mathematics Journal, vol. 39(1), (January 2008), pp. 1–11, which includes (pp. 9f.) a summary translation of Huygens’ 1691 paper in the Acta Eruditorum. 25 Cf. S. Ohly, Johann Bernoullis mechanische Arbeiten 1690 bis 1713, Augsburg, 2004, and in particular chap. 3, pp. 117–189 (Fallstudie 1: Die Kettenlinie). 26 Cf. J. Renn, P. Damerov, S. Rieger, D. Giulini, “Hunting the white elephant: when and how did Galileo discover the law of fall?”, pp. 29–149, in: J. Renn (ed.), Galileo in context, Cambridge, 2001, and in particular (regarding the catenary) pp. 96–104.

Introduction: The Core Themes

23

privy to Johann Bernoulli’s solution or that Leibniz und Johann might have had common artifices at their disposal, which had been denied to himself. Another year was to pass before a further contest aroused mathematical passions. Since Leibniz had, through the intercession of his friend and associate Bodenhausen in Florence, fervently tried to demonstrate to Vincenzo Viviani – a disciple and biographer of Galileo – and his compatriots the superiority of the differential calculus over the simple geometrical methods of contemporary Italian mathematicians, a retaliation move was in the offing. Viviani had secretly prepared the ‘Florentine problem’ (as it was later to be designated) and it was circulated in a pamphlet of April 4, 1692. This Aenigma geometricum de miro opificio testudinis quadrabilis hemisphaericae called for the cutting out of four windows from a hemisphere such that the remaining surface area be squareable. Leibniz received the pamphlet through the Florentine envoy in Vienna on May 27, 1692; he solved the problem on the same day and sent his solution with a letter to the Florentine hereditary or crown prince Ferdinand on May 29. At the same time he had the single-page problem enunciation with his own solution printed in the June number of the Acta Eruditorum. Jacob Bernoulli’s solution appeared in the same journal two months later. On July 12, 1692, Bodenhausen forwarded to Leibniz the solution of L’Hospital having discovered it, and partially transcribed it, at the Florentine court. L’Hospital’s solution had been achieved in cooperation with Johann Bernoulli but it remained unpublished at the time. After Huygens had seen Viviani’s solution in the latter’s tract Formazione e misura di tutti i cieli (1692), he too solved the problem, but hesitated and then reneged on his intention of forwarding it to Leibniz. But even Leibniz proved not to be infallible in this contest and Jacob Bernoulli was able to point out a mistake in his solution – in a letter sent to Otto Mencke in July 1692 – following which Leibniz published an “Additio” in the January 1693 number of the Acta Eruditorum. Yet another mathematical problem frequently mentioned in Leibniz’s correspondence at this juncture was the so-called ‘Bernoulli problem’, formulated by the younger Bernoulli brother, Johann, in the Acta Eruditorum in May 1693. The call here was for the determination of the curve whose axis intercept from the origin to the intersection with the tangent (“resecta”) has a constant proportion or ratio (m/n) to the length of the tangent. Bernoulli revealed at the outset that for m/n =1 the curve is a circle and that for a rational ratio (m/n) the curve in question would be geometrical whereas for an irrational ratio it would be transcendental. In the course of the year 1693, Bernoulli’s older brother Jacob, Leibniz, L’Hospital and Huygens published or communicated their solutions of the Bernoulli problem. Huygens communicated his solution of the problem – at which he had arrived in consultation with L’Hospital – to Leibniz

24

Introduction: The Core Themes

on September 17, 1693. This problem, the solution of which had posed problems for Huygens, led to an admission on his part that his skepticism about the power of Leibniz’s calculus was possibly unfounded; it appeared to him that it might possibly be superior to his own much appreciated geometrical methods. And he acknowledged his change of mind not only in private correspondence but also in his publication “De problemate Bernoulliano” in the Acta Eruditorum (October 1693). This long-awaited moment of recognition of the value of his new calculus from his mentor of the Parisian years was a source of joy for Leibniz and he reciprocated, in his reply on October 11, with praise both for a new curve of Huygens – until then only communicated in encrypted or enciphered form – namely a limiting curve of a tautochrone or isocrone double pendulum (analogous to the cycloid as limiting curve of a simple tautochrone or isochrone pendulum) and for his treatment of the involute of the catenary viz. the tractoria or tractrix. First and foremost, however, Leibniz relished the recognition of his differential calculus on this occasion and the fact that Huygens had taken the trouble to grapple with it. Notwithstanding Huygens’ words of praise for the differential calculus, in his letter of September 17, 1693, however, Leibniz’s relationship with his former mentor was complex, and at times strained. This was manifest particularly in their discussions and disputes about the so-called ‘Leibniz series’ for the arithmetic quadrature of the circle, the solutions of the catenary problem, and the proposed exchange of inverse-tangent methods between Leibniz and Huygens’ collaborator at the time, the Swiss mathematician Nicolas Fatio de Duillier.27 Besides the three public contests that dominated Leibniz’s mathematical correspondence in early 1690s, a wide variety of topics appeared in his mathematical publications and correspondence between 1691 and 1693. These included one of the central questions that had led to the discovery of the differential calculus during his years in Paris, namely quadrature methods, involving the determination of an area under a given curve (quadrature), of the arc length (rectification) as well as of the connection between quadrature and rectification. In the triennium in question these issues were discussed in Leibniz’s correspondences with Huygens, Tschirnhaus, L’Hospital and Newton. A further example concerns the (plane) curve representation methods – discussed 27 Cf. J. G. O’Hara, “Huygens, Leibniz and the ‘petit demon’: Agreement and dissension in their mathematical correspondence”, Christiaan Huygens: De Zeventiende Eeuw, vol. 12(1), (1996), pp. 151–160; F. Chareix, “Geometrization or mathematization: Christiaan Huygens’s critiques of infinitesimal analysis in his correspondence with Leibniz”, chap. 2 (pp. 33–50), in: Dascal, M. (ed.), The Practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010.

Introduction: The Core Themes

25

in Leibniz’s correspondence with Huygens among others – which were of great importance for his mathematical thought and understanding. Yet another significant example relates to the inverse tangent method by which, from the properties of tangents or sub-tangents, the corresponding curves could be determined. Leibniz considered this to be his most important mathematical discovery of his years in Hanover. His interest and that of his correspondents in diverse aspects of the inverse tangent method was likewise evident in his mathematical and scientific correspondence after 1690. However, in his publications in the early 1690s, this inverse tangent method had not yet become an autonomous topic nor did Leibniz reveal related general solution procedures. The proposed exchange of methods with Nicolas Fatio de Duillier, under the aegis of Huygens, failed to materialize when Leibniz decided to forego the exchange. Nonetheless, Leibniz felt obliged to communicate (on October 5, 1691) a summary account of the basics of his inverse tangent method. A point of culmination as regards inverse tangent method then was an article of August 23, 1694, entitled “Considerations sur la difference entre l’analyse ordinaire et le nouveau calcul des transcendants”, in the Journal des Sçavans in which Leibniz skillfully summarized the essence of the method in question. For mathematical tasks derived from the physical world in particular, the value of the inverse tangent method is evident, as for example in the determination of curves like the catenary. From the multitude of special curves treated in Leibniz’s correspondence in the early 1690s, those having real-world applications deserve particular mention here like, for example, the Archimedean spiral, the catenary and auxiliary or related curves. In the discussion of the catenary problem Leibniz pointed out, for example, the connection with the loxodrome or rhumb-line curve – that is the line cutting all meridians at the same angle and that which is followed by a ship sailing in a fixed direction – specifically in his correspondence with Huygens on July 24 and September 21, 1691. In the years between 1694 and 1696 Leibniz’s mathematical renown reached its zenith, with the pinnacle in the frequency of the mathematical journal articles published by him also being attained in these years. At the same time the Bernoulli brothers, Jacob and Johann, and L’Hospital emerged as formidable supporters of the new infinitesimal methods. All these mathematicians continued to show reverence to Leibniz acknowledging him without reservation as an imaginative discoverer and doyen of modern mathematics. And, in 1696, L’Hospital published the first textbook on differential calculus with the title Analyse des infiniment petits pour l’intelligence des lignes courbes. Of the mathematical problems treated in Leibniz’s correspondence in mathematics, science and technology between 1691 and 1693, one still remained to be solved in 1694, namely that concerning the ‘isochrona paracentrica’. This

26

Introduction: The Core Themes

was in fact an extension of the first challenge question posed by Leibniz in 1687, namely to determine that curve along which a body under the influence of terrestrial gravity approaches the earth’s surface at a constant velocity (viz. the isochrone) and, when he published his solution of the problem in April 1689, he presented a further challenge question, namely to find the curve under the modified condition that the body, still under the influence of terrestrial gravity, veer away from a given point at constant velocity. This problem was to remain unsolved for a few years and Jacob Bernoulli was the first to publish a solution in June and September 1694 in the Acta Eruditorum. In the month of August of that year, Leibniz presented his own solution in the same journal and two months after that, in October, there followed Johann Bernoulli’s solution. Huygens – to whom Leibniz had forwarded the solution of Jacob Bernoulli (on July 27) – identified, in his reply (of August 24), some shortcomings but was happy merely to give passing mention of these in his article in the Acta Eruditorum in September of that year. Finally, L’Hospital was unable to cope with this problem and he accordingly failed to provide a solution. Whereas the series of mathematical task assignments or challenge questions did not fade away entirely after 1693 – as is evidenced for instance by Jacob Bernoulli’s inverse tangent problem in the Acta Eruditorum of October 1694 – they no longer had the intensity or consistency of previous years. In April 1695, for example, Leibniz commented on the drawbridge problem of Joseph Sauveur  – viz. the challenge to find the curve along which a counterweight continually keeps a drawbridge in balance – which had already been solved by L’Hospital in the late summer of 1692 but whose special solution (the ‘limaçon’ or snail of Pascal) first appeared in print only in February 1695. In that number of the Acta Eruditorum there also appeared the solution of Jacob Bernoulli and his brother Johann’s generalized conceptual formulation. Subsequently, Leibniz turned his attention to other mathematical questions and only in mid-1696 was he enthused by the very beautiful task setting of Johann Bernoulli in the Acta Eruditorum, of June 1696, namely the brachistochrone problem, or the task of determining the curve of fastest descent of a body under the influence of terrestrial gravity between a certain point and a lower point which is not directly below the first. Having been informed about the task formulation by Johann, on June 19, Leibniz at once (on June 26) communicated his solution (a cycloid) to Bernoulli. Johann reciprocated by sending Leibniz – with a letter of July 31 – two solution procedures, one utilizing the law of refraction of light and another direct method that was however to remain unpublished. Johann had to resort to a printed flysheet to remind mathematicians of his challenge question after the original deadline set (the end of the year 1696) had passed. The challenge questions referred to here were by no means the only mathematical issues that got Leibniz’s attention between 1694 and 1696; in fact they

Introduction: The Core Themes

27

were not even the dominant issues in his mathematical correspondence. At the center of interest for him was still without doubt his new analysis within which the development of a not insignificant number of sub-disciplines became increasingly apparent. These included, as previously, especially the theory of differential equations, integration theory, differential geometry, and the theory of series; to these were now added fundamental questions of his ‘scientia infiniti’. In comparison, Leibniz’s other areas of mathematical interest such as algebra, elementary geometry, his ‘analysis situs’, number theory and Diophantine arithmetic proved to be of lesser importance in these years. Discussion of dyadic or binary mathematics  – that had not been treated in Leibniz’s mathematical and scientific correspondence for more than a decade – continued to be missing in the period from 1694 to 1696. From the spring of 1696, however, this topic came to the fore again in his general political and historical correspondence with duke Rudolf August of Wolfenbüttel, as for example the exposé of the binary number system given in an attachment to a letter of May 18, 1696, he sent to the prince. Finally, binary arithmetic, and in particular the binary number system, was presented in a philosophical vein in the famous ‘New Year’s Letter’ of January 12, 1697, to duke Rudolf August. In the year 1694 we find Leibniz’s first announcements of a planned work about a ‘scientia infiniti’. Over a longer period he had stressed the necessity of an explanation of the elements of this higher geometry, for example in a letter to Augustinus Vaget (Vagetius) on January 6, 1694. Then, in a no longer extant letter from February 24 (or March 7) 1694, he confided to Otto Mencke his plan to incorporate contributions of other mathematicians into the work as is evident from Mencke’s reply of March 17. There the editor of the Acta Eruditorum recommended that Leibniz include a resumé of his planned work in order to achieve the participation of other mathematicians. A couple of weeks later, on March 31, Leibniz also reported to Johann Bernoulli (who was likewise a correspondent of Mencke) about his desire to write a work about the principles of higher mathematics with the possible title ‘Scientia infiniti’. There then followed in relatively close succession references to the projected work in letters Leibniz sent to several additional correspondents, including Erhard Weigel (on May 20), Huygens (on June 22), Johann Andreas Schmidt (on August 13), L’Hospital (on August 16), and Adam Adamandy Kochański (on August 20), whereas, on the other hand, he failed to act on the suggestion of Mencke to include an outline of his conception of the work in the Acta Eruditorum. That which can be gleaned about the content of the planned work is relatively vague and general. It was to contain a theory of quantities, which should make fundamentally clear the different nature of finite quantities (algebra) and infinite quantities (infinitesimal calculus). Similarly, the important research results of leading mathematicians in the field of the new analysis were to be

28

Introduction: The Core Themes

presented, as is evidenced by the invitations sent in 1694 to Johann Bernoulli and his brother, to Huygens and to L’Hospital; in fact, Leibniz even wanted to have Newton participate in his work, as can be seen from his letter to Huygens of June 22 of that year. At this juncture the so-called priority dispute,28 or “quarrel between Newton and Leibniz”,29 already had a long prehistory and was destined to continue until Leibniz’s death and thereafter.30 By 1694 the controversy had been going on for over a decade having arisen primarily from the circumstance that neither Leibniz nor Newton had been informed early on about the achievements of the other in the area of infinitesimal analysis. The English mathematicians knew almost nothing until 1684 about Leibniz’s method, in particular about the date of its discovery and the chronology of its elaboration. Leibniz, for his part, had been informed by letters from the secretary of the Royal Society about certain results and, during his second London visit in October 1676, he had access to Newton’s manuscript De analysi per aequationes numero terminorum infinitas of 1669 but, until 1693, he had no knowledge either of the method of fluxions or of the chronology of its development. The result was that both sides could rightfully consider themselves to be the founder of infinitesimal mathematics and – in as far as not just the results but also the methods were comparable – believe that the other side could have borrowed from them. Of particular significance in relation to the smoldering priority dispute was the role played by Nicolas Fatio de Duillier. The latter – following a year-long cooperation with Huygens – lived in London from 1687 where he developed his own inverse tangent calculus and gained the trust of Newton by 1689 at the latest. There followed a second period of residence in Holland lasting more than a year during which time Fatio had regular contact again with Huygens. Leibniz however learned nothing at the time about the views of Fatio. All in all then, the view had arisen among several English mathematicians that Newton had discovered much earlier the infinitesimal calculus, which at the time was flourishing on the continent and was being attributed to Leibniz 28 Cf. T. Sonar and E. Knobloch (Epilogue), Die Geschichte des Prioritätsstreits zwischen Leibniz and Newton: Geschichte – Kulturen – Menschen, Berlin-Heidelberg, 2016; The history of the priority di∫pute between Newton and Leibniz: Mathematics in history and culture, Basel, 2018. 29 Cf. A. Rupert Hall, Philosophers at war: The quarrel between Newton and Leibniz, Cambridge 1980 and 2009. 30 Cf. C. Wahl, “‘ich schätze Freunde mehr als mathematische Entdeckungen’ – Zum Prioritätsstreit zwischen Leibniz und Newton”, pp. [111]–143 in: M. Kempe (ed.), 1716 – Leibniz’ Letztes Lebensjahr: Unbekanntes zu einem bekannten Universalgelehrten. Hanover: Gottfried Wilhelm Leibniz Bibliothek – Forschung 2 (vol. 2), 2016.

Introduction: The Core Themes

29

and, furthermore, that the Leibnizian method could only be a redraft with a different notation of the Newtonian fluxional calculus. This seemed all the more plausible since Leibniz had been caught ‘in flagranti delecto’, in flagrant delight as it were, having gained an insight – during his second London visit in 1676 – into Newton’s papers and, in addition, had received two detailed letters with Newton’s results, namely the so-called ‘epistola prior’, viz. Newton’s letter to Oldenburg for Leibniz and Tschirnhaus of June 23, 1676, and the so-called ‘epistola posterior’, viz. Newton’s letter to Oldenburg for Leibniz of November 3, 1676. To achieve public acceptance both for this view and for the achievements of the English mathematicians, evidence on Newton’s behalf needed to be promptly published. This concerned, on the one hand, Newton’s still unpublished fluxional calculus and, on the other hand, all communications of the results of the English mathematicians that had been sent to Leibniz. Wallis was the first who resolutely attempted to implement this plan in the context of his Opera Mathematica (vols 1, 2 and 3, published in 1695, 1693 and 1699). Since, however, Newton was unwilling to give his unrestricted approval to the effort, Wallis had to be satisfied at first with extracts from the relevant material. Leibniz first learned from Huygens of the intended publication of Newton’s method of fluxions in a letter of January 12, 1693, but he failed to react to the intelligence. He was then informed directly by Newton himself, in a letter of October 26, 1693, about the publication of extracts from the two ‘epistolae’ of 1676 and the solution or divestiture of an anagram there in the context of the revised Latin version of Wallis’ Algebra (in his Opera, vol. 2). Again in this case there was no reaction forthcoming from Leibniz. Huygens received the Opera volume in question, which appeared at the beginning of September 1693, from the author and he informed Leibniz accordingly on May 29, 1694. Since Leibniz did not possess a copy of the work, he asked Huygens, in a letter of June 22, to copy for him those parts of Wallis’ opus containing Newton’s new findings relating to the inverse-tangent method. And it was in this letter to Huygens that he articulated a proposal to include appropriate contributions of Newton, as they appeared in Wallis’ Opera Mathematica, in his planned ‘Scientia infiniti’ in order to do justice to his rival. On August 24, Huygens was able to send him a relevant extract which he had received from David Gregory. In the opening paragraph of his reply to Huygens, on September 14, Leibniz then remarked that although he had found agreement between the two forms of the infinitesimal calculus, he had nevertheless been irritated on not finding any new light being thrown on the inverse tangent method. This was in fact Leibniz’s one and only known, and immediately communicated, reaction to volume 2 of Wallis’ Opera. Essentially, while expressing his disappointment that only one of the two procedures for the solution of differential equations, namely the

30

Introduction: The Core Themes

formal power-series method, had been published, he passed over any questions of a chronological or temporal priority and a possible interdependence of Newton’s and his own infinitesimal methods although he did acknowledge the alleged similarity of the two methods. In point of fact, however, a totally new situation had now arisen and he could henceforth no longer assume two fundamentally different versions of the infinitesimal calculus with the inevitable questions of priority and plagiarism arising from this. The next volume of Wallis’ Opera appeared in mid-April 1695. In the “Ad lectorem praefatio” to this ‘first’ volume, Wallis had turned once again to the infinitesimal calculus of Newton and Leibniz with the intention of giving the impression that Newton’s calculus of fluxions had already been made known to Leibniz in the aforementioned letters of 1676.31 On November 23, 1695, Otto Mencke sent a copy (presumably of the two volumes that had appeared) to Leibniz, who significantly proposed including a short announcement or advertisement rather than a review of the work in the Acta Eruditorum. Contrary to Leibniz’s proposal, however, Mencke insisted on a detailed review of Wallis’ Opera in the Acta Eruditorum. In the light of Leibniz’s reluctance and dilatory approach in supplying a review text, Mencke felt justified in sending him a reminder. At last, on June 30, 1696, Mencke was able to express his thanks for Leibniz’s review but not without mentioning that Newton had given him a present of Wallis’ Opera. At the same time he offered – albeit in vain – his services as an intermediary in transmitting messages to Newton, to whom he wished to express his gratitude for the generous gift. In his anonymous review,32 in June 1696, Leibniz followed the strategy of not alluding to questions of priority and independence of the infinitesimal methods but rather of prioritizing his criticism of the fact that Wallis had (indeed for lack of knowledge) paid too little tribute to the achievements of the continental mathematicians in comparison with their English counterparts. Leibniz’s view of Wallis as an English nationalist is also reflected in a passage (deleted before dispatch) from a letter he sent to Thomas Burnett of 31 Cf. N. Guicciardini, “John Wallis as editor of Newton’s Mathematical Work”, Notes and Records of the Royal Society, (2012), pp. 3–17, in particular note 44 (p. 16). In the ‘Epistola prior’ and ‘Epistola posterior’ Newton was explicit about his debt to Wallis who, for his part, had by 1676 already completed a large part, possibly the first seventy-two of the hundred chapters, of his A Treatise of Algebra (London, 1685). Newton’s ‘epistola posterior’ probably then prompted him to add a further twenty-five chapters to this work; cf. also J. A. Stedall (ed., trans.), “Introduction: The arithmetic of infinitesimals”, pp. xi–xxxiii (in particular pp. xxxiif.) in Sources and studies in the history of mathematics and physical sciences:The arithmetic of infinitesimals[:] John Wallis 1656, New York, 2004. 32 Cf. A. H. Laeven, L. J. M. Laeven-Aretz, The authors and reviewers of the Acta Eruditorum 1682–1735, Electronic Publication Molenhoek (NL), 2014.

Introduction: The Core Themes

31

Kemney half a year earlier, on December 2, 1695. That Wallis would not accept Leibniz’s view was foreseeable and thus it was no surprise that Wallis complained about this review in the opening letter of his correspondence with Leibniz on December 11, 1696. In the mid-1690s Leibniz was also criticized for the first time for alleged deficiencies in the epistemological foundations of his infinitesimal calculus.33 The Dutch physician Bernard Nieuwentijt published two books entitled Considerationes circa analyseos ad quantitates infinite parvas applicatae principia, et calculi differentialis usum in resolvendis problematibus geometricis (1694) and Analysis infinitorum, seu curvilineorum proprietates ex polygonorum natura deductae (1695), respectively, in which he accused Leibniz of inconsistencies and lack of principles in his calculus. Since the author had his books forwarded directly to Leibniz and seemed authentic as regards the vein of his criticism, Leibniz thought he could lay the matter to rest with an equable reply published in the Acta Eruditorum in June 1695. In this assumption he was however mistaken. The central objections of Nieuwentijt,34 which were also directed against Pierre de Fermat and others, were outlined by Leibniz in letters to L’Hospital, Huygens and Johann Bernoulli in late June and early July, 1695. These objections were, in Leibniz’s view, aimed at the very definition of a mathematical magnitude. Thus, the ‘infinite parvum’ was for Nieuwentijt a nonentity or nothing. Accordingly, two magnitudes were only equal if their difference was zero. If Leibnizian dx differentials were equal, then the dy differentials were also. Higher-order differentials were all equal to zero. Finally, Leibnizian calculus was considered to be not applicable to exponential equations. Leibniz countered Nieuwentijt’s criticism with the simple ascertainment that experience had confirmed the results obtained with his mathematical magnitudes outlining his views, for example, in a letter to Detlev Clüver 33 Cf. P. Mancosu, Philosophy of mathematics and mathematical practice in the seventeenth century, Oxford, New York, 1996, in particular chap. 6, pp. 150–177 (Leibniz’s differential calculus and its opponents) and specifically, regarding the prolonged discussions about the foundations of the calculus with Bernard Nieuwentijt and Detlev Clüver, chap. 6,2 (pp. 156ff.). 34 Cf. R. H. Vermij, “Bernard Nieuwentijt and the Leibnizian calculus”, Studia Leibnitiana, vol. 21, (1989), pp. 69–86; R. H. Vermij, Secularisering en Natuurwetenschap in de zeventiende en achttiende eeuw: Bernard Nieuwentijt: Nieuwe Nederlandse Bijdragen tot de Geschiedenis der Geneeskunde en der Natuurwetenschappen, no. 38, Amsterdam-Atlanta (GA), 1991, in particular “Nieuwentijt als wiskundige” and “Nieuwentijt als experimenteel natuurkundige”, pp. 16–50; F. Nagel, “Nieuwentijt, Leibniz, and Jacob Hermann on infinitesimals”, pp. 199–214 in: U. Goldenbaum and D. Jesseph (eds.), Infinitesimal differences: Controversies between Leibniz and his contemporaries, Berlin, New York, 2008.

32

Introduction: The Core Themes

a year later at the end of June or early July, 1696. In his contribution for the Acta Eruditorum (in July 1695), he also dealt with the details of the difficulties raised by Nieuwentijt. A month later, he even appended Addenda to demonstrate the comparability of higher-order differentials with those of first order. Johann Bernoulli too publicly rejected the objections of Nieuwentijt in the Acta Eruditorum (in February 1696) but, notwithstanding all this, Nieuwentijt was still not willing to concede. From a letter of April 18, 1696, received from Mencke, Leibniz learned that Nieuwentijt had prepared a detailed rejoinder for the Acta Eruditorum, from which however Mencke was prepared to publish only an extract. Thereupon the author decided to publish his Considerationes secundae circa calculi differentialis principia et Responsio ad … G. G. Leibnitium as a book at Amsterdam in 1696 which was then reviewed by a third party, namely Martin Knorr(e), in the Acta Eruditorum in March 1697. All in all, the years between 1690 and June 1696 marked a most fruitful period for Leibniz in which he proposed and solved mathematical problems of his own, as well as working on problems proposed by others. This activity was reflected in his correspondence with a number of mathematicians and resulted in several publications in each of those years. In the following thirty-month period from mid-1696 to the end of 1698, it was above all in his voluminous correspondence with Johann Bernoulli that mathematical questions were discussed. In this correspondence at this juncture, an important mathematical issue was the continuing and widespread interest in the brachistochrone problem. The solution of the problem, or the curve of fastest descent in question, was found to be a segment of a cycloid.35 On June 19, 1696, Bernoulli communicated the brachistochrone problem to Leibniz and it was also made public in the same month in the Acta Eruditorum. Bernoulli likewise informed Leibniz that he had forwarded the problem to France and to England, namely to Pierre Varignon and John Wallis, respectively. Leibniz shared Bernoulli’s excitement about the problem and joined the effort to make it known through correspondence and in journal articles. Bernoulli himself had a flysheet about the problem printed in Groningen with the title Acutissimis qui toto orbe florent mathematicis (1697). A six-month deadline was 35 The solution of the brachistochrone problem has found a place both in the history of mathematics and in mathematical pedagogy; cf. J. A. van Maanen, Een complexe grootheid: leven en werk van Johan Bernoulli 1667–1748, Utrecht, 1995 and Amsterdam, 2016; J. A. van Maanen, Leibniz (1646–1716) and the curve of quickest descent, Conference: Curves in honour of Leibniz’s Tercentenary, Gresham College with the British Society for the History of Mathematics, Bernard’s Inn Hall, London (27 October 2016). Online (last accessed on March 1, 2023): https://www.gresham.ac.uk/lectures-and-events/leibniz -and-the-curve-of-quickest-descent.

Introduction: The Core Themes

33

announced at first but it was subsequently extended to Easter 1697 in order to enable mathematicians from Italy and France to participate in the challenge competition to solve the problem. Already on June 27 and 28, 1696, Leibniz had communicated the problem to Antonio Magliabecchi and to Bodenhausen, respectively, in order to have it announced in the Giornale de’ Letterati. Leibniz’s proposal to make the problem known in Florence and Pisa was implemented by Bodenhausen in the form of a flysheet announcing it that he distributed in the circles around Vincenzo Viviani and Alessandro Marchetti also with his personal ulterior motive of piquing the followers of Galileo. On his own initiative Bodenhausen also passed the problem on to the Tuscan prince Giovanni Gastone, as he confided to Leibniz in his letter of November 24, 1696. His draft for an announcement of the problem in the Giornale de’ Letterati was however superseded by a communication sent by Leibniz himself in September 1696 to Bernardino Ramazzini and which appeared in the same month in the Giornale. Bodenhausen provided Leibniz with detailed information about the reaction in Italy. To his disappointment he had to report that the Italians attributed their unwillingness to tackle the problem not to any inability to solve it but rather to other preoccupations. Bodenhausen himself, notwithstanding some knowledge of the differential calculus, had no luck in solving the problem, and he informed Leibniz accordingly in a letter of November 24, 1696. In the Netherlands the brachistochrone problem was disseminated through Johann Bernoulli’s flysheet. In addition Bernoulli prompted the publication of a note on the problem in the Rotterdam journal Histoire des Ouvrages des Savans in February 1697. His efforts met with a mixed response. Having failed to arouse the interest of Johannes Makreel – a friend of the critic of the differential calculus Bernard Nieuwentijt – Leibniz reflected on who might be a contender to solve the brachistochrone problem in a letter of March 5 to Bernoulli. Christiaan Huygens, had he still been living, would not have rested until he had found the solution, he thought. The only mathematicians from whom a solution might be expected were L’Hospital, Johann’s brother Jacob Bernoulli and also Newton; an afterthought was given to Johannes (or Jan) Hudde, the ‘burgemeester’ or mayor of Amsterdam, but who was most likely no longer a contender, it was thought. Johann Bernoulli, as he reported to Leibniz on March 30, received a further reaction from a professor in Harderwijk, namely Gerard Wijnen, who considered the problem to be not at all difficult whereas his explanations had revealed his lack of understanding. The sole contribution with a solution to the problem from the Netherlands came (anonymously) from Nicolaas Dierquens, the son of Salomon Dierquens, the court president in Den Haag; although based on the differential calculus it was, alas, flawed.

34

Introduction: The Core Themes

In France, Leibniz publicized the problem in the Journal des Sçavans in November 1696. Already in May of that year it had been forwarded by Pierre Varignon to L’Hospital, and some others, and L’Hospital duly presented it to the Académie des Sciences. Through L’Hospital, Bernoulli received a solution attempt by the Parisian mathematician Joseph Sauveur which he then forwarded to Leibniz as an attachment to his letter of January 29, 1697. The mistakes in this attempt, which followed from a false application of the differential calculus, were contentiously analyzed in the on-going correspondence between Leibniz, L’Hospital and Johann Bernoulli in 1697. In a letter of March 17, L’Hospital expressed the hope that his textbook on the differential calculus, namely the Analyse des infiniment petits (1696), might make a contribution in the struggle of the new calculus against the established methods. In this vein Bernoulli explained to Leibniz, on August 24, that Varignon too had complained about certain mathematicians of the old school who would do anything and everything to depreciate the differential calculus, whereby Bernoulli suspected that in particular the Abbé (François) de Catelan, Michel Rolle, Philippe de La Hire and some other more obscure persons were the ones intended here. From Basnage de Beauval, Bernoulli learned that La Hire had arrived by three different routes each time at the same incorrect solution, namely a semicubical parabola, as he informed Leibniz in a letter of June 17. L’Hospital’s solution of the brachistochrone problem, presented to the Académie des Sciences on April 20, 1697, was then an important victory over the opponents of the infinitesimal calculus. In his letter of August 24 to Leibniz, Johann Bernoulli could then include an extract from a letter, of August 6, from Varignon regarding L’Hospital’s success and the blow dealt to his opponents. Leibniz was happy to pass on this report to others, for example to Otto Mencke and to Etienne Chauvin at the end of August or early September of that year. The brachistochrone problem first reached England in the form of a communication from Johann Bernoulli to John Wallis in the summer of 1696. In addition Bernoulli sent two copies of his flysheet to Wallis and Newton, respectively, in January 1697. The brachistochrone problem was the only mathematical contest in Leibniz’s ambit in which Newton participated. It provoked a plagiarism allegation from the side of Fatio de Duillier and initiated thereby a new phase of the priority dispute. In the light of this, English reactions to the brachistochrone problem, as well as those in Leibniz’s circle to Newton’s solution, have special significance. Already in March 1697, Bernoulli received from Basnage de Beauval an anonymous solution to the problem from England – without details of the exact approach taken  – which had appeared two months earlier in the Philosophical Transactions. Bernoulli sent a copy to Leibniz on March 30 and

Introduction: The Core Themes

35

he correctly concluded that Newton was the author of the solution in question. The author of the piece had acknowledged that he had received two flysheets with the problem and Bernoulli considered Newton to be more familiar with recent developments in infinitesimal calculus than Wallis and in fact Bernoulli even believed at this moment that Wallis had died. For Leibniz, the fact that Newton had needed only a single day to solve the problem – as he had indicated in presenting his solution – was a welcome proof of the effectiveness of the infinitesimal calculus since, as he told Bernoulli on April 25, for someone who was in command of the method, a day was more than enough whereas, for those not versed in the method, even a period of years would not suffice. The view that Leibniz presented to Bernoulli here was that Newton had partly studied the differential calculus and partly an analogous method. Words of a similar tenor, namely that only those had been able to solve the problem who had used the differential calculus, are to be found in a letter of May 7 to Etienne Chauvin, which was then partly reproduced in the Nouveau Journal des Sçavans in May–June 1697 and in Leibniz’s own contribution regarding the brachistochrone problem in the Acta Eruditorum in May 1697. The latter article did not however take Newton’s solution into account since Leibniz had already sent his own contribution to Mencke before he received that of Newton. The fact that he did not send a subsequent amendment to the journal editor was indeed a conscious decision on his part which he justified, in his letter to Bernoulli on April 25, with the behavior of his English rivals who, without waiting for the deadline to pass, had published the solution of the problem and had not even sufficiently acknowledged the services of Bernoulli himself. In May 1697, Thomas Burnett of Kemney confirmed Leibniz’s assumption that Newton was indeed the author of the solution in question and Leibniz, for his part, instructed this correspondent, on May 28, to convey his esteem to Newton. In addition, Leibniz emphasized that he was not the one who had sent Newton the brachistochrone problem but rather Johann Bernoulli. He himself, on receiving the problem from Bernoulli, had solved it as rapidly as Newton had, namely while travelling on a coach between Hanover and Wolfenbüttel and then on arrival at his lodgings. Later, following the allegations made against him by Fatio de Duillier in his solution published in 1699 – which included the allegations of plagiarism of Newton – Leibniz wrote to Wallis that Bernoulli had sent the flysheet to Newton without his knowledge and, furthermore, that it was not his style to provoke men of merit with problems. In fact, Leibniz had mentioned the brachistochrone problem neither to Wallis nor to Tschirnhaus. He did, however, recommend on November 28, 1698, that Bernoulli, his brother, or others, send further problems to Newton for the sake of the advancement of

36

Introduction: The Core Themes

science. In a letter of September 8, 1699, from John Wallis, Leibniz was likewise informed, albeit belatedly, about yet another anonymously-published English solution of the brachistochrone problem, namely that of David Gregory in the Philosophical Transactions. The only correct solutions then of the brachistochrone problem, which reached Mencke before the deadline had elapsed, came from Johann Bernoulli, his brother Jacob, L’Hospital and Newton. Johann Bernoulli had already sent his solution to Leibniz on July 31, 1696, with the request that he forward it on time to Mencke. Leibniz complied with this request but he also persuaded Johann to keep one of his two solution approaches secret. The first approach, which he characterized as indirect, established an analogy to the problem of finding the path of a ray of light in homogeneous media. This allowed him to embrace a general hypothetical connection between path and velocity in place of Galileo’s law of falling bodies. From the law of refraction, as it applied to the infinitely small, Bernoulli derived his differential equation. In the second or direct solution approach, as he called it, he compared infinitely small sections of the curve of different curvatures but with a common circle of curvature center, and derived from this an equation for the curvature radius. In addition, he showed by a synthetic proof that the cycloid was the only possible solution. Leibniz saw potential in Bernoulli’s direct approach and persuaded him not to publish either this or the synthetic proof. For the same reason, Leibniz also declined to publish his own solution. Bernoulli’s brother Jacob sent his solution directly to Mencke, as he informed Leibniz on February 6, 1697. L’Hospital first sent, on February 25, a solution attempt to Johann Bernoulli who forwarded it to Leibniz on March 5; he then returned it to L’Hospital on March 8. Finally, on March 17, L’Hospital sent his final solution to Leibniz for forwarding to Leipzig. In his own contribution or introduction to the four solutions being published, Leibniz – having withheld his own solution – could only comment on the competition describing that which he considered novel in this kind of extremal problem. And, furthermore, through his intensive occupation with the brachistochrone problem it had become clear to him how far his analysis was still removed from perfection. From Tschirnhaus, who rejected the differential calculus, no solution of the brachistochrone problem was to be expected from the outset especially in view of the fact that he had previously failed to provide a solution to the catenary problem although he had been publicly invited to do so after he had announced a new method of his own. This, and further announcements in Tschirnhaus’ article “Nova et singularis geometriae promotio” of November 1695, led to the skepticism and criticism expressed by the Bernoulli

Introduction: The Core Themes

37

brothers in letters to Leibniz in 1696 and 1697. Johann, for example, in a letter of January 29, 1697, compared Tschirnhaus to an alchemist who touted his secrets in pompous words without ever producing anything. Leibniz’s criticism was also in evidence in the drafts of his letters whereas his dispatched texts, like that sent to Jacob Bernoulli at the beginning of April 1697, were more diplomatic. Tschirnhaus’ article “De methodo universalia theoremata eruendi” of May 1697, which Mencke had placed among the solutions of the brachistochrone problem, provoked further criticism in Leibniz’s correspondence with Johann Bernoulli and L’Hospital. In his article Tschirnhaus only briefly mentioned the problem. He presented the cycloid as the solution but he left open the question as to whether he had solved the problem himself or not. Both Bernoulli and Leibniz suspected that he had most likely learned the solution from Mencke during the Leipzig Spring Fair of 1697. In conclusion, it may be recalled that the brachistochrone problem was a mathematical problem rooted in the physical world and the considerations concerning it were subject to physical influences. Thus, for example, in connection with the solution of this problem Leibniz and Johann Bernoulli discussed orthogonal trajectories, or specifically a family of curves in a plane that intersect a given family of curves at right angles. Methods for the determination of orthogonal trajectories had already been developed in 1694 by Leibniz and Bernoulli. An important influence here came from physics and in particular from ‘Huygens’ Construction’ – which was published in the Traité de la lumiere (1690)36 – in the theory of light propagation in which the light waves were shown to be orthogonal to the rays. In connection with the presentation of his solution of the brachistochrone problem, Jacob Bernoulli challenged his brother Johann to solve other mathematical problems, among which was the isoperimetric problem. Jacob’s problem was a generalization of the classical isoperimetric problem, which calls for the determination of the plane figure of the largest possible area whose boundary has a specified length. He asked Leibniz, on February 6, 1697, to help make the problem known in France and Italy. Replying at the beginning of April, Leibniz recalled however that the brachistochrone problem had shown that nothing was to be expected from France (with the exception of L’Hospital) and Italy and so he did nothing to help circulate the isoperimetric problem. Thus, the Bernoulli brothers were to remain the only ones to seriously tackle this problem. Already on June 17, 1697, Johann could announce his solution of 36 Cf. F. J. Dijksterhuis, Lenses and waves: Christiaan Huygens and the mathematical science of optics in the seventeenth century, Dordrecht, New York, Boston, London, 2004, and in particular chap. 6, pp. 213–254 (1690 – Traité de la lumière).

38

Introduction: The Core Themes

the problem in a letter to Leibniz but, as Jacob had not specified the procedure for adjudicating and awarding the prize money he had offered for the solution of this problem, there ensued a long drawn-out conflict with his brother. Jacob suspected that Leibniz had taken the side of Johann and the dispute about the isoperimetric problem may have been the reason for the disruption of Leibniz’s correspondence with Jacob. The latter may also have taken offence at Leibniz’s letter of early April 1697 in which he expressed reserved criticism of Jacob’s behavior towards his brother Johann. This letter remained unanswered until 1702. In a further skirmish concerning David Gregory in 1697, which had relevance for the smoldering priority dispute with Newton, the editorial policy of Mencke became an issue.37 In a letter of August 8, 1698, to Johann Bernoulli, Leibniz accused Mencke of giving preferential treatment to foreigners in order to ensure their goodwill. The cause for Leibniz’s complaint was Mencke’s decision to reprint Gregory’s solution for the catenary problem from the Philosophical Transactions of August 1697 in the Acta Eruditorum in July 1698. Leibniz considered the publication to be inappropriate as Gregory’s solution was coming far too late, a sentiment he confided to Johann Bernoulli in a letter of September 1, 1698. When, in addition, the solution turned out to defective, Leibniz wrote an anonymous reciprocation which Mencke then reluctantly published in the Acta Eruditorum in February 1699. When Gregory in turn reacted in the Philosophical Transactions to Leibniz’s anonymous criticism, Mencke saw himself obliged to reprint this reply in the Acta Eruditorum in July 1700 and avoid any accusations of censorship, as he informed Leibniz in advance in a letter of November 11, 1699. When Johann Bernoulli, in a subsequent letter of January 25, 1701, desired a resolute reaction in which fresh contradictions in Gregory’s solution would be laid bare, Leibniz composed a response three days later in which he called for Gregory to obtain Newton’s approval of his proof. Perhaps, however, Leibniz did not pursue this demand in order not to tax Mencke’s patience too much. The episode with Gregory had nonetheless repercussions for the smoldering priority dispute. And so, when Leibniz complained to Wallis about Fatio de Duillier’s accusations against him, Wallis compared, on September 8, 1699, Fatio’s behavior to the critique of Gregory’s solution of the catenary problem. 37 Cf. U. Mayer, “‘Kein tummelplatz, darauff gelehrte leute Kugeln wechseln’  – Principles and practice of Mencke’s editorship of the Acta eruditorum in the light of mathematical controversies”, pp. 49–59 in: J. Pfeiffer, M. Conforti, P. Delpiano (eds.), Les journaux savants dans l’Europe modern: Communications et construction des saviors, (Archives Internationales d’ Histoire des Sciences, vol. 63, no. 170–171), 2013.

Introduction: The Core Themes

39

In the person of Wallis, with whom he established contact at the end of 1695 by means of a billet, Leibniz had once again a correspondent from Newton’s milieu interested in mathematics. Another billet addressed to Newton himself had produced no reply. It was nonetheless a favorable moment for the exchange of views on the emerging disgruntlement between the mathematicians around both Leibniz and Newton. Wallis’ De algebra tractatus of 1693 (in Opera, vol. 2), contained a short presentation of Newton’s calculus of fluxions that had previously not been published. Leibniz’s calculus was only referred to as being similar to that of Newton. As indicated already, Leibniz had received from Huygens in 1694 the relevant extract from the second volume and, on November 23, 1695, Mencke had sent him the first two volumes of Wallis’ Opera. In his anonymous review in the Acta Eruditorum in June 1696 Leibniz criticized the one-sided representation by Wallis. In a letter to Leibniz of August 10, 1696, Bernoulli commented that the differential calculus had not received appropriate praise from Wallis and two weeks later, on August 25, he conjectured that Newton had developed the calculus of fluxions on the foundation of information he had received from Leibniz. Replying on September 2, Leibniz relativized Bernoulli’s suspicion without however contradicting him. It was true that he had, twenty years earlier, communicated the foundations of the differential calculus to Newton and before the latter had communicated anything about his methods. However, whether or not this had helped Newton, he could not really say and he was unwilling to pass judgement in the matter. Wallis, in his first letter to Leibniz on December 11, 1696, defended himself against the criticism expressed in the review, the author of which he correctly assumed to be none other than Leibniz himself. Wallis was familiar with only two articles of Leibniz, one of which, namely “The true proportion of the circle to the square” had appeared in the Philosophical Collections in April 1682, two months after the publication of the Latin version in the Acta Eruditorum. Acceptance of the fact that often the limited circulation of scholarly results, rather than malicious intentions, was the reason for their non-percipience, enabled Wallis and Leibniz to unbiasedly discuss priority issues in their correspondence and accusations of plagiarism did not arise. Leibniz wrote, in a letter to Wallis of June 7, 1697, that he had first learned about the similarities between his own and Newton’s calculus through the brief reference in Newton’s Principia Mathematica (1687) and the presentation in Wallis’ Opera. Wallis, in his reply of August 9, did not take a stance regarding priority in the matter of the differential or fluxional calculus but merely stressed that for him the difference between Leibniz’s calculus and that of Newton was simply a question of nomenclature. He offered examples of further mathematical concepts which had appeared under different names in the writings of different

40

Introduction: The Core Themes

authors, before expressing his desire for an elucidation of the similarities and differences of the two forms of the calculus. Wallis also pointed to a relationship of the differential calculus with other forms of calculus like, for example, his own tangent method. While, at first, he appeared to acknowledge the advances made by the differential calculus in comparison with other methods, he later – for example in his letter of August 1, 1698 – reverted to a comparison of the differential calculus with his own method of tangents and described the two forms as being essentially equivalent. Leibniz, for his part, in a letter of June 7, 1697, objected to the equalization of his own and Newton’s calculus, except perhaps under the broader heading of infinitesimal analysis. And a year and a half later, in a letter of January 8, 1699, in opposition to any suggestion of such identicalness, Leibniz pointed out the fundamental differences between his and Wallis’ method and those of others, like Fermat and even Archimedes, recalling in particular the recognition accorded him for his calculus by Christiaan Huygens towards the end of his life. The form of parlance in Leibniz’s correspondence with Wallis was accommodating, even then when achievements and the honor of the respective nations were at stake.38 Nonetheless, Wallis’ unuttered motivation and agenda was to help the calculus of fluxions assert itself against the differential calculus. Wallis had learned of the success of the differential calculus on the continent, specifically in the Netherlands, shortly before his correspondence with Leibniz began, as he mentioned in his first letter to Leibniz on December 11, 1696. Thereafter Wallis pursued the goal of having Newton’s letters to Leibniz of June 23 and November 3, 1676, respectively (viz. the ‘epistola prior’ and the ‘epistola posterior’) published. When he learned of the existence of Leibniz’s replies to these letters, he tried to obtain them. Newton proved to be anything but cooperative in this matter and Wallis’ enquiry met with no success at first. Already in his first letter to Leibniz he requested copies of the Newton letters. Later, however, he did receive transcriptions of Leibniz’s letters from Newton and Hans Sloane. His academic colleague at Oxford, David Gregory, was likewise actively involved in obtaining the letters. Whereas at first the issue had only been to establish that Newton was already in possession of the calculus of fluxions in 1676, the possibility of plagiarism was now in the air. 38 Cf. S. Probst, “Leibniz und Wallis: Eine Übersicht über neuere Quelleneditionen und Forschungen”, pp. 89–101, in: G. Wolfschmidt (ed.), Festschrift – Proceedings of the Scriba Memorial Meeting  – History of Mathematics, Hamburg, 2017; S. Probst, “The relation between Leibniz and Wallis: An overview from new sources and studies”, in: Quaderns d’història de l’enginyeria, vol. 16, (2018), pp. 189–208.

Introduction: The Core Themes

41

In correspondence with Leibniz, however, Wallis referred only to a scholarly interest as motivation for his plan to edit the letters. He even offered Leibniz the possibility of preventing the publication of his letters or of undertaking changes. Leibniz, who was not able to locate his versions of these letters himself, expressed his trust in Wallis. The Newton letters were then printed in the third volume of Wallis’ Opera Mathematica (1699). And, in the conflict that ensued from the accusations brought forward by Fatio de Duillier against Leibniz and that were printed by the Royal Society, Wallis actually defended Leibniz, indeed successfully, at the Society. The success of the differential calculus led not only to envy, as Leibniz and Johann Bernoulli continued to suspect, but also to criticism of its foundations. By 1696, discussions along these lines with Bernard Nieuwentijt and Detlev Clüver had already been carried on for some time. After the technical aspects had been exhaustively treated, the central question in Leibniz’s circle was how to deal with persistent and obstinate critics. Nieuwentijt considered among other things the use of differentials of second and higher order to be contradictory and he devised an alternative to the differential calculus from which these had been eliminated. Leibniz had defended his calculus in the Acta Eruditorum against Nieuwentijt’s objections and exposed mistakes that he had made. Nieuwentijt’s reciprocation, the publication of which in the Acta Eruditorum had been refused by Mencke, was then printed in Amsterdam as Considerationes secundae circa calculi differentialis principia et responsio ad  … G. G. Leibnitium (1696). In this tract Nieuwentijt renewed his criticism of the differential calculus. In addition, Mencke received a further manuscript of Nieuwentijt that replied to an article of Johann Bernoulli. On July 28, 1696, Mencke delegated to Leibniz the decision about the best course of action to be taken in the matter of this manuscript. Leibniz then forwarded the manuscript to Johann Bernoulli who in turn added marginal notes for Mencke to add in the form of a commentary – in the event of the manuscript being published – before returning it to Leibniz on August 25. Thereafter, Leibniz moderated somewhat the twang of Bernoulli’s interjections before finally returning the manuscript to Mencke. At the same time he advised Mencke against publication with the result that three quarters of a year later Nieuwentijt had to enquire about the fate of his work. Mencke replied, on March 2, 1697, that the contribution had failed to find any resonance there. Nieuwentijt’s Considerationes secundae were likewise no longer taken seriously by Leibniz and Bernoulli, since they found the work to be no more than a repetition of the author’s former objections and an adventurous treatment in dealing with the infinite. Their discussions in late 1696 and early 1697

42

Introduction: The Core Themes

concentrated mainly on how best to react to Nieuwentijt. The fact that Mencke too was disconcerted in this matter led to further complications. At first, Leibniz considered keeping his counsel to be the best course of action for him in the matter: as long as Nieuwentijt was not prepared to listen and defended his position stubbornly, then he ought to be treated like a heretic who, according to the bible – as he wrote to Bernoulli on January 7, 1697 – ought to be avoided once admonitions had proved to be of no avail. Johann Bernoulli, however, prepared a response to Nieuwentijt’s critique of his treatment of exponential equations. Mencke did not want to alienate Nieuwentijt and considered it unwise to publish Bernoulli’s harsh criticism without first having presented Nieuwentijt’s Considerationes secundae in the Acta Eruditorum. Accordingly, he requested Bernoulli to provide an objective summary account of the tract. This was however preempted by a review of the work submitted by Martin Knorr(e) which duly appeared in the Acta Eruditorum in March 1697. Immediately following this review, a toned-down version of Bernoulli’s rejoinder was printed. Notwithstanding Mencke’s efforts, Leibniz considered the book to have been overrated in the review and he prepared a compilation of the (in his view) most absurd passages from Nieuwentijt’s tract with the motto – formulated in his letter of March 10 to Mencke – “recitasse est refutasse” in mind. Reluctantly, Mencke conceded and published the series of extracts as he informed Leibniz on March 23, 1697. Finally, Jacob Bernoulli also replied to Nieuwentijt by pointing out – in his solution of the brachistochrone problem – the value of second order differentials. In 1686–1687 Clüver published a couple of enigmatic articles in the Acta Eruditorum, which included in particular his “Quadratura circuli infinitis modis demonstrate” (July 1686), in which he also announced a new ‘scientia infiniti’. This matter was however first discussed in correspondence with Leibniz only in the year 1694 although the two had already been in sporadic contact over a longer period. Clüver explained his principal criticism in a letter of June 14, 1694, which, however, only reached Leibniz a year later. According to Clüver, the differential calculus was not sufficient to achieve ultimate geometrical precision. The supposition that the relationship of unity to infinity (one over infinity) be equal to zero was impossible and that, he insisted, was the source of the imperfection. Clüver’s objections were directed not just against Leibniz’s differential calculus but also against Archimedes’ quadrature of the parabola and were debated not only in correspondence with Leibniz but also with Jacob Bernoulli. The responses of both Leibniz and Bernoulli make clear the degree of accuracy they ascribed to the differential calculus as well as their different attitudes to dealing with critics. As regards Clüver’s correspondence with Leibniz, a point was finally reached where the dispute no longer seemed

Introduction: The Core Themes

43

meaningful to Leibniz and he advised the correspondent to henceforth devote himself to astronomy and other areas of mathematics. In a letter of June 3, 1697, he explained to Clüver, in diplomatic terms, his approach in dealing with critics referring in particular to Nieuwentijt. In the year 1698 a new critic arrived on the scene in the person of Burchard de Volder; in contrast to Nieuwentijt and Clüver, however, he could quickly be convinced. Johann Bernoulli reported to Leibniz about de Volder’s difficulties with the infinitesimal calculus, having made his acquaintance in Leiden during a journey through the Netherlands. In contrast to Nieuwentijt and Clüver, de Volder had no alternative conception. He had occupied himself with the infinitesimal calculus out of interest and, while considering the quadrature of the hyperbola, had encountered a (supposed) contradiction. De Volder’s mathematical difficulties were no doubt dispelled following Johann Bernoulli’s explanations and their main effect was to initiate a lengthy discussion between Bernoulli and Leibniz about the nature of the infinite. In general, then, the main allegation brought against the differential calculus  – as indeed against the fluxional calculus of Newton39 – was that its proofs did not have the same rigor as those of the ancients or of classical mathematics. This was however, according to Leibniz, not the ambition of the differential calculus which was essentially an analytical method for obtaining results. As a member of the Académie des Sciences, Philippe de La Hire was one of the most influential supporters of the old methods. Leibniz availed of the sole letter to him, on October 18, 1697 – in which terrestrial magnetism and not mathematics was at the center of interest – to deal with the correspondent’s skepticism regarding the calculus. Finally, L’Hospital’s textbook on the differential calculus, namely the Analyse des infiniment petits pour l’intelligence des lignes courbes, which appeared in 1696 and which Leibniz received via Tschirnhaus in November of that year, represented a major contribution to the spread and dissemination of the differential calculus. L’Hospital’s opus contained material assimilated from private lessons which Johann Bernoulli had given him in Paris in 1691 and 1692, as well as from Bernoulli’s letters to him. Notwithstanding L’Hospital’s acknowledgement of Bernoulli’s influence in the preface, and annual payments made by the author to him since 1694 for the relinquishment of scholarly results, Bernoulli experienced the publication as an affront although he did manage to keep his counsel in public. L’Hospital did not include the integral calculus in his 39 Cf. M. Kline, Mathematics in western culture, Oxford, London, New York, 1953 and 1964, in particular chap. 15, pp. 214–233 (Grasping the fleeting instant: The calculus), specifically p. 231.

44

Introduction: The Core Themes

textbook in order not to preempt Leibniz’s planned – but never completed – opus on ‘scientia infiniti’. Leibniz’s satisfaction following the appearance of L’Hospital’s textbook is in evidence in numerous letters he wrote. In particular, the fact that the author had, in the foreword to the book, characterized Leibniz’s calculus as being superior to Descartes’ geometry, was a particular source of pleasure for Leibniz and a backing for him against Cartesian critics. To those correspondents interested in the differential calculus Leibniz recommended the book as an introduction as, for example, in letters to Domenico Guglielmini and to Johann Balthasar von Wernher. To the latter he expressed the desire that the book be translated into Latin and he arranged for the work to be reviewed in the Nouveau Journal des Sçavans (in September 1696) and in the Acta Eruditorum (in March 1697). The fact that John Wallis was acquainted with the book, when writing his letter of August 9, 1697, is evidence not just of its rapid and widespread distribution but also of the fact that the development of the differential calculus was now also being followed with attention in England. Besides L’Hospital’s textbook on the differential calculus, Leibniz’s interest in the communication and dissemination of mathematical knowledge also found expression in his correspondence in the second half of 1696 and in early 1697 with Augustinus Vagetius, where the conception of a textbook for teaching mathematics was at the center of interest. In comparison with previous years, mathematics was no longer center stage in Leibniz’s correspondence between 1699 and 1701. One reason for the reduced importance of mathematics, specifically in his correspondence with Johann Bernoulli, was a shift in his mathematical interests. Leibniz now devoted himself increasingly to binary calculus which was discussed mainly in his correspondence with Philippe Naudé and Pierre Dangicourt whereas his exchanges with Johann Bernoulli petered out on this issue. Likewise the discussion between Leibniz and Johann regarding the existence of the infinite and the infinitely small, which had begun in 1698, ended with Leibniz’s clarification of his conception of the infinite but without agreement being reached between the two. Leibniz’s correspondence with Jacob Bernoulli was interrupted at this juncture. The estrangement between the two led to a brief alliance between Jacob and his compatriot Nicolas Fatio de Duiller. Jacob’s correspondence with Fatio between July 1700 and August 1701 mirrored Leibniz’s dispute with Fatio. However, following Fatio’s return to England from his temporary residence in his native Swiss municipality (Duillier) and Jacob’s admission to the Berlin Society of Sciences in 1702, the alliance evidently ended. Leibniz’s dispute with Fatio however went public in the year 1699. In the summer of that year, Fatio sent a short tract of his entitled Lineae brevissimi descensus investigatio

Introduction: The Core Themes

45

geometrica duplex (1699) – which was attached to a work entitled Fruit-walls improved … or, a Way to build walls of fruit-trees; whereby they may receive more sun shine and heat than ordinary (1699) – to both L’Hospital and to Varignon, who in turn referred to it in a letter to Johann Bernoulli on July 12, 1699; both correspondents found it to be outrageous. It contained a belated solution of the brachistochrone problem as well as the derivation of the problem of the solid of revolution of least resistance (for rarified fluids) which Newton had included (without proof) in his Principia mathematica (1687). Already on the first page of the tract, Fatio took umbrage at Leibniz’s Communicatio, in which he had commented on the solutions of the brachistochrone problem in the Acta Eruditorum of May 1697. There Leibniz had insisted on the vigor and superiority of his calculus, stressing the difficulty of the task in hand and praising the solutions that had been submitted. Fatio felt that he had been demoted, since Leibniz had not included him among those, like Newton, he attested the ability to solve the problem and to whom he had communicated the enunciation of the problem in advance. Fatio’s criticism was however of a more fundamental nature. He accused Leibniz of acting, as it were, from a mathematical throne and of distributing praise at his own discretion and he condemned the practice of posing mathematical challenge questions. Towards the end of the tract Fatio placed the accusation that surely was most offensive to Leibniz. To begin with, Fatio stated that he himself had developed similar methods to those of Leibniz and Newton and he went on to insinuate that Leibniz could even have plagiarized Newton. Fatio was referring here to the contemporaneously-published third volume of Wallis’ Opera in which the correspondence of 1676 between Leibniz, Oldenburg and Newton had been published. L’Hospital forwarded Fatio’s tract to Leibniz on July 13, 1699, and also pointed to Wallis’ edition whose purpose he saw as part of an effort on the side of the English to claim the glory for the invention of the differential, or rather fluxional, calculus. Johann Bernoulli, who felt himself under attack because he had disseminated the brachistochrone problem announcement, also informed Leibniz of Fatio’s invectives: he passed on Pierre Varignon’s letter of July 12 in which these were quoted in detail. Bernoulli was especially surprised since he had (in 1691) instructed Fatio’s older brother Jean Christophe in the differential calculus and he now suspected Fatio himself could have profited from this. Varignon likewise judged Wallis’ edition to be an attack on Leibniz’s right to claim the invention. In point of fact however, Leibniz, who regarded his earlier correspondence with Oldenburg and Newton as innocuous, had been consulted in advance by Wallis and had granted him permission to publish the letters as he then explained to Bernoulli (on August 4) and to L’Hospital (on August 7).

46

Introduction: The Core Themes

Leibniz was nevertheless surprised at the intensity of Fatio’s allegations. At first he did not see any connection with the previous history to which Fatio was to refer a year later in a letter, of August 30, 1700, for him and for Otto Mencke. In fact, Leibniz did have indirect contact with Fatio through Christiaan Huygens in 1691–1692 with the objective of arranging an exchange of their respective inverse tangent methods. Leibniz had in the end declined Fatio’s offer to reveal his method which he thought he could deduce for himself. For Fatio, the fact that he had been overlooked in the competition to solve the brachistochrone challenge problem amounted to a deliberate exclusion. However, Leibniz and Bernoulli had little sympathy for Fatio’s apparent desire for recognition. In their eyes this ought to be earned and exactly those challenge problems, which had been criticized by Fatio, offered an opportunity of doing so. The fact that the idea of a competition of methods had arisen here also led to disgruntlement elsewhere. Thus, after Leibniz had criticized David Gregory’s belated solution of the catenary problem in an anonymous contribution in the Acta Eruditorum in February 1699, Wallis complained to him, on September 8 of that year, as did Gregory to Mencke, who duly informed Leibniz on November 11. Leibniz then orchestrated a two-track reaction to Fatio’s publication, namely in the form of a complaint to the Royal Society – whose imprimatur the work contained – and by means of official rejoinders in the Acta Eruditorum in November 1699. The complaint he directed to Wallis in a letter of August 16, whereby he kept his counsel regarding any accusation of plagiarism. Wallis forwarded Leibniz’s suit to Hans Sloane and both of them, without having seen Fatio’s tract, condemned Fatio’s actions at once. Wallis included, with his letter of September 8 to Leibniz, an extract from Sloane’s letter to him of September 5 in which it was asserted among other things that the Society had known nothing of the matter in advance, had great veneration for Leibniz and regretted the interruption of the epistolary commerce with him. Thus, Leibniz actually profited from the dispute with Fatio in that he gained a new correspondent in the guise of Sloane and was thus in official contact once again with the Royal Society. Sloane even offered to send Leibniz the Philosophical Transactions to which he otherwise had only irregular access. For his public response to Fatio, Leibniz obtained a placet in advance from Mencke  – who, in general, was anxious to keep his journal free from such disputes – addressing the matter in a letter of August 2, 1699, to which Mencke replied on August 8. On August 7, he sent a draft to Johann Bernoulli who, in his reply of August 17, provided some additional commentarial information about Fatio and added his derivation of the problem of the solid of revolution of least resistance for the publication of which he now granted Leibniz permission. Bernoulli was horrified however when Leibniz – overriding the resistance

Introduction: The Core Themes

47

of Mencke who, in his letter of November 11, 1699, accused both of them of defamation of character – published not only the solution but also Bernoulli’s letter in only a slightly tempered and shortened form in the November number of the Acta Eruditorum. For Bernoulli the issue had arisen at an unfavorable moment. He had just publicly described Wallis as an overzealous defender of English glory in the belief that the latter had died, as he explained to Leibniz in a letter of December 1. He now feared not only the wrath of Wallis but also that Fatio’s anger would be directed against him, as he explained in a letter to Leibniz of April 17, 1700. In addition, it adversely affected his position in relation to Mencke who had become increasingly less inclined to publish the polemical exchanges of the Bernoulli brothers. In his reply of April 25, Leibniz excused his behavior with the circumstance that Bernoulli had reacted with little enthusiasm to the mathematical result attached to his response and, finally, in accordance with Bernoulli’s wishes, he published his response in a revised form in his May 1700 article entitled “Responsio ad Dn. Nic. Fatii Duillierii imputationes”, which was then applauded by Bernoulli in a letter to him of June 19 of that year. Fatio de Duillier in turn responded both to Johann Bernoulli and to Leibniz sending both replies through Jacob Bernoulli to Mencke along with permission for their publication. Leibniz had the response intended for Johann Bernoulli sent to him and he arranged for its publication in a – in part at least – considerably shortened and revised form. In particular he replaced in the derivations of the isochrone and of the solid of revolution of least resistance – which were once again included there – the notation of the Newtonian method of fluxions with that of the differential calculus. He himself answered Fatio in a letter of January 4, 1701. In this way he conformed with Mencke’s desire to fill his journal with “realia” and not with polemical disputes. Fatio communicated his closing reaction only to Jacob Bernoulli with whom he had found agreement in his complaints about Leibniz’s hegemonic dominance in the republic of letters. An instance of this, Jacob saw in the foundation of the Berlin Society of Sciences. Fatio gave Jacob an account of the English resentment against Leibniz resulting from Wallis’ edition. Because of the close connection between Leibniz and Henry Oldenburg, it was assumed in England that Leibniz had been informed about Newton’s calculus. Fatio likewise expressed his views in a letter for Mencke and Leibniz of August 30, 1700, to which Leibniz replied on January 4, 1701. As Fatio had admitted that Newton did not approve of his attacks against him, Leibniz could present himself here as someone who enjoyed the support of Wallis and Newton and who had found support in his strategy of not taking accusations of plagiarism seriously.

48

Introduction: The Core Themes

While the admission of Leibniz and the Bernoulli brothers to the Académie des Sciences represented an endorsement for the differential calculus, it could not hide the fact that it was still rejected by a number of powerful members of the French academy. Supporters like Varignon and L’Hospital were confronted by powerful opponents like Michel Rolle. While L’Hospital’s solution of the brachistochrone problem silenced the opponents at first, Rolle’s criticism of the foundation of the calculus – about which Varignon informed Johann Bernoulli in September 1700 – marked the beginning of a long lasting dispute. Although, in the autumn of 1701, the Académie set up a commission to settle the conflict, an expansion of the dispute was in evidence at the end of 1701. This dispute, like that between the Bernoulli brothers, is also reflected in Leibniz’s mathematical correspondence at this juncture. All in all then, Leibniz’s correspondence throughout the 1690s and in the first years of the new century throws light on his diplomatic skills in relation to his publication policy and his conflict management policy both in situations where he defended his discovery claims and in those where he acted as a mediator (as for example in the dispute between the Bernoulli brothers).40 Dyadic (or binary) mathematics began to appear more frequently in Leibniz’s correspondence around 1700. Already in 1696, he had, in discussion with duke Rudolf August of Wolfenbüttel, lauded the dyadic or binary number system with which one could represent, like in a mirror, the creation or the origin of things out of ‘God’ and ‘Nothing’. He had even suggested using it in the foreign missions. Such philosophical thoughts he had likewise communicated to the China missionary Claudio Filippo Grimaldi in January or early February 1697. To the latter he had also indicated that he saw the main use of binary arithmetic in the investigation of the properties of numbers. However, in his mathematical correspondence, binary arithmetic had previously played hardly any role, although he had, in the early 1680s, referred to it in letters to Ferguson, Clüver and Tschirnhaus. Some reasons for the long silence on binary mathematics, and the interruption of this silence around 1700, can be deduced from Leibniz’s correspondence. To L’Hospital he explained on September 26, 1701, that he had wanted to advance his investigations further but, because of his numerous other occupations, he now feared that his ideas might be lost. Already on March 23, 1699, he had expressed sentiments to L’Hospital concerning his analysis situs that surely also applied for binary mathematics. In February 1701 – as he informed 40 Cf. C. Wahl, “Diplomat in der Gelehrtenrepublik  – Leibniz‘ politische Fähigkeiten im Dienste der Mathematik”, pp. [273]–291 in: Wenchao Li (ed.), Komma und Kathedrale: Tradition, Bedeutung und Herausforderung der Leibniz-Edition, Berlin, 2012.

Introduction: The Core Themes

49

L’Hospital on April 4 – he sent an Essay d’une nouvelle science des nombres to Bernard le Bovier de Fontenelle to encourage the Académie des Sciences to undertake further investigations on binary mathematics. He refused to provide a publication however since, as he explained to Fontenelle, that which he had at his disposal would not yet be sufficient to create excitement about dyadic or binary mathematics. Leibniz’s assessment was confirmed in the brief exchange on this topic with Johann Bernoulli in the spring of 1701 that quickly came to an end. Binary arithmetic reminded Bernoulli – as he announced in his letter of April 11 of that year – of Erhard Weigel’s publication entitled Tetractys, summum tum arithmeticae tum philosophiae discursivae compendium (1673). Leibniz defended himself, on April 19, with the argument that number systems other than the decadic or decimal system were generally known before Weigel who had been his professor during his studies in Jena in the summer semester of 1663.41 Leibniz saw his own contribution not so much in the discovery of the binary system but rather in its number theoretical applications. That the consideration of other number systems was in the air, he had already illustrated at this juncture with examples in the Essay sent to Fontenelle. The fact that binary mathematics was increasingly discussed in Leibniz’s correspondence around 1700 was no surprise. The necessary investigations and test calculations could now easily be delegated and the academies offered a suitable forum for realizing this. Through these institutions Leibniz hoped then to obtain personnel and assistants. Accordingly, during his visit to Berlin in the summer of 1700, he made the effort, through the intermediation of Philippe Naudé, to motivate Pierre Dangicourt to devote himself to binary mathematics. The introduction of Dangicourt to dyadics duly led to a co-operation under Leibniz’s direction that culminated in a publication of Dangicourt, entitled “De periodis columnarum in serie numerorum progressionis arithmeticae dyadice expressorum”, in the Miscellanea Berolinensia in 1710. However, since the exchange of ideas took place viva voce, by word of mouth, during Leibniz’s visits to Berlin, it is sparsely documented in his correspondence. With the Académie des Sciences, Leibniz was less successful. L’Hospital proposed Antoine Parent as a suitable mathematician for research on binary mathematics but Leibniz was not in a position to provide the requisite funding. In addition he had doubts concerning Parent’s suitability for the 41 Cf. K. Müller, G. Krönert, Leben und Werk von G. W. Leibniz: Eine Chronik, Frankfurt am Main, 1969, in particular pp. 6f. (1663; Jena und Leipzig); M. Palumbo, “„Praeceptor, Fautorque meus colendus  …“ – Weigels Werke in der Privatbibliothek von Leibniz”, pp. 249–268, in: K. Habermann, K.-D. Herbst (eds.), Erhard Weigel (1625–1699) und seine Schüler: Beiträge des 7. Erhard-Weigel-Kolloquiums 2014, Göttingen, 2016.

50

Introduction: The Core Themes

task in hand. In quite a different sense the China Jesuit missionary Joachim Bouvet took up dyadic mathematics after Leibniz had, on February 15, 1701, communicated to him the theological interpretation and his latest results. The key element to success on that front was  – as Bouvet’s communications on November 4, 1701, reveal – that the correspondent saw an analogy to Chinese figures of Fohy (‘FuXi hexagrams’), which are found in the binary (and indeed, by implication, octal and hexadecimal) Fohy (or FuXi) sequence and which Leibniz elaborated in a letter sent from Berlin to Hans Sloane on April 17, 1703, an extract from which was forwarded to John Flamsteed.42 3

Natural Philosophy Mon sentiment est fondé en raisons et en experiences. Leibniz to Denis Papin, November 17, 169543

3.1 Dynamics The history of Leibniz’s principal work on dynamics, namely, his planned opus Dynamica de potentia et legibus naturae corporae,44 begins in the year 1689, 42 Cf. E. J. Aiton, “An unpublished letter of Leibniz to Sloane”, Annals of science, vol. 38(1), (1981), pp. 103–107; E. G. (and M.) Forbes, L. Murdin, F. Willmoth (eds.), The correspondence of John Flamsteed, first astronomer royal, vol. 3 (1703–1719), Bristol and Philadelphia, 2002, and in particular Letter 902 (Sloane to Flamsteed dated June 22, i.e. July 3, 1703, with an enclosed extract from Leibniz’s letter to Sloane dated April 17, 1703), pp. 2–6 (including Sloane’s letter p. 2, the enclosed extract from Leibniz’s letter pp. 2f., an English translation of the enclosure pp. 3f., annotations pp. 5f., and specifically annotation 9 regarding the figures of Fohy); the letter publication (A III,9, N. 84, viz. Leibniz an Hans Sloane, Berlin, 17. April 1703); D. Guangbi, “The book of changes and mathematics”, pp. 125–135 in: F. Dainian, R. S. Cohen (eds.), Chinese studies in the history and philosophy of science and technology, Dordrecht, Boston, London, 1996 (Boston Studies in the Philosophy of Science, vol. 179); R. Widmaier, M.-L. Babin (eds.), Philosophische Bibliothek: Gottfried Wilhelm Leibniz: Briefe (1694–1716) über China. Die Korrespondenz mit Barthélemy des Bosses S.J. und anderen Mitgliedern des Ordens, Hamburg, 2017, specifically Letter 3 (Leibniz an Giovanni Battista Tolomei S.J.) and note 5 (p. 443). 43 Cf. A III,6 N. 172, p. 533. Translation: My sentiment is rooted in reason and practical experience or experiment. 44 Cf. for example R. S. Westfall, Force in Newton’s physics: The science of dynamics in the seventeenth century, London, New York, 1971, in particular chap. 6 (Leibnizian dynamics); R. S. Westfall, The problem of force: Huygens, Newton, Leibniz, pp. 71–84 in: A. Heinekamp (ed.), Leibniz’ Dynamica: Symposion der Gottfried-Wilhelm-Leibniz-Gesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, (Studia Leibnitiana, Special issue, no. 13), Stuttgart,1984; W. Kutschmann, Die Newtonsche Kraft: Metamorphose eines wissenschaftlichen Begriffs, (Studia Leibnitiana, Special issue, no. 12), Wiesbaden, 1983; D. Garber, T. Tho,

Introduction: The Core Themes

51

and it is documented primarily in his correspondence with Rudolf Christian von Bodenhausen. During and following the Italian journey, Bodenhausen was for Leibniz not just an industrious correspondent but also an assistant and editor of his Dynamica. Accordingly, in their correspondence, one meets not only problems of the organization and reorganization of this work but also, in respect of content, questions and definitions of core concepts such as for example specific gravity, mass, and homogenous magnitudes. Bodenhausen had already begun to prepare the fair copy, when, on February 20, 1690, Leibniz forwarded to him from Venice a further installment of the work in question, which included among other things a section containing the “modus aestimandi velocitates, impetus, effectus, potentias mobilium”. And further chapters, like one on varied or varying accelerating and decelerating motions (“ein caput De Motu varie accelerato et retardato”), were announced. On March 4, Leibniz announced once again the prospect of supplements including a whole chapter on the applications of dynamics to machines (“ein ganzes caput applicationis dynamicae ad Machinas”) that he wanted to complete during the return journey to Germany. With a letter of March 11, there followed further additions to the Dynamica including the first sheet of the chapter on varied or varying accelerating and decelerating motions (“einige supplementa und in specie das erste folium des capitis De Motu varie accelerato aut retardato”). With a letter of March 18, Leibniz sent Bodenhausen from Venice further parts of the Dynamica and, as an attachment, a revised version of an appendix containing a reprint of his article on the differential calculus of October 1684, namely the “Nova methodus pro maximis et minimis”. The new classification of the work included two main parts which corresponded to his pair of systematic early physical works,45 namely those on motion from the year 1671  – viz. the Theoria motus abstracti and the Theoria motus concreti, (from the Hypothesis physica nova) – and were to include “dynamica simplicia seu a rebus abstracta” and “dynamica concreta”. Bodenhausen was accordingly informed in the letter of March 18, 1690, in which Leibniz presented a detailed outline of the projected work with a breakdown according to part, section and chapter. As a result of this rearrangement, the completion of the Dynamica was considerably delayed not least because Bodenhausen was now compelled to recopy a large portion of the work. Leibniz was himself also “Force and dynamics”, chap. 17 (pp. 304–330), in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. 45 Cf. P. Beeley, “De abstracto et concreto: Rationalism and empirical sciences in Leibniz”, chap. 4 (pp. 85–98) in: M. Dascal (ed.), Leibniz: what kind of rationalist? Logic, epistemology, and the unity of science, vol. 13, Dordrecht, 2009: P. Beeley, “Early physics”, chap. 16 (pp. 290–303), in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

52

Introduction: The Core Themes

unable to complete the work as planned on the return leg of his Italian journey. Back in Hanover, notwithstanding his increasing commitments, he was still hoping, on July 6, 1690, to find the time to complete the supplements and conclude the work on the Dynamica as a whole but he had to concede that a delay was inevitable. In a letter Bodenhausen sent from Florence, on November 11, 1690, the correspondent told of his continuing efforts for the Dynamica and of further additions he was expecting to receive from Leibniz. Nonetheless, at the beginning of 1691 central parts of the Dynamica were still missing like the conclusion of the chapter on impact, and topics like the “problema staticum generale”, string tension, the construction of the thermometer and finally an entire section about machines as Bodenhausen’s letter of January 19, 1691, reveals. On June 23, 1691, the correspondent expressed himself quite indignantly concerning Leibniz’s inactivity and placed all his hopes in an early conclusion of the time-consuming ‘opus historicum’ that seemed to be keeping Leibniz from higher-order thought and from discoveries concerning the advancement of the sciences and in particular from supplying the outstanding parts in his “Opere Dynamico”. Here Bodenhausen echoed the sentiments of Christiaan Huygens who, in his letter of September 17, 1693, likewise expressed his regret that Leibniz should be sacrificing his time for his Codex Juris Gentium opus. Bodenhausen’s judgement that Leibniz had been preoccupied with historical research and had, accordingly, been inactive in the field of natural philosophy and dynamics was however premature in this instance. Leibniz had in fact written to him just one day earlier telling that he had communicated to Antonio Alberti (alias Amable de Tourreil) his thoughts about the nature of bodies, as well as about the overestimation of their physical extension, and that he had requested that Alberti pass on the text in question to their mutual friend Bodenhausen. Alberti, for his part, had independently turned to Bodenhausen with the request that he should try to motivate Leibniz to explain the cause of gravity. At the same time he had expressed the desire to learn the publication date of Leibniz’s Dynamica. And so, on December 1, 1691, Bodenhausen could inform Leibniz that he had to console Alberti in the light of the inevitable delays and he added that he would request Alberti to forward Leibniz’s demonstrations about the nature of matter which he had not received. The aforementioned letter concerning the question as to whether the essence of bodies consists in their extension, which Leibniz sent to Alberti, was in fact published in the Journal des Sçavans of June 18, 1691, as an “Extrait d’une letter … sur la question, si l’essence du corps consiste dans l’étendue”. Also, in a letter to Paul Pellisson-Fontanier from the second half of July, 1691, Leibniz developed his fundamental thoughts about force (“force”, “l’effort”, “conatus”)

Introduction: The Core Themes

53

as the most important property of bodies and further expanded these formulations in a subsequent letter of November 19 (or 29) to include concepts like active and passive force. In the course of this initiative, he also sent important documents from his disputes in the 1680s with the Abbé Catelan and Nicolas Malebranche to France. He likewise referred to his discussion at that time with Antoine Arnauld and, accordingly, Pellisson initiated contacts with members of the Académie des Sciences. And so, at the turn of the year 1691–1692, Leibniz saw himself obliged to compose a written summary of his central thoughts on dynamics. This was perhaps also the reason why Leibniz asked the completely perplexed and irritated Bodenhausen, in a non-extant letter of December 23, 1691 – referred to in Bodenhausen’s reply of January 12, 1692 – to forward his fair copy of the Dynamica to Hanover. In a subsequent letter of February 25, 1692, he was able to conciliate the correspondent with the explanation that he had asked for the “Manuscriptum dynamicum” in order to refresh his mind regarding the content. In the meantime he had sent a newly composed text with the title Essay de dynamique or Élémens de dynamique, together with a letter of January 18, 1692, to Pellisson, but not without emphatically pointing out the difference to his planned Dynamica. And it was his desire that the Essay be examined by Nicolas Malebranche. Unfortunately, this initiative on Leibniz’s part led to no more than a mere reading of the Essay de dynamique before the Académie des Sciences on July 28, 1692 by Philippe de La Hire and to the production of transcripts; a public discussion about it, or even the requested transmission of a copy to Malebranche, never did materialize. This envisaged copy, had it been forwarded on time, might well have influenced Malebranche’s tract Des loix de la communication des mouvemens which appeared in the summer of 1692. Immediately after receiving this tract, Leibniz made notes on Malebranche’s text and, through the intercession of Daniel Larroque, had them delivered to Malebranche. The latter replied to Leibniz directly with a letter of December 8, 1692, that was dispatched to him together with L’Hospital’s first letter of December 14 and, apparently under the influence of Malebranche’s tract, he undertook a further revision of the Essay de dynamique at the end of 1692. L’Hospital’s first letter to Leibniz of December 14, 1692, was written in the hand of an unidentified amanuensis. In fact, virtually all of the approximately 20 letters which L’Hospital wrote to Leibniz between December 1692 and June 1701 were written in Paris and signed “Le M. De Lhospital” by the correspondent’s wife, namely the mathematician Marie-Charlotte de Romilley de la Chesnelaye, the marquise de L’Hospital. These letters written in the hand of Charlotte de L’Hospital were surely the work of a mathematical assistant

54

Introduction: The Core Themes

rather than of just an amanuensis and the lady in question was probably the only female mathematician (albeit incognito) on the frontline of Leibniz’s mathematical discourse in this period. On July 12, 1692, Bodenhausen was able to report the dispatch to Venice of his fair copy of the Dynamica, and Leibniz confirmed its delivery in Hanover on October 5. Once he had perused the work, he realized that he would require more time than he then had in order to complete it. For his part, Bodenhausen believed he could accelerate the completion of the work in this way by forwarding his clean copy, yet Leibniz politely declined in a letter of July 22, 1693, since for him the overriding problem was the lack of time to proceed with the work. Already in the spring of 1692 Leibniz had undertaken a second attempt to gain the backing of French scholars for his Descartes critique and the establishment of dynamics on a new foundation. On May 6, 1692, he sent a paper about the resultant of forces acting in different directions with the title Règle générale de la composition des mouvemens par M. d. L. to Pellisson, intending it as a contribution for the Journal des Sçavans. However, when Pellisson died on February 7, 1693, Leibniz’s text had still not appeared in print. L’Hospital’s communication of June 15 resulted in Leibniz undertaking in great haste a revision of his Règle générale which he hurriedly sent, on July 23, to Paris since he had reason to fear antecedence by a publication of L’Hospital on the same topic as is evident from a letter of L’Hospital to Johann Bernoulli of September 21. Finally, Leibniz had success; in the September 1693 number of the Journal des Sçavans there appeared his contribution “Règle générale sur la composition des mouvemens” and, in addition, two application examples. The Essay de dynamique, on the other hand, was to remain unpublished during his lifetime. Leibniz had already corresponded with Simon Foucher before his research tour to Austria and Italy and, on his return to Hanover, he strove to revive this epistolary exchange. For this purpose he sent several letters to Paris. To his letter of March 23, 1691, to Christophe Brosseau, to which the aforementioned extract from his letter to Alberti was attached, he finally received a reply from Foucher dated May 30. When Foucher referred, in his following letter of December 31, to the manuscript he had left behind in Florence, Leibniz felt obliged to report to him in detail, in January 1692, about the state of his Dynamica which had been left in the hands of Bodenhausen for edition and publication. Although in an advanced state, and lacking only a wrap-up contribution from himself, he was confronted with the dilemma that his renewed consideration of the subject constantly led to a mêlée of new thoughts for which he did not have the leisure to sort out. Parts of this letter to Foucher appeared in the Journal des Sçavans of June 2, 1692, and in this way a public discussion with Leibniz about philosophical assumptions was initiated by

Introduction: The Core Themes

55

Foucher that continued until August 1693. In addition, Foucher helped Leibniz to reestablish contact with Jean Gallois and he convinced the latter to send Leibniz the numbers of the Mémoires of the Académie des Sciences that had hitherto been published and for which Leibniz expressed his gratitude in a letter to Gallois on December 8, 1692. Gallois even offered Leibniz the option of publishing his works in the Mémoires and he reacted by recommending the printing of his Essay de dynamique that had been sent to Pellisson. Following the latter’s death Foucher regularly informed Leibniz about the whereabouts of the first version of this Essay, which he himself was yet to see half a year later. To begin with, it had remained among the papers in the sealed estate of Melchisédech Thévenot (who died on October 29, 1692) and then (in July 1693) it was in the hands of Pierre Varignon for appraisal. Towards the end of 1693 the correspondence between Leibniz and Foucher – in which, among other things, Leibniz’s Hypothesis physica nova of 1671, infinite divisibility and effective infinity were discussed – suffered more and more from the public dispute between the two philosophers in the Journal des Sçavans, and finally it was interrupted for two years. In the April 1695 number of the Acta Eruditorum, Leibniz’s “Specimen dynamicum” (or “A specimen of dynamics”)46 was published. It represented a renewed attempt on his part to circumvent the completion of the final version of his envisaged major opus Dynamica, which then had been in the hands of Bodenhausen in Florence for more than five years. On several occasions Leibniz had referred to this more than 200-page long planned work with the result that not only his French followers but also his German friends, in Otto Mencke’s circle, continued to remind him ever more distinctly of the commitment he had given. However, just as the French scholars had to be satisfied with surrogate contributions in the Journal des Sçavans, their German counterparts had to make do with the “Specimen dynamicum” in the Acta Eruditorum, the second part of which, although promised for the following month, never did in fact appear. Starting with a scrutiny of the concept of movement in the “Specimen dynamicum”, Leibniz arrived at a concept of force, in which he distinguished, on the one hand, between a metaphysical “vis primitiva” and a physical “vis derivativa”, respectively, and on the other hand, between a virtual “vis mortua” and a real “vis viva”, respectively. For forces associated with corporeal 46 Cf. [G. W. Leibniz,] “A specimen of dynamics toward uncovering and reducing to their causes: Astonishing laws of nature concerning the forces of bodies and their actions on one another”, part 1, chap. 16 (pp. 117–138) in: R. Ariew, D. Garber (eds., trans.), G. W. Leibniz: Philosophical essays, Indianapolis, Cambridge, 1989.

56

Introduction: The Core Themes

or substantial states, total and partial forces, respectively, were to be considered separately and furthermore, in the case of the latter, the “vis respectiva” (internal force) and “vis directiva” (outward-operating or outward-manifesting force), respectively, were to be regarded separately. Leibniz duly arrived at a central conclusion of the work, according to which, from the connection of metaphysical laws and the laws of extended (or physical) bodies, the actual, systematic laws of motion arise. This connection was however not to be misunderstood to imply that Leibniz wanted to explain physical phenomena using metaphysical laws. In fact it simply implied that physical laws have their foundations not in themselves but in metaphysical principles. Finally, he differentiated between efficient causes and final causes, whereby the latter are not accessible to humans in the same manner that the former are. Nonetheless, they could certainly be employed in particular cases in physics with success, as for example in the case of extremal principles like, for example, in optics. As first important consequence from the systematic laws of movement, Leibniz cited the true quantification of forces as a product of mass and the square of velocity for the example of movement under the influence of terrestrial gravity. 3.2 Vis Viva About the same time as he produced the first comprehensive conceptual design of his philosophical system in the form of his Discours de metaphysique (1686), Leibniz composed an article for the Acta Eruditorum in which he believed he could exemplify his long-standing criticism of the philosophy of Descartes on the basis of an easily recognizable mistake, namely regarding the principle of the conservation of momentum or impulse. This was to become the starting point of a prolonged dispute about whether the forces in dynamics should be characterized by the velocity or by the square of the velocity and about which of these entities is conserved in nature.47 Whereas Descartes considered the product of mass and velocity to be a key magnitude of kinetics, Leibniz proposed an alternative, namely the product of mass and square of the velocity whose conservation he saw as a fundamental feature of nature. His “Brevis demonstratio erroris memorabilis Cartesii”, in the Acta Eruditorum in March 1686, provoked – following its translation and publication in French in the Nouvelles de la République des Lettres in September 1686 – intense and lasting reactions from the side of the Cartesians which were led by the Abbé Catelan’s article “Courte remarque de M. l’Abbé D.C. où l’on montre à Mr. G. G. Leibnits la paralogisme contenu dans l’objection precedente”, also 47 Cf. T. Tho, “Vis vim vi: Declinations of force in Leibniz’s dynamics”, Studies in History and Philosophy of Science, vol. 46, Cham (Switzerland), 2017.

Introduction: The Core Themes

57

in the Nouvelles de la République des Lettres of September 1686. In April 1689, Denis Papin then joined the fray with an article in the Acta Eruditorum entitled “De gravitatis causa et proprietatibus observationes”. Leibniz then saw himself obliged to respond to Papin in the May 1690 number of the Acta with an article entitled “De causa gravitatis et defensio sententiae suae de veris naturae legibus contra Cartesianos”. This was to be the prelude then to an extensive correspondence between Leibniz and Papin which was initiated a little time later and of which the famous ‘vis viva controversy’ was a core element.48 Leibniz’s interest in the fundamental questions of natural philosophy and, in particular, in his most important contribution in the area of mechanics namely the determination of that physical quantity that is conserved in all mechanical changes (i.e. “vis viva”) was indeed very much alive following his return to Hanover after his Italian journey in 1690. The factors that contributed to this continuing interest included the unfinished state of his Dynamica, the appearance of Huygens’ Discours de la cause de la pesanteur (1690), and especially the correspondence with Papin that now came about through the mediation of Johann Sebastian Haes. Newton’s Principia mathematica too continued to be an influence and, last but not least, the idea of his French correspondents Paul Pellisson-Fontanier and Simon Foucher – namely of realizing a contrasting juxtaposition of the Cartesian and Leibnizian convictions for the purpose of disquisition by adept mathematicians – resulted in a continued striving on Leibniz’s part for more succinct and comprehensible explanations of his most important propositions. Leibniz’s acquaintance with Denis Papin can be traced back to their time together in Paris where Papin served (from 1673 to 1675) as assistant to Huygens at the laboratory of the Académie des Sciences. A correspondence between the two did however not develop at first. Since Papin’s views on natural philosophy had been shaped by Descartes’ philosophical thought, it was inevitable that Leibniz would encounter Papin’s opposition to his assault on Cartesianism launched with the publication of his article “Brevis demonstratio” in March 1686. Papin’s aforementioned rejoinder “De gravitatis causa et 48 Cf. C. Iltis, “Leibniz and the vis viva controversy”, ISIS: Journal of the History of Science Society, vol. 62(1), (1971), pp. 21–35; D. Papineau, “The vis viva controversy: Do meanings matter?”, Studies in History and Philosophy of Science, vol. 8(2), (1977), pp. 111–141, and chap. 47 (pp. 198–216) in: R. S. Woolhouse (ed.), Gottfried Wilhelm Leibniz: Critical assessments, vol. III, London, 1994; S. Kühn, “Gelehrte Streitkultur und Wissenskollektive: Das Beispiel des Denis Papin”, pp. 273–280 in: U. J. Schneider (ed.), Kulturen des Wissens im 18. Jahrhundert, Berlin, 2008; I. Shimony, “Leibniz and the vis viva controversy”, chap. 3 (pp. 51–74) in: M. Dascal (ed.), The Practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010.

58

Introduction: The Core Themes

proportionibus observationes” appeared however only after an interval of three years, in April 1689, after he had taken up a mathematical professorship and settled in Marburg in the landgraviate of Hesse-Kassel. Papin’s defense of the natural philosophy of Descartes was directed not only against Leibniz but also against Johann Christoph Sturm and Jacob Bernoulli among others. Papin’s central argument rested on the assumption that the cause of gravity is an ether vortex which acts on a body with infinite velocity (at least in comparison the velocity of the body). Since this action at any instant occurs by virtue of an equal number of equally strong blows to the body, it is proportional to the elapsed time (and accordingly to the velocity of the body attained) and is not proportional for instance to the traversed distance (and accordingly to the square of the velocity of the body attained). The same proportionalities applied also for the resistance encountered by bodies in motion. Leibniz, following his return to Germany from Italy, encountered Papin’s article in the course of working through the Acta Eruditorum and he composed at once (probably in Augsburg) his aforementioned response “De causa gravitatis” which he dispatched from Vienna, at the end of April 1690, to Otto Mencke in Leipzig and which duly appeared in the May number of the Acta Eruditorum. Following a general rejection of Papin’s arguments – which included references to proofs from his own projected opus Dynamica – Leibniz turned, under the twelfth and final heading of his “De causa gravitatis”, to the attacks of Papin against himself. From his definition of force Leibniz concluded that it is conserved in the collision of bodies, regarding which view he felt certain of agreement from Papin’s side. From this definition, however, it follows of necessity that the forces are proportional to the product of weight and height (under the influence of terrestrial gravity). Otherwise, as he demonstrated by means of a thought experiment,49 the possibility of a “motus perpetuus mechanicus” would arise, which was of course considered to be absurd.50 The condition for the validity of this conclusion on Leibniz’s part was the complete substitutability of the bodies incorporated in the definition 49 Cf. S. Roux, “Introduction: The emergence of the notion of thought experiments”, pp. 1–142 in: K. Ierodiakonou, S. Roux (eds.), Thought experiments in methodological and historical contexts, (Series: Medieval and early modern philosophy and science, vol. 15), Leiden, 2011; R. T. W. Arthur, “Thought experiments in Newton and Leibniz”, chap. 6 (pp. 111–127) in: M. T. Stuart, Y. Fehige, J. R. Brown (eds.), The Routledge companion to thought experiments, Abingdon (Oxon), New York, 2018. 50 Cf. the following preprint and publication: G. Freudenthal, Perpetuum mobile  – The Leibniz-Papin controversy, Berlin: Max-Planck-Institut für Wissenschaftsgeschichte (Preprint 127), 1999, pp. 1–58, and appendix with translation (pp. [i]–xv) and facsimile of Papin’s “Synoppsis controversiae”; Publication in: Studies in History and Philosophy of Science Part A, vol. 33(3), (2002), pp. 573–637.

Introduction: The Core Themes

59

of force and the complete transferability or transmission of the force between bodies. In conclusion Leibniz attempted to provide proof that the source of the error on the side of the Cartesians was to be found in the circumstance that many philosophers considered the total movement in the world to be a perpetual and inalterable or invariable magnitude. Papin’s reply followed after five months, even though it first appeared in print only in the January 1691 number of the Acta Eruditorum under the title “Mechanicorum de viribus motricibus sententia”. This time Papin changed his argumentation strategy in that he consciously adapted it to that of his antagonist. First of all, having given his definition of force, he remarked that the effect should be measured neither by the distance covered nor by the duration of the motion but rather exclusively by the resistance to be overcome. On the basis of these preconditions he then refuted Leibniz’s thought experiment whereby he denied above all the possibility of a complete transferability or transmission of the force from one body to another. In this very assumption he saw the source of Leibniz’s error. Leibniz now also allowed himself more time sending his next contribution only in August 1691, as is evidenced by Mencke’s reply to Leibniz’s non-extant letter of August 16, 1691. The article entitled “De legibus naturae et vera aestimatione virium motricium contra Cartesianos” then appeared one month later in the Acta Eruditorum. A week before this mailing to Mencke, Leibniz had dispatched his first (non-extant) letter to Johann Sebastian Haes in Kassel in the form of an attachment to a letter addressed to Friedrich Lucae. Leibniz hoped to obtain information from Papin’s confidant Haes about the activities of his opponent and perhaps even to initiate a direct correspondence with him. In the article “De legibus naturae” Leibniz attempted above all to refute Papin’s argument regarding the non-transferability or non-transmissibility of the total force of a body in that he declared the pure-thought assumption of such a transfer to be sufficient. He considered himself not to be obliged to offer the means of realizing such a transfer. He also believed that, in the event that cause and effect were not equivalent, the wisdom of the Creator would be derogated. The proof – demanded by Papin – of the complete transfer or transmission of force from a body of greater mass to one of lesser mass he provided once again by means of a thought experiment. He also formally defended the possible existence of a body having perfect or total hardness that had been denied by Papin. The issue for Leibniz was not that such perfect hardness might actually exist in the real world and for him it would suffice that it be conceivable without contradictions. In addition, the deviation from the condition of perfect hardness might be assumed to be arbitrarily small. Subsequently, Leibniz offered new arguments to support his views: for him equal forces would then

60

Introduction: The Core Themes

exist if an equal number of elastic springs, each having the same resilience or tension force and being in the same state of stress, were to be traversed or overcome. Only the real and true measure of force would fulfill the transferability or transmission requirement of the laws of nature. Following a further letter from Leibniz to Haes at the end of November 1691, the stage was finally set for a direct correspondence with Papin. Haes’ reply (of January 31, 1692) had as an enclosure the first letter (of January 23, 1692) from Papin to Leibniz together with an addendum in which Papin articulated his reply to Leibniz’s “De legibus naturae”. With this step the dispute, which had until then been conducted publicly in the Acta Eruditorum, was relocated to the private correspondence between Leibniz and Papin.51 This was much to the satisfaction or pleasure of the editor of the journal, Otto Mencke, who expressed his desire, on April 16, 1692, to publish a summary account of the outcome once the dispute had been resolved. In the first phase of the correspondence between Leibniz and Papin (between January and December 1692) sixteen letters were exchanged between the adversaries in the dispute. This correspondence included a piece written by Papin in late October or early November for the Acta Eruditorum with the title “Synopsis controversiae circa legitimam virium motricium aestimationem excerpta a D. Papin” that was forwarded to Leibniz who added more than fifty marginal annotations and commentaries. In November he himself also composed three drafts for a piece of his own, likewise intended for the Acta Eruditorum, either before or after receiving Papin’s “Synopsis controversiae”. Leibniz probably failed either to return Papin’s piece to Leipzig or to dispatch his own piece to Mencke or Papin. Subsequently, the correspondence was interrupted for a period of two and a half years  – with the exception of a single communication from Papin forwarded with Haes’ letter of May 11, 1693 to Leibniz – until the summer of 1695. A central conclusion of Leibniz’s “Specimen dynamicum” (of April 1695) was that the actual systematic laws of motion arise from the connection of metaphysical laws and the laws of extended (or physical) bodies. To the context of a metaphysical foundation of the laws of dynamics – and following from this, the partly a priori and partly a posteriori derivations of the true measure of force – belongs also the treatment of dynamics by Leibniz in his correspondences from 1695 with Johann and Jacob Bernoulli, L’Hospital and of course above all with Denis Papin.

51 Cf. A.-L. Rey, “The controversy between Leibniz and Papin: From the public debate to the correspondence”, chap. 4 (pp. 75–100) in: M. Dascal (ed.), The practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010.

Introduction: The Core Themes

61

The rekindled correspondence with Papin in 1695 had, at this point, a long and grief-stricken history in the course of which ever increasing similarities to a legal battle being imposed on Papin became apparent. Whereas Papin was by and large willing to let the scholarly public decide in the matter of the competing concepts of force, Leibniz tried again and again to convince him of the falsehood of his stated positions. In this matter they could see eye to eye neither regarding the terminology and the theory underlying this nor regarding the physical phenomena and their interpretation. Thus, Papin had a fundamentally different understanding to Leibniz of the concepts of “effectus” and “vis” and he interpreted most dynamic processes by resorting to very rapid percussions in an almost massless ether. Accordingly, his argumentation – concerning events taking place over the moment of time under consideration – led again and again to what was later to become known as “momentum” or “impulse” while he insisted above all on the conservation of this quantity. Leibniz, on the other hand, understood “effectus” to represent an ascent or descent under the influence of terrestrial gravity, or a spring tension or spring force, having in mind what was later to be known as “energy” and he, for his part, insisted on the conservation of that quantity. Since, however, he had no clear conception of the physical processes involved in processes like the force transmission from a falling body to other bodies or that arising in the case of two bodies impacted at the same instant by a third body, or like the tensioning or straining (or the relaxation or relief) of a spring, he was unable to convince Papin either by means of his thought experiments or by drawing a theoretical distinction between a “vis mortua” and a “vis viva”. Thus, with the statement that his sentiment was rooted in reason and practical experience or experiment (“Mon sentiment est fondé en raisons et en experiences”) – the leading quotation in the heading of this section that was expressed in his letter of November 17, 1695 – he was to come to grief and encounter outright failure in his efforts to convince Papin on both of these explanatory grounds, namely of reason and experiment, notwithstanding (in relation to the former, viz. “en raisons”) his formalization efforts using syllogism chains  – to which he first resorted in his letter of April 19, 1696 – which were however to prove to be of no avail. In relation to the latter (“en experiences”), viz. physical experiment or engineering practice, Leibniz thought he could reduce the controversy to a simple consideration in the letter of November 17, 1695. Thus, he thought the controversy could be reduced to a consideration of two identical bodies having the same simple velocity and whose joint force would be double that of either of the bodies on its own. In the same way, four such identical bodies would have quadruple of the force of any one of the bodies on its own. Now, however, an individual body having double the velocity in question could

62

Introduction: The Core Themes

impart the simple velocity not simply to two but rather to four other identical bodies. Therefore, one of the bodies on its own having a twofold velocity value would have quadruple the force of another one of the identical bodies having the simple velocity, which for Leibniz was that which was to be demonstrated. And, furthermore, for him, an estimation of the force as the product of magnitude or mass and velocity, i.e. the quantity of movement, had to be incorrect, and the error involved would, he thought, be very considerable in practice. In his reply of December 9, Papin found that Leibniz had proposed two instances here that could be illustrated by an experimental arrangement with bodies (weighing 1000 and 2000 pounds, respectively) which were placed in turn at the circumference of a horizontal wheel whose vertical axle and shaft passed through a cylindrical drum below; a rope wound around the drum and passing over a pulley was connected to a weight or load which on falling caused the horizontal wheel above to rotate. In Papin’s view, Leibniz was proposing that (in the first experimental arrangement) the weight on descending two feet would give the load of 1000 pounds above a sufficient velocity to complete four rotations in a minute of time, and that (in the second experimental arrangement) the weight on descending just one foot would give a load of 2000 pounds above a sufficient velocity to complete two rotations in a minute of time. From this Leibniz claimed to have proved that the force communicated to the load of 1000 pounds in the first instance was double that communicated to the load of 2000 pounds in the second instance because the weight had descended double the vertical distance in the first case. To this Papin replied that he judged the two experiments to be the same in the sense that the impact on the falling weight would be the same in both cases. Writing on January 1, 1696, Leibniz insisted that Papin had misconstrued his argument and that he had never considered a weight descending from two different heights but rather from the same height in both experimental arrangements, and he then reformulated the problem in his sense as one an engineer might be confronted with. Thus, an undershot vertical water wheel in a stream below powered a horizontal wheel above by means of the intervening cog-wheel and lantern-pinion mechanism, and accordingly a weight or load on the circumference of the horizontal wheel was made rotate at a certain velocity. According to Leibniz, to double the velocity of the weight by doubling the size of the horizontal wheel on whose circumference it rested, it would be necessary to quadruple the cross section of the stream (keeping the depth of the current and the slope constant) and to enlarge the surface area of the radial vanes of the vertical water wheel by a factor of four. The same effect could also be achieved by quadrupling the specific gravity of the fluid while keeping the

Introduction: The Core Themes

63

current and the area of the vanes constant. Accordingly, Leibniz insisted that Papin’s thought experiment would ultimately lead to a four-fold force increase. According to Leibniz, an engineer who claimed to be expending the same force in the two experiments driving, firstly, a load of 1000 pounds resting on a horizontal wheel of a certain diameter at a certain velocity and, secondly, a load of 2000 pounds on a horizontal wheel having a diameter reduced to half and moving at half the previous velocity, would be deceiving either himself or the public. To drive the load of 2000 pounds at a velocity of half that of the first velocity, a current having a magnitude of merely half of that required to drive the load of 1000 pounds at the first velocity was required, a matter which, he insisted, could be demonstrated in advance either from a consideration of the force of gravity acting on the water or by modelling the water using balls or globules. At all events, he hoped that Papin might at least accept that with identical stream depths and inclinations of the currents considered, the forces would vary as the current breadths. His focus on finding differences in terms of such magnitudes had the intention of not having to have to resort to disputed measures like that of force. On January 15, 1696, there promptly followed Papin’s rejoinder. While accepting the legitimacy of Leibniz’s representation (alongside his own) of the force supplied to drive the weights on the circumference of the horizontal wheel, he could see no advantage in this. In a reference to Leibniz’s “Brevis demonstratio” of March 1696, he claimed that Leibniz was once again presenting – albeit in disguised form – his original arguments of almost ten years earlier in which he had attempted to show that (according to the Cartesian interpretation) levers of double and single length would impart double and single velocity values, respectively, to the two bodies under consideration which was nonetheless impossible. In his consideration of the horizontal wheels of different diameters, Leibniz had revived his earlier argumentation since wheels represented a type of lever which once again would be of no avail. Finally, on February 3, Leibniz abandoned the discussion of the horizontal wheel drive. He had believed that in their consideration and discussion of the weight carried by a horizontal wheel, as in case of two bodies impacted at the same instant by a third body, Papin had laid aside his Cartesian philosophical view and deigned to restrict himself to proofs based on sensible matter and capable of experimental proof. However, the correspondent’s renewed retrenchment in his former positions had, in Leibniz’s view, ended his hope of a resolution of their dispute. In his letter of June 18, 1695, Johann Bernoulli began his discourse on Leibniz’s “Specimen dynamicum” with praise for the definitions given of the

64

Introduction: The Core Themes

fundamental concepts of dynamics, in particular those for “vis mortua” and “vis viva”, for which he immediately suspected parallels to the infinitesimal calculus. The Leibnizian “aestimatio virium” he chose however not to follow, at least at first. As a counter-example he introduced the penetration depths of two equal bodies that encounter a homogeneous resisting medium at different velocities. The depths of penetration into the medium would not be proportional to the square of the velocities but rather to the simple initial velocities. Leibniz replied, on July 4, that not every arbitrary effect could be drawn upon for the estimation of force but only those in which the force which was taken in or absorbed could also be given back or emitted once again, as in the case of tensioned springs or of attained heights of fall in terrestrial gravity. In the letters that followed, Leibniz persistently refused to go into the details of Bernoulli’s counter-example. Instead, on August 8, he instructed Bernoulli in detail in his general “ars aestimandi”, which postulated homogeneity, substitutability and additivity. Finally, a point was reached, in Leibniz’s letter of January 2, 1696, where he was at last prepared to introduce the special problems of “resistentia medii” as the reason for the non-applicability of Bernoulli’s experiment. However, by the time of Bernoulli’s reply of January 28, 1696, the correspondent had read Papin’s bilingual edition Recueil de diverses pieces (or Fasciculus dissertationum), and the correspondence took a completely different turn. Following the study and contemplation of Leibniz’s conflict with Papin, Bernoulli had come to the conclusion that Leibniz’s conception was the only tenable one and that Papin was simply seeking subterfuges in order not to have to concede. He provided additional evidence favoring Leibniz’s definition of force in order to help corner their opponent. Whereas Leibniz had previously believed that he could refute Papin using the example, or thought experiment, of an oblique or slanting impact of bodies, he found that exactly that was now being proposed by Bernoulli. He had, however, consciously desisted from playing this trump card, as he confided to Bernoulli on February 7, 1696, seeing the correspondent henceforth as an ally in the dispute. And, further on in this letter, he conceded that, notwithstanding the extended dispute with the Cartesians, he had long been aware that analytical mechanics was founded conjointly on two conservation laws, of which the second or law of the conservation of progress (“conservatio quantitatis progressus”) – namely that which specified the velocity rather than the square of the velocity  – differed from the conservation law of Descartes only in that the directions of the velocities were being taken into account. Accordingly, the second of Leibniz’s two conservation laws agreed with Descartes’ rule, as he thought he should once again emphasize in his letter to Johann Bernoulli, on March 18, 1696. In the further

Introduction: The Core Themes

65

course of the correspondence with Johann Bernoulli then, topics like the laws of impact of bodies, compound and conjoint movement, the resistance of a medium, center-of-gravity principles and statements concerning centers of oscillation and percussion were interpreted anew on the basis of the two conservation laws. In addition, Bernoulli pursued pertinaciously the question of the origin of gravity (viz. ether percussion) as did Leibniz regarding the possibilities of a formal and a virtual, or a priori, proof or reasoning in dynamics. Even the course of the Leibniz-Papin correspondence was occasionally commented on in the continuing correspondence with Johann Bernoulli. Already, on October 4, 1690, Leibniz had requested the opinion of Johann’s brother Jacob about the dispute with the Cartesians. Then on December 12, 1695, he sent Jacob a (relatively short) instruction in the most important basic principles of his dynamics having received a letter from him, of October 19, from which it was evident that Jacob had not been convinced by the explanations given in the “Specimen dynamicum”. Because, however, Jacob introduced the elasticity of the air even in Leibniz’s example of the tensioning of springs placed along a horizontal plane, and because he felt insufficiently informed about the ongoing treatment of this matter in Leibniz’s correspondence with his brother Johann, Leibniz was unable to convince him (at least at first) of the correctness of his force concept. With Leibniz’s concept of force L’Hospital likewise had great difficulty. In particular, it appeared to him, as he made clear in a letter of December 1, 1695, that “quantité de mouvement” and “force” lay in close proximity to each other. This incomprehension on L’Hospital’s part provided Leibniz with the welcome opportunity of presenting to him, in his reply of January 25, 1696, the main features of his dynamics as convincingly as possible. Here he stressed on several occasions that his concept of force did not need to be proved by experience or experiment since it could be derived solely from the principle of the equality of cause and effect. Of interest is likewise Leibniz’s allusion to the circumstance that the difference between Papin’s “quantité de mouvement” and his own “quantité de progrès” lay solely in the directionality of the velocities. Alas, in the letters that followed, L’Hospital failed to respond to Leibniz’s efforts to convince him. The thirty-month period between July 1696 and December 1698 saw the greatest density in Leibniz’s continuing correspondence with Papin with as many as 40 letters being exchanged in this timespan. In this correspondence, Leibniz attempted again and again, but to no avail, to persuade Papin of the fallacy of his standpoints. The antagonists were unable to agree either about the terminology, and the theory upon which it was based, or about the physical phenomena and their interpretation. As Leibniz had no clear notion of the physical processes involved in the tensioning (or the release of tension) in a

66

Introduction: The Core Themes

spring or in the transmission of force between colliding bodies or from a falling body to other bodies, he was unable to convince Papin either by means of his thought experiments or by drawing a theoretical distinction between “vis mortua” and “vis viva”. For the refutation of his opponent, Leibniz availed of, among other things, the method of syllogisms beginning with his letter of April 19, 1696. However, even these formalization efforts proved to be of no avail. In the further course of the correspondence with Papin, matters such as composite movement, the laws of colliding bodies and the example of oblique collision were discussed using thought experiments. In this context the physical quantity action (or “actio”52) was introduced and explained by Leibniz. As regards the formulation of the laws of colliding bodies, Leibniz could on his fiftieth birthday (July 1, 1696) look back at developments over a period of half a century and more. Writing to Papin on that day, he mentioned in particular the contributions of Galileo Galilei, Joachim Jungius, the Jesuit Johann Marcus Marci von Kronland, Giovanni Alfonso Borelli, Christiaan Huygens, Christopher Wren, John Wallis and Edme Mariotte. He then offered the prospect of further proofs for his measure of force, and indeed, independent of experiment but, in his reply of July 12, Papin reacted with skepticism. In Leibniz’s view, expressed in his next letter of July 26, two bodies separate following a collision as a result of the elasticity of their constituent parts that could be represented by an intervening spring. The bodies first mutually repel each other only after they have lost the total force with which they had previously impacted each other and after their relative velocities have fallen to zero. Independent of their respective forces, viz. those the bodies have at the beginning of the impact, they are reduced to a state of rest relative to the intervening spring. In that instant the law of “vis mortua” (like that of equilibrium) becomes operative and such that the respective values of the two bodies are reciprocally or inversely proportional to their masses. Following separation, the change of velocity resulting from the elastic resilience of the spring is, at every instant, infinitely small. Two bodies having unequal forces, but with velocities that are inversely proportional to their respective masses, mutually cause each other to reverse their motions. The equilibrium of the “vis mortua” values leads however to an inequality of the “vis viva” values, which for Leibniz was the true measure of force. He illustrated the difference between the two measures of force with the help of an analogy from geometry comparing the dead forces to lines and living forces to squares or square figures. 52 Cf. A. G. Ranea, “Poiein and prattein: The concept of actio and the measurement of motive force”, pp. 226–232 in: H. Breger, J. Herbst, S. Erdner (eds.), Natur und Subjekt: IX. Internationaler Leibniz-Kongress, (Supplementary volume), Hanover, 2012.

Introduction: The Core Themes

67

Since Papin saw no reason for making a distinction between a “vis viva” and a “vis mortua”, and could not conceive infinitesimal velocity changes, he elaborated his position yet again in his next letter, of August 7, to Leibniz, who in turn responded on August 20 by explaining his understanding of infinitesimal physical changes, resorting once again to a comparison with mathematics likening such infinitely small changes to the infinitely small flexure or curvature changes of line curves. Nonetheless, in his letter of August 30, Papin continued to reject the introduction of a “vis viva” and he insisted that for him the law of “vis mortua” was valid everywhere. For Leibniz, as he outlined in his letter of September 24, the “vis mortua” was effective only in relation to relative effects which manifested themselves as instantaneous infinitely small velocities. Bodies having the same quantity of motion were indeed in a position to mutually stop each other in their tracks, but they did not have to have the same “vis viva” which operated in relation to absolute effects and was subject to force conservation. In order to establish contradictions in Leibniz’s argumentation, Papin, in his reply of October 4, conceived a thought experiment involving the collision of a larger with a smaller body. Between the two bodies there is a spring. In the instant in which the velocity of the smaller body is reduced to zero, it is replaced by a much larger body which absorbs the recoil of the spring and the impact of the other body. Since the distribution of the quantity of motion follows the law of “vis mortua”, the surrogate body has a lower velocity (and less “vis viva”) after the collision than the smaller body had before the collision. Accordingly, there would be a loss of force in the world following the event and this represented a contradiction in Leibniz’s conservation principle. In his reply on November 11, Leibniz maintained that, in this experiment, a portion of the force of the stalled body is transferred to its spring, that is into the form of motion of its constituent parts. The replacement of a body by a larger body was only admissible if the “vis viva” lodged in the spring of the body were to be transferred to the surrogate body. Leibniz’s position now meant that Papin saw himself constrained to investigate more closely the exact mechanism of such a substitution process. The 13th syllogism, which was enunciated in Papin’s letter of November 15, was now at the center of the dispute and was founded on a thought experiment in which two perfectly hard bodies A and B meet and, through the collision, tension is produced in the intervening spring C. In the instant in which the smaller body B almost comes to a stand-still, it is struck from the side by a considerably larger body D whose velocity is just sufficient to effectuate that it replaces B and (as soon as the recoil of the spring C becomes operative) it receives the total force that had previously been transferred from B to C. The surrogate body D would

68

Introduction: The Core Themes

therefore have less force than B had before the collision and the total force would thus have decreased. The interpretation of this thought experiment is intimately connected with the possible existence of a perfect hardness of physical bodies. Both of the adversaries in the dispute quickly agreed that such a state of complete hardness was unattainable in reality. Nevertheless, Leibniz believed, as he explained in his letter of November 19, that, on the assumption of an almost perfect hardness, a substitution would be possible, viz. that only a small part of the force would be transferred to the parts of the bodies A and B with by far the greatest portion going to the spring C. In spite of this, there would be no loss in the quantity of force. The surrogate body D would namely experience the impact of the recoil of the spring not centrally (like B) but rather partly off-centered and would therefore be subject to a rotation which would lead to a diminution of its resistive potential and there would be no overall loss of force or “vis viva”. Papin then responded, on November 25, by formulating a syllogistic premise, which, while taking account of the rotation effect, still entailed a loss of “vis viva”. And, on the basis of a numerical example, he claimed to have demonstrated the correctness of this premise before elaborating a variant of his earlier thought experiment. In the last letter of the year 1696 to Papin, on December 24, Leibniz denied at once the validity of the premise arguing that the total force following the collision was composed of the force of the movements of the bodies A and D as well as the elastic resilience of the intervening spring C. Papin, replying on January 14, 1697, then saw a contradiction in Leibniz’s explanations. Thus, whereas Leibniz had, in his letter of November 19 of the previous year, assumed an almost perfect hardness of the bodies A and B and an almost total transfer of the force to the spring C, he had subsequently, in the letter of December 24, talked about an elastic body B with tensioned parts in which a portion of the force was retained. One could however, according to Papin, reduce the elastic resilience of the parts of the body to almost zero so that it would be negligible in comparison with the loss of force in the total substitution process. It would, furthermore, be possible to arrange in the substitution process for the body D to advance fast enough (or for its broadside to be accordingly altered) in order for it to absorb the recoil of the spring at its central point. At the beginning of the year 1697 Leibniz suspended the intensive exchange with Papin for two months in order to thoroughly consider the matters at issue. When, on March 7, he resumed the correspondence he had reconsidered the course of the debate since July 1696. In this renewed consideration, he had arrived again at Papin’s 13th syllogism. As a concession to his opponent he now declared his willingness to put aside for the time being his objections relating

Introduction: The Core Themes

69

to the hardness of the bodies and the practical execution of the substitution. The manner of carrying out of the substitution would not play a role as long as there was neither gain nor loss of force involved. He maintained, however, that the entire force that is transferred from the body B to the spring C is returned to the surrogate body D. To make his assertion clear, he presented an example with numerical values for the masses and velocities of the bodies involved. His result was based on the assumption that the spring C would experience a greater resistance from the body D than it did from the body B. In the spring of the year 1697, Papin had other commitments and he for his part announced, on May 13, a time-out in the contest with Leibniz and it was not until October 24 that he saw himself in a position to continue the dispute. After Leibniz had appeared to concede regarding the feasibility of carrying out a substitution, Papin was confident that he could soon bring the controversy to an end. He then conceived the following experiment: A body A (of mass 10 and velocity 4) collides with a body B (of mass 1 and velocity 10) and later (in a separate thought experiment) with a body D (of mass 2 and velocity 5). On the basis of his calculations, Papin believed he could present a proof that, in substituting D for B, a loss of force would occur whereas inversely, in the substitution of B for D, a gain of force would result. The process could be continued in that one continually reduced the mass of B and correspondingly increased its velocity. This argumentation would of necessity then lead to a violation of the conservation of force requirement. In his reply on November 18, Leibniz countered with the argument that it would be impossible by means of two separate collisions of A with B and D, respectively, to produce the same conditions as those which resulted from the substitution of the body B with D following impact with A. The bodies A and D would have to be provided with movements such that, in the course of their collision, three conditions would be met, namely that, firstly, D would have to come to a stand-still, secondly, A would receive the same movement through the impact as in the case of the collision with B that brings the latter body to a stand-still and, thirdly, the tension of the spring between A and D would have to be the same as between A and B in the instant of the stand-still. These conditions were, in Leibniz’s view, not being fulfilled in the experiment conceived by Papin; in particular there was absolutely no consideration relating to the third condition. Leibniz maintained that he had determined the stress conditions of the spring in three ways; he then proceeded to explain the simplest of the three calculations using a numerical example. His conclusion was that the two situations were not equivalent and, accordingly, that the forces of the bodies A and D after collision would not be the same as those of the bodies A and B. At the heart of the matter in Leibniz’s view was the circumstance that

70

Introduction: The Core Themes

Papin had based his considerations on the law of “vis mortua” whereas, for an explanation of the substitution process, the “vis viva” would have to be taken into account. On December 5 then, Papin replied that the two bodies D and B would (on the basis of the law of the “vis mortua”) have the same effect on the spring due to the reciprocity of their masses and velocities. Even the circumstance, accepted by Leibniz, that the bodies B and D produced the same effect in colliding with the body A, required the same tensioning of the spring. Papin recalled that he himself had in his earlier letter of August 30, 1696, introduced yet another objection, namely that, according to Leibniz’s interpretation of the process, it would be possible that, following a collision, the stronger of the two bodies would be forced into reverse whereas the weaker of the two could continue on its path. Once again, Papin contested some fundamental distinctions introduced by Leibniz, in particular the existence of a “vis viva” alongside a “vis mortua”. Leibniz, in his final letter of the year 1697 to Papin, on December 12, emphasized that it would be sufficient for his line of argumentation if Papin were to concede the following two points, namely that, firstly, two bodies of different magnitudes can be provided with the same quantity of force and, secondly, a substitution can be carried out in such a way that the quantity of force of the bodies is conserved. In the collisions of the body A with B and D, respectively, the intervening spring would experience a different tension in each case although A behaved in exactly the same way in both cases. Here the body A might even be replaced by a wall. From this consideration, he conceived the following thought experiment to help provide a decision in the dispute: against a spring that is attached to a wall on one side two bodies, designated L (of mass 6 and velocity 1) and M (of mass 1 and velocity 6), respectively, impact the other side of the spring in separate trials. In each case a considerable difference in the tensioning of the spring was to be expected. Accordingly, L and M would have unequal forces although both of them would in turn be stopped in the collision. In the context of the thought experiments pertaining to the nature of percussion and elastic spring, Leibniz once again pointed to a further conservation law of his, namely that of the quantity “progress” (“progrès”) which was given as the product of mass and directional velocity and was the counterpart of “force morte”. Regarding Papin’s objection that – according to Leibniz’s interpretation – in the collision of two bodies the stronger one might possibly be forced into reverse while the weaker one could continue in its path, Leibniz maintained that this circumstance would depend on the definition of “stronger” and “weaker” and in any case would lead to linguistic paradoxes. For this very reason it was necessary to introduce two very different kinds of force

Introduction: The Core Themes

71

that were compared to angles and lines in mathematics. Leibniz characterized these two forces as active or living, productive, absolute and spatial (the first) and as passive or dead, disabled, relative and plane (the second), respectively. The first force is that which is conserved in nature. Also, the circumstance that Papin found so strange, namely that the tensioning of a spring arises from the law of the “vis mortua” while contemporaneously the “vis viva” is consumed, was explained by Leibniz by referring to the relationship between peripheries and areas of geometrical figures: in consuming all of the dead force (like the peripheral lines) the living force (like the areas) would also be consumed. The ascent of a weight against the force of gravity was in this respect similar to the tensioning of a spring. The “vis mortua” represented the distributive law of the changes whereas the “vis viva” embodied the collective law of conservation. Papin’s designation of an effect in which a body is brought to a standstill as “absolute” induced Leibniz to explain his use of the terms “absolute” and “relative”, the former being applicable to the production of a certain force, where there is a certain determined movement, and the latter to the determination or regulation of a body like preventing its advance or forcing its reversal of direction. Papin, in his first letter of the year 1698 to Leibniz, on January 6, then rejected the allegation of a paradox resulting from his interpretation and maintained the paradoxes that had arisen only existed within Leibniz’s system. He explained that, notwithstanding different tensions in the spring, an equal breaking effect could be achieved since the duration of the event had also to be taken into consideration. The correspondent proceeded to explain the difference between his and Leibniz’s approach by means of an analogy. Two observers arrange for the collision of two bodies A (of mass 1 and velocity 2) and B (of mass 2 and velocity 1) in a space devoid of air without gravitational influence and they establish the existence of equal quantities of motion and of equal forces, also for other relations of mass and velocity. Then, the observers are transferred to another location in space where a hailstorm is raging. The non-observable particles of the hail are unimaginably small and their velocity is extraordinarily large. The observers now observe two bodies having the same magnitude that are moving against the hail stream. They notice to their surprise that the bodies lose their movement after travelling a short distance and subsequently move backwards apparently without having encountered other bodies. The amazement of the observers increases once they establish that the traversed distances (until the loss of their respective movements) are not proportional to the quantities of motion. A body with double the quantity of motion of its counterpart has to traverse four times the distance before coming to a halt. The first observer (Papin’s alter ego) explains the occurrence by

72

Introduction: The Core Themes

supposing the existence of the hailstorm and seeing the laws of colliding bodies at work whereas the second observer (Leibniz by proxy) prefers to introduce a new force to explain the event which Papin considered superfluous if not embarrassing. In his reply on January 26, Leibniz then complained about a certain prevailing camp thinking in which the two contenders in the dispute, like hostile armies following a skirmish, claim victory for themselves among their partisans without ever having joined battle. Accordingly, he sought to reply in a formal fashion citing articles like in a legal dispute. Leibniz attempted to show that Papin’s interpretation must, in the final analysis, lead to the possibility of a perpetuum mobile; this could happen, for example, if the principle of the equality of cause and effect were to be infringed at the location in space where Papin had placed his observers. Leibniz then introduced two basic principles from which the laws of colliding bodies could be derived, namely the equality of cause and effect and the conservation of progress, or of the directional quantity of motion. In order to prove his standpoint solely on the basis of the law of “vis mortua”, combined with the rules for the composition of movements, Leibniz conceived the following thought experiment. A ball or sphere passing along the diagonal of a square strikes simultaneously two other balls of the same magnitude resting at one corner (the upper right-hand corner) of the square. The first ball comes to rest at the upper right-hand corner and its movement is transferred to the other two balls which then move off along the extension of the upper horizontal side and the extended right-hand vertical side of the square, respectively. The velocity of the ball moving along the diagonal is represented by the diagonal length and those of the other two balls by lengths equal to that of the side of the square. Leibniz concluded from the Pythagorean theorem that it is not the movement (or velocity) but rather the force (or square of the velocity) that is conserved. The collision event could also take place in reverse with the two balls travelling in reverse coming from the corresponding directions and simultaneously striking the first ball resting at the upper right-hand corner of the square; there their movements would be transferred to the first ball and they would come to rest, whereas the other (or first) ball would move forth from the upper right-hand corner along the diagonal of the square with a velocity represented by the length of that diagonal. In this manner a quantity of force would have been transferred from a greater to a smaller part of matter. For Leibniz, this showed that his interpretation would apply not only on earth but also in free space without gravitational force. The hail, imagined by Papin, would however have to be taken into account in considering the quantity of motion. Leibniz also dealt with the effects, arising from his standpoint,

Introduction: The Core Themes

73

which Papin experienced as paradoxical, as for example, the circumstance that two bodies which mutually arrested each other might produce the same effect. While two bodies A (of mass 2 and velocity 1) and B (of mass 1 and velocity 2) would put each other into reverse, B would produce double the effect of A. Furthermore, a body at rest could, without force and by virtue of its inertia alone, bring a moving body of the same magnitude to a halt. A measure of force based on the capability to stop moving bodies would of course become infinite. The true measure of force, which is conserved in nature, was to be measured in terms of the production of other forces. While Papin continued to find Leibniz’ interpretation paradoxical, for Leibniz the explanation of Papin was not just paradoxical but also absurd. He insisted that, in his treatment of the matter, he had shown that the position taken by Papin offended against reason and might sometimes result in a perpetuum mobile. Leibniz reported optimistically that he had found a criterion by means of which, and with the support of a physical experiment, a decision in the dispute could be reached. Inevitably for him, in the case of two bodies that produced a certain degree of tension in a spring, it was always the sum of the forces and not that of the quantities of motion that remained constant. Papin was, however, still not impressed by Leibniz’s arguments, as he made clear in his reply of April 20, 1698. Solely Leibniz’s thoughts concerning the impact of a ball against two stationary balls at an oblique angle of incidence appeared to him to be cogent. Four months later, on August 28, Papin finally entered into the details of the matter. He now argued that the two bodies in Leibniz’s thought experiment when they are simultaneously impacted by the body moving along the diagonal of the square, are not impacted for as long and not as forcibly as in the case when each of them is impacted separately. Each receives a smaller velocity than that represented by the side of the square. Also, when the collision process takes place in reverse, the course of events would be different to what Leibniz imagined. Papin claimed to be able to prove that, in the case of the simultaneous impact of the two moving bodies against the stationary body at the upper right hand corner of the square, the entire force would not be transferred but only a portion of it and that the two moving bodies would continue their movements after the impact and without change of direction. The velocity of the first body along the diagonal would be greater than the velocity represented by the side of the square but less than that represented by the diagonal. Papin was now also convinced that the matter could be decided by a physical experiment and that he himself would be in a position to carry out such an experiment. Alas, his overwrought situation at that juncture did not allow him the time and leisure to follow this course.

74

Introduction: The Core Themes

Leibniz for his part, in his letter of September 7, now also favored an experimental decision in the matter of the collision or oblique impact of a body against two other bodies at rest as he sensed an opportunity of obtaining a submission on the issue from Papin. He contradicted Papin’s argumentation however. The force transfer would be independent of whether the body moving along the diagonal encountered the second body on its own or the second and third bodies together at the corner of the square. The same applied when the collision process takes place in reverse, that is regarding whether the second body impacts the stationary first body on its own, or simultaneously with the third body. He then expressed his intention of pursuing the experimental approach to complement reason in the matter. In the meantime, however, Papin had his doubts once again about whether the matter could after all be decided in the short term by means of a physical experiment, and he retracted his previous conviction in his letter of October 9. Both the adversaries remained stubborn and, at the end of the year 1698, neither party had budged from its own view of things. Papin maintained at first, in a letter of November 17, that the first body, which was set in motion along the diagonal of the square, yielded to the two bodies faster than to only one of them and consequently offered less resistance or consumed less force. Both bodies together would lose less force compared to the situation where they individually impacted the body at rest. On November 28, Leibniz countered with the argument that the resistances, just like the velocities, were geometrically compounded and could be resolved into components. In the final communication of the year 1698, on December 11, Papin maintained that, if the first body moving along the diagonal of the square impacted the second body with reduced force (because of the skew angle of inclination), the reaction of the second body to the first would be similarly reduced which leads to the same result as if the collision had taken place centrally with a velocity represented by the diagonal. Besides the dispute about the correct measure of force, the discussion about the concept of ‘action’ (“actio”) was an important issue in Leibniz’s correspondence with Papin from the summer of 1696. The starting point was a proposition formulated by Leibniz at the end of his letter of August 20 of that year. There he presented the following assertion regarding a body moving uniformly without gravity or resistance through a space of a league or mile over time spans of one, two or three hours, namely that the body that covers a league in one hour displays a performance rate that is double (or triple) that which it would display if it were to cover the same distance in two (or three) hours. At the end of his letter of November 11, he then stated his proposition more precisely. The basic statement was that a body has double the action of another

Introduction: The Core Themes

75

body if it covers a certain distance in half of the time taken by that other body, and he offered to provide a demonstration of this for Papin. However, in his reply of November 15, Papin doubted the very cogency or validity of the concept of action. Citing the maxim “omne agens agendo repatitur” he insisted that there is no action in nature without re-action. Since the body encounters nothing against which it could act or through which it could be changed, the process represented nothing other than a continuing state. There then followed, in Leibniz’s letter of November 19, a more precise specification of the concept of action from his side, namely that action exists by virtue of the movement of a body. If a body moves more quickly it covers a greater distance in a given time and its action increases; in the case of constant velocity the action also increases if the body continues its movement over a longer period. For him movement per se represented a kind of action. He was, however, prepared to accept a different terminology which might appeal to Papin like “changement” (or “mutation”) or “changement de lieu”. Papin reacted with skepticism on November 25. He was unable to comprehend Leibniz’s distinction between force and action. And, furthermore, he could not identify Leibniz’s change of location (“changement de lieu”) with the distance covered by a body. Leibniz responded, on December 24, expressing the view that a force also manifests itself there where no resistance is to be overcome. This would be the case if the force of a body acts on its own mass, for example when it rotates about its axis. This exercise of force is conservative just like that of the universe as a whole. The action of a body meant for Leibniz the succession of the states of the body during a change of location. Papin’s assertion, that the change of location also depends on the movements of other bodies, was affirmed by Leibniz, with the caveat, however, that in each of these bodies a part of the total change is to be found. While Papin attributed an intrinsic movement to a body, Leibniz wanted to assign it a true “action”, determined both by its celerity and the duration (“intension”) or the extension of its movement (“extension”). Papin, in his reply of January 14, 1697, then argued that, in absolute terms, all bodies with the same mass possess the same force. A body at rest would exert the same force as a moving body in the sense that it would be in a position to offer the same resistance. A moving body, which is in motion without resistance and without consuming force, operates with the same ease as a body at rest. Papin concluded his consideration of the topic action with an offer to continue their discussion of the issues involved. The exchange of ideas concerning action was however interrupted for an entire year before Leibniz returned to the matter once again early in 1698. On January 26, 1698, he could then announce to Papin a new insight into the proportionality between action and his measure of force. He emphasized,

76

Introduction: The Core Themes

however, that he was only willing to share his thoughts on the matter with those who had expressed approval for his views. Only three months later, on April 24, after a certain degree of agreement with Papin (regarding the composition of mechanical movements) had been achieved, did Leibniz finally present his proposition for the uniform motion of a body, namely that action is proportional to the product of path and velocity, and thus also to that of time and the square of velocity. And from his conservation law for force – but not from that of Papin and the Cartesians – Leibniz then concluded that the quantity of action in the world was conserved. In his belated reply, on August 4, Papin rejected Leibniz’s proposition regarding the uniform motion of a body on the grounds that that, which he had always contested, was being postulated here. As far as he was concerned, the resistance to be overcome had to be measured and this was not necessarily proportional to the velocity. To this Papin added a criticism of Leibniz’s syllogistic argumentation and insisted on the need for proof of a certain assertion or premise before a particular demonstration could have validity. Leibniz then reacted almost immediately, on August 8, with a formal counter-argument that was again, like a legal document, divided into articles. In a medium without resistance, and free of gravity, a body is transported from one location to another. By virtue of its natural inertia, the body offers resistance to the movement. Then, the action of the body is taken to be proportional to the traversed path and to the velocity. As a result, actions over equal time intervals (“actions contemporaines”) are proportional to the squares of the velocities. All other assumptions as, for example, that actions are proportional to the velocities and to the times, or to the traversed paths and to the reciprocals of the times, lead inevitably to absurdities. Solely through his measure of force, combined with his principle of action, could such contradictions be ruled out. The error in the common or Cartesian interpretation lay, in Leibniz’s view, in the confusion of quantity of action with quantity of movement. In this letter, Leibniz also verified his measure of action in detail in the following manner: it is assumed that the action involved in traversing two feet, or units of path, in two seconds is double that involved in traversing a single unit in one second and that the latter is twice as great as that for the passage through one unit of path in two seconds. From this Leibniz concluded that the action involved in traversing two units of path in two seconds is four times that involved in the passage through one unit of path in two seconds. Only with the proviso that with action no force is consumed, was Papin willing, in his letter of October 9, to concur with Leibniz’s syllogistic reasoning and proof in the letter of August 8. He recalled once again that for him action arose solely through the overcoming of resistance. From this Papin concluded that

Introduction: The Core Themes

77

he himself and Leibniz were employing different definitions of the concept of action. And, for his concept of action, Leibniz’s arguments had no validity. In fact, in his letter of September 7 to Papin, Leibniz had also differentiated between two forms of action, namely between such actions in which the acting force is conserved and those actions, which he designated as “actions violentes ou contingentes”, in which this acting force is consumed. However, his main focus of attention was the first form, which he wished to call formal action because of its essential connection with force, and that action was equal to the product of force and time. Whereas he also had had thoughts about the second form of action, he had found the a priori nature of the formal action to be of fundamental importance. Both forms of action would nonetheless lead to the same measure of force. Now, in the letter of October 9, Papin actually contested the view that the existence of a force always implied an action. He believed that all bodies, with the same volume, have the same force, and indeed independently of whether they are in motion or not. In his reply, in the third week of October, Leibniz rejected Papin’s claim and once again referred to the inertia that a body in motion must overcome and for which force is required. This is equal to the resistance it has to overcome. The resistance, for its part, is nothing other than the repugnance or aversion to the production of such a force. Leibniz distinguished between an absolute resistance (which was involved here) and a relative resistance. In fact, the distinction between absolute and relative made here corresponded to Leibniz’s differentiation elsewhere between absolute and relative forms of force, action and velocity. Then, on November 17, Papin withdrew his endorsement of the designation of action as resistance-free movement of a body. He negated that the quantity of action is determined by the time and the path traversed. Furthermore, he contested Leibniz’s claim that a body in motion continually acts on itself. Also, Leibniz’s distinction between force and inertia had become incomprehensible for him. In his reply to this, on November 28, Leibniz tried once again to find a common vantage point. Even if his opponent was not willing to designate the change of location of a body as action, it would be sufficient if he could accept that an alteration was involved. For, since location and time were being changed, the alteration would also have to be measured by location and time. Papin’s measure of force (the quantity of motion) was in the last analysis likewise rooted in space and time; this ought also to apply for his (Leibniz’s) measure of force. Finally, in this last letter of 1698 to Papin, Leibniz referred to the correspondent’s remarks concerning inertia and made his own position clear once again. Inertia would always exist in a body, whether it was in motion or not, and its magnitude would depend on the quantity of matter involved. Force, on the other hand, existed only if the body was in motion and

78

Introduction: The Core Themes

it varied with the velocity. Inertia was to be counted among the passive abilities or acquirements (“potentia”) of a body, whereas, on the other hand, force belonged to its active abilities or acquirements. And so, at the end of 1698, the dispute was once again reduced to the conflicting definitions of force. In his final letter of the year to Leibniz, on December 11, Papin also remained totally intransigent as regards his understanding of action and his uncompromising adherence to the Cartesian definition of force, and thus the year ended with both parties in the dispute entrenched in their starting positions. In Leibniz’s correspondence with Papin, the disputes concerning the true measure of force and the correct concept of action were continued in the new year of 1699 with unabated intensity and passion. In the 30-month period that ended in December 1698 a total of 40 letters had been exchanged between Leibniz and Papin. In the 36-month period that followed from January 1699, 20 letters were exchanged of which 19 had been dispatched by the spring of the year 1700 when the debate finally came to a standstill. In the course of the debate with Papin, the themes of the previous years were once again played through time and time again in 1699 and early 1700. In January 1699, Leibniz began to have doubts about the forthrightness and the probity of his correspondent, as the beginning of the never-dispatched first draft version of his letter to Papin of January 1699 reveals. He expressed himself more diplomatically at the beginning of the second dispatched version of this letter where he attributed the (for him) incomprehensible argumentation of Papin to inattention on the part of the correspondent. His desire was for a return to a formal argumentation regime with the help of a series of syllogisms. Accordingly, Leibniz summed up, in the form of syllogisms, the state of the debate regarding the principal points at issue, namely his concept of action and his thought experiment regarding the impact of a spherical body moving along the diagonal of a square figure against two similar bodies resting at a corner. As regards Papin’s argument that there could be no action without the body experiencing resistance, Leibniz had initially proposed using the term ‘changes’ in place of ‘actions’, viz. “changemens” instead of “actions”. This however had only added to the confusion since Papin had replaced – in the syllogism with which Leibniz had expressed the action for uniform motion as depending on the traversed distance and the velocity  – the expression traversed spaces (“espaces parcourus”) with changes of location (“changemens de lieu” or “mutationes loci”). Papin did in fact differentiate between produced and producing changes, viz. between “mutationes loci productae” and “mutationes loci producendae”, and was therefore not confronted with a

Introduction: The Core Themes

79

contradiction in Leibniz’s syllogism. Nonetheless, that was not what Leibniz intended. Accordingly he then tried, on the one hand, to explain the difference between “changemens des espaces” and “espaces changés” and, on the other hand, to return to the concept of action which he needed to make plausible in another way. He discussed in detail why action also existed in the event of a resistance-free movement, a matter which Papin had previously rejected, and he presented further reasons for presupposing an action. For the collision along the diagonal of a square involving the three bodies, Leibniz assumed that the resultant of the event consisted of two components, namely the mutually independent movements of the first and the second spheres and of the first and the third spheres, respectively. Papin had rejected this, with the argument that the first sphere, in its movement along the diagonal, would, in the event of a simultaneous meeting of the three balls, experience less resistance from each individual sphere or, in the reversal of the process, be pushed off faster than in the case of separate collisions. The total result therefore would not be the sum of the individual collisions. Leibniz replied here that what mattered was not how rapid the repulsion of the first sphere (that moved along the diagonal) would be, but rather what the velocities along the extended sides of the square figure would be. Both of these themes, namely the interpretation and the measure of the action as well as the understanding of the diagonal collision, were at the center of the Leibniz-Papin correspondence until its extended interruption in the spring of the year 1700. Accordingly, the different positions were recapitulated again and again, reformulated and stated more precisely without however a convergence of those positions being achieved. In his reply of February 23, 1699, to Leibniz’s letter of January, Papin also regretted the lack of agreement in the matters at issue but he did insist however that he was motivated solely by the search for truth and he went into detail regarding Leibniz’s main argument. In his view, Leibniz’s explanations concerning the distinction between “espaces changés” and “changemens d’espaces” failed at this point to clarify the issues of terminology. Papin proposed equating the concept of action with perseverance or persistence within the same manner of being (“perseverance dans la même maniere d’être”), which however was independent of the movement. As regards the diagonal-collision thought experiment, the situation, assumed by Leibniz, of the simultaneous collision of two balls against a third at rest, was for Papin only valid in the first instant when the diameter of one ball meets the diameter of the ball resting at the corner of the square. In the case of the simultaneous collision of the three balls, the ball at rest would receive less force from the first of the two moving balls than in the case of the sole impact with just one of those moving balls.

80

Introduction: The Core Themes

The discussion about the role of the resistance also led to considerations about inertia and mass. The conflicting positions remained, in Leibniz’s eyes, unreconciled alongside each other as he remarked in his reply of March 10. Notwithstanding this, Leibniz did find that they were in agreement about the circumstance that a body resisted a change from a state of motion to that of rest and vice versa. However, while for Papin there was no fundamental difference between the states of rest and motion, for Leibniz, in the state of rest, which he regarded as a simple deprivation (“une simple privation”), the mass or the inertia of matter resisted motion. For bodies in motion however an entelechy – namely, an inherent or intrinsic and purposive force which realized or made actual what was otherwise merely potential53 – provided for the maintenance of the state. Mass constantly reacted against or resisted this entelechy. Thus, action and reaction would take place here within a body. Papin’s assumption of a general inclination for the conservation of a body’s manner of being (“inclination generale pour conserver sa maniere d’estre”) contradicted however the phenomenon, since, for a movement along a flexuous line or curve, only the direction and not the curvature was conserved after the constraining force was removed. Which magnitudes in nature were really conserved would have to be scientifically established. Leibniz proclaimed here that he had established that the measure of force as well as the measure of action (but not the quantity or measure of motion, viz. the momentum or impulse) were conserved. Leibniz did however consider Papin’s objections against his explanation of the diagonal-collision thought experiment to be well founded. In the abstract consideration of the event, however, one could assume perfect hardness and an instantaneous or momentary collision of the three balls and, therefore, that the force of both the moving balls would be totally transferred to the stationary one. The total transfer (and conservation) of the quantity of motion from the combined or double mass of the two moving bodies to the single mass of the body at rest would however result in a perpetuum mobile. Papin, in his letter of April 2, adhered to the notion of “changement de lieu” which he considered to be decidedly more distinct than that of “action” or “actio”. His assumption of an absolute indifference for every kind of manner of being (“indifference absolue pour toutes sortes de manieres d’être”) appeared to him to be more natural, simpler and more complete than Leibniz’s 53 Cf. the discussion of the importance of the Aristotelian entelechy concept for Leibniz’s understanding of force in E. Rudolph, “Die Bedeutung des aristolelischen Entelechie­ begriffs für die Kraftlehre von Leibniz”, and in G. Gale, “Leibniz’s force: Where physics and metaphysics collide”, pp. 49–54 and pp. 62–70, respectively, in: A. Heinekamp (ed.), Leibniz’ Dynamica: Symposion der Gottfried-Wilhelm-Leibniz-Gesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982 (Studia Leibnitiana, Special issue no. 13), Stuttgart, 1984.

Introduction: The Core Themes

81

distinction between the states of rest and motion. Leibniz’s concept of the entelechy meant for him an added complication or, in his words, to “multiplier les êtres”. Papin considered the movement of bodies along a flexuous line or curve to be in conformity with his assumption which he explained by the example of centrifugal force. The bodies would possess this force in order to conserve their state. As regards the diagonal collision, Papin stuck to his conviction that, even with the assumption of a perfect hardness, the sum total of the quantities of motion following the collision would be less than before the event. It was similar to the case of free fall in terrestrial gravity. If an arbitrarily hard ball were to fall freely and rebound from an anvil, it would never rise again to the height from which it fell. However, there were instances in which the quantity of motion might indeed be increased following collision. Leibniz, replying in the second half of April, then resolved to no longer speak of action and instead insisted on hearing Papin’s view of the assertion that to traverse a league in one hour was more than to traverse this distance in two hours (“parcourir une lieue en une heure est plus que parcourir une lieue en deux heures”).54 The exact proportion of 2 to 1 (“en raison de deux à un”) could be determined later. The question concerning inertia and the entelechy was for Leibniz not decisive. A simpler, more natural and more understandable hypothesis would however be worthless if it did not conform with the phenomena of nature as was to be seen in the comparison of the Keplerian ellipses with the circular planetary paths of the ancients. If matter were indifferent, as Papin maintained, then a smaller body in motion could carry off a larger body at rest without suffering loss. However, Papin would also have to presuppose an inherent or intrinsic predisposition of the body, namely that of being present. The inertia and the entelechy represented for Leibniz nothing other than such a preference for the existing states of rest and motion, respectively. The inertia was of an essential nature whereas, in contrast, the entelechy was changeable. As regards the diagonal-collision thought experiment, Leibniz contradicted Papin’s assertion that the alteration of the quantity of movement – be it an increase or a decrease – would be only small and as a result would inevitably – following the common or Cartesian interpretation – lead to perpetual motion. The example of free fall (and rebound from an anvil) was of a different nature; for a small change in height it would be scarcely noticeable, whereas, for a small change in the direction of oblique impact, there would in time be an accumulation or continued divergence with the obliquity increasing as the lines moved further apart. 54 underlining by Leibniz.

82

Introduction: The Core Themes

Regarding Leibniz’s question, as to whether the covering of a distance in half the time amounted to more, Papin replied, on May 7, that an increase of velocity was involved here but not a change of place or location (“changement de lieu”). Since the change of place is compounded of velocity and duration, a compensation occurs; both of the activities were identical. He considered that Leibniz had the obligation to prove his hypotheses about inertia and the entelechy. And he interpreted the encounter of a small body in motion with a large body at rest differently to Leibniz. In the meeting of bodies in incompatible states (e.g. those of rest and motion), both have to concede equally, for otherwise matter would not be indifferent but would have a penchant for a particular state like that of motion. Furthermore, one could often not distinguish between bodies in motion and those at rest. For Papin, movement along a curve constituted not a single state but rather a concatenation of an infinite number of states. Only when the body in motion is freed from constraint, does it remain in a single state. And, finally, he insisted that in a collision there would inevitably always be a loss of quantity of motion with the result that a perpetuum mobile would never be produced. In his next letter, written in the second half of May or the first half of June, 1699, Leibniz assessed Papin’s answer to his question as to whether traversing a distance in half the time amounted to more – namely that the velocity increases but not the change of location – as a partial agreement of their standpoints, which he now stated more precisely using the concepts of “extension” (viz. extensive or spatial change) and “intension” (viz. intensive or temporal change). If one could agree about the proportionality factor, the dispute could be resolved at least on this point, Leibniz thought. He then presented to that end a formal proof in the guise of a syllogism whose major and minor premises stated, respectively, that “in doubling the path and the time, one obtains more in the proportion 2:1” and “exactly the same proportion results if for a constant path the time be halved”. In the context of the major premise, the “extension” is doubled (while the “intension” remains constant) whereas, in the case of the minor premise, it is the “intension” which is doubled (while the “extension” remains constant). Taken together a factor of 4:1 ensues and, accordingly, Leibniz’s understanding was that in this way Papin’s proposition  – namely that the changes of place behaved like the product of velocity and time – had been refuted. As regards an understanding of the collision process, the rival positions were still far apart. Leibniz argued that the force lost in the transfer would be small with the result that the Cartesian measure of force would lead to a perpetuum mobile. As regards the difference between rest and motion, Leibniz emphasized that he was concerned with the true (real or actual) and not an apparent

Introduction: The Core Themes

83

(or potential) state of rest. This had the same relation to motion that zero had to the positive numbers in mathematics. Just the same, Leibniz saw here a certain proximity to Papin. Rest could also be regarded as inertia and would then be nothing other than Papin’s concept of incompatibility or of resistance. Movement along a flexuous line or curve was also for Leibniz a concatenation of states. However, one could understand every movement, even uniform movements, in the following way: there is a past state, a future state and a third state, namely the location change itself, which is conserved. However, the change of direction too is a state which is altered. Leibniz explained this difference on the grounds that motion was attributable to an intrinsic principle, namely the entelechy, which forms the basis of the distinction between real and apparent movement. The change of direction was, however, attributable to an external cause just like an acceleration, a retardation or any change of speed whatsoever. As soon as the external cause ceased to be operative, the change would also come to an end. And here he stated more precisely that this involved not just a simple change but rather the change of a change. In his reply, on June 18, Papin emphasized that, without external resistance, slow and fast motion would have the same force, perfection, and reality. Since the quantity of the location changes depended only on the traversed path, he considered an a priori proof of Leibniz’s standpoint to be impossible. Furthermore, his own position could be refuted neither by the power of judgement nor by experiment. While Papin did concede to Leibniz that the assumption of a complete transfer of the quantity of motion would inevitably result in a perpetuum mobile, he continued to insist that the laws of motion would prevent this ever happening, since there would always be a loss. In addition, Papin made clear once more why the loss of velocity in the collision of a small moving body with a larger body at rest could be explained by an indifference of matter. There was no reason why only the large body would experience a change while its smaller counterpart did not. In principle, in the collision of two balls, the quantity of change of both would tally or be in agreement. Finally, Papin could not comprehend that, for Leibniz, not only curvilinear motion but also uniform motion consisted of several states. If one were to keep intrinsic and extrinsic factors apart, one would not find any such plurality. Naturally, the position of a body in relation to other bodies could change, but that would only affect the external circumstances. Leibniz, writing on July 4, insisted once again on the importance of formalization, which he justified with the abstractness of the subject matter and for which one could not simply resort to numbers or figures for support. The essential touchstones for him were (a priori) the form and (a posteriori) experience or experiment. The first matter of dispute, namely as to whether

84

Introduction: The Core Themes

traversing a certain path in half the time was more, or represented a gain, Leibniz considered to have been decided in his favor now that Papin had (in his view) in effect concurred with him. He thus considered his standpoint to have been confirmed and the opposing standpoint to have been reduced to absurdity. Papin’s continuing opposition represented for him simply tactics for the purpose of saving face. Also, in regard to the second matter of dispute viz. the collision of a body moving along the diagonal of a square with two bodies resting at a corner, Leibniz saw a toing and froing on Papin’s part. The latter had accepted that a total transfer of the quantity of motion would lead to a perpetuum mobile but had assumed, in practice, a loss from the transferred quantity. Leibniz was now of the opinion that this loss could be kept arbitrarily small by replacing the balls with long thin cylinders. Regarding collision, Leibniz proceeded to state the differing standpoints more precisely. While Papin held the states of the bodies involved to be incompatible, for Leibniz movements were fundamentally compatible; on bringing them together in a single body, the result would be that they move with the compounded motion. If one assumed an indifference of matter, then, in the collision, each body would receive the movement of the other in addition to its own which would lead to the previously mentioned contrariety that a smaller body might carry off a larger one. As regards movement along a curvilinear path, Leibniz repeated and elaborated his interpretation. Here a state was involved but, however, not a single state but rather a compound one. Indeed even the much simpler rectilinear motion was for Leibniz a composite entity. A conservation of state was involved in rectilinear motion but not in curvilinear motion. Responsibility for this lay in the circumstance that the change of location had an internal cause whereas the change of direction was attributable to an external cause. A differentiation between intrinsic and extrinsic properties of bodies was essential for Leibniz. Regarding this point he saw a certain degree of agreement with the correspondent. On the basis of this distinction, he insisted, Papin should finally recognize that a greater velocity would lead to greater perfection independent of external resistances. Replying on September 21, Papin then rejected Leibniz’s reproach that he was not abiding by the agreed formalized forms of argumentation. As regards the question as to whether the passage through a certain distance in a shorter time was more than when a longer time interval was involved, Papin stated his position more precisely. His principal objection here related to the general expression “it is more” (“c’est plus”). Identical bodies would have the same force independently of the velocity. This was so because for every force acting in a particular direction there was a compensating weakness (“foiblesse”) operating in the opposite direction. As far as the velocity was intended, he was

Introduction: The Core Themes

85

able to be in accord with this; however if it was intended that the movement would be something stronger, more real or more perfect than the state of rest, then he was still in denial about it. As regards the diagonal-collision thought experiment, Papin doubted that losses could be avoided by substituting long thin cylinders for the colliding balls. He justified his concept of incompatibility with the circumstance that, in a collision, one (or both) of the bodies would of necessity have to change its state (or their states). Leibniz’s splitting of the regular motion into several states meant for Papin nothing less than an unnecessary complication, or, in his words, to “multiplier les êtres sans necessité”. He rejected the idea of an intrinsic reason for the regular movement and accordingly also Leibniz’s concept of the entelechy. Leibniz’s replique, on October 30, was short, since further discussion with Papin now appeared to him to be superfluous and he added that he was satisfied that his measure of force had been demonstrated in principle or in his words: “il me suffit que mon estime soit demonstrée ex hypothesi et à leur egard”. Papin in turn, writing on December 3, only briefly dealt with the dispute about the measure of force and returned to his entrenched position, insisting on the superiority of the Cartesian measure over that of Leibniz with the words: “Je tiens que pour faire cette estime il faut se servir de nôtre methode et non pas de la vôtre”. Then, in his final letter of 1699 to Papin, on December 27, Leibniz briefly expressed his incomprehension that Papin wanted to incorporate a weakness in the opposite direction to the force since naturally the core of the matter was an action in the direction of motion. Finally, in the spring of the year 1700, the exchange of views with Papin about the true measure of force gathered pace once again and entered its final phase. In his letter of March 4, Papin recapitulated his view of the respective positions as follows: Leibniz had maintained that the location changes of bodies moving along a certain path depended on the velocities. He even assumed that a faster motion would lead to greater perfection and greater reality. He himself, on the other hand, held the view that all states had the same degree of force, perfection, and reality. In a certain sense, however, a rapid motion would actually have an advantage over a slower motion because the path would be completed in a shorter time. The actions which Papin equated, as he had previously done, to changes of location, manifested themselves, in his view, as the product of the times and velocities. Once again Papin referred here to Leibniz’s statement that it was more to cover a certain distance in one hour than in two hours. With respect to the velocity, this would be correct. As far as he was concerned, however, it was only a matter of the distance covered. The circumstance, that one body required double the time span whereas another body had double the velocity, resulted in a compensation or equalization. Whether one considered

86

Introduction: The Core Themes

the quantity of changed locations, or that of changes of location, would be of no consequence here. All in all then, Papin considered that he had responded adequately to the issues Leibniz had raised. Less than a week later, on March 10, Leibniz replied. He now tried to portray Papin’s views as absurd or beside the point. The whole world would prefer a more rapid movement to a shorter counterpart and would consider it to be more perfect. If duration and velocity were to mutually compensate, or offset each other, that should also hold for liabilities and assets, like for debts and wealth assets, for that which one person lacks would be in the possession of another. Furthermore, Papin’s assumption would, according to Leibniz, lead to the situation that the actions of all movements would be equal since, for bodies in motion, a reciprocal relationship between velocities and times always exists. This would only apply, however, if the covered distances were to be equal. In the general case (with Papin’s assumption) a proportionality would result between action and the product of distance and time. This would then lead to the absurd consequence that a uniform movement, in which two units of length were covered in two hours, would have fourfold the action of a movement in which one unit of length was covered in one hour. And so, for Leibniz, it followed that the acceptance of his measure of force was the only means of avoiding this embarrassment. Four weeks later, on April 8, Papin once again insisted that a more rapid movement had advantages but that, in relation to their states (“manieres d’être”), bodies at rest would have exactly the same amount of force, perfection and reality as those in motion: while a body in motion acts more strongly in the direction of motion, a body at rest acts more strongly in the reverse direction. He denied that velocity and time always stood in a reciprocal relation to one another and he then demanded from Leibniz a formal proof for the minor premise of the syllogism under consideration. In his final letter to Papin dealing with the measure of force and action, written in the second half of April 1700, Leibniz elaborated his views about the still unanswered matters of dispute under nine headings in an attempt to structure the discussion. Then, he accused Papin of not having answered all his arguments and he once again emphasized that the essence of the matter was the measure of action in the direction of motion. Having at first attempted to provide a proof for the minor premise of the syllogism referred to, he finally backed off with the consoling words “on vera alors, si j’ay encor besoin de preuve”. A reply from Papin to this letter has not been found. Perhaps Leibniz’s letter of April 1700 did not reach the correspondent since he had embarked on a journey to Holland. The outcome was that the correspondence between the two was interrupted for a period of a year and a half. In Papin’s last communication

Introduction: The Core Themes

87

to Leibniz of the year 1701, on December 5, no further reference was made to the dispute about the correct measure of force and the concept of action. Nonetheless, Papin’s continuing correspondence with Leibniz after 1701 (especially between 1704 and 1707) may contribute to a better understanding of the controversy including how the dispute was first unleashed in 1689.55 4 Physics Argumentum Neutoni contra vortices mihi stringere non videtur. Leibniz to Augustinus Vagetius, January 6, 169456

A series of physical writings of Leibniz from his first three years in Hanover (1677–1679) relate directly to questions raised, or left unsolved, by Descartes.57 Here it was above all the Cartesian laws of motion and laws of refraction which, along with Leibniz’s efforts for a further development of his Hypothesis physica nova (1671), provided occasion for scientific discussion with correspondents like Honoré Fabri. Already during his four years in Paris, from 1672 to 1676, Leibniz had set himself the task of reducing mechanics to geometry and in doing so assigned a key role to the principle of the equality of cause and effect. These studies in natural philosophy achieved a first lasting result in his outline entitled De corporum concursu (1678) with the introduction of the product of mass and the square of the velocity as the measure of force. In letters to Philipp Lohmeier, François de la Chaise, Adam Adamandy Kochański, and Friedrich Schrader, Leibniz referred to this result and stressed the importance of reducing mechanics to geometry. Then, in the early 1680s, there is evidence of increased attention being paid to concrete science, and physics in particular, in Leibniz’s correspondence. In this effort he was not satisfied with 55 Cf. A. G. Ranea, “Theories, rules and calculations: Denis Papin, before and after the controversy with G. W. Leibniz”, pp. [59]–83 in: M. Kempe (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung, vol. 1, 2013. 56 Cf. A III,6 N. 2, p. 13; Translation: Newton’s argument against vortices in the theory of planetary motion does not appear to efface my position. 57 Cf. D. Garber, “Leibniz: Physics and philosophy”, chap. 9 (pp. 270–352), in: N. Jolley (ed.), The Cambridge Companion to Leibniz, Cambridge, 1995, 1996, 1998; J. K. McDonough, “Leibniz’s philosophy of physics” (Includes: “The historical development of Leibniz’s physics”, “Leibniz on matter”, “Leibniz’s dynamics”, “Leibniz on the laws of motion”, “Leibniz on space and time”, and “Bibliography”), in: E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2019 Edition; last viewed December 2022), .

88

Introduction: The Core Themes

the mere accumulation of experimental data, a practice which he associated with the work of Robert Boyle in particular. While he very much appreciated Boyle’s judgement and experimental industriousness (“judicium et industriam experimentalem”), as he wrote in the letter of March or April 1681 to Friedrich Schrader, he criticized what he saw as Boyle’s reticence in drawing conclusions. According to Leibniz, experimental results should be ordered and structured by means of principles and an attempt ought to be made to explain phenomena in terms of form, magnitude, and movement. Accordingly, the paradigm to be followed involved the accumulation of empirical observations (like those of Francis Bacon or Robert Boyle) and of calculations (like those of Galileo or Descartes), in the organizing and carrying out a system of experiments, in the refining of calculations by means of experiments, and thus advancing mathematics and physics. Mariotte was for Leibniz the most interesting correspondent on questions of physics at the end of the 1670s and in the early 1680s. He reported to Leibniz in detail about his own experimental research as well as about books in progress. In addition to the nature of an elastic collision and the mode of operation of the wedge, motion in a resisting medium received particular attention. In a letter from the first half of June, 1682, Leibniz enquired of Mariotte about experiments carried out by the Académie des Sciences on this topic, in the hope of obtaining support for the mathematical treatment of the process of resisted motion leading to the science of ballistics, and he referred in particular to the third and fourth days in Galileo Galilei’s Two New Sciences, viz. the Discorsi e dimostrazioni matematiche, intorno a due nuove scienze attenenti alla mecanica & I movimenti locali (1638).58 4.1 The Pneumatic Engine Leibniz had visited Boyle during his first visit to London on February 12, 1673; thereafter, through his correspondence with Heinrich (or Henry) Oldenburg, the German-born secretary of the Royal Society and editor of the Philosophical Transactions, Leibniz repeatedly conveyed greetings to Boyle, directed questions to him and sought to establish contact with him. Boyle’s words too, which reached Leibniz through Oldenburg, were pronounced friendly, as for example in letters of April 22, 1675, and of March 4, 1677. Even after Oldenburg’s death, in September 1677, Leibniz learned that Boyle had enquired about him as, for 58 Cf. S. Drake (transl., intro, notes), Galileo Galilei: Discourses and mathematical demonstrations concerning two new sciences pertaining to mechanics and local motions, Madison (Wis.), 1974, and also: R. Raphael, Reading Galileo: Scribal technologies and The two new sciences, Baltimore, 2017.

Introduction: The Core Themes

89

example, from a letter of Friedrick Slare on July 18, 1680. Even six years later, at the end of June 1686, Detlev Clüver could report Boyle’s continuing interest in Leibniz’s work but the correspondent regretted being unable to report to Boyle about Leibniz’s chemical studies. In his reply to Clüver, at the end of July 1686, Leibniz elaborated his thoughts on Boyle’s works and presented a characterization of his own contribution to the study of metals. In his official correspondence, Leibniz usually expressed his reverence for Boyle and he tried to encourage him to make known or publish his results as, for example, in a letter to Henri Justel – the royal librarian at St. James’s Palace in London under William III – on October 20, 1690. In his epistolary exchanges with other correspondents there are also indications of the topics discussed during his meeting with Boyle on February 12, 1673, for example, in a letter to Oldenburg on March 8, 1673, less than a month after that meeting. However, the only direct correspondence between Leibniz and Boyle materialized after the latter had sent, through an intermediary, a sample of an Indian seed to duke Johann Friedrich of Hanover. At the end of October 1677, Leibniz then wrote a short official acknowledgment and expression of gratitude to Boyle for the gift received. Whereas the sole letter Leibniz sent to Boyle, and the exchanges of greetings through intermediaries, were of a cordial nature, a range of critical remarks regarding Boyle are also to be found in Leibniz’s correspondence as, for example, in the previously cited letter of March or April 1681 to Friedrich Schrader. As regards practical science, and physics in particular, the question of priority in the development of the vacuum pump proved to be a point of contention. Boyle, together with Robert Hooke who in his early career (c.1657/8) worked as Boyle’s research assistant,59 had improved the vacuum pump that had originally been developed by Otto (von) Guericke and, equipped with this pneumatic engine, Boyle had embarked on his epoch-making experiments on the properties of air. However, in Leibniz’s view, Boyle had unjustly received acclamation for the development of the vacuum pump, to the detriment of Guericke with whom he had discourse and had corresponded with in 1671 and 1672.60 59 Cf. for example, S. Inwood, The man who knew too much: The strange and inventive life of Robert Hook, 1635–1703, London, 2002 (and 2011), and The forgotten genius: The biography of Robert Hooke, 1635–1703, San Francisco, 2003 (and 2005); R. D. Purrington, The first professional scientist: Robert Hooke and the Royal Society of London, Basel, Boston, Berlin, 2009. 60 Cf. for example, F. Krafft, “Die aus der Literatur bekannte Korrespondenz des Otto von Guericke (d. Ä.)”, Technikgeschichte, vol. 45, (1978), pp. 37–54; F. Krafft (ed.), Otto von Guerickes Neue (sogenannte) Magdeburger Versuche über den Leeren Raum. Mit einer einleitenden Abhandlung, Düsseldorf, 1996, pp. X–LXXXVIII; F. Krafft, “Die Schwere der

90

Introduction: The Core Themes

In fact, however, the discovery of the new device by Guericke had first been made widely known through an appendix in Caspar Schott’s Mechanica hydraulico-pneumatica (1657) in advance of Boyle’s publication. The following title of Schott’s appendix had left no doubt as to the priority of Guericke in this discovery: “Experimentum Novum Magdeburgicum, … Inventum primo Magdeburgi a Ottone Gericke Urbis illius consule”. Then, three years later, at the outset of his New experiments physico-mechanicall, touching the spring of the air, and its effects, (made for the most part, in a new pneumatical engine), Boyle acknowledged his indebtedness (regarding the pneumatic engine) to Guericke, referring to Schott’s book as his source of information. His own contribution lay in the removal of deficiencies and the further development of the pneumatic engine. Notwithstanding this, Leibniz claimed for Guericke the status of “inventor primus” of the vacuum pump in his correspondence from the middle of the 1670s as, for example, in a letter to the English physician Nehemiah Grew in July or August 1679. His conviction in this matter endured into the 1690s and found expression, for example, in a planned (but never dispatched) letter to Christiaan Huygens from the first half of October 1690. Apart from any personal antipathy towards Boyle, Leibniz saw here a manifestation of prejudice against Germany and the Germans. In another deleted (and never-dispatched) text passage forming part of a draft of a letter to John Wallis of March 29, 1697, Leibniz claimed that no other nation was as outstanding as the German nation in acknowledging the achievements of others, and that the result of this exemplary behavior was that the Germans themselves were often disadvantaged. In this context, he then added the following statement that all recognized, or acknowledged, what an outstanding man Robert Boyle had been: “Agnoscimus omnes quantus Vir fuerit Robertus Boilius”.61

61

Luft in der Diskussion des 17. Jahrhunderts: Otto von Guericke”, pp. 135–170 in: W. Klewer (ed.), Die Schwere der Luft in der Diskussion des 17. Jahrhunderts, (Wolfenbütteler Arbeiten zur Barockforschung, vol. 29), Wiesbaden, 1997; F. Krafft, “Alt und Jung: Die Kontakte zwischen Otto von Guericke und Gottfried Wilhelm Leibniz: virtutes mundanae und ‘Einhorn’”, pp. 263–282 in: B. Heinecke, I. Kästner (eds.): G. W. Leibniz und die gelehrte Welt Europas um 1700, Aachen, 2013; F. Krafft, “Gottfried Wilhelm Leibniz oder Otto von Guericke: Protogaea oder Experimenta nova Magdeburgica? Die Rekonstruktion des vermeintlichen Einhorns von Quedlinburg”, Sudhoffs Archiv, vol. 99, (2015), pp. 166–208; B. Heinecke, W. Knapp, P. Rubini, P. Streitenberger (eds.), Leibniz und Guericke im Diskurs: Die Exzerpte aus den Experimenta Nova und der Briefwechsel, Berlin, Boston, 2019. Regarding certain critical remarks about Boyle in Leibniz’s correspondence, cf. J. G. O’Hara, “‘Agnoscimus omnes quantus Vir fuerit Robertus Boilius’ – kritische Anmerkungen über Boyle in Leibniz’ Korrespondenz”, pp. 319–332, in: B. Heinecke, I. Kästner (eds.), Wettstreit der Künste: Der Aufstieg des praktischen Wissens zwischen Reformation und Aufklärung, (Europäische Wissenschaftsbeziehungen, vol. 17), Aachen, 2018. For a broader scientific,

Introduction: The Core Themes

91

To his German correspondents, Leibniz expressed very similar sentiments, as for example in a letter to Christoph Pfautz, co-editor of the Acta Eruditorum, on March 4, 1691. Leibniz recalled there an unidentified letter he had written to Oldenburg – perhaps that of March 8, 1673 – in which he had pleaded for a rehabilitation of Guericke. However, the ex-patriot Oldenburg did not wish – according to Leibniz  – to derogate the reputation of Boyle or to slight the English in this matter, a position that deeply alienated him, as he then told the correspondent. In a letter to the medical professor in Wittenberg Georg Franck von Franckenau, on January 6, 1694, Leibniz once again referred to his letter to Oldenburg as well as to the latter’s anonymous review of Guericke’s Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio (1672) in the Philosophical Transactions. In this context, Oldenburg was represented by Leibniz almost as a turncoat since he had not asserted and defended Guericke’s priority in the development of the vacuum pump. Even as regards the investigation of the physical properties of the air, Guericke was, in Leibniz’s view, the leading figure and Boyle his subaltern. In his correspondence with Samuel Reyher, specifically in letters of September 8, 1679, and of August 20, 1680, Leibniz dealt with the respective contributions of Boyle and Guericke, referring in particular to the defective static barometer type they both used, and years later, in a letter of January 1697 to the Italian physician and medical professor Bernardino Ramazzini, he continued to insist on the leading role of Guericke as the principal developer here whom Boyle had followed (“maximus hujus doctrinae promotor quem Boilius est secutus”). All in all then, while Leibniz considered Boyle to be (or to have been) an outstanding experimentalist, he doubted that he had drawn hitherto unknown conclusions in his mechanical philosophy. Boyle’s air (or vacuum) pump in particular was, in Leibniz’s eyes, simply a further development of Guericke’s discovery. However, this instance of injustice he saw as not being without precedent. At the end of his drafted, but never dispatched, letter of October 1690 to Huygens, he recalled a similar injustice in the case of Willebrord Snell van Royen, the Dutch discoverer of the law of refraction which was later attributed to Descartes and Kepler. But here, Leibniz insisted, even the latter had suffered injustice at the hand of the former having been denied the credit for being the first to suggest an explanation of gravity based on the centrifugal force experienced by rotating bodies. philosophical and theological consideration of Leibniz and Boyle, see for example: S. Brown, “Leibniz and Robert Boyle: Reason and faith: Rationalism and voluntarism”, chap. 6 (pp. 83–94) in: P. Phemister, S. Brown (eds.), Leibniz and the English-speaking world, Dordrecht, 2007.

92

Introduction: The Core Themes

Finally, in relation to the pneumatic engine or the air-pump,62 Leibniz’s own idea, expressed in his letter to Huygens on November 24, 1690, of using a vacuum or pneumatic extractor to remove objects from bodies, was indicative of future technical applications for which the time had not yet come. Theory of Matter, Elasticity, Sound and Acoustics, Strength of Materials The kernel of Leibniz’s theory of matter is his theory of elasticity which occupies a central place in the entire corpus of Leibnizian physics.63 It was the basis of his theory of sound generation and sound propagation and of the breaking or rupture strength of materials.64 In the late 1670s and early 1680s, Leibniz’s occupation with a variety of topics in concrete science was often prompted by a particular correspondent. Thus, for example, the medical professor in Helmstedt Günther Christoph Schelhammer confided to him, in Janurary 1681, that he was working on a book about hearing and he requested Leibniz’s views on this matter. Leibniz seized the opportunity to elaborate his thoughts on acoustics in letters of February–March 1681 and January 1682. Schelhammer duly acknowledged Leibniz’s contribution in the section of his book De auditu (1684) that treated the propagation of sound. When Mariotte brought up the same topic, in letters of March–April and August 8, 1681, Leibniz repeated his detailed explanations for the French physicist in a letter from the second half of the same month. Alas, Leibniz failed to publish his thoughts on sound and acoustics. A planned publication, in the form of an appendix to Schelhammer’s book, failed to materialize as did sporadic plans for a publication in the Acta Eruditorum. In a letter of April 28, 1682, to Christoph Pfautz, Leibniz referred to the draft of an article he presumably wrote at the beginning of 1682 with the title “De soni generatione …; excerpta ex Epistolis G. G. L.” which however never did appear in the Acta Eruditorum and his published correspondence for the early 1680s is the only evidence for the independent development of Leibniz’s thought on sound and acoustics at this time.

4.2

62 Cf. also S. Shapin, S. Schaffer, Leviathan and the air-pump: Hobbes, Boyle and the experimental life, Princeton, Oxford, 1985 and 2011. 63 Cf. H. Breger, “Elastizität als Strukturprinzip der Materie bei Leibniz”, pp. 112–121 in: A. Heinekamp (ed.), Leibniz’ Dynamica: Symposion der Gottfried-Wilhelm-LeibnizGesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, (Studia Leibnitiana, Special issue, no. 13), Stuttgart, 1984. 64 Cf. H. Breger, “Physics: Leibniz’s principles of research into natural phenomena”, pp. 65–79 in: K. Popp, E. Stein (eds.), Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000.

Introduction: The Core Themes

93

According to Leibniz’s line of thought, as outlined in his letter to Schelhammer of February–March 1681, referred to above, the hitherto existing theories of acoustics failed to address the heart of the matter in that they neglected the most important aspect, namely the elasticity of the air. Only in terms of this property of the air could it be explained how pitch is propagated so exactly. Regarding the creation of sound, Leibniz explained that, while the remote cause might be a blow to a body, i.e. a percussion, the true or immediate cause would be its restoration, or a repercussion, which would manifest itself in the form of a vibration or oscillation. The constancy of pitch was thus a consequence of the general principal of the isochronism of elastic vibrations or oscillations. Leibniz explained in detail the reasons for the fact that different pitches can be transmitted in the air and that the ear can be simultaneously in resonance with different sonorous bodies. Schelhammer objected, in his reply of April 23, 1681, that not every sound was a vibration or oscillation giving the example of a blow to a cushion. Leibniz replied, on January 23, 1682, that the blow could be so strong that the cushion would be ruptured. However, anything that is ruptured must have previously been in a state of tension. To produce a sound, a blow would suffice that strained the threads of the cushion and thus generated a striving for the restitution of the original state. On the occasion of the appearance of Schelhammer’s book De auditu (1684) Leibniz explained his understanding of sound production, sound propagation and of hearing in a letter of May 16, 1684, to Friedrich Schrader. In this letter, he recalled that some three years earlier, in August 1681, he had communicated similar thoughts in French to Mariotte. Before Leibniz and Mariotte, sound and hearing were already understood as involving the sympathetic resonance between the vibrating air and various parts of the inner ear.65 The work of Claude Perrault, for example, who had treated the matter (Du bruit) in his Essais de physique ou Récueil de plusieurs traitez touchant des choses naturelles (1680), was referred to by Mariotte in a letter to Leibniz of August 8, 1681. The cause of sound, according to Leibniz and outlined in his reply of the second half of August, lay in the vibrations of tiny air particles. By means of such oscillations, the sound was carried from the resonating body to the ear. Independently of the sound level or loudness, or the sonority, the sound was transmitted at a constant speed. Accordingly, the oscillations of a resonating body having a given tension were always isochronous and so the same tone pitch was produced.

65 Cf. for example, V. Erlmann, Reason and resonance: A history of modern aurality, New York, 2010.

94

Introduction: The Core Themes

As far as the human experience of sound was concerned, Leibniz believed that there existed an organ within the ear, which on being stimulated by the vibrations or oscillations of the air, produces a corresponding sound in the ear. The organ in question, namely the “ossicula” (viz. the ossicles, or ossicular chain), actually conveys sound from the tympanic membrane, or ear drum, to the cochlea or inner ear. The experience of pitch is related to the frequency of the received oscillations. Leibniz also considered the question as to how this organ could be consonant with all the resonating bodies and how the eardrum could reproduce the corresponding sounds. Here he compared the ear to a musical instrument (like a zither or a lute) in which many different strings are stretched and which sonorously render many different sounds and in harmony with other instruments. The elasticity of the air also played an essential role in Leibniz’s theory of heat. As in the case of acoustics, Leibniz’s occupation with this topic during the 1680s can be attributed to the appearance of a tract by one of his correspondents. When, in March 1684, he learned from a letter of Friedrich Schrader of the appearance of a dissertation, over the defense of which the correspondent was presiding, he immediately expressed his interest. He then elaborated his view that in the same way that metals in a furnace are liquefied, or that water over a fire evaporates, the sun takes care that, by virtue of different internal movements it produces in bodies, fluids remain in their physical condition or state of matter. Also, the effects of heat and cold in the human body could be attributed to the motion of particles. Once the flux or the movement of these particles reaches a certain degree, the feeling of warmth is evoked in man. If, on the other hand, the human body is debilitated, and the body humors are under attack, then the human being experiences the sensation of cold. In relation to this, reasons are also given for the circumstance that water in a vessel, on being frozen solid, expands and may even burst its container. Leibniz attributed this to the fact that the air, being present in only small bubbles, is not in a position to make its elastic properties operative since, due to a lack of convection, it is prevented from forming larger bubbles. Analogous processes also take place, for example, in the explosion of gunpowder where scattered air pockets are only able to unite and form larger bubbles through the application of fire. Yet another example was that of a river, which was normally regulated by means of lumbering using large tree trunks but which might, under certain circumstances, have the capability of sweeping away large obstacles like a bridge. In essence then, Leibniz’s theory is based on the assumption of the existence of small elastic particles which, as long as they are isolated and mutually obstructive, are not in a position to break down certain barriers.

Introduction: The Core Themes

95

Elasticity as an explanatory principle was ultimately also at the center of the theory of the strength of materials developed by Leibniz and Edme Mariotte in their correspondence in years 1682 and 1683. Regarding the development of the strength of materials in the seventeenth century – as revealed in publications and secondary literature in the field – Mariotte and Robert Hooke have been seen as major figures following in the footsteps of Galileo, whereas the epochality of Leibniz’s contributions in this area has been attributed more to his publications on differential and integral calculus which became the starting point for the rapid development of the infinitesimal calculus and specifically for the investigation of elastic curves by mathematicians like Jacob and Johann Bernoulli.66 The argument, that every break or fracture is preceded by elastic tension, is the fundamental idea behind the theory of the breaking or fracture strength of materials developed jointly by Leibniz and Mariotte in their correspondence. Whereas Galileo had considered – in his Discorsi (1638) – the body to be absolutely rigid, and had assumed a sudden break, Mariotte supposed that the body consisted of elastic fibers or filaments which bend before breaking, as he first explained to Leibniz in a letter of April 28, 1678. Mariotte had encountered the problem of fracture strength in the course of investigations of aqueducts or conduits for the royal waterworks. In a letter of July 20, 1682, he communicated to Leibniz his experimental results, as well as his critique of the theory of fracture strength developed by Galileo. Corresponding to the different theoretical assumptions, Galileo had obtained a proportionality factor of 1/2, whereas Mariotte held a value of 1/4 to be correct. Leibniz, who at the time did not have access to a copy of the Discorsi, believed at first that both theoretical assumptions would lead to more or less the same result, as he told the correspondent in a letter of late July or early August, 1682. However, Mariotte could, he thought, convince him of the truth of the opposite view. The discussion continued over several letters, between August 1682 and January 1683, and finally resulted in Leibniz’s demonstration in March–April 1683, on the basis of Mariotte’s assumption of elastic fibers or filaments, that the correct proportionality factor was 1/3. Mariotte, writing on June 5, 1683, accepted the value found by Leibniz. This result  – that was published by Leibniz as “Demonstrationes novae de resistentia solidorum”, in July 1684, in the Acta Eruditorum and by Mariotte in 66 Cf. for example, S. P. Timoshenko, History of strength of materials: With a brief account of the history of theory of elasticity and theory of structures, New York, Toronto, London, 1953 (reprint 1983); see chap. I, pp. 7–24 (The strength of materials in the seventeenth century), and chap. II, pp. 25–28 (Elastic curves: the mathematicians Bernoulli).

96

Introduction: The Core Themes

1686 in his Traité du mouvement des eaux – has gone down in the history of elasticity and of the strength of materials as “the Mariotte-Leibniz theory”.67 The genesis of this theory is documented above all in their correspondence. A query of Jacob Bernoulli, of December 25, 1687, concerning the beams of precision balances and Leibniz’s aforementioned article “Demonstrationes novae de resistentia solidorum”, was only comprehensively answered by Leibniz following his Italian journey on October 4, 1690. A month later, on November 5, he also informed Bodenhausen about Bernoulli’s question. At the center of the considerations was the quest for the form and configuration of a uniform break-proof beam. Although Leibniz considered his starting hypothesis, namely that the strain or extension of the carrier beam fibers is proportional to the tensioning or straining force, to be uncertain, he was convinced that his demonstrations could also be valid under different premises. In his letter to Jacob Bernoulli of October 4, 1690, the profile of a uniform fracture-resistant carrier beam, which was subjected to both its own weight and an additional load (like an attached weight), was at the center of the considerations. Leibniz had omitted this additional loading in his article of July 1684 and Bernoulli had not been able to find the solution on his own, since it depended on Leibniz’s “analysin extraordinariam” or infinitesimal calculus, as he tried to make clear in his letter of November 5, 1690, to Bodenhausen. Galileo, he told this correspondent, had already treated the issue “de resistentibus figuris” but “alio sensu” and “abstrahendo ab ipsarum pondere proprio” which was mathematically a much simpler task. It was Leibniz’s conviction that they were dealing here with a task which simply could not be solved using ordinary analysis and required rather the application of his infinitesimal calculus. Besides his focus on dynamics, Leibniz’s interests in the 1680s also included statics, albeit to a lesser extent. A dispute in the years 1684 and 1685 with the Italian Jesuit Giovanni Francesco Vanni about the static moment of a heavy body on an inclined plane led Leibniz to write the article “Demonstratio geometrica regulae apud staticos receptae de momentis gravium in planis inclinatis”, which appeared in November 1685 in the Acta Eruditorum. A direct correspondence between the adversaries never materialized, however, and the exchange of opposing arguments took place through third parties (Antonio

67 Cf. I. Todhunter (K. Pearson, ed.), A history of the theory of elasticity and of the strength of materials. Volume 1: From Galilei to Saint Venant, Cambridge, 1886 (and 2014), in particular p. 6 (the Mariotte-Leibniz theory); C. Truesdell, The rational mechanics of flexible or elastic bodies 1638–1788: Introduction to Leonhardi Euleri Opera Omnia vol. X et XI seriei secundae, Zürich, 1960, and in particular pp. 59–64 (Mariotte and Leibniz on elastic beams, 1684).

Introduction: The Core Themes

97

Magliabechi and Otto Mencke) and Leibniz’s objections in the Acta Eruditorum remained anonymous. 4.3 Terrestrial Magnetism A further theme, portrayed in detail by Leibniz in the late 1670s and early 1680s, was from the field of geophysics and was concerned with the variation of magnetic declination. Johann Georg Volckamer and Georg Christoph Eimmart had observed in Nuremberg the temporal variation of the magnetic declination – a phenomenon which, although previously known, was new to them – and they had communicated their findings in letters to other scholars. When Leibniz learned of this, he contacted, in the fall of 1680, Sebastian Scheffer, a member of the ‘Academia Naturae Curiosum’ (the ‘Academia Leopoldina’) living in Frankfurt, with the proposal that the Academy arrange to carry out a series of corresponding measurements at different places in the German empire. From such corresponding temporal and spatial measurements, Leibniz expected decisive results in a relatively short time on the basis of monthly observations repeated over a period of a year. With the help of a natural law for the spatial and temporal variations of magnetic declination, he thought that one of the most discussed practical problems of the time might be solved, namely the problem of the determination of longitude at sea. Regarding this point in particular, Volckamer and Eimmart  – to whom Scheffer had passed on Leibniz’s proposal – reacted in a joint letter for Leibniz, in early May 1681, with a degree of skepticism.68 Volckamer forwarded a transcribed copy of an essay by Erasmus Bartholin, which revealed that the values for the magnetic declination in Copenhagen and on the neighboring island Ven varied appreciably with the changes being discontinuous and accordingly without apparent practical value. Thereupon Leibniz presented in a further representation, in a letter of June 20, 1681, that was sent to Scheffer for forwarding to Volckamer, his detailed thoughts on the matter supported by a profound knowledge of the relevant literature. Two essential assumptions in particular were defended by Leibniz, namely the validity of a law for the 68 Cf. G. Wolfschmidt (ed.), Astronomie in Nürnberg: Anläßlich des 500. Todestages von Bernhard Walther (1430–1504) und des 300. Todestages von Georg Christoph Eimmart (1638–1705), Hamburg: tredition science, (Nuncius Hamburgensis  – Beiträge zur Geschichte der Naturwissenschaften, vol. 3), 2010, and in particular: G. Wolfschmidt, “Astronomie in Nürnberg – Zentrum des Instrumentenbaus”, chap. 1, sect. 1.9, pp. 92–101 (Die Eimmartsche Sternwarte und die instrumentelle Ausstattung), and H. Gaab, “Die Eimmart-Sternwarte in Nürnberg”, chap. 6, pp. 213–234. Regarding the determination of longitude at sea, cf. for example, R. Dunn, R. Higgitt, Finding longitude: How ships, clocks and stars helped solve the longitude problem, Glasgow, 2014.

98

Introduction: The Core Themes

variation of magnetic declination and his heuristic principle or law of continuity. Descartes had attributed declination to randomness in the make-up and structure of the earth, whereas Leibniz was convinced of the existence of a regularity that could be detected by relatively simple means. This law would also satisfy the requirements of the heuristic continuity principle. Referring to various measurements, including those from a sea voyage, Leibniz showed that, in general, the magnetic declination only changed slowly and gradually and, accordingly, was probably spatially and temporally continuous. On July 21, 1684, Leibniz approached the then secretary of the Académie Royale des Sciences in Paris, Jean-Baptiste Du Hamel, with a query regarding observations of the variation of the magnetic needle being carried out under the direction of the Académie. Later it was Huygens – who had given an account of his Traité de l’aimant to the Académie des Sciences in 1679 – from whom Leibniz most likely expected to obtain an explanation of the phenomena of magnetism and electricity. Thus, in his drafted, but never dispatched, letter from the first half of October 1690, and again in his letter of November 7, Leibniz asked Huygens about the laws of terrestrial magnetism. Alas, in his reply of November 18, Huygens did not see himself in a position to give a satisfactory explanation for the variation of terrestrial magnetism and for known electrical phenomena. In his reply of November 24, 1690, Leibniz then alluded to Otto von Guericke’s experiment in which electric sparking had been obtained with a ball of sulfur,69 to his own correspondence with Guericke in 1671 and 1672, as well as to his knowledge of observations of the variation of terrestrial magnetism at sea. In the wake of this, Huygens referred to his familiarity with Guericke’s Experimenta Nova (1672) and he provided some further thoughts concerning his own electrical experiments (carried on since 1672) and theories in his final letter of the year, on December 19, 1690. Finally, terrestrial magnetism, and astronomy were also touched on in Leibniz’s correspondence in the year 1701. On July 9 of that year, Hans Sloane informed Leibniz about the journeys of the buccaneer-scientist and global circumnavigator William Dampier and of Edmond Halley and forwarded a map prepared by Halley of the seas he had traversed (between 1698 and 1700) and in which also the variation of the magnetic declination had been recorded.70 69 Cf. J. L. Heilbron, Electricity in the 17th and 18th centuries: A study of early modern physics, Berkley, Los Angeles, London, 1979, in particular part 2 (Electricity in the seventeenth century) and (regarding Otto von Guericke), chap. 6, pp. 213–219. 70 Cf. for example A. Cook, Edmond Halley: Charting the heavens and the seas, Oxford, 1998, and “Edmond Halley and the magnetic field of the earth”, Notes and Records of the Royal Society of London, vol. 55(3), (2001), pp. 473–490; published 22 September 2001 (https://doi.org/10.1098/rsnr.2001.0158).

Introduction: The Core Themes

99

4.4 Meteorology In the year 1679, through the encouragement of Mariotte, a further focus of geophysical investigation was added in Leibniz’s correspondence, namely meteorology; this encompassed the use of measuring instruments like the barometer, thermometer and hygrometer, and found expression particularly in the correspondences with Philipp Lohmeier and Samuel Reyher. Already in a letter of December 7, 1677, Mariotte had outlined his idea of undertaking corresponding simultaneous weather observations at different locations in Europe. The idea was immediately adopted by Leibniz, and he passed it on to some of his other correspondents in the form of a request for them to undertake similar observations themselves. Whereas, in early January 1680, Lohmeier in Lüneburg was having difficulties in acquiring the requisite instruments, Reyher, amongst others, sent (on September 8, 1680) weather observations which Leibniz forwarded to Mariotte and for which he received in return, in March–April 1681 and for purposes of comparison, Mariotte’s own observations. Mariotte had previously sent Leibniz weather observations (in mid-January 1680) and he reported (on July 5, 1680) in particular about a storm in France and he enquired about wind conditions on the same day in Germany. During and after Leibniz’s Italian journey, Bernardino Ramazzini was his internationally most renowned correspondent in the medical field, but this correspondent also made significant contributions in field of physics and, in particular, by undertaking thermometric and barometric investigations in the subterranean wells of Modena following a suggestion of Leibniz himself. During his stay in Modena, from December 30, 1689, to February 2, 1690, Leibniz had proposed the undertaking of temperature measurements in the subterranean wells there. These measurements were then conducted along with atmospheric pressure measurements beginning in October 1690. At the end of September 1696, Ramazzini then sent Leibniz copies of his medical and barometric ephemerides. Leibniz, for his part, referred to the measurements undertaken in the subterranean wells of Modena, along with similar investigations of the Académie des Sciences from the year 1679, in a letter to Ramazzini in January 1697. Leibniz may even have contemplated undertaking barometric investigations himself when, at the end of 1697, he entrusted Rudolf Christian Wagner with the construction of a portable barometer. When, in a letter to Ramazzini, on April 22, 1699, Leibniz once again recalled the temperature and atmospheric pressure measurements, which the correspondent had made in the wells of Modena, his interest was to establish whether there existed, as had been claimed, an antiperistasis, or whether they were dealing with an illusion

100

Introduction: The Core Themes

or a false perception. Replying on June 17, Ramazzini then promised to undertake further measurements as soon as new wells would be excavated. In Leibniz’s correspondence with Ramazzini in 1699 and 1700 there was also a detailed discussion about the correspondent’s dispute with Günther Christoph Schelhammer concerning the rise and fall of the barometric mercury column accompanying weather changes. The fact that the level fell in rainy weather – with the consequence that the air must be lighter than during brighter weather – seemed to contradict intuition. Leibniz followed the debate with interest since he too had sought an explanation of the phenomenon, as he confided to Ramazzini in his letter of April 22, 1699. He thought the problem might be settled by proofs and mechanical experiments, as he explained to Ramazzini on January 7, 1700. His solution of the problem he then outlined to Ramazzini, on March 18, by means of a thought experiment, which envisaged a horizontal beam balance on which there hangs at one end a pipe filled with water in which, in turn, a hollow ball is floating and, at the other end, a weight such that the balance is in equilibrium at first; however as water slowly enters the ball it gradually sinks. The sinking process leads to an infringement of the equilibrium state and the water pipe as a whole rises while the weight, at the other end of the beam, sinks. According to Leibniz, this was analogous to the behavior of the barometer, with the sinking ball being equivalent to a rain drop in the air, and the balance weight at the other end of the beam corresponding to the mercury column of the barometer. Leibniz’s suggested balance instrument has in fact been seen by historians of science as a precursor of the aneroid barometer, first developed in the nineteenth century, namely an instrument that measures air-pressure not by the height of a fluid column but rather by its action on an elastic lid of an evacuated box.71 Friedrich Hoffmann likewise made a contribution to the debate in a Dissertatio  … de potentia ventorum in corpus humanum, ubi simul agitur de ascensu et descensu argenti vivi in barametro (1700), over which he had presided, and which he sent to Leibniz with a letter of March 1700, requesting his opinion. Hoffmann’s work in turn induced Leibniz to send him a year later, with 71 Cf. W. E. Knowles Middleton, The history of the barometer, Baltimore, 1964 (and 2002), and Taunton (UK), 1994, and in particular chap. 2 (The Torricellian experiment), chap. 3 (The ‘Extraordinary effervescence’), and chap. 4 (Seventeenth-century experiments and speculations); W. E. Knowles Middleton, A history of the theories of rain and other forms of precipitation, London, 1966; H. H. Frisinger, “Mathematicians in the history of meteorology: The pressure-height problem from Pascal to Laplace”, Historia Mathematica, vol. 1(3), (1974), pp. 263–286, and in particular (regarding John Wallis and Leibniz) pp. 268f.; T. S. Feldman, “Barometer”, pp. 26f. in: J. L. Heilbron (ed.), The Oxford guide to the history of physics and astronomy, Oxford, 2005.

Introduction: The Core Themes

101

a letter of March 19, 1701, a text with his explanation of the barometric phenomena, alas too late for inclusion in Hoffmann’s opus, entitled Observationes barometrico-meteorologicae, et epidemicae Hallenses anni MDCC (1701). In a letter of May 30, 1699, Johann Bernoulli reported to Leibniz about his new process for measuring the heaviness, or the weight, of the air. Bernoulli maintained that, while other processes were based on an attenuation or rarefaction of the air, his was a condensation or compaction method which would lead to an error reduction as well as a power-requirement reduction. Bernoulli subsequently presented his ideas in a publication entitled Dissertatio philosophica de aeris gravitate et elasticitate (1701).72 Replying to Bernoulli, on July 6, 1699, Leibniz pointed to the experiments of Robert Boyle – published in New experiments physico-mechanicall, touching the spring of the air, and its effects (1660) and defended in A defence of the doctrine touching the spring and weight of the air (1662)  – on the relation between density, temperature and expansion force (“vis dilatandi”), which had revealed a perturbation or violation of the expected proportionalities and, accordingly, deserved further investigation. Leibniz referred here specifically to Boyle’s first formulation of a certain law, later to known as ‘Boyle’s Law’, and he even proposed a clarifying experiment himself. This interrelationship, of air density, expansion force and temperature, was discussed in detail in further correspondence with Bernoulli, in 1699 and early 1700, with the help of thought experiments and physical models for the air. However, Leibniz and Bernoulli could not agree even about the fundamental properties of the air. Bernoulli’s processes were based on a proportionality between density and weight and Leibniz, writing on August 4, 1699, objected that there might be incompressible parts involved. In a letter of October 6, Bernoulli argued that, notwithstanding this, the proportionality would be maintained: either the air as a whole would be incompressible, like water, or, although it might contain incompressible parts, it would nevertheless be compressible, like for example steam. Still there remained the question, as to whether or not a compression would be possible to the extent that the incompressible parts might touch each other, as Leibniz thought. Leibniz and Bernoulli were only in agreement about the circumstance that nothing in nature was totally incompressible, as Leibniz’s letter of October 30 and

72 Cf. D. Speiser, “Johann Bernoulli’s work on the theory of gravitation and on the weight of the atmosphere”, pp. 187–208 in: W. Klewer (ed.), Die Schwere der Luft in der Diskussion des 17. Jahrhunderts, (Wolfenbütteler Arbeiten zur Barockforschung, vol. 29), Wiesbaden, 1997, reprinted (pp. 105–121) in: K. Williams, S. Caparrini (eds.), Discovering the principles of mechanics 1600–1800: Essays by David Speiser, Basel, Boston, 2008.

102

Introduction: The Core Themes

Bernoulli’s reply of December 1, reveal. In the end, on January 22, 1700, Leibniz concluded that further experiments were necessary to decide the matter. 4.5 Astronomy and Celestial Mechanics Matters relating to astronomy and celestial mechanics had only marginal importance in Leibniz’s correspondence in the late 1670s and early 1680s. Tschirnhaus, for example, reported about the planetaria of Ole Christensen Rømer and of Huygens. Scheffer was able to report about a fiery celestial appearance, which he regarded as something supernatural. Tschirnhaus, on the other hand, referred to Edmond Halley’s comet and Pfautz and Samuel Reyher mentioned the comet of 1680. Pfautz, in particular, requested Leibniz’s expert opinion about this comet that was observed over several months from November 1680. Newton and Gian Domemico Cassini had  – in contrast to John Flamsteed and Jean Charles Gallet – incorrectly concluded that two comets were involved. And so, on October 29, 1681, Pfautz referred the matter to Leibniz. The observation of two comets was based on a false assumption or interpretation and, despite the fact that he had not been able to undertake observations himself, Leibniz was able, in December 1681, to provide an appropriate reply to Pfautz’s question as to whether one or two comets were involved, referring to observations of another comet from December 1664, with perhaps the explanations given by Adrien Auzout or Johannes Hevelius regarding that earlier comet in mind. Before Leibniz’s Italian journey (and his absence from Hanover between late 1687 and mid-1690) topics in celestial mechanics such as comets continued to have only marginal importance in his correspondence as, for example, when Christoph Pfautz referred to observations (in the summer of 1683) of a comet and (in the summer of 1684) of a solar eclipse, which had been reported in the Acta Eruditorum and in the Journal des Sçavans, respectively. Spurred on by the appearance of Newton’s Principia mathematica in 1687, Leibniz worked intensively on celestial mechanics, and specifically on the mathematical and dynamical theory of planetary motion,73 during the tour of southern Germany, Austria 73 Cf. the following seven publications by E. J. Aiton, “The celestial mechanics of Leibniz”, Annals of Science, vol. 16(2), 1960 [published 1962], pp. 65–82; “The celestial mechanics of Leibniz in the light of Newtonian criticism”, Annals of Science, vol. 18(1), (1962) [published 1964], pp. 31–41; “The celestial mechanics of Leibniz: A new interpretation”, Annals of Science, vol. 20(2), (1964) [published 1965], pp. 111–123; “An imaginary error in the celestial mechanics of Leibniz”, Annals of Science, vol. 21 (3), (1965) [published 1966], pp. 169–173; The vortex theory of planetary motions, London, New York, 1972, and in particular chap. 1 (Introduction) and chap. 6 (The harmonic vortex of Leibniz); “The mathematical basis of Leibniz’s theory of planetary motion”, pp. 209–225 in: Heinekamp, A.(ed.), Leibniz’

Introduction: The Core Themes

103

and Italy. Shortly before his departure from Vienna, his principal contribution on this topic appeared in February 1689 in the Acta Eruditorum with the title “Tentamen de motuum coelestium causis”.74 In this article – as already in the Hypothesis physica nova of 1671 – Leibniz hypothesized a rotating ether vortex around the sun as the cause of planetary motion. The motion of planets resulting from this vortex he resolved into a circular motion, or “circulatio harmonica” having a rotational velocity which was inversely proportional to the radius, and a radial motion, or “motus paracentricus” which corresponded to the force of gravity or centrifugal force. The combination of both components of the motion yielded the elliptical planetary motion as well as Kepler’s first two laws. According to Leibniz, Johannes Kepler had been the first to adumbrate the true cause of gravity. After Kepler, Ismael Bouilleau (or Boulliau, 1605–1694) and the astronomy professor, controversial divine and predecessor of John Wallis as holder of the Savilian chair at Oxford Seth Ward (1617–1689) had derived the law of equal areas for planetary motion with the help of mathematical constructions (circles, epicycloids, etc.) but without being able to give a physical explanation for the law, or at least to frame hypotheses or conceptions of gravity and its mechanical cause.75 With the introduction of harmonic circular Dynamica: Symposion der Gottfried-Wilhelm-Leibniz-Gesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, Stuttgart, 1984 (Studia Leibnitiana, Special issue no. 13); “Polygons and parabolas: Some problems concerning the dynamics of planetary orbits”, Centaurus, vol. 31, (1989), pp. 207–221. Furthermore, cf. D. Bertoloni Meli, Equivalence and priority: Newton versus Leibniz including Leibniz’s unpublished manuscripts on the Principia, Oxford, 1993 and 2002, and “Cosmology”, chap. 24 (pp. 438–452), in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018; P. Bussotti, The complex itinerary of Leibniz’s planetary theory: Physical convictions, metaphysical principles and Keplerian inspiration, (Science networks: Historical studies, no. 52), Cham (Switzerland), 2015. 74 Cf. English translation: “An essay on the causes of celestial motions”, part 2, chap. 6 (pp. 126–142) in: D. Bertoloni Meli, 1993 and 2002 (note 73). 75 Cf. C. A. Wilson, “From Kepler’s laws, so-called, to universal gravitation: Empirical factors”, Archive for History of Exact Sciences, vol. 6, (1969–1970), pp. 89–170, in particular pp. 106–136 (From Boulliau’s hypothesis to Newton’s ‘propositio notissima’); I. Bernard Cohen, The Newtonian revolution with illustrations of the transformation of scientific ideas, Cambridge and New York, 1980 and 1983, in particular pp. 222–279 (on Newton’s and Kepler’s laws); F. van Lunteren, Framing hypotheses: Conceptions of gravity in the 18th and 19th centuries (Doctoral dissertation, Rijksuniversiteit te Utrecht) Utrecht, 1991, and in particular chap. 1 (The seventeenth-century background) and chap. 2 (The reception and interpretation of universal attraction, 1687–1740); F. van Lunteren, “Nicolas Fatio de Duillier on the mechanical cause of universal gravitation”, pp. 41–59 in: M. R. Edwards (ed.), Pushing gravity: New perspectives on Le Sage’s theory of gravitation, Montreal, 2002; S. Probst, “Infinity and creation: The origin of the controversy between Thomas Hobbes and the Savilian professors Seth Ward and John Wallis”, British Journal for the History of Science, vol. 26(3), (1993), pp. 271–279; R. A. Hatch, “Between

104

Introduction: The Core Themes

motion, Leibniz considered that he himself had at last succeeded in going a step further and presenting a basis for a physical explanation of all three of Kepler’s laws of planetary motion in his “Tentamen”, which was appearing seventy years after the first formulation of Kepler’s third law in 1618.76 During his tour of Austria and Italy, Leibniz continued his work on planetary theory in the course of which he came to the conclusion that an overhaul of his “Tentamen” was essential, and he subsequently undertook a revision of the article. In Rome, where he met a number of members of the Accademia Fisico-Matematica, like Francesco Bianchini, Vitale Giordani and Domenico Quarteroni, he was able to present his ideas on planetary motion to Adrien Auzout who, for his part, encouraged a further publication on this topic. In a letter to the French numismatist Nicolas Toinard, in May or June 1689 and shortly after that meeting in Rome, Leibniz reported about his conversations with Auzout as well as about his planned publication und he emphasized the simplicity of his celestial mechanics and its agreement with Kepler’s laws. Leibniz became a member of the Accademia Fisico-Matematica, and he composed for it his tract Phoranomus seu de potentia et legibus naturae.77 His desire to return to Hanover via Paris, and to have discourse there on astronomical topics in particular, proved not to be feasible because of the war with erudition and science: The archive and correspondence network of Ismaël Boulliau”, chap. 4 (pp. 49–71) in: M. Hunter (ed.), Archives of the scientific revolution: The formation and exchange of ideas in seventeenth-century Europe, Woodbridge, UK and Rochester, NY, 1998; I. Bernard Cohen, G. E. Smith (eds.), The Cambridge companion to Newton, Cambridge, 2002, in particular the Introduction (pp. 1–32); C. Wilson, “Newton and celestial mechanics”, chap. 6 (pp. 202–226) in: I. Bernard Cohen, G. E. Smith, (eds.), The Cambridge companion to Newton, Cambridge, 2002 and (regarding Boulliau in particular), p. 204; P. Beeley, S. Probst, “John Wallis (1616–1703): Mathematician and divine”, chap. 23 (pp. 441–457), in: T. Koetsier, L. Bergmans (eds.), Mathematics and the divine: A historical study, Amsterdam, Boston, Heidelberg, 2005. 76 Cf. E. Meyer, “Das Rätsel um Johannes Keplers Wohnort in der Linzer Hofgasse  – Zum Jubiläum (2018): 400 Jahre Drittes Keplersches Gesetz”, chap. 2 (pp. 19–48) in: G. Wolfschmidt (ed.), Internationalität in der astronomischen Forschung (18. bis 21. Jahrhundert) / Internationality in the Astronomical Research (18th to 21th Century), Proceedings der Tagung des Arbeitskreises Astronomiegeschichtein der Astronomischen Gesellschaft in Wien 2018, (Nuncius Hamburgensis: Beiträge zur Geschichte der Naturwissenschaften, vol. 49), Hamburg, 2019. 77 Cf. A. Robinet (ed.), G. W. Leibniz: Phoranomus seu de potentia et legibus naturae, Rome, Juillet 1689, Florence (published in: Physis, vol. 28 (2 and 3, N.S.) 1991. Regarding the Accademia Fisico-Matematica, cf. F. Favino, “Beyond the ‘Moderns’? The Accademia Fisico-Matematica of Rome (1677–1698) and the vacuum”, pp. 120–158, in: S. Dupré, S. Kusukawa (eds.), History of universities, vol. XXIII/2, (Special issue: The circulation of news and knowledge in intersecting networks), Oxford, 2008.

Introduction: The Core Themes

105

France. On the return journey, on March 18, 1690, he wrote to Bodenhausen from Venice about the need to extend his article in the Acta Eruditorum to cover matters like the inverse-square law of gravitational attraction. Also, following his return to Hanover, the theory of planetary motion was repeatedly referred to, for example in letters to Erhard Weigel in September 1690 and to Otto Mencke in October 1690. The appearance of Leibniz’s “Tentamen”, however, also presented a difficulty for him in relation to ecclesiastical policy, which is reflected in his correspondence with Bodenhausen and Francesco Bianchini and which is evidence for the circumstance that an open discussion of the Copernican system among scholars in Italy in the last decade of the seventeenth century was still problematical. Thus, at the end of February 1690, Bodenhausen had to explicitly inform Leibniz that, in an intended Italian reprint of his “Tentamen” from the Acta Eruditorum, it would be necessary to omit the names of Kepler, Galileo and Copernicus, and some further text, to avoid conflict with the Inquisition. Again, in the following month, on March 18, 1690, Leibniz turned to Bianchini – who was close to Pope Alexander VIII and enjoyed the pontiff’s patronage – with the request that he exert an influence on him. Alas, however, he was to be confronted with the fact that Bianchini could not see, in his reply of April 7, any hope of amelioration in the matter in question. Celestial mechanics was also a focus in Leibniz’s newly revived correspondence with Christiaan Huygens from 1690. As early as February 8 of that year, Huygens had sent Leibniz his recently published twin tracts Traité de la lumière … avec un discours de la cause de la pesanteur (1690). Leibniz only received the work in question in the second half of September 1690, but then he immediately embarked on intensive studies of both Huygens’ Traité … discours and of Newton’s Principia mathematica, as is to be seen from his drafted, but never dispatched, letter addressed to Huygens from the first half of October. His commentaries on the theories of Newton and Huygens, chronicled therein, are provided with annotating remarks regarding his own celestial mechanics. Leibniz found himself unable to endorse the opinions of Newton about gravity and planetary motion resulting exclusively from gravitation. In fact, he considered the supposition of an ether for the explanation of the motion of the planets, or that of the moons of Jupiter and Saturn, to be absolutely essential. His overt adherence to Cartesian vortices, in his correspondence with Huygens, is indicative of an indispensable centerpiece of his planetary theory. Leibniz, in fact, assumed the existence of two vortices rotating about the sun. The first caused gravitation and terrestrial magnetism while the second coarser vortex provided a ‘fluidum deferens’ which moved the planets. In Leibniz’s comments about Newton’s Principia mathematica, admiration and rejection go hand in

106

Introduction: The Core Themes

hand. Thus, he found an explanation of gravity, and indeed of the law of gravity, to be wanting in Newton’s work. For both the law of gravity and the photometric inverse-square law, Leibniz suspected analogous explanations. As regards Huygens’ explanation of gravity, he found similarities with his own conceptions of a centrifugal force produced by the rotating ether. Leibniz’s explanation of these phenomena was based on the principle of equality of the active force (being proportional to the square of the velocity) in the respective orbits of the bodies rotating around the sun. And, on the basis of this model, he saw a means of deriving both Kepler’s third law and the law of gravity. In Leibniz’s correspondence with Huygens, in the final quarter of the year 1690, he also enquired about the correspondent’s opinion regarding Newton’s explanation of the ebb and flow of the tides as well as of the tails of comets. Unlike Newton, Leibniz considered the tail of a comet to be not of a material nature but rather an optical phenomenon comparable to the rainbow. Since Huygens had spoken with Newton a number of times during a visit to England in the summer of 1689, Leibniz thought it possible that he might well have taken the opportunity of verbally articulating objections regarding the Principia mathematica to its author, and so he hoped in this way to learn, at least indirectly, something about Newton’s views regarding these issues. Alas, these hopes were dashed, as Huygens, in his reply on November 18, 1690, communicated mainly his own thoughts about the tides and the tails of comets. Huygens did however indicate that, while he considered Newton’s explanation of ebb and flow to be partly absurd and without foundation, he did feel much more comfortable with Newton’s theory of cometary tails. Leibniz’s explanation of gravity on the basis of the centrifugal force of a very subtle fluid also led him to the supposition of rays of attraction, to which he referred in a letter to Huygens on April 11, 1692. His vortex theory allowed him also to explain further phenomena like the round or spherical form of the terrestrial globe and of water drops, respectively, as well as the parallelism of the earth’s axis and those of the other solar planets. For Huygens, on the other hand, Leibniz’s theory was inapprehensible as he made clear in his reply of July 11, 1692. Neither the published “Tentamen”, nor Leibniz’s explanations in his letters, could convince Huygens of the confirmability of his theory. Although Huygens continued to be more than skeptical, Leibniz resolutely continued his efforts to show an equivalence or agreement between their rival systems. He firmly believed that the very different conceptions could be harmonized, and he expressly included the Newtonian position in this. However, Huygens upheld his rejection of Leibniz’s understanding of things. Notwithstanding some concededly positive aspects of the vortex theory, he expressed his conviction of the superiority of his own theory, in his letter of

Introduction: The Core Themes

107

January 12, 1693. Whereas with Leibniz’s vortex theory certain phenomena – as, for example, the fact that the planets all rotated in the same direction – were easy to explain, with others – like the constant eccentricity of the planetary orbits, the acceleration and deceleration of celestial bodies along their orbital paths or the movement of comets through rotating vortices  – explanation proved more difficult. Although Leibniz conceded these difficulties, in his letter of March 20, 1693, he upheld the possibility of bringing the competing systems into mutual agreement. Towards Newton he had likewise been expressly conciliatory in a letter  – the first in their direct correspondence  – he wrote three days earlier.78 Closely connected with the theory of planetary motion were questions regarding sun spots, referred to in correspondence with Augustinus Vagetius, who had presided over the examination of a dissertation entitled Dissertatio de maculis in sole visis (1693), and also questions about the nature and motion of comets in the solar system. These matters were discussed in letters for Edmond Halley (on June 3, 1692), from Erhard Weigel (on February 18, 1693), to Vagetius (on October 7, 1693) and from Newton (on October 26, 1693). Leibniz considered the observed tails of comets, in particular, to be purely optical phenomena, whereas others accorded them a material character. Another astronomical topic, discussed after 1690, was Huygens’ work on parhelia, or mock suns, from 1670. On March 2, 1691, Leibniz directed a query about these together with an exhortation for the publication of Huygens’ tract on dioptrics to the correspondent. In his reply, on March 26, Huygens wrote that his treatment of parhelia would indeed be published in his Dioptrica which, alas, only appeared posthumously in the year 1703. In Leibniz’s correspondence with Huygens, in the early 1690s, the shape of the earth was a further topic considered. At the center of attention here was Leibniz’s critical assessment of the value of a book published by Johann Caspar Eisenschmidt entitled Diatribe de figura telluris elliptico-sphaeroide (1691), in which the author postulated an elliptical-spheroidal shape of the earth. Unlike Newton and Huygens, however, Eisenschmidt assumed the earth to have an excess of mass at the poles rather than at the equator. In letters of January 8 and February 19, 1692, Leibniz sought Huygens’ opinion about the matter. Although he had only read a short account of the work in the Acta Eruditorum of July 1691, Huygens likewise doubted the correctness of Eisenschmidt’s conclusion, a view he expressed in his reply of March 15, 1692. While Huygens attached 78 Cf. M. Dascal, E. Firt, “Leibniz’s conciliatory approaches in scientific controversies”, chap. 6 (pp. 137–168), in: M. Dascal (ed.), The practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010.

108

Introduction: The Core Themes

considerable doubt to the hypothesis of Eisenschmidt, he reserved nonetheless a final judgement in the matter until reliable results of the then ongoing longitude determinations became available. Through the clocks, which he himself had developed for these measurements, Huygens was directly involved in this effort.79 On July 11, 1692, he finally reported to Leibniz that he had, having at last read Eisenschmidt’s opus, compiled a list with several objections. Notwithstanding these, however, he was left with a good impression of the work in question. In several correspondences between 1694 and 1696, Leibniz expressed his views about the cause of gravity, which he attributed to a physical fluid in motion, or an ether, as for example in a letter of November 17, 1695, to Papin, and he compared his explanation to his understanding of that given by Papin. For Leibniz, the force of gravity experienced by an ascending heavy body did not come from space or elevation but rather from physical percussion effects or blows it received. On the other hand, Papin’s explanation was based on the effect of a resisting, insensible fluid. Leibniz, for his part, rejected such an insensible fluid and a possible explanation of gravity on the basis of philosophical suppositions or hypotheses rather than mathematics. Writing to Johann Sebastian Haes, on February 3, 1696, he spoke of “l’ether auteur de la gravité” whereas, in a letter of July 4, 1695, to Johann Bernoulli, he referred to a “gravitas, cujus causam esse ab abiente non nego” and in a subsequent letter to Johann’s brother Jacob, in the spring of 1696, he referred to a certain “materia gravifica … quod motu suo est causa gravitatis”. The most important discussions about gravity or gravitation between 1694 and 1696, however, are to be found in Leibniz’s correspondence with the Newton confidant Fatio de Duillier and with Huygens. Leibniz’s renewed interest in gravitation was provoked by Fatio’s letter for him of April 9, 1694, sent through the Hanoverian representative in London, Wilhelm de Beyrie. Fatio had presented his tract De la cause de la pesanteur from the years 1688–1690 to the Royal Society of London, and had discussed the matter in person both with Newton and Huygens before approaching Leibniz in written form. In this letter, Fatio emphasized his adherence to 79 Cf. M. S. Mahoney, “Christiaan Huygens, the measurement of time and longitude at sea”, pp. 234–270 in: H. J. M. Bos et. al (eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979, Lisse, 1980; A. R. T. Jonkers, “Finding longitude at sea: Early attempts in Dutch navigation”, and E. Schliesser, G. E Smith, “Huygens’s 1688 report to the directors of the Dutch East India company on the measurement of longitude at sea and its implications for the non-uniformity of gravity”, pp. 186–197 and pp. 198–214, respectively, in: L. Palm (guest ed.), Christiaan Huygens: De Zeventiende Eeuw, vol. 12(1), (1996).

Introduction: The Core Themes

109

Newton’s theory of gravitation, and he endorsed his universal declaration of mutual attraction and of the inverse-square law. For Newton and Fatio, the universe consisted for the most part of empty space, for otherwise the celestial bodies would be exposed to a large resistance from the particles of an ether, and would accordingly be decelerated. With reference to various passages in the “Addition” to Huygens’ Discours de la cause de la pesanteur, Fatio elaborated Newton’s criticism. Fatio rejected both Huygens’ hypothesis of matter in motion to explain the gravitation of the planets in the solar system, as well as his interpretation of gravity as a centrifugal force. He then proceeded to elaborate his own mechanical explanation of gravity. In addition to terrestrial matter, which was constituted of the smallest homogeneous particles, there existed everywhere in the universe an almost infinitely thin form of matter. The particles of this thin matter, which were subject to high-speed rectilinear motion in all directions, were the cause of gravity. Whereas Fatio enjoyed the approval of Newton, drawn-out investigations were required to rebut the objections of Huygens. The essence of these objections was that, as a consequence of Fatio’s theory, the matter surrounding the earth would become increasingly dense. Notwithstanding this, Fatio was confident of victory. In Leibniz’s reply of May 18, 1694, that was sent to De Beyrie for forwarding to Fatio, he showed an open mind regarding Newton’s interpretation of gravity, but he stressed the necessity of a mechanical explanation of gravity, or gravitation, as an inherent property of matter. He himself was undecided and he alluded to his public dispute with Papin in the Acta Eruditorum from April 1689. The competing theories to explain gravitation assumed physical processes based on the effects of circular motion (Huygens) and rectilinear motion (Newton), respectively. In the case of circular motion, centrifugal force was able to provide a sufficient explanation of gravitation but an inverse-square law (analogous to the photometric inverse-square law) could not be derived from it, Leibniz insisted. This was followed by a report about his own efforts to find an explanation for gravity and, indeed, both on the basis of a circular-motion hypothesis as of one assuming rectilinear motion. He described in greater detail his second approach (based on rectilinear motion), elaborating his “explosion” theory of gravitation, comparing it to an incendiary process in which coarse matter enriched with fine matter is attracted to rarefied matter at the center of attraction, or in a flame. As a consequence of the ensuing explosion, or ignition, and the accompanying rarefaction, the fine matter is expelled to the periphery where it serves for alimentation of the coarse material there and, as a result, for the continuation of the cycle or process. Such an explosion would be comparable to the movement of light and, accordingly, the inverse-square law, analogous to the photometric inverse-square law, would also be valid. Finally, he

110

Introduction: The Core Themes

thought nature might opt for a combination of circular and rectilinear motion, its style being to seek the optimal minimum-redundancy solution. Huygens was informed by Leibniz on May 6, 1694, about Fatio’s letter of April 9, 1694, and on this occasion, Leibniz elaborated once again his “explosion” theory of gravitation. In the context of this emission theory then, he had succeeded in deriving the inverse-square law of gravity, or gravitation. He was however, he told the correspondent, still contemplating how he might arrive at the same result on the basis of the (to him) seemingly very plausible interpretation of the force of gravity as a centrifugal force. In his reply, on May 29, Huygens characterized Fatio’s theory, which in essence accorded with that given by Pierre Varignon in his Nouvelles conjectures sur la pesanteur (1690), as a chimera. Against Huygens’ objection, that a consequence would be a concentration of the ether-like matter above the earth’s surface, Fatio had countered with the argument that the concentration of this material would not lead to any appreciable increase of mass. As regards Leibniz’s “explosion” theory, Huygens was likewise very skeptical. In his next letter to Huygens, on June 22, 1694, Leibniz defended and further elaborated his notion of an “explosion” theory. The ether particles that produce light, magnetism and gravity might contain a compacted fine matter, since they themselves were still relatively large. This compressed matter would be expelled as soon as the bodies were shattered on impacting the sun or a similar body. Yet another conception of the explosion process involved the effects of a fine material, comparable to an infinite number of little air guns enshrined within the coarser matter that produced light, magnetism and gravity. Thus the spring of the coarse material would be attributable to the effects of the fine material it contained. To counteract a possible concentration of the fine ether-like matter around the earth and other bodies subject to gravitation, and to meet Huygens’ objection, Leibniz conceived a dissipation of such matter in a fashion similar to the activity of sunspots. Huygens continued however to adhere to his objections against Fatio’s theory of gravitation. In his letter to Leibniz of August 24, 1694, he adamantly disputed Fatio’s claims to the contrary. Furthermore, Leibniz’s repeated call for him to derive an inverse-square law from his theory of gravitation failed to impress him. Right up to his death, he was convinced of the correctness and completeness of his own theory. Leibniz’s attitude towards Huygens remained conciliatory, however. He henceforth characterized the different theories about gravity, or gravitation, as being essentially equivalent and he attributed the different opinions that had emerged mainly to different linguistic usage by the adversaries in the dispute as, for example, in his letter of September 14, 1694.

Introduction: The Core Themes

111

Likewise, as regards explanations of planetary motions and the tails of comets, Leibniz tried to harmonize (at least partially) the theories of Newton with his own perceptions. These astronomical topics are found in his correspondences at this time with Detlev Clüver, Fatio, Huygens and Vagetius. In this matter, Leibniz emphasized again and again to his correspondents his commitment to a vortex theory of planetary motion and his opposition to the theory of Newton, based exclusively on gravitation. At the same time he adopted a conciliatory position (at least at first) in his letter to Vagetius of January 6, 1694. The observed phenomenon that all planets of the solar system, and all satellites of a planet, rotate in almost the same plane and in the same direction of rotation, could for Leibniz only be explained using an ether-vortex model. And, in addition, there was a further reason for his ether-vortex, namely the analogy to the phenomenon of terrestrial magnetism in the guise of a magnetic rotation or curl. Leibniz’s position thus seemed to himself to be sufficiently consolidated, or – in the sense of his words cited in the leading quotation in the heading of this section – that Newton’s argument against vortices in the theory of planetary motion did not appear to detract from his own position. Even for the paths of comets, it seemed to Leibniz that the ether did not present obstacles since the rare ether-vortex scarcely impeded the trajectory of a comet. However, as regards the tails of comets, the views of Leibniz and Newton were irreconcilable. Newton allowed the tails a material character whereas Leibniz was convinced that they were simply optical phenomena. The theory of planetary motion was also an important topic in Leibniz’s correspondence with Huygens, and the exchange of views relating to Huygens’ Discours de la pesanteur (1690) continued in 1694. Just as with the explanation of the theory of gravitation, Leibniz adhered to his notion of an ether-vortex circulating around the sun, whereas Huygens saw centrifugal force as being decisive. However, this force was also included by Leibniz in the considerations presented in his letter to Huygens on May 6, 1694, and it appeared to him to be possible to bring the two possible causes under consideration into harmony with one another. Once again, Leibniz introduced here the corresponding motion of the planets of the solar system and the analogy between the supposed ether-vortex and that of magnetism as arguments against the Newtonian gravitational theory of planetary motion. A day later, on May 7, 1694, Leibniz addressed the same theme in a letter to Clüver, whereby he enquired here especially about the cause of those phenomena of celestial mechanics which he believed he could easily explain with his vortex theory, and he referred, among other things, to the action of a terrella or a small magnetized model ball representing the Earth. Continuing this line of thought, he then alleged that Newton could only resort to chance

112

Introduction: The Core Themes

in his explanatory model. As an argument against Newton’s explanation of comet-tail appearances as real or material emissions, he objected that the fact, that the tails were observed to be confined to the plane of motion of the comet around the sun, contradicted such a material interpretation. Fatio, for his part, had his mind made up on this issue. Thus, in his letter of April 9, 1694, he suggested that since the tail emissions were in the planes of movement of the comets, they had to be real or material emissions. Leibniz reacted, in his reply of May 18, with the counter argument that the fact, that the comet tails were in the plane of rotation passing through the sun, would suggest they were of an emphatic nature (“emphases ou phenomenes emphatiques”), whereas real or material emissions would not necessarily be confined to the plane of rotation. Here, he likewise defended his vortex theory of planetary motion against Fatio, presenting the same evidence as in his letters to Huygens and Clüver. 4.6 Resisting Media and Motion in Resisting Media The appearance of Newton’s Principia mathematica also led Leibniz to turn to other topics in physical research. Thus, during and after his Italian tour, Leibniz paid increasing attention to the topic of the resistance of a medium or of movement in a resisting medium.80 From these efforts emerged the article or schediasm on the resistance of a medium and on the motion of heavy projectiles in a resisting medium, entitled “Schediasma de resistentia medii et motu projectorum gravium in medio resistente”, which appeared in the January 1689 number of the Acta Eruditorum. The intention of writing such an essay was by no means new. Already in the years 1683 (on August 22 and December 2) and 1684 (on March 23), Leibniz’s attention was drawn to this problem when Mariotte sent him accounts of his thoughts, and experimental investigations, concerning the fall of a body taking account of the resistance of the air. Furthermore, François Blondel’s L’art de jetter des bombes (1683) dealt with this topic although, in Leibniz’s view, it contained nothing which went beyond the explanations given by Galileo and Descartes for the motion of a projectile whose trajectory was supposed to be a parabola. This assessment he expressed in a letter to Detlef Clüver in London, at the end July 1686, and he intimated for the first time an intended publication in which he would broach the issue of the resistance of the air which had been disregarded by Galileo and Torricelli.

80 Cf. E. J. Aiton, “Leibniz on motion in a resisting medium”, Archive for the History of the Exact Sciences, vol. 9, (1972), pp. 257–274.

Introduction: The Core Themes

113

Leibniz’s “Schediasma” appeared after Newton’s Principia mathematica (1687) but in advance of Huygens’ Discours de la cause de la pesanteur (1690), two works in which comparable research results were presented. The results announced by Leibniz in this article were based on a successful application of his differential calculus, although in fact he withheld the details of the mathematical elaboration. He distinguished between two forms of resistance, namely “resistentia absoluta” and “resistentia respectiva”, which are, for the same time intervals, proportional to the velocity and the square of the velocity, respectively. Here Leibniz’s theory of absolute and respective or relative resistances corresponded roughly to Newton’s much more elaborate treatment of this topic in Book II, Sections I and II of the Principia mathematica.81 Leibniz did not consider a combination of the two forms of resistance, as treated by Newton in Book II, Section III. The corresponding results, published by Huygens in 1690, had in fact been obtained more than twenty years earlier. Leibniz first learned of these results from the Discours whereby his reception of Huygens’ thought went hand in hand with his own efforts to revise and extend the Schediasma, which is evident from their correspondence in November and December 1690. In elaborating his propositions, Leibniz made some ‘faux pas’ which, although he was able to correct them quickly, added to the difficulty of reaching an understanding with Huygens. The latter’s lack of familiarity with the infinitesimal calculus contributed likewise in no uncertain fashion to the communication obstacles between the two. The fruit of this epistolary exchange, at the end of 1690 and in early 1691, was Leibniz’s article “Additio ad schediasma de medii resistentia”, which appeared in the Acta Eruditorum in April 1691. The “Additio” was referred to in a letter Leibniz wrote to Huygens on July 24, 1691. Already, on February 23 of that year, Huygens had come to realize that Leibniz had adopted a different definition of resistance to his and that of Newton, namely that, while for Leibniz the effect of the resistance was synonymous with the resistance itself, for Newton and himself the resistance was the pressure of the medium against the surface of the body. Leibniz considered, as he made clear in his reply of March 2, that he had sufficiently explained his position but he did not underestimate the danger of such misunderstandings. Also related to the topic of motion in resisting media were a number of other issues which were treated both in the non-dispatched letter to Huygens, from the first half of October 1690, and in the further epistolary exchanges with the same correspondent. These issues included the nature of an extended and 81 Cf. N. Guicciardini, “Isaac Newton, Philosophiae naturalis principia mathematica, first edition (1687)”, chap. 5 (pp. 59–87) in: I. Grattan-Guinness (ed.), Landmark writings in western mathematics 1640–1940, Amsterdam, Boston, 2005.

114

Introduction: The Core Themes

resisting medium, the admissibility of a perfect hardness of matter and, finally, the question of the existence of atoms in a space devoid of air and matter. 4.7 Astronomy and Calendar Reform (1700) On September 23 (old style or Julian)/ October 3 (new style or Gregorian) 1699, the ‘Corpus Evangelicorum’ – the Protestant Imperial Estates at the Perpetual Diet at Regensburg – introduced the so-called improved calendar.82 Following a leap from February 18 to March 1, 1700, the Julian calendar was merged with the Gregorian calendar. For the architects of the change, there was one major unsolved issue remaining, namely the determination of the calendrical date of Easter. It was defined as falling on the Sunday following the full moon that follows the northern spring equinox. Instead of the solar and lunar cycles used to determine Gregorian Easter, the German Protestant states now decided to use, from 1700, an astronomical Easter based on a determination of the spring equinox and full moon following the ‘Rudolphine Tables’ of Johannes Kepler (and Tycho Brahe) – the Tabulae Rudolphinae of 1627. Leibniz, for his part, supported the intention of the reform, namely of achieving the greatest possible agreement regarding both the civil and ecclesiastical calendars in the confessionally-mixed German empire, as he explained, for example, in a letter to Hans Sloane on February 9, 1700. He likewise helped carry the discussion about the calendar reform beyond the German Protestant territories, as for example in his letter to Ole Christensen Rømer on March 5, 1700, advocating an equitable discussion between Catholics and Protestants in the adoption of the Gregorian calendar. At the beginning of 1700, he also called on the Académie des Sciences, through his correspondents Jean-Paul Bignon and Christophe Brosseau, to show that the Gregorian Easter calculation was in agreement with astronomical truth. The outcome was that – following a directive of Louis XIV – the astronomer Gian Domenico Cassini established contact with the Vatican with the intention of making clear that the Gregorian Easter calculation was indeed capable of improvement. The reaction from Rome was positive and, on March 5, 1700, Leibniz reactivated his correspondence with 82 Cf. W. Kokott, “Umwege zur Kalendereinheit: Der »Verbesserte Kalender« (1700 bis 1775) und die Gründung der Berliner Sternwarte”, pp. 43–48 in: W. R. Dick, K. Fritze (eds.), 300 Jahre Astronomie in Berlin und Potsdam, Frankfurt am Main, 2000; K. Habermann (ed.), Die Kalenderbriefe des Georg Albrecht Hamberger im Kontext der Kalenderreform von 1700, Göttingen, 2012, in particular pp. 18–21 (Die Rolle Erhard Weigels bei der Kalenderreform) and pp. 21–26 (Die Osterfestrechnung); E. Koller, Strittige Zeiten: Kalenderreformen im Alten Reich 1582–1700, Berlin, Boston, 2014, in particular chap. 4, pp. 278–408 (Die Gelehrte Kalenderdebatte des 17. Jahrhunderts), and chap. 5, pp. 409–526 (Der Weg zur Datumseinheit – der Verbesserte Kalender 1700).

Introduction: The Core Themes

115

the Roman astronomer Francesco Bianchini. Through him, Leibniz hoped for, among other things, contact to the Curia, and in particular to the cardinals Marco Delfini and Gian Francesco Albani, who was destined to become pope Clemens XI. Shortly after the latter began his pontificate, and in a memorandum intended for him and attached to a letter of late February, 1701, Leibniz picked up on Cassini’s assessment and suggested – as he had previously done with Bianchini – a course of action that Protestants could also follow. These initiatives met with no reaction at first with the result that Leibniz had to resort to contacting Bianchini once again, on December 27, 1701, following the establishment of a Calendar Congregation at the Vatican in the autumn of 1701. The reply would follow one year later. From his own coreligionists, Leibniz kept his involvement secret in order not to endanger the process through outside criticism, and he informed Johann Bernoulli accordingly on April 25, 1700. In accordance with the goal of advancing the formation of opinion in the matter, Leibniz promoted – in his correspondence – communication between astronomers, and he commented on, evaluated and disseminated their proposals, without however presenting a precise standpoint of his own. Rømer pointed out in a memorandum entitled “Dubia circa novam correctionem calendarii Evangelicorum”  – which had been prepared in accordance with a directive of the Danish king for communication to the Imperial diet and which was attached to his first letter to Leibniz, of December 29, 1699 – that in Regensburg not just the question as to the best set of astronomical tables had been left open; also unclear was, for example, the question of whether the determinations of equinoxes and full moons were to be based on actual or average astronomical movements. For the year 1704 alone, this distinction would lead to different dates for Easter. The astronomer of the Berlin Society of Sciences, Gottfried Kirch, had complained about this und further points of uncertainty; in Regensburg his opinion had been regarded as being amiss, a matter he confided to Leibniz in early April 1701. The decisions of the Council too were questioned. Thus, Rømer – in a memorandum entitled “De Paschate correcti calendarii” and attached to his letter of February 3, 1700, to Leibniz – established that the new calculation of Easter was considerably more tedious than its Gregorian counterpart, although in end effect both were usually in agreement. His alternative suggestion was radical: Easter ought to be always celebrated on the Sunday between April 5 and 11 which, although a simplification for civil life, would have meant a radical departure from the Catholic calculation. In his reply of March 5, Leibniz wrote that he considered this suggestion to be hardly realistic as the purpose of the reform had been to establish the greatest possible unification of the calendars. Nonetheless, Rømer forwarded his proposals to Ulrich Junius in Leipzig, and to

116

Introduction: The Core Themes

Gottfried Kirch in Berlin, for their judgements in the matter. Junius’ reply from the second week of April, 1700, and that of Kirch from early April, 1701, were sent to Leibniz. Argumentation diametrically opposed to Rømer’s came from Samuel Reyher and Joachim Tiede in Kiel, who advocated using solar and lunar cycles developed by the latter and that were supposed to be more exact than the Gregorian lunisolar calendar. Leibniz, as he informed Hans Sloane on December 27, 1701, considered the rearrangement of the leap years – arising from Tiede’s cycles – to be politically unenforceable. Nevertheless, the cycles seemed to be well suited for negotiations with the Vatican by virtue of the small deviation from their Gregorian counterparts, as he made clear in a letter he wrote to Tiede on November 16, 1701. Leibniz had sent a corresponding report to Bianchini, on March 5, 1700, and he now persuaded Reyher and Tiede to write a letter to Cardinal Enrico Noris, whom he had met in 1689 during his Italian journey and who was a member of the papal Calendar Congregation. Furthermore, Leibniz sought external opinions about Tiede’s cycles, from Gottfried Kirch and, in particular, from the Royal Society – which had excellent astronomers like John Flamsteed, Edmond Halley and Isaac Newton among its members – and from Cassini through an intermediary, namely the permanent secretary of the Académie des Sciences, Bernard Le Bovier de Fontenelle. In addition, Leibniz enquired about attitudes in other lands to the calendar reform. Thus, on April 25, 1700, he asked about the situation in the Netherlands in a letter to Johann Bernoulli. At the beginning of a letter of January 25, 1701, Bernoulli then enthusiastically reported the adoption of the new style calendar by the provinces Friesland and Groningen at the turn of the year 1700–1701. Already, in February 1700, Leibniz had informed both the Royal Society and the Académie des Sciences about the improved calendar and had requested their views. Thus, in his first letter to the secretary of the Royal Society, Hans Sloane on February 9, he gave details of the Protestant calendar reform that had, however, not been adopted in England. John Wallis was one of the few individuals who fundamentally criticized the Gregorian reform notwithstanding its precision. This is surely to be seen in the light of the confessional and theological antagonism found in Wallis’ mathematics and philosophy. As an Anglican minister, he repeatedly made disparaging remarks about Catholics, particularly the pope and the Jesuits.83 83 Cf. A. D. Richter, “John Wallis and the catholics: Confessional and theological antagonism in Wallis’s mathematics and philosophy”, Notes and Records of the Royal Society, vol. 72(4), (2018), pp. 487–503.

Introduction: The Core Themes

117

With a letter of July 15 (dated “London July 4 s.v. 1700”), Sloane sent Leibniz an extract copied from a letter received from Wallis of May 22 (dated “Oxford May 11th 1700”). Wallis saw no necessity for an astronomically-exact fixing of the civil year. The Julian calendar was simpler and the ecclesiastical year could be uncoupled from the civil year, he thought. He therefore predicted that in the future many countries would not adopt the new calendar. Besides the Rudolphine Tables, Wallis also referred to the Tables and rules for the moveable, and immoveable feasts in the 1662 version of the Book of common prayer and of further tables in Thomas Streete’s Astronomia Carolina (1661) and The description and use of the planetary systeme (1674), as well as in John Flamsteed’s The doctrine of the sphere (1680). Besides the Royal Society, and learned individuals in England, Leibniz also lobbied for the acceptance of the calendar reform in political circles there. In a letter of February 9, 1700, to the English diplomat James Cressett, he referred to his letter to Sloane of the same day and elaborated his vision for the calendar reform. As regards France, in addition to his secretive personal initiatives, Leibniz also sought the judgement of the Académie des Sciences in an official letter, written on February 8, 1700. In this – as in the letter a day later to Cressett – he pleaded for a course of action in line with astronomical truth. Thus he thought, for example, that the mathematicians of the Académie might adopt a comparable role as once the astronomers of Alexandria, or the members of the Calendar Office in China, did. In particular, Leibniz saw in the decision of the “Corpus Evangelicorum” at Regensburg an opportunity to advance astronomy which, in his opinion, was still in its infancy. Earlier observations he considered to be uncertain and erroneous; one did not even know for sure if the solar year was constant or not. His interest in the quality of astronomical tables was rooted above all in the desire for an increase of knowledge rather than in a correct determination of the date of Easter. But, even in respect to the latter problem, Leibniz called for a transnational and an inter-confessional exchange. The fact, that the Tabulae Rudolphinae were founded on erroneous observations, had been known even to Kepler himself. Thus, he wrote to Rømer, on March 18, 1700, that the calculation of the vernal equinox, on the basis of Kepler’s data, deviated systematically by three hours from later more exact calculations. Ulrich Junius had – in a short tract entitled Epistola de dispositione ephemeridum ad seculum XVIII conficiendarum – presented his project for more exact tables based on ephemerides, and he called for representations from others in the matter. Leibniz forwarded this tract to the Académie des Sciences, with a letter of February 8, 1700, and to Rømer, whose commentary of February 3 he

118

Introduction: The Core Themes

in turn sent to Junius and to Gottfried Kirch. Furthermore, through Wagner’s letter of July 21, 1700, Leibniz learned of Cassini’s recommendations for Junius. Already from this limited number of responses, fundamental differences became apparent: Rømer and Kirch recommended taking the tables of a single author as a basis while Junius wished to follow an eclectic or comprehensive approach, as he wrote to Rømer on March 18, 1700. Rømer, however, considered Kepler’s tables to be adequate once a small number of corrections had been undertaken. Other points that were in part controversial related to true or average movement, the use of right ascension and declination versus longitude and latitude as well as of heliocentric versus geocentric positions. Rømer wanted to exclude aspects that were important for astrology, and he found himself on this point in agreement with the “Corpus Evangelicorum”, which sought to preempt the abuse of astrology in the calendar reform. Kirch, for his part, was however more pragmatic and would not rule out all meanings or actions of real celestial bodies. Similarly, regarding the quality of available data, there was no consensus. In the meantime a multitude of newer astronomical tables had become available. Whereas Junius wanted to take those of Johannes Hevelius, John Flamsteed and Philippe de La Hire as a basis for solar and lunar considerations, Wallis considered the English-language ones to be the most exact – as his letter of May 22, 1700, to Sloane reveals – although they had already become out of date once more, a matter Leibniz pointed out in his letter to Rømer on March 18. The most recent results of Flamsteed and Newton on solar and lunar motions had not yet been published. Leibniz received nonetheless through Sloane a short summary, that had been written by Newton and inspected by Flamsteed. This he lent out to Kirch for his judgement, and he also passed it on to Fontenelle whose reply contained an advisory comment from the Académie des Sciences. Although Kirch, Newton and La Hire were in agreement that the maximum of the midpoint equation of the sun, as calculated by Kepler and Hevelius, was much too large – being above 2° instead of about 1° 57´ – they were not of one mind about its precise value. Following Kirch’s letter from the beginning of April 1701, Leibniz sent this correspondent’s value for the midpoint equation to Sloane, on May 15, 1701, and he in turn presented it to Halley, as he reported to Leibniz on July 9. As regards the values for lunar motion calculated by Newton, both Kirch and the Académie des Sciences could only recommend verification by observation. This was because a satisfactory mathematical description of the motion of the moon, which was required for forecasts, did not yet exist. Newton’s own theory, about which Leibniz enquired among correspondents and visitors, only appeared in 1702.

Introduction: The Core Themes

119

Even Kepler’s theory of elliptical planetary motion proved not to be infallible.84 Fontenelle confirmed to Leibniz that Cassini still preferred ovals to the Keplerian ellipses, and La Hire appeared not to opt for a particular curve, as Leibniz informed Sloane on May 15, 1701. Furthermore, in this letter to Sloane, he requested Newton’s opinion. However, both this and a parallel enquiry to Newton through Christoph Bernhard Crusen  – in Leibniz’s letter to Crusen on July 14, 1701 – proved to be in vain. Alas, Newton, because of his commitments in the monetary and academic fields in London and Cambridge, respectively, was scarcely to be encountered as Crusen’s reply, of October 11 from London, revealed. Flamsteed appeared to have taken an important step towards confirmation of the heliocentric world picture with his observation of the parallax of the fixed stars, which was reported in a letter of December 30, 1698, to Wallis; the latter included it in the third volume of his Opera, and he informed Leibniz accordingly, on April 30, 1699. The fact that astronomers had quickly cast doubts on this was not referred to in Leibniz’s correspondence at this juncture. In point of fact though, Leibniz too was skeptical since similar earlier observations like that of Robert Hooke – published in An attempt to prove the motions of the earth from observations (1674) – had not proved convincing.85 This he confided to Tschirnhaus, on April 17, 1701. However, he did not consider a proof of the Copernican world view, based on stellar parallax, to be at all necessary, as he had already explained to the physician Georg Wolfgang Wedel in a letter of September 9, 1699. Wedel had opened the correspondence with Leibniz, on August 24, 1699, by expressing his objections against the movement of the planet earth. According to him, this would contradict the story of genesis or of the creation from the Book of Moses, according to which the earth had been created first, and later the sun and other celestial bodies. Leibniz, however, 84 Cf. B. S. Baigrie, “The justification of Kepler’s ellipse”, Studies in History and Philosophy of Science, vol. 21(4), (1990), pp. 633–664; A. Mazer, The Ellipse: A historical and mathematical journey, Hoboken (New Jersey), 2010, in particular chap. 7, pp. 275ff. (Kepler and Newton: Aristarchus redeemed); R. Rössler, “Hypothese, Abweichung und Traum: Keplers Ellipsen”, pp. 65–76, in: R. Rössler, T. Sparenberg, P. Weber (eds.), Kosmos & Kontingenz: Eine Gegengeschichte, Paderborn, 2016; V. Remmert, “Die Ellipse als Epochensignatur?: Von Kepler am Weißen Haus vorbei zu Warburg”, pp. 274–282, in: M. Chihaia, G. Eckert (eds.), Kolosale Miniaturen: Festschrift für Gerrit Walther, Münster, 2019. 85 Cf. for example, M. Hoskin, Stellar astronomy: Historical studies, Chalfont St Giles, 1982, and Cambridge (Science history publication), 1986, in particular sect. A, chap. 3 (Hooke, Bradley and the aberration of light); H. Siebert, “The early search for stellar parallax: Galileo, Castelli, and Ramponi”, Journal for the History of Astronomy, vol. 36(3), (2005), pp. 251–271.

120

Introduction: The Core Themes

pleaded for a metaphorical and not a literal interpretation of the bible; in the case of dubiety or ambiguity, that interpretation was to be followed which was in accordance with the nature of the thing itself, or the science of nature, he told the correspondent. Flamsteed’s observation, and the doubts that had arisen about it, underlined the importance of precise astronomical values. For this reason, Leibniz canvassed the Berlin Society of Sciences, advocating the acquisition of good astronomical instruments, as is evident from an excerpt he made from a letter from John Wallis of November 16, 1700. Moreover, through his correspondents, he gathered proposals for the building and equipment of the planned Berlin Observatory that was to be located on the roof of the new pavilion. Rømer argued, in a letter of December 15, 1700, that the building should be designed to accommodate the instruments if it were intended to serve the purpose of utility rather than of pomp; he recommended the construction of a meridian circle, which he himself had designed. In a letter to Wagner, on April 9, 1700, Leibniz commissioned him, and Johann Andreas Schmidt  – who had contacts in southern Germany – to make enquiries regarding the observatories of Erhard Weigel and Georg Christoph Eimmart, in Jena and Nuremberg, respectively. Wagner also had contact with the master builder Johann Heinrich Gengenbach in Zeitz, whom Leibniz decided to consult in a letter written in the last week of March 1700. 4.8 Optics Leibniz’s interest in optics was in evidence throughout the 25-year period under consideration (1676–1701) and beyond. In the years 1677–1679, questions from certain areas of optics like, for example, concerning the theory of colors and optical instruments, such as the telescope and the microscope, were a pronounced interest in Leibniz’s correspondence, especially in that with Mariotte and Huygens. This interest in optics was to continue in the early 1680s. With the indefatigable experimenter Mariotte, whose tract De la nature des couleurs (1679–1681) he avidly awaited, he discussed problems regarding colors. Leibniz’s suggestion of a possible attribution of the color of blood to refraction was convincingly rejected by Mariotte, without Leibniz conceding defeat on the question, however. Already before the publication of his principle of the easiest light path, in the article entitled “Unicum opticae, catoptricae et dioptricae principium”, in the Acta Eruditorum in June 1682, Leibniz discussed this principle in correspondence with Huygens. Then, following the publication of his article, objections voiced by Basilius Titel and Pierre Ango and reported by Christoph Pfautz in a letter of November 18, 1682 – to which Leibniz replied on February 17, 1683 – provided a further reason for him to express his views on

Introduction: The Core Themes

121

the matter. Pierre de Fermat (1607–1665), as well as the Jesuits Ignace Gaston Pardies (1636–1673) and Pierre Ango – the latter in his L’Optique divisée en trois livres (1682) – had formulated a principle of the shortest time and had supposed that light moved more slowly in a denser medium. According to Leibniz, however, the light followed the “via facillima”, whereby a greater resistance of the medium leads to a greater velocity.86 After Pfautz referred once again, on May 8, 1683, to the issues raised, Leibniz responded, on May 14, stating clearly that he did not claim priority in the formulation of the minimal principle of optics. Just the same, he stressed that he could – by means of his differential calculus – provide a considerably shorter proof of the minimal principle than Fermat in particular had done. 4.8.1 Theories of Light: Newton and Huygens In the late 1680s Leibniz’s thoughts on optics were largely determined by his interest in the works of Newton and Huygens. His only significant publication during this period – the article “De lineis opticis” in the Acta Eruditorum of January 1689 – was closely connected with the “Tentamen de motuum coelestium causis” and the “Schediasma de resistentia medii”, both of which had come into being under the influence of the recently published Principia mathematica (1687) of Newton. Shortly after Leibniz’s return to Hanover, Huygens informed him, on August 24, 1690, about hints Newton had given him – on the occasion of their meeting in the summer of 1689 – regarding a planned work on optics, as well as about new experiments on the theory of colors. The delivery of Huygens’ gift of his Traité de la lumière in the second half of September 1690 also proved to be a major influence on Leibniz’s thinking about optics, as is evident from his drafted but never dispatched letter to Huygens from the first half of October of that year. Leibniz was exceedingly impressed by Huygens’ presentation of his wave theory of light, and he referred in particular to the propagation of a wave represented using Huygens’ construction of wave fronts, his derivation of the laws of reflection and refraction, and his explanation of the phenomenon of double refraction in Iceland spar on the basis of spherical wave propagation.87 In the drafted letter intended for Huygens, Leibniz did not forget to recall the efforts of predecessors in the development of the wave theory, namely Pardies and 86 Cf. A. I. Sabra, Theories of light from Descartes to Newton, Cambridge, 1981, in particular chap. V and chap. VII. Regarding Leibniz’s contributions to optics, cf. J. K. McDonough, “Optics”, chap. 23 (pp. 425–437), in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. 87 Cf. A. I. Sabra, (note 86), chap. 8, and O. Darrigol, A history of optics from Greek antiquity to the nineteenth century, Oxford, 2012, in particular chap. 2, sect. 2.3.

122

Introduction: The Core Themes

Ango. Huygens’ presentation of the laws of reflection and refraction, as well as of double refraction, found Leibniz’s unconditional support. However, as regards the phenomenon of double refraction, Leibniz saw in Huygens’ treatment only a description and not an explanation of the observed appearances. Such an explanation, he presumed, would simultaneously provide the key to the theory of colors. For this reason, he expressly requested that Huygens communicate to him his understanding of the nature of colors, especially as this topic had been left out of consideration in the Traité de la lumière. Leibniz to all appearances never carried out experiments himself in order to explain the phenomenon of double refraction in Iceland spar, although he may possibly have had the intention of doing so. As early as September 10, 1683, Georg Mohr had sent him a quantity of Iceland spar with the promise to send him more of this mineral. Once again, on December 19, 1690, he was reminded of this matter by a letter of Johann Jacob Spener, who reported that he had received samples of Iceland spar with which he had obtained experimental results. Among other things, Spener claimed to have found a better method than Huygens of polishing the crystal, namely by employing aqua fortis (nitric acid). Leibniz’s thoughts on optics after 1690 continued to be influenced by the works of Huygens and Newton. From the fall of 1690, he had occupied himself with the Traité de la lumière, but an intended detailed discussion he put off again and again with the result that, on March 26, 1691, Huygens had to remind him of his treatise on optics and to request Leibniz’s opinion about the explanation given of double refraction in Iceland spar. Only after more than a year had elapsed, on April 11, 1692, did Leibniz finally express his views to the author regarding his wave theory of refraction and double refraction. Leibniz was most pleased with Huygens’ explanation of double refraction, and he found only a single circumstance where an explanation was lacking, having in mind perhaps the polarization of light, a phenomenon which Huygens had observed but not explained. Huygens’ explanation of colors, which Leibniz found wanting in the Traité, also interested him very much. Already on August 24, 1690, Huygens had informed him about intimations made by Newton, during a meeting they had in the summer of 1689, concerning a planned work of his on optics as well as about new experiments on the theory of colors. Thereupon Leibniz requested further information, first of all from Huygens, on January 8, 1692, then from Halley, on June 3, 1692, and finally from Newton himself, on March 17, 1693, in the letter which marked the beginning of their direct correspondence. While Newton confirmed Huygens report, in his reply of October 26 of that year, he was not prepared to reveal his results. Even his intended work on optics was put in a long-term perspective, not least in order to avoid controversy.

Introduction: The Core Themes

123

Leibniz was most impressed by the power and capability of Huygens’ wave theory of light, especially by the derivation of the law of refraction it facilitated, as he made clear in correspondence with Tschirnhaus. In this context, Huygens had outclassed his predecessors Pardies and Ango, he explained in a letter to Tschirnhaus on January 30, 1693. For all that, a theory of light lacking an explanation of colors remained for him incomplete, as he explained to Tschirnhaus. In the years between 1694 and 1696, the works of Newton and Huygens, and in particular the latter’s Traité de la lumière, unabatedly dominated Leibniz’s thoughts on optics. As regards Newton’s experiments, he hoped for more precise information from his correspondence with Fatio de Duillier. It was therefore a welcome development that Fatio, for his part, addressed the topic in his letter of April 9, 1694, referring in particular to the corpuscular theory. And so, Leibniz was able to enquire, in his reply of May 18, about an explanation of colors, referring to the hypothesis formulated by Edme Mariotte in his De la nature des couleurs (1681)  – which was in opposition to the view held by Newton – namely that light rays do not possess any primitive constant colors but rather that their colors change, for example following refraction.88 Alas, a reply by Fatio to Leibniz’s questions never materialized. Leibniz reported to Huygens, on May 6, 1694, about Fatio’s letter not without making clear his own skeptical position regarding the corpuscular interpretation. Also, Huygens  – following his discussions with Newton (in the summer of 1689) and with Fatio (between June 1690 and September 1691) – was an opponent of the Newtonian corpuscular theory. For him, the very high velocity of light, that had been demonstrated by Ole Christensen Rømer and reported in his article “Demonstration touchant le movement de la lumière”, in the Journal des Sçavans (1676), was an important argument against this theory, as he made clear in his letter of May 29, 1694, to Leibniz. Huygens had already confronted Fatio with the latter objection, alas to no avail. Huygens saw a further touchstone for Newton’s theory in the explanation of refraction, and in particular of double refraction, referring to this as an “Experimentum Crucis”. And, as regards the explanation of colors, in Huygens’ view, neither the investigations of Newton, which had been presented in A letter of Mr. Isaac

88 Cf. for example, A. E. Shapiro, “Artists’ colors and Newton’s colors”, Isis: Journal of the History of Science Society, vol. 85(4), (1994), pp. 600–630; A. Rupert Hall, Isaac Newton: Eighteenth-century perspectives, Oxford, New York, Tokyo, 1999, in particular Part II, chap. 5 (Bernard le Bouvier de Fontenelle’s Eloge), and specifically “anatomy of light” and “primitive rays” (pp. 66f.).

124

Introduction: The Core Themes

Newton, containing his new theory about light and colors (1672),89 nor his own had brought sufficient clarity. Leibniz had, up to the 1690s, repeatedly attempted to obtain more detailed information about the optical experiments of Newton. Then, in his letter of July 9, 1694, he reminded Huygens once again about his desire to learn about these. After these efforts had been to no avail, and in the wake of Huygens’ death, on July 8, 1695, he turned once again directly to Newton himself. On a slip of paper, intended for Newton and dated December 16, 1695, with which Leibniz attempted to revive their correspondence that had been in abeyance for a year and a half, the call for Newton to publish his research concerning colors as soon as possible occupied a central position. Leibniz included this note with a letter sent to Thomas Burnett of Kemney, probably at the end of January 1696, for forwarding to Newton. Whether or not Leibniz’s note reached the addressee is unknown. A reply, or response, from Newton probably never materialized and, as regards the theory of colors, Leibniz had to wait for most of a decade for the publication of Newton’s seminal work Opticks: or a treatise of the reflexions, refractions, inflexions and colours of light (1704), or Optice: sive de reflexionibus, refractionibus, inflexionibus et coloribus lucis libri tres (1706). Prior to Huygens’ demise, Leibniz had likewise hoped to obtain valuable clues, from the correspondent’s investigation of Iceland spar, about the nature of colors as well as an explanation of the polarization of light in the context of the wave theory. All in all, Leibniz was highly impressed by the effectiveness and capability of Huygens’ wave theory of light. In this, Leibniz thought, Huygens had far surpassed his predecessors like the two Jesuits Pardies and Ango, and of course Robert Hooke. In his appreciation of Huygens’ achievements in optics, Leibniz also had occasion to recall his own contribution, namely his article “Unicum opticae, catoptricae et dioptricae principium” of June 1682. The reason for this was the consignment to Huygens, on May 6, 1694, of a copy of a dissertation, over which Martin Knorr(e) had presided, entitled Dissertatio dioptrica de refractione luminis (1693). Huygens’ reaction, however, was one of disappointment that Knorr had failed to appreciate the significance of his own Traité de la lumière, placing his wave theory of light on a par with those of his predecessors like that of Hooke – given in Micrographica (1665) – and that of Pardies, who had laid the foundation for Ango’s L’Optique (1682). Huygens, in his reply on May 29, saw the essential leap forward on his own part, 89 Cf. for example, P. Fara, “Newton shows the light: A commentary on Newton (1672) ‘A letter … containing his new theory about light and colours …’”, Philosophical Transactions A (Math Phys Eng Sci.), 2015 (April 13): 373(2039): 20140213 (https://doi.org/10.1098/rsta.2014.0213).

Introduction: The Core Themes

125

in comparison with his predecessors, in the explanation of the phenomenon of double refraction in Iceland spar. For Leibniz, on the other hand, Huygens’ explanation of wave propagation was the essential innovation. His criticism of Ango – which he had previously expressed in his drafted, but never dispatched, letter for Huygens from the first half of October, 1690, and in a communication on January 30, 1693, to Tschirnhaus – was now finally articulated in his letter to Huygens of June 22, 1694. All of Huygens’ predecessors had failed, in Leibniz’s view, to explain either the refraction of light or the phenomenon of double refraction. 4.8.2 Catoptrics, Dioptrics and Optical Instruments In a letter to Bodenhausen, on July 22, 1693, Leibniz praised the Dioptrica nova published by William Molyneux of Dublin in 1692.90 In this work, which was the first treatise in English on dioptrics, the author had presented parts of Leibniz’s article “Unicum opticae, catoptricae et dioptricae principium” (1682) in an English translation, and he had given Leibniz priority for the formulation of the correct minimization principle of optics, which was clearly preceded in time by that of Fermat.91 Specifically, in his 1682 article, Leibniz had suggested that light follows the path of least resistance, in contrast to Fermat’s principle of least time of 1662. Leibniz’s interpretation was also that preferred by William Molyneux in his Dioptrica nova. Molyneux’s treatise likewise contributed to Huygens’ resumption of his work on dioptrics in the spring of 1692. The latter undertook a detailed examination and critique, which was later published with the title “Ex Dioptrica nova Guilielmi Molyneux. Edita 1692”. It was primarily to the third part of his posthumously-published Dioptrica,92 viz. “Des telescopes et des microscopes”, that Huygens’ attention was now directed. While Huygens expressed approval of the work in general, Leibniz, for his part, was flattered by Molyneux’s use of his 1682 article and, in his correspondence and writings, he referred to Dioptrica nova as an excellent work on a number of occasions.93 90

Regarding Molyneux, cf. J. G. Simms (P. H. Kelly, ed.), William Molyneux of Dublin 1656–1698, Dublin, 1982; J. G. O’Hara, “Molyneux, William (1656–1698), experimental philosopher and constitutional writer”, Oxford Dictionary of National Biography (Published in print/online: September 23, 2004). 91 Cf. chap. 5 in: A. I. Sabra, (note 86), and chap. 2 in: O. Darrigol, (note 87). 92 Cf. F. J. Dijksterhuis, “Huygens’s dioptrica”, in: L. Palm (guest ed.), Christiaan Huygens: De Zeventiende Eeuw, vol. 12 (1), (1996), pp. 117–126. 93 Cf. J. G. O’Hara, “‘Leibnutz’s Universal principle in optics’: William Molyneux’s translation and interpretation of Leibniz’s Unicum opticae”, pp. 915–918 in: H. Poser et al. (eds.), Nihil

126

Introduction: The Core Themes

Leibniz’s interest in new works appearing in the field of dioptics continued until Huygens’ death and beyond. When he learned, from a review in the Journal des Sçavans, of the appearance of Nicolaas Hartsoeker’s Essay de dioptrique (1694), his main interest proved to be the explanation of the law of refraction given there, as he made clear to L’Hospital in a letter of March 18, 1695. For Huygens, Leibniz surely had great expectations and longed for an early publication, as is evident from his impatient question in his letter of September 14, 1694: “N’aurons nous pas bien tost vostre Dioptrique?” Alas, Huygens’ work on dioptrics was destined to appear only posthumously in 1703. Optical instruments and equipment routinely attracted the attention of Leibniz and his correspondents. In letters exchanged with Tschirnhaus, there were already in the years 1681 and 1682 reports about the construction of concave mirrors. There is also evidence in Leibniz’s correspondence, in the years that followed, of Tschirnhaus’ long-standing involvement in the improvement of such mirrors. On September 4, 1683, the correspondent wrote to Leibniz that he was having a copper mirror made with a diameter of seven quarters of a lower-arm length (“7 viertel der Ellen”). Furthermore, he told that he intended to commission a second mirror of three lengths (“3 Ellen”) diameter. In the following letter, of December 7, 1683, he then informed Leibniz about the finest requirements for the construction of such mirrors. His own mirror, he emphasized, provided admirable results exceeding expectations and was unique among its kind in Germany. Two years later, Tschirnhaus submitted an article on new optical experiments entitled “Novae quaedam experientiae opticae” to the editors of the Acta Eruditorum, a copy of which was sent by Christoph Pfautz, in September 1685, to Leibniz asking for his expert opinion. Pfautz desired in particular an explanation of an experiment described using a microscope without a lens. Tschirnhaus claimed that, by the placement of the object in proximity to the observing eye, an enlargement was achieved. In his reply, Leibniz recalled a similar observation of an object through a slit close to the eye that had once been described by Christoph Scheiner in his opus: Oculus, hoc est fundamentum opticum (1619). Notwithstanding Leibniz’s positive verdict on Tschirnhaus’ investigation, the article in question never did appear in the Leipzig journal. By the early 1690s, optical instruments and devices had been the subject of Leibniz’s correspondence with Tschirnhaus for more than a decade. For Tschirnhaus, practice was the priority, as he made clear in a letter to Leibniz Sine Ratione: Mensch, Natur und Technik im Wirken von G. W. Leibniz, VII. Internationaler Leibniz-Kongreß: Vorträge 2. Teil, Berlin, 2001.

Introduction: The Core Themes

127

on January 13, 1693. And, he believed he possessed special abilities in the construction of telescopes and microscopes. In both telescopy and microscopy, he had succeeded in considerably improving the illumination of the instruments. Similarly with concave mirrors, his long-standing commitment had led to substantial progress towards perfection. Finally, Tschirnhaus raised the prospect of an impending breakthrough, possibly resulting in a sensation, through his work on optical instruments, and he thought this might prove comparable to the appearance of the Sidereus nuncius, Galileo’s ‘Sidereal Messenger’ publication of 1610 which came in the wake of the invention of the telescope. Leibniz emphatically supported Tschirnhaus’ practice-related optical investigations, as he told the correspondent in his reply on January 30, 1693, but he valued improved microscopes more than a new sidereal or starry messenger, he told the correspondent. Although resolution capacities of such optical instruments would inevitably reach their limits, the objective for Leibniz was to approach these limits as closely as possible. Tschirnhaus’ commitment to optics, and in particular to the perfection of concave mirrors and convex lenses or burning glasses, extended back to the early 1680s and continued to manifest itself in his correspondence with Leibniz in the 1690s. Following a renewed avowal of his commitment to optics as his overriding field of activity, he informed Leibniz, on February 27, 1694, about a new machine he had developed for the manufacture of glass convex lenses of up to two feet diameter, and having a performance superior to the mirrors he had previously made. Furthermore, he explained that, in his most recent work, he had been able to produce, within seconds, glass spheres or beads from the ashes of paper and vegetable matter or from molten porcelain, talc or asbestos. And he maintained that, with his burning glass, it would be possible to burn a fleck or black spot in wood located under water; it could render molten many materials like pitch, sulfur or colophony (rosin resin); it even reduced metals to a glass form, and gold to ruby glass. Particularly interesting, as regards the state of technology at the time, was Tschirnhaus’ listing of the main advantages of convex lenses in comparison to concave mirrors, namely that they were highly effective, while being not as heavy and large as their specular counterparts and therefore easily transportable. In addition, the refracted rays travelled below or underneath the lens and could be aimed at fluids and powders of all kinds and, lastly, their polish or glaze, which in mirrors was difficult to restore, was enduring. Although Tschirnhaus had found a series of noble buyers for his burning glasses, this did not cover his expenditure and, therefore, he sought to offer his lenses to a wider public in Holland. His real intention, however, was to establish

128

Introduction: The Core Themes

a fund for the advancement of the sciences out of the proceeds from the sale of his optical products. Leibniz lauded Tschirnhaus’ idea in no uncertain fashion but, as regards its realization, he remained skeptical. In the fall of 1694, Leibniz and Tschirnhaus met up twice in Hanover. During his stay, Tschirnhaus also demonstrated his burning glasses at the court of Hanover in the hope of finding purchasers not only for a burning glass but also for a large concave mirror, as is evident from a later letter he wrote to Leibniz on October 22. In Amsterdam also, Tschirnhaus offered concave mirrors for sale. From a letter written by Johann Daniel Crafft, on December 30, 1694, Leibniz learned about Tschirnhaus’ business relationship with Ameldonck Block (or Bloeck) and Huygens’ final letter to Leibniz, on December 27, 1694, told of Tschirnhaus’ visit and about his inability to demonstrate a burning glass on that occasion due to unfavorable weather conditions. Huygens, for his part, had a preference for the fabrication of concave mirrors from glass with a diameter of up to 4 feet, having a coating on the back side and, in addition, a small plane mirror near the focal point in order to direct the rays to the combustible material. In his intended reply, written on July 1, 1695, a week before Huygens’ death, Leibniz wished to inform him that a large mirror of Tschirnhaus was to be seen in Amsterdam,94 as well as about the production of convex mirrors in Nuremberg. 4.8.3 Microscopy In November 1676, when Leibniz was on his way to Hanover for the first time, he visited the Dutch pioneer of microscopy Antoni van Leeuwenhoek in Delft. Leibniz’s continuing interest in Leeuwenhoek and his work found its expression in the years and decades that followed, in the form of numerous utterances regarding him in letters to a variety of correspondents. However, it was only in the summer of 1715 that a direct correspondence between the two finally developed. And so, in the last fifteen months of Leibniz’s life, at least eight letters were exchanged between the two.95 94 Cf. F. J. Dijksterhuis, “Foci of interests: Optical pursuits amongst Huygens, Leibniz and Tschirnhaus 1680–1710”, pp. [261]–283 in: M. Kempe (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung, vol. 1, 2013. 95 Cf. Letters 316–320, 322, 323, 326 in: L. C. Palm, H. J. Zuidervaart, D. Anderson, E. W. Entjes (eds.), Alle de Brieven van Antoni van Leeuwenhoek. Uitgegeven, geillustreerd en van antekeningen voorzien door een Commissie van Nederlandse Geleerden, Deel XVII / The Collected Letters of Antoni van Leeuwenhoek. Edited, illustrated and annotated by a committee of Dutch scientists, vol. XVII, London, 2018; J. G. O’Hara, “‘J’aime mieux un Leewenhoek qui

Introduction: The Core Themes

129

The first report, about Leibniz’s meeting with Leeuwenhoek in Delft, is to be found in a letter from Amsterdam, which he wrote shortly after the encounter, on November 28, 1676, to Henry Oldenburg in London. As regards Leeuwenhoek’s microscopic observations in particular, Leibniz expressed his delight and underlined their importance for the advancement of science. Then, shortly after his arrival in Hanover (in the last days of the year 1676), he reported (in January 1677) to duke Johann Friedrich about his most important contacts in the Netherlands. These included, first and foremost Christiaan Huygens, whose opus on the pendulum clock Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae (1673) he alluded to,96 and four others, namely Jan Hudde, Baruch de Spinoza, Theodor Cranen and, of course, Leeuwenhoek. In the first draft of a letter for Jean Paul De La Roque from the end of 1677, Leibniz reported about Leeuwenhoek in the context of microscopy, and of lens optics in particular. He stressed the value of microscopic observation for medicine and the medical arts, referring specifically to Leeuwenhoek’s observation of animate beings or little animals in water interfused with pepper, which he most likely had learned about during their meeting in Delft in November 1676 and which had been published in the Philosophical Transactions in March–April 1677. Following Oldenburg’s death, in September 1677, Leeuwenhoek sent a series of reports about his microscopic investigations to the Royal Society. All in all, between September 1677 and April 1679, he sent eight such reports, including that concerning the production and nature of mammalian or human sperm entitled “Observationes de natis e semine genitali animalculis”, which were duly published in the Philosophical Transactions. Accordingly, Nehemiah Grew, who acted as secretary of the Society from 1677 to 1679, was able to inform me dit ce qu’il voit, qu’un Cartesien qui me dit ce qu’il pense’: Leibniz, Leeuwenhoek und die Entwicklung der experimentellen Naturwissenschaft”, pp. 145–175 in: M. Kempe (ed.), 1716 – Leibniz’ Letztes Lebensjahr: Unbekanntes zu einem bekannten Universalgelehrten. Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung, vol. 2, 2016. Regarding microscopy before Leeuwenhoek, cf. C. Lüthy, “Atomism, Lynceus, and the fate of seventeenth-century microscopy”, Early Science and Medicine, vol. 1(1), (1996), pp, 1–27. 96 Cf. “Christiaan Huygens, pendulum clocks, and a curve ‘not at all considered by the ancients’” and “Appendix: Part five of Horologium Oscillatorium”, pp. [75]–94 in: S. G. Gindikin, A. Shuchat (trans.), Tales of physicists and mathematicians, Boston, Basel, 1988; D. Speiser, “Le « Horologium Oscillatorium » de Huygens et les « Principia »”, Revue Philosophique de Louvain, vol. 72, (1988), pp. 485–504; J. G. Yoder, “Christiaan Huygens’ book on the pendulum clock (1673)”, chap. 3 (pp. 33–45) in: I. Grattan-Guinness (ed.), Landmark writings in western mathematics 1640–1940, Amsterdam, Boston, 2005.

130

Introduction: The Core Themes

Leibniz, on August 4, 1678, about Leeuwenhoek’s continuing commitment to microscopic research and he referred in particular to the discovery of millions of minute animate beings in water interfused with pepper. Three months later, on November 6, 1678, Johann Sigismund Elsholz wrote to Leibniz from Berlin and he recalled a visit by Johann Daniel Crafft, in the previous summer, during which microscopy was discussed. Elsholz now hoped to obtain a microscope from Holland through Leibniz’s influence. Evidence of Leibniz’s own interest in the spherical (or globular) microscope is found in a letter to Christian Philipp in Leipzig, written on November 22, 1678, in which he informed the correspondent that microscopes of that type had been first developed by Jan Hudde and later improved, and successfully employed, by Leeuwenhoek. From Elsholz’s letter to Leibniz of February 8, 1679, it is evident that the correspondent was already in possession of such a spherical (or globular) microscope with a single lens (“unica lenticula vitrea”) and that he had in mind a compound instrument with two lenses (“microscopium globularium”). Johann Georg Graevius, of the University of Utrecht, likewise informed Leibniz about Leeuwenhoek’s activities, in a letter of March 24, 1679, and he referred specifically to the extraordinary numbers of little animals (or animalcula) observed under the microscope in blood and human semen and to the communication of results to the Royal Society of London. In the months before his Italian journey, Leibniz expressed his views about Leeuwenhoek in his philosophical correspondence with Antoine Arnauld (in 1686 and 1687), referring in particular to Leeuwenhoek’s “Observations” (or “Observationes”) that had been published in the Philosophical Transactions in 1677 and 1678. In this context, Leibniz referred specifically to Leeuwenhoek’s observations of animate beings, or little animals, in water interfused with pepper and those concerning mammalian or human sperm. Here, he also alluded to Leeuwenhoek’s animalculist theory of preformation. According to this theory, an entire organism was pre-formed in the little animals (or animalcula) found in human or mammalian sperm, and it had only to unfold or de-convolve itself in the process of fertilization. From a philosophical point of view, the generation (and later death) of an animal represented merely a transformation from one state to another, a view Leibniz expressed in a letter to Arnauld, on December 8, 1686. Then, on April 30, 1687, he wrote, in a further letter to Arnauld, that there was a prodigious quantity of little animals to be observed in a drop of water imbued with pepper. Again, in September 1687, he wrote to the same correspondent that, putting philosophy aside and from the results of experimental science alone, entire organisms appeared to be present in the form of still imperceptible little animals. Finally, on October 9,

Introduction: The Core Themes

131

1687, Leibniz wrote again to Arnauld about his penchant for Leeuwenhoek’s sentiments, while referring also to an “autre grand observateur et Anatomiste”, namely Jan Swammerdam, with his work entitled Miraculum naturae sive uteri muliebris fabrica (1672) in mind. In the years following his Italian journey, Leibniz retained his interest in the microscopic observations of Leeuwenhoek, and he referred to him again and again in his correspondence. Leibniz’s meeting with the microscopist Marcello Malpighi in Italy proved to have had a special influence on him. On July 25, 1690, for example he reported to Huygens about his encounters with mathematicians and physicists in Italy; these included Adrien Auzout (in Rome), Vincenzo Viviani (in Florence), Stefano degli Angeli (in Padua) and of course Malpighi (in Bologna). Writing to Huygens, on March 2, 1691, Leibniz drew a dividing line between philosophical thought and practical or observational science. Distancing himself from the Cartesian world view, he introduced the observer Leeuwenhoek as the preferential antipole to a contemplative Cartesian with the words: “j’aime mieux un Leewenhoek qui me dit ce qu’il voit, qu’un Cartesien qui me dit ce qu’il pense”. To this sentiment he added, however, that, in the final analysis, it behooved one to bring together reasoning and experimental observation: “Il est pourtant necessaire de joindre le raisonnement aux observations”. In a letter to Melchisedech Thévenot, on September 3, 1691, Leibniz referred to the auspicious work of the microscopists Malpighi and Leeuwenhoek, alluding in particular to the latter’s vast collection of instruments. Again and again, Leibniz recalled his meeting with Leeuwenhoek in Delft, in November 1676, and he often extended greeting to him through travelers. Leeuwenhoek’s work on microscopy continued to attract Leibniz’s interest throughout the 1690s. A particular wish of his was to persuade Leeuwenhoek to publish some of his research results in the Acta Eruditorum of Leipzig. Alas, his efforts were to be of no avail, as is evident from a letter of February 26, 1695, from Johann August Haberstroh in Leiden. In a letter of December 6 (or 16), 1695, to Haberstroh, Leibniz appears to have made a further attempt to convince Leeuwenhoek to submit his research results to the Acta Eruditorum, as is apparent from Haberstroh’s reply from Leiden on January 29, 1696. In the course of the year 1695, Leeuwenhoek’s Arcana naturae detecta, in which he documented his numerous discoveries, was published in Delft. The work was dedicated to Antonio Magliabechi, who then, in a letter from Florence on October 22, 1695, informed Leibniz about the new publication. At about the same time, at the end of October 1695, in the draft of a letter for the physician Justus Schrader in Amsterdam, Leibniz stressed the importance of the

132

Introduction: The Core Themes

observer, and the experimentalist, in the art of medicine, referring specifically to the two Dutch microscopists, Jan Schwammerdam and Leuwenhoek. Later in the decade, in 1697 and 1698, the work of Leeuwenhoek continued to attract Leibniz’s interest, and microscopy then became the main focus for him in optics. Leibniz now used his correspondence with Hendrik van Bleiswijk (or Bleiswyck), the influential burgomaster of Delft, to revive his contact with Leeuwenhoek there. In a letter to Bleiswijk, on May 7, 1697, he elaborated his interest in Leeuwenhoek and his work. He pleaded for measures to be taken, for the preservation for posterity of Leeuwenhoek’s methods and instruments, by arranging timely assistance for the master by apprentices and students. In this context, Leibniz distinguished between  – on the one hand  – great discoverers or innovators, like Christiaan Huygens and Jan Hudde, who excelled by virtue of their ingeniousness and intellectual prowess, and – on the other hand – great observers like Leeuwenhoek, who stood out because of their special abilities and their assiduity. Leibniz saw the latter as being subordinate, or ancillary, to the former, but he stressed, in this context, that he appreciated an observer like Leeuwenhoek more than a painter of the Italian Renaissance like Raphael of Urbino. Half a year later, on November 7, 1697, Bleiswijk answered Leibniz’s letter. From this communication, it is apparent that Bleiswijk agreed with and supported Leibniz’s recommendation and that he had even shown Leibniz’s letter to Leeuwenhoek. In Leibniz’s following letter to the burgomaster, on January 3, 1698, his admiration for Leeuwenhoek once again found expression in a comparison with Raphael, Michelangelo and the “Oracle delphique”, namely Hugo Grotius (1583–1645). Leibniz saw great benefits for medicine coming from an increased commitment to microscopy and microscopic observation. From Bleiswijk’s reply of February 17, 1698, it is evident that Leibniz planned a journey to Holland and the Netherlands. Bleiswijk had once again forwarded Leibniz’s letter to Leeuwenhoek, primarily in order to reinforce the effort to persuade him to work for the conservation for posterity of his secret observational methods. However, the letter reveals that Leeuwenhoek was insisting that he himself had taken appropriate measures in this respect. In a letter to Bleiswijk, on January 6, 1699, Leibniz continued to advocate an effort for the conservation of Leeuwenhoek’s observations, and observational methods, including the granting of a pension to him by the Dutch republic, which would serve both for the advancement of science and the honor and glory of the town of Delft, he argued. Ultimately, however, Antoni van Leeuwenhoek, who was Leibniz’s senior by almost fourteen years, would outlive him by almost seven years.

Introduction: The Core Themes

5

133

Energy Conversion, Transmission, Storage and Power Technology Ego hac aestate occupabor in absolvendis tandem meis molendinis ventaneis, quae fodinis applico.97 Leibniz to Ehrenfried Walther von Tschirnhaus, May 23, 1681

5.1 Mining in the Harz Mountains Leibniz’s activities in the Harz mines after 1679 have in the past been described as coming in the wake of a period of two centuries of German ingenuity in the fields of mining and metallurgy, whereby the epochality of Leibniz’s own contributions to engineering has been attributed more to his publications on differential and integral calculus in 1684 and 1686, respectively, than to new approaches taken in relation to energy conversion, transmission and storage, as well as power technology.98 However, the concept of a power technology did have, even in Leibniz’s time, a long tradition going back 400 years and more to the medieval exploration of mechanical power when a range of active minds – stimulated both by technological successes in their time and led on by a certain will-o’-the-wisp (or gleam in the eye) of a perpetual motion – began to generalize the concept of mechanical power and came to think of the cosmos as a vast reservoir of energies waiting to be tapped. The fantasies and imaginations of the power-conscious technicians and engineers of the Late Middle Ages were to be the foundation for the Early-Modern development of power technology in the Western World.99 The present work pays particular attention to the latter aspects and seeks to provide a revised view of Leibniz’s commitment to the development of energy and power technologies in the fields of mining, transport, and beyond.

97 A III,3 N. 233, p. 428; Translation: I will be occupied this summer in completing at last my windmills which I am applying in the mines. 98 Cf. W. H. G. Armytage, A social history of engineering, London, 1961 and 1970, in particular chap. 7, pp. 60–66 (German miners and metallurgists, 1450–1650); D. S. L. Cardwell, “Power technologies and the advance of science, 1700–1825”, Technology and Culture, vol. 6(2), (1965), pp. 188–207, and “Some factors in the early development of the concepts of power, work and energy”, British Journal for the History of Science, vol. 3(3), (1967), pp. 209–224 (also published online by Cambridge University Press: 05 January 2009). 99 Cf. L. White Jr., Medieval technology and social change, London, Oxford, 1962, in particular pp. 129–134 (The concept of a power technology) and notes; B. S. Hall, D. C. West (eds.), On pre-modern technology and science: A volume of studies in honor of Lynn White Jr., (Humana civilitas: Sources and studies relating to the middle ages and the renaissance), Malibu, 1976, in particular Introduction; S. A. Walton, Fifty years of medieval technology and social change, New York, London, 2019.

134

Introduction: The Core Themes

Leibniz’s published correspondence reveals that, following a first preparatory stay in the fall of 1679, he commenced his activity in ore mining in the Harz mountains in the summer of 1680. With the construction of windmills, he aimed to tap into a renewable energy and power source which, although known since medieval times, was surely an innovation as regards applications to operate the pumping and winding machinery in the mines.100 Previously, water wheels had been employed in the Harz mining district in order to operate the pumping machinery for draining the mines. These water wheels were powered using rainwater collected in ponds or reservoirs. Thus, the operation of the ore mines had depended on the available quantity of rainwater and, in times of drought, ore production was considerably reduced. At first Leibniz anticipated relatively problem-free and rapid success with his plans to employ windmills, notwithstanding the protracted negotiations with the local mining authority and with duke Ernst August in Hanover. In the course of events, however, his commitment only ended in the summer of 1685 and then without a satisfactory outcome. Difficulties arose repeatedly forcing him to continually alter his plans. Thus, for example, an iron crankshaft was at first envisaged as part of the transmission system supplying energy to power the pumping machinery. Since, however, the requisite furnace was inoperative for a lengthy period, an alternative construction had to be devised, and the miller and master carpenter Hans Linsen informed him accordingly, on December 12, 1680. This temporary arrangement then led to further repair and maintenance work. Only in the summer of 1682, did it become possible to install the crankshaft weighing 13 hundredweight, as is evident from Linsen’s letter of August 2 of that year. Three weeks later, on August 24, Linsen informed him that, for the transport of an iron shaft in the hilly country, as many as 16 horses were required. To such extraneous influences, the prevailing weather conditions can be added. Operations had to be suspended during the winter months; on April 7, 1681, for example, Leibniz complained to Johann Daniel Crafft about the diabolic weather conditions that were holding up operations and causing him to lose time in the Harz mountains. In addition to such external factors, internal difficulties of Leibniz’s own designs also played a role in the delays. The transfer ratio in the cog and rung internal transmission of the windmill – that is, between the cogs of the cogged wheel and the vertical staves of the 100 Cf. J. G. O‘Hara, “Quellen zur Geschichte der Nutzung regenerierbarer Energiedargebote – Mühlen- und Maschinenbücher”, pp. 95–111 in: G. Bayerl (ed.), Wind-und Wasserkraft: Die Nutzung Regenerierbarer Energiequellen in der Geschichte, (Series: Technikgeschichte in Einzeldarstellungen), Düsseldorf, 1989; U. Hasenöhrl, J.-H. Meyer, “The energy challenge in historical perspective”, Technology and Culture, vol. 61(1), (2020), pp. 295–306, in particular, pp. 297–299 (The alternatives – Historicizing renewables).

Introduction: The Core Themes

135

lantern pinion – had to be altered several times in 1681–82 from its initial state in June 1680. Likewise, the success of a project involving power transmission by means of compressed air  – referred to in letters to Linsen in September and October 1682 – proved not to be feasible with the materials available. In addition, the lack of cooperation on the part of the local mining authority, and the mining officials, added greatly to the difficulties. Thus, in an underhanded manner, the Harz project, that Leibniz had hoped to complete successfully in just one or two summers – as his remark to Tschirnhaus, on May 23, 1681, cited in the heading of this section, reveals – developed into a time-consuming preoccupation over several years. In the 42 month period between January 1680 and June 1683 Leibniz travelled fourteen times to the Harz district, and he spent a total of 18 months there. On the occasion of one of the few palpable successes, which however soon proved to be fleeting, Leibniz told Johann Daniel Crafft in retrospect, on March 26, 1682, that he could have ceded on a hundred occasions to the multifarious opposition forces he was confronted with, if he had not wanted to show that it was a core feature of his mindset not to let up until he had carried out what he had set out to do. Leibniz’s unusual stubbornness here is remarkable and may perhaps be attributable to the fact that at stake was, not just the proof of the practicality of a theoretical idea, but also his reputation at court and his future influence on the new duke. The correspondences relating to windmill construction in the early 1680s – namely those with Hans Linsen, Heinrich Schütz, Reinhart Pfeffer and Johann Hagen – include estimates of costs, design drawings, receipts concerning wages paid and smithy costs, reports of the master carpenter Linsen during Leibniz’s absence as well as his instructions for Linsen. From these correspondences, as well as from that with duke Ernst August and the mining office, certain insights can be gained concerning Leibniz’s plans, his visits to the mining district and the progress of operations. Naturally, Leibniz’s commitment to his windmill venture, as well as his interest in discoveries and innovations in this area, are also reflected in a range of other correspondences. Thus, in a letter from the end of November or early December 1679, he informed Huygens about his windmill project for draining the mines that was intended to replace the water wheel-powered system that suffered especially in times of drought. He specified, for the depth at which the water lay in the mine, a value of the order of 100 mining measures of length (“jusqu’à 100 toises et plus”), and he requested the correspondent’s opinion. In his answer to this query, Huygens communicated his opinion in the closing paragraph of a letter of January 11, 1680. He proposed using a paternoster system, using chains and buckets, for lifting the water from the mine. Although

136

Introduction: The Core Themes

technically possible for depths of 100 “Lachter” or “Berglachter” (about 180 meters), Huygens thought any investment in machinery ought to match the expected return. He recalled learning from a Scottish gentleman about such a chain and bucket pumping system, which had been successfully employed in coal mining, albeit using horse mills. In his reply, on February 5, 1680, Leibniz then elaborated on his Harz project. A special difficulty was the corrosiveness of the water in the pits, which would damage the metal components of a bucket and chain pumping system. Instead it was necessary to employ a score of pumps (having wooden cylinders) arranged in tiers, one above the other, which were powered by water wheels. His idea, Leibniz explained, was to avail of wind power to service and replenish the reservoirs, while retaining the existing system of pumps and tiers of pumps. There remained the difficulty that the wind supply was erratic, and he explained that he had thought of an arrangement, where the windmill sails might be rotated a little in order to remain in the direction of the wind, and where the inclination of the axis of the sails might be varied according to the strength of the wind. Leibniz’s collaborator Crafft appears to have informed him belatedly, but then frequently, about the state of the windmill enterprise. As an experienced project developer himself, Crafft realized at the outset (in September 1680) the complex essence of the matter, and he cautioned that, while Leibniz’s ideas were good in theory, only time could tell if they would survive the test of practice and, a month later, he warned Leibniz that such things always prove more difficult than anticipated. As regards Leibniz’s interests in mining then, the years from 1680 to 1687 saw both a continuity, in the form of his pursuits of earlier interests, as well as a departure in the guise of the emergence of new applications or fields of activity. These efforts included, in particular, the multifarious proposals for the improvement of ore mining and, in addition, for the requisite water resources management in the Harz mountains.101 Already in the fall of 1679, a contract between Leibniz and the local mining authority  – the Board of Mines in Clausthal – had been ratified by duke Johann Friedrich. This was for 101 Cf. J. Gottschalk, “Theorie und Praxis bei Leibniz im Bereich der Technik, dargestellt am Beispiel der Wasserwirtschaft des Oberharzer Bergbaues”, Studia Leibnitiana, Supplementary vol. 22, (1982), pp. 46–57; J. Gottschalk, “Windmills and water-mills”, pp. 108–128 in: K. Popp, E. Stein (eds.): Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000; A. Wakefield, “Leibniz in the mines”, Osiris: Annual journal of the History of Science Society, vol. 25, (2010), pp. 171–88; H. Hecht, J. Gottschalk, “The technology of mining and other technical innovations”, chap. 30 (pp. 526–542) in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

Introduction: The Core Themes

137

a one-year trial of the use of windmills for draining the Dorothea Landskron colliery, an undertaking which was moved to the Catharina colliery in the spring of 1680. The plan was to raise the pit water from the mine by means of a pump assembly attached directly to a windmill, the so-called direct, or immediate, windmill (“immediate Windkunst”) solution. In August of 1680, Leibniz then presented a new arrangement in the form of a plan, which had been first devised by a Dutchman, namely by the mining official Peter Hartsinck (or Hartzingk) who died in that year. This alternative plan – which Leibniz had previously rejected but now advocated – envisioned that the windmills would not be used to power the pumping machinery directly, but would rather form part of a pumped-storage system. The service water, which was used to drive water wheels attached to the pumping machinery, was to be returned from the collecting pond below the prime mover to its original storage pond above the water wheel by the use of wind power. This was the so-called indirect or ‘mediate’ windmill (“mediate Windkunst”) solution. A commission then decided that the direct or “immediate” system should continue in operation at the Catharina colliery, while, simultaneously, the indirect or “mediate” system should be deployed at the Zellbach colliery, thus making use of two separate windmills. The preferential trials of the direct system proved to be very protracted, due to a variety of circumstances. To begin with, the employment of new pumps proved to be controversial, as did the use of control mechanisms for a steadier, or more uniform operation, of the windmill and, in addition, the aforementioned system of power transmission using compressed air was contemplated. As a result, the costs increased to over 2000 Taler by the middle of the year 1683 and, on December 6 of that year, duke Ernst August ordered the suspension of payments by his court to the mining company until the efficiency of the windmills could finally be established. Leibniz, who previously had to contribute only a third of the costs, now agreed to the continuation of the trials for a further year entirely at his own expense. Two new test series, using the direct or “immediate” method, were carried out in 1684 in the absence of Leibniz himself at the Catharina colliery but, alas, with only partial success, mainly as a consequence of the erratic wind supply in the mountainous environment. Because of the varying strength and direction of the wind, Leibniz pursued simultaneously, from the beginning of 1684, his “mediate” or indirect project using horizontal windmill technology.102 In this system, the vanes of the wind turbine rotated horizontally about a vertical axis which allowed the wind power to be 102 Cf. for example, R. L. Hills, Power from wind: A history of windmill technology, Cambridge, 1994, in particular chap. 2 (The horizontal windmill).

138

Introduction: The Core Themes

better and more uniformly regulated. For the construction of such a horizontal windmill, which was considerably cheaper but also correspondingly less efficient in comparison to a conventional windmill, the duke had promised the payment of a sum of 200 Taler on January 31, 1684. This horizontal windmill operated presumably satisfactorily at the location of the lower Eschenbach pond, but not, however, under full-load conditions. An actual practice test with piston pumps, or an Archimedean water screw system, attached to raise water was probably never carried out. Finally, after a third test series – this time in Leibniz’s presence at the beginning of 1685  – at the Catharina colliery with a directly-attached windmill failed to prove an unreserved success, the duke ordered the termination of the windmill trials, on April 14, 1685. Notwithstanding this setback, Leibniz was unable to free himself from his commitment to the Harz undertaking. In September 1685, he presented a new proposal to the duke, this time for improvement of the winding, or ore-hoisting, machinery in the ore mines using a closed-loop, or endless cable, to be powered by water wheels, and to be put to the test at three pits, owned by the duke, in the Thurm Rosenhofer mountain range. Scarcely a year later, Leibniz considered the practicability and advantage of this system to have been proven, but he nevertheless accepted (at least for the time being) the termination of the test series in the light of outstanding repair and maintenance work at the pits. At the end of the year 1686, Leibniz finally departed from the Harz mountains, where he had spent a considerable portion of the previous seven years. Almost another seven years were to intervene before (in 1693) the challenge of improving the Harz mining processes would once again capture his interest. Leibniz’s activity in the Harz mining district for the period from February 1684 to August 1686, i.e. during the time of the final three test series with the direct or “immediate” wind-mill technology at the Caterina colliery, as well as with the horizontal windmill technology and the ore-lifting techniques at the Thurm Rosenhof pit, is reflected above all in his general political and historical correspondence at this time. Leibniz’s most important correspondent in relation to his mining interests was surely Jobst Dietrich Brandshagen, who supervised the trials and experiments during his absence and recorded the financial accounting in writing on his behalf. Leibniz’s correspondence with Brandshagen (between 1677 and 1690) is spread between his general political and historical correspondence and his correspondence in mathematics, science and technology, for this period. On the other hand, reports, accounts and sundry communications, sent by the master carpenter Hans Linsen to Leibniz, belong to his correspondence in the area of engineering and technology and include, firstly, those from the summer and fall of 1683 relating to work on the direct or “immediate” windmill at the Catharina colliery, secondly, those

Introduction: The Core Themes

139

relating to a probably failed effort in 1685 to secure an order or commission for the implementation of the horizontal windmill technology, and thirdly, those for the period between November 1685 and March 1686 during which the use of a closed-loop or endless cable in the winding machinery was being investigated at the Thurm Rosenhof mine. For his part, Linsen was, throughout the period in question, willing and in a position to assist Leibniz in acquiring wooden models for his technical designs. In relation to this important correspondence with Linsen, stands a range of minor correspondences and communications with tradesmen, smiths and material suppliers, which document above all financial accounts and reveal expenditure for materials and labor. Leibniz’s knowledge of mining was not limited to his own practical experience in the Harz district. Contacts with persons from other mining districts in Germany and Europe frequently came to the fore. Early in 1687, for example, there developed an extended correspondence between Leibniz and the mining engineer Friedrich Heyn, who had recently returned from England. In a letter of November 30, 1686, to the Harz resident and apothecary, Johann Christian Wachsmuth, Heyn lauded the knowledge he had gained during his stay in England, referring among other things to Robert Boyle’s process for making phosphorus, to a process for the desalination of sea water, and to a process employed by Prince Rupert of the Rhine for tempering iron, or for the production of the alloy named after him (‘Prince Rupert’s metal’). On the basis of his practical experience in English mining, and of his familiarity with English mineral ores, Heyn was in a position to introduce himself to Leibniz as a prospective assistant on February 6, 1687. In this letter from Lüneburg, he reported about a new powerful water wheel-powered pumping machine, with rod engine-like sectional components, that had been designed by Johann Joachim Becher and successfully deployed and operated, following Becher’s untimely death in 1682, in the mining district of Cornwall. The new machine, Leibniz was told, incorporated neither a standard “suck and press” pumping-system, nor a scoop water wheel system, but consisted rather of a “Taschenkunst” or rag and chain pump (also known as a chain of beads, or paternoster pump) of a type previously used in Hungary and that had already been described by Georg Agricola in De Re Metallica Libri XII (1556). The novelty of the Cornish technology,103 as Leibniz was told, was that it incorporated not just a single chain pump but rather a series of stages, comparable to the sections of a “Stangenkunst”, or rod-engine transmission system, and involving 103 Cf. G. Hollister-Short, “Leads and lags in late seventeenth century English technology”, History of Technology, vol. 1, (1976), pp. 159–183, and “The vocabulary of technology”, History of Technology, vol. 2, (1977), pp. 125–155.

140

Introduction: The Core Themes

pumps of a kind that might operate using several pipes of different measure, in either perpendicular or inclined shafts, and at depths of up to 100 or more fathoms. The power supply could come from wind-power, water power, horse power or even manpower. In a further letter of March 26, 1687, Heyn reported further, but now in a more cautionary fashion, about the new machine in Cornwall. The perfection of this machine had taken three years and had involved an investment of more than 15 thousand Taler. Once fully functional it had brought the operating company a monthly return on its investment of eleven hundred Taler, or two hundred and fifty pounds sterling. Alas, his most recent intelligence from England was that the machinery had, in the meantime, come to a complete standstill, as a consequence of the vein having been cut off and of a mining accident. And Heyn offered to reveal the details of the Cornish machine to Leibniz using a model of the device. Heyn also provided Leibniz with further information about Becher’s demise, his family situation, his legacy, and liabilities. He also informed him about Becher’s writings – his chemical writings in particular – and specifically about the satirical work entitled Närrische Weißheit und weise Narrheit (foolish wisdom or wise foolery/ folly’ish wisdom or wise folly) of 1682, in which the author had ridiculed discoveries and projects of a range of contemporaries including Leibniz himself. Though not mentioned in Heyn’s letter, the work in question contained, as an appendix, an additional work entitled Dr. Bechers kurtzer doch gründlicher Bericht von Wasserwercken und Wasser=Künsten, where an invention the author claimed  – perhaps that referred to by Heyn in his letters to Leibniz  – is alluded to. This was essentially a variant of the “Stangenkunst”, or rod engine technology, involving a double rotary crank mechanism and an intervening double rod mechanism. Regarding the long-established German “Stangenkunst” technology, Becher explained that it was essentially a power transmission system connecting regular, or circular, motions at both ends by means of an irregular, or retrograde linear (or alternating), motion in between. It connected a prime mover  – supplying wind power, water power or horse power – with a distant load like a flour mill. Becher’s report on waterworks and water wheels is at all events a further instance of his activity as an engineer and discoverer.104 In Heyn’s next letter to Leibniz of July 1687 – which followed a meeting of the two in Lüneburg in late June or early July – the correspondent recalled that 104 Cf. H. Breger, “Becher, Leibniz und die Rationalität”, and U. Troitzsch, “Johann Joachim Becher als Techniker und Erfinder”, pp. 69–84 and pp. 85–102, respectively, in: G. Frühsorge, G. F. Strasser (eds.), Johann Joachim Becher (1635–1682), Wiesbaden, 1993.

Introduction: The Core Themes

141

he had informed Leibniz during their meeting about yet another water mill near Ehrenfriedersdorf, in the Freiberg mining district of Saxony, that was likewise compared to the “Stangenkunst” or rod engine technology. The machine in question was most likely nothing other than a technically improved version of the so-called “Ehrenfriedersdorfer Radpumpe”. This was essentially a piston-pump system, which consisted of several pump stages, arranged one above the other, and powered by a single prime mover. Just as with the machine of Becher’s design in Cornwall, the focus in Heyn’s account of the machine in Saxony was the mechanism which transmitted the power of a horse mill, or water wheel, to two or three such pump stages, arranged likewise one above the other. It had been employed – Leibniz was told – at a pit which had previously stood still for years due to a lack of adequate pumping machinery. The piston-pumps with flap valves, just like the rag and chain, or paternoster pumps, represented a conventional technology which was, however, still capable of improvement through the reduction of friction losses, as for example in the leather packing or sealing of valve-pistons. While Heyn was convinced and excited about the possibilities for the use of machines like those in Cornwall or Saxony, Leibniz viewed the prospects in a more sober vein. The modification of a machine, like that in Ehrenfriedersdorf, would in Leibniz judgement – as he outlined in his reply to Heyn of mid-July 1687 – not lead to any increase in efficiency. He then presented the following simple calculation to illustrate the point. For a mine shaft with total lifting height requirement of a hundred lachters (about 200 meters), and a desired delivery volume of half a hundredweight of water from the mine for each revolution of the water wheel above ground, a head (equal to the diameter of the water wheel) of some 5 lachters (or 30 feet), and a volume of at least 10 hundredweights of water, would be required in order to power each such rotation of the wheel. In reality, however, one would require a great deal more to compensate for the considerable frictional losses in the transmission mechanism. With this train of thought, Leibniz broached the fundamental problem in all such mechanical power transmission systems, namely the enormous frictional losses between the constituent parts of the mechanism. In his letters to Leibniz, Heyn also reported about his professional experience in salins, or salt works, and he enquired about a salt refinery being set up near the town of Einbeck. As Heyn’s attempts to find employment at such salt works proved unsuccessful, he opted to accompany Leibniz on his research tour as far as Vienna. By the time of Leibniz’s return from Italy, Heyn had become a mining official, a tax gatherer and inspector in Ilmenau. On June 6, 1690, he sent Leibniz, from Leipzig, mineral ores in which fossilized plants were to be seen. Then, in a subsequent letter from Ilmenau, on November 14,

142

Introduction: The Core Themes

1690, he expressed his pronounced interest in a new translation of A. A. Barba’s work, entitled Arte de los metales (1640), which was then being prepared by Christoph Pratisius in Hanover.105 The apothecary Wachsmuth, who had brokered Heyn’s role as Leibniz’s companion on the first leg of the Italian journey, and who had even contemplated accompanying Leibniz himself to Italy, served him not only as a supplier of medication. He also provided Leibniz with important information about the Harz mining towns, and their administration, as well as about learned travelers in the Harz mountains such as, for example, in a letter of July 19, 1687, about the Swedish mining expert Eric Odelius who, while fulfilling a royal commission, was exploring the Harz district and who – having been provided with a letter or recommendation from Wachsmuth – then desired to meet Leibniz, in Hanover, on his return journey to Sweden. On July 31, 1683, the Dutch mathematician Johann Jakob Ferguson reported to Leibniz about a technically interesting wind-powered water elevator, which he had seen during an inspection of the new fortifications of the town of Breda. The machines in use, the “Slang-molens”, required a strong wind and their performance was apparently equivalent to that of three “Ketting-molens” or chain mills. Leibniz then informed the correspondent, on August 25, about his own horizontal windmill concept, and he even raised the possibility of introducing such systems in Holland. To this he added a query about the so-called “Slang-molen” or “Ketting-molen” designs. In his reply from Amsterdam, on September 11, Ferguson compared the operation of the former to a rotating wooden spiral or helical staircase, i.e. an Archimedean screw,106 and the latter to a chain elevator system in which the water was lifted by a system of troughs, which were attached to the chain and arranged one above the other. While Leibniz’s most important innovation in mining was no doubt the exploitation of wind power, he was also very much occupied with waterpowered and water-raising machines, and in this regard too, he tried to obtain information about corresponding developments, and corresponding technologies, in other European countries. Thus, Noel Douceur (on December 20, 105 Cf. J. P. Melero, “The scientific revolution and enlightenment in Spanish American mining and metallurgy”, pp. 51–61 in: G. D. Rosenberg (ed.), The revolution in geology from the renaissance to the enlightenment, (The Geological Society of America, Memoir 203), Boulder, Colorado, 2009, and in particular pp. 55–57 (Álvaro Alonso Barba: The last in the alchemistic tradition). 106 Cf. G. J. Henderson, “Turn, turn, turn: The construction of the architectural spiral fluted column in the ancient mediterranean world”, Technology and Culture, vol. 59(2), (2018), pp. 363–409, and in particular, regarding the origins and development of the water screw, pp. 376–385.

Introduction: The Core Themes

143

1680), Mariotte (in March–April 1681) and Brandshagen (on November 5, 1682) reported to Leibniz about new water-lifting machines in Paris and Copenhagen and, through the intercession of Ferguson, Leibniz received, in November 1682, accurate and detailed construction drawings of a Dutch windmill. Then, in July 1684, Leibniz himself requested information about relevant publications, and projects, of the Académie Royale des Sciences in Paris, in a letter to the secretary Jean-Baptiste Du Hamel. Leibniz enquired here specifically about the activities of Samuel Morland, who had been sent to France in early 1682, by the English king Charles II, in order to gain knowledge and experience for the further improvement of English waterworks and water-lifting machines. Morland’s involvement was in the scheme, which Louis XIV had in hand, known as the Machine of Marley,107 an installation that was planned and carried out between 1681 and 1683. In January 1685, Leibniz enquired once again about the scheme, this time in a letter to Claude Comiers. Leibniz’s involvement in mining continued until August 1685, when duke Ernst August ordered the cessation of his activities in the mines against his clearly formulated wishes. Nonetheless, by the middle of 1687 at the latest, Leibniz had come to terms with the fact that his involvement in Harz mining was not desired. Six years later, however, a proposal made by two moneyers, Johann Jacob Jenisch and Rudolf Bornemann, to increase the production in ore mining by employing a small number of horses to power the winding machinery, led to a revival of Leibniz’s interest in the ore mines. When he learned of this undertaking, at the end of March 1693, the authorization procedure was already at an advanced stage. Accordingly, he immediately approached both the chamber in Hanover and his sovereign Ernst August – who ultimately had to grant approval for the proposed venture – claiming his own priority in the matter. Since the means of realizing a profit increase had not been clearly presented by Jenisch and Bornemann, Leibniz feared that his own idea of weight compensation using an endless rope or cable might actually be applied in the enterprise. In the summer of 1693, he finally succeeded in convincing Ernst August that his work on the history of the dynasty would not be retarded by a revival of the Harz project, since he would be able to delegate the execution and supervision of the work to others. Thus, the trial of Leibniz’s proposals, at his own expense, received short-term approval until the end of the year 1693. The application of his rivals was then put on hold for the time being. For the execution of the skilled manual work, Leibniz was able to obtain the services of Hans Linsen and fellow craftsmen or tradesmen and, for 107 Cf. H. W. Dickinson, Sir Samuel Morland: Diplomat and inventor, 1625–1695, Cambridge, 1970, in particular pp. 74f.

144

Introduction: The Core Themes

supervision and procurement of materials, Balthasar Ernst Reimers was engaged as his managing agent and, as a skilled pitman, the senior mining official from Clausthal, Daniel Flach, was to be present at operation trials of the winding machinery. Details of the allocated pit, as of its nature and condition, along with the difficulties encountered in the trials are revealed in Leibniz’s extensive general political and administrative correspondence relating to his mining involvement in the years 1693–1696. As might have been expected, in light of the ill-fated series of trials of Leibniz’s proposals for the improvement of engineering methods in the mines carried out during the first half of the previous decade, he once again greatly underestimated the operability and requisite time span for his undertaking and so, at the end of 1693, he found himself trudging through a mammoth task, whose end was not in sight and which would earn him more disappointment than recognition. The years between 1693 and 1696 then marked Leibniz’s second period of activity in the Harz mining district. The improvement of the mine-dewatering pumps, and an increase in the efficiency of the winding machinery for hoisting ore, were at the center of his interest at this point. He contemplated the possibility of replacing horse mills, as well as the overshot reversible water wheel, as power sources by using a rod-engine power transmission system from a remote water wheel to the pithead, and not just for operating the pumping machinery alone, as had previously been done, but also for the winding or hoisting machinery. In order for such a combined system to function properly, the overall power requirement needed to be significantly reduced, and Leibniz thought of achieving this, on the one hand, by employing an endless or closed-circle winding cable or chain. In addition, he conceived a tugging or towage device, having a switchable pinion gear mechanism, that would transform the above ground alternating linear motion, firstly, into the vertical alternating linear motion of the pump or piston rods, by employing a standard cross-shaped lever-system located at the pithead and, secondly, into the circular motion of the winding machinery, by means of a capstan or roller drive also at the pithead. Thus, in theory at least, the objective would be achieved of powering both the pumping machinery (vertical alternating linear motion) and the winding machinery (circular motion) using a single vertical water wheel,108 with its rod-engine transmission system. Progress towards the completion of the construction, and testing, of the requisite machines proved, however, to be very protracted. It was only in 108 Cf. T. S. Reynolds, Stronger than a hundred men: A history of the vertical water wheel, Baltimore (Maryland), 1983, and in particular chap. 3, pp. 122–195 (Continuity: The traditional vertical water wheel at its pinnacle, c.1500 to c.1750).

Introduction: The Core Themes

145

February 1694, that Leibniz was able to connect, for test purposes, the tugging system, being powered by the rod-engine transmission line, with the capstan or roller drive of the winding machinery at the pithead. Here the additional tugging system was mounted on a linkage along the transmission line, located at a switching point about halfway between the water wheel and the pithead. The system proved to be functional at first and was demonstrated, on February 18, 1694, in Leibniz’s presence, to the mining officials. On the occasion of that demonstration, 4 tons of ore were hoisted in an hour before the machinery came to a standstill. In the course of later hoisting trials, further dysfunctions were experienced and there ensued contention and conflict with the Mining Office in Clausthal, a matter which was duly reported to the Chamber in Hanover. Leibniz delegated the supervision of the trials at the pits to Balthasar Ernst Reimers during his absence, whereas the juror Zacharias Pöhler emerged as his main opponent or adversary in the undertaking. On April 16, 1694, Leibniz reported to Crafft about damage (perhaps even sabotage) to the rod-engine machinery, and about the opposition and obstruction being experienced from the jurors and engineering officials. He also included a sketch of the damaged rod engine system, illustrating the water wheel location, the pithead, the rod-engine transmission line and the point where the towage system, for the winding machinery, was connected to it, and he completely rejected any blame on his part for the damage incurred. Crafft kept Leibniz informed und up-to-date about the matter, for example in his letter of May 20, 1694. The rival party, he was informed, had in the meantime conceded that Leibniz’s combined system could function under certain favorable conditions as, for example, when the residual water level in the mine was low. However, in the event of the quantity of water in the pit being considerable, the entire power of the prime mover would have to be applied in order to operate the pumps alone. According to Crafft’s report, the senior mining official, Otto Arthur von Ditfurdt, was attempting to bring the rival factions to their senses by pointing out that, in the event of a continuation of the trials, one of the parties would in the end have to bear the costs. The Chamber president and privy counsellor, Albrecht Philipp von dem Bussche, too had advocated the suspension of the trials. And even Crafft himself could not exclude the possibility that the juror Pöhler might indeed be vindicated in the end. And so, after the situation for Leibniz’s efforts to improve the ore-hoisting methods had considerably deteriorated, he reverted to the mine pumping machinery in the knowledge that his idea could only be successful in the long-run, if he were to succeed first in constructing energy-saving pumps. Instead of using leather obturator rings, he wanted to provide the pump cylinders with valves in order that the previously

146

Introduction: The Core Themes

existing friction losses might be reduced. The task of fabrication of the pumps, Leibniz once again entrusted to Reimers, who in turn kept him informed about the progress of the work in hand. In September 1694, the new pump was ready for use, but the testing and trials were drawn out into the year 1695, in particular because of lack of cooperation on the part of the mining office and the mining officials. Reimers’ letter, from early February 1695, in which the correspondent reported about the preparation of the trial operation, contains the final report about Leibniz’s efforts at the time for improvement of the pumping machinery. 5.2 Transportation To the field of power technology belong certain themes from the area of transportation technology, and which also arose occasionally in Leibniz’s correspondence. In September 1683, Georg Mohr reported about Nicolaas Witsen’s tract on ancient and contemporary shipbuilding, entitled Aeloude en hedendaegsche Scheeps-Bouw (1671), a work that also attracted Leibniz’s interest and from which he made extracts. In preparing his Italian journey, Leibniz established contact with a certain G[-] S[-] Schmid from Sulbeck, near the town of Einbeck, concerning the improvement of coaches and carriages. However, in the sole surviving item of this correspondence, dated July 17, 1687, Schmid had to admit his inability to complete the fabrication of his “Schese rolandte”, but he did include a detailed drawing of such a carriage or coach. Leibniz’s vision of a stage (or post) coach that could travel from Hanover to Amsterdam in six hours was reported, perhaps inadvertently, by Johann Daniel Crafft to Johann Joachim Becher, and it was ridiculed by the latter in his satirical work Närrische Weißheit und weise Narrheit (1682). Five years later, this was referred to, not only by Heyn (in his letter of March 26, 1687) but also by Friedrich Meurs von Blauenstein in a letter he wrote from Dresden, on February 28 of that year. 5.3 The Steam Pump and Steam Engine By mid-1696, the second period of Leibniz’s involvement in mining in the Harz mountains had by and large come to an end. Power technology continued, nonetheless, to be an important topic in his correspondence after 1696, above all in the context of the exchange of ideas with Papin about his steam pump as well as about the possibility of using steam, and other vapors, to power a machine or a vehicle. The starting point was Leibniz’s conjecture, in his letter to Papin of November 18, 1697, that the explosive effect of gunpowder could be attributed to the compression pressure of the air. As is clear from Papin’s reply, on December 5, this line of thought reawakened memories for him of his earlier work Nouvelles experiences du vuide, avec la description des machines

Introduction: The Core Themes

147

qui servent à les faire (1674), from the time when he was assistant to Huygens in Paris, and perhaps also of his more recent article “Excerpta … ex litteris … de novo pulveris pyrii usu”, in the Acta Eruditorum of September 1688. On the basis of his calculations carried out while in Paris, he had concluded that the air contained in gunpowder causes the force released in gunfire. In order to be able to make more advanced pronouncements here, he explained to Leibniz that he would need to carry out further research on the powder and its constituent parts. Then, a week later, on December 12, 1697, Leibniz greeted their mutual agreement about the nature and power of gunpowder on the basis of experiment. On April 20, 1698, Papin then reported that the landgrave, Charles of HesseCassel (Karl von Hessen-Kassel), had charged him with the determination of the origin of the salt contained in salt or brine wells. In connection with this, he had carried out experiments on lifting water from a depth using the power of fire, or of steam. In addition, he announced that he had conceived far more important applications for the new power source than pumping water from a depth. Thereupon, on April 24, Leibniz enquired, as to whether Papin had made use of a principle of dilation, or of expansion, in raising water by means of the power of fire or steam. This was indeed a matter, which he himself had also contemplated and, concerning the realization of which, he now wished to consult the correspondent. Then, on August 4, Papin confirmed that he had in fact employed the expansion of steam, but in such a way that he could exploit both the suction and compressive effects. Referring to his article “Nova methodus ad vires motrices validissimas levi pretio comparandas”, in the Acta Eruditorum of August 1690, in which he first published the principle of the atmospheric steam engine, he expressed the conviction that the power of fire or steam might indeed find other applications besides the raising of water. Papin related that he had constructed a model of a vehicle, powered by steam, that operated on water in a pan or pot. However, he doubted that this form of propulsion would be suitable for normal wagons or carriages on land, above all because of the imperfections of existing roadways. On the other hand, he believed that he himself possessed the competence to build a marine vehicle powered by steam. Leibniz, replying four days later, on August 8, concurred with the view that the expansion of steam could produce a greater effect than the atmospheric pressure accompanying the condensation of steam. The expansion of steam had the same effect as the explosive power of gunpowder in a receptacle, whereby water had the advantage of not behaving so explosively on ignition. Like Papin, he had also contemplated the possibility of employing the expansion of other liquors or vapors in place of water vapor or steam. Water was,

148

Introduction: The Core Themes

however, more practical as it was freely and plentifully available everywhere, he told the correspondent. Furthermore, he greeted the fact that experiments, which he himself had contemplated – but had been unable to carry out due to a lack of resources in Hanover – in order to test the superiority of a steam engine over a pneumatic engine, had now been carried out by Papin. He himself, just like Papin, had previously contemplated the use of such an engine to power a vehicle and to facilitate transport. Then, Leibniz outlined his own ideas about the use of pneumatic machines, referring to a device he had contemplated, which would use mercury for sealing or making airtight the contact between a piston and a pump cylinder. This idea came no doubt from his practical experience in the Harz mining district, where wooden rather than metal pumps were being employed. In the highly corrosive environment there, water was used for making the contact between the piston and the cylinder airtight. The idea, which he now presented to Papin, was that mercury could balance (or equalize) the air pressure inside the cylinder produced following the expansion of water vapor. At first, he had contemplated such machines for improving transportation, but then he had become skeptical regarding their aptitude (or suitability) for the purpose. Following further experiments, Papin reported, on August 28, that he had been able to pump water only to a height of 70 feet using steam power. His recently gained knowledge included ascertainment of the fact that a small increase in the degree of heat would lead to greater effect. He believed one could achieve – through the further development of such machines and the use of higher degrees of heat – that a pound of water would produce a greater effect than a pound of gunpowder. As regards Leibniz’s ideas for the improvement of transportation, Papin underlined their importance and urged Leibniz, in the event of him being unable to implement these in practice, to at least make them available to posterity through publication. However, Papin cast doubt on the functionality of Leibniz’s mercury-pump idea, primarily because it contained three interlaced tubes. The alternating movement of the tubes, and the mercury, would inevitably lead to considerable resistance losses. Furthermore, he had, through experimentation, gained the insight that the effect of gunpowder increases with the resistance to be overcome. It appeared that gunpowder would then set off its charge more completely and, accordingly, provide a greater effect or yield when confronted with a high resistance, for example in raising a column of water. Finally, he insisted that the means to control the expansion of the exploding gunpowder conglomerate would need to be researched, and found, in order to obtain the greatest benefit.

Introduction: The Core Themes

149

As regards the connection between the strength of the expansion force, and the height attained in lifting a body by means of steam power, Leibniz argued – in his reply on September 7 – that consideration ought to be given to the circumstance that force was actually being lost through the cooling of the steam during expansion, that is, that energy was being transferred to the surroundings not only as work, a premonition perhaps of what was later to become known in thermodynamics, or the science of heat,109 as an adiabatic process. Leibniz wanted to organize his thoughts concerning transport or transportation and, accordingly, passed over the matter in this letter. As regards Papin’s objection to his mercury pump idea, he responded that, the greater the length of the pump cylinder (and accordingly of the stroke of the piston), the smaller the friction would be in relation to the performance of the pump, since the friction increased in relation to the cylinder diameter while the performance grew in proportion to the square of the diameter. As Papin was not able or willing to communicate any further details of his research on the steam pump – as he made clear in his letter of October 9, 1698 – the considerations regarding the matter ended at this juncture. Papin, however, did report to Leibniz, on June 18, 1699, about the steam pump constructed by Thomas Savery,110 and the patent granted to him by the English parliament for the invention.111 However, the pump had failed to live up to the expectations raised by its inventor, Leibniz was told. Alas, Papin was not in a position to provide him with a design description. Savery’s tract The miners friend: or, an engine to raise water by fire appeared in 1702 and, in the year 1704, he was (no doubt with Leibniz’s knowledge) invited to provide a description of his steam pump, and to demonstrate his invention, at the Court in Hanover. The visit 109 Cf. D. S. L. Cardwell, From Watt to Clausius: The rise of thermodynamics in the early industrial age, Ithaca (NY), 1971 and Ames (Iowa), 1989, in particular chap. 1, pp. 1–31 (The origins of the science of heat). 110 Cf. for example C. Matschoss, Geschichte der Dampfmaschine: Ihre kulturelle Bedeutung, technische Entwicklung und ihre großen Männer, Berlin, 1901 and Hildesheim, 1983, in particular part “B. Die technische Entwicklung der Dampfmaschine”, pp. 32–43; H. W. Dickinson, A short history of the steam engine, Cambridge, 1939 (reprinted 2010 in the Cambridge Library Collection, Books of enduring scholarly value), in particular Part I, chap. II, pp. 18–28 (Savery and his fire engine), and (facing p. 22) plate I; D. S. L. Cardwell, Steam power in the eighteenth century: A case study in the application of science, London, 1963; R. L. Hills, Power from steam: A history of the stationary steam engine, Cambridge, 1989 and 1993 (reprinted 1995, 1997), in particular chap. 2, pp. 13–30 (The impellant force of fire; The first steam engines, Savery, Newcomen (1600–1730)). 111 Cf. S. Bottomley, The British patent system during the industrial revolution 1700–1852: From privilege to property, Cambridge, 2014, in particular chap. 8, pp. 231–240.

150

Introduction: The Core Themes

to Hanover never did materialize, however, and Savery’s letter of October 7, 1704, marks the end of Leibniz’s indirect correspondence with him. As regards Papin, he sent (in the year 1707) a monograph to the Royal Society, in which he described a design of an engine which he had developed on high-pressure principles and, in the following year, he returned to London to seek support for his invention. Whereas Leibniz had admired it, and suggested refinements, Newton turned it down, and Savery criticized it most severely, even accusing Papin of poaching his ideas.112 5.4 Other Enginery Some other discoveries of Papin were also discussed in correspondence with Leibniz. Thus, in his letter of September 21, 1699, the correspondent reported how, in a coal mine, he had successfully employed the centrifugal pump of whose merits he had long sung the praises, namely the so-called ‘Hesse pump’, together with a long air conduction pipe made from wood and serving as a mine aeration or ventilation system. In his reply, on October 30, Leibniz referred to the connection between breathing difficulties and the extinguishing of lamp flames in the pits, both of which he attributed to inadequate air circulation. Already in the year 1692, the Hesse pump had been employed for the air exchange in Papin’s submergible vehicle, during its trials on the river Fulda. It was now also to be the key element of a machine, for seawater desalination, and with which fuel use might be economized. Papin sent Leibniz a detailed report, on December 3, 1699, about the first successful experiments with the machine, and about the role played by the Hesse pump. Leibniz, as he informed Papin, on March 10, 1700, was acquainted with a new process, for transporting earth, used by the renowned French military engineer, Sébastien Le Prestre de Vauban, between 1699 and 1703 on the construction site of the fortification works at Neuf-Brisach (Neu-Breisack).113 Here new machines, which were driven using manpower and horsepower, were in operation. In Leibniz’s view the discovery was “pas fort considerable” but, 112 Cf. their remarks accompanying a translation from the French of Papin’s monograph and transcripts of his proposals in: A. Smith, “A new way of raising water by fire: Denis Papin’s treatise of 1707 and its reception by contemporaries”, History of Technology, vol. 20, (1998), pp. [139]–181, and also A. Smith, “‘Engines moved by fire and water’: The contributions of fellows of the Royal Society to the development of steam power, 1675–1733”, Transactions of the Newcomen Society, vol. 66, (1995), pp. 1–25; D. P. Miller, “A new perspective on the natural philosophy of steams and its relation to the steam engine”, Technology and Culture, vol. 61(4), (2020), pp. 1129–1148, and in particular pp. 1132–1134 (Steam and the natural philosophy of the vacuum). 113 Cf. J.-D. G. G. Lepage, Vauban and the French military under Louis XIV: An illustrated history of fortifications and strategies, Jefferson (North Carolina), 2010, in particular p. 23.

Introduction: The Core Themes

151

nevertheless, he sent Papin a sketch or drawing as a sign of respect for the landgrave. Here Leibniz also referred to a news report in the Gazette d’Amsterdam, of February 25, 1700, with information about a new machine with the help of which one could transport a large quantity of sand from one location to another. In Leibniz’s correspondence between 1699 and 1701 with other correspondents, like Magnus Gabriel Block, other recent developments in technology and engineering were discussed. Thus, on January 10, 1699, Block informed Leibniz, about machines of the Swedish engineer Christopher Polhammar (later called Polhem),114 which were being used for quarrying out stone. Polhammar had developed a conveyor system, with special conveying machinery, for the ‘King Charles XI mineshaft’ at Falun, where he had been head of the mining machinery operations since 1698 and where, at the beginning of 1700, he was elected to the position of senior mining engineer (“Kunstmeister”). As Block wrote to Leibniz, on June 24, 1699, Polhammar’s machine was particularly suitable for inclined or slanting pits. Leibniz, replying on September 8, was able to point out – indeed from his personal experience – that the mine pits in the Harz mountains were not only slanting but that, in addition, their slope varied along the veins. 6 Engineering Mais je estimeray peu tout cecy, si je ne voyois moyen de reduire les problemes de Mechanique aux termes de la pure geometrie, et de mettre les machines en calcul tout comme les figures.115 Leibniz to François de la Chaise, April–May 1680

6.1 Ballistae – Military Engines and Engineering At the beginning of the reign of duke Ernst August in 1680, there arose a contentious dispute about the Douceur cast-iron process, referred to above in the context of Leibniz’s biography. He had purchased from the French engineer, Noel Douceur, during the reign of Johann Friedrich and with his mandate, a process for the ostensible production of malleable cast iron, a process that was 114 Cf. W. A. Johnson (trans.), Christopher Polhem: The father of Swedish technology, Hartford, Conn., 1963. 115 A III,3 N. 61, p. 192; Translation: But I would esteem all of this very little, if I did not see the means of reducing the problems of mechanics to the terms of pure mathematics, and of rendering machines as machine-equivalent figures for calculation.

152

Introduction: The Core Themes

alleged to render cast iron malleable and had an obvious military significance, in particular for improvement in the production of canons. Once in possession of the Douceur process, Leibniz could at least pride himself with the achievement in various places, such as at the Danish court. On July 6, 1683, Brandshagen reported from Copenhagen that he had spoken to king Christian V about, among other matters, the cast iron process and had read aloud to the monarch, on that occasion, the postscript of a letter from Leibniz. The full technical details of this process were, on the occasion of its original communication in 1679, kept a secret from all except duke Johann Friedrich. However, Leibniz had been informed to the extent that, in a text intended for duke Ernst August entitled “Bedencken betreffend eine Proposition von verbeßerung der Eisen Stuck und ander Eisen-manufacturen” (Thoughts concerning a proposition for the improvement of [cast] iron and other iron manufactory processes) from June 23, 1684, he was able to describe the Douceur roasting or annealing process. A similar process, one comparable to that of Douceur, was the production of quality damascene steel, which had been a subject of interest at European courts since the late middle ages.116 The matter arose in the letters of Brandshagen and Martin Elers sent to Leibniz from Copenhagen, in August or September 1683 and August 1684, respectively. Elers also enquired on this occasion about a military bridge which, according to reports, had been tested by the duke of Celle. He claimed to have made a similar discovery himself. Military technologies were likewise the subject of Leibniz’s correspondence with Brandshagen in Denmark. On July 6, 1683, Leibniz was informed about the correspondent’s activities with the Danish artillery. Four years later (on July 23, 1687), after he had quit Danish service, Brandshagen reported to Leibniz about a meeting in Hamburg with a former lieutenant of the Danish artillery. The latter had revealed to him the layout of French ballistic mortars, intelligence which Brandshagen was willing to make available to Leibniz. In the following letter to Leibniz, on August 27, he enquired about a possible trial of such a mortar. In addition, he offered Leibniz plans or layouts of Danish howitzers, and of grenade or artillery shell launchers. On September 24, 1686, Friedrick Meurs von Blauenstein reported from Dresden about his investigations of iron and steel production, which he had 116 Cf. A. Williams, The knight and the blast furnace: A history of the metallurgy of armour in the middle ages & in the early modern period, Leiden and Boston, 2003, in particular Sect.1, Appendix 2, pp. 14f., and The sword and the crucible: A history of the metallurgy of European swords up to the 16th century, Leiden and Boston, 2012, specifically chap. 3, pp. 36–38.

Introduction: The Core Themes

153

undertaken with a particular focus on military applications. On February 28, 1687, in reply to a query from Leibniz, the same correspondent referred to the production of damascene blades, and to a smelting furnace for the mass production of steel in Saxony. However, most of his innovations, referred to in this letter, served exclusively military purposes as, for example, a light armor, halberds, grenade throwers and copper coatings for canon muzzles. Civil Engineering: Urban Water Supply, Garden Design and Architecture Leibniz, and his correspondents, also contemplated the use and improvement of pumps, and pumping machinery, outside of mining in his correspondence during the 1690s. Crafft, for example, in a letter from Amsterdam on June 14, 1695, professed his interest in a type of pump with a four-sided, or rectangular, section that had been referred to by Leibniz in a no-longer extant letter of May 1695. Crafft had read the description of such a pump with pyramidal form, in the Journal des Sçavans from the year 1679, and he was hoping to obtain further information from Leibniz, as is to be seen from his letter of February 23, 1696. The new pumps, which were also to be employed for pumping water into elevated reservoirs and which in turn would serve as a reserve supply for the watermills, were intended to overcome above all the unreliability of the traditional fluvial water mills. In his reply, on March 2, Leibniz then generally elaborated the mode of operation of such flour mills, which could be powered by wind, water or horse power. Even four-sided, or rectangular, pumps could be employed, he maintained, having established himself the advantages of pumps of this kind by means of an experiment with a pump assembly, having a quadrangular cross section of 8-inch width, a 4-foot length and a 3½-foot piston stroke length. Leibniz’s involvement in the design of waterworks, like cascades, waterfalls and ornamental fountains, for the electoral gardens at Herrenhausen (in Hanover) commenced in mid-1696.117 This involvement, and commitment, is reflected above all in his correspondence with the military engineer, Andreas Du Mont. The draft of Leibniz’s letter to Du Mont, of July 21, 1696, reveals that Leibniz had received a commission, from the elector Ernst August, to work for the provision of the waterworks and fountains at the gardens in Herrenhausen. In this matter, Leibniz sought the expert advice of authorities like Du Mont. In his letter to this correspondent, Leibniz elaborated three options for the 6.2

117 Cf. K. Popp, E. Stein (eds.): Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000, in particular pp. 133–137 (Herrenhausen Waterworks).

154

Introduction: The Core Themes

development of the waterworks and fountains. The first option envisaged the construction of a vertical water wheel on the river Leine flowing through Hanover, directly opposite the gardens at Herrenhausen, with which water could be raised into a tower tank. From there, it would pass through pipes, either directly to the fountains in the gardens, or into a reservoir. Alternatively, the water wheel might be erected on a branch of the river, in the vicinity of Hanover’s new town district (the “Neustadt”), and be used additionally for urban water-supply there. This option had a disadvantage, namely that the water for the fountains would have to be delivered, through a lengthy system of wooden pipes, from the town to the remote gardens. The third – and in Leibniz’s view the best – possibility would involve the construction of a canal passing through the gardens. From a location on the river, it would pass in a straight line to the gardens, before veering back to another location further along the course of the river. The costs, Leibniz claimed, would be moderate as long as the only function was to supply water for the fountains. The exploitation of the canal for other purposes, such as navigation, would of course lead to additional expense. Because of the considerable head of water it could provide, the canal might also be used to supply water mills along its course. The engineering hydraulics works, along the canal, would be less exposed to dangers than any alternative engineering works, along the main river, and would entail no impairment of shipping traffic along the course of the river. The water could be raised into a tower tank, and from there be directed to fountains in the immediate vicinity, or alternatively be conducted by means of a ditch or a hydraulic flume supported on stands – like those used in mining in the Harz district – to other locations in the gardens. Gondolas might even be used on the canal for transportation and would represent an added attraction, he thought. The water supply to Hanover’s new town district – and perhaps the establishment there of a ‘water network’, like in London,118 or of a ‘water supply piping network’ of the type that had been developed in German, and other, cities throughout Europe,119 in the fifteenth and sixteenth centuries – would then have to be realized independently of the plans for the gardens at Herrenhausen. In his expert’s report, which was attached to a letter of July 30, 1696, Du Mont also argued in favor the construction of a canal between the river and the gardens. In addition, he recommended using the earth, obtained in the excavation 118 Cf. L. Tomory, “London’s water supply before 1800 and the roots of the networked city”, Technology and Culture, vol. 56(3), (2015), pp. 704–737. 119 Cf. C. Shulman, “The groundbreaking water supply systems of central and eastern European cities, 1300–1580”, Technology and Culture, vol. 60(3), (2019), pp. 726–769.

Introduction: The Core Themes

155

works, to build a dike as a protective measure against flooding, specifically on the side facing the town. A lock should be built at the location, where the canal and river would meet, in order to keep the water level of the canal constant, and to regulate the quantity of water for the operation of the water wheel. Such a canal might serve as a waterway for gondolas operating between Hanover and Herrenhausen. For the return flow of the water into the river, a cascade would have to be built. This would also allow for the canal to be drained on occasions in order to undertake cleaning operations. The second suggestion of Leibniz – namely that of combining the water supply of Hanover’s new town district with that for the garden fountains at Herrenhausen, by means of an extended system of water pipes – was rejected by Du Mont as being impractical. While the proposal for the construction of a canal, as envisaged by Leibniz, found the support of Du Mont in principle, he pointed out that a number of difficulties would arise, like the task of dealing with the sandy and swampy ground near the river. To avoid an erosion of the sides of the canal, the cladding of its walls would be necessary and this would greatly add to the costs. Furthermore, a lock would be required – as in the case of the first proposal – in order to regulate the water flow and to protect the canal and garden. Du Mont failed to meet Leibniz during a visit to Hanover in mid-August 1696. As is evident from entries in Leibniz’s diary, for August 13 and 14, consultations were taking place at that time, at the court in Hanover, about the planned water-fountain system at Herrenhausen. On that occasion, the decision was taken to build the facility in accordance with Leibniz’s first proposal and to forgo the construction of the canal because of the costs involved. Accordingly, Leibniz reported to Du Mont, on August 20, 1696, that a Persian or scoop wheel, of 50-foot diameter, was to be built on the river opposite Herrenhausen and, furthermore, that it was to be combined with a mill to help offset the costs. The water would pass through pipes to a reservoir, which would then supply the fountains. Leibniz regretted the rejection of his proposed plan to build a canal and he cast doubt on the calculation of the costs involved. He believed that extensive and costly hydraulic construction measures, on the main river, would be necessary and that such expense might have been avoided by the provision of a canal. Furthermore, since the canal would have been connected with an arm of the river, it would have been protected from the current and from ice formation on the main river. In contrast, the planned scoop wheel and mill, at their respective locations on the river, would be exposed to all the forces of nature. From Du Mont’s final letter to Leibniz, from the last week of August 1696, it is clear that he shared Leibniz’s skepticism about the durability of a scoop wheel on the main river. He likewise continued to adhere to his view, namely that the construction of a canal with a dike would be the best option.

156

Introduction: The Core Themes

The construction of such a canal, projected and favored both by Leibniz and Du Mont, was however never realized during their lifetimes. In the spring of 1697, Leibniz’s correspondence with the miller and master carpenter Hans Linsen enjoyed a resurgence. Linsen – who worked at the Heyersum salt works, near the town of Hildesheim  – had apparently been entrusted by Leibniz with the task of producing and testing a piston for a water pump. Furthermore, as is evident from a note of May 23, 1697, to Leibniz, Linsen had also been engaged by Leibniz to work on a model for a carriage. Linsen’s water pump was possibly intended for the waterworks at Herrenhausen; at all events, Linsen offered Leibniz his services for the undertaking on this occasion. In August 1697, the master builder Leonhard Christoph Sturm – the son of the renowned astronomer and mathematician, Johann Christoph Sturm120 – having been appointed professor at the military academy in Wolfenbüttel, in succession to Johann Balthasar Lauterbach,121 commenced a correspondence with Leibniz. Sturm had edited, and posthumously published, the chief civil-engineering work of Nicolai Goldmann (1611–1665) with the title Vollständige Anweisung zu der Civil Bau-Kunst (1696). In a letter of October 12, 1697, Sturm enquired about the possibility of his being appointed master builder in Hanover and, in a further letter of January 3, 1698, he presented himself as a master builder, a mathematics professor and a prospective preceptor at the court in Hanover. Finally, in a letter of February 3, 1698 – written just one day after the death of Leibniz’s sovereign Ernst August – Sturm additionally offered his services as draughtsman, architect, poet and polymath for the design of a “castrum doloris”, or castle of grief, in honor of the deceased elector. Following journeys to the Netherlands (in 1697), and to France (in 1699), Sturm finally obtained an appointment as mathematics professor in Frankfurt an der Oder, in 1702. The British architect John Smeaton (1724–1792) may well have been the first person to call himself a ‘civil engineer’ in English, a term that would come to refer to one who designs and constructs roads, bridges, water-supply and sanitation systems, or other other publicly funded and utilized projects, whereas in France the term ‘ingénieur civil’ (with a broader meaning than ‘civil engineer’) first appeared in the early 1800s. Overall the emergence of the civil engineer, as distinct from the military engineer, was a manifestation of 120 Cf. S. Kratochwil, “Johann Christoph Sturm und Gottfried Wilhelm Leibniz”, pp. 104–118 in: H. Gaab, P. Leich, G. Löffladt (eds.), Johann Christoph Sturm (1635–1703), (Acta Historica Astronimiae, vol. 22), Frankfurt am Main, 2004. 121 Cf. H.-H. Grote, Johann Balthasar Lauterbach (1663–1694): Professor für Mathematik, Landbaumeister und Ingenieur am Wolfenbütteler Fürstenhof, Braunschweig, 1995.

Introduction: The Core Themes

157

a development which saw the continuing attenuation of the age-old connection between engineer and soldier in the period between the seventeenth and nineteenth centuries.122 Leibniz’s correspondence with Leonhard Christoph Sturm, in 1697 and 1698, reveals at all events that the term “Civil Bau-Kunst” (or the art of civil engineering) was already well established in Germany at the end of the seventeenth century. Before his death in 1719, Leonhard Christoph himself witnessed the publication of his father Johann Christoph’s posthumous work Kurtzgefasste Mathesis Oder Erste Anleitung zu Mathematischen Wissenschafften (1717), whose 12 chapters or sections included those on military engineering (“Der Kriegs=Bau=Kunst”), and on civil engineering (“Der bürgerlichen=Bau=Kunst”), as well as his own Architectura Civili-Militaris (1719). 6.3 Engineering Manufactories In the fields of engineering and technology (as in natural philosophy and physics), Leibniz’s correspondence with Papin was the most important from the mid-1690s. From his letter of August 30, 1696, Papin’s inventive genius and richness of ideas, but also his frustration, are evident; here he explained to Leibniz that he had conceived numerous new machines of which he could hope to realize not even half during his lifetime. Leibniz, in his reply on September 24, encouraged the correspondent to continue to dedicate himself to the progress of technology and he promised him his support in the endeavor. In this context, Leibniz too complained that he was not in a position to realize his own engineering discoveries. He specifically mentioned, in this context, his calculating machine which, even after 24 years of development, still had not been completed, principally due to lack of time and assistance. In the fall of 1696, Papin submitted a petition for his release from the service of landgrave Charles of Hesse-Kassel, a copy of which he sent to Leibniz on October 4. In this petition, Papin emphasized the importance of his centrifugal ‘Hesse pump’ of 1689 (called the “Rotalis Suctor et Pressor Hessiacus”), especially for shipping and navigation. He desired to return to England, because navigation had a special significance there. Leibniz expressed his skepticism, and he was relieved when Papin’s petition to the landgrave was rejected, as he 122 Cf. for example C. Mitcham, “Engineering as a productive activity: Philosophical remarks”, pp. 80–117 in: P. T. Durbin (ed.), Critical perspectives on nonacademic science and engineering, (Research in Technology Studies, vol. 4), Bethlehem (PA), London, Toronto, 1991, in particular pp. 82ff. (Where engineering comes from); A. W. Skempton, M. M. Chrimes, R. C. Cox, P. S. M. Cross-Rudkin, R. W. Rennison, E. C. Ruddock (eds.), Biographical dictionary of civil engineers in Great Britain and Ireland. Volume 1: 1500 to 1830, (The Institution of Civil Engineers), London, 2002, in particular pp. xvii–xxxiv (The practice of civil engineering 1500–1830).

158

Introduction: The Core Themes

learned from a letter of January 14, 1697. Four months later, on May 13, Papin was able to report that, while his main objective in submitting the petition had not been achieved, he had been successful in having some of his demands met. Thus, he was given better conditions for certain research activities that were concerned with glass-kiln development, in particular for the improvement both of a process for glass melting, using his ‘Hesse pump’, and of a newly-developed oven. His efforts were directed, first of all, to testing and bringing to perfection a scaled-down version of the process. The realization on a large scale, however, was to be subject to a directive of the landgrave. Replying on May 25, Leibniz stressed the importance of glass melting for optics and recalled Tschirnhaus’ research on concave mirrors and convex lenses. Papin was then able to report, on June 19, that his trials on small-scale glass melting had, in the meantime, been successfully concluded. He was confident that a scaled-up version of the process would also work. The landgrave had observed Papin’s experiment, and he had given instructions for the construction of a laboratory for the continuation of the series of experiments. Nonetheless, Papin had to show patience since, to begin with, a new oven had to be constructed. Then, on April 20, 1698, he could report to Leibniz that construction was under way. The new melting furnace – a key element of which was Papin’s own ‘Hesse pump’ – was, however, not intended for the production of polished sheet or mirror glass, but solely of iron retorts or alembics. Finally, on October 9, 1698, Papin sent Leibniz a detailed description and a drawing of his new blast furnace. In this blast furnace, the air was passed both above and below the burning wood using a centrifugal pump. The flames were blown by the ventilator pump in the direction of the melting crucible, and were simultaneously drawn to there by the suction effect of the smokestack. Through openings in the upper oven wall, a heating plate could be introduced and used for the extraction of the glass melt. This could also be carried out using a machine, the correspondent reported. The blast and suction air regulation would prevent the flames from rising through the openings (and thus impairing the servicing of the melting crucible, or even causing the curtailment of the fire). Papin informed Leibniz that the glass melt produced in the oven could be used for various product applications, such as mirrors, window glass or hollow cylinders. Furthermore, the oven could also be used for the production of iron products, by virtue of the great heat impact of the fire. Papin conceded, however, that he had not been able to realize the full potential of his invention, since his blast furnace was not large enough. In particular, the height of the smokestack was restricted to two feet.

Introduction: The Core Themes

159

In his reply from the third week of October, 1698, Leibniz recalled his own earlier experiments with melting furnaces, especially those carried out, in the summer of 1679, at the time of his cooperation with the discoverer of phosphorus, Heinrich Brand, as well as the ovens built by Johann Daniel Crafft. All these experiments had, however, not been undertaken using a blast furnace. Leibniz, although impressed by Papin’s innovation, was of the opinion that, to begin with, ordinary bellows might be employed. Since the fire could now be regulated, the use of a heating plate for the removal of the molten glass seemed to him to be superfluous. The melting operations could be carried out entirely on such a plate, provided the intensity of the fire was not so great as to be able to damage the plate. Leibniz acknowledged that he himself had often contemplated the process of glass melting, and he continued to have the ambition to develop new ideas regarding it. Papin, writing on November 17, emphasized the superiority of his method in comparison with the normal process, especially as regards the production of plate or mirror glass. In the conventional process, the glass melt was drawn from the oven and then polished. With the new process, the molten glass was to be drawn onto oven plates. To begin with, he wanted to test this, using smaller plates. However, the key innovation in his new oven was that the flame passed both above and below the material to be heated. Leibniz, for his part, as he wrote in his reply of November 28, was not really convinced that Papin’s process was entirely new. In his view, such oven plates were already being used in the production of mirror glass. However, like Papin, he considered it worthwhile to render the polishing of the plate superfluous. Papin’s final letter of the year 1698, written on December 11, contained a request to Leibniz for additional information regarding the normal process of producing plate or mirror glass. Papin confessed that his own knowledge was based on observations made on the island Murano, near Venice, in the year 1681. There, parts of a hollow cylinder were moved on a large stone into an oven. The molten glass was then spread out over the stone with the help of a draw-plate, or drawing die, before the whole was again removed from the oven. Magnus Gabriel Block, in a letter of June 24, 1699, to Leibniz, described (with the help of a sketch) a smelting process of Francesco Maria Levanto, who was one of a number of foreign smelters and chemists who attempted to improve copper smelting at the Falun mine in Sweden.123 Leibniz had already asked 123 Cf. H. Fors, The limits of matter: Chemistry, mining and enlightenment, Chicago and London, 2015, and in particular chap. 3, pp. 43–75 (Chemists in the mining business), and specifically (regarding Levanto) p. 66.

160

Introduction: The Core Themes

correspondents on a number of occasions about this process as, for example, on January 16, 1694, in a letter to Gustav Daniel Schmidt, and on July 23, 1697, in letters to Lorenz Hertel and to Johann Gabriel Sparwenfeld. At the heart of the process was a reverberatory furnace – or, one that isolates the material being processed from contact with the fuel, but not from contact with combustion gases – for roasting, or calcination, that could be fueled with twigs or branches. The roasted blende, or the ore produced by calcination, was then to be melted in an air furnace but was, however, carried away by the wind. As the desired success failed to materialize, Levanto was out of pocket following the trials of the process. This fate Levanto shared with Johann Kunckel von Löwenstern, who subsequently tried out the process, according to Block’s report. Leibniz proposed operating the roasting furnace, and the air furnace, in a different way. He wrote to Block, on September 8, 1699, that one ought to leave the material longer in the roasting oven, in order that it becomes thicker, and to power up the air furnace slowly in dependence on the consistency of the material. Reverberatory furnaces (alongside blast and cementation furnaces) were also employed in the eighteenth century Britain and Europe,124 for tempering and annealing bar or rod iron, as well as for china or porcelain ovens,125 and for glass ovens in manufactories, and presumably also in Tschirnhaus’ new glass making plant, about which he informed Leibniz, in letters on May 18 and October 16, 1700, respectively. He had even set up a grindery, or grinding shop, for precious stones and jewels. The second of these communications provided details about his new glass-making plant and his plans for the production of convex lenses for telescopes and burning glasses. While Tschirnhaus lauded his lenses, in particular in his letters to Leibniz, the latter obtained technical details about Tschirnhaus’ laboratories from Wagner. While on an exploratory tour through Saxony – having been spurred on to undertake it by Leibniz – Wagner visited Tschirnhaus in Dresden. His host showed him the glassworks, or glass kiln, regarding which Wagner sent a drawing and a detailed description to Leibniz. As regards the ingredients used to manufacture glass, Wagner learned little or nothing, other than the fact that arsenic and borax were not being used, since they would give glass a dark color. The visit to Tschirnhaus’ 124 Cf. C. MacLeod, “The European origins of British technological predominance”, pp. 111–126 in: L. P. de la Escosura (ed.), Exceptionalism and industrialisation: Britain and its European rivals, 1688–1815, Cambridge, 2004; C. Evans, A. Withey, “An enlightenment in steel? Innovation in the steel trades of eighteenth-century Britain”, Technology and Culture, vol. 53(3), (2012), pp. 533–560. 125 Cf. the following volume of the terminated Tschirnhaus Edition: E. Knobloch, C. Krautz, M. Ullmann (eds.), Johann Friedrich Böttgers Tätigkeit am Dresdner Hof: Ehrenfried Walther von Tschirnhaus Gesamtausgabe, Series II (Official Writings), Leipzig, Stuttgart, 2000.

Introduction: The Core Themes

161

laboratory for precious stones proved to be even more secretive. The king of Saxony – or, more precisely, the elector of Saxony, Friedrich August I (and king August II of Poland) – had forbidden visits by strangers, as well as the issue of materials from there. In spite of this, Wagner was able to take a quick look inside and to take a sample away with him. He had, however, to abandon any hope of visiting Tschirnhaus’ private laboratory on his estate in Kieslingswalde, since his host had proved very secretive in the matter. Wagner, in letters on June 26 and July 21, 1700, revealed to Leibniz the tricks with which he tried to elicit as much information as possible from his conversation partners. He also went to see the architect Johann Heinrich Gengenbach, during which visit he was able make numerous drawings of a fortification model, and of other discoveries and curiosities as, for example, a pull-out or fold-out table, an Italian andiron, as well as carriages and lanterns, as he reported to Leibniz on August 1 of that year. Previously – on the occasion of the discussion of the failed trials of Levanto – Leibniz, in a letter to Block on September 8, 1699, pointed to the general difficulties in the realization and implementation of such engineering innovations. Large-scale trials often proved expensive. But these were necessary, not only for testing discoveries but also in order to establish trust in them, and so to counter the widespread skepticism towards innovations. Late in 1699, Jobst Heinrich Voigt – the head bailiff, or administrator, of the location Aerzen in the Weser Uplands – presented to Leibniz a drawing of a threshing-machine of his design. This was attached to a letter, of November 28, sent to Leibniz by another official, Cord Plato von Gehlen, in which it was claimed that the machine in question could be operated by a single person, do the work of fifteen others and, accordingly, reduce costs considerably.126 Leibniz, in his reply in mid-December 1699, expressed his appreciation of the new machine, but he did make a proposal for the optimization of the threshing-machine transmission system, namely by replacing a three cogged wheel-lantern pinion element – a central cogged wheel in a vertical plane engaging the horizontal staves of a lantern pinion on each side – with a two-wheel pulley system and, accordingly, reducing resistance. Leibniz reacted not only by proposing technical improvements like this. He also expressed his opinion regarding the widely-held view, namely that such machines actually deny the poor of potential earnings. In this context, he recalled a further instance of social change accompanying technological progress, namely that which led 126 Regarding technology and social change, cf. L. White Jr. (note 99). Regarding the threshing machine, cf. T. S. Reynolds (note 108), and in particular p. 138 (Figure 3–5, showing a water-powered threshing machine from the year 1735).

162

Introduction: The Core Themes

to the proscription of the ribbon-loom (“die strumpf und bandmuhlen”) in the year 1685 by the emperor, Leopold I, following a recommendation of the Imperial Diet at Regensburg in 1681. Leibniz rejected such concerns regarding the loss of employment through mechanization. Even if there were to be such lay-offs, there would be enough other useful occupations for those affected. At most there would be readjustment difficulties at the beginning. Leibniz also referred to Voigt’s threshing-machine, in a letter to him from the second half of January 1700. Again his basic opinion on the matter, expressed in this letter, was that one ought not to refuse the assistance of machines, or the art of engineering, on the grounds of such a pretext. Besides, there would be an infinity of alternative occupations for the hands set free by mechanization. He also referred here to a similar threshing-machine being developed at the location Linden (near Hanover) by count Franz Ernst von Platen and of which he subsequently made a drawing. The drawing of Voigt’s threshing machine reveals a human operator turning a camshaft to operate the thresher-cylinders. The carriage, to which the threshers were attached, was moved or pedaled along the threshing-floor by means of a rack and pinion gear mechanism. To deal with the faineance of workers, Leibniz proposed remuneration of the operatives on the basis of performance, namely in terms of recorded tours or working shifts. Leibniz also contemplated here the use of water and wind as alternatives to manpower as a prime mover for the threshing-machine. The former option, he found, would require the availability of a water raceway. On the other hand, in order to avail of wind power, a pumped-storage system involving the use of a windmill and a water reservoir system – similar to that contemplated for use in the Harz mining district – would be required, in order to ensure operation of the machinery throughout the autumn and for part of the winter, he told the correspondent. 6.4 Process or Chemical Engineering Further key aspects of the correspondence between Leibniz and Papin, in the late 1690s, included chemical or process engineering, and techniques for the conservation of foodstuffs. On June 19, 1697, Papin indicated that he was working on a discovery of practical importance, through which chemical processes could be carried out in fresh air, and he promised to keep Leibniz informed. A little later, on August 5, he reported that he had achieved a breakthrough. For the distillation of sulfur, he had developed distillation equipment consisting of six alembics, or retorts, in series. The outlet of the final distillation flask led into the open air, and in this retort a considerably greater quantity of spirit of sulfur, or oil of sulfur, was liquefied in comparison with the first retort. By the use of additional retorts, a complete liquefaction could be achieved without having

Introduction: The Core Themes

163

acid fumes escape into the air. Papin stressed here that his method might also be used with other combustible materials and could provide insights into other chemical processes. And, in a later letter of October 24, he continued this line of thought, referring to flowers of niter purified by sublimation, and to the extraction or production of sulfuric acid. Leibniz recognized at once the importance of Papin’s new process for the production of the strong acids, like oil of vitriol (sulfuric acid), aqua fortis, spirit of niter or saltpeter acid (nitric acid), and spirit of salt (hydrochloric acid), as is evident from his letter to Papin of November 18. Papin in turn, in his letter of December 5, 1697, emphasized the importance of spirit of sulfur, particularly for chemistry and medicine, but also for the conservation of meat. And, as he explained in his first letter to Leibniz of 1698, on January 6, the spirit of sulfur, when diluted with water, could serve as a conservation fluid for foodstuffs. He had, himself, successfully conserved pears, raspberries, apples, and plums, as well as several types of meat and vegetables. In addition, he intended investigating the conservation of fish and he offered to make such conserved products available to Leibniz. In addition, in letters of December 12, 1697, and January 6, 1698, respectively, Leibniz and Papin discussed certain medical benefits in connection with the conservation of meats, fish and fruit, like, for example, the application of the spirit of sulfur as a remedy for scurvy. 6.5 Engineering Science: Mechanics of Fluids Leibniz’s meetings in Italy, in 1689–1690, with major figures of the second generation of Galileo’s disciples included the renowned physician Bernardino Ramazzini, who was also interested in problems of hydraulics and hydromechanics, and these topics then became central issues in his correspondence with Leibniz in the year 1690. Included in their epistolary exchanges were fundamental considerations in fluid mechanics, which involved, for example, the beginnings of the theory of streamlines.127 The starting point here was the intelligence Leibniz received that Domenico Guglielmini – a physician, mathematician and engineer with whom he would correspond over several years – intended to treat fundamental questions of fluid mechanics in a tract, with the title Aquarum fluentium mensura nova methodo inquisita (1690–1691). In addition to this, Leibniz was interested in a work, planned by Ramazzini, on the 127 Cf. C. S. Maffioli, Out of Galileo: The science of waters 1628–1718, (Nieuwe Nederlandse Bijdragen tot de Geschiedenis der Geneeskunde en der Natuurwetenschappen, no. 49), Rotterdam, 1994; J. G. O’Hara, “The mathematician as engineer in the seventeenth century: Leibniz and engineering hydraulics”, pp. [77]–89 in: M. C. Duffy (ed.), Engineering and engineers: Proceedings of the XXth International Congress of History of Science (Liège, 20–26 July 1997), vol. XVII, Turnhout, 2002.

164

Introduction: The Core Themes

springs or wells of Modena, and which duly appeared in 1691 under the title De fontium Mutinensium admiranda scaturigine tractatus physico-hydrostaticus, a work that was also to have an impact on Leibniz’s ideas on earth history, which appeared in his posthumously-published Protogaea.128 In the discussions Leibniz had with Ramazzini in Modena, between December 30, 1689, and February 2, 1690, he had learned that his vis-à-vis wanted to experimentally investigate the flow of water around an obstacle in a stream. From discussions with Guglielmini, whose acquaintance he had made in Bologna about a week before his arrival in Modena, he also knew of the latter’s plans to write a tract about the laws of fluid motion in open channels. Although, Galileo’s disciple, Benedetto Castelli (1578–1643), had formulated one of the fundamental laws of fluid mechanics, namely the continuity law, in his book Della misura dell’acque correnti (1628), several other basic questions had remained unanswered as, for example, about the vertical velocity distribution in a stream. Even in the third edition of Castelli’s book of 1660, the corresponding proposition – which postulated a linear velocity distribution increasing from the river bed to the water surface – had proved to be unsatisfactory. Motivated by this, Guglielmini sought to place the laws of open-channel flow on a new foundation. When, on February 25, 1690, Leibniz enquired of Ramazzini about the progress of Gugliemini’s undertaking, the correspondent  – in his reply of April 15  – reported instead about another planned work, entitled De motu mechanico, by yet another engineer of Modena, namely Giovanni Baptista Boccabadati whom Leibniz had also met during his stay in that city. Boccabadati had been concerned above all with the problem of flooding along the Po tributaries, Panaro and Secchia, and, during the recent inundations, at the beginning of April 1690, he had undertaken observations and measurements along these rivers, an activity about which Ramazzini reported to Leibniz in this letter of April 15. In commenting on Boccabadati’s practical experience, Leibniz, in his reply of July 16, then brought up Castelli’s theorem about the vertical velocity distribution in a stream. Leibniz doubted that an exact rule for this velocity distribution in natural waters could be given, and he posed an additional question, namely concerning the increase of the velocity of flow downstream from a point where the channel depth suddenly increased, having in mind perhaps a structure at a bend or turn in the stream (like an earth wall, levee or dam), similar to that built in the river Tiber by the Dutch hydraulic engineer, Cornelis Meyer (1640–1694), and about which Tschirnhaus had previously informed him in a letter from Rome, on April 10, 1678. Meyer 128 Cf. C. Hodoba-Eric, “Artificial apertures: The archaeology of Ramazzini’s De fontium in 17th-century earth historiography”, Centaurus, vol. 62(3), (2020), pp. 522–541.

Introduction: The Core Themes

165

was a member of the ‘Accamemia fisico-mathematica romana’ and author of a tract on the fluvial navigation of the river Tiber, entitled L’arte di restituire a Roma la tralasciata navigazione del suo Tevere (1683). Leibniz’s conviction was that, at a greater distance from such a point, the velocity increase of the stream would be negligible. Then, following his return to Hanover, he received several reports about Boccabadati, and about the planned work of his on mechanics that was to be founded on the practical experience of the author in the floodplain, or flood zone, around Modena. Thus, Ramazzini referred, on April 15, 1690, to an interruption of Boccabadati’s efforts on his planned mechanics tract, that was to based entirely on restoration efforts along the Po tributaries Panaro and Secchia, and two years later, on March 30, 1692, Ramazzini reported about a further delay in the completion of the work, which, alas, was still unpublished at the time of Boccabadati’s death in 1696. As regards Guglielmini’s forthcoming tract, Leibniz, in his letter of July 16, 1690, to Ramazzini, expressed his skepticism about whether an exact rule to supersede Castelli’s might be formulated, but he did express his pleasure at the prospect of the appearance of Ramazzini’s own tract on the springs, or wells, of Modena. Leibniz learned about the appearance of the first part of Guglielmini’s tract from a letter of Bodenhausen, of September 16, 1690, and in his reply of November 5, he immediately requested that the correspondent send him information about the most important propositions in Guglielmini’s work and their foundation. Then, in the first half of November, Leibniz received a review copy of the work from Otto Mencke and, a little time later, on November 17, he sent a first opinion about Guglielmini’s book to Bodenhausen. At the center of Leibniz’s interest was Guglielmini’s postulated parabolic velocity increase from the water surface to the river or canal bed. This “scala fallacy”, as it was later called, was based of the false assumption of the applicability and validity of Torricelli’s efflux law in an open stream.129 Whether Leibniz immediately recognized, that the mistake in Guglielmini’s proposition was rooted in an inadmissible application of the Torricelli law, is not clear. In any event, he emphatically asserted that the velocity distribution postulated by Guglielmini could have no validity in real rivers and canals. However, in his anonymous 129 Cf. S. Leliavsky Bey, “Historic development of the theory of the flow of water in canals and rivers”, The Engineer, vol. 191, (1951), pp. 466–567, specifically p. 466, p. 498, p. 533, p. 565, and pp. 601–603; J. C. I. Dooge, “Historical development of concepts in open channel flow”, pp. 205–229 in: G. Garbrecht (ed.), Hydraulics and hydraulic research, Rotterdam, Boston, 1987; L. Boschiero, “Machines, motion, mechanics: Philosophers engineering the fountains of Versailles”, Technology and Culture, vol. 61(4), (2020), pp. 1108–1128, and in particular pp. 1111–1114 (Hydrostatics in the seventeenth century: From Galileo to Pascal).

166

Introduction: The Core Themes

review of the first part of Guglielmini’s Aquarum fluentium mensura nova methodo inquisita, in the Acta Eruditorum of February 1691, Leibniz desisted from any kind of criticism and restricted himself to an account of the basic tenets of the work. Guglielmini’s treatment of fundamental questions of fluid flow in open channels, in his Aquarum fluentium mensura (1690–1691), instigated Papin to publish a critique, entitled “Observationes quaedam circa materias ad hydraulicam spectantes”, in the May 1691 number of the Acta Eruditorum. This in turn provoked a réplique from Guglielmini in the form of two open letters, one addressed to Antonio Magliabechi, and the other, dated December 24, 1691, addressed to Leibniz, which were published with the title Epistolae duae hydrostaticae (1692). The dispute was essentially concerned with the issues of whether Galileo’s laws of falling bodies were valid in fluid flow, whether the velocity in the upper layers of a stream was influenced by the movement of the lower layers, and how the efflux velocities of a fluid out of an orifice, near the bottom of a cylindrical container, compared with that from an orifice of the same diameter in the bottom itself, under the same pressure head. Papin’s response to Guglielmini’s Epistolae duae hydrostaticae only appeared in 1695 in the form of two open letters, addressed to Huygens, with the titles “Lettre, touchant la mesure des eaux courantes” and “Epistola … de fluentium aquarum mensura”, respectively, as part of Papin’s bilingual miscellany entitled Recueil de diverses pieces touchant quelques nouvelles machines and Fasciculus dissertationum de novis quibusdam machinis, respectively. Here Papin repeated his objections in greater detail than in his “Observationes quaedam” of 1691. In doing so, he desisted from using mathematical or technical proofs and restricted himself to the consideration of analogies or differences between solid bodies and fluids. In this way, he believed he had refuted, or made superfluous, the objections of Guglielmini. Papin’s Recueil was reviewed (probably by Leibniz) in the August 1695 number of the Acta Eruditorum, and thus became known to Guglielmini. However, on June 22, 1696 – when Guglielmini commenced his correspondence with Leibniz – he still did not have Papin’s work to hand and, accordingly, he did not feel obliged to provide a response, or a rejoinder. He did, however, request Leibniz’s help in acquiring a copy of the work. A month later Papin had two copies of his Recueil sent to Leibniz, one of which, although forwarded by Leibniz, never did reach its intended addressee in Italy. Subsequently (on January 7, 1697), Leibniz sent Guglielmini hand-written extracts from the work. For his réplique to Papin’s criticisms in 1697, Guglielmini once again chose the form of two open letters, addressed to Leibniz and Magliabechi, respectively. However, the publication of Guglielmini’s letter (of June 5, 1697) to Leibniz in

Introduction: The Core Themes

167

the Acta Eruditorum was refused, in view of its length, and so the long-aspired to publication was finally procured by Leibniz himself only thirteen years later – namely in the first volume of the Miscellanea Berolinensia (1710) – thus bringing the dispute to a conclusion in the year of Guglielmini’s death. Guglielmini’s letter of June 5, 1697, was concerned, among other things, with his postulated parabolic velocity distribution and increase from the water surface to the canal bed on the basis of Torricelli’s efflux law, the applicability of Torricelli’s theorem to open-channel water flow (over both horizontal and inclined canal beds), and the general validity of Galileo’s laws of falling bodies in fluvial mechanics. According to Guglielmini’s Aquarum fluentium mensura (of 1690–1691), the laws of fluid flow were to be explained exclusively by the fall (or head) of the channel, the slope or inclination of the water surface, and the pressure of the water. Neither gravitation nor resistance forces were taken into account. This abstract mathematical approach could not, of course, be automatically applied to conditions prevailing in real rivers and canals. However, in his letter of June 22, 1696, Guglielmini informed Leibniz that he was preparing a new tract, which would not be subject to such restrictions. Leibniz delighted in the new knowledge emerging in the context of Guglielmini’s fluvial mechanics, including that about the nature of curl or vorticity flows, as his letter of January 7, 1697, to Guglielmini reveals. And so with the appearance (in 1697) of Guglielmini’s main work – that was based on actual engineering practice rather than mathematical abstraction – entitled Della natura de’ fiumi trattato fisico-mathematico, the academic dispute with Papin about the fundamentals of fluid mechanics lost its importance to a great extent. 7 Projects Solcher sterilitat nun zu hülffe zu kommen habe ich den vorschlag gethan gehabt, wie man unzahlbare neue und nüzliche anmerckungen die schohn unter den leuten sind, nur daß sie den gelehrten nicht bekand, herfür geben könne.130 Leibniz to Sebastian Scheffer, Mid-April 1682

The world of projects and of projectors, at the end of the seventeenth century, was symbolized by an interaction of artisans and practitioners with the world 130 A III,3 N. 342, pp. 588f.; Translation: To counter such sterility, I had made a proposal regarding how the countless new and useful annotative expressions prevalent in the population, although unknown among the learned, might be used to this end.

168

Introduction: The Core Themes

of learning. It was the lack of such interaction in Nuremberg that Leibniz complained so bitterly about in his letter to Scheffer cited here. In contrast, this interaction is clearly evident, for example, in Leibniz’s correspondence in relation to his calculating machine. 7.1 Calculating Machines The history of Leibniz’s calculating machine can be traced back to the years of his sojourn in Paris, between 1672 and 1676.131 Following early designs, dating from his time in Mainz before his stay in Paris, he had presented a wooden three-place demonstration model to the Royal Society on the occasion of his first London visit in 1673. The presentation, on February 1 of that year, was recalled by Oldenburg in a letter to him on February 9. Subsequently, an improved version of the machine, made of metal and with six entry and twelve result positions (powers of ten), came into being in Paris and it was presented to the Académie des Sciences early in 1675. It was referred to, in an entry of January 9, 1675, in the Procès-verbaux of the Académie. However, the final version of this first metallic model still remained to be presented at the time of Leibniz’s departure from Paris in 1676. Accordingly, he attempted in the years that followed to entice the Parisian clockmaker Ollivier, who had been entrusted with the construction of the machine, to come to Hanover, and the clockmaker may possibly have arrived in Hanover at the end of 1679, or in early 1680, although there is no clear proof that he actually did. At all events, when the model was finally completed, in the mid-1680s, Leibniz commissioned a larger machine with eight entry and twelve result positions. The work on this so-called ‘older machine’ was finally brought to a conclusion by the Hanover clockmaker Georg Heinrich Kölbing, in 1694, following a construction period of almost ten years.

131 Cf. L. von Mackensen, Die Vorgeschichte und die Entstehung der 4-Spezies-Rechenmaschine von Gottfried Wilhelm Leibniz, nach bisher unerschlossenen Manuskripten und Zeichnungen mit einem Quellenanhang der Hauptdokumente, Doctoral Dissertation (TU Munich), 1968; M. R. Williams, A history of computing technology, Englewood Cliffs, N.J., 1985 (and Los Alamitos, CA, 1997), in particular chap. 3, pp. 122–158 (Mechanical calculating machines); L. von Mackensen, “Calculating machines”, pp. [84]–107 in: K. Popp, E. Stein (eds.): Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000; E. Stein and F.-O. Kopp, “Konstruktion und Theorie der leibnizschen Rechenmaschinen im Kontext der Vorläufer, Weiterentwicklungen und Nachbauten. Mit einem Überblick zur Geschichte der Zahlensysteme und Rechenhilfsmittel”, Studia Leibnitiana, vol. 42(1), (2010), pp. 1–128; M. L. Jones, “Calculating machine”, chap. 29 (pp. 509–525) in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

Introduction: The Core Themes

169

Leibniz’s efforts for the completion of his four-function (viz. addition, subtraction, multiplication, division) calculating machine, from between 1680 and the mid-1690s, can be traced in his correspondence in this period. His efforts to develop his calculating machine  – about which he informed various correspondents in the spring of 1680 – appear to have also suffered due to lack of time. Detlev Clüver’s admonition, on July 26, 1680, that the completion of the calculating machine was more important than work for the Hanoverian court proved to be of no avail, not least because of Leibniz’s commitment at the time to his time-consuming windmill project in the Harz mountains. A further difficulty was the lack of a suitable skilled craftsman in Hanover for work on the machine. At all events, Leibniz was pleased to be informed by Ferguson, on November 10, 1682, about two prospective young Dutch clockmakers, brothers who were willing to travel to Hanover and take up employment there. Leibniz’s English correspondents Clüver and Robert Hooke – to whom he turned to through the intercession of Theodor Haak  – were the ones who emphatically enquired about progress in the construction of the calculating machine,132 not least because the machine appeared to be a part of a larger project for the mechanization of thought predicated on an interdependency of philosophical principles and mathematical-scientific results. To Haak, for example, Leibniz wrote in February, 1680, that a general script was conceivable with the help of which one might be able, for every topic, to calculate and prove just like in algebra and arithmetic. He also recalled, in this letter, his visits to London (in 1673 and 1676) and his meetings there with Henry Oldenburg, and he expressly desired the involvement of Hooke. Two machines, about which Leibniz reported in his correspondence with Bodenhausen and Huygens, deserve particular mention. In the summer of 1691, Leibniz possibly intensified his efforts to have the construction of the so-called ‘older model’ of his four-function calculating machine completed; perhaps, however, he was inspired to consider such machines because of a recommendation to the Tuscan hereditary or crown prince Ferdinand he was contemplating. At all events, at the end of a letter to Bodenhausen, on June 22, 1691, he referred to his “Arithmetische Machinam” and his desire to complete its construction. That the study of mathematical curves produced by movement would also require an apparatus, or machine, to draw them was obvious and was discussed in detail by Leibniz, both in a published article

132 Cf. M. L. Jones, Reckoning with matter: Calculating machines, innovation, and thinking about thinking from Pascal to Babbage, Chicago and London, 2016, and in particular (regarding Leibniz and Hooke) chap. 2, pp. 56–87.

170

Introduction: The Core Themes

entitled “Supplementum geometriae dimensoriae”, in the Acta Eruditorum of September 1693, and also in his letter to Huygens of October 11, 1693. In the period 1694–1696, calculating machines came to the fore again, and were referred to more frequently in Leibniz’s correspondence in these years than at any time in the previous two decades. An important reason for this was, no doubt, the completion in 1694 of his ‘older model’. The elation in his accounts of the device served to motivate his correspondents to recall their own knowledge in the field. The great variety of models discussed in this context also clearly illustrates the extent to which the completion of such mathematical devices reflected the spirit of the time. When the landgrave, Karl of Hesse-Kassel, expressed his interest in the mode of operation of a machine he had received from his brother, Leibniz was enticed to provide a detailed report  – in a letter sent to Johann Sebastian Haes on April 8, 1695  – about the recent history of mathematical calculating machines. In fact, the letters Haes sent to Leibniz, on March 28 and May 23, 1695, and Leibniz’s corresponding letters, sent on April 8 and at the end of May or early June of that year, are of special significance here. These communications contained reports about the improvement of the ‘Pascaline’ (the calculator of Blaise Pascal)133 by the Parisian watchmaker René Grillet, about variants of Samuel Morland’s machine type,134 that used slide rules and Napierian logarithms and that was to be seen in the guise of an exemplar in possession of the landgrave, about a little machine which Haes himself had made more than ten years earlier and which had previously been made known to Leibniz, about yet another little machine of Charles Cotterell and about the calculating cylinders of Caspar Schott and Pierre Petit. The adding machine of Haes, referred to in his letter of May 23, 1695, and a gearless machine conceived by Tschirnhaus, were, on the other hand, no doubt independent developments. The latter correspondent, on hearing of the completion of Leibniz’s ‘older machine’, reported about his own very different device on February 27, 1694. A first reference to the completion of the ‘older machine’ by Kölbing may be found in a letter (from which only an extract is extant) to L’Hospital of August 16, 1694, and in the correspondent’s reply of November 30. In fact, L’Hospital immediately reacted to Leibniz’s communication concerning the completion of the work on the first exemplar by commissioning a duplicate of the machine in return for appropriate remuneration. In the years between 133 Cf. H. Loeffel, Blaise Pascal 1623–1662, Basel, Boston, 1987, in particular chap. 3 (Die Erfindung der Rechenmaschine). 134 Cf. H. W. Dickinson, Sir Samuel Morland: Diplomat and inventor, 1625–1695, Cambridge, 1970, in particular pp. 28–33, and plates I–VII.

Introduction: The Core Themes

171

1694 and 1696, L’Hospital continued to remind Leibniz about this order. In a letter to Bodenhausen, on October 13, 1695, Leibniz also referred to the completion of the machine almost a year earlier and – as in the case of L’Hospital – he was flattered and obliging when Bodenhausen requested further details of the machine, no doubt with the intention of enticing the duke of Tuscany to order a duplicate. Yet another indication of the completion of the ‘older machine’ from the year 1694 is found in Leibniz’s letter to Nicolas Toinard of October 14 (or perhaps 24) of that year. Furthermore, there can be little doubt that Crafft was able to give Huygens an account of Leibniz’s calculating machine from his perspective, as we learn from Huygens’ letter of December 27, 1694, to Leibniz. The machine was likewise presented to visitors in Hanover, as for example on the occasion of a passing visit by Tschirnhaus, in September or October 1694, which is recorded in Leibniz’s letter to Jacob Bernoulli from the spring of 1696, albeit with the caveat that only a part of the machine was complete on that occasion. There is also evidence of a presentation of the machine for Thomas Burnett of Kemney, which took place in Hanover in April 1695, and which was referred to in Leibniz’s final letter addressed to Huygens, on July 1, 1695. At about the same time as the completion of the first exemplar of the ‘older machine’, work began on the second version, or so-called ‘younger machine’, which offered, for the same number of entry positions, sixteen result positions, as Leibniz explained in detail in his letter to Bodenhausen on December 23, 1695. However, in the four years that followed, the calculating machines played no great role in Leibniz’s correspondence. Then, on February 25, 1700, the death took place of Hans Adam Scherp, who had been working on Leibniz’s ‘younger’ calculating machine. The clockmaker Johann Levin Warnecke, from Helmstedt, became his successor having been recommended by Wagner, who himself assumed the role of a supervisor of the ongoing work on the machine. This course of events proved to be a stroke of good fortune, not least for posterity. Thus, on the basis of his reports concerning progress and problems in the construction of the machine, its coming into being can be retraced step-by-step. Already, in the month following Scherp’s death, both the ‘younger machine’ (then under-construction) and the completed ‘older machine’, which served as a model for the new machine, were transferred to Helmstedt, together with a letter of March 15 addressed to Wagner. The latter succeeded in striking a balance between the respective interests of Leibniz and Warnecke, and he made the delays, which inevitably arose, plausible to the impatient Leibniz. Thus, in order to reduce expenditure, Leibniz at first wanted to have to pay only for the overhaul and reworking of individual parts, as he indicated in a letter of March 18. Wagner, replying on March 23, guaranteed Leibniz a daily control of

172

Introduction: The Core Themes

the work in progress, to prevent waste or deceit, but he did point out, that the unobstructed interaction of the parts of the machine in itself demanded trials, lasting days at times, and that the remuneration would have to be orientated towards the effort involved rather than just the final product. The circumstance that progress was slow, Wagner attributed, in letters of early February, 1701, to other work commitments of Warnecke, to his diligence and painstakingness, to the difficulty of working long hours by candle light in winter and, above all, to the desolate state in which Wagner claimed Scherp had left the ‘new machine’. Thus, progress and setbacks went hand in hand. At the beginning of February 1701, Wagner could report the completion of the drawing spindle for moving and positioning the carriage. However, Wagner and Warnecke had ascertained here that holes could not be drilled uniformly, and had to be provisionally repaired, and also that rods could not be mounted at right angles with the result that, at that juncture, the machine could only be operated by applying force. Warnecke’s predecessor had used neither compass nor protractor, Leibniz was told. The rotary disk was completed but, in putting the parts together, fresh imprecisions, construction defects, as well as evidence of tinkering and botching, became apparent, all matters which found expression in Wagner’s letters to Leibniz in February and March, 1701. On April 7 then, Wagner once again expressed his frustration regarding Warnecke’s deceased predecessor. The latter had, Wagner asserted, been like a child. He had exploited Leibniz and only wanted to secure his income in order to indulge his passion for liquor, Leibniz learned from this communication. Leibniz surely felt piqued when he wrote his reply four days later, on April 11, in which he also recalled, in contrast to Scherp, his predecessor, namely the clockmaker Georg Heinrich Kölbing. Pragmatically, however, he had come to terms with the shortage of such qualified tradesmen or craftsmen. Wagner, in contrast, in his letter of August 12, considered Scherp’s work to have been useless. Warnecke, he claimed, could have constructed a new machine in the time he spent doing repair work on the older model. He then proceeded to give precise details of three specific corrections that had been carried out on the machine. In all of this, however, both Leibniz and Wagner were in agreement about the quality of the ‘older machine’ and about the fact that the structure of the ‘new machine’ was superior to that of the older one. On April 26, 1701, Wagner reported the completion of the upper part of the machine and, from July, Warnecke devoted himself to the improvement of the ‘older machine’. On this device, Wagner also carried out the first calculation examples which he reported to Leibniz, on July 29. Instead of multiplying a four digit number (4286) by 4, as intended, Wagner – after the operating rules had slipped his mind – carried

Introduction: The Core Themes

173

out the addition of this four digit number and a two digit number (16). The result he obtained contained an error in the third place (i.e. 4202 instead of 4302), which revealed that the decimal carrying operation was incomplete. A further addition (of 16), did however lead to the correct final result (4318). In his non-extant reply, Leibniz surely pointed to the role of the series of pentagonal disks, incorporated in the carrying mechanism, which served for the manual through-connection of all those positions that were, although activated, not brought to completion. Although Wagner heeded these disks in his following calculations (reported on August 5), these multiplication examples were also flawed. Wagner and Warnecke then developed a correction procedure, which combined the requisite corrective horizontal positioning of the pentagonal disks with a renewed manual rotation of the crank that operated the value transfer mechanism  – between the setting mechanism (or input) and the result mechanism (or output) – of the machine. They were also able to eliminate some further errors by making precision-engineering alterations, whereas other errors Wagner considered to have already been eliminated in the ‘new machine’, as he reported on August 12. Then, for a short time at the end of our period, late in the year 1701, everything was once again in the balance when Warnecke became gravely ill. To Wagner, who observed night vigils at the bedside of the patient, the development of the calculating machine appeared for a time to be cataclysmal, with the impending death of the clockmaker coming after that of his predecessor in the previous year. However, in his final letter of the year 1701, on December 16, Wagner was able to announce to Leibniz the recovery of the patient and the resumption of work on the calculating machine. The work on the perfection of the calculating machines was to continue for the rest of Leibniz’s life, and thereafter.135 7.2 Steganography and Cryptography A central theme in Leibniz’s correspondence with the court archivist in Kassel, Johann Sebastian Haes, was the cryptograph or cipher code developed by the correspondent and printed in book form (and in a very limited edition), with the title Steganographie nouvelle (1693). The author included one copy of the work (with a dedication to the elector, Ernst August of Hanover) with a letter dispatched to Leibniz on May 4, 1693, and with the request that he pass it on to Franz Ernst von Platen, the prime minister in Hanover. The story of the coming into being of this work, as well as of its repudiatory reception at the 135 Cf. F.-S. Morar, “Reinventing machines: The transmission history of the Leibniz calculator”, British Journal for the History of Science, vol. 48(1), (2015), pp. 123–146.

174

Introduction: The Core Themes

Hanoverian court, is documented in Leibniz’s correspondence with Haes from its commencement in July 1691. Steganology, copology (or deliberate deception), and specifically here steganography, represented a medium for the concealment of information and with the help of which a secret message could be hidden in an unsuspicious text. In the foreword to his Steganographie nouvelle, Haes stated that his cipher code would be particularly useful in diplomatic communications, being easy to write but difficult to decipher for the uninitiated. The author provided an historical summary of the development of cryptography, and he referred to pioneers like Johannes Trithemius (or Johann Trittenheim, 1462–1516), who was perhaps the first theoretician in the field, Gustavus Selenus (alias Augustus the Younger, duke of Brunswick-Lüneburg-Wolfenbüttel, 1579–1666), who was author of Cryptomenytices et Cryptographiae libri novem (1624), and the German Jesuits Athanasius Kircher (1602–1680) and Caspar Schott (1608–1666).136 Leibniz  – who was honored with an anonymous acknowledgment in the “Avertissement” of the Steganographie nouvelle – had first made the acquaintance of Haes when he visited the natural-history collection of the landgraviate library in Kassel, at the beginning of November 1687, on which occasion various projects were discussed. That these included the projected stenographic tract is evident from Haes’ first letter to Leibniz, on July 30, 1691. Subsequently Haes’ interest was concentrated on the Steganographie nouvelle, the completion of which was drawn out into the year 1693. He praised, again and again, the advantages of his cipher code, however without revealing any details. When, at the end of 1692, the tract had taken on a concrete form, Haes was finally willing to provide Leibniz with an insight into his system of encryption, which involved giving a different sense to individual letters or words with the help of tables, which he referred to in a letter of December 11, 1692. Putting the final touches to the work proved, however, to be most tedious, since the author wanted, for security reasons, to leave gaps in the text to be filled in by hand and to send encoding examples separately, and in handwritten form. With the consignment of May 4, 1693, Haes then sent his Steganographie nouvelle, together with an accompanying letter for Leibniz and a letter for prime minister Von Platen, as well as a separate package with additional tables and handwritten supplements to Hanover. The copy of the work in 136 Cf. for example, N. F. Johnson, Z. Duric, S. Jajodia, Information hiding: Steganography and watermarking-attacks and countermeasures, Dordrecht, 2001 (and New York, 2003), in particular chap. 1, sect. 2, pp. 2–4 (Steganography throughout history); G. Kipper, Investigator’s guide to steganography, Boca Raton (FL), London, New York, Washington (DC), 2004, in particular chap. 3, pp. 15–36 (History).

Introduction: The Core Themes

175

question – now preserved at the ducal library in Wolfenbüttel – with numerous marginal entries by the author consists of, in addition to the previously mentioned “Avertissement”, thirteen chapters as well as a handwritten “Addition”. In the course of the correspondence with Leibniz, Haes provided further annotations, examples and supplements to his opus. The appropriateness of the cipher code was made clear by the author’s choice of examples, which were derived from contemporary military conflicts. In the Steganographie nouvelle, reference is made to the siege of the town Montmélian (in 1691) in the form of a letter of the duke of Savoy, Victor Amadeus II, sent to Carlo Girolamo del Carretto, the Marchese di Bagnasco. In relation to this letter, further examples of encoding using the cipher were sent to Leibniz on July 1, 1693. Leibniz, for his part, had at first hesitated to pass on the copy of the Steganographie nouvelle he had received, together with the supplements, to prime minister Von Platen, as he informed the correspondent, on June 1, since the author’s dedication of the work to the elector Ernst August had met with a mixed response in Hanover. Finally, on the insistence of the correspondent, Leibniz forwarded the material to the court. At first Haes was confident of receiving recognition and reward from Ernst August, as he indicated to Leibniz on June 11. However, when a decision of the Hanoverian court in his favor proved not to be forthcoming, he made no secret of his disappointment in a letter of June 30. Yet another letter to Von Platen, which was attached to a letter to Leibniz of July 31, proved to be of no avail. In his final letter of the year 1693, on October 8, Haes expressed to Leibniz his great disappointment at the outcome, notwithstanding which, however, he remained convinced of the merits of his cipher code. In the course of their mathematical correspondence, in the late 1690s, Leibniz attempted (alas without success) to persuade John Wallis to share his knowledge of cryptography.137 To begin with, on March 29 and October 12, 1697, and again on April 3, 1698, he attempted to persuade the 80-year-old correspondent to impart his knowledge to the younger generation. Later, from the end of 1698, Leibniz pleaded for the sending of a younger man to Wallis to partake in his knowledge. To this end, he turned to the hereditary or crown prince 137 Cf. P. Beeley, ““Un de mes amis”: On Leibniz’s relation to the English mathematician and theologian John Wallis”, chap. 5, pp. 63–82, in: P. Phemister, S. Brown (eds.), Leibniz and the English-speaking world, Dordrecht, 2007; P. Beeley, “Breaking the code: John Wallis and the politics of concealment”, pp. 49–81 in: W. Li, S. Noreik (eds.), G. W. Leibniz und der Gelehrtenhabitus. Anonymität, Pseudonymität, Camouflage, Köln, Weimar, Wien, 2016. Regarding Leibniz’s interest in the theory and practice of cryptography and cryptanalysis, cf. Part 1, in particular, of: N. Rescher, Leibniz and cryptography: An account on the occasion of the initial exhibition of the reconstruction of Leibniz’s cipher machine, Pittsburgh, 2012.

176

Introduction: The Core Themes

Ferdinand of Tuscany, on November 3, 1698, as well as in the following year to the courts of Brandenburg (on February 24) and of Sweden (on April 17). Leibniz’s motive was surely not the political benefits that accompanied a knowledge of cryptography (even if these played a role in his argumentation at court), but rather the advancement of the “ars inveniendi”, as well as the fear that Wallis’ cryptographic knowledge could be lost to posterity, just as in the case of the death of François Viète (1540–1603) almost a century before.138 Regarding the latter concern, he had quoted from his review  – in the Acta Eruditorum of June 1686 – of Wallis’ A Treatise of Algebra (1685), in his letter to the author on March 29, 1697. In this review, Leibniz had, in addition to the appeal to Wallis to share his knowledge, placed cryptography in the proximity of algebra and compared the author to Viète. Regarding Wallis as a cryptographer, and his cryptographic knowledge,139 Leibniz had already committed his desire to paper as early as 1673 and he continually repeated it to other English correspondents in the 1690s. Wallis’ reaction was, however, noncommittal. As a specimen of his capability, he sent an encoded letter, with his notes for its decoding, to Mencke who, however, because of political considerations, refused publication and informed Leibniz accordingly on June 1, 1697. Hereupon, Wallis published the letter in the third volume of his Opera. Although he chose not to react to Leibniz’s proposals, Wallis did benefit from Leibniz’s interest in negotiations with the English court, which duly granted him a pension, in order to enable him to instruct his grandson, William Blencow, in cryptography. Ultimately, Wallis’ work on cryptography, from the year 1653, was posthumously edited and published by John Davys – in An essay on the art of deciphering – in the year 1737.140 While Leibniz’s attempts to persuade John Wallis to share his cryptographic knowledge proved to be futile  – at least until the end of 1698 – the matter continued to be a topic in their correspondence in 1699 and 1700. Following persistent pressure, Wallis finally admitted that political considerations had influenced his decision not to respond to Leibniz’s request to publish his 138 Cf. D. Kahn, Codebreakers: The story of secret writing, New York, 1967 (and 1996), and in particular (regarding Viète) pp. 116–188; P. Pesic, “François Viète, father of modern cryptanalysis – two new manuscripts”, Cryptologia, vol. 21(1), (1997), pp. 1–29. 139 Cf. D. E. Smith, “John Wallis as a cryptographer”, Bulletin of the American Mathematical Society, vol. 24, (1917), pp. 82–96. 140 Cf. J. Davys, An essay on the art of decyphering. In which is inserted a discourse of Dr. Wallis. Now first publish’d from his original manuscript in the publick library at Oxford, London, 1737, pp. 9–58; K. Ellison, A cultural history of early modern English cryptography manuals, London, New York, 2017, in particular pp. 1–20 (Introduction: Crises of expression in seventeenth-century criptography manuals).

Introduction: The Core Themes

177

methods, or at least to educate someone in these matters. Encryption was often necessary in negotiations, and a dissemination of cryptographic methods was therefore not at all desirable. Furthermore, as he informed Leibniz on April 9, 1700, he was unwilling to part with his knowledge in this area without the express consent of his sovereign. A further reason, as he explained in a letter of January 26, 1699, lay in the nature of the matter itself. Cryptography was difficult to transmit, since it consisted not merely of a method but rather of a clouded pursuit, in the course of which the method of operation needed to be continually adapted. 7.3 Military-Related Projects (Submarines, etc.) The letters of Martin Elers in particular suggest that Leibniz had shown an interest, and had requested further details from his correspondents, regarding projects having military applications. This applies, for example, to Elers’ work on the production of mail armor made out of silk. When, at the end of August 1681, Leibniz remarked that armor of that kind was obtainable in England at a high price, Elers replied, on September 2, that the kind of armor he had in mind – in which apparently a network of brass wire was incorporated – would be considerably cheaper. With the elector of Brandenburg, Elers did not have any success in promoting his new armor idea, and on December 30, 1681, he informed Leibniz that the elector had already received a similar coat of arms, in the form of a gift from king Charles XI of Sweden, and had tested the extent to which it was resistant to musket balls or shot, namely by having a condemned soldier, awaiting execution, wear the armor and serve as a target. Although the musket balls of the firing weapon did not penetrate the armor, the proband collapsed and the shot was found to have produced a bloated, purulent and bloody wound, and would have required surgery to treat. Jobst Dietrich Brandshagen reported, on November 5, 1682, from Copenhagen, where preparations for a war with Sweden were underway, about certain bellicose inventions, like setting ships on fire with cannonballs. Brandshagen’s subsequent account, on May 15, 1683, of the components of these incendiary cannonballs interested Leibniz, as did the function of a rifled gun in which the powder was automatically transferred to the priming pan. Remarkable was a ballistic mortar, allegedly made out of board or pasteboard by Brandshagen, and reported in a letter sent to Leibniz, on April 3, 1683. Because of the easy transportability, the mortar, from which nine grenades had already been fired, was superior (according to Brandshagen) to mortars made from metal. The suggestion to use the peculiar material for the weapon had apparently come from Leibniz himself, who had been inspired by an article entitled “Extrait d’une lettre  … touchant une nouvelle invention de faire des pendules de

178

Introduction: The Core Themes

carton”, by the French Jesuit astronomer, Jean Bonfa, in the Journal des Sçavans in January 1679. Leibniz received intelligence, in the years 1691 and 1692, concerning Papin’s Hessian pump (the “Rotatilis suctor et pressor Hassiacus”) and, in particular, regarding its employment in the development of a submersible vessel in Kassel,141 for example in a letter from Haes, on June 11, 1692, who reported about the trial of such a vessel in the presence of the landgrave, Karl of Hesse-Kassel. The centrifugal pump had first been developed by a tradesman in Stuttgart and had been made public in a work of Salomon Reisel in 1684 entitled Sipho Würtembergicus, sive Sipho inversus cruribus aequialtis fluens et refluens hactenus inauditus. Papin had studied this innovation intensively, while in London, and then (from 1688) in Marburg. Half a year after Papin first gave an account of this work, in the context of his article “Rotatilis suctor et pressor Hassiacus” in the Acta Eruditorum of June 1689, Reisel’s book Sipho Wurtembergicus per majora experimenta firmatus (1690) was published, and then reviewed in the March 1690 number of the Acta Eruditorum. To this, Papin then responded with an account of his investigation “Examen siphonis Wurtemburgici”, in the May 1690 number of the journal. Finally, after an interval of five years, Papin published his concluding study of the centrifugal pump in his bilingual collection Recueil de diverses pieces touchant quelques nouvelles machines and Fasciculus dissertationum de novis quibusdam machinis (1695), respectively. The lift pump, or the suction pump or suction lift pump, had been developed in Europe in the late middle ages and existed alongside the force pump, which was known since Hellenistic times, as a reciprocating pump for raising water. A newer development then was the ‘suck and press’ pump, developed by Reisel and Papin, which was powered by the uniform movement of a human hand, and which operated with the fluid (water or air) entering the machine in the direction of the axis and escaping in a tangential direction.142 It then became a central element in Papin’s trials of a submersible vessel (his “navis urinatoria”) in 1691 and 1692. According to the accounts  – given by Robert Boyle (in 1660/ 1661) and Balthasar Monconys (in a posthumous publication of 1666) – about the experiments of Cornelis Drebbel (1572–1633) with a 141 Cf. F. Tönsmann, “Wasserbauten und Schifffahrt in Hessen um 1700 und die Forschungen von Papin”, pp. 89–104 in: F. Tönsmann, H. Schneider (eds.), Denis Papin: Erfinder und Naturforscher in Hessen-Kassel, Kassel, 2009. 142 Regarding the lift pump, the suction pump and the ‘suck and press’ pump, cf. G. HollisterShort, “On the origins of the suction lift pump”, History of Technology, vol. 15, (1993), pp. 57–75; M. T. Wright, “On the lift pump”, History of Technology, vol. 18, (1996), pp. 13–37; E. Gerland, Leibnizens und Huygens’ Briefwechsel mit Papin nebst der Biographie Papin’s, Berlin, 1881 and Wiesbaden, 1966, in particular pp. 37–41.

Introduction: The Core Themes

179

submersible vessel on the Thames, in about 1620, the requisite air exchange or renewal had been achieved by chemical or alchemical means using drops of a quintessence. Papin’s trials of his submersible vessel then gave Leibniz occasion to recall once again the methods Drebbel was thought to have employed more than seventy years earlier. A correspondent in Marburg, Hermann Peikenkamp, who informed Leibniz about Papin’s efforts, recalled Drebbel’s submersible vessel in a letter of August 3, 1692. Whether or not the air renewal took place, by the use of hoses or tubing to connect the submerged vessel with the atmosphere, as in the case of Papin’s “Navis urinatoria”, was considered in a further letter from Peikenkamp, written on October 12, 1692. In this letter, the correspondent also attributed a dubious role to Boyle in the matter, through his sequestering of first-hand accounts of the undertaking.143 In a letter he wrote to Papin, almost three years later, in the first half of August 1695, Leibniz expressed the view that burning spirit of wine might well have been the quintessence in question. Even if this spirit of wine had not been a substitute for fresh air, it might well have had a beneficial effect. In this connection, he recalled that he had, while in London, discussed Drebbel’s submarine passage across the Thames, both with Boyle (presumably on February 12, 1673) and with Drebbel’s daughter, Katharina, together with her husband Johann S. Kiefler (or Kuffeler). He had not, however, been able to ascertain from any of them, whether or not fresh air had been supplied to the submersed vessel. Papin of course attached little credibility to a procedure for air exchange or renewal, which was to be achieved by chemical means, and in the construction of his underwater vessel, he employed, first, a ventilator pump and, then, the centrifugal pump to achieve an efficient intake of fresh air and, likewise, for the expulsion of the foul or exhaust air. This air exchange through hosepipes or tubing, between the submerged vessel and the water surface, was of course crucial for the boat occupants, supplying both the human respiratory system and a lamp flame for illumination. To build and set up the submersible vessel, Papin had travelled from Marburg to Kassel, in June 1691, and the Kassel resident Haes was able to report regularly to Leibniz about Papin’s activities there. In its first design, the boat consisted of a rectangular parallelepiped box made of tinplate, with a hull made of wood and iron guide rails, as Papin informed Huygens, in a letter of August 26 of that 143 Cf. L. E. Harris, The two Netherlanders: Humphrey Bradley and Cornelis Drebbel, Leiden, 1961, in particular chap. 14, pp. 160–170 (regarding Drebbel and submarine navigation) and p. 173 (regarding the question of breathing, or the supply of air, in a submerged boat, and regarding the role of Boyle).

180

Introduction: The Core Themes

year. The vessel was provided with lockable openings, in the floor and roof, that were not, however, to be opened simultaneously. The upper hatch served the purpose of entry and exit, before and after immersion, respectively, whereas the bottom hatch provided an opening for sculling, or for grabbing objects, while submersed. A hole was bored in the roof of the vessel, and a cylinder was soldered in there. At the outlet of this cylinder, a leather tube – having been reinforced on the inside with spiral springs – was fixed. By means of this tube or hose, at whose upper end a piece of light wood was attached to act as a buoy on the water surface, the vessel was to maintain contact with the atmosphere while submerged. The lower end of the cylinder was located inside the vessel, within an additional cylinder which was provided with a downward-opening valve. Through an up and down movement of this second cylinder air would be drawn into the interior of the vessel. According to Archimedes’ Principle, the weight of the immersed boat, with its machinery and occupants, should be equal to that of the displaced volume of water. To make the vessel sink, recesses in the floor were to be filled with lead ballast. Through the bottom hatch, this ballast was then to be offloaded again in order to make the vessel rise to the surface once more. To measure the depth, a barometer was installed in the interior of the submersible vessel. In order that the bottom hatch could be opened, the pressure inside the vessel had to be equal to the sum of the atmospheric air pressure and the hydraulic thrust in order to prevent the intrusion of water from below into the interior. In addition to the barometer, a compass was supplied to aid the navigation of the vessel. On July 30, 1691, Leibniz too was informed – both by Friedrich Lucae and Haes – about the progress being made in the construction of this vessel. When, in mid-August, the boat was being launched it was considerably damaged in an accident, concerning which event Haes sent a detailed report to Leibniz, on November 19. According to this account, a crane being employed to help lower the vessel onto the river failed to hold its load, and the vessel crashed into the water and sank. Already, about a week after the accident, in his letter of August 26, Papin sent a detailed report about his submersible vessel, and its demise, to Huygens in which he also dealt with the utilization of his invention, suggesting that its purpose had been purely experimental. In the same letter, Papin likewise informed Huygens about his design for a new, improved bathyscaphe. In the spring of 1692, Papin was once again able, with the support of the landgrave, to travel to Kassel to undertake fresh experiments with the new submersible vessel. The new boat was – according to the account sent to Huygens on August 26, 1691 – of oval shape and made of wood. In the cabin, or machine room (with measurements: 6.5 feet height, 5 feet width and 3 feet depth), three

Introduction: The Core Themes

181

persons could be accommodated. There was no longer an opening and hatch in the floor of the vessel; instead there were openings at the sides, which were sealed with leather, and intended for the operation of oars. The centrifugal pump was now employed in combination with the hose, or tubing, reaching to the water surface for the supply of fresh air. The removal of foul, or exhaust, air was achieved by means of a separate hose. In order to submerge the vessel, water was let in using a faucet and collected in receptacles or ballast tanks. The rise of the submarine vehicle, from a depth below the water surface, was to be achieved by pumping the water in the receptacles out of the vessel. The depth of the vessel under water was to be determined using a manometer. Again on this occasion, Haes informed Leibniz about the progress of Papin’s efforts, first of all in a letter of May 1, 1692. Then, in a further letter of May 22, Haes praised especially the superiority of the method of air exchange and renewal being employed, in comparison with Drebbel’s supposed procedure. Finally, on June 11, 1692, Haes was able to report about a successful demonstration of the submersible vessel in the presence of the landgrave, and he used the occasion to give a detailed description of the form of the new ship, the air exchange system, the method of submergence and reemergence, the illumination of the machine room, and the instruments for navigation. This report was complemented by a further letter from Haes, of October 23, 1692, in which the principal innovations of Papin were accentuated. In contrast to the first design of the previous year – that had been conceived solely for the purpose of salvaging objects and carrying out tasks under water – the new design envisaged journeys under water and attacks on hostile vessels. Once again, Haes highlighted the centrifugal pump, combined with tubing for air exchange, as well as the water containers, or ballast tanks, fitted with water pumps as important improvements. Independently of Haes’ accounts of the two submersible vessels, Leibniz received an independent report, written on October 12, from Hermann Peikenkamp, who related that he had been informed by Johann Philipp Heppe, an engineer and artillery officer; the latter’s account of events, as reported to Leibniz, was in good agreement with that of Haes in all essential points. With the appearance of Papin’s bilingual work Fasciculus dissertationum and Recueil de diverses pieces, in 1695, which contained chapters entitled “Navis urinatoriae … constructae descriptio”, and “Description du Batteau plongeant”, respectively, questions relating to the submersible or diving vessel were discussed in Leibniz’s correspondence with the author. Whereas Haes had raised the issue of the quintessence – allegedly used by Cornelis Drebbel and concerning the composition of which Leibniz had long tried to gain an insight – both Leibniz and Papin were decidedly skeptical about the possible effect of

182

Introduction: The Core Themes

such a quintessence. To Papin, Leibniz wrote, in the first half of August 1695, that he conjectured that the substance used by Drebbel might have been the spirit of wine, viz. an aqua vitae prepared by distilling wine. A further more general question Leibniz posed, in this context, concerned the possible use of spirit of wine as a fuel to power a two-stroke piston engine – with a combustion or rarefaction stroke followed by a compression or condensation stroke – similar to the use of water vapor from water held over a lamp flame. Papin answered, on September 1, that the flame producing the fumes of the spirit of wine, as well as all other flames aboard the submersible, would only further pollute the air within the submerged vessel. And he announced that Leibniz’s conjectures, about the power of spirit of wine as a fuel, were in agreement with experiments he had carried out, but that the costs involved in the use of this fuel would be prohibitive. In a further letter of early October, 1695, Papin dealt in more detail with the use of a spirit of wine lamp in a submersible or diving vessel. Once the connection with the outside atmosphere was removed, the flame would be extinguished, just as if it were an oil lamp, and would add to the pollution of the air inside the vessel. As regards the possible use of a cycle of rarefaction and condensation, using the spirit of wine rather than water vapor as part of a piston engine, Papin admitted that his experimental investigation of the idea had never attained the necessary precision to allow a judgement on the matter. He was, however, skeptical as to whether the cylinder and piston would be impermeable, as they were generally found not to be completely impervious to the water that was used as a seal over the piston. In connection with seafaring and the demands of navigation  – be it in a civil or military context – stood the development of sea-worthy and precise clocks. Leibniz had been active in this area in his younger years, as is evidenced, for example, by “An Extract of a Letter of the Learned Dr. Gothofredus Guil. Leibnitz, concerning the Principle of exactness in the portable Watches of his invention”, which was part of his letter for Jean-Paul de La Roque of mid-March 1675. Huygens’ efforts in this area in the early 1690s met, no doubt, with Leibniz’s approval. After this correspondent had reported the completion of a new clock at the end of his article “De problemate Bernoulliano”, of October 1693, he addressed the matter once again in a letter of May 29, 1694, to Leibniz. Navigation, and in particular the method of steering and maneuvering a sailing ship, was also the subject of a public dispute between Huygens and Bernard Renau d’Eliçagaray, concerning which Leibniz’s opinion was requested. Renau’s anonomously published book De la théorie de la manoeuvre des vaisseaux (1689) was criticized by Huygens in his “Remarque  … sur le livre de la manoeuvre des vaisseaux” (1693). Renau duely replied with his

Introduction: The Core Themes

183

“Reponse … à la Remarque de M. Huguens” (1694), which in turn was countered by Huygens with his “Replique … à la Reponse de Mr. Renau” (1694). On May 29, 1694, Huygens had requested Leibniz’s judgement for inclusion in the “Replique … à la Reponse”. As Leibniz had not seen Huygens’ “Remarque”, and had only vague memories of his study of Renau’s book, he desisted from giving a definitive judgement and only presented a single point of criticism – namely the author’s failure to take the center of gravity of the ship into consideration – in his letter to Huygens of June 22. He welcomed, however, the practical nature of Renau’s work, and he recalled that the author had cited comte de Tourville’s Exercice en général de toutes les manoeuvres qui se font à la mer (1693). On August 24 then, Huygens reiterated once again his highly critical standpoint regarding Renau d’Eliçagaray. However, even after L’Hospital had sent Leibniz the documents relating to this dispute, he restricted himself, in writing to this correspondent, to rather general comments concerning issues of force, speed, and leeway or windward drift of a vessel, like, for example, in a letter of June 24, 1695, and again on September 30, 1695. Nevertheless, Leibniz thought that he could obtain the correct rule for leeway, or drift, and he believed that the time he should invest in the study of Renau’s book would be rewarded, and, indeed, would give him occasion to show the power of his own dynamics. 7.4 Economic and Techno-Economic Projects In the late 1670s and early 1680s, there was no shortage of economic and technical project conceptions in Leibniz’s correspondence, and new schemes were constantly being discussed or implemented. Two correspondents, in particular, epitomized a type of Baroque discoverer, or projector, namely the merchant Martin Elers and Leibniz’s associate Johann Daniel Crafft, who was a pioneer in manufacture and manufacturing in Germany.144 With Elers and Crafft, Leibniz discussed a multitude of enterprises, or undertakings, intended to provide national economic benefits. Most such projects were of a kind that required the financial support of, and the granting of privileges by, a prince. Thus, the technical and economic proposals were discussed, for the most part, in the context of the realization chances at one or other European court. And so we find Elers at the ducal court in Celle, at the court of the elector of Brandenburg in Berlin, and finally at the court of the Danish king in Copenhagen, busy in each instance with his efforts to convince the prince in question, alas mostly without success. Correspondingly, Crafft repeatedly 144 Cf. W. Loibl, “Johann Daniel Crafft (*Wertheim 1624-+Amsterdam 1697): Ein Chemiker, Kameralist und Unternehmer des 17. Jahrhunderts”, Wertheimer Jahrbuch 1997, pp. 55–251, Wertheim, 1998.

184

Introduction: The Core Themes

reported about discussions and negotiations with the Saxon mercantile community – whose trade was being adversely affected by the establishment of manufactories in their territory – as well as with ministers, and with the estates or the broad orders of social hierarchy, of the territory. The difficult ambient conditions, combined with the lack of maturity of many a project, was not without effect on the cooperation of Leibniz and the two correspondents in question. Good agreement, mutual recommendations, and common intentions, alternated with intrigues and scheming in which, for example, letters were tactically withheld from addressees, or regurgitated. Following a suggestion of Leibniz, both he and Crafft adopted a cryptographic script or cipher (viz. intentional alteration of individual alphabetic characters in order to hamper the decryption by other parties) in their letters, which, however, occasionally led to confusion or misunderstanding on Crafft’s part, as a result of false encryption, or of vague intimation in non-encrypted text passages. In the mercantile policy, that he and Crafft wanted to propose to the emperor, Leibniz saw a secret formula, not only for restoring Germany unscathed to an integral whole, but also for achieving happiness and for rendering his imperial majesty formidable once again. In an aide-mémoire for Crafft, written in the second half of July 1680, Leibniz proposed that the correspondent write to Philipp Wilhelm von Hörnigk – the brother of the Imperial privy counsellor in Vienna, Johann Moritz von Hörnigk – introducing the thoughts of an unnamed reference person, or third party, namely Leibniz himself. It was argued that with the establishment of manufactories in the German empire – along with the introduction of import barriers for French goods – wealth and tax intake would be increased and, at the same time, the power of France would be weakened. Furthermore, according to Crafft, the establishment of manufactories should be recommended to the German princes at the diplomatic conference on reunifications, meeting at Frankfurt, since all or most of that pertaining to the prosperity of Germany was rooted in such disprized manufactories, as Crafft wrote, in his letter of September 2, 1681, to Leibniz. Of course Crafft knew from experience that those wielding power failed to realize that the greatest benefit for themselves lay in the provision of sustentation for their subjects, as he wrote in his letter of October 3, 1680. Leibniz developed the same train of thought, but without an anti-French accentuation, in the draft of a letter written for Crafft, in the second half of July 1680, which was to be sent to the elector of Brandenburg. In order not to come into conflict with the foreign policy of the elector, Leibniz stressed that the embargo on French goods would not be required, since domestic goods, like silk and wool products, could be produced better and more inexpensively with the result that, in the long term, even the export of manufactured goods might be conceivable.

Introduction: The Core Themes

185

Crafft placed particular hopes in his invention of new machines for textile manufacture. He told Leibniz, in a letter of December 6, 1680, that he had wonders in hand and would teach the world a lesson, having developed a veritable philosopher’s stone. Crafft stressed in a letter  – composed the end of May 1681 during a meeting with Leibniz  – to the pensionary of Haarlem, Michael ten Hove, the usefulness of a new invention, namely the ribbon-loom, or mola limbolaria, which was known in Germany as ‘Mühlstuhl’, ‘Schnurmühle’ or ‘Bandmühle’, and which has long been a matter of interest in social and economic history.145 Although the loom needed to be deployed in a purpose-built building, Crafft nevertheless believed he could market the device even in Holland. Then, in a letter of January 8, 1682, he requested that Leibniz approach Jan Hudde in Amsterdam in this matter. On December 25, 1682, Crafft forwarded a fabric sample and recommended to Leibniz that he get the opinion of a braid and lace maker concerning it. He had, however, also to confess that his three machines were idle and needed to be replaced by a modified machine, since, contrary to all expectations, the fabric in question had gone out of fashion. At the end of 1680, and in early 1681, Crafft and Leibniz followed with interest the efforts of Elers to persuade the duke of Celle to establish a new town, near Harburg (south of Hamburg), for emigre Huguenots. The duke of Celle insisted on financial participation in the scheme by the duke in Hanover, who, in turn, insisted on the fulfillment of certain other conditions. A decision about the matter was delayed, and Elers finally had to depart without success, at the end of 1681. Another one of several proposals that Elers presented to the Brandenburg court, proved likewise to be a failure. The Brandenburg-African company was to bring a large number of Africans into the territory, and the elector would then make them available to farmers (in return for payment), as slaves or farm laborers. In addition, it was argued, if the Africans were to be trained once a week in the use of fire arms, then the elector would acquire cheap and good soldiers since these were, by their very nature, hardy and strong. Elers outlined his project in a letter of February 7, 1682, to Leibniz. Crafft was likewise approached by Elers in the matter, and his judgement was that the project was totally impractical, and that the projector could expect 145 Cf. U. Troitzsch, Technischer Wandel in Staat und Gesellschaft zwischen 1600 und 1750, pp. 9–267 in: A. Paulinyi, U. Troitzsch, Mechanisierung und Maschinisierung 1600–1840, (Propyläen-Technikgeschichte, vol. 3), Berlin, 1991, in particular pp. 156f. (Bandmühle); R. Reith, “Technische Innovationen im Handwerk der frühen Neuzeit? Traditionen, Probleme und Perspektiven der Forschung”, pp. 21–60 in: K. H. Kaufhold, W. Reininghaus (eds.), Stadt und Handwerk in Mittelalter und früher Neuzeit, Cologne, Weimar, Vienna, 2000, and in particular (regarding the ribbon loom) pp. 35–41.

186

Introduction: The Core Themes

to experience more dishonor than honor with this proposal, as he wrote to Leibniz, on February 24, 1682. Leibniz’s letter to Elers, of February 17, 1682, has not been found, but it was referred to at the beginning of the correspondent’s reply, on March 1, 1682. There Elers related that a copy of his proposition had been taken to Vienna for presentation to the emperor. From this reply, an insight can be obtained into Leibniz’s thoughts on the matter. In the context of the foundation of the Brandenburg-African Company, Leibniz must have recalled that the Dutch had forbidden the holding of serfs, or slaves, in the republic itself.146 Elers had not heard of such a total prohibition of the slave trade in the Dutch republic, but simply that slavery and serfdom in the county itself was prohibited and the ruling that black people, brought into the country, should enjoy freedom. Just the same, Elers insisted that no small number of black people were being held in Holland, even among the Jews there. Once again he insisted that the black laborers, once provided with appropriate clothing and following a period of acclimatization, would be hardier than their European counterparts. Following this, Elers recalled Crafft’s skepticism about the prospects for the project, and he suggested that Crafft’s views were very much at variance with Leibniz’s opinion on the matter. Crafft was to have the last word on Elers’ project relating to black Africans (“wegen der Schwartzen”), namely, in a letter to Leibniz, on May 7, 1682. He was of the opinion that the demographics of Germany differed from those of certain north American territories, like Canada, where the rural settlement of black Africans might indeed make economic sense. He also believed that Elers’ resettlement project would – like many another project of his – in due course die a natural death. The trend found in the epistolary exchanges of the late 1670s, where questions arose regarding the possible application of machines, for example, in the mechanization of silk and wool manufacture, continued in the early 1680s. In a letter from Dresden, on January 30, 1680, Crafft referred to a wool, or silk, manufactory, and to a proposal, which had been submitted to the elector of Saxony, for the establishment of a workhouse, and orphanage, in connection with a bag cloth and stockings manufactory. For the duchies of Brunswick and 146 Cf. J. Postma, The Dutch in the Atlantic slave trade, 1600–1815, Cambridge, New York, Melbourne, 1990; J. Postma, “The dispersal of African slaves in the west by Dutch slave traders, 1630–1803”, chap. 10, pp. [283]–300, in: J. E. Inikori, S. L. Engerman (eds.), The Atlantic slave trade: Effects on economies, societies and peoples in Africa, the Americas, and Europe, Durham, NC, 1992 (and 1998). Regarding the Brandenburg-African Company (1682–1721), cf. H. Weiss (ed.), Ports of globalisation, places of creolisation: Nordic possessions in the Atlantic world during the era of the slave trade, Leiden, 2016, in particular chap. 1 (Introduction), p. 12.

Introduction: The Core Themes

187

Lüneburg, he also proposed the establishment of a bag cloth manufactory, and his exchange of ideas with Leibniz, about the possibility of steel production in the Harz district, resulted in Leibniz turning to duke Ernst August in the matter. Even greater was the diversity of the projects in which Elers was involved. During a visit to the glassworks in the hills of the Weser Uplands, he found a process to facilitate the making of burning glasses or lenses, as he informed Leibniz from Hanover, on May 15, 1681. From Dresden, on July 8, 1681, he informed Leibniz about his quest for a new kind of wax bleachery, and from Berlin he reported, on December 30 of the same year, that he had informed the elector there about an inventor, who claimed to have a means of preventing ships from sinking. Over several months, Elers promoted a so-called “infallible project”, as he informed Leibniz in a letter from Dresden, on September 2, 1681. The intention here was to market a wallpaper, consisting of silk printed with gold or silver, and Elers enclosed samples with his letter to Leibniz. Crafft, for his part, as he informed Leibniz on May 7, 1682, considered this project to be impractical and inefficient. Elers finally abandoned the project for lack of start capital. Although there exists no statement from Leibniz about this particular project, the letters of Crafft and Elers leave no doubt that he had shown an interest, and had requested further details from his correspondents. Communications and discussions of technological, or engineering, projects were not limited to the correspondences with Elers and Crafft, however. On March 21, 1682, Tschirnhaus reported that he had seen in Paris a recently discovered repeater clock that could be made to chime on awakening in the night. In finance and commerce, Leibniz’s interests encompassed calculations of interest and discount, of bonds and debentures, as well as the evaluation of life annuities and insurance (reflected in his correspondence with Johann Jakob Ferguson between July 1683 and March 1684). In an article in the Acta Eruditorum entitled “Meditatio juridico-mathematica de interusurio simplice”, in October 1683, Leibniz treated the problem of determining the current value of a loan repaid ahead of schedule. The difficulties Leibniz experienced following the publication of this article  – which included the accusation that he was an advocate of the then frowned-upon method of compound interest (“Anatocismus”) – can be followed in his correspondence with Christoph Pfautz, in August, and on December 21, 1683. Leibniz’s proposals for improvement of monetary systems are to be found in his correspondence and collaboration with Crafft, specifically in their joint memorandum for the emperor written in Vienna, in the second half of 1688, and in discussions Leibniz had, also in Vienna, with the metallurgist and refiner of metals, Christian Holeysen, at the end of April or in the first half of May, 1690. Questions of cost effectiveness, and economic feasibility, of processes and of

188

Introduction: The Core Themes

undertakings and business ventures, were also taken to heart by Leibniz. Thus, he excerpted passages from the papers of Holeysen concerning the economic efficiency of the Hungarian mines. He also carefully noted Crafft’s communication of a claim, namely that gold could be made from the best iron slag, during discussions they had in Graupen (now Krupka), at the end of January 1688. Without discussing the truth or validity of such gold extraction processes, Leibniz found that, because of the cost of related ingredients, such processes could simply not be cost-effective. But other more legitimate processes, such as salt production, referred to in letters from Georg Mohr (on February 5, 1686) and from Friedrich Heyn (on November 30, 1686, and March 26, 1687), or the introduction of street illumination, using oil as a fuel for lamps, referred to by Crafft (on June 26, 1689, and on July 15, 1690) were always assessed by Leibniz from the viewpoint of cost effectiveness. In addition to such considerations of cost effectiveness, there was yet another aspect which determined Leibniz attitude to the projects and processes under consideration, namely cameralism, or a German variant of mercantilism, which developed at the end of the 17th century. It was, in essence, an approach to government and administration, involving police order and supervision. It incorporated a set of practically-orientated academic disciplines, concerned with state administrative organization, and a form of a ‘science’, dedicated to reforming society while promoting economic development.147 Within the sphere of cameralism, and the cameral sciences, the concept and economic doctrine of technology emerged in Germany in the eighteenth century. The Anleitung zur Technologie (1777) of Johann Beckmann (1739–1811),148 a prominent figure in German cameralism, was the first work that self-consciously developed the concept of technology as a discipline devoted to the systematic description of handicrafts and industrial arts.149 At the beginning of this development, almost a century before Beckmann, stands Leibniz’s rival, and adversary, Johann Joachim Becher, whose satirical work entitled Närrische Weißheit und weise Narrheit (foolish wisdom or wise foolery/ folly’ish wisdom or wise folly) of 1682 has been referred to above. The subtitle of the work 147 Cf. for example, A. Wakefield, The disordered police state: German cameralism as science and practice, Chicago, 2009; M. Seppel, K. Tribe, Cameralism in practice: State administration and economy in early modern Europe, Woodbridge (Suffolk) and Rochester (NY), 2017. 148 J. Beckmann, Anleitung zur Technologie oder zur Kenntnis der Handwerke, Fabriken und Manufacturen, vornehmlich derer, die mit der Landwirtschaft, Polizey und Cameralwissenschaft in nächster Verbindung stehn, Göttingen, 1777. 149 Cf. C. Mitcham, E. Schatzberg, “Defining technology and the engineering sciences”, pp. 27–63 in: A. Meijers (ed.), Philosophy of technology and engineering sciences, (Techno­ logy, engineering and the sciences, vol. 9, part I), Amsterdam, 2009, in particular p. 36.

Introduction: The Core Themes

189

in question “Ein Hundert so Politische alß Physicalische Mechanische und Mercantilische Concepten und Propositionen” (A hundred both political as physical, mechanical and mercantile, concepts and propositions) reveals the standpoint of the author, who has been seen as a pioneer in the development of ideas regarding technology, or in technological thinking.150 On the basis of such a mercantilist-cameralist conviction then, Leibniz’s interest developed in silk and wool manufactories, referred to by Brandshagen (in late August or early September, 1683) and in the memorandum of Leibniz and Crafft for the emperor (from the second half of 1688), in iron and steel production and in the wine trade, referred to in Leibniz’s discussions with Crafft in Graupen and in the memorandum for the emperor, in the production of armor, referred to by Elers (on August 1, 1684), in textile printing, referred to by Brandshagen (in late August or early September, 1683), in the improvement of the luster of pearls, referred to by Elers (on August 12, 1684), and in a range of other economic projects. Furthermore, Leibniz’s correspondence reveals a wide range of proposals he made in the area of governmental economic planning and administration, both at state level in Hanover as at the Imperial level in Vienna. Thus, in the memorandum, intended for presentation to the emperor, that had been prepared in Vienna in the second half of 1688, we find Leibniz, in the guise of Crafft, advocating the establishment of a “Bergkollegium”, an Imperial mining college or council that would establish and coordinate the occurrence of mineral and ore deposits within the empire. To this end, a laboratory was to be set up and a chamber of arts maintained, where the most important mechanical inventions and innovations would be presented. This mining institution was intended to preempt the import of ores and minerals, that were already available in Germany, and to play an important role in the colonization of those regions of Hungary that had, shortly before, been freed from Turkish rule, that is after the ending of the siege of Vienna and the defeat of the Turks, in 1683, and the Habsburgs’ reconquest of Hungary that followed. At the outset of his 150 Cf. U. Troitzsch, Ansätze technologischen Denkens bei den Kameralisten des 17. und 18. Jahrhunderts, (Schriften zur Wirtschafts- und Socialgeschichte, vol. 5), Berlin, 1966, in particular chap. 1, pp. 11–19. Regarding the history of the notion, or concept, of technology, cf. A.-F. Garçon, “The three states of technology: An historical approach to a thought regime, 16th–20th centuries”, pp. 11–26 in: M. Faucheux and J. Fores (eds.), New Elements of Technology, (Collection Sciences Humaines et Technologie, UTBM: l’université de technologie de Belfort-Montbéliard), Sevenans, 2012; A.-F. Garçon, “Technologie: histoire d’un régime de pensée, xvie–xixe siècle”, pp. 73–102, in: R. Carvais, A.-F. Garçon, A. Grelon (eds.), Penser la technique autrement: En hommage à l’oeuvre d’Hélène Vérin, Paris, 2017; E. Schatzberg, Technology: Critical history of a concept, Chicago, 2018.

190

Introduction: The Core Themes

petition to the emperor, Crafft (or rather Leibniz) provided a brief account of his life and studies, his travels in Europe and in the American colonies, his professional life in the service of the electors in Mainz and Saxony, and his experience over a broad spectrum of manufactories. Chemical substances too, like paints, were available in nature and were of interest from the viewpoint of their economic utilization. On July 10, 1687, Heyn reported, for example, about veins of iron ore which he had observed on the river Elbe. Several of these veins, when mixed with crude ores, were found to be suitable as paint, providing fine umbra and brown ocher pigments. Likewise, in the long memorandum composed jointly by Leibniz and Crafft for the emperor, the experience gained by Crafft and Heyn in producing and applying paints was emphasized. A complete factory, or plant, for the processing of mineral ores was contemplated here in the light of ongoing building activity in Hungary, and Lower Austria, where such paint products would be particularly useful, especially for the conservation of wood and even of stone. A range of physical and chemical issues arose in Leibniz’s correspondence, both in the context of scientific and engineering applications and of techno-economic projects. Examples from the 1680s from the latter category included, for example, the dyeing of garments, production of ruby glass, perfection of pearls, retrieval and extraction of gold and silver, phosphorus production, and the desalinization of sea water. Thus, in Leibniz’s correspondence with Ramazzini, the desalination of seawater being pursued by a certain Nathan Lacy, an Englishman living in Modena, was referred to by Leibniz in a letter from Venice on February 25, 1690. Even the topic of emissions from laboratories, and protection against such emissions, arose in Leibniz’s correspondence. At the end of 1689, Leibniz made the acquaintance in Modena not only of the physician Ramazzini but also of the chemist Bernardino Corradi. With the approval of Ramazzini, Leibniz supported Corradi in a dispute, with a certain Giovanni Paolo Stabe de Cassina, about dangerous emissions being produced in applications, or processing, using vitriol. Leibniz’s backing took the form of a contribution to Corradi’s polemical pamphlet against his opponent, entitled Raccolta di tutto quello che fin ora estato scritto nella virtuosa gara iatro-chimica (1690). Leibniz’s contribution consisted of a letter sent to both Ramazzini and Corradi, on January 24 and 26, 1690, respectively, and it was essentially an historical note about the “Historia inventae tincturae Scarlatinae”, or the discovery of scarlet dye by the Dutch innovator Cornelis Drebbel (1572–1633). Leibniz referred here specifically to Drebbel’s tract entitled, in its German translation, Ein kurzer Tractat von der Natur der Elementen (1608). Political economy, and the application of mathematics to economicopolitical matters, was yet another interest of Leibniz in the early 1690s, and

Introduction: The Core Themes

191

later. The work of William Petty (1623–1687), in particular, had attracted his interest at this time, as is evident from remarks in letters sent to Ludwig Justus Sinold (alias von Schütz), on October 20, 1690, and to Henri Justel, on January 23, 1691, in which he referred to Petty’s works on political arithmetic,151 namely Deux essays d’arithmetique politique, touchant les villes de Londres et Paris (1686) and Two essays in political arithmetick, concerning the people, housing, hospitals &c. of London and Paris (1687). In the years that followed, Leibniz continued to refer, or allude, to Petty’s work on political economy in his correspondence, for example, in a letter of February 11, 1697, to Thomas Burnett of Kemney, in a memorandum attached to a letter to Johann Theodor Jablonski, on March 19, 1701, and in a letter to Christian Titius, on April 12, 1702, where he referred once again to the seminal work of Petty as being a specimen from the field of political arithmetic (“quodam Arithmeticae politicae genus, cujus specimen dedit Guilielmus Pettius Anglus”). In the early 1690s, topics in the area of mercantile economics continued to have a special significance in Leibniz’s correspondence. These included the improvement of the system of coinage and of the wine and brandy trade, the economic development of kiln technology for ore and glass smelting, increasing of agricultural production by the use of manures, and the possibility of silk production through the growing of mulberry trees in combination with the rearing of silkworms. Likewise of importance in these years was the discussions, that emerged or continued, regarding metal refinement or ennoblement, specifically for gold, silver and lead production, and regarding pearl cleansing procedures, or about retort manufacture, about salt production and oil production processes, and much more besides. However, the considerations of these processes, or process improvements, did not have the importance they had in earlier years, a situation reflected, for example, in remarks made by Crafft, in a letter of March 5, 1691, about the futility of entrepreneurial involvement in manufactories without princely or baronial participation. Likewise, in the years between 1693 and 1696, Leibniz did not find any great sphere of activity as regards his interest in economic and trade advancement. Although he was informed by his correspondents about a range of different projects, he failed in several instances  – for example, regarding salt works, linen drapery or wallpaper manufacture – to advance beyond the reception, or intake, of intelligence or, at best, he could only offer encouragement to others as, for example, regarding glass working for optical equipment or porcelain manufacture. In end effect, apart from his renewed activities in mining in the Harz region, there was but a single undertaking in the economic field, in which 151 Cf. T. McCormick, William Petty and the ambitions of political arithmetic, Oxford, 2009.

192

Introduction: The Core Themes

he was seriously involved in this period, namely that for the production of brandy from native sugar. This project was also motivated in part by his obligations towards his old, and in the meanwhile luckless, associate, namely Crafft. In the course of the War of the Grand Alliance (1688–1697), the helplessness of the German empire, in the face of the conquest-oriented French king, caused Leibniz to reflect very early on possible counter-measures on the economic front. To this end, a trade war seemed to be an option and, by a favorable coincidence, Crafft learned, in the fall of 1693, of a projected brandy manufactory in the town of Münden, an enterprise in which he immediately involved himself. In the same vein, Crafft had been able to inform Leibniz, on October 19 of that year, about a new ferment that had been developed in Hamburg. Since the greatest part of the brandy and cognac, consumed in Germany, was imported from France, it seemed that considerable economic damage might be inflicted on the enemy through the domestic production of such distillates. Unlike the French brandy production from wine, sugar solutions (syrup or treacle) were to be employed in the contemplated German scheme. After Crafft had reconnoitered the processes used for such distillates in Holland, he and Leibniz signed a contract for the formation of a company, whose aim was the production of brandy or a brandy substitute. According to the contract – that was done at Hanover on May 14, 1694 – a quarter of the proceeds of the company were to be used for pious or charitable purposes. A final stipulation was that the company so formed be limited to the two signatories to the agreement, a clause that in the end would prove to be ominous for Crafft. Since Leibniz was not yet convinced of the profitability of the production process, he ordered, on the one hand, further trials to be carried out with, among other things, the goal of producing vinegar from the residue of the distillation process – a matter which was referred to in Crafft’s letter of August 8, 1694 – and, on the other hand, he carried on detailed negotiations with a merchant in Hamburg, called Danneberg, about the process he employed. There was also contention between the parties to the contract regarding the location of the production facility. While Crafft advocated England as the place of production, Leibniz favored Holland, as is to be seen from a passage in Crafft’s letter of early October 1694. And so it was agreed to undertake the initial preparations in Holland, to where both of them travelled at the beginning of November. In Amsterdam, during the second half of November, they wrote a series of memoranda and letters, which were intended for the Stadhouder (or head of state of the Dutch republic),152 William III, and (in the wake of the revolution of 152 Cf. for example, J. I. Israel, The Dutch republic: Its rise, greatness, and fall, 1477–1806: The Oxford history of early modern Europe, New York, 1995.

Introduction: The Core Themes

193

1688–1689 and the Dutch invasion) king of England, for his diplomat George Stepney, and for the general field marshal of the forces of the States-General, and governor of Mastricht, duke Johann Adolf of Holstein-Sonderburg-Plön. The half-English prince of Orange (son of Maria Henriette or Mary Stuart and grandson of Charles I) had come to power in 1672, the so-called calamity year in Dutch history which saw, in the spring of that year, the outbreak of the ‘Third Anglo-Dutch War’ (1672–1674), in which England fought in alliance with France against the Dutch republic, and additional declarations of war by the German bishoprics of Münster and Cologne.153 The threat of full invasion, and the ensuing domestic fury and civil strife, then culminated in the brutal assassinations of the ‘grand pensionary’ of Holland, namely the mathematician and author of Elementa curvarum linearum (1661), Johan de Witt, together with his brother Cornelis de Witt, in August of that year.154 Apart from their very extensive literary estate,155 a series of references to the de Witt brothers are also to be found in Leibniz’s manuscript papers and correspondence, and the Elementa curvarum linearum was alluded to, for example, in letters exchanged with John Wallis (on August 9, 1697, and January 8, 1699),156 and with L’Hospital (on March 23, 1699).157 Also to be found among Leibniz’s manuscript papers, and in his correspondence, are numerous reports about William’s campaign in Ireland in 1690 following the revolution of 1688–1689.158 Thereafter William also advanced in terms of personal wealth and, with his acquired fortune at the time of his death in 1702, he was to head the list of the 500 richest individuals in the 153 Cf. Q. Barry, From Solebay to the Texel: The third Anglo-Dutch war, 1672–1674, Warwick, 2018. Regarding the ‘year of disaster’ in particular, cf. K. E. Hollewand, The banishment of Beverland: Sex, sin, and scholarship in the seventeenth-century Dutch republic, Leiden, Boston, 2019, in particular the ‘Prologue’ (p. 25). 154 Cf. for example, H. H. Rowen, John de Witt, Grand pensionary of Holland, 1625–1672, Princeton, 1978. Regarding Johan de Witt’s mathematical work, cf. F. van Schooten (ed.), J. de Witt, Elementia curvarum linearum, in: R. Descartes, Geometria, vol. 2, Amsterdam, 1661, pp. [153]–340; A. W. Grootendorst, Jan de Witt’s Elementa curvarum linearum: Liber primus, (Sources and studies in the history of mathematics and physical sciences), London, Dordrecht, Heidelberg, New York, 2000; A. W. Grootendorst, Jan de Witt’s Elementa curvarum linearum: Liber secundus, (Sources and studies in the history of mathematics and physical sciences), London, Dordrecht, Heidelberg, New York, 2010. 155 Regarding the mammoth De Witt epistolary estate, cf. Bodleian Libraries, University of Oxford, EMLO: Early Modern Letters Online (http://emlo.bodleian.ox.ac.uk/). 156 Cf. A III,7 N. 128, p. 528, and A III,8 N. 3, p. 11. 157 Cf. A III,8 N. 21, p. 77. 158 Cf. J. G. O’Hara, “Leibniz and the Jacobite war: Reports and reflections on the battle of the Boyne and events in Ireland, 1689–91”, Proceedings of the Royal Irish Academy, vol. 91C, (1991), pp. 1–20.

194

Introduction: The Core Themes

Dutch republic during the whole of the 17th and 18th centuries.159 And so, in approaching the king of England in November 1694, seeking support of their enterprise for brandy production, Leibniz and Crafft were in fact knocking on the door not just of a head of state, but also of a prince with enormous personal wealth. Of the two letters, written by Leibniz and Crafft and addressed to William III, only that of November 18, 1694, was actually dispatched. It was included as an attachment to a letter, dictated by Leibniz and written by Crafft, to Stepney on the same day. It was, however, never presented to the addressee, as is evident from Stepney’s letter to Leibniz of March 4, 1695. Stepney reported that he had handed Crafft’s latter to Charles Talbot, the duke of Shrewsbury and ‘secretary of state’, who was not willing, however, to pass it on, since Crafft had not been prepared to disclose the details of his secret process. In the letter in question addressed to William III, Leibniz and Crafft argued that part of the strength of France lay in trade in foodstuffs and merchandising, on which its neighbors were dependent. Their research had then revealed a method of circumventing this French trade monopoly, namely by enabling the English, together with their allies, to independently obtain the requisite products in great quantity, of high quality and at a low price, a development which would, in due course, lead to irreversible damage to French foreign trade. Furthermore, it was claimed that such a trade war might even be legitimately continued in times of peace and would thus inflict long-term damage and, in effect, be tantamount to the destruction of a French province. Such damage would of course affect only the adversaries of England and Holland, and would promote commerce in the provision of the requisite raw materials, give increased turnover, and serve to increase the wealth and power of the allies, promoting navigation and plantations, a development which might even lead to overseas expansion, like in south America. Thus, in end effect, it was claimed that France would be mortified, or humiliated, while William and his allies would be the beneficiaries. For the realization of such projects, a company should be formed and provided with prohibitive privileges to exclude any French influence. In effect, they were requesting a Royal privilege for the protection of participating entrepreneurs, and they expressed their willingness to particularize the details together with a minister appointed by the king.

159 Regarding the 500 wealthiest persons, and wealth, belief, power and culture in the Dutch republic, cf. K. Zandvliet, De 500 rijksten van de republiek: Rijkdom, geloof, macht en cultuur, Zutphen, 2018.

Introduction: The Core Themes

195

Finally, their submission called for a portion of the company’s profits to be set aside for the promotion of pious or charitable causes, and of the practical arts, under the guidance of the applicants. On December 26, 1694, following Leibniz’s return to Hanover, Crafft was able to report, from Amsterdam, for the last time about a general acceptance of the project. Thereafter, there followed a succession of bad news reports and evil tidings in relation to the project. At first – as reported in Crafft’s letter of December 30, 1694 – there arose contractual difficulties. These were followed by reports of the need for a better ferment, and for the establishment of smaller subsidiary companies, all of which contributed to delays. In due course, a disappointed Leibniz had to abandon all hope of a successful conclusion of the enterprise, and he wrote off the advance payments he had made, the sole consolation for him being that his lost investment had been in the service of the commonweal, as he wrote in his letter to Crafft of July 5, 1695. After an extended period of silence, Crafft finally acquiesced, on February 23, 1696, to Leibniz’s decision in listing economic factors that had made the death of the undertaking inevitable. In particular, he suggested that sugar and syrup prices were only low enough in America to enable the profitable production of brandy from this raw material. However, the imaginative and relentless Crafft did propose a new project, which he had encountered in connection with his personal fight against gout, namely for the removal of the fusel oils from fruit and corn liquor by means of distillation with quicklime. But Leibniz’s reaction, in his reply on March 2, was cool, noncommittal, and even recriminatory. By mid-1696, the brandy project seemed wholly and permanently debilitated. And so Crafft’s economic survival became increasingly difficult, and he was forced to seek new possibilities to secure his livelihood. The frequency of letters to Leibniz decreased and the two long-time companions became increasingly estranged. In the last nine months of his life, Crafft wrote a total of three letters to Leibniz from Amsterdam. The final stroke, that would wipe the slate clean in this correspondence that had been conducted since 1671, was inflicted by Leibniz, on March 8, 1697, just one month before Crafft’s death. Initially however, on September 26, 1696, Crafft could, in spite of all, report progress on the brandy project to Leibniz. He was still hoping to be able to live from the project in the future and even to generate surpluses. In addition, he informed Leibniz about contacts to a German business partner, named Ludwig Wilhelm von Stauff zu Löwenstadt, whom Leibniz, however, regarded as dubious and unsavory. Notwithstanding his optimistic outlook, Crafft now found himself in the role of solicitant before Leibniz. Efforts for the relocation of his wife to join him in Amsterdam, and payments to an assistant there, had led to a financial shortfall so that he was now forced to request a payment of

196

Introduction: The Core Themes

40 Taler from Leibniz. When, on February 26 1697, he complained to Leibniz about the outstanding payment, he must have realized that their relationship had suffered. He presented, among other things, a follow-up project to the brandy project that would be much better and to which he had aspired over a period of forty years. Being gout-ridden, however, he had been prevented from pursuing this and further projects. Crafft’s desperate situation was repeatedly articulated in between moments of excitement about his conceptions and discoveries. He suggested that Leibniz should seek financial support for the brandy project from the court in Celle. Furthermore, he once again insisted that Leibniz should send him money. Leibniz’s reply, on March 8, reveals the fact that he had already supported Crafft financially to a considerable degree and that he had, as a quid pro quo, called for a continuation of their correspondence on a regular basis. He had, however, been bitterly disappointed by Crafft’s failure to meet this condition. Leibniz complained, above all, about the circumstance that the promised communication of information had not materialized. He felt himself exploited and treated “like a cow being milked”, and he insisted that he was not pursuing personal advantage but rather the public interest. He expressed doubts concerning the prospects for the brandy project, in particular, and on the practicability of Crafft’s projects, in general, demanding presentable results in advance of any further financial support. He reproached Crafft with the circumstance that his ambitious plans, in collaboration with Baron von Stauff, had come to nothing since there had been no further mention of them. In the final sentence of this final letter, Leibniz then laid down strict and rigorous conditions for a continuation of their business partnership and, in doing so, he effectively terminated an association, and even friendship, that had existed for more than 25 years. A month later, on April 9, 1697, Crafft died ill and poverty-stricken in Amsterdam. In connection with the death of Johann Daniel Crafft stood Leibniz’s correspondence with Crafft’s widow, Dorothea Crafft, as well as with the Dutch correspondents Nicolaas Listingk and Ameldonck Block. Leibniz had met Listingk during his stay in Amsterdam, in November 1694, and it was from this correspondent that he learned – in reply to a query of his – of Crafft’s death from a letter of July 9, 1697. In mid-July 1697, Leibniz then passed on the sad tidings from Listingk’s letter to the widow. In this letter, he justified his dealings with Crafft, pointing out that his financial support for the deceased had been misappropriated again and again. Almost twenty years before Crafft’s death, and during a previous visit to Amsterdam in mid-July 1677, Leibniz  – in a letter sent from Hanover to

Introduction: The Core Themes

197

Friedrich Adolph Hansen and Henri Justel in Paris, for forwarding to Jean Paul de la Roque – had given the correspondents a detailed account of Crafft’s association with Heinrich Brand, the discoverer of phosphorus. The opening words of this letter characterized Crafft as an inquisitive person working in Holland for the sake of personal fortune and glory: “Monsieur Krafft est un curieux, qui travaille en Hollande pour sa fortune et pour sa gloire”. Then, in the wake of Crafft’s death, Leibniz once again spoke critically of him, in his letter, of mid-July 1697, sent to Ameldonck Block with whom Crafft also had debts. Here it becomes evident how objectionable and malodorous Leibniz had found Crafft’s business relationship with Baron von Stauff, whom he referred to as “un certains Baron Allemand”, and which ultimately had led to his demise. While Leibniz praised Crafft as a chemist and technician, he attested him impaired judgment and inability in managing money, and he complained about his ingratitude and greed for profit. Crafft had hoped through a great discovery to become rich someday. Leibniz claimed that he had, again and again, cautioned and advised him to follow an ordinary profession and, like himself, to work for the common good. Furthermore, he explained how he had supplied Crafft with money, that was partly his own, and that he had been willing to continue doing so, provided Crafft adhered to the terms of the agreement between them. 7.5 The Organization of Science and Education Throughout the 1680s and 1690s, Leibniz had a pronounced interest in the establishment or promotion of academies and learned societies, both in Germany and in other European countries.160 Besides his personal ambition to receive recognition of the Académie des Sciences, both a draft of a letter addressed to Jean Baptiste Colbert and one dispatched to Jean Gallois, in October 1682, reveal a particular commitment on Leibniz’s part to the organization and the advancement of science with government or princely support. The fact, that the French Académie was in a position to carry out large-scale projects, was repeatedly revealed to Leibniz through his correspondence with Mariotte. The latter not only reported continuously about regular meetings of the Académie but also, for example, about the journey of a group of savants to the equatorial region, in the course of which the astronomer Jean Richer’s disputed measurements of the length of the seconds pendulum in Cayenne, in French Guiana, were confirmed. A further group of academicians undertook

160 Cf. H. Rudolph, “Scientific organizations and leraned societies”, chap. 31 (pp. 543–562) in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

198

Introduction: The Core Themes

journeys for the preparation of an improved map of France and, furthermore, they were to dissect samples of rare fish species. Whereas the correspondence with Nehemiah Grew – who had relinquished his office as secretary of the Royal Society of London at the end of 1679 – was interrupted in the spring of 1680, Leibniz was kept informed about the activities of the Royal Society by Theodor Haak, although not as comprehensively and regularly as by Mariotte regarding the activities of the Académie des Sciences. Leibniz was also able to maintain contact with the Leopoldina, the Academia Naturae Curiosorum in Halle, with the help of the Frankfurt physician Sebastian Scheffer. Through the intercession of Leibniz, an article about an oversized kidney from the Journal des Sçavans appeared, under Scheffer’s name, and in a Latin translation with the title “De rene monstroso”, in the Miscellanea Curiosa Medico-Physica, the journal founded by the Leopoldina in 1670. Leibniz had of course used his contact to Scheffer to propose, to the Academia Leopoldina, a system of corresponding terrestrial magnetic observations. This proposal in turn gave Johann Georg Volckamer reason to consult with Johann Christoph Sturm about the creation of a mathematical-magnetic association for such an undertaking. Sturm, for his part, wrote an Epistola invitatoria ad observationes magneticae variationis  … instituendas (1682), in which the learned and the scholarly were called upon to undertake corresponding observations. Sturm’s appeal – following the initiating step taken by Leibniz and revealed in his correspondence with Scheffer, between June and September 1681, and on August 18, 1682 – may not have had quite the desired success, yet it did find a greater resonance than similar previous invocations. With another proposal Leibniz was less successful, namely, that to encourage the Leopoldina to pursue utile activities. Leibniz prompted Volckamer, through Scheffer, to encourage the physicians of the town of Nuremberg, for the sake of science, to establish contact with the renowned tradesmen or craftsmen of that city, and to publish the results of such discussions. Volckamer’s reply, quoted in Scheffer’s letter to Leibniz of April 3, 1682, was to the effect that, while the suggestion was by no means bad, no scholar would be willing to communicate his knowledge to tradesmen or craftsmen, especially without financial compensation or remuneration. As Leibniz confided to Scheffer, in his reply in mid-April (see the leading quotation in the heading of this introductory section), he considered the reaction from Nuremberg to be ludicrous. His vision was that the bookish erudition of the scholars should be annotated with countless and useful explanatory notes of the practitioners and craftsmen. Here Leibniz broached a topic which would find the interest of historians of science in the twentieth and early twenty-first centuries, namely the relation of the scholar or scientist to the craftsman, artisan and practitioner, since the

Introduction: The Core Themes

199

Renaissance, and particularly at the time of the Scientific Revolution.161 The French pedagogical reformer Petrus Ramus (1515–1572), for example, believed that a way to unify theory and practice could be drawn out of the mix of practical mathematics and artisanal activity going on in Nuremberg and, in 1568, he visited the workshops of artisans there.162 Likewise, the mathematician and instrument maker Georg Hartmann (1489–1564) moved to Nuremberg, where he set up an instrument shop and where he made globes, astrolabes, sundials and quadrants.163 It was likewise in Nuremberg, that an expanding cumulative knowledge, acquired from minting coins, was first documented in the mid fifteenth century; this invention was at the heart of the central European mine boom, producing increased yields of silver.164 The scholar / craftsman cleavage was of course not confined to Nuremberg but was also evident, for example in England,165 and in many places in continental Europe,166 where the reality of practical mathematics and the role of mathematical practitioners was manifest. It was, however, the physicians and surgeons of Nuremberg towards whom Leibniz’s ire was directed, a professional group to whom technical knowledge

161 Cf. for example, A. R. Hall, “The scholar and the craftsman in the scientific revolution”, pp. 3–23, and the following commentaries by R. K. Merton (pp. 24–29) and F. R. Johnson (pp. 30–32), in: M. Clagett (ed.), Critical problems in the history of science, Madison (Wisconsin), 1969; D. Raven, W. Krohn, R. S. Cohen (eds.), Edgar Zilsel [(1891–1944)]: The social origins of modern science, (Boston Studies in the Philosophy of Science, vol. 200), Dordrecht, 2003; P. H. Smith, The body of the artisan: Art and experience in the scientific revolution, Chicago, 2004 (and 2012); P. O. Long, Artisan / practitioners and the rise of the new sciences, 1400–1600, Corvallis (Oregon), 2011. 162 Cf. P. H. Smith, (note 161), p. 66. 163 Cf. P. O. Long, (note 161), p. 98. 164 Cf. p. 110. 165 Cf. E. G. R. Taylor, The mathematical practitioners of Tudor and Stuart England, Cambridge, 1954 and 1967, and The mathematical practitioners of Hanoverian England, Cambridge, 1966; S. Johnston, “The identity of the mathematical practitioner in 16th-century England”, pp. 93–120 in: I. Hantsche (ed.), Der “mathematicus”: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, (Duisburger Mercator-Studien, vol. 4), Bochum, 1996; G. Wickel, “Landvermessung als praktische Geometrie in England um 1600”, pp. 263–280 in: B. Heinecke, I. Kästner (eds.), Wettstreit der Künste: Der Aufstieg des praktischen Wissens zwischen Reformation und Aufklärung, (Europäische Wissenschaftsbeziehungen, vol. 17), Aachen, 2018; P. Beeley, “Practical mathematics and mathematical practice in later seventeenth-century London”, British Journal for the History of Science, (Special issue: London 1600–1800: Communities of natural knowledge and artificial practice), vol. 52(2), (2019), pp.[225]–248. 166 Cf. L. B. Cormack, S. A. Walton, J. A. Schuster (eds.), Mathematical practitioners and the transformation of natural knowledge in early modern Europe, (Studies in History and Philosophy of Science, no. 45), Cham (Switzerland), 2017.

200

Introduction: The Core Themes

was indeed transferred at times, for example in the development of artificial limbs and of prosthetic technology in early modern Europe.167 Shortly after the accession of duke Ernst August in 1680, Leibniz proposed to his prince the establishment of a military academy in Hanover, or Göttingen, perhaps with the ulterior motive of assembling a circle of scholars nearby. As mathematics professor for the proposed academy Leibniz had the Dutch mathematician Ferguson in mind and, perhaps, the aristocratic Tschirnhaus as its director. Later, writing from Paris on May 27, 1682, and again on August 6 of that year, Tschirnhaus informed Leibniz about a plan of his own to assemble a group of scholars around him at his manor in Kieslingswalde, near Görlitz. Tschirnhaus aspired to a pension from the Académie des Sciences, with which he hoped to pay salaries to the Danish mathematician Georg Mohr, to a tradesman, a physician as well as an individual versed in algebra, all of whom would work to carry his inventions to execution. Although, in the case of Tschirnhaus, the pension never did materialize, Leibniz surely followed his plans with interest, just as in the case of the foundation of a scientific academy in Venice, by Ambrose Sarotti, the secretary of the republic of Venice, which was referred to by Friedrich Schrader in a letter of April 23, 1682. Sarotti had returned from a diplomatic mission to England and drew inspiration for his academy from the Royal Society and, while in London, he had arranged for Denis Papin to participate in the enterprise. From Schrader and Scheffer, Leibniz requested further details in July–August of the same year and Scheffer, replying on August 18, raised the prospect of soon being able to provide him with further details about Sarotti’s undertaking. During the early 1690s, Leibniz continued to be interested in the establishment or promotion of academies and societies as well as of institutions like the “Collegium Imperiale Historicum”, in Vienna, the “Kunst- Rechnungs- liebende Societät”, in Hamburg, or a projected “Societas Germana” that might be independent of the grace and favor of a sovereign. As regards the organization of science in England, and its institutions, there was also a long-standing interest of Leibniz that continued after 1690. Following his return from Italy, he had resumed his correspondence with Henri Justel, on October 20, 1690. Through this channel he received, between 1691 and 1693, information about English scientists and about the Royal Society including, for example, the appointment of Robert Southwell as President and that of Edmond Halley as secretary of the

167 Cf. H. Hausse, “The locksmith, the surgeon, and the mechanical hand: Communicating technical knowledge in early modern Europe”, Technology and Culture, vol. 60(1), (2019), pp. 34–64.

Introduction: The Core Themes

201

Society, as well as about the latter’s planned research journey in the Atlantic, during which the variation of the magnetic needle was to be investigated. After Leibniz had learned from Justel, in a letter dated “le 25 mars 92”, that Halley was prepared to correspond with him, he undertook the first step to initiate this correspondence. His letter of June 3, 1692, was forwarded by Justel to the prospective correspondent. However, Halley’s answer failed to materialize, and there was to be an interval of eleven years until the correspondence between the two eventually developed in July 1703. From Justel and Halley, as the letter of June 3 reveals, Leibniz hoped above all for information about the literary bequest and manuscript estate of Robert Boyle, and about the scientific treasures this was thought to contain. More detailed information about recent English advances in science and technology was also requested. Thus, Leibniz was interested in a sea-water desalination process of the English physician and Modena resident Nathan Lacy, in an English mining engineer called Kirckby (or Kirkby), who was involved in mining in the Erzgebirge or Ore Mountains in Saxony, and in the extraction yield of a recently discovered silver mine in Wales. Leibniz likewise enquired about English scientists and mathematicians he had previously been acquainted with, like John Collins (1625–1683), John Pell (1610–1685), Robert Hooke, Christopher Wren, John Wallis, and of course Newton whose reaction to the objections to his Principia mathematica – formulated by Huygens in the Discours de la cause de la pesanteur (1690) – was of particular interest. In the 1690s, Leibniz was able to uphold his life-long ambition, firstly, to establish and advance societies, colleges and institutions for the collection, advancement and resourcing of knowledge and practical skills and, secondly, to improve and extend existing institutions in order to serve the commonweal, or “bonum commune”, in both theory and practice. The nature of his engagement, or commitment, included the conception of plans and memoranda to support the initiatives of kindred spirits, and even the exertion of influence in the filling of vacancies and appointments. The spectrum of institutions and associations considered was quite broad. It included, on the one hand, renowned and established academies (like the Académie des Sciences, the Royal Society of London, and the Leopoldina), universities (like in Gießen, Helmstedt and Wittenberg), military academies (like the one in Wolfenbüttel), grammar schools (like that in Göttingen) and, on the other hand, scholarly coteries (like the “Kunst- Rechnungs- liebende Gesellschaft” in Hamburg, and the “Collège de curieux” in Kassel). Thus, when on January 31, 1695, Leibniz was informed by Haes that landgrave Karl wanted to establish such a “Collège de curieux” in his principality – in which Papin was to be one of the first members – he was prompted to provide a detailed representation on the matter, which he

202

Introduction: The Core Themes

included with his reply to Haes of March 6 for presentation to the landgrave. From the extant penultimate version of this reply, it can be seen that Leibniz was sending the landgrave a proposal for the establishment of an Academy of Sciences and Arts (“Akademie der Wissenschaften und Künste”). Haes could, in turn, inform Leibniz, on March 28, of the admiration and gratitude of the landgrave. The birth of this academy (the “Collegium Illustre Carolinum”) was, however, to be delayed until the year 1709. The projects of Leibniz’s former mathematics professor (at Jena in 1663) Erhard Weigel, like his “Collegium artis consultorum” project, his pedagogical ideas and his school reform project,168 and even his calendar reform efforts in the year 1700,169 deserve special attention in this context. A (non-identified) letter Weigel wrote to Leibniz, on February 18, 1693, as well as letters and attachments Leibniz sent to Huldreich von Eyben (in June 1693), to Wilhelm Ernst Tentzel (on June 29), and to Tschirnhaus (at the end of June), contained proposals for the improvement of the organization of science. Among such proposals was Weigel’s project for a “Collegium artis consultorum”, which he referred to in a letter to Leibniz of April 26, 1694. This project provided occasion for Leibniz to think once again about scientific institutions that would not be dependent on the grace and monetary support of princes. The issue of the “Collegium” was likewise addressed, not only in Leibniz’s correspondence with Tschirnhaus, but also in the first letter of November 29, 1694, that Leibniz received from the physician Alexander Christian Gakenholz following a meeting of the two, in Hanover, shortly before. By 1693, Weigel’s commitment to pedagogy had already persisted for more than a decade.170 In fact, the year 1681 had marked the beginning of a creative period in Weigel’s life which was dominated by pedagogy. He approached both the Imperial Diet (the “Reichstag”) in Regensburg (in 1683), and also princes willing to invest in his schemes and, furthermore, he campaigned for support in realizing his school reform enterprise. In the year 1683, he started a private school project in his own house. Based on this experience, and following the 168 Cf. L. Friedrich, “Pädagogische Perspektiven zwischen Barock und Aufklärung: Die Pädagogik Erhard Weigels”, pp. 39–68 in: R. E. Schielicke, K.-D. Herbst, S. Kratochwil (eds.), Erhard Weigel –1625 bis 1699: Barocker Erzvater der deutschen Frühaufklärung, (Acta Historica Astronomiae, vol. 7), Frankfurt am Main, 1999; K. Habermann, K.-D. Herbst, Erhard Weigel (1625–1699) und seine Schüler: Beiträge des 7. Erhard-Weigel-Kolloquiums 2014, Göttingen, 2016. 169 Cf. J. Hamel, “Erhard Weigel und die Kalenderreform des Jahres 1700”, pp. 135–156 in: R. E. Schielicke et al. (eds.), note 168 above. 170 Cf. W. Hestermeyer, Paedagogia Mathematica: Idee einer universellen Mathematik als Grundlage der Menschenbildung in der Didaktik Erhard Weigels, zugleich ein Beitrag zur Geschichte des pädagogischen Realismus im 17. Jahrhundert, Paderborn, 1969.

Introduction: The Core Themes

203

completion of the necessary building measures, there followed a public school project in 1690. An outstanding aspect of Weigel’s School of Virtue (“Kunstund Tugendschule”), as it was called, was the range of teaching materials he developed himself. At the core of his method of teaching was the activity concept, with the children being taught in such a way that they remained active as much as possible during the learning process. In this context, Weigel developed a so-called “Schreibregel”, or writing rule, that availed of a mechanical instrument he had designed. This was used in elementary instruction, for the training of the motor function in learning to write, and it allowed the simultaneous execution of scribal movements by a large number of children. In addition to this writing rule, there was also a so-called “Leseregel”, or reading rule, for school starters and, for teaching arithmetic, a corresponding learning aid was made available. A special attraction of Weigel’s private school was the so-called “Schwebeclaß”, or floating class, which was intended to enable the scholars to accompany their memory exercises with swaying movements. It consisted of desks mounted on a floor plate or platform made of wooden planks. The platform was suspended by means of strong ropes attached to iron hooks, and it was constantly maintained in a horizontal position parallel to the ground. In this way, a pleasant tranquility in the midst of movement was achieved, and the rhythmic movements of the individual children were combined with the common movement of the entire class. The syllabus of instruction combined rhythmics and calculation, reading and swinging, on the “Schwebeclaß” platform. Weigel’s dynamic instruction retained, by and large, the traditional syllabus but shifted the emphasis more towards mathematics and science. The vernacular language, or tongue, was introduced as a full-fledged medium of instruction. Weigel chose not to curtail the amount of material, that had to be learned, but rather the time that had previously been required. His commitment to pedagogy and learning was reflected in his correspondence with Leibniz, for example in his letter of April 26, 1694, in which he elaborated his school reform plans. Replying on May 20, 1694, Leibniz strongly praised Weigel’s efforts and he announced his continuing support for these in political circles. In connection with the establishment in the year 1700 of the Berlin Society of Sciences,171 or the Prussian Academy of Sciences,172 membership was 171 Cf. H.-S. Brather (ed.), Leibniz und seine Akademie: Ausgewählte Quellen zur Geschichte der Berliner Sozietät der Wissenschaften 1697–1716, Berlin, 1993. 172 Cf. E. Knobloch, “Mathematics at the Prussian Academy of Sciences”, pp. 1–8 in: H. G. W. Begehr, H. Koch, J. Kramer, N. Schappacker, E.-J. Thiele (eds.), Mathematics in Berlin, Basel, Boston, Berlin, 1998.

204

Introduction: The Core Themes

offered to mathematicians, scientists and physicians, like Johann Bernoulli, Friedrich Hoffmann, Philippe Naudé, Pierre Dangicourt and Georg Wolfgang Wedel. In taking this step, Leibniz was guided as well by his own interests as, for example, in the construction of an astronomical observatory. While he hoped for support from Hoffmann, in the realization of his long-entertained project for gathering medical and meteorological ephemerides, he tried to influence Naudé and Dangicourt to do research on dyadic or binary mathematics. Leibniz would have liked to be able to entice Johann Bernoulli into his proximity – possibly by providing him with a mathematical professorship at Frankfurt an der Oder – but the Berlin Society did not have the requisite resources, as his letter of June 24, 1701, to Bernoulli reveals. The foundation of the Society did indeed meet with goodwill, but the dilatory start also led to some skepticism. At first, Bernoulli hoped that the new society would – in comparison with its foreign counterparts – develop like a cypress among the fellow botanical species viburnum or arrowwood, as he wrote to Leibniz on October 16, 1700. However, nine months later, Bernoulli had the impression that the Society was moribund again, a sentiment he expressed in his letter to Leibniz, on July 9, 1701. Hoffmann reported, on August 30, 1701, that many were beginning to seriously have doubts about the prospects for the success of the Society. In Hoffmann’s view, expressed in his letter of October 4, only Leibniz’s influence and involvement could guarantee the success of the undertaking. In a letter of November 8, Hoffmann likewise expressed the fear that too many members had been accepted, and that this was to the detriment of the reputation of the Society abroad. Writing to Tschirnhaus, on April 17, 1701, Leibniz referred to the fact that the financing of the project was a major problem. It is understandable, therefore, that Leibniz did not respond to Bernoulli’s repeatedly expressed desire for financial support for his experiments. Interesting for Bernoulli  – whose articles were on occasions rejected by Otto Mencke, the editor of the Acta Eruditorum, because of the provocations they contained – was the prospect of having access to a journal of his own, a matter alluded to by Leibniz in letters of September 6, 1700, and September 13, 1701. However, the first volume of the Society’s envisaged journal, namely the Miscellanea Berolinensia, only appeared in the year 1710. Also unresolved, at the end of the year 1701, was the financing of Hoffmann’s lectures in experimental physics in Halle which, while not directly connected with the Berlin Society, was rooted in the broader context of the promotion of science by the court at Berlin. Leibniz backed this endeavor, in the wake of his meeting with Hoffmann in Halle in September 1700, since he was convinced of the great benefit to be gained from experimental science. In his letter of November 1, 1701, Leibniz informed this correspondent that the authorities had provided about a hundred Taler per

Introduction: The Core Themes

205

year for his lectures. In this context, Leibniz expressed a remarkable sentiment, namely that a single lesson of a “collegium experimentale” – concerned with physical-mathematical inventions and experiments – had a greater value for him than a hundred corresponding lessons in metaphysics, logic or ethics. Hoffmann’s problem was, however, not just of a financial nature, as he reported to Leibniz on November 8, 1701. His advocacy of an empirical science, built on the foundation of a mechanical world view inspired by Descartes, was being thwarted at the University of Halle by Christian Thomasius, who offered his own experimental lectures to promote his spiritualistic approach. Leibniz attempted to communicate enthusiasm for science to the Prussian king Friedrich I – who was also elector Friedrich III of Brandenburg-Prussia – by means of spectacular experiments. Thus, on February 16, 1701, Leibniz requested that Hoffmann confide to him a recipe for a fiery spirit (“spiritus igneus”), by which two oils catch fire on being mixed together. The spectacle, he thought, would benefit both the Society and the correspondent himself. The circumstance that Johann Bernoulli applied, on October 16, 1700, for membership in the Berlin Society, by presenting mercury vessels that could be made to glow following shaking, also proved to be highly welcome. Leibniz suggested to Hoffmann (on March 19, 1701), and to Wagner (in a letter sent to Johann Andreas Schmidt on February 12, 1701), that they produce, with the aid of Bernoulli’s process, curiosa such as luminescent insignia, scepters and crowns, as well as a luminous showcase or “museolum”, which he might present to the king in the name of the Society. The attempts to replicate Bernoulli’s experiments had a prominent place in Leibniz’s correspondence with Wagner, in the months of February and March 1701. In the vessels, a vacuum had to be created, and Wagner had first to construct the requisite instruments. In his letter of March 29, he revealed to Leibniz that he had succeeded in producing a luminescence which, however, was not comparable to that of Bernoulli. In the end, a luminous vial, sent by Bernoulli, was presented by Leibniz himself at the court, and then reported to the correspondent on December 27, 1701. Thereafter, the interpretation of Bernoulli’s experiments played only a secondary role, even though Bernoulli had provided starting points for an explanation. In addition to impressing the king, Leibniz hoped – as his letter of December 31, 1700, to Bernoulli reveals – through a comparison of different illuminant or luminescence phenomena, like mechanoluminescence – or the luminescence resulting from mechanical action on a solid, such as the sparkle produced when hard sugar is broken or scraped in the dark – to gain an insight into the cause of refulgence, or of luminescence in general. In spite of all difficulties, the Society’s project of establishing a system of medical ephemerides appeared to have achieved success by the end of the year 1701. Leibniz presented Hoffmann’s “spiritus igneus” to the royal family, in the

206

Introduction: The Core Themes

autumn of 1701, following which the king mandated the establishment of the ephemerides program, as Leibniz informed Hoffmann on November 1, 1701. This success marked the conclusion of a long-standing commitment. Shortly after Hoffmann had established contact with him, at the end of 1699, Leibniz took up again the project that he had initiated back in 1691. On January 19, 1700, he then asked Hoffmann to endeavor to establish a system of annual observations, under the aegis of the Academia Leopoldina, following the example of Bernardino Ramazzini in Modena. Just like the efforts of the theologians and mathematicians in their support of the calendar reform, physicians could, he thought, serve the public interest by collecting observations. Leibniz had indeed found the right addressee, since Hoffmann himself had for years been recording barometric, thermometric and hygroscopic data, as well as producing occasional ephemerides, as he informed Leibniz at the end of January 1700. His goal had been to understand the connection between weather and maladies, as well as the mode of operation of the barometer. Hoffmann most likely did not make the requisite effort to obtain an involvement of the Leopoldina, an institution that had previously not gone beyond a reprinting of Ramazzini’s ephemerides from the early 1690s. However, he did keep his promise to publish, for the following year, observational data that he had been systematically collecting in consultation with practitioners. The publication, entitled Observationes barometrico meteorologicae, et epidemicae Hallenses anni MDCC (1701), was dedicated to Leibniz and sent to him with a letter of April 10, 1701. That Leibniz was flattered by the dedication of the work to him, is evident from the beginning of his letter of April 18, 1701, to Hoffmann. The appearance of this work prompted Leibniz’s proposal to work towards achieving that the Prussian king decree the public funding of physicians in the provinces, in order to record weather and ephemeral data following Hoffmann’s example. Thereafter, Leibniz and Hoffmann strove to achieve this goal during visits to Berlin, and in correspondence with the court. The measure, that would be easy to implement, and cost nothing, could – as Leibniz wrote to the Brandenburg-Prussian minister Paul von Fuchs – provide an incomparable treasure of knowledge for human life. The theologian Daniel Ernst Jablonski, however, considered it advisable to await the constitution of the Berlin Society, as Hoffman informed Leibniz on June 15, 1701. Nonetheless, Leibniz and Hoffmann continued to plan the concrete organization and implementation of the royal mandate. Hoffmann translated a part of his Observationes into German and conceived a project, initially entitled “Entwurf zur Einrichtung von medizinisch-meteorologischen Beobachtungen” (Plan for the establishment of medical-meteorological observations), and sent to Leibniz with a letter of October 4, 1701.

Introduction: The Core Themes

207

Hoffmann also compiled, as an example, the data for a month, prepared drafts for a mandate, and proposed the names of certain suitable physicians. And, from his “Entwurf” or plan, it is clear that he considered it necessary that, at every location, the data be recorded by two physicians for purposes of mutual control. Besides weather and illnesses, they should also observe the living conditions and circumstances of the population at the specific locations, and in addition, the welfare of animals and field crops in order to explain the connection with illnesses. Hoffmann did not insist on the employment of barometers and thermometers but, rather, only recommended them, since Leibniz had expressed doubts, in his letter of September 23, 1701, that all participants would have access to such instruments. Hoffmann lauded the undertaking, not only with the expectation that insights into the occurrence and prevention of epidemics were to be expected, but he also hoped to throw light on the connection between weather, the human condition and planetary aspects. Although astrology was rejected by most philosophers and astronomers, at this juncture, nonetheless experience seemed to suggest a certain influence of celestial bodies. Hoffmann recalled that even Kepler had been affine to an “astrologiam meteorologicam”. Leibniz formulated the edict for king Friedrich I, along with detailed instructions based at least in part on Hoffmann’s drafts. Thus, borrowing from Hoffmann, he referred to lunar and solar phases but not, however, to the planetary aspects. An annotation with the words “non communic[atum]”, found on a copy of the edict, is indicative of the fact that this part of the project came to grief in its final stages. At the end of 1701, however, Leibniz was – as he reported to Sloane on December 27 – still optimistic about a mandate, that had been approved by the king, for the carrying out of such annual observations in the provinces by learned physicians. Further projects of the Belin Society played only a subordinate role in Leibniz’s correspondence at this juncture. In 1701, first on March 15 and then on December 27, he enquired of Wagner and Johann Bernoulli, respectively, about fire engines which the Society was willing to finance. The projects, which he mentioned to Tschirnhaus in his letter of April 17, 1701, included a calendar monopoly, the drainage of swamps and marshlands, and the idea of producing a German technical or specialized dictionary. Besides the Berlin academy, Leibniz also had his sights on other national academies. In 1699, Denis Papin was offered the post of curator of experiments by the Royal Society of London, and he was considering returning to England, as he confided to Leibniz on June 18, 1699. Leibniz, however, in his reply of July 4, advised the correspondent against pursuing this offer. The commitment of the Royal Society was not as great as in former times, he insisted, and furthermore the landgrave, of whose “curiosité grande et universelle” he had a

208

Introduction: The Core Themes

high opinion, could effectuate more for Papin. Leibniz had already expressed to Wallis, on April 9, 1699, his desire that the Royal Society be reinvigorated, just like the restructured Académie des Sciences. In his reply on April 30, Wallis informed him about new rules that would support scientific investigations, but he did not fail to acknowledge the contrasting financial endowments, and the corresponding possibilities, of the two academies. On the occasion of the appearance of Leibniz’s Novissima Sinica (1697), Wallis had reported about journeys to China by English merchants, which were also concerned both with Christian missionary ambitions and with the advancement of science. Then, on April 9, 1700, the English correspondent could inform Leibniz that mathematical instruments were to be acquired in China. Leibniz announced to Wallis, in his reply of September 3, that the Berlin Society wished to support the mission along the overland route to the orient, and could accordingly contribute to the advancement of the Anglican missionary efforts.173 That the propagation of the faith, with the aid of science, was an objective of the Berlin Society, Leibniz also confided to Sloane, on December 27, 1701, after he had learned of the newly founded ‘Society for the Propagation of the Gospel’. 8

Alchemy and Chemistry et experimenta lucifera magis quam lucrifera quaerimus.174 Leibniz to Johann Andreas Stisser, April 3, 1699

In Leibniz’s correspondence with Heinrich (or Henning) Brand, Johann Daniel Crafft and Georg Hermann Schuller during the first three years in Hanover (1677–1679), issues of alchemy and chemistry came to the fore, with questions arising about phosphorus and about the centuries-old problem of gold extraction, or reduction, and of the improvement or ennoblement of base metals viz. Chrysopoeia, the process of transmuting base metals into gold.175 White 173 Regarding Leibniz’s missionary zeal, cf. for example: F. J. Swetz, “Leibniz, the Yijing, and the religious conversion of the Chinese”, Mathematics Magazine, vol. 76(4), (2003), pp. 276–291. 174 A III,8 N. 25, p. 85; Translation: and we require ‘luciferous’ or enlightening experiments more than ‘lucriferous’ (viz. enriching or profit-bringing) experiments. 175 Cf. A.-L. Rey, “Alchemy and chemistry”, chap. 28 (pp. 500–508) in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018; L. M. Principe, “Wilhelm Homberg: Chymical corpuscularianism and chrysopoeia in the early eighteenth century”, pp. 535– 556 in: C. Lüthy, J. E. Murdoch, W. R. Newman (eds.), Late medieval and early modern

Introduction: The Core Themes

209

phosphorus was first discovered in 1669, or in the early 1670s, by the Hamburg alchemist and pharmacist Brand, concerning which discovery Leibniz later published an account, entitled “Historia inventionis phosphori”, in the first volume of the Miscellanea Berolinensia (1710). The new substance was first scientifically studied by Johann Kunckel (von Löwenstern from 1693) and Robert Boyle and publicized in their works Phosphorus mirabilis (1678) and The aerial noctiluca (1680), respectively.176 When Leibniz met Boyle in London, on February 12, 1673, their discussions evidently embraced a phosphorus-like substance. Seven years later, in a letter to Nehemiah Grew, on March 19, 1680, Leibniz reported the visit to Hanover of an Englishman named Roger Breatridge, who claimed to have a kind of powder that would ignite spontaneously after a certain time, and, in this context, he recalled the discussions he had with Boyle and the reference made to such a substance on that occasion. Also, about 1674, Christian Adolph Balduin (1632–1682) prepared a phosphorescent form of calcium nitrate, by mixing chalk and nitric acid, about which he published a tract entitled Phosphorus hermeticus, sive magnes luminaris (1675). This development was made known to Leibniz in a discussion with Crafft, on March 12, 1677, following which he made a note about the preparation of the so-called “Phosphorus Balduini”. corpuscular matter theories, (Series: Medieval and early modern philosophy and science, vol. 1), Leiden, Boston, 2001; L. M. Principe, L. De Witt, Transmutations: Alchemy in art: Selected works from the Eddleman and Fisher collections at the Chemical Heritage Foundation, Philadelphia, 2002, pp. 1–41, and in particular “Alchemy-chemistry in the seventeenth century” (p. 2), “The transmutation of metals, or chrysopoeia” (pp. 2f.), “Chemical medicine, or iatrochemistry” (p. 4), “Chemical industry” (p. 5), “The ambiguous status of chemistry” (p. 6), and “The marriage of art and alchemy” (pp. 8ff.). 176 Cf. C. Wahl, ““Im tunckeln ist ein blinder so guth als ein sehender”: Zu Leibniz’ Beschäftigung mit Leuchtstoffen”, pp. [225]–259 in: M. Kempe (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung vol. 1, 2013; H. Peters, “Kunckels Verdienste um die Chemie”, Archiv für die Geschichte der Naturwissenschaften und der Technik, vol. 4, (1912), pp. [178]–214; H. Peters, “Leibniz als Chemiker”, Archiv für die Geschichte der Naturwissenschaften und der Technik, vol. 7, (1916), pp. [85]–108, [220]–235, [275]–287; J. R. Partington, “The early history of phosphorus”, Science Progress, vol. 30, no. 119, (1936), pp. 402–412; J. Golinski, “A noble spectacle: Phosphorus and the public cultures of science in the early Royal Society”, ISIS: Journal of the History of Science Society, vol. 80(1), (1989), pp. 11–39; H. Kragh, Phosphors and phosphorus in early Danish natural philosophy: Historisk-filosofiske Meddelelser, 88, 2002. Det Kongelige Danske Videnskabernes Selskab; The Royal Danish Academy of Sciences and Letters Commission, Copenhagen, 2003; H.-J. Kruse, “Johann Kunckel – der bedeutendste Plöner?”, Jahrbuch für Heimatkunde im Kreis Plön, vol. 42, (2012), pp. 89–150 and, regarding phosphorus in particular, pp. 100–104 (and notes 98–141).

210

Introduction: The Core Themes

Crafft had also become acquainted, in February or March 1676, with Brand’s phosphorus and its discoverer and a little time later he received a sample of the new chemical substance. Then, in mid-May 1677, he presented the substance at the court in Hanover and, no-doubt, confided the name of the discoverer to Leibniz. At all events, in his letter of mid-July 1677, which he sent to Friedrich Adolph Hansen and Henri Justel in Paris for forwarding to Jean Paul de la Roque, Leibniz gave the correspondents a detailed account of Crafft’s (or Brand’s) phosphorus, which was referred to as “Le Phosphore de M. Krafft”. In this letter, he also informed the correspondents that Balduin had sent a sample of his phosphorus to king Charles II. Leibniz had in fact previously been informed by Henry Oldenburg, on March 4, 1677, about the phosphorus sent by Balduin to the king. In July 1678, during a visit to Hamburg, Leibniz availed of the opportunity to call on Brand and to negotiate a contract with him for the divulgement of his secret, and the optimization or perfection of the production process. The outcome was the completion of a contract between the two, that was done at Hamburg on July 24, 1678. Brand had first aspired to the position of personal physician to duke Johann Friedrich in Hanover, but in the end settled for an appointment as “Medicus” and “Chymicus”. He then accompanied Leibniz to Hanover, where they arrived around September 5 of that year. The circumstances of, and events surrounding, Brand’s employment in the service of the duke of Hanover are reflected in his correspondence with Leibniz in 1678, 1679 and between 1680 and 1683. In a letter of September 2, 1682, for example, Brand requested the payment of the final installment of his salary from his employment in Hanover during 1678 and 1679. Notwithstanding such restitution claims, Brand was clearly referred to in Leibniz’s letters as the “inventor primus” of the new substance. In fact, this attitude on Leibniz’s part mirrored the fashion in which he referred to Otto von Guericke’s role in the development of the vacuum pump, that was subsequently improved by Boyle. Thus, for example, in a letter of July or August 1679 to Grew, Leibniz characterized Guericke as the “inventorem primum” of the vacuum pump and he referred to the “phosphorum fulgurantem, quem ut nostis primus invenit Henricus Brand”. Like Leibniz, Robert Boyle learned of the discovery of phosphorus from Crafft, who visited him in London, on September 25, and on October 2, 1677.177 In his tract The aerial noctiluca, presented to the Royal Society in December 1680, Boyle referred to the discovery, and his knowledge of it, in the opening 177 Cf. M. Boas, Robert Boyle and seventeenth-century chemistry, Cambridge 1958 and 2015, and, regarding phosphorus in particular, pp. 137, 139, 193, 226f.; J. Golinski (note 176), and specifically regarding Crafft’s meetings with Boyle, p. 19.

Introduction: The Core Themes

211

prefatory address where he referred in particular to Crafft’s role in disclosing to him the nature of the new substance, or in his words: “After the experienced Chymist Mr. Daniel Krafft had, in a Visit that he purposely made me, shewn me and some of my Friends, both his Liquid and Consistent Phosphorus … he … confest to me at parting, that at least the principal matter of his Phosphorus’s, was somewhat that belong’d to the Body of Man”. By the early 1680s, phosphorus was becoming internationally well-known and this was also reflected in Leibniz’s correspondence. Thus, at the end of a letter of July 18, 1680, from London, Friedrich Slare referred to the various forms of phosphorus, and to the intelligence about the new substance provided by Crafft during his visit in 1677 and the ongoing effort to produce it. Robert Hooke too was interested in the new substance and, in a letter of July 22, 1680, he sent to Theodor Haak, for forwarding to Leibniz, he requested that “If Dr Leibnitz knows any thing of the composition thereof I should take it as a great favour if he would please to Impart any thing concerning it”. Leibniz, who had produced phosphorus in Hanover with the assistance of Brand, informed Tschirnhaus, at the end of June 1682, about both his own (superior) process and about the (inferior) one of Boyle, both of which involved heating and repeated and protracted distillation procedures, starting with the requisite raw material, namely human urine. In the production process, a series of intermediate products were produced, namely concentrated urine (“dicken urin”), oil of urine (“oleum urinae”), a so-called “caput mortuum oleosum” containing a hard superfluous salt and a black loose or soft material (“eine schwarze lückere materi”), and then an amber-like hard stone (“eine ganz harte materi wie ein börnstein”). The final product was characterized by its brightness and property of glowing in the dark but the core fire-containing substance was the “caput mortuum oleosum”. In fact, the superiority of his own process over that of Boyle, Leibniz saw in an additional step that involved the refinement of the “caput mortuum oleosum” giving a hard salt byproduct and the core soft black matter. Tschirnhaus’ letter of May 27, 1682, to Leibniz contains the intelligence that in Paris a secret formula for the production of phosphorus was being offered for sale by an Englishman and, Mariotte’s letter, of April 13 of that year, revealed that various members of the Académie des Sciences were experimenting with the substance. While in Copenhagen, Jobst Dietrich Brandshagen had the opportunity to produce a large quantity of phosphorus, but, when he presented the product to the king, the latter saw in the new substance a source of amusement and, to the dismay of the correspondent, besmeared the entire consignment in the course of an evening. In his letter of mid-January 1682, Brandshagen also related that, in order to enhance phosphorescence in the

212

Introduction: The Core Themes

dark, he himself had rubbed the substance into his own face, which resulted in severe nausea along with a feeling of having nothing under the skin, and the following morning his whole face had an ulcerous or pyogenic appearance. Besides such playful applications, which made phosphorus most suitable for public performances, Leibniz saw an eminent theoretical importance of this novel fiery substance. And Tschirmhaus wrote, in his letter from the end of June 1682, that he knew of no better process which squared with the three universal alchemical principles, namely mercury, sulfur and salt, since the end product, or fiery substance, derived neither from a solid state, or a fixed salt, nor from a volatile or mercurial spirit, but rather from an intermediate oily or sulfuric liquid. The Académie des Sciences too was appreciative of the fact that Leibniz was willing – for the sake of supporting the advancement of his compatriot Tschirnhaus – to disclose the production process for phosphorus, in exchange for other scientific secrets, as Mariotte acknowledged in a letter of June 22, 1682. Leibniz received two such secrets from the Académie through Tschirnhaus, referred to as a “Sel vegetans; et l’or rendu volatile sans fulminer”, the first of these being a salt which grew like a plant in water. The experiment of an Italian, who had demonstrated a smoking or fuming liquid at the court in Celle, was described by Leibniz in a report for the Journal des Sçavans, sent to the editor Jean Paul de La Roque, in January or early February, 1681. In September 1680, it had led to a discussion with the professor of medicine in Helmstedt, Günther Christoph Schelhammer, who in turn involved Georg Wolfgang Wedel, a professor in Jena. Schelhammer had conjectured, in a letter of June 14, 1680, that the smoke rising from the liquid was attributable to an inner fire in the fluid, and he seized the opportunity, in this letter to Leibniz, to enquire about phosphorus. Replying on September 24, 1680, Leibniz made clear that the smoking liquid had nothing in common with phosphorus, and he in turn enquired of Schelhammer about where Wedel’s description of the smoking liquid had been published. The properties of afterglow, or phosphorescence, and ignitability were in the seventeenth century the principal motive for investigating phosphorus. However, other methods of encapsulating fire and combustion also attracted the interest of Leibniz and his correspondents. Thus, for example, Leibniz recorded – in the memo of a conversation with Christoph Pratisius between 1683 and 1687 – a means of distilling without fire which the conversation partner had learned about from a carbonarius or charburner. To this was added a further application, namely that of preserving heat over an extended period during a journey.

Introduction: The Core Themes

213

As in the years prior to 1683, phosphorus continued to be an important topic in Leibniz’s correspondence in that year, and indeed throughout the decade. Thus, Brandshagen reported from Copenhagen, in July 1683, about the distrust he was experiencing there because of his reluctance to provide information about his mortar bombs, and about phosphorus. Sometimes, Leibniz himself even received incorrect or inaccurate reports from his correspondents. As regards the transfer of knowledge about phosphorus to England, for example, Friedrich Heyn reported, on November 30, 1686, that intelligence about this German discovery had been communicated by Johann Joachim Becher to Robert Boyle, who then had his German laboratory assistant produce it. Boyle’s more accurate version of events, as given in his The aerial noctiluca (1680), was that he had received the essential intelligence about the production process from Crafft, and from another German informant referred to as “A. G. M. D.”, a reference probably to Ambrose Godfrey Hanck(e)witz.178 Leibniz corrected the text of Heyn’s letter, introducing the correct name of the discoverer (“D. Brand”), and correcting the name of Boyle’s informant by replacing Becher’s name with the words “ist ein ander”, and adding the name “Hangwiz”. In mid-year 1687, Leibniz commissioned Brandshagen to carry out chemical experiments in Hanover, including on phosphorus production, and he duly compiled a list of what was required to produce phosphorus. During Leibniz’s absence from Hanover, in late April and early May 1687, the master tailor Curd Reimers had to make sure that Brandshagen was able to collect enough urine for the phosphorus production and that he was accordingly compensated. On the eve of his Italian journey then, and almost twenty years after its discovery, Leibniz was able to pride himself on his knowledge of the discovery, and of the production process, of phosphorus. Three years later, on February 20 and March 4, 1690, in fulfillment of a promise made to prince Ferdinando in Florence, he sent from Venice details of the production process, as well as verses he had composed regarding this wondrous substance, to Bodenhausen, the prince’s tutor. Then, on August 12, 1690, Bodenhausen was able to report that he had recited the details of the process in Leibniz’s name to the prince, who immediately joined in a disputation with him. In addition, Bodenhausen reported that the prince’s younger brother  – prince Gian Gastone  – had expressed his admiration and praise for Leibniz and the recited verses about phosphorus. Even after 1690, Leibniz’s interest in the discovery and investigation of phosphorus continued. In 1692, in the Mémoires of the Académie des 178 Cf. L. M. Principe, L. DeWitt (note 175 above), and regarding Ambrose Godfrey Hanckwitz (1660–1741) see p. 5 (with engraving).

214

Introduction: The Core Themes

Sciences, he found an account of the history of the discovery of phosphorus, from the viewpoint of Wilhelm Homberg, which became a subject of discussion in his letters to Simon Foucher (on October 27, 1692) and to Bodenhausen (on January 23, 1693). Alas, his own “Historia inventionis phosphori” would only appear in the first volume of the Miscellanea Berolinensia (1710). A multitude of chemical considerations in Leibniz’s correspondence may be categorized under the heading of the economic utilization of chemical processes. Often the dividing line to the techno-economic projects is difficult to draw. Thus, for example, writing to Grew on March 18, 1680, Leibniz desired to learn whether the Royal Society could produce a fluid gold paint with which clothing might be dyed. In the production process of ruby glass (“artificiall Rubine”), Leibniz and Robert Hooke were equally interested. In the letter of July 22, 1680, sent by Hooke to Theodor Haak for forwarding to Leibniz, the correspondent requested information concerning the production of both phosphorus and ruby glass. In Crafft’s and Elers’ endeavors for the perfection of pearls, the correspondents believed themselves to be in a position to report initial success at the beginning of September, 1681. Above all, however, it was the range of very different chemical processes for the preparation of gold and silver, that repeatedly played a role in the correspondences with these two projectors. Leibniz apparently esteemed such projects less than the techno-economic processes, referred to above, and he was accordingly impatient on occasions as, for example, in his letter to Crafft, on April 7, 1681. Nevertheless, there can be no doubt about Leibniz’s interest in the preparation, or separation, of gold and silver from suitable raw materials or chemical precursors. Thus, we find Elers reporting, at the beginning of September 1681, about his efforts – together with the personal physician at the court in Hanover, Christof Pratisius  – to obtain silver from cinnabar through the application of sulfur and lead. Crafft, Christoph de Rojas y Spinola – the Dutch-born Franciscan priest and Bishop of the Viennese new town district (“Wiener Neustadt”) – and Leibniz himself, discussed the possibility of obtaining silver from the liquation, or segregation, of Spanish copper coins, as is to be seen from Crafft’s letter to Leibniz of December 25, 1682. In January 1680, both Leibniz and Crafft had followed attentively the efforts of various chemists in Dresden seeking to obtain gold from copper, mercury, and silver. In July 1682, Elers reported the sale of a process for obtaining gold – on the basis of intelligence obtained from Leibniz – to a Berlin chemist for a sum of 8000 Taler. Alas, he appears not to have received the sum in question, a part of which was intended for Leibniz. A much larger sum, namely 20,000 Taler, was mentioned in relation to the offer of the Dutch punchcutter and engraver, Christoff Adolphi, whom Leibniz had probably first encountered during his time as a student in Leipzig. In January 1680, Adolphi

Introduction: The Core Themes

215

offered Crafft different chemical secrets, including a process to obtain mercury from all metals except gold, and in addition, to separate sulfur and mercury. Crafft forwarded this proposal to Leibniz who, in early February 1680, duly requested further details from Adolphi, as well as a demonstration of the truth of his propositions. A reply from Adolphi proved not to be forthcoming. Leibniz also used contacts with his correspondents to clarify problems that arose in his reading of chemical literature, or to make inquiries about further investigations. In a letter to Sebastian Scheffer, in March 1682, he referred to a polemical work from the year 1656, which was directed against Johann Rudolf Glauber (1604–1670)179 – and specifically against his opus Widerlegung oder vielmehr Warnung vor der groß prallenden Explicatio Miraculi mundi, und der betriegerischen genandten Wolfahrt Teutschlands Johann Rudolph Glaubers (1656) – in which the author, Christoph Fahrner, had referred to a chemical process through which ostensibly, and with little effort, an appreciable quantity of silver could be obtained from lead. In January–February 1683, Leibniz asked Scheffer – who in his youth had worked as an assistant with Fahrner – for information about the process in question. Scheffer duly consulted his former mentor about the matter before replying to Leibniz, on February 27, 1683, with the information that Fahrner was at the time indisposed and unable to comment on the issue. The production of gold and silver from tin – along with a passage in a work of Glauber – were also at the center of an enquiry Leibniz sent to Crafft at the end of August 1681. In connection with this query, which he was unable to answer, Crafft made a remark – in his reply on September 2 – that epitomizes chemical research at the time, namely that he was from day to day becoming more and more confirmed in his conviction, that all was possible and available in nature and required only to be diligently sought and dealt with by means of the correct aptitude or ingenuity. This belief, that everything seemed possible, implied also that there could be a quest for very remarkable things in nature. Thus, for example, Crafft was persuaded by an alchemist at the Leipzig Fair that a non-wetting water existed in nature, as he reported to Leibniz on November 11, 1682. While Leibniz’s response to this has not been found, it seems that his attitude may well have been characterized by a cautious skepticism. Indeed, even Crafft himself relativized – in a letter

179 Cf. J. R. Partington, A history of chemistry, vol. 2, London, 1961, in particular chap. X (Glauber and Kunckel), and specifically pp. 341–361 (Glauber); H. Gebelein, R. Werthmann, and S. Nomayo (ed.), Johann Rudolph Glauber: Alchemistische Denkweise, neue Forschungsergebnisse und Spuren in Kitzingen, (Series: Schriftenreihe des Städtischen Museums Kitzingen, vol. 4), Kitzingen, 2009.

216

Introduction: The Core Themes

of December 25 – his search for this mysterious fluid with a degree of melancholic self-reprobation. In the fall of 1681, Leibniz invited the alchemist Jakob Vierort to a presentation of an alleged transmutation of his, which was to take place at the court in Hanover. Leibniz had made thorough enquiries in advance about Vierort, contacting, among others, the renowned medical professor in Helmstedt, Heinrich Meibom, and of course Crafft. The latter, on September 2, 1681, recommended a strategy for exposing the presumed swindler. In the end, Leibniz demanded that the alchemist himself not be present during the performance of the transmutation. Since Vierort rejected this condition, it is probable the planned performance, in the presence of duke Ernst August, never did take place. Saltpeter was – as the main ingredient of gunpowder – also of great interest at that time, whereby the focus was on improved processes for its manufacture rather than the investigation of its chemical properties.180 Thus, in a letter from Copenhagen, on August 1, 1684, Elers referred to a hypothetical process, by which one might be able to establish a perpetual saltpeter works – at low cost and providing a high weekly production output – without having to leach and concentrate in ditches or trenches in the usual fashion. In January 1688, Leibniz also noted, after a conversation with Crafft in Graupen, the damming opinion of his conversation partner about a suggestion for the improvement of saltpeter production using a vault or dome – in which the product might appear on rocks following blasting – without the need for leaching and concentrating. The range of chemical issues, that were subjects of discussion in Leibniz’s correspondence, included processes for obtaining precious metals and, in particular, gold and silver. The work of the assayers along with their analytical methods – in the circle of Leibniz and his correspondents – forms part of a German tradition extending back to the Middle Ages.181 On August 1, 1684, Elers reported from Copenhagen about the trial of a chemical process  – 180 Regarding the history of gunpowder, and gunpowder artillery, cf. B. S. Hall, Weapons and warfare in renaissance Europe: Gunpowder, technology and tactics, ( Johns Hopkins Studies in the History of Technology), Baltimore, 1997; J. R. Partington, and B. S. Hall (Intro), A history of Greek fire and gunpowder, Baltimore, 1999, in particular “Introduction, 1999”, pp. xv–xxix, and chap. 7, pp. 298–339 (Saltpeter); B. J. Buchanan (ed.), Gunpowder, explosives and the state: A technological history, Oxford, New York, 2006 (and 2016), in particular Part two (The production of saltpetre and gunpowder in Europe); E. de Crouy-Chanel, Le canon au moyen âge et à la renaissance: 1338–1559, Tours, 2020. 181 Cf. D. Thorburn Burns, R. K. Müller, R. Salzer, G. Werner, Important figures of analytical chemistry from Germany in brief biographies: From the middle ages to the twentieth century, Berlin, 2014, in particular chap. 1, and specifically “Introduction and overview” (pp. 1–10) and “Important figures in analytical chemistry: From the middle ages to the nineteenth century” (pp. 11–47).

Introduction: The Core Themes

217

communicated by Leibniz – for the reduction of gold powder in aqua fortis (nitric acid). Regarding the course of the trials, it was reported that, at the outset, the correspondent could have sworn that the actual outcome would be six times the anticipated result. However, it transpired that, after the preparation had been left standing for a certain time, all of the product was consumed once again. A repeat of the trial, with fresh acid, also fell short of expectations, and this had accordingly shattered the correspondent’s belief in the process. In his discussion with Crafft in Graupen, in January 1688, Leibniz learned details about the technique of gold panning in rivers. A few years earlier, he had received from the Académie Royale des Sciences through Tschirnhaus – in exchange for the communication of the phosphorus process, as outlined above – a description of two other processes, referred to as “l’or rendu volatile sans fulminer” and “un sel vegetant”, respectively. After Tschirnhaus had given him an account of these processes, at a meeting in October 1682, he included written transcripts with his letter of September 4, 1683. Alas, Leibniz displaced these copies and he had to request them again, both in a letter to Jean-Baptiste Du Hamel, on July 21, 1684, and in the postscript to a letter of October 17, 1684, sent to Tschirnhaus. Often such processes were treated as secrets as, for example, one “pour rendre le plomb en couleur de bronze à la fonte” that Douceur had promised him in January, and again on August 6, of the year 1683. From Venice, Christof Pratisius reported, on October 26, 1685, about the activity of several hundred Italian alchemists, all of whom were occupied with the investigation of a certain cinnabar process. After Leibniz learned that Bodenhausen wanted to join this effort, he wrote to him, in August 1690, approving the study of the chemical process in question, which involved a remarkable chemical reaction, or “transplantatio”, as it was called. He had also been informed about an adulteration of the process, by falsifying the cinnabar using lead oxide, and the possible use of cinnabar of antimony.182 A central concern in Bodenhausen’s chemical experiments was the study and investigation of mercury. In this connection, he reported to Leibniz, on September 16, 1690, about his work on the writings of the famous eastern Arab writer on alchemy, Geber (or Gebir, i.e. Jabir ibn Hayyan, fl. c.721–c.815) and, in particular, about Geber’s edited work, entitled Chymia sive traditio summae perfectionis et investigatio magisterii (1668).183 In his reply, on November 5, 182 Cf. W. R. Newman, L. M. Principe, Alchemy tried in the fire: Starkey, Boyle, and the fate of Helmontian chymistry, Chicago, London, 2002, and specifically, regarding cinnabar of antimony, chap. 2, p. 104, note 34. 183 Cf. S. Nomanul Haq, “Jabir ibn Hayyan”, pp. 459f. in: H. Selin (ed.), Encyclopaedia of the history of science, technology, and medicine in non-western cultures, Dordrecht, Boston, London, 1997; H. S. Redgrove, Alchemy: Ancient and modern, London, 1911 and later, most

218

Introduction: The Core Themes

1690, Leibniz advised the correspondent to record his experiments in writing, and in the form of a diary, for the benefit of science. In addition, Leibniz could report the establishment of a chemical laboratory in Hanover under the direction of Pratisius. Although Leibniz was impressed by the alchemist Geber, and considered his writings to be well-founded, he had certain doubts about the correctness of Geber’s results and, as an instance of this contrariness or inconsistency, he cited the chapter on the sublimation of mercury. Being unable to undertake experiments himself, Leibniz hoped to obtain clarification of important questions from those of Bodenhausen. As regards Geber, he was willing to keep an open mind, notwithstanding his predominating skepticism. Even the clarification of a specific point in this complex matter could amount to a breakthrough, he told the correspondent. Bodenhausen then reported to Leibniz, on November 11, 1690, that one of his princely students – presumably the hereditary or crown prince Ferdinando  – was adept at doing chemical experiments and had, a few days before, produced mercury in his chambers from the regulus of antimony – viz. the metallic antimony reduced from its ore – without any mercurial addition, an experiment that Bodenhausen himself also hoped to repeat. Leibniz regularly used his contacts, with correspondents, associates and friends, to obtain new information about known chemical processes. On June 26, 1689, he obtained intelligence from Crafft about the efforts of Johann Elias Rothmaler in Vienna to demonstrate a transmutation of metals, a demonstration which, it was claimed, the whole world ought to heed as a proof of the veracity of the transmutation of metals. However, Leibniz, for his part, wrote the following skeptical comment about the steadfastness of the matter between the lines of Crafft’s text: “vereor ne sit stantiarismus”. On another occasion, in August 1689 and April 1690, Crafft likewise reported about a process, named after a certain count Lobkowitz, for the transmutation of silver into gold and silver, using, among other substances, mercury. Yet another example was the separation process of Christian Holeysen. The latter resided in Vienna from 1688 to 1692 in order to present his purported process, for an improved yield of gold from auriferous silver, to the emperor. At the end of April, or in the first half of May 1690, Leibniz was able to make detailed excerpts from Holeysen’s submissions to the emperor, and to carry on conversations with him which he recorded in writing. Besides the possible production and extraction of gold and silver, by means of the chemical transmutation of metals, Leibniz was especially interested in an improvement in the processing of ores – referred recently Sweden (Ulwencreutz Media), 2008, Washington (DC), 2016, and New York, 2018, in particular chap. 3, sect. 32.

Introduction: The Core Themes

219

to as the “maturation” of metals – not just for obtaining new knowledge, but also for greater economic benefit, as he explained to the mining official Johann Christian Orschall, in a letter sent from Hanover in August 1687. In the early and mid-1690s, alchemy and chemistry played only a minor role in Leibniz’s correspondence. During his final two and a half year stay in Amsterdam, Crafft, for example, reported about projects based on chemical knowledge. Thus, on April 22, 1695, and again on February 23, 1696, he reported about projects for desalination and salt extraction from seawater, including one on the basis of a chemical precipitation process. Leibniz, although skeptical regarding the prospects for such projects in general in the Dutch climate, did nonetheless express an interest in the latter method in his reply on March 2, 1696. With a letter of May 24, 1698, Johann Andreas Stisser, who was a university professor at the University of Helmstedt (the Academia Julia), initiated a correspondence with Leibniz. The prelude to this correspondence was the transmission, as an attachment to Stisser’s letter, of a work on chemistry of his, entitled Actorum laboratorii chemici in Academia Julia specimen tertium medico-chemica observata quaedam rariora exhibens (1698). This work dealt with, among other things, a certain “Tinctura vitrioli”, and to which Leibniz referred in his reply to Stisser on June 1. In doing so, he recalled the medieval alchemical text “Turba philosophorum”, in which mercury was treated as a basic principle of metals. Leibniz now saw vitriol in this role. Leibniz – like other contemporary philosophers of nature including Robert Boyle and Isaac Newton  – had a long-standing and profound interest in alchemy. As regards Newton, he sought to make advances in the knowledge of alchemy, through laboratory experiments and the study of alchemical texts.184 He studied alchemical literature extensively, and he treated the language of alchemy as a code to be deciphered, thus providing recipes for laboratory applications, including the decomposition or transmutation of metals, not least with the hope of making gold. Boyle, for his part, as a natural philosopher, ranks alongside Newton as a remarkably wide-ranging, penetrating and rational thinker, who was a pioneer of the modern experimental method and a champion of a novel mechanical view of nature. While Boyle (like Newton) reflected deeply on philosophical and theological issues related to science, he

184 Cf. N. Guicciardini, Isaac Newton and natural philosophy, London and Chicago, 2018, in particular pp. 105–108; W. R. Newman, Newton the alchemist: Science, enigma, and the quest for nature’s “secret fire”, Princeton, 2019.

220

Introduction: The Core Themes

was also fascinated by alchemy and magic, and plagued with doubts about faith and conscience, which was at odds with his rational thinking.185 As for Leibniz, his interest in alchemy had existed since his stay in Nuremberg – between the spring and autumn 1667 – when, as a twenty-year-old, he became secretary of an alchemical society there. Almost thirty years later, on August 10, 1696, after Gottfried Thomasius had reported to him about an alchemist called Friedrich Kleinert, Leibniz recalled, in his reply of December 17, the names of certain alchemists of earlier times including Ramon Lull, Nicolas Flamel, Daniel Keller, Johann Conrad von Richthausen (a baron with the title “Freiherr von Chaos”), as well as a former monk called Johann Wenzel Seyler. Keller was a practitioner of the art of the gold-maker, in sixteenth-century Augsburg, whereas Baron Chaos had demonstrated, in Mainz in 1658, an alleged process for the transmutation of mercury into gold. Wenzel Seyler possessed a powder, with the help of which gold could allegedly be produced, and he stood in high regard until his process was found to be fraudulent. On his way to Italy, on May 17, 1688, Leibniz had inspected – at the Imperial Treasury in Vienna – the counterfeit, or fake, gold from the workshops of Chaos and Seyler. He told his correspondent Thomasius, in his letter of December 17, 1696, that he had personally witnessed the demise of practitioners in the field, like Johann Joachim Becher and others, and he urged circumspection in judging alchemical activity. His Swedish correspondent, Magnus Gabriel Block, who had lived in Florence, had the same cautious attitude to alchemy as Leibniz himself, which was epitomized in the quotation of an old Spanish proverb in his letter of July 1, 1698. Thus, Block wrote on that occasion: “je approuve le proverb des Espagnols Alequimia provada es tener rienta y no gastar nada”, an admonition to the effect that the true philosopher’s stone is to have wealth and not spend it. In his correspondence between 1699 and 1701 – more than thirty years after his stay in Nuremberg – Leibniz’s continuing interest in the field is reflected in letters exchanged with, besides Block, Peter Moller, Johann Andreas Stisser and Georg Wolfgang Wedel. Block enquired about Leibniz’s views on astrology, palmistry (palm reading or chiromancy), necromancy (necromantia), and the branch of alchemy concerned with transmutation (chrysopoeia). Leibniz’s skeptical reaction, in a non-extant letter of April 17, 1699, can be sensed from the tenor of Block’s reply two months later, on June 24. Leibniz warned, again 185 Cf. M. Hunter, Boyle: Between God and science, New Haven, CT, 2009. Regarding Newton, cf. for example, J. E. Force, R. H. Popkin (eds.), Newton and religion: Context, nature and influence, (International Archives of the History of Ideas, no. 161), Dordrecht, Boston, London, 1999; R. Iliffe, Priest of nature: The religious worlds of Isaac Newton, Oxford, 2017.

Introduction: The Core Themes

221

and again, against investing time and money in the search for possible transmutations. The probability of success would be less than 1:100,000. But, one ought not to discredit or abandon alchemy entirely, which was the tenor of his reply to Block of September 8, 1699. He did not fundamentally cast doubt on the notion of a transmutation, which he certainly considered to be possible. However, many claims of such transformations failed to pass the test of proof, as he maintained in a letter to Block, written between mid-December 1699 and the end of January 1700. Unlike contemporaries (and correspondents) like Gottfried Kirch, and Friedrich Hoffmann, Leibniz condemned outright “astrologia judiciaria”, and saw himself here in the company of renowned astronomers like Cassini, Huygens and Hevelius, as he wrote in his letter of September 8, 1699, to Block. He proposed exposing, or unmasking, the astrologists by means of a statistical experiment that would show that the fulfillment, or coming true, of their predictions was entirely accidental. For Leibniz, the fact that a transmutation was difficult to achieve, and at best only revealed to adepts in well-informed circles, was a work of providence that in turn contributed to the maintenance of the world order, and for the same reason, the quest for it seemed to him to make no sense. That one might find a small particular or singular process which worked, he considered to be more likely. Writing to Peter Moller of Hamburg, on January 2, 1699, he complained that in spite of his contacts to renowned chemists, his intensive study of alchemistic writings, and his visitations to laboratories, he had witnessed no credible transmutation but, on the contrary, had encountered a number of impostors. Moller, replying on January 7, found it hardly surprising that Leibniz had had little success in his dealings with chemists of fame, since the true adepts in the field – in contrast to those imposters – operated incognito, and worked secretly. Moller claimed that he had contact with several alchemists, who were working more or less in secret, and about whom he reported to Leibniz. He had, for example, just learned from an old acquaintance that he was involved in alchemy. Alas, the individual in question could only survive as a “capitalist”, and not as a chemist. He recalled yet another adept who had resigned from his employment in Brandenburg, because he had been discovered, and had then moved to Hamburg. Moller was impressed by Leibniz’s early involvement with alchemy, more than thirty years before, and, although he himself had seen a lot, he admitted that he had not carried out any laboratory work due to lack of instruction in the field. The discoverer of phosphorus, Heinrich Brand, was still living in Hamburg and, in a letter of November 7, 1698, he touted to Leibniz an ostensibly very lucrative process for metal ennoblement. Leibniz then sought the judgement of Moller in the matter. The latter, however, – in his reply of January 7,

222

Introduction: The Core Themes

1699 – considered Brand to be a braggart who, although he had come far, had in fact not discovered phosphorus himself at all. Furthermore, Moller suggested, Brand was too poor to finance laboratory work. For the claimed effect, a universal or pansophist knowledge, which Brand simply did not have, would be required. Moller had not yet met such a person, but he was convinced that an acquaintance of his did possess a very lucrative particular, or singular, process, about which he promised to inform Leibniz, as soon as he received intelligence in the matter, as he wrote in a second letter of July–August 1699. According to Stisser, Johann Joachim Becher had (in the 1670s) hoped, and tried in vain, to become rich by means of a process that purported to turn sand into gold.186 Stisser himself had been a witness to one such demonstration by Becher – carried out both in Amsterdam and Hamburg – but one where the announced effect had failed to materialize. This he now reported to Leibniz, in a letter of February 5, 1699, in which he replied to a query about the transmutation of salts, with or without useful applications. Stisser confirmed, on this occasion, that he himself was aware of some transmutations of salts, albeit without particular use and only in small quantities. For Leibniz, as he wrote in his reply of April 3, 1699, the gain of enlightening experimental knowledge – like concerning the transmutation of salts – meant more than that of lucrative or lucre-bringing experimental knowledge, namely the leading quotation of this section (“et experimenta lucifera magis quam lucrifera quaerimus”). Although efforts were indeed being made everywhere, to bring chemistry into the form of an art, hitherto little light had been shed on the foundations of the subject, he thought. Many had postulated principles that were more melodious than veritable. He hoped, therefore, that Stisser might advance chemistry through a combination of method and experiment. Stisser then promised, on June 2, to actively work for the consolidation of chemistry provided the means were made available to him for the meticulous experimental examination of the entire subject. And, he communicated to Leibniz some examples of salt transmutations from all three kingdoms of nature, namely the mineral, vegetable and animal realms. For Leibniz however, in his reply on December 22, it remained unclear whether, in fact, in each of these examples, a “transmutatio” was involved and not just a “transplantatio” in which chemical substances were merely exchanged in the reaction or process. Taking the example of Glauber’s salt –treated in the third part of Johann Rudolph Glauber’s Prosperitatis Germaniae or Theütschlandes Wohlfahrt (both 1659) – and, considering also Robert Boyle’s discussion of Glauber’s works in 186 Cf. H. A. M. Snelders, “Johann Joachim Becher und sein Gold-aus-Sand-Projekt”, pp. 103–114 in: G. Frühsorge, G. F. Strasser (eds.), Johann Joachim Becher (1635–1682), Wiesbaden, 1993.

Introduction: The Core Themes

223

Some specimens of an attempt to make chymical experiments usefull to illustrate the notions of the corpuscular philosophy (1661),187 Leibniz considered different alternative explanations of the transmutation of chemical substances  – including the revivification or transanimation of Glauber’s salt – for which he also proposed further investigation. Chemical substances could be veiled or unveiled in reactions, and the products of such a process might be already contained as subtle particles in the starting substances, and could possibly alter their form depending on their environment. Stisser’s open letter, of February or March, 1700, addressed to Leibniz and entitled De variis erroribus, chemiae ignorantia in medicina commissis dissertatio epistolaris, maked the end of the correspondence. The author and correspondent died on April 21 of that year. Leibniz’s reply, written before he learned of Stisser’s passing, is erroneously dated May 25 instead of the probable date, April 25. In his Dissertatio epistolaris, Stisser had, to begin with, characterized chemistry as the oldest of the arts. This prompted Leibniz, in his reply, to consider the importance and reliability of tradition, from the ancient times, in relation to chemistry. He did believe that chemical knowledge had existed in antiquity and that distillation had been known then. However, he considered chemical interpretations – for example the legend of ‘The Golden Bough’ from the Aeneid, the epic of the Roman poet Virgil (70–19 BC) – to be more elegant than credible. And, the portrayal of the Egyptian art of gold making – found in the Byzantine encyclopedia of the ancient Mediterranean world, the Suda – he considered to be hardly reliable either, since other authors chose not to mention it. The fact that he himself had once pursued the idea of editing the

187 Regarding seventeenth-century atomism and the corpuscular philosophy, cf. C. Meinel, “Empirical support for the corpuscular theory in the seventeenth century”, pp. 77–92 in: D. Batens, J. P. van Bendegem (eds.), Theory and experiment: Recent insights and new perspectives on their relation, (Synthese library series, vol. 195), Dordrecht and Boston, 1988; C. Meinel, “Early seventeenth-century atomism: Theory, epistemology, and the insufficiency of experiment”, ISIS: Journal of the History of Science Society, vol. 79(1), (1988), pp. 68–103; C. Meinel, “‘Das letzte Blatt im Buch der Natur’: Die Wirklichkeit der Atome und die Antinomie der Anschauung in den Korpuskulartheorien der frühen Neuzeit”, in: Studia Leibnitiana, vol. 20, (1988), pp. 1–18; C. Lüthy, J. E. Murdoch, W. R. Newman (eds.), Late medieval and early modern corpuscular matter theories, (Series: Medieval and Early Modern Philosophy and Science, vol. 1), Leiden, Boston, 2001, in particular “Introduction: Corpuscles, atoms, particles and minima”, pp. 1–38; W. R. Newman, “The significance of ‘chymical atomism’”, Early Science and Medicine, vol. 14(1/3), (2009), pp. 248–264; M. P. Banchetti-Robino, The chemical philosophy of Robert Boyle: Mechanicism, chymical atoms, and emergence, Oxford, 2020, in particular chap. 3, sect. 2, pp. 84–90 (Boyle’s corpuscular theory of matter).

224

Introduction: The Core Themes

alchemical writings of the ancients, he had previously admitted to Block in a letter of September 8, 1699. Leibniz had likewise, as he wrote in his final letter to Stisser, attempted to motivate the Dutch classicist Jacobus Tollius (1633–1696) to obtain alchemical information from mythology, not least with the intention of dissuading him from pursuing any further what he saw as a senseless undertaking. After Georg Wolfgang Wedel had sent him two writings regarding ‘The Golden Bough’, Leibniz, referring to Plato and Aristotle, made clear to this correspondent – in a letter written between February and April, 1700 – how difficult it was to identify substances described in the writings of antiquity, not least because of the strange terminology employed. Wedel’s solution of an alchemical number puzzle of George Starkey – published under the pseudonym ‘Philalethes’ – appeared also to Leibniz to be uncertain, and he pointed out, in this letter to Wedel, that there was an infinite number of solutions. To begin with, one ought to convince oneself of the scientific pedigree of the author. The vague notation of Philalethes gave the impression that one was dealing with a sophist, rather than an adept in the field. Wedel had searched in vain in Erfurth for a manuscript on quintessence of Basilius Valentinus, and he asked Leibniz, on August 24, 1699, to search for it in the library at Wolfenbüttel. In his reply, on September 9, Leibniz had to disappoint the correspondent. However, in contrast to the writings of Philalethes and others, those of Basilius Valentinus – although he considered them to be feigned  – stood out above the rest in Leibniz’s opinion because of their concrete character. The identities of alchemical authors, and the contents of alchemical records, were often the subjects of speculation in Leibniz’s correspondence. On November 28, 1699, Block reported to him from Stockholm that his then deceased correspondent and collaborator in Florence, namely Rudolf Christian von Bodenhausen, had left behind numerous records and notes on chemical processes and concerning transmutation. One particular note of Bodenhausen provided the intelligence – derived from a conversation with the, in the meantime, likewise deceased personal physician at the court in Hanover, Christof Pratisius – that Leibniz possessed the manuscript of a work entitled Lucerna salis philosophorum, which had been published in 1658 under the pseudonym ‘Sendivogius filius’, and that Johann Joachim Becher was possibly its real author. This was disputed by Leibniz in his reply to Bloch, in December 1699 or January 1700. He told Block that he himself had indeed known the author in Nuremberg, whose real identity was Johann Harprecht and who was synonymous with Johann Hiskia Cardilucius. Becher, on the other hand, had preferred the pseudonym Solinus Salzthal Regiomontanus. Yet another pseudonym, namely ‘Eirenaeus Philalethes’, was in reality the American physician

Introduction: The Core Themes

225

and alchemist, George Starkey (1628–1665), who had died in the great plague of London. He was alluded to, for example, in Georg Wolfgang Wedel’s aforementioned letter to Leibniz on August 24, 1699.188 In his letter of June 24, 1699, Block also promised Leibniz transcriptions of Bodenhausen’s alchemical records, some of which had never been intended for dissemination. To prevent the scribe, or amanuensis, from understanding these, Block planned to encrypt them and he sent Leibniz the secret-key encryption. In addition, following a request by Leibniz on September 8, Block passed on – with his letter of November 28 – a recipe of a process of Amund (Anund) Tyresson for making iron malleable (and hard again), that surely evoked memories for Leibniz of the Douceur process, which had been acquired more than twenty years before. 9

Earth Sciences: Geology, Mineralogy, Paleontology and Ethnography, Etymology j’ay trouvé des choses si éloignées de l’opinion commune touchant l’origine des mineraux, et cependant si aisées à demonstrer par des raisons entierement mechaniques.189 Leibniz to Jean Gallois, mid-October 1682

Leibniz’s first years in the Harz mountains saw the beginning of the investigations that would culminate in his posthumously-published Protogaea sive de prima facie telluris (1749).190 This work was composed in the early 1690s, 188 Regarding the identities of the alchemical authors, cf. P. H. Smith, The business of alchemy: Science and culture in the Holy Roman Empire, Princeton, 2016, in particular pp. 40f. (regarding Becher’s “pseudonym of Solinus Salzthal of Regiomontanus”); W. R. Newman, Gehennical fire: The lives of George Starkey, an American alchemist in the scientific revolution, with a new Foreword, Chicago, London, 2003; W. R. Newman, From alchemy to “chymistry”, chap. 21, pp. 497–517, and in particular pp. 513f. (regarding George Starkey), in: K. Park, L. Datson (eds.), The Cambridge History of Science: Volume 3, Early modern science, Cambridge, 2006; W. S. Shelley, Science, alchemy and the great plague of London, New York, 2017, in particular chap. 2, pp. 23–32 (George Starkey and Eirenaeus Philalethes); C. Wahl, “Zum Leibniz-Korrespondenten Johann Hiskias Cardilucius  – alias Johann Fortitudo Hartprecht”, Studia Leibnitiana, vol. 49(1), (2017), pp. 111–116. 189 Cf. A III,3 N. 407, p. 725; Translation: I have found things far removed from the common opinion regarding the origin of minerals, and nonetheless so simple to demonstrate solely on the basis of mechanical reasoning. 190 Cf. C. Cohen, A. Wakefield (trans. and eds.), Protogaea: Gottfried Wilhelm Leibniz, Chicago, 2008; Ch. L. Scheid, and W. von Engelhardt, F.-W. Wellmer (trans., eds.), Gottfried Wilhelm Leibniz: Protogaea sive de prima facie telluris et antiquissimae historiae vestigiis in ipsis

226

Introduction: The Core Themes

and it was publicly announced for the first time in an advertisement in the Acta Eruditorum in January 1693, where it was designated “Protogaea” for the first time. A first intimation of an intended article for the Acta Eruditorum is found as early as October 22, 1681, in a letter to Otto Mencke. As is evident from another letter of mid-October 1682 to Jean Gallois, Leibniz had arrived at results regarding the formation of minerals, which strongly deviated from the received view, and which he thought might easily be given a mechanical foundation and verified accordingly. He explained to Gallois that he had made important discoveries regarding the formation of rocks and of the ore deposits found in lead and copper mines. In addition, he told the correspondent that he had made unique discoveries regarding copper mines and had found an explanation for a certain wonder of nature, which was probably a reference to the fish fossils he had come across. In practical terms, Leibniz’s frequent journeys to the Harz mountains provided him with a welcome opportunity for geological and mineralogical studies, in view of the fact that he considered a scientific treatment of all matters relating to mining to be a desideratum. In a letter to Nehemiah Grew, on March 19, 1680, Leibniz posed the question as to whether amber found in the ground, near the location Wunstorf (not far from Hanover), could have originated there. In January and March, 1682, Ferguson replied to queries received from Leibniz about a goldmine on Sumatra. Already, on November 24, 1681, Leibniz had requested information from the rich treasure trove of experience of the director of that mine, Benjamin Olitsch, a former Saxon mining official who had joined the Dutch East India Company. In this letter to Olitsch, Leibniz referred to fossilization specimens found in Mansfeld slate, which had revealed the likes of natural fish, and which he found to be of particular interest. About the time Leibniz composed his letter to Olitsch, in October–November 1681, an inspector of the mint in Zellerfeld named Becker enquired, in conversation with him, about the processing procedures for various ores, on which occasion reference was also made to ores from other regions of geological or mining interest, like Muscau (near Görlitz in Saxony), or in Poland and even in East India. In the mid-1680s, having accepted the commission as court historian, Leibniz began to extend his project to write a history of the House of Welf (or Guelph) and to include prehistory. His long-standing interest in the natural history of regions, like the Harz district, accordingly led him to include earth naturae monumentis dissertatio, Göttingen, 1749; Stuttgart, 1949; Hildesheim, Zürich, New York, 2014; A. Wakefield, “The origin and history of the earth”, chap. 25 (pp. 453–465) in: M. R. Antognazza, The Oxford Handbook of Leibniz, Oxford, 2018.

Introduction: The Core Themes

227

history, or the geological history of the Welf territories. In relation to the genesis of this work – that was originally conceived as the prelude to the history of the Welfs and largely founded on his knowledge of the Harz mountain range – there exists a report, in the form of an extract from a letter of January 1687, sent to the clergyman named Barthold Meier, whom he probably met on a visit to the Harz mountains in late October or early November 1685. This report concerned the “Baumannshöhle”, a cave near the small town of Rübeland, which he visited during that journey in the fall of 1685. In addition there are some scattered reports in Leibniz’s correspondence, between 1683 and 1690, about interesting prehistorical finds. Thus, at the end of a letter to Georg Mohr in the second half of July 1683, Leibniz wrote that he had discovered fish fossils in shale, and that he suspected that the fish had lived in water before being petrified. Likewise, in his letter to Jean-Baptiste Du Hamel, on July 21, 1684, Leibniz reported about his recent studies, and views, concerning earth history and, in particular, about the formation of rocks and minerals (mineralogenesis), which were at variance with those of Agricola, Descartes and Nicolas Steno (Niels Stensen), the Danish physician, geologist, Catholic theologian and apostolic vicar in Hanover, under duke Johann Friedrich, with whom Leibniz had discussions, for example on December 7, 1677.191 191 Cf. K. Müller, G. Krönert, Leben und Werk von G. W. Leibniz: Eine Chronik, Frankfurt am Main, 1969, p. 50. Regarding Leibniz’s connection with Stensen, cf. A. Vibeke Vad, “Polidore and Théophile: The rationalist and the faithful observer”, pp. 39–47, in: K. Ascani, H. Kermit, G. Skytte (eds.), Niccolo Stenone (1638–1686): Anatomista, Geologo, Vescovo, Atti del seminario organizzato da Universitetsbiblioteket i Tromsø e l’Accademia di Danimarca lunedi 23 ottobre 2000 (Proceedings of a Conference on October 23, 2000), (Analecta Romana Instituti Danici, Suppl. XXXI), Rome, 2002; M. Lærke, “Leibniz and Steno, 1675–1680”, chap. 3, pp. 63–84, in: R. Andrault, M. Lærke (eds.), Steno and the philosophers, (Studies in Intellectual History, vol. 276), Leiden, 2018. Regarding Steno and the natural history of the earth, cf. the following chapters in this work: J. E. H. Smith, “Thinking from traces: Nicolas Steno’s palaeontology and the method of science”, chap. 7 (pp. 177–200), and D. Garber, “Steno, Leibniz, and the history of the world”, chap. 8 (pp. 201–230). Regarding Stensen’s biography and papers, cf. T. Kardel, P. Maquet (eds., trans.), Nicolaus Steno: Biography and original papers of a 17th century scientist, Berlin, Heidelberg, 2013 (and 2018). Regarding ‘mineralogenesis’, cf. J. E. H. Smith, Divine machines: Leibniz and the sciences of life, Princeton and Oxford, 2011, in particular chap. 6 (pp. 228f.). Finally regarding Leibniz’s geological research in the Harz mountains (including his trip to the Baumannshöhle cave), cf. H.-J. Waschkies, “Leibniz’ geologische Forschungen im Harz”, pp. 187–210, in: H. Breger, F. Niewöhner (eds.), Leibniz und Niedersachsen: Tagung anläßlich des 350. Geburtstages von G. W. Leibniz, Studia Leibnitiana, (Special issue vol. 28), Stuttgart, 1999; J. Mattes, “Mapping the invisible: Knowledge, credibility and visions of earth in early modern cave maps”, British Journal for the History of Science, vol. 55(1), (2022), pp. 53–80, in particular pp. 60–62.

228

Introduction: The Core Themes

The same line of thought is found in a letter he wrote to Detlev Clüver, at the end of July 1686. Concerning the formation of metals, Georg Agricola had supposed  – in De ortu et causis subterraneorum (1546)  – that mineral veins were formed when groundwater permeated the rocks and was boiled by subterranean heat, to attain a certain denseness and so to form metal ore deposits. Leibniz attributed the process of the subterranean formation of minerals by fire to spirits trapped in the mines, and he insisted that he could reproduce the process in experiments. Descartes had, in his Principia philosophiae (1644), disputed Agricola’s hypothesis, that groundwater was the source of the subterranean fluids from which minerals form, and he suggested instead that they are formed from molten rock. Leibniz considered Descartes’ account to be particularly meager and off the mark, the author having had no experience in the mines and having been beguiled by written sources. Finally, on June 6, 1690, Friedrich Heyn sent Leibniz samples of mineral ores, from the Ilmenau mines, specifically shale and limestone, in which fossilized plants were to be seen. Leibniz’s projected work Protogaea also forms the context of his correspondence with the Hamburg pastor, Caspar Büssing, and, in particular, the exchange of views regarding the theories of Thomas Burnet and William Whiston. Büssing, in his work De situ telluris paradisiacae et chiliasticae Burnetiano, ad eclipticam recto, quem T. Burnetius in sua Theoria sacra telluris proposuit, dissertatio mathematica (1695), published a critique of Burnet’s views expounded in his two-volume work entitled Telluris theoria sacra, originem et mutationes generales orbis nostri, quas aut jam subiit, aut olim subiturus est, complectens. Accedunt archaeologiae philosophicae, sive doctrina antiqua de rerum originibus (1681–1689). In a letter of October 16, 1696, Büssing then informed Leibniz about his “Dissertatio Anti-Burnetiana”. He was not sure, however, if his publication had reached England, and if Burnet would heed it. Büssing’s opus was reviewed by Christoph Pfautz in the Acta Eruditorum, in November 1695, and subsequently referred to by Leibniz in his correspondence with, among others, Thomas Burnett of Kemney and Wilhelm Ernst Tentzel. On December 26, 1696, Büssing reported to Leibniz that he had just received Burnet’s publication Archaeologiae philosophicae; sive doctrina antiqua de rerum originibus, libri duo (1692). This work had angered some English theologians, but Burnet, enjoying the protection of the king, was able to retain his standing. Büssing was also disappointed by Burnet’s publication, and he was of the opinion that it represented no more than a literary tale (“historiam quandam literarariam”) and failed to dispel any of the doubts that had been raised. Leibniz could then inform Büssing, on January 3, 1697, about William Whiston’s A new theory of the earth, from its original to the consummation of all things wherein the creation of the world in six days, the universal deluge, and the general conflagration, as laid

Introduction: The Core Themes

229

down in the Holy Scriptures, are shewn to be perfectly agreeable to reason and philosophy (1696). In this work, Whiston had postulated the origin of the earth from the atmosphere of a comet, and all major changes in the earth’s history were attributed by him to the action of comets.192 It was also directed against Burnet’s Archaeologiae philosophicae and, concerning which, Leibniz had been informed from a letter sent from London, by Burnett of Kemney, to the electress Sophie of Hanover, on December 16, 1696. Burnet had presented the view that God had created the earth in a perfect and regular form, but that it had been transformed into its present form by the deluge. Büssing’s alternative scenario assumed a spongy solidification of the earth’s crust through which, as a result of the subsidence or settlement of the earth’s surface, subterranean waters had been pressed upwards causing the deluge. Büssing’s explanatory model of the deluge appealed to Leibniz, as is evident from his letter of January 3, 1697. He was, however, of the opinion that a sinking of the earth’s surface would not have been possible without fissures being created in the existing crust of the earth. Leibniz’s skeptical questions in this letter, as to where such a quantity of water might have disappeared following the deluge and whether, for example, the water had sunk back into cavities in the earth’s interior, remained no doubt unanswered by the correspondent. On August 16, 1699, Leibniz reported to John Wallis about Gustav Daniel Schmidt’s geographical explorations of the coasts of the North Sea and of 192 Regarding Thomas Burnet and William Whiston, cf. M. Farrell (F.C.J.), The life and work of William Whiston, Ph. D. thesis submitted to the Faculty of Technology of the University of Manchester, 1973, and New York, 1981, in particular chap. 2 (Speculations in earth history 1660–1700: Whiston’s contribution to this debate); cf. also the following more recent studies: P. Rossi, L. G. Cochrane (trans.), The dark abyss of time: The history of the earth and the history of nations, Chicago and London, 1984, in particular chap. 10, pp. 66–69 (Burnet’s Heritage); J. E. Force, William Whiston: Honest Newtonian, Cambridge, London, New York, 1985, in particular chap. 2, pp. 32–62 (Whiston, the Burnet controversy, and Newtonian biblical interpretation); T. Heidarzadeh, A history of physical theories of comets: From Aristotle to Whipple, (Archimedes: New Studies in the History of Science and Technology, vol. 19), Cham, Switzerland, 2008, in particular pp. 129–135 (The post-Newtonian theory of comets: William Whiston and Edmond Halley); W. Poole, The world makers: Scientists of the restoration and the search for the origins of the earth, Oxford, 2010, in particular chap. 5, pp. 55–74 (The world makers: Burnet, Woodward, Whiston); T. Rossetter, The theorist: Thomas Burnet and his sacred history of the earth, Thesis submitted for degree of Doctor of Philosophy, Department of Philosophy, Durham University 2019 (E-Theses Online: http://etheses.dur.ac.uk/13080). Finally, regarding the development of geological, geomorphological, cosmological and cosmogenic theorizing, which served to undermine the strict historical veracity of the biblical narrative, cf. pp. 16–19 (Natural History) in: I. Leask, “Constant process: The science of Toland’s Pantheisticon”, Eighteenth-Century Ireland / Iris an dá chultúr [Ireland of the two cultures], vol. 34, (2019), pp. 11–27.

230

Introduction: The Core Themes

the Baltic Sea. Leibniz was also interested in the geological formation history of the English Channel, and accordingly in being able to establish temporal changes of the earth’s surface. Following inducement by Leibniz, Schmidt had prepared a questionnaire, on the configuration of the coasts near Calais and Dover, which Leibniz sent to the Abbé Jean-Paul Bignon and to Hans Sloane, on May 14 and 15, respectively, of the year 1701. Furthermore, in correspondence with Wallis,193 Leibniz discussed Olof Rudbeck’s geographical interpretation of mythology which, although rooted in literary legend, might just contain some truth, as he thought and wrote in a letter to Wallis, on April 30, 1699. Rudbeck had located Atlantis and Odysseus’ journey in northern Europe. Magnus Gabriel Block considered Rudbeck’s hypotheses to be ridiculous, and these sentiments about his compatriot he expressed to Leibniz in his letter of January 10, 1699. Block also reported in this letter about rejoinders to Rudbeck’s theory. In addition to questions of the geological configuration of the European Atlantic coastline, there was the issue of the pre-Christian Celticization of the lands and islands along and off these shores.194 It is not surprising then, that historical linguistics, in general, and, in particular, the theory of the relationship of languages, and alphabets, developed by the astronomy professor Edward Bernard, became an interest of Leibniz in the early 1690s. The discussion in his correspondence of the interrelationship, and development or evolution, of the Celtic languages, or protolanguages, and of Irish (or Proto-Irish) in particular, probably began in 1694.195 In a letter to Bernard, on January 6 of that 193 Cf. P. Beeley, “Physical arguments and moral inducements: John Wallis on questions of antiquarianism and natural philosophy”, Notes and Records of the Royal Society, vol. 72(4), (2018), pp. 413–430. 194 Regarding Celticization, cf. for example: B. Cunliffe, J. T. Koch (eds.), Celtic from the west: Alternative perspectives from archaeology, genetics, language and literature, (Celtic Studies Publications, book 15), Oxford, Philadelphia, 2012; Exploring Celtic origins: New ways forward in archaeology, linguistics, and genetics, (Celtic Studies Publications, book 22), Oxford, Philadelphia, 2019. 195 Cf. E. Poppe, “Leibniz and Eckhart on the Irish language”, Eighteenth-Century Ireland / Iris an dá chultúr [Ireland of the two cultures], vol. 1, 1986, pp. 65–84. Regarding the language “evolutionary theory” and the concept of a “protolanguage”, cf. W. Wildgen, The evolution of human language: Scenarios, principles, and cultural dynamics, (Series: Advances in consciousness research), Amsterdam, 2004, and in particular, chap. 8, pp. 159–184 (The form of a “protolanguage” and the contours of a theory of language evolution). More generally, regarding a possible analogy between Leibniz‘s ‘language dynamics’ and his dynamics in natural philosophy and physics, cf. W. Wildgen, Dynamische Sprach-und Weltauffassungen (in ihrer Entwicklung von der Antike bis zur Gegenwart), Philosophische Grundlagen der Wissenschaften (Book series of the Center for the Philosohical Foundations of the Sciences), vol. 3, Bremen, 1985, and 2005 (in electronic/digital form), and in particular pp. 25–32 (Naturdynamik und Sprachdynamik bei Leibniz).

Introduction: The Core Themes

231

year, Leibniz referred to John Wallis’ Grammatica linguae Anglicanae (1653 and 1674), in which the author had criticized Joseph Justus Scaliger’s Diatriba de Europaeorum linguis (1610), and other works, for separating Irish from Welsh and placing it among the “matrices” – viz. the isolated or unrelated languages – of Europe like Basque, Hungarian, Finnish and Lappish. Near the end of his letter to Bernard, Leibniz ruled out a connection between the Irish and Basque languages. In a letter to Daniel Larroque a month later, on February 5, Leibniz suggested once again that Irish seemed to be one of the languages of Europe which appeared isolated and difficult to relate to others, although there were people (like Wallis) who saw a connection with Welsh and Breton. A connection between Irish and Welsh, based on a comparison between contemporary Irish and Welsh texts of the Lord’s Prayer, was also a focus of Leibniz’s correspondence with Thomas Smith, in late 1694 and early 1695. The origins of the peoples and languages of Great Britain and Ireland were again considered in Leibniz’s correspondence with Wallis, at the end of the decade. Thus, Leibniz’s words in his letter of December 4, 1699, refer to the Anglo-Saxon settlement and reveal an inkling of the later formulated division of the Celtic peoples and languages into two groups, namely the Brythonic or P-Celtic (“Cymraeos  … vel Cambros”) and Goidelic or Q-Celtic (“Scotos antiquos seu Hibernos”). Leibniz alluded here to recent works of the Welsh naturalist, botanist, linguist, geographer and antiquary, Edward Lhuyd, including his catalog of fossils entitled Lithophylacii Britannici ichnographia, sive, lapidum aliorumque fossilium Britannicorum singulari figura insignium … distributio classica (1699) – which had been published with the financial assistance of the author’s friend Isaac Newton196 – and, specifically, the author’s observations concerning Irish Gaelic (“de Lingua Hibernica quaedam non vulgaria observasse”). Lhuyd had noted the similarity between the two linguistic families, namely P-Celtic (Breton, Cornish and Welsh) and Q-Celtic (Irish Gaelic, Manx and Scottish Gaelic). The first formulation of the P-Q split of the Celtic languages, advanced by Lhuyd and referred to by Leibniz in his letter, of December 4, 1699, to Wallis, is however generally traced back in the literature to Lhuyd’s glossography (or study of ancient words or languages) of 1707, namely his Archaeologia Britannica, which was published after Wallis’ death in 1703.197 Subsequently, in the years following Wallis’ demise, Leibniz 196 Cf. R. S. Westfall, Never at rest: A biography of Isaac Newton, Cambridge, 1983, specifically p. 581. 197 Cf. for example, J. MacKillop, Myths and legends of the Celts, London, 2005, and specifically, regarding the Celtic languages in general, pp. xi, xiv, xvi, xvii, xviii, 6, 47, 146, and regarding the so-called P-Q split in particular, pp. xvif.; J. Lennon, Irish orientalism: A literary and intellectual history, Syracuse (NY), 2004 and 2008, in particular chap. 2

232

Introduction: The Core Themes

(alongside Johann Georg Eckhart) also developed a more complex theory, in which the Irish language was integrated into his concept of the history and the relationship of the European languages. The most prominent Irish speaker – with a lifelong interest in the Celtic languages and their cultures – known to Leibniz was surely John Toland,198 particularly during the latter’s Hanoverian years (1701–1707).199 Ultimately, the culmination and conclusion of Leibniz’s efforts in this field, together with Eckhart, was no doubt the posthumous publication of his Collectanea Etymologica, illustrationi linguarum, veteris Celticae, Germanicae, Gallicae, aliarumque inserventia, in 1717. 10

Biology and Life Sciences Ex pollinis autem granulis spirituosum aliquid perductum ad ovarium, ut sic dicam, vel siliquam penetrare, atque ova vel semina illic foecundare.200 Leibniz to Alexander Christian Gakenholz, April 23, 1701

The interests of Leibniz and his correspondents in the living world were closely connected with the growth of biological thought in the seventeenth century and later. This encompassed questions of the meaning and diversity of life, the science of classifying – specifically pre-Linnaean classification, or the classification of plants and animals before Carl Linnaeus (1701–78) – and the science of species, as well as the characteristics of living organisms that distinguish them from inanimate systems. The latter category of characteristics included capabilities for evolution, and specifically for self-replication or reproduction, as well as for growth and differentiation, binding and releasing (Ogygia, pp. [58]–114), and specifically p. 90 (regarding the P-Q split of Celtic languages as advanced by Lhuyd). 198 Cf. A. Harrison, Béal eiriciúil as Inis Eoghain: John Toland (1670–1722) [Heretical voice from Inishowen: John Toland (1670–1722)], Dublin, Belfast, 1994, in particular chap. 3 (John Toland mar Ghaeilgeoir [John Toland as a Gaelic speaker], pp. 57–93, and regarding Leibniz in particular p. 64); A. Harrison, “Sur les origines celtes de John Toland”, Revue de Synthèse, vol. 116 (2/3), (1995), pp 345–355. (https://doi.org/10.1007/BF03182049). As regards the Gaelic language used in the Urris region of Inishowen, cf. E. Evans, “The Irish dialect of Urris, Inishowen, Co. Donegal”, Lochlann: A Review of Celtic Studies (Norsk tidsskrift for sprogvidenskap, Universitetsforlaget, Oslo), vol. 4, (1969), pp. 1–130. 199 Cf. M. Brown, A political biography of John Toland, London, New York, 2012 (and 2016), in particular chap. 3 (Hanover, 1701–7). 200 A III,8 N. 253, p. 660; Translation: Moreover, from the pollen grains a kind of spirit is led to the ovary, so to speak, or penetrates the pod and fecundates there either the eggs or the seeds.

Introduction: The Core Themes

233

of energy, self-regulation, and response to stimuli through perception and sense organs.201 Alongside the development of biological theory, practical issues and experiments were also often considered in Leibniz’s recorded discussions and correspondence. For example, the topics of discussion in Leibniz’s interlocution with the Marburg physician and Cartesian Johann Jakob Waldschmidt, on November 6, 1687, included two experiments of a botanical or zoological nature involving a vacuum pump. In the first experiment, the leaves of a plant were inserted into a vacuum flask while the roots remained outside and, in the second experiment, vice versa. When the vacuum pump was put in operation, water and vital spirit, or sap, were drawn from the roots through the meatus to the leaves, but not with the inverse experimental arrangement. Waldschmidt attributed the effects observed to the presence of valves in the vessels of the plants, through which liquids flow, whereas Leibniz supposed that inflected fibers were operative. The second experiment discussed by Leibniz and Waldschmidt involved introducing a small fine tube into the vein of a dog, and then pumping air into this tube. The outcome was the immediate death of the animal, because the blood was suddenly pumped through the veins to the heart and the blood circulation accordingly blocked. This conversation also touched on a bell mouth (speaking tube or trumpet), or acoustic horn, discovered by Waldschmidt and referred to by Leibniz as “eine redende Trompete” for voice transmission over a distance of a quarter or half a mile. In Leibniz’s letter to Hendrik van Bleiswijk, on January 6, 1699, the theory of animal origins and development is referred to in connection with a recent 201 Cf. for example, E. Mayr, The growth of biological thought: Diversity, evolution, and inheritance, Cambridge (MA), London, 1982, in particular Part I (Diversity of life), and specifically chap. 4 and chap. 6 (concerning the ‘Science of classifying’ and the ‘Science of species’, respectively), and Part II (Evolution), specifically chap. 7 and chap. 8 (concerning ‘Origins without evolution’ and ‘Evolution before Darwin’, respectively); E. Mayr, This is biology: The science of the living world, Cambridge (MA) and London, 1997 and 2001, in particular chap. 1 (What is the meaning of “life”?, treating the physicalists, the vitalists, the organicists, and distinguishing characteristics of living organisms). Furthermore, cf. G. Toepfer, Historisches Wörterbuch der Biologie: Geschichte und Theorie der biologischen Grundbegriffe, 3 vols, Stuttgart, Weimar, 2011, and in particular vol. 1, pp. 481–539 (Evolution, and concerning Leibniz’s thought, pp. 486f.), and pp. 577–605 (Reproduction, and concerning Leibniz’s thought, pp. 579f.). Regarding medieval thought on evolution, cf. G. Wicklein, “Die explication: Ein mittelalterliches Denken von Evolution”, pp. 13–24 in: C. Asmuth und H. Poser (eds.), Evolution: Modell – Methode – Paradigma, Würzburg, 2007. Regarding Leibniz’s conception of organism, cf. M. Echelard-Dumas, “Der Begriff des Organismus bei Leibniz: „biologische Tatsache“ und Fundierung”, Studia Leibnitiana, vol. 8(2), (1976), pp. 160–186.

234

Introduction: The Core Themes

discovery of Antoni van Leeuwenhoek, but one which was distinct from his earlier discovery of ‘animalcula’, or so-called little animals, in mammalian sperm.202 The discovery in question may, however, be that referred to in an article by Martin Lister, that had been published in September 1698 in the Philosophical Transactions with the title “An objection to the new hypothesis of the generation of animals from animalcula in semine masculino”. However, Leibniz’s line of thought here might also be connected with two communications, which he received from Johann Bernoulli, in Gronningen, during the second half of 1698. In a letter of August 2, Bernoulli, in contemplating the infinite and the infinitely small in mathematics  – like in the coexistence of lines and surfaces, of surfaces and bodies, or of differentials and integrals – drew parallels to the ongoing dispute between ovists and animalculists, in the theory of preformation, and he alluded to works by William Harvey (for example, Exercitationes de generatione animalium of 1651) and by Leeuwenhoek (for example, Observationes de natis e semine genitali animalculis of 1677–1678). In a second letter of November 18, where the relationship between infinity and the infinitely small was likewise at issue, the mathematician Bernoulli – alluding to his discussions in 1697 and 1698 with Pierre Varignon on these issues  – referred to the micro-cosmos, and the world of the animalcula observed by Leeuwenhoek, and he suggested that those animalcula might in turn, if provided with appropriate microscopes, observe a further micro-cosmos within their own, and so forth. Referring then to Leeuwenhoek’s observation of animate beings or little animals in water interfused with pepper (Observations … concerning little animals observed in rain- well- and snow-water, as also in water wherein pepper had lain infused of 1677), Bernoulli envisaged yet another sub-cosmos within the greater one. The interest of Leibniz, and of his correspondents, in botany and zoology is also reflected in other correspondences between 1696 and 1698. Although chemistry was the main focus of the correspondence with Johann Andreas 202 Regarding van Leeuwenhoek, cf. C. Dobell, Antony van Leeuwenhoek and his “Little animals”; being some account of the father of protozoology and bacteriology and his multifarious discoveries in these disciplines, New York, 1932, and 1958 (another first edition); N. Lane, “The unseen world: Reflections on Leeuwenhoek (1677) ‘Concerning little animals’”, Philosophical Transactions of the Royal Society, (2015), B370: 20140344 (http://dx.doi.org/10.1098/rstb.2014.0344). Regarding early theories of sexual generation in general, cf. C. Pinto-Correia, The ovary of Eve: Egg and sperm and preformation, Chicago and London, 1997, in particular chap. 3, pp. 105–109, and p. 326 (notes); J. Klein, N. Takahata, Where do we come from? The molecular evidence for human descent, Berlin, Heidelberg, New York, 2002, in particular pp. 16f. (Vapors, little worms and eggs): M. Cobb, The egg & sperm race: The seventeenth-century scientists who unlocked the secrets of sex, life, and growth, London, 2006.

Introduction: The Core Themes

235

Stisser in Helmstedt, botany was also an interest of this correspondent. Stisser had set up a botanical garden in Helmstedt, in 1692, and he was the author of a work, entitled Botanica curiosa (1697). Zoology, and in particular the anatomical investigation of large mammals, was likewise an important topic in Leibniz’s correspondence at this juncture. It was stimulated by reports of the study of the skeletons of dead or extinct animals. The more general context of Leibniz’s interest in the anatomy of large mammals was, however, his commitment to natural history and, in particular, regarding the history and form of the earth. On January 3, 1697, for example, Caspar Büssing asked Leibniz about the excavation of bones of an elephant-like creature at Gräfentonna (Tonna in the territory of Thuringia), an event that had been reported by Wilhelm Ernst Tentzel in his journal Monatliche Unterredungen, in April 1696, and in an open letter addressed to Antonio Magliabechi, entitled Epistola de sceleto elephantino Tonnae nuper effoso, published in Latin and German in the same year. Tentzel, for his part, hoped to obtain a report from the addressee of his Epistola about the skeleton of an elephant in Florence. In a letter to Leibniz on April 22, 1696 – to which the official judgement of the ‘Collegium Medicum’, in Gotha, concerning the discovery at Gräfentonna was attached – Tentzel referred specifically to two additional publications, namely Allen Mullen’s twin tracts entitled An anatomical account of the elephant accidentally burnt in Dublin on Fryday June 17 in the year 1681 … Together with a relation of new anatomical observations in the eyes of animals (1682), which were addressed to William Petty and Robert Boyle, respectively,203 and John Ray’s Synopsis methodica animalium quadrupedum et serpentini generis (1693). Tentzel’s letter to Leibniz, of April 22, thus reveals that, fifteen years after the event, Mullen’s dissection of the elephant was still attracting attention. Similarly, in a report on Tentzel’s Epistola de sceleto elephantino, in the Journal des Sçavans four months later, on August 20, 1696, the reviewer commented on Mullen’s autopsy of the elephant and he drew comparisons with the more recent discovery at Gräfentonna. In addition to the autopsy of the elephant, the physician Mullen had recorded his observations on the eyes of fowl and of fish, as well as on the ears of fowl, drawing inferences between the organs of animals and of humans. Whale hunting, and the import of exotic animals from distant lands, offered yet another means of studying the anatomy of the largest mammals. On September 28, 1697, Georg Franck von Franckenau – then personal physician 203 Cf. K. T. Hoppen (ed.), Papers of the Dublin Philosophical Society 1683–1709, Dublin: Irish Manuscripts Commission, 2008, 2 vols, in particular vol. 1, nos. 184–189, pp. 399–413 and vol. 2, pp. 959f.

236

Introduction: The Core Themes

to the king of Denmark – reported to Leibniz that he had received precious minerals, as well as coral, or coral algae, from the mining official Heinrich von Schlanbusch in Trondheim, Norway. In addition, the remarkable penis, as well as the mandible or lower jaw – commonly known as boning or ‘Fischbein’ – of a whalebone or baleen whale had been received. The same correspondent also reported that he had obtained specimens of exotic animals, like a large spotted civet cat and tiger, a long-tailed monkey and a brown squirrel, from East India. After he had learned of the impending return of the Jesuit priest, Joachim Bouvet, to China, the president of the Leopoldina, Lucas Schröck, commenced a correspondence with Leibniz, on January 16, 1698. As an attachment, Schröck sent a non-sealed letter addressed to Andreas Cleyer – who was originally from Kassel and had become a physician, botanist, pharmacist and respected figure in the Dutch East India Company’s Batavian society – as well as a questionnaire, also intended for Cleyer, about, among other things, the musk plant and the Levant wormseed (“semen sanctum”). Two weeks later, on January 30, Leibniz forwarded Schröck’s letter (and questionnaire) for Cleyer to Joachim Bouvet, together with an accompanying letter. As is evident from Bouvet’s reply – sent from La Rochelle on February 28 – the correspondent intended having Schröck’s letter copied and gathering relevant information himself. Cleyer had already published Specimen medicinae Sinicae, sive opuscula medica ad mentem Sinensium (1682), about heartbeat or cardioplegia, and had edited the edition of Michael Boym’s Clavis medica ad Chinarum doctrinam de pulsibus (1686). In a letter to Leibniz, of July 17, 1698, Schröck also made reference to Georg Eberhard Rumpf from Hanau. Like Cleyer, the latter had gone as a physician to East India and had become consul and senior merchant of the Moluccan Island Ambon.204 In the service of the Dutch East India company, he wrote a number of works about the natural history, and the natural science of the Moluccan Islands, and devoted himself to the study of botany. Schröck, in this letter to Leibniz, referred to another letter of Rumpf, from September 1696, that had duly been published in the Miscellanea Curiosa under the title “De caryophyllis regis Ambonicis”. In addition, Schröck referred to a joint publication of Cleyer and Herbert de Jager, who had investigated a species of flowering plants called “artemisia abrotanum” (southernwood or southern wormwood) in Persia. Moreover, Schröck provided Leibniz with intelligence, received from Christian Mentzel and Rumpf himself, about a planned six-part botanical opus of Rumpf, the first part of which had, following dispatch, unfortunately been 204 Cf. G. Yoo, “Wars and wonders: The inter-island information networks of Georg Everhard Rumphius”, British Journal for the History of Science, (Special Issue: Science and Islands in Indo-Pacific Worlds), vol. 31(4), (2018), pp. 559–584.

Introduction: The Core Themes

237

lost in a shipwreck, while en route to Holland in 1692. Alas, following Rumpf’s death in 1702, his posthumous multi-volume work Herbarium Amboinense was only published decades later, between 1741 and 1750.205 In the spring of 1701, Leibniz’s correspondence with Alexander Christian Gakenholz gained a special significance, particularly in the fields of biology and medicine. Following a discussion with Leibniz (probably in March 1701), Gakenholz composed an open letter addressed to him, dated April 14, 1701, with the title Ad illustrem atque excellentissimum virum Dominum Godefr. Guilielmum Leibnitium … epistola … de emendanda ac rite instituenda medicina. The first printed version, of this Epistola on the emendation and correct practice of medicine, was sent as an enclosure to Gakenholz’s letter to Leibniz dated April 21, 1701. The correspondent attributed the inspiration for his composition to the discussion he had with Leibniz a few weeks earlier. Leibniz had proposed considering roots as the basis for a system of plant classification. Following up on this proposal, Gakenholz had, in his Epistola, discussed various established classification systems, which were based on fruit, seeds and, more recently, flowers. As in his remarks concerning medicine, Gakenholz complained here also about the predominant orientation towards antiquity, where writings were interpreted, annotated and even provided with plant illustrations without any comparison with the real world having been undertaken. That had only begun to change in recent decades, he maintained. However, the new methods, that strove for mathematical exactness, were hardly suitable for general use, since classification on the basis of flowers and fruit made long-term observation necessary. The advantage of roots, as a basis for a classification system, was that they were constantly available. However, the fact that roots did not present any great number of variations made them unsuitable as a sole classification characteristic, although otherwise easy to deal with. The central message of Gakenholz’s Epistola then was that, besides anatomy and chemistry, botany had a particular significance. And a special desideratum in the subject area of botany was the development of a taxonomy, or classification system, on the basis of parts of plants, such as flowers, fruit, seeds or roots. From Leibniz’s reply of April 23, 1701, it is clear that Gakenholz had picked out and developed suggestions, which had been introduced by Leibniz himself at their meeting some weeks earlier, including thoughts about the taxonomy of 205 Cf. W. Buijze, Leven en werk van Georg Everhard Rumphius (1627–1702): Een natuurhistoricus in dienst van de VOC, Den Haag (The Hague), 2006, and in particular the second appendix about persons in Rumphius’ ken (“Bijlage 2: Personen in Rumphius’ Wereld”) pp. 214–339, and specifically Andreas Cleyer (pp. 228–246), Herbert de Jager (pp. 282–296), and Christian Mentzel (p. 309).

238

Introduction: The Core Themes

plants. Thus, from this letter, it is evident that a classification of plants according to a single criterion, such as the form of flowers, fruit, seeds or roots, was for Leibniz insufficient. Combinatorics, and in particular his own dissertation on the combinatorial art – viz. the Dissertatio de arte combinatoria of 1666 – appeared to offer a way forward.206 In addition to mathematics, philosophical (and even juridical) categories also seemed to have a certain relevance for the development of botanical systematics and classification systems. That the criteria depended on the focus of the particular discipline, he illustrated by making reference to geometry. Here he alluded to Ramist geometry (based on the teachings of the Parisian pedagogical reformer Petrus Ramus, 1515–1572), which, despite its crudity, had enjoyed popularity in the late sixteenth-century, and in the early seventeenth-century, providing a method of systematizing all branches of knowledge. It did not heed proofs, like those of Euclidean geometry, and it judged figures on the basis of their form, with practical geometry putting the focus on benefit or usefulness. In terms of the organization of learning, the radical innovator Ramus had, in fact, authored innovative treatises on subjects including grammar, dialectic, rhetoric, and of course mathematics.207 While the knowledge derived from Ramist geometry was inferior to that obtained from Euclidean geometry, it was of benefit to those not capable of understanding higher mathematics. According to Leibniz, botany found itself on an analogous level, since the internal structures of the machines of nature, viz. of plants  – founded perhaps in René Descartes’ natural philosophical approach to the vegetal realm208 – were not yet known. For Leibniz, therefore, further progress seemed to depend above all on an improved knowledge of the inner workings of these machine-like entities. For him, organic bodies produced by nature, like plants, animals and the human body, represented machines for the fulfillment of certain duties and functions, such as nutrition,

206 Cf. E. Knobloch, Die mathematischen Studien von G. W. Leibniz zur Kombinatorik, Studia Leibnitiana, (Supplementa, vol. 11 and vol. 16), Wiesbaden, 1973 and 1976, respectively; E. Knobloch, “Renaissance combinatorics” and “The origins of modern combinatorics”, pp. 123–146 and 147–166, respectively, in: R. Wilson, J. J. Watkins (eds.), Combinatorics: Ancient & modern, Oxford, 2013. 207 Cf. P. H. Smith, The body of the artisan: Art and experience in the scientific revolution, Chicago, 2004 (and 2012), in particular p. 66; A. T. Grafton, “Textbooks and the disciplines”, pp. [11]–36, in: E. Campi, S. De Angelis, A.-S. Goeing, A. T. Grafton (eds.), Scholarly knowledge: Textbooks in early modern Europe, Geneva, 2008, in particular p. 22 (regarding Ramus). 208 Cf. F. Baldassarri, “The mechanical life of plants: Descartes on botany”, British Journal for the History of Science, vol. 52(1), (2019), pp. [41]–63.

Introduction: The Core Themes

239

reproduction and the preservation and perpetuation of knowledge.209 Just as one differentiated between theoretical and practical mathematics, one ought to distinguish between theoretical biology, on the one hand, and practical biology and medical practice, on the other hand. To theoretical biology belonged the classification of plants according to one criterion, or several criteria. Plants, animals and humans were, for him, machines that were adapted for certain tasks: humans for contemplation, and plants and animals, among other things, for helping humans in the fulfillment of such tasks. The challenge then was to explain these tasks, as well as the mechanisms involved in their realization. Leibniz had long been interested in the animate beings of earlier epochs, and in the science of these creatures. It may be recalled, for example, that he had obtained intelligence (in 1696 and 1697) regarding a trove of bones in Gräfentonna. In his letter to Gakenholz, on April 23, 1701, he then employed concepts from the field of comparative anatomy (such as “collatio animalium”) and from reproductive, developmental and evolutionary biology (like “plantarum cum animalibus connexio” or “transitus a plantis ad animalia majora per intermedia”). Thus, he spoke of a link between plants and animals on the common basis of respiration, or respiratory organs, and of insects as an intermediate form between plants and animals, particularly with Jan Swammerdam’s Historia insectorum generalis, ofte Algemeene verhandeling van de bloedeloose dierkens (1669) in mind.210 A further influence on Leibniz thought, in relation to the classification and, in particular, the reproduction of plants, was no doubt the letter sent to him by Johann Heinrich Burckhard, on February 21, 1701, also following a 209 Cf. R. Andrault, “The machine analogy in medicine: A comparative approach to Leibniz and his contemporaries”, chap. 7 (pp. 95–114), in: J. E. H. Smith, O. Nachtomy (eds.), Machines of nature and corporeal substances in Leibniz, Dordrecht, Heidelberg, London, New York, 2011; F. Duchesneau, “Physiology and organic bodies”, chap. 26 (pp. 466–484) in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Regarding the machine analogy / metaphor, cf. the following editions of Canguilhem’s works and their English translations: G. Canguilhem, La connaissance de la vie, Paris, 1952, and 1965, 1992, 2003, respectively, and in particular “Machine et organisme”, pp. 124–159 and pp. 129–164, respectively; M. Cohen, R. Cherry (trans.), “Machine and organism”, pp. 44–69, in: J. Crary, S. Kwinter (eds.), Incorporations, New York, 1992, and P. Marrati, T. Meyers (eds.), and S. Geroulanos, D. Ginsburg (trans.), Knowledge of life, New York, 2008; O. Fiant, “Canguilhem and the machine metaphor in life sciences: History of science and philosophy of biology at the service of sciences”, Transversal: International Journal for the Historiography of Science, (Graduate Program in History of Federal University of Minas Gerais / Universidade Federal de Minas Gerais), vol. 4(4), (2018), pp. 149–162. 210 Cf. S. Klerk, “Natural history in the physician’s study: Jan Swammerdam (1637–1680), Steven Blankaart (1650–1705) and the ‘paperwork’ of observing insects”, British Journal for the History of Science, vol. 53(4), (2020), pp. 497–525.

240

Introduction: The Core Themes

meeting between the two in Wolfenbüttel a few days earlier. In Leibniz’s letter to Gakenholz of April 23, Burckhard’s reference to the work of the Tübingen professor Rudolph Jacob Camerarius, entitled De sexu plantarum epistola (1694), was duly acknowledged. In his letter of February 21, Burchard had provided him with a detailed representation of the sexual organs of plants and, in particular, of the phenomena of monoecy and dioecy, viz. of monoecious and dioecious plants. Leibniz, in his letter to Gakenholz of April 23, saw in the reproduction process in plants – described by Burckhard and set in connection with the reproduction of animals  – a connecting element between the vegetable and animal kingdoms. Accordingly, the pollen of seed-producing, or flowering, plants corresponded to mammalian sperm. Similarly, the style of a flower corresponded to the vagina in placental mammals, and the ovary at the bottom of the style corresponded to a mammalian ovary. Fertilization occurred when a kind of spirit – a non-physical element, or a vital force, contained by the living organism – coming from the pollen, penetrates the ovary, whereby either the eggs or the seeds are duly fecundated there (“atque ova vel semina illic foecundare”).211 In this context, Leibniz recalled the rival theories of preformation of Antoni van Leeuwenhoek and of the anatomist Theodor Kerckring. In the ovist-animalculist controversy, Leibniz saw here a possible reconciliation, but his own position was close to that of the animalculist Leeuwenhoek and removed from that of the ovist Kerckring. The preformist theory assumed that the entire organism was preformed, either in the sperm (the animalculist position) or in the egg (the ovist position), of the mammal and had only to unfold, or deconvolve itself, in the process of fertilization. Here again Leibniz saw a connection between the vegetable and animal kingdoms. 211 Cf. G. Toepfer, Historisches Wörterbuch der Biologie: Geschichte und Theorie der biologischen Grundbegriffe, 3 vols, Stuttgart, Weimar, 2011; see vol. 3, pp. 692–710 (Vitalismus) and in particular pp. 693f. (Stahl und Leibniz); F. J. Martínez, “Vitalism in Leibniz: A dileuzian approach”, chap. 10 (pp. 159–170) in: J. A. Nicolás, J. M. Gómez Delgado, M. Escribano Cabeza (eds.), Leibniz and hermeneutics, (Cambridge Scholars Publishing), Newcastle upon Tyne, 2016. Regarding vitalism or vitalists, cf. E. Mayr, 1997 and 2001 (note 201 above). Concerning Newton’s position with regard to the nature of a vital force, see pp. 12–16 (Vitalism beyond Mechanism) in: I. Leask, 2019 (note 192). Regarding Leibniz’s communications concerning sexual reproduction, cf. J. G. O’Hara, ““ova vel semina … foecundare”: Sexual reproduction in Leibniz’s scientific correspondence”, in W. Li, U. Beckmann, et. al. (eds.), “Für unser Glück oder das Glück anderer”: Vorträge des X. Internationalen Leibniz-Kongresses, Hanover, 18.–23. Juli 2016, 5 vols, Hildesheim, Zürich, New York, 2016, in particular vol. II, pp. 431–448. Regarding preformationism and the work of Camerarius, cf. L[incoln] Taiz and L[ee] Taiz, Flora Unveiled: The discovery and denial of sex in plants, Oxford, 2017, in particular chap. 12, pp. 322–349 (The difficult birth of the two-sex model).

Introduction: The Core Themes

241

Following his correspondence with Gakenholz in 1701, Leibniz continued to refer to the theory of preformation in his learned correspondence. Thus, for example, in a letter to queen Sophie Charlotte and John Tolland, in early December 1702, Leibniz explained his views on preformation, referring to Swammerdam’s Historia insectorum generalis (1669) and Leeuwenhoek’s article “Observationes de natis e semine genitali animalculis” (1677/78). Leibniz, referring to Leeuwenhoek in his major philosophical writings composed between 1704 and 1714, admitted his penchant for the latter’s interpretation of the theory of preformation, particularly in the Nouveaux Essais sur l’entendement humain (1704), in the Essais de theodicée sur la bonté de Dieu, la liberté de l’homme et l’origine du mal (1710), and in the Lehr-Sätze über die Monadologie (1714 and 1720). In the Nouveaux Essais, he expressed the view that Leeuwenhoek had enhanced the status of the male sex, and accordingly degraded the female sex, which merely provided a nutrient medium for the seed. Finally, on August 5, 1715 – almost forty years after their meeting in Delft in November 1676 – Leibniz commenced a direct correspondence with Leeuwenhoek, and a total of eight letters were exchanged between the two before Leibniz’s death on November 14, 1716. A final letter of Leeuwenhoek, dated November 17, was written before he learned of Leibniz’s passing.212 11 Medicine Wolte Gott daß Medicinalia und dergleichen concreta so wohl in potestate wären. Gleichwohl ist gewiß, daß auch diese dinge, in so weit sie rationi unterworfen, auch in calculum zu bringen. Denn calculus nichts anders als aptissima et compendiosissima ratiocinationum expressio.213 Leibniz to Rudolf Christian von Bodenhausen, February 20, 1690

212 Cf. L. Palm, et al. (eds.), note 95; J. G. O’Hara, note 95; A. Becchi, “Between learned science and technical knowledge: Leibniz, Leeuwenhoek and the school for microscopists”, pp. 47–79 in: L.Strickland, E. Vynckier, J. Weckend (eds.), Tercentenary essays on the philosophy and science of Leibniz, Basingstoke, 2016. 213 A III,4 N. 236, p. 462; Translation: [May it be that] God wanted that medicinalia, and the like, exist both concretely and potentially [viz. be both concrete and abstract]. Nonetheless, it is certain that these things, in as far as they are subject to reason, can also be reduced to calculation. For, indeed, calculus is nothing other than a most appropriate and compendious expression of reasoning or rational thought.

242

Introduction: The Core Themes

11.1 Anatomy, Physiology In the field of medicine,214 questions arising included those regarding the circulation of the blood, and the form of blood vessels, and were an important consideration in Leibniz’s correspondence with the professor of Medicine in Helmstedt, Heinrich Meibom, in the early 1680s. Following a meeting with Meibom in Hanover, in September or early October 1681, Leibniz wrote to him, on January 23, 1682, referring to Meibom’s observations of triangular vascular formations discussed at their meeting. Here Leibniz took an anatomical observation of the correspondent  – whose exact investigation and verification with the aid of a microscope he considered to be essential – as a starting point for a lengthy theoretical consideration about the form of blood vessels. Assuming the blood vessels to be elastic, and to have a polygonal cross section, they represented what he termed a most simple hydraulic machine, which, notwithstanding the irregular entry of the blood, guaranteed a regular rate of flow. Thus, resorting to trigonal prismatic geometry to describe the shape of such blood vessels – whose cross section was represented by a circumscribed polygon that might range from a triangle (the best case), through multi-faceted polygons, to a circle (the worst case) – he imagined a hollow triangular prism, or tube, filled with water and continually supplied through an orifice, as the most simple hydraulic machine to emulate blood flow. However, the experiment entailed a mechanical problem of reconciling the intermittent, or pulsed, intrusion with the continuous extrusion of the fluid, and the solution of this mechanical problem did not seem to Leibniz to be at all simple. Immediately following this line of thought, Leibniz elaborated a further consideration in which elasticity emerged as an explanatory principle in anatomy, while adhering to his triangular prism or tube model for the form of blood vessels. The longer and fewer the sides of the circumscribed polygon were, the more flexible they would be. He then proceeded to present his views on acoustics, and he concluded that something must exist in the hearing organ which can be of uniform tension or tonus, viz. be homotonic (and thus belong to the same gamut or pitch range) with every sonorous body. He encouraged Meibom, in the letter of January 23, 1682 – as he had done previously with Günther Christoph Schelhammer in a letter of February–March 1681 – to pursue this outstanding anatomical problem of identifying the missing entity. Otherwise, Leibniz considered the main questions of acoustics to be essentially solved.

214 Cf. J. E. H. Smith, “Medicine”, chap. 27 (pp. 485–499) in: M. R. Antognazza (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

Introduction: The Core Themes

243

New observations about kidneys, and urinary tracts, were reported or discussed in various correspondences in the early 1680s. Sebastian Scheffer had good contacts in Padua and he forwarded, on May 23, 1682, an anatomical discovery of Domenico Marchetti – reported also in the June number of the Journal des Sçavans  – which Leibniz in turn passed on, without comment, to Friedrich Schrader a couple of months later. Likewise, Scheffer’s letter, of January 1681, reveals that Leibniz had acted as an intermediary between him and Henri Justel, regarding the publication, in the Miscellanea Curiosa in 1678–1679, of his description of an extremely enlarged kidney. Schelhammer’s investigations in this area were initiated following his acceptance of a medical professorship in Helmstedt, in November 1680. In relation to medical science, it was an anatomical investigation of the sexual organs of the mole that became the starting point of a discussion between Schelhammer and Leibniz, and that was continued over several letters in 1680 and 1681. The overture to this discussion was a brief meeting between the two in Hanover. Following Leibniz’s first letter, of June 2, 1680, and Schelhammer’s reply on June 14, the topic of discussion was extended in Leibniz’s next letter, of September 24 and the focus moved from the anatomy of the mole to the question of sexual reproduction in general. In the contemporary controversy about the constituent parts of mammalian semen – in particular, between the Dutch physicians and medical professors Johannes van Horne (Hoorn), Reinier de Graaf, and Jan Swammerdam – Schelhammer, writing to Leibniz on November 18, expressed his belief that he had identified the existence of three separate constituents of the seminal fluid which were being continually produced in testicles, prostate or prostatic glands and seminal vesicles, and then effused into the urethra for removal from the body. On December 16, Leibniz then expressed his skepticism and interjected that it should be investigated whether all three constituents were equally necessary for animal reproduction. However, the question could not be answered by the correspondent in his reply on January 10, 1681, and, notwithstanding his knowledge of medical literature and the considerable thought he had given to the matter, he readily conceded that Leibniz’s objection was valid. A veritable sensation among scholars was caused by the arrival of Denis Papin’s digester, in which animal bones could be rendered soft and made edible. Papin first presented his pressure pot at the Royal Society, in May 1679, and the first publications regarding it came from Robert Boyle, in his Experimentorum novorum physico-mechanicorum continuatio secunda (1680), and from Papin himself, in his work entitled A new digester, or engine for softning bones (1681), and reviews were published in the newly-established Acta Eruditorum in April and October 1682. Furthermore, Mariotte informed Leibniz, on June 4, 1681,

244

Introduction: The Core Themes

about a presentation of the digester at the Académie des Sciences. Leibniz had previously been informed, in a letter of July 18, 1680, by Frederick Slare following which he negotiated with Slare, in the early months of 1681, about the purchase of such a digester. While Schelhammer was curious to learn what was causing the softening of the bones, and thought the invention might have useful applications in medicine, Friedrich Schrader saw in Papin’s steam digester an analogy to rachitis, or rickets, which likewise made bones soft. However, he was more interested in the opposite problem, namely as to how one might petrify, and indurate, the parts of animals and innards so that they would retain their form and position, and he informed Leibniz accordingly, on December 8, 1681. The knowledge which Schrader had gained on his journeys about the embalming of corpses, and related matters, as well as through reading and experiments, was greeted with acknowledgement by Leibniz, in a letter of July–August 1682. A pronounced interest in anatomy, and in new anatomical insights, on Leibniz’s part was also apparent in the 1690s. In the early months of the year 1695, the surgeon Jacques M. B. Bouquet accompanied prince Maximilian Wilhelm of Hanover on a tour to Italy. On March 3, Bouquet reported to Leibniz from Padua that discussions about anatomy were very much in vogue in his circles there. In Padua, Bouquet had assisted a dissector with the postmortem examinations of a series of corpses. Two of these autopsies, Bouquet considered particularly worthy of mention. In the first case, in carrying out the postmortem examination of a corpse, they had found a spleen split in two, with one part in the breast area and the other in the abdomen. In the second case, they were seemingly confronted with a corpse having two livers separated from each other. One liver was found in the normal location, and it had normal proportions. The second liver was discovered within the coverings of the diaphragm. According to Bouquet’s report, it had the size of two fists, and it weighed about two to three pounds. Furthermore, it had an approximately round figure and a small lobe. Below this second liver passed the vena cava, which led to the remaining veins and numerous arteries, he reported to Leibniz. After Leibniz had requested further details, Bouquet addressed the two autopsies once again in his next letter of June 11, 1695. First of all, he explained the circumstances of the investigation of the corpse with the two livers. Together with the dissector, he had examined an organ, between the membranes of the diaphragm, that was at first construed to be the heart. Through further investigation, however, similarities with a liver were established. The form and substance of the organ, the path of the vena cava, as well as the distribution of the veins and arteries throughout the whole body, indicated that the organ was indeed a liver. The gallbladder, and the gallbladder passage to the

Introduction: The Core Themes

245

intestines, were found to be missing. Bouquet then elaborated on the special circumstances of this second autopsy. In that, they had been confronted with the corpse of a crippled or maimed man, a school master who had never been able to walk. As a result of his illnesses, and the circumstances of his disability, the organs of the lower abdomen were swollen or overblown, pressed together and pushed upwards. The circumstances of the man’s life also provided an explanation for the split spleen in the first corpse. A part of the oversized organ had, in fact, been pressed into the chest, or breast area, by an extension of the diaphragm. For Bouquet, these deformities represented a grotesqueness of nature, from which no new insights into the normal functions, and functioning, of the organs involved could be expected, he told Leibniz. As regards anatomical studies, Georg Franck von Franckenau emerged as Leibniz’s most important correspondent in the late 1690s. Physicians’ reports about postmortem examinations of corpses, as well as reports about birth deformities, had long been a source of information for Leibniz in the area of anatomy. Both are to be found in a report of Franck von Franckenau, in his letter of September 28, 1697, about a monstrous birth and, specifically, the postmortem examination of the remains of a dead-born two-headed female child. In August of that year, the wife of a schoolmaster near Copenhagen, who was already mother of several children, gave birth to this two-headed girl. The still-born child was brought to the Royal Palace, where the remains were examined by Franck von Franckenau, then personal physician to the king, and the correspondent duly informed Leibniz. His eldest son, Georg Friedrich Franck von Franckenau, had carried out the post-mortem examination, Leibniz was told. It was found that several organs were duplicated, and these included the trachea or wind-pipe with outgrowths, the oesophagus or gullet, the stomach, with the small intestine extending to the middle of the ileus and terminating in an ample or spacious sac, the spine, the lungs and the ribs. The remaining organs were found singly, and these included the heart, the liver, the spleen, the kidneys, the adrenal glands, the urinary bladder, the uterus, the pancreas, the mesentery and the cunt. The body had two arms and two legs, all provided with nails. Finally, following the exenteration, and a public viewing by a large number of visitors at his residence, the remains were laid in a container filled with a fluid of florantibalsam (“spiritus balsamicus”), and then taken to the Royal Museum for preservation, Leibniz was informed. Following the death of Leibniz’s correspondent and collaborator at the Court in Florence, Rudolf Christian von Bodenhausen, an autopsy was likewise carried out on the remains. Previously, on July 28, 1696, Bodenhausen himself had informed Leibniz about his insistence on self-treatment during illness and his reluctance to seek medical assistance in Italy. Bodenhausen’s reservations

246

Introduction: The Core Themes

were centered on a perceived abuse of phlebotomy there. When his death ensued in May 1698, the corpse was duly dissected. The twenty eight year old Swedish physician to-be, Magnus Gabriel Block, who assisted during the postmortem examination, availed of the opportunity to commence a correspondence with Leibniz, whom he informed, on May 12, 1698, about the passing three days earlier of his correspondent and collaborator, and about the cause of his death. The autopsy had shown that Bodenhausen died of an abscess of the liver in which, it was reported, four pounds of pus had been found. Medicine  – anatomy and physiology in particular  – received a critical appraisal in the open letter (dated April 14, 1701) by Gakenholz addressed to Leibniz. In his Epistola … de emendanda ac rite instituenda medicina, Gakenholz complained that the subject was still in its infancy while other sciences, mathematics in particular, had been making great strides. He put the blame for this on a superstitious veneration for the ancients and wrong priorities in medical studies and training. He propagated an anatomy of fluids, and he pleaded for a reform of the system of anatomical, or postmortem, examination that should be guided by a particular understanding, namely that the body was to be viewed simply in the context of the vessels and organs. One ought, he maintained, to begin with the circulation of the blood, with particular interest being paid to the arteries, veins, and the heart chamber, to avoid incisions, and to pay attention to connectivity and interrelation. He himself had tested injections and re-injuries of vessels in corpses. Experimental infusions, as well as blood transfusions, could be undertaken with animals, he thought. Gakenholz emphasized the role of chemistry in medicine, and he insisted that physicians ought to study this subject in order to understand the processes in nature. At the same time, he criticized the excrescence of chemical pharmacy, which had produced a multitude of salts where, he reckoned, a single specimen might be sufficient. He recommended the study of plants with regard to their powers of healing, but he considered the established methods not to be very meaningful. Besides color, odor, taste and combustion or incineration properties, the reaction of plant sap with blood had been investigated in order to establish the effect on the human body. Gakenholz maintained that there were differences in the reactions with arterial and venous blood. Furthermore, the effectiveness of such a medicament, following intake and digestion, was not at all clear. On April 23, 1701, Leibniz excused himself for entering solely into Gakenholz’s further remarks on botany, being unable to contribute further to the discussion of medicine. He pointed out, however, his special interest in public health and he acclaimed his proposed project with Hoffmann – a project referred to above – for the collection and annual publication of meteorological-medical observational data.

Introduction: The Core Themes

247

In the same month, April 1701, there appeared a summary and review in German of Gakenholz’s work in Leibniz’s house journal Monat[h]licher Auszug. In this review the writer (perhaps Johann Georg Eckhart) outlined Gakenholz’s criticism of the existing system of medical studies. There the reader learned that the core of medical studies, according to Gakenholz, should be anatomy, the science dealing with the structure of plants, animals and the human body, which was to be considered as a machine or automaton. The heart was the prime mover of the machine, and anatomy served the purpose of the meticulous study of the vessels emanating from the heart in their natural state. Thus, the circulation of the blood would be revealed and, for example, the passage of blood from the heart through the largest artery, the aorta, and then through the body to the kidneys illustrated. Furthermore, the reviewer reported that blood and other body fluids were the focus of the anatomy of fluids, and that here experimental science, and particularly chemistry, had a special role to play. Aspirants in the field of chemistry ought to be mainly concerned with the subject as revealed in the works of nature with, for example, the chemical reactions of life, and the seat of most illnesses, being found in body fluids 11.2 Pathology, Therapeutics, Pharmacology Therapeutic and pharmaceutical topics were likewise not wanting in Leibniz’s correspondence in the early 1680s. Regarding the spectacular application of cinchona bark, in particular by the English physician Sir Robert Talbot, Leibniz sought (in 1680) to obtain the opinions of the Royal Society and of the personal physicians at the court in Celle, namely Heinrich Christoph Ebell and Dietrich Conerding. Leibniz’s question, about the appropriate use of antimony preparations, was answered in detail by Schrader in letters of August 14, 1681, and April 23, 1682, and Ferguson was able to inform him, in the spring of 1680, about a skin cosmetic, which Leibniz then designated as “Cosmeticum Fergusoni”. In January 1681, Scheffer reported the use of sulfur as medication against cough and, on August 18, 1682, he reported that he had concocted an “antepilepticum” (an antiepileptic or epilepsy drug) from the hearts of frogs. The age-old conflict between physicians and apothecaries also raised its head in Leibniz’s correspondence in the early 1680s. Schelhammer complained, in the first half of September 1680, that he, as a medical professor, had to leave the production of medication to the apothecaries. In this dispute, Leibniz endorsed the standpoint of the physicians, as he informed Schelhammer in his reply on September 24. The Chinese method of diagnosing diseases by pulse observation also aroused Leibniz’s interest. In January, 1681, Scheffer answered a query from

248

Introduction: The Core Themes

Leibniz, and he referred to a letter of November 20, 1679, which he had received from the botanist, and physician, Andreas Cleyer, which contained mussels from Jakarta and from which excerpts were later published (in 1685) in the Miscellanea Curiosa. Scheffer’s letter contained a reference to “Clayers methodo” which involved the diagnosis of illnesses by means of pulse observations, and which was treated by Cleyer in his publications, entitled Clavis medica ad Chinarum doctrinam de pulsibus (1680), and Specimen medicinae Sinicae, sive, Opuscula medica ad mentem sinensium, continens I. De pulsibus libros quatuor e sinico translatos. II. Tractatus de pulsibus ab erudito europaeo collectos (1682), respectively.215 In a subsequent letter to Leibniz, on August 18, 1682, Scheffer once again referred to his correspondence with Cleyer, and subsequently, extracts from a letter of December 20, 1683, sent by Cleyer from Malacca to Scheffer, were referred to in a letter to Leibniz of October 23, 1685, and were published in the Miscellanea Curiosa in the same year. In the final letter, of December 8, 1685, that Leibniz received from Scheffer – before the correspondent’s death on January 20, 1686 – there is a final reference to Cleyer’s contributions for the Miscellanea Curiosa. In Leibniz’s correspondences with Friedrich Heyn and Christian Wachsmuth, in 1686 and 1687, a multiplicity of medicinal products are referred to. Besides medicaments like Peru balsam syrup, smelling salts (“Schlagbalsam”), sweet almond oil, white candied sugar, which Leibniz obtained from Wachsmuth, other products, like medication against dysentery and the pest, Armenian bole (referred to in Heyn’s first letter of February 6, 1687) or white Armenian bole, also deserve mention. Herbal remedies too were popular like, for example, an emetic from America, which was referred to (in Heyn’s letter of November 30, 1686, to Wachsmuth) as a “Planta aus America so vomitus ohne beschwerung macht”. In a letter to Bodenhausen, on January 13, 1690, Leibniz tried to get information about a herbal remedy against podagra or gout. The Jesuit missionary Claudio Filippo Grimaldi had brought the plant in question from China, and it was then to be found in the garden of the grand duke in Florence. The correspondent Bodenhausen then reported, on January 28, that he too had been promised this “curam podagrae”, and that he intended to investigate the Chinese plant in question. Several months later (on July 6), however, Leibniz had to remind the correspondent about the matter, requesting details once again of the “plantae chinensis Antipodagricae”. 215 Cf. L. L. Barnes, Needles, herbs, gods, and ghosts: China, healing, and the west to 1848, Cambridge (MA), London, 2005, in particular chap. 3, pp. 72–125 (Model state, medical men, and “mechanick principles”: 1660–1736), and specifically pp. 73–75 (The reporters). Regarding Cleyer, cf. p. 75 and pp. 92–99 (Perfect knowledge of the pulse).

Introduction: The Core Themes

249

It was also Bodenhausen who, on September 16, 1690, drew Leibniz’s attention to a panacea against chronic diseases, which was being claimed by Samuel Ledel from Görlitz, and which had been treated by him in the Miscellanea Curiosa in 1688. It was the subject of a note drafted by Leibniz, in connection with his reply to Bodenhausen of November 5, 1690. He had  – he told the correspondent  – in the meantime tried to obtain further details about this alleged universal remedy, specifically by asking Pratisius to write to a well-known physician in Görlitz on the matter. The fact that Leibniz, and his correspondents, were always interested in remedies and therapies can be seen from a passage in a letter of December 7, 1683, received from Tschirnhaus, in which a method for preventing and treating women’s breast diseases was highlighted. Breastfeeding women were often found to have painful breast diseases and breast ulcers which, if not treated, might often lead to malignant diseases, like breast cancer. A common resort for such patients was a painful operation at the hands of a barber-surgeon,216 which the correspondent now sought to replace with milder treatment methods. Attached to a letter of December 16, 1695, which Leibniz sent to Ramazzini with collegial greetings to friends and acquaintances in Italy, was a copy of his tract about “Ipecacuanha” – a recently discovered medicinal plant from South America  – entitled Relatio  … de novo antidysenterico Americano (1696). The healing effect of “Ipecacuanha” had previously been described by the Dutch physician and naturalist Willem Piso, in his opus entitled Historia naturali Brasiliae … In qua non tantum plantae et animalia, sed et indigenarum morbi, ingenia et mores describuntur et iconibus supra quingentas illustrantur (1648), but it had subsequently fallen into oblivion. Leibniz had learned about this plant for the first time from a letter of April 8, 1695, which he had received from Christophe Brosseau in Paris. Leibniz’s Relatio was then conceived as a communication to the Academia Leopoldina. In addition, he arranged for the Relatio to be published as an appendix to Martin Lister’s Sex exercitationes medicinales de quibusdam morbis chronicis (1696).217 Leibniz also reported to Bodenhausen, in a letter of December 23, 1695, about the new “Antidysentericum Americanum”.

216 Cf. M. Fishbein, “The barber surgeons and the liberation of surgery”, Journal of the International College of Surgeons, vol. 27, (1957), pp. 766–779; J. E. McCallum, Military medicine: From ancient times to the 21st century, Santa Barbara, Denver, Oxford, 2008; regarding barber surgeons cf. pp. 36f. 217 Cf. A. M. Roos, Web of nature: Martin Lister (1639–1712), the first arachnologist, (Series: Medieval and early modern philosophy and science, vol. 16), Leiden, 2011, in particular part 4, chap. XIII, pp. 335–374 (Publication and prestige: The sex exercitationes medicinales and the Royal College of Physicians).

250

Introduction: The Core Themes

Besides being a remedy against dysentery, Leibniz envisioned further possible therapeutic applications against other diseases. In addition to his letter to Bodenhausen, the issue of the new antidysentericum from America was likewise broached in Leibniz’s correspondence with Johann Bernoulli in the first half of the year 1696. Thus, in the PS to a letter of February 7, Leibniz elaborated the circumstances of the rediscovery of the new “emetica sine violentia”, and he requested information about similar emetics recently introduced in the Netherlands, like the “Cortex Peruviana” (also “Cortex Peruvianus”) and “Herba Paraguay”, and he expressed his desire that the intelligence be imparted to Johann’s brother, the pharmacist Hieronymus Bernoulli. Thereupon Bernoulli made enquiries about the plant, and he conferred with, among others, the medical professor in Groningen, Theodorus van Essen, whereby the two medicinal plants from South America  – the “Herba Paraguay” and the “Cortex Peruvianus” – were also considered and referred to in the PS to Bernoulli’s letter of March 3 to Leibniz. A little later, on March 13, Bernoulli then forwarded to Leibniz the report of a renowned apothecary from Amsterdam about “Ipecacuanha” and further medicinal plants. Leibniz reacted to this, on the March 18, by forwarding a copy of his Relatio, as well as a set of notes about medicinal cortices or barks. Furthermore, he enquired about possible sources of supply, and about the usage of “Ipecacuanha” in the Netherlands. Cinchona, or Peruvian bark, was obtainable in Hanover even though not of best quality, he told the correspondent. And he even placed an immediate order for a supply of the Peruvian bark, and added a query about the “Herba Paraguay”. This order Bernoulli was able to fulfill a month later, on April 17. As for “Ipecacuanha”, Leibniz was informed about suppliers and purchase price in Amsterdam. As regards this medicinal plant, as well as the “Herba Paraguay”, Bournoulli could announce that he had obtained supplies for Leibniz, but he still wanted to obtain additional information elsewhere about the application and use. Information from van Essen concerning dosage, and the shortfall, of the “Herba Paraguay” as an effective nauseant, or emetic, was also communicated to Leibniz. Finally, on May 25, 1696, Leibniz dealt with this ineffectiveness of the “Herba Paraguay”, and he addressed in this context the broader issue of adulteration of medication or medicinal remedies. Leibniz’s involvement in a discussion of pharmacology, and pharmacological advances, was surely derived only in part from an academic interest in advances in medical science. His commitment was likewise influenced by his own health and therapy requirements and, in fact, in the years 1693 to 1695 he was often indisposed. Thus, for example, he wrote on May 12, 1693 to Otto

Introduction: The Core Themes

251

Grote, the Chamber president in Hanover, about a feeling he had of health deterioration. Thus, a subjectively-felt pressure of work, or overwork, in connection with the history project in particular may have contributed to his illness pattern – with possible psychovegetative disorders viz. physical or vegetative dysfunctions on the basis of a neurotic or high-strung development – at this juncture.218 On October 24, 1694, we find him enquiring in the PS to a letter to Johannes Teyler about “une Herbe des Indes qui fait vomir sans effort”, about which Robert Boyle had once informed him, and which he thought might be similar to one then obtainable in Amsterdam. Likewise, in a no longer extant letter to Bodenhausen, Leibniz had complained about health problems. And so, in his reply of November 17, 1694, the correspondent commented and attributed Leibniz’s indisposition to a lifetime of overwork. He recommended that Leibniz rest himself, observe a diet, and get more exercise. Likewise, in Bodenhausen’s letter of May 26, 1695, we find the correspondent assuming that Leibniz was suffering from a biliousness that was revealed though external inflammation (phlogosis), painful urination, and in the effects of medical drinks. In fact, he saw part of Leibniz’s problem in the medication he had taken, like lemon juice, and he recommended instead mild acids in fruit drinks (“acida … welche nicht zu starck agiren”). Bodenhausen recalled a well-known case he was familiar with, in which drops of vitriol had been successfully employed against an infectious dysentery epidemic in Italy, and he recommended among other things the intake of this remedy about which he informed Leibniz. Considering Leibniz’s symptoms, Bodenhausen recommended, furthermore, that he take a vitriolic emetic under the supervision of a physician, and he described the mode of operation of the emetic, but he advised caution at the same time. Above all, Leibniz should not delay the treatment and he ought to avoid every form of exertion, he was told. Leibniz’s reaction to Bodenhausen’s proposals is to be found in his letter of June 24, 1695. As far as the acidic and vitriolic remedies were concerned, he was not averse to trying them out. As regards the application of an emetic or vomitive, as suggested by Bodenhausen, he hesitated and wanted to think the matter over first. All in all, Leibniz enjoyed good health for most of his life but, in his last twenty years and at the end of his life in particular, he suffered from lower limb, or foot

218 Cf. E. Görlich, Leibniz als Mensch und Kranker, Doctoral dissertation, Hanover: Medical faculty (Medizinische Hochschule), 1987; regarding Leibniz’s psychovegetative complex of complaints around the year 1695, see pp. 110ff.

252

Introduction: The Core Themes

ulceration (‘ulcus cruris’), as well as articular or joint trouble like gout,219 the consequences of which probably ultimately led to his death in 1716.220 Leibniz also regularly received reports about the health problems and conditions of his correspondents, or indeed queries regarding medication and medicinal products as, for example, on April 16, 1696, from Johann Sebastian Haes regarding “la teinture aperitive du Dr [Gottfried] Moebius et spiritum Martis volatile striatum, du Dr [Friedrich] Hoffman [senior]”. Johann Daniel Crafft complained again and again about his gout pains, and he sought the right medication to relieve his suffering as, for example, on September 20, 1694, when he referred to two letters of Christoph Fahrner, written to Jonas Zipffell and published in Zipffell’s work Podagrischer Triumph (1659). Just like gout, which was known as the ‘Patrician Malady’,221 the topic of phlebotomy, or bloodletting, arose again and again in Leibniz’s correspondence as, for example, in Bodenhausen’s letter of July 28, 1696. In his letter of May 1698 to Franck von Franckenau, Leibniz told that he had received a work hostile to bloodletting, written by Dominico La Scala and entitled Phlebotomia Damnata (1696). Leibniz himself, however, favored the moderate application of bloodletting, the value of which was evident from application with animals, he told the correspondent. In his letter to Block, on July 30, 1698, Leibniz justified his standpoint with the following argument: bloodletting might work in the same way that arsenic could act as an antipyretic. Thus, nature reacts to the artificially-produced health threat and reverses the path previously taken. In his letters to Franck von Franckenau and Block, from the summer of 1698, Leibniz referred to the positive effects of the method in treating animals. Block, in his letter of October 30, agreed with Leibniz, and he wrote that with fever, blood heat, unconsciousness or disturbance of consciousness, or with blood congestion in the lungs or heart, bloodletting could indeed be applied. Bloodletting was, however, the last resort of the Galenists and, in France, Spain and Italy, there was an enormous abuse of the method in evidence. Finally, the fact that Leibniz was fully aware of this abuse is evident from his letter to Ramazzini of April 22, 1699, in which he once again referred to La Scala’s opus, and requested the correspondent’s judgement on the issue. 219 Cf. E. Görlich (note 218 above), pp. 118–120 (Das Ulcus cruris-Leiden), pp. 162–166 (Die Therapie der Ulcera cruris), pp. 120–126 (Die Gelenkbeschwerden) and pp. 166–177 (Die Therapie der Gelenkbeschwerden). 220 Cf. also pp. 199–221 (Leibnizens letzte Krankheit-Tod und Begräbnis). 221 Cf. for example, W. S. C. Copeman, A short history of the gout and the rheumatic diseases, Berkeley, Los Angeles, 1964; D. P. Mertz, Geschichte der Gicht: Kultur- und medizinhistorische Betrachtungen, Stuttgart, New York, 1990; R. Porter, G. S. Rousseau, Gout: The patrician malady, New Haven, London, 1998.

Introduction: The Core Themes

253

By 1699, accounts of autopsies had long been a source of information for Leibniz in the field of anatomy. The post-mortem examination of corpses was important, however, not only for obtaining new anatomical knowledge, but it also served for the development of examination and treatment methods for physicians, and even for obtaining medicaments and medicinal or pharmaceutical products. In this context then, Leibniz came into contact with medical cannibalism that was then in widespread use.222 Thus, on October 30, 1699, he requested information from Papin about the so-called “king’s drops”, which he had learned about from a traveler, namely an unnamed English musician, who had been to Muscovy and had shortly before come from Kassel. He related that the Electress Sophie, at the court in Hanover, had also heard wonderful, or miracle-like, stories about this medicament. The basis of these drops was a recipe for the liquefaction of material taken from the inside of human skulls, often from executed prisoners. The distillate has found a place in the history of medicine under the name ‘Goddard’s drops’ – after the discoverer Jonathan Goddard – or otherwise as “king’s drops” after the Stuart king Charles II, who carried out such distillations in his private laboratory. Whether or not Leibniz knew what kind of medicament was involved is not clear. At all events, Papin’s response, on December 3, 1699, was short and decidedly skeptical about what he termed “ces sortes de remedes”. Also the remedy “mumia” – a substance obtained from pulverized Egyptian mummies  – is referred to in Leibniz’s correspondence. Wagner related, on March 15, 1701, that he had, as a result of clumsiness, suffered a breast injury and then obtained, as a remedy from the apothecary, the following substances: crab’s eyes, dragon’s blood, prepared mumia, prepared native cinnabar and diaphoretic antimony. A note which the surgeon Jacques Bouquet handed to Leibniz, on August 5, 1701, provides an example of the use of parts of corpses for therapeutic purposes. A woman from the French émigré community, then living in the town of Hameln, had in the past suffered from a wart, or a swelling, on her hand over a period of time. After a variety of plasters had proved useless, it was recommended that she rub the swelling, or growth, with the fingers or hand of a corpse, where the person had died following a lengthy illness. Some years earlier, while resident in Hamburg, a neighbor of a general, whom she had served there as a governess, died. This first opportunity for her to test the proposed treatment method proved unsuccessful. Later, however, the general himself 222 Cf. R. Sugg, Mummies, cannibals and vampires: The history of corpse medicine from the Renaissance to the Victorians, London, New York, 2011, and in particular chap. 2, chap. 8 and the conclusion.

254

Introduction: The Core Themes

died, and she tried the procedure again of rubbing the swelling with the hand of the corpse and was on this occasion – according to the note Leibniz received – permanently cured in a short time. Both in the use of medicaments derived from human remains (such as the “king’s drops”), and in the application of corresponding therapies (like in Bouquet’s communication), the death struggle and the mortal agony of the deceased was an essential aspect of the presumed medicinal benefit. The agonal state of tortured and executed prisoners, of soldiers in their death throes on the battlefield, or of long-suffering patients could lead to the production of substances having curative, or immunizing, effects, and which might serve as ingredients for medication. The prevailing positive attitudes towards phlebotomy, or bloodletting, were perhaps akin to those relating to medical cannibalism. Thus, bloodletting might contribute to improved defense mechanisms of the body under attack. Leibniz received regular reports from Wagner, who also worked as a physician, concerning both his own ailments, as well as illnesses he was confronted with, and the therapies which were applied. In the spring and summer of 1701, Wagner reported about a female patient of his, from the town of Halberstadt, who had a swelling or tumor on the cheek, and which he illustrated in a drawing. He was able to provide relief at first and the swelling declined. However, an accident, or mishap, had led to an undermining of the recovery process, according to the correspondent. In 1699 and 1700, several university professors at Helmstedt died in quick succession, whereas others suffered from chronic illnesses. Thus, Wagner reported, on April 21, 1699, to Leibniz about the recurring hemorrhages experienced by Johann Andreas Schmidt, a hemophiliac who had to observe a strict diet. A little later, Wagner assisted the medical professors Heinrich Meibom and Friedrich Schrader in the treatment of a fourteen year old, who complained about hoarseness, coughing, intense headache as well as the accompanying fear of asphyxia. On May 5, 1699, Wagner elaborated for Leibniz his explanation of the course of the disease, and he explained that an opening of the temporal artery had brought little relief. Then, on May 16, Leibniz recalled, in this context, a new treatment method for headache involving the opening of the temporal artery, and about which he had been previously informed by Johann Gebhard Rabener. Then, on March 23, 1700, Wagner reported that Meibom himself had been infected with a pleurisy, through contact with the vice rector of the university, Christoph Tobias Wideburg, whom he had treated. Bloodletting proved to be of no avail on this occasion, and three days later, on March 26, Wagner reported the passing of Meibom on that day, and he elaborated in detail the

Introduction: The Core Themes

255

course of the illness that had led to the professor’s demise. Just two weeks later, Ilse Stisser (née Petersen), the wife of Johann Andreas Stisser, died in childbirth (on April 8) leaving her distressed husband with six children. Stisser himself then suffered a collapse, resulting from grief and exhaustion, as Wagner reported to Leibniz on April 10. Furthermore, Wagner reported, on this occasion, that another colleague, Caspar Cörber, the professor of eloquence, had fever and that his sallow complexion was frightening. Cörber survived just a week with this condition. That the news of the death of Stisser himself, on April 21, devastated the correspondent is hardly surprising. Wagner too had been suffering from headache and lassitude, a condition which was then aggravated by hot flushes and states of anxiety. The narrative of his short but intense illness, accompanied also by a fear of dying, was related by Wagner to Leibniz in great detail, as soon as he began to feel better a few days later, namely on April 27. Recovery, he reported, had come following consumption of large quantities of medicinal beer made from Scorzonera, or “Schwarzwurzeln”. The study of diseases was a particular interest of Leibniz’s internationally most renowned correspondent in the field of medicine, namely Bernardino Ramazzini. His teaching assignment for theoretical medicine included the area of occupational or industrial medicine.223 In the course of his investigation of the water springs of Modena, Ramazzini also investigated the working conditions of laborers in the well pits and shafts, and about which he reported to Leibniz on May 4, 1691. He did not hesitate to descend himself into the shafts in order not to have to rely on accounts of others. The knowledge gained in the course of these investigations is to be found in the surely most important, and most renowned, work of Ramazzini that, however, was only to appear almost a decade later, namely his tract on the diseases of workers and tradesmen with the title De morbis artificum diatriba (1700).224 In replying to Leibniz’s letter of 223 Cf. for example, J. S. Felton, “The heritage of Bernardino Ramazzini”, Occupational Medicine, vol. 47(3), (1997), pp. 167–79; R. B. Añón, “Medical biographies and their historical significance: The figure and the work of Bernardino Ramazzini (1633–1714)”, Medicina y Seguridad del Trabajo, (Special issue / Suplemento extraordinario, no. 2), (2014), pp. 34–41; G. Franco, Meglio prevenire che curare – Il pensiero di Bernardino Ramazzini, medico sociale e scienziato visionario, 2015 (eBook). 224 Cf. B. Ramazzini, De morbis artificum diatriba, Modena, 1700; B. Ramazzini, [E.] W. C. Wright (ed., trans.), De morbis artificum diatriba: Diseases of workers  … The Latin text of 1713, revised with translation and notes, (History of Medicine series), Chicago, 1940; B. Ramazzini, [E.] W. C. Wright (ed., trans.), G. Rosen (Introduction), Diseases of workers. Translated from the Latin text De morbis artificium of 1713, (New York Academy of Medicine, History of Medicine series, no. 23), New York, London, [c. 1964]; P. Di Pietro, “Le fonti bibliografiche nella « de morbis artificum diatriba » di Bernardino Ramazzini”, History and Philosophy of the Life Sciences, vol. 3(1), (1981), pp. 95–114; A. Gils, Bernardino Ramazzini

256

Introduction: The Core Themes

April 22, 1699, Ramazzini announced, on February 24, 1700, his forthcoming tract about the diseases of workers with the words “Tractatum meum de morbis Artificum inter caeteras meas nugas abjeceram”. Leibniz for his part, in his letter of March 18 to Ramazzini, referred to works on the ailments of miners and pitmen by Georg Agricola, who himself had been a representative of the medical profession (“qui ipse erat Medicus reique metallariae scientissimus”), and above all by the physician Samuel Stockhausen, from Goslar in the Harz mining district, who had published a work entitled Libellus de lithargyrii fumo noxio morbifico (1656). The latter had described the lung diseases that occurred among miners, namely the pulmonary disease “Bergsucht”, or occupational lung cancer,225 – later to be called “Schneeberg disease” – and the pulmonary phthisis, or consumption, known as “Hüttenkatze”. Stisser’s open letter, of February–March 1700, addressed to Leibniz  – De variis erroribus, chemiae ignorantia in medicina commissis dissertatio epistolaris (1700) – was a passionate plea for a pronounced inclusion of chemistry in medicine, and in the study of medicine. To those who professed to be enemies to chemistry – whom he characterized as “misochemists” – he pointed out the omnipresence of the subject. Foodstuffs, like bread, beer or wine, were prepared with the help of chemical processes, just as with the pretended non-chemical medicaments. His argumentation was founded, on the one hand, on Hippocrates and numerous other deceased and living authorities and, on the other hand, on case studies in which wrongly prepared medication had brought about undesired reactions. Leibniz – in his last letter to Stisser (probably) of April 25, 1700 – complained about the enormous multiplicity of pharmaceutical products, but he was otherwise in agreement with the correspondent. To abstain from using chemical medicaments, would be tantamount to forgoing great advantages of the natural world. More effective medication against illnesses, that affected the body fluids, could, in Leibniz’s opinion, be found, either simply by accident or as a result of advances in chemistry.

(1633–1714): Leben und Werk, unter besonderer Berücksichtigung der Schrift “Über die Krankheiten der Künstler und Handwerker” (De morbis artificum diatriba), Doctoral dissertation, Göttingen (Universität Göttingen), 1994. 225 Cf. P. D. Blanc, “Historical perspective of occupational and environmental lung disease”, chap. 1 (pp. 1–26), in: Y.-C. T. Huang, A. J. Ghio, L. A. Maier (eds.), A clinical guide to occupational and environmental lung diseases, New York, Heidelberg, Dordrecht, London, 2012, in particular pp. 6–8 (1500–1750).

Introduction: The Core Themes

257

11.3 Epidemiology, Demography Pestilence and epidemics featured strongly in Leibniz’s correspondence in the early 1680s. At the end of 1679 the plague afflicted Vienna and spread in the following years via Prague and Leipzig, without however reaching the territories of the principalities of Brundswick and Lüneburg. On May 24, 1680, the physician Crafft wrote that Leibniz should not put off a planned journey to Dresden, and that the rumors circulating about the plague there were false, and possibly even fabricated by surgeons to advance their own financial interests. Leibniz lingered in Saxony in the first half of July 1680. That the pestilence began spreading there at this time is evident, not only from the relief of Christof Pratisius, expressed in his letter of July 20, following Leibniz’s return, but also from Crafft’s communication of August 6 telling of the spread of the contagion in recent weeks. The plague had, we learn from Crafft’s letter of early September, spread almost exclusively among the common people, and there had been scarcely any cases recorded among people who had taken precautions, and been able to care for themselves and their kin. The outbreak of the plague restricted considerably the movement of travelers within Leibniz’s ken at this juncture. Crafft was unable to travel to Berlin from Dresden, as he informed Leibniz on April 4, 1681. Likewise, Christoph Pfautz and Otto Mencke, who were preparing the launch of their journal Acta Eruditorum with a journey to the Netherlands, and to England, beginning in at the end of May or early June 1680, had, on their return journey to Leipzig, to linger for some months in the town of Oldenburg, from where Pfautz informed Leibniz on January 18, 1681. Leibniz developed ideas not only for health care policy decisions to combat the spread of the plague – for example his “Vorschläge gegen die Pest” (1681?), addressed to duke Ernst August, and involving the closure of borders – but he also pursued medical deliberations on the matter. In a letter, from the end of September 1680, to Crafft, there is a reference to a “Medicina infusoria” which he thought might be a most efficacious remedy against the pestilence, since he was convinced that the malady resided especially in the body’s humors, and above all in the blood. Leibniz concluded his considerations regarding the plague by calling on Crafft to use his good rapport to the Saxon vice chancellor, Johann David von Oppel, to thoroughly investigate the cause of the pestilence and, in particular, the changes in the blood of those afflicted by the malady. Other less formidable suggestions included that of the resident diplomat of the elector of Mainz in Vienna, Johann Christoph Gedenus, who proposed onions as an amulet against the plague, and which was communicated at the end of a letter to Crafft of August 25, 1680, and then forwarded to Leibniz in early September.

258

Introduction: The Core Themes

In the field of medicine Bernardino Ramazzini emerged as Leibniz’s most important correspondent during and following his Italian journey. In the course of their conversations in Modena, between late December 1689 and early February 1690, Leibniz encouraged Ramazzini to intensify his observations, not only in the medical field but also in areas of science and technology, and to work towards their publication. These efforts soon began to bear fruit when, already in 1690, Ramazzini published his first epidemiological work. At short intervals there then appeared several further works which were to make Ramazzini known far beyond the borders and shores of Italy, especially in the fields of epidemiology and occupational, or industrial, medicine. Leibniz actively supported the dissemination of Ramazzini’s writings and significantly contributed to his success, and fame, north of the Alps. Through the use of the thermometer, barometer and hygrometer, it became possible, at the end of the seventeenth century, to establish a relationship between illnesses, or diseases, and the prevailing weather conditions. In addition, statistical investigations were gaining a foothold in medicine. Accordingly, mortality, morbidity and population development could be quantitatively recorded for the first time. Demography, or the statistical study of population, contributed in turn to progress in medicine. Increasingly, prevention became a principal task for the physician. The causes of diseases were sought and found in almost all areas that affected the lives of people as, for example, in weather and occupational conditions, and in the living environment. Parallel to general preventative measures, physicians began to pay particular attention to the causes, and circumstances, of the occurrence of epidemics. This then was the general background to Ramazzini’s achievements in medicine. In the history of epidemiology in the seventeenth century, Ramazzini stands out following in the footsteps of the English physician Thomas Sydenham (1624–1689). He emerged, like Sydenham, as an epidemiologist of the Hippocratic ilk. Sydenham, who coined the concept and term “Constitutio” – viz. the epidemic constitution of a year or season – was the first to strive for the annual publication of such “constitutiones epidemicae”.226 Ramazzini continued these efforts, and he published “Constitutiones” for the years 1690 to 1694, which appeared in three installments. The epidemic constitutions De constitutione anni 1690 ac de rurali epidemia, quae Mutinensi agri et vicinarum regionum colonos graviter afflixit, dissertatio (1690) and De constitutione anni 1691 (1692)  – which were dedicated to Antonio Magliabecchi and Leibniz, 226 Regarding Sydenham’s study of London epidemics and his textbook Observationes Medicae (1676), cf. K. Dewhurst, Dr. Thomas Sydenham (1624–1689): His life and original writings, London, 1966, and Oakland, CA, 2021, in particular, pp. 30–59 (The Physician) and pp. 71–78 (Sydenham’s Original Writings).

Introduction: The Core Themes

259

respectively  – appeared separately, whereas those for the years 1692 to 1694 were published together, as De constitutionibus annorum M.DC.XCII., XCIII., et XCIV., in Mutinensi civitate, et illius ditione, dissertatio (1695). All five annual constitutions finally appeared in a single collection, almost twenty years, later as Constitutionum epidemicarum Mutinensium annorum quinque (1714). In these works, Ramazzini described all epidemic diseases that had occurred in the region around Modena in the respective year. They contained exact information, and data, about symptoms and the progression of diseases, about applied therapeutics, and about assessments of their effectiveness. Ramazzini also analyzed the weather, in the respective years, with regard to possible weather and climatic influences on the occurrence of diseases. He even took account of the welfare of useful, or crop, plants like wheat or vine, as well as of the health of farm animals and livestock. He observed which sections of the population, and in what manner, were affected by a particular epidemic, and he tried to find an appropriate explanation. In the Emilia-Romagna region of northern Italy, there occurred, in the years 1690 to 1694, in particular malaria and typhoid epidemics. Thus, the extreme precipitation in the year 1690, that caused flooding along the Po tributaries – as Ramazzini reported to Leibniz on April 15, 1690 – led to a malaria epidemic, which primarily affected the rural population. In his epidemic constitution for the year in question, Ramazzini described the course of this epidemic in detail in relation to the individual seasons. He also described attending ills, like cereal or wheat rust, and animal diseases. The following year (1691) was in contrast dry and warm. On that occasion, the malaria epidemic primarily affected the poorer urban population, whereas the rural population largely escaped the contagion. In the years 1692 to 1694, notwithstanding very different weather and climatic circumstances, typhoid afflictions dominated Ramazzini’s attention. He held the view that the transmission of these infectious diseases occurred through the air, and that the south wind had brought the pestilence from Africa to Italy. An obvious source of danger, arising from the deployment of troops in war time in the region, was, on the other hand, seen as innocuous by Ramazzini. Like many important physicians of the time, Ramazzini belonged to the iatrochemists (or chemical physicians), so that the diagnostic and therapeutic teachings of the chemiatric school are reflected in his works. Thus, the aetiological theories, and the therapeutic strategies he proposed, show his acquaintance with the iatrochemistry of the seventeenth, and early eighteenth, centuries.227 Since his “Constitutiones” were very successful, and seminal, in the area of 227 Cf. B. Cavarra, “Filosofia e scienze nell’opera di Bernardino Ramazzini, Medicina nei secoli arte e scienza”, Giornale di Storia della Medicina, Nuova Serie ( Journal of History of Medicine, New Series), vol. 23(2), (2011), pp. 411–423.

260

Introduction: The Core Themes

epidemiology, Leibniz was able to persuade Johann Georg Volckamer  – the president of the Academia Leopoldina – to reprint Ramazzini’s report for the year 1690 as an appendix to the Miscellanea Curiosa for the year 1691. The second installment of the “Constitutiones” likewise appeared in the Miscellanea Curiosa, and these publications helped make Ramazzini well-known north of the Alps. Again on Leibniz’s recommendation, the Leopoldina accepted Ramazzini as its 201st member in November 1693. Leibniz considered Ramazzini’s epidemiological works to be particularly important, and he repeatedly recommended them to familiar and well-established physicians, suggesting that they write similar works for other regions and time intervals. A case in point here was Leibniz’s letter to Paul Pellisson-Fontanier of December 1, 1692. In Leibniz’s correspondence in the early 1690s, several instances of Ramazzini’s epidemiological considerations are to be found. In the accompanying letter, of May 4, 1691, to the consignment of his De constitutione anni 1690 ac de rurali epidemia, Ramazzini described the plight of the “Modenese” region at that time. The economic decline, as a consequence of the climatic and epidemic situation in the previous two years, had been aggravated by the threat of war and a possible French intervention. Thus, these three afflictions were referred to in this letter, or to quote the correspondent: “sic jam nobis triplex flagellum imminet”. The difficulties and shortages, that had arisen in the provision supply of the Italian and allied Bavarian troops deployed near Modena, were sketched by Ramazzini in a later letter of March 30, 1692. He also suspected a connection between the shortages and epidemics of those years, on the one hand, and phenomena like malformation and mortality of infants, on the other hand. Here, anatomical, physiological, pathological and demographic aspects were combined in Ramazzini’s considerations. Specifically, he related the details of a case where a German woman at a camp at Spilamberto, located near Sassuolo (south of Modena), had given birth to stillborn deformed female twins, who were conjoined at their breasts and abdomens, but were otherwise of normal proportions. The remains of the stillborn twins were presented to the ducal authorities in Modena where a post-mortem examination was carried out. Ramazzini explained that the pathologist, who dissected the remains, discovered that the twins had but a single, or shared, heart, a single stomach, and a single liver. Otherwise each individual had its own intestines and internal organs, including a bladder, kidneys, spleen, etc. Finally, the remains were handed over to Ramazzini himself for anointment and conservation among other cimelia. And, he added that he had learned of the ominous occurrence of a similar monstrous birth in Bologna and, finally, he posed a rhetorical question as to what the sum of these occurrences did in fact portend. Ramazzini was aware of the important role that Leibniz had to play in his scientific life. His esteem for Leibniz was reflected not only in the dedication of

Introduction: The Core Themes

261

his work De constitutione anni 1691 apud Mutinenses, but also in his accompanying letter of March 30, 1692. That the reprint of Ramazzini’s De constitutione anni 1690 in the Miscellanea curiosa resulted from a suggestion of Leibniz is evident from the fact that, when he revived his correspondence with Johann Georg Volckamer, on July 26, 1691, this was his principal concern. Already in the years 1681 and 1682, Leibniz had carried on a correspondence with Volckamer in which ideas were exchanged about corresponding terrestrial magnetic observations. And, during his sojourn in Nuremberg (from December 31, 1687 to January 6, 1688) at the outset of his Italian journey, he and the correspondent had met, as is evident from the opening words of his letter to Volckamer from the summer of 1691. In this letter, Leibniz presented his principal request to the president of the Academia Naturae Curiosorum, or Academia Leopoldina. First, he told of his meeting with the learned Ramazzini in Modena, and of his exhortations that the Italian commit his results to print. Then he explained how he had recently received Ramazzini’s De constitutione anni 1690, a work which he prized so much. And, above all, as he explained, Ramazzini had committed to continuing his medical ephemerides in the future. Leibniz hoped that the Academia Leopoldina might follow the Italian example and he emphatically pointed out the importance, and necessity, of collecting medical statistics in Germany also. The Leopoldina should use its influence to promote such undertakings and to collect the results of such inquiries from all over the empire. On November 2, 1691, Leibniz thanked Volckamer for reprinting Ramazzini’s De constitutione anni 1690, expressing the hope that, through Volckamer’s influence, similar undertakings might be successful in Germany. An exemplary case that Leibniz was able to announce involved the personal physician of the elector Ernst August in Hanover, Christoph Pratisius, who had promised to publish medical observations soon. A further topic from the field of epidemiology, which occupied both Leibniz and Volckamer, was the medical treatment of dysentery. On January 15, 1691, Henri Justel had reported from London about the mysterious plant root called Ipecacuanha, mentioned above, that had been used in France as a remedy in the treatment of dysentery. Leibniz, in turn, informed Volckamer about this on August 25, 1691. Since the root in question had found use as a medicament with the French army, Leibniz hoped that this rhubarb-like plant might soon be employed by the allied forces also. Volckamer was pleased about the intelligence regarding the new remedy and recommended, for his part, the treatment of dysentery with vegetable, or herbal, remedies like sorrel, or common or garden sorrel, the recipe for which he was happy to communicate to Leibniz. Throughout the 1690s, Leibniz continued to regularly receive communications from correspondents regarding the plague and other epidemics as, for example, on March 29, 1695, from Augustinus Vagetius in Wittenberg,

262

Introduction: The Core Themes

who referred to the crawling expansion of the plague and epidemic disease throughout Germany. In the field of epidemiology, however, Bernardino Ramazzini remained his most important correspondent, although the direct correspondence between the two was very much in abeyance in the mid 1690s. In the years that followed the publication of Ramazzini’s Constitutiones epidemicae for the years 1690 to 1694, Leibniz repeatedly recommended to physicians he knew that they carry out, and publish, similar medical compilations for other regions. At the beginning of 1694, on January 6, he sent such a request to the renowned physician Georg Franck von Franckenau in Wittenberg, lauding Ramazzini’s achievements at the outset of his appeal. As things transpired, Franck von Franckenau was certainly prepared to support this call, and to pass it on to medical colleagues in Wittenberg, Dresden, Torgau, Leipzig, Zerbst, Halle, Magdeburg and Berlin, as is evident from his reply almost half a year later, on June 22, 1694. For his own part, however, Franck von Franckenau failed to provide a compilation of the type envisioned, not least perhaps for the reason that he would soon become personal physician to the Danish king, Christian V, in Copenhagen. The project for the annual publication of medical-meteorological observations pursued by Leibniz and Hoffmann, under the aegis of the Berlin Society of Sciences, referred to above, was of course inspired above all by the ephemerides which Ramazzini had published for the years from 1690 to 1694 and in which he described the epidemic outbreaks that had occurred around Modena in those years. The publications for the years 1695 and 1696 failed to appear which motivated Leibniz to enquire about the continuation of the series, in his letter of April 22, 1699. Replying, on February 24, 1700, Ramazzini justified the interruption on the grounds that the data collection had proved cumbersome for physicians, not least due to the lack of remuneration, but also because there had been no new notable epidemic occurrences in the meantime. In a previous letter, on June 17, 1699, Ramazzini had announced the republication of his collected ephemerides in a single volume which of course only appeared in 1714. Leibniz also advocated data collection even in times when there were no special occurrences. At least one would then know that no change had taken place, he wrote in his letter to Ramazzini of March 18, 1700. 11.4 The Medical Profession, Mathematization, Rationalization The medical profession, including studies and qualification, was of special interest to Leibniz. On two occasions in the early 1680s, the actions of academically unqualified physicians were graphically described in Leibniz’s correspondence. On the first such occasion, an individual named Scradetzky had apparently found a cure for gout, and seemed to have worked miracles

Introduction: The Core Themes

263

in Berlin, even curing the elector himself, according to the account of May 7, 1682, that Leibniz received from Crafft. As a reward, the individual in question was granted the right to import wines tariff-free, as Elers reported to Leibniz on August 22, 1682. A similar case involved the vicissitudes experienced by another charlatan, a Roman whose departure from several courts Scheffer characterized (on August 18, 1682) as malodorous. Statements of Leibniz regarding an amulet – which had been presented to the elector of Brandenburg and was referred to by Elers, on August 22, 1682 – against pain caused by stone (kidney, ureter and urinary stone), or indeed regarding the question posed by Schrader, on December 8, 1681, concerning the age-old issue of the influence of the moon on the body humors, have not been found. The blacksmith’s laborer, who claimed to be able to diagnose all diseases by urine observation, as reported by Scheffer, on May 23, 1682, was at all events not taken seriously by Leibniz. Two years before embarking on his grand tour of Austria and Italy, Leibniz received a damming report, sent by Pratisius from Venice on October 26, 1685, about the situation there with regard to medical practice and practitioners. Similar sentiments were expressed regarding the pharmaceutical system, and about the methods of treatment there. Leibniz’s Italian journey then provided him with a welcome opportunity for oral discourse on medical subjects with Italian physicians and scientists. Whereas, in Leibniz’s exchange of ideas with Ramazzini while in Modena, matters of engineering and technology were predominant, he was particularly impressed in the case of other ‘medici’ by their mathematical abilities. Thus he wrote to Huygens, on July 25, 1690, about his meetings with Domenico Guglielmini and Francesco Spoleti, who were referred to as “tous deux bons Mathematiciens” and “deux Medecins, bien versés dans les Mathematiques”. In this context, Leibniz advocated treating medicine as an exact science and he pleaded for its mathematization. Thus, in a letter from Venice sent to Francesco Bianchini, on March 18, 1690, he referred to his high expectations for Spoleti, and he recalled having exhorted him “ut mathematicum in re medica agat, quoad ejus fieri potest”. Leibniz’s vision of medicine rooted in calculus – essentially an appropriate and precise form of expression in the process of reasoning or in the application of rational thought – was even more pronounced in another letter, sent to Bodenhausen from Venice, on February 20, 1690, which provides the leading quotation for this section on medicine. Leibniz’s deliberations on the medical profession, on medical progress, on medicine as an empirical science, and on the application of mathematics in medicine were topics that continued to be discussed in his correspondence in the 1690s. Thus, he wrote to Huygens on June 22, 1694, that medicine had hitherto been a purely empirical science. Empiricism in itself was no bad thing, he

264

Introduction: The Core Themes

thought, but, since medicine had become a profession, its practitioners were often more concerned with saving appearances. Leibniz even envisaged a religious order of friars, like the Capuchins, embracing medicine as a charitable endeavor. Huygens, in his letter of August 24, signaled his assent to Leibniz’s perceptions, but did not enter further into a discussion of them. The mathematician Johann Bernoulli, who had studied medicine and was author of two works entitled Dissertatio chymico-physica de effervescentia et fermanttatione (1690) and Dissertatio inauguralis physico-anatomica de motu musculorum (1694), was admonished by Leibniz on July 4, 1694 – particularly with reference to the latter dissertation on the movement of muscles  – to continue and maintain his commitment to medicine. More than a year later, Leibniz referred to this proposal again in a letter to Johann’s brother, Jacob Bernoulli, on December 12, 1695. In his reply, on March 14, 1696, Jacob then emphasized, in particular, the possibilities and the benefits of applying mathematics in medicine, citing his brother’s Dissertatio … de motu musculorum as an example. Considerations by Leibniz regarding the medical profession, advances in the medical field, and medicine as an empirical or rational science, were continuing themes in his correspondence in the late 1690s. After Block had explained, in a long letter of July 1, 1698, why – following studies in history, law and theology – he had opted for the medical profession, Leibniz, in his reply of July 30, welcomed the decision and expressed the view that medicine had previously been primarily an empirical science, and that most of the theories and hypotheses in the field were hardly reliable or useful. For that reason, it was also the desire of the renowned physician, Heinrich Meibom, that the discipline be established on an empirical foundation. Nonetheless, Leibniz himself welcomed the conjectures of competent physicians. Writing on October 30, 1698, from Stralsund on his journey home to Sweden, Block, for his part, also desired “istitutioni di Medicina”, which would not be speculative, or concerned with occult speculation, but rooted rather in empiricism. He had his doubts, however, that medicine could be built up solely on the foundation of experience. He compared the subject-matter of medicine, namely the human body, to a closed machine, like a clock, that one could not correct without opening it up, and thus risking its destruction. A possible way out of this dilemma, Block saw in the form of a panacea or universal remedy. Leibniz’s reply, in his letter of December 2, was that hypotheses and conjectures served as tentative solutions on the way to the establishment of the truth. Above all, it was important to separate certain from provisional knowledge. The mainstay of medicine was empiricism and practice. As regards the possibility of finding a panacea or universal remedy, Leibniz recalled the

Introduction: The Core Themes

265

investigations of the recently-deceased English physician Richard Morton. The renowned Morton had established that, in the case of fever patients, a remission often occurred that makes it possible for the physician to save the patient. In the event of an extreme weakness of the body, on the other hand, such a recovery would no longer be possible. Morton had never been able to find a means for the procurement of such a remission. Leibniz himself chose, nonetheless, to continue to adhere to this idea. Leibniz advocated a comprehensive scientific training of medical doctors. Writing to Franck von Franckenau, in May 1698, he recalled a meeting in Paris with Gui-Crescent Fagon, the personal physician of Louis XIV. Fagon had arranged – Leibniz told the correspondent – for a law to be enacted that would filter out in advance charlatans and quacksalvers, by requiring that henceforth medics, and persons in the medical profession, should have to produce evidence of their knowledge of anatomy, botany and chemistry. According to Leibniz, Fagon also wanted to get rid of the accusation – disseminated not least by Jean-Baptiste Poquelin, alias Molière, the satirist of seventeenth-century French medicine228 – that the repertoire of treatment methods of French physicians was limited to the application of clysters, enemata, purgatives or cleansing enemas, and venesection or phlebotomy. Of significance here is Leibniz’s reference to Fagon, Molière and of course to their patron, and enlightened despot, the ‘sun king’, who consciously used the arts and sciences to assert his own importance and grandeur.229 Remarkable in particular is the fact that, during the reign of Louis XIV, rational and critical thought came into being revealing two facets – a bright side and a dark side – of his rule. Foreigners with talent in the arts and sciences were enticed to come and work in Paris for the academies, or institutions, set up during Louis’ reign. Astronomers, mathematicians and scientists like Giovanni Domenico Cassini (from Genua) and Christiaan Huygens (from The Hague) were invited to lead the royal observatory and the Académie des Sciences, respectively. And, of course, it was in Paris that Leibniz (under his mentor Huygens) first developed the differential and integral calculus.230 New areas of investigation in the arts and sciences emerged under the ‘sun king’, which in turn led to an unexpected development of critical thinking. His political communication needed 228 Cf. for example, H. Gaston Hall, “Molière, satirist of seventeenth-century French medicine: Fact and fantasy”, Proceedings of the Royal Society of Medicine, (Section of the History of Medicine), vol. 70, (June 1977), pp. 425–431; A. Calder, Molière: The theory and practice of comedy, London, 1993, in particular chap. 12 (Medicine). 229 Cf. J. Op de Beeck, De Zonnekoning: Glorie & Schaduw van Lodewijk XIV, Antwerp, 2018, in particular pp. 449, 452, and pp. 539–541 (with a portrait of Gui-Crescent Fagon, 1638–1718). 230 Cf. J. Op de Beeck, chapters 5, 7, and 8 (in particular pp. 178f.).

266

Introduction: The Core Themes

the arts as a medium, and he supported and funded, for example, the dramatist Molière who accordingly gained respectability and fame among an ever wider public. Versailles became the fertile ground for a seldom-seen creative drive in the arts and sciences during Louis’ reign. Artistic freedom existed in as far as it served the king’s ideals, and the chance of social promotion became an attraction for artists and scientists of various kinds. Molière, in particular, needed the king, not only for royal commissions for court performances, but also for protection against the growing number of social groups, like the physicians referred to in Leibniz’s letter to Franck von Franckenau in May 1698, which his plays infuriated and antagonized.231 Leibniz’s thoughts on the idea of a rational medicine found expression in his correspondence, and above all in his epistolary exchanges with the “medico-mathematicus” Domenico Guglielmini in the year 1697. To the latter, in a letter of January 7, he expressed the hope that mathematics might, with the support of the correspondent, find a place in medicine. Guglielmini, writing on June 18, expressed his intention of attempting to deduce mathematical laws in physiology. However, thoughts about the organization of medicine as an exact science, or the training of “medico-mathematici”, Guglielmini considered to be wishful thinking and removed from reality. Medics were, as a rule, not versed in mathematics and would spurn rather than approve such ideas. Leibniz replied at the end of September with a profession of faith in the higher value of rational over speculative thoughts in medicine, whereby plausible hypotheses ought to replace less certain conjectures. As he had previously done with Block, Leibniz stressed here how important it was to keep certain and provisional knowledge separate. Conjectures should be taken into consideration only to the extent to which they were expedient or purposeful. And so, from Guglielmini, he hoped for no mean contribution for the advancement of a rational medicine. Between 1699 and 1701, it was above all to Friedrich Hoffmann that Leibniz turned for progress in the area of the development of a rational medicine. Hoffmann, in a work of 1699, had picked up on the public part of the metaphysical controversy between Leibniz and Johann Christoph Sturm. Hoffmann’s dispatch of his work – in particular the dissertation over which he had presided, entitled Dissertatio inauguralis physico-medica de natura morborum … mechanica  – to Leibniz, in September 1699, was to be the overture to their correspondence. In his reply, on October 7, Leibniz treated Hoffmann’s work in detail and commented on the mechanical world picture, on substance and 231 Cf. for example the introduction to: R. Bolt (trans.), N. Dromgoole (Introduction), Molière: The school for wives, a new translation, London, 1998, and 2012 (electronic/ digital).

Introduction: The Core Themes

267

on the soul. However, he quickly changed over to his ideas on the representation of nature. Since one could not immediately establish the mechanism of nature,232 from the Cartesian principles of magnitude, figure and motion,233 one ought to reduce composite principles to simpler ones in the same way that chemists reduced many things to secondary principles. However, he criticized their oftentimes vague terminology, stressing that for principles firm concepts should be chosen. In this sense then, Leibniz desired a contribution from Hoffmann towards the development of a rational medicine, or in his words “Itaque aliquando a Te expecto quaedam rationalis Medicinae elementa”. Alas, Leibniz did not live to see the publication of Hoffmann’s multi-volume work, entitled Medicina rationalis systematica (1718–1734), or its English translation entitled A system of the practice of medicine (1783).234 232 Cf. D. Bertoloni Meli, Mechanism: A visual, lexical, and conceptual history, Pittsburgh, 2019. 233 Cf. for example, C. Mercer, Leibniz’s metaphysics: Its origins and development, Cambridge, New York, Melbourne, 2004, in particular Part 2 (Metaphysics of substance), pp. 110–114. 234 Cf. F. Hoffmann, Medicina rationalis systematica, 6 vols., Halle, 1718–1734; English translation: A. Duncan (ed.), W. Lewis (trans.), A System of the practice of medicine, London, 1783. Also, cf. S. Naragon, “Friedrich Hoffmann (1660–1742)”, pp. 346–348 in: H. F. Klemme, M. Kuehn (eds.), The Bloomsbury dictionary of eighteenth-century German philosophers, London, New York, 2010 and 2016.

The Correspondence: Core Texts

∵

Chapter 1

1676–June 1683 Ego nullum problema Geometricum curo, nisi sit vel valde elegans; vel valde utile ad rem mechanicam aut physicam; vel denique novam methodum nobis ostendat ad infinita alia problemata solvenda.1 Leibniz to Christoph Pfautz, April 28, 1682

∵ 1

Biographical Background (1676–June 1683)

Leibniz’s correspondence in mathematics, science and technology in the seven and a half year period under consideration can be considered in two phases, namely the late 1670s and the early 1680s, corresponding to his periods of service under the reigning Hanoverian dukes Johann Friedrich and Ernst August, respectively. His correspondence in the late 1670s, viz. in the period between November 1676 and December 1679 – consisting of 261 epistolary communications, extant in manuscript or printed form – with almost fifty individuals, can be ordered both in terms of their voluminosity and of their scholarly importance in the history of science, technology and medicine.2 The most voluminous correspondence – constituting more than a sixth of the whole – during this thirty-eight month period was that with the physician, alchemist, friend of Baruch Spinoza, and Amsterdam resident Georg Hermann Schuller. The following four places are occupied by the then Saxon councilor of commerce Johann Daniel Crafft, the medical practitioner and discoverer of phosphorus Heinrich (or Henning) Brand, from Hamburg, the French physicist Edme Mariotte, who was one the first members of the Académie des Sciences, and the Cartesian and former professor at the Hessian university in Rinteln, Arnold Eckhard. The top five correspondents –regarded in terms of their scholarly and historical importance – were no doubt the physicist, mathematician and mentor for 1 A III,3 N. 345, p. 597; Translation: I do not tackle any mathematical problem unless it is either particularly elegant, particularly useful in matters of mechanics or physics, or finally, shows us a new method for solving an infinity of other problems. 2 Cf. H.-J. Hess, A III,2, Introduction, pp. [XXVI]–XXIX.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_003

272

Chapter 1

Leibniz, during his years in Paris from 1672 to 1676, Christiaan Huygens,3 the editor of the Journal des Sçavans, Jean Paul de La Roque, the previously listed Edme Mariotte, the secretary of the Royal Society of London, Heinrich (or Henry) Oldenburg, who served as intermediary for Leibniz’s correspondence with his later rival Isaac Newton, and the mathematician, physicist and philosopher Ehrenfried Walther von Tschirnhaus, who was to remain a friend and associate of Leibniz over a time span of more than forty years. These five exemplary correspondences reflect Leibniz’s intellectual and scholarly activity during his first three years in Hanover, while at the same time documenting the advanced state of knowledge, as well as the ingenuity and inventiveness found among the most important representatives of the European republic of letters of the seventeenth century. In terms of Leibniz’s own biography, his mathematical, scientific and technological correspondence, in the late 1670s, documents a phase of development of his thought and action which – following the years of rich intellectual creativity, and of official and political independence, spent in Paris – was directed towards the exact sciences, and was shaped by the circumstances at the ducal residence in Hanover, with its totally different intellectual environment, and its limited material and human resources, as well as political influence. Of Leibniz’s correspondence in mathematics, science and technology in the early 1680s, namely in the three and a half years between January 1680 and June 16834 – consisting of 344 extant missives with more than sixty individuals – the four most extensive epistolary exchanges constitute in fact half of the whole. Three of these four correspondences represent continuations of existing exchanges. The correspondences in question (in order of their voluminosity) were those with Crafft, the Dutch mathematician Johann Jakob Ferguson, Edme Mariotte and Tschirnhaus. Important aspects of Leibniz’s biography, between 1680 and June 1683, were his continuing duties for the Hanoverian court and his personal plans. The beginning of the year 1680 marked an important change in Leibniz’s life. With the death of duke Johann Friedrich (on December 28, 1679), he had lost a prince with scholarly interests, and an open-minded conversation partner or, as he expressed himself in a letter to Huygens on February 5, 1680: “I have suffered a great loss with the death of my late master, who was without doubt one of the greatest men I have known, 3 Cf. HO: Oeuvres Complètes de Christiaan Huygens, publiées par la Société Hollandaise des Sciences, 22 vols, Den Haag (The Hague), 1888–1950 (http://www.dbnl.org/tekst/huyg003o euv00_01/); J. Yoder (ed.), Catalogue of the manuscripts of Christiaan Huygens including a concordance with his Oeuvres Complètes, Leiden, Boston, 2013. 4 Cf. H. Breger, A III,3, Introduction, pp. [XXIX]–LIX.

1676–june 1683

273

not to mention his quality as a prince”.5 Nonetheless, Leibniz was soon able to count on the continuation of his standing at court, and on his appointment as court counselor and librarian.6 And so, he could sanguinely observe the accession to power of the new duke, namely Ernst August. In February 1680, he travelled to Osnabrück where he received his official appointment documents, and even his fervidly pursued windmill project in the Harz mountains, which at first seemed to be in doubt, was approved by the new duke in the spring of 1680. However, he was never able to establish a similar bond of trust with Ernst August as had previously existed with Johann Friedrich. The new duke was primarily interested in political rather than in scholarly matters, as his predecessor had been. A striking example for this is seen in the contentious discussions about the Douceur cast-iron process. Leibniz had purchased, during the reign of Johann Friedrich and with his mandate, a process for the ostensible production of malleable cast iron from the French engineer Noel Douceur, a process that was considered to be potentially valuable in the production of canons. However, due to the lack of qualified technical personnel, it proved not to be possible to appropriately verify the process even in the course of an extended period of time.7 Douceur received half of the agreed purchase price of 1000 livres at once and, as a precaution, the other half was entrusted to Mariotte, with the intention that it be paid out once the process had been successfully tested. A difficult situation then ensued for Leibniz when, without deficiencies in the process having been established – and thus clearly in breach of contract  – duke Ernst August refused to sanction the payment of the outstanding sum. Leibniz was accused of having induced the deceased duke into sanctioning superfluous expenditure, since – it was claimed – Prince Rupert of the Rhine had already been in possession of a similar, or even better, process for tempering iron.8 The somewhat inept Douceur had the good fortune to have the backing of a powerful advocate in the guise of the trustee Mariotte who, for his part, vigorously pressed his compatriot’s claim, or as he wrote to Leibniz in May 1681: “Concerning the affair of Mr Douceur, I believe he has grounds for complaint”.9 Following Leibniz’s request, Mariotte then reappraised the process and arrived 5 “J’ay fait une grande perte par le mort de feu Maistre, qui estoit sans doute un des plus grands hommes que j’aye connu, sans parler de sa qualité de Prince” (A III,3 N. 22, p. 73). 6 Cf. A III,3 N. 13 and N. 14. 7 Cf. A III,2, p. XXIX. 8 Prince Rupert of the Rhine (1619–1682)  – known in German as ‘Prinz Ruprecht von der Pfalz’ – was the brother of Duchess Sophie of Hanover. 9 “A L’Egard de l’affaire de Mr Douceur, je crois qu’il a sujet de se plaindre” (A III,3 N. 239, p. 434).

274

Chapter 1

at a (for Douceur) positive result,10 which in turn put Leibniz in a very difficult situation, or as he expressed himself in his letter to Mariotte in the first half of August: “The affair of Mr Douceur is proving extremely embarrassing for me”.11 A number of compromise suggestions proved to be of no avail. The idea of including Michel Raison – a valet of duke Ernst August who was then travelling in France – as a co-adjudicator of the process also proved not to be feasible.12 When Mariotte refused to act as a broker, or creditor, for the impoverished Douceur, Leibniz reacted with a letter written on August 25, 1681, the unusually irritated ring of which clearly reveals his difficult situation. Here he wrote: “In the meantime I have been in agony here with this contradictory matter, and have incurred the wrath almost of those in power, which is an entirely different matter to the solicitations of Mr Douceur”.13 Nevertheless, Mariotte referred relentlessly to his verification of the process, and he wrote accordingly, on November 29: “As far as I am concerned, if I were in your place, I would much prefer to lose the 500 livres, rather than to renege on my commitment”, to which he added that “there remains nothing to be done other than to satisfy Mr Douceur”.14 Early in 1682 then, on February 16, Leibniz finally conceded,15 and accordingly, a further 400 livres were paid out to Douceur on March 17, 1682.16 The Hanoverian court was presumably not informed of this payment, as Leibniz had previously written, on August 25, 1681, to Mariotte that: “it is desirable that no others learn as yet that Mr Douceur has received a further payment”.17 The final installment of 100 livres was only paid out in 1685. In the first year of the reign of Ernst August, Leibniz also undertook two attempts to persuade his master to cover expenditure for scientific purposes. Firstly, Leibniz was interested in a fuming liquid,18 which was discussed in 10 11 12 13 14 15 16 17 18

Cf. A III,3 N. 240 and N. 241. “L’affaire de Mr Douceur m’embarasse furieusement” (A III,3 N. 264, p. 466). Cf. A III,3 N. 212. “Depuis j’ay essuyé icy sur cette matiere des contradictions, et me suis presque brouillé avec des personnes puissantes, ce qui est bien autre chose que les solicitations de Mons. Douceur” (A III,3 N. 273, p. 487). “Pour moy[,] si j’estois en vostre place[,] j’aimerois mieux perdre le 500 lb que de ne point effectuer ma parole” and “et ainsy il ne reste plus qu’à satisfaire Mr Douceur” (A III,3 N. 297, p. 520). Cf. A III,3 N. 323. Cf. Mariotte’s receipt (A III,3 N. 334) sent with a letter of Christophe Brosseau to Leibniz on April 10, 1682 (A I,3 N. 459). “il est apropos que d’autres ne sçachent pas encor que M. Douceur a recue quelque chose de nouveau” (A III,3 N. 273, p. 487). Cf. A I,3 N. 42.

1676–june 1683

275

correspondence with the medical professor in Helmstedt Günther Christoph Schelhammer,19 and concerning which he published a short account in the Journal des Sçavans.20 Secondly, Leibniz wished to purchase an exemplar of Denis Papin’s steam digester21 – the precursor of the pressure cooker  – and he corresponded with Frederick Slare about the matter.22 In both cases the purchase did not materialize and, at least in the first case, the duke appears to have reacted with skepticism, if not disapproval. This was further motivation for Leibniz to produce tangible results, and to demonstrate the value of a scientific and rational approach, in his windmill project in the Harz mining district. Accordingly, the continuing lack of progress in this undertaking must have been all the more bitter for him. Leibniz was unusually often away from Hanover in the early 1680s. To Mariotte he wrote, in August 1681, the following words: “My almost continual journeys have prevented me once again from replying to you”,23 and these words surely applied also for other correspondents. Besides his inaugural visit to Osnabrück, referred to above, and his regular journeys to the Harz mountains in connection with the windmill project, other destinations included Brunswick, Celle, Neuhaus in Westphalia and, still further afield, Saxony. There he met up with the mining official Benjamin Olitsch and carried out chemical experiments in Dresden together with Johann Daniel Crafft.24 In Hanover too, Leibniz found new conversation partners. Christof Pratisius, the personal physician of the duke, relocated from Osnabrück to Hanover. Furthermore, the merchant and chemist Martin Elers, the physician Friedrich Schrader, and Tschirnhaus visited Leibniz in Hanover, and extended stays by both the jurist Simon de la Loubère, and the mathematician Ferguson, provided opportunities for discussion. In the summer of 1680, Leibniz made an effort to obtain a court appointment in Vienna, where the position of librarian at the imperial court had become vacant. Crafft encouraged Leibniz to make every effort to secure this 19 Cf. A III,3 N. 69, N. 109, N. 110 and N. 124. 20 Cf. “Extrait de deux lettres écrites à l’auteur du Journal, l’une d’Hanovre par M. de Leibnitz, Conseiller de S.A.M. le Duc d’Hanover, touchant une expérience considérable d’une eau fumante, et l’autre d’Oxford, par M. Hansen”, Journal des Sçavans, (February 17, 1681), p. 46, and also A III,3 N. 163. 21 Cf. A I,3 N. 66. 22 Cf. A III,3 N. 84, N. 178, and N. 218. 23 “Mes voyages presque continuels m’ont empeché encor de vous repondre” (A III,3 N. 264, p. 466). 24 Cf. A III,3 N. 63 and N. 184.

276

Chapter 1

position, since, in his view, direct access to the emperor would greatly benefit their planned joint economic projects.25 Leibniz himself pursued a prospective appointment, as librarian and privy counsellor, at the imperial court with the argument – revealed in a ‘promemoria’ for Crafft,26 from the second half of July 1680 – that, through such economic projects, the house of Austria might once again be in the ascendant. Those who were approached to support Leibniz’s effort to obtain this appointment included an old acquaintance, namely the Polish Jesuit and polymath, Adam Adamandy Kochański (in a letter from the second half of July or August 1680),27 and the chancellery assessor Christoph Gudenus (documented in Gudenus’ letter sent with a letter to Crafft at the beginning of September 1680).28 However, Leibniz was soon to learn from Crafft that another candidate had been preferred and appointed imperial librarian, and that their deliberations had been to no avail. Thus, Crafft wrote from Dresden, at the beginning of September: “Herewith the deliberations in the matter have come to an end, and it will be for ever regrettable that the well-conceived combination could not be realized in reality”.29 Likewise, Leibniz’s efforts to become a member of the French Académie des Sciences proved to be in vain. Following a first unsuccessful attempt while still in Paris, he once again turned to Christiaan Huygens, in September 1679, in this matter.30 Huygens reported, on January 11, 1680, about a consultation with Jean Gallois concerning the matter. The latter had been, according to Huygens’ words at the beginning of that letter, positively disposed to the proposal, and he had even given an assurance of his commitment to its realization.31 However, the correspondence with Huygens was interrupted before the initiative could be further pursued. An ulterior motive for Leibniz’s letter to the Jesuit confessor of Louis XIV, François de la Chaise,32 may well have been the procurement of the support of such an influential figure for his aspired admittance to the Académie des Sciences. However, when La Chaise failed to reply, 25 26 27 28 29

Cf. A III,3 N. 93, p. 247. Cf. A III,3 N. 82. Cf. A III,3 N. 91. Cf. A III,3 N. 104. “Hiemit haben die deliberationes daruber ein End, vnd ist immer Schad dafur, daß die wohlgefaste combination nicht wurcklich hatt gemachet werden könen” (A III,3 N. 103, p. 257). 30 Cf. A III,2 N. 346; HO, 8, pp. 218f. 31 “je le trouvay de luy mesme fort disposé à vous procurer du bien  … m’assurant qu’il n’obmettroit point d’occasion pour cela et qu’il avoit mesme conceu quelque moyen pour l’effectuer” (A III,3 N. 4, p. 48; HO, 8, pp. 256–258). 32 Cf. A III,3 N. 61.

1676–june 1683

277

and Huygens departed from Paris in 1681, Leibniz’s prospects of a decision in his favor dwindled accordingly. Notwithstanding this setback, he subsequently supported with remarkable altruism the candidacy of Tschirnhaus for appointment to the Académie des Sciences, in the following year. In a letter to Gallois, he lauded Tschirnhaus’ scholarly achievements and solicited the correspondent with the words: “I will be obliged to you as much as if I had received the honor myself”.33 Furthermore, Leibniz generously made available, in a long letter at the end of June 1682 to Tschirnhaus – intended for communication to the Académie – details of the process for the production of phosphorus which, at that juncture, was known to only a few persons.34 Near the end of an earlier equally long letter of May 27, 1682, from Paris, Tschirnhaus had referred to Leibniz as a “philosophical friend”,35 and, at the beginning of a further letter of August 6, 1682, as a “good and reliable friend, who had done him a great favor in disclosing details of the phosphorus process”.36 Thus, the communication of the phosphorus process, in particular, was for Tschirnhaus an act of exceptional generosity, on Leibniz’s part, to which the correspondent’s words of gratitude in this letter testify. In the course of events, Tschirnhaus was successful in being accepted as a member of the Académie des Sciences. Leibniz, encouraged by the success of his compatriot, then drafted a letter to the founder of the Académie, Jean Baptiste Colbert, in first half of October 1682,37 but it was dispatched instead, in mid-October, as a letter to Jean Gallois, of whose continuing esteem he had been informed by Tschirnhaus. In this letter, Leibniz expressed his desire to be admitted to the Académie as a foreign member entrusted with duties in the field of geological research in the Harz mountains. Thus he wrote: “I could supply the Academie Royale from time to time with curious or singular observations about such matters, and even minerals in nature”, to which, he added, that he would try to draw conclusions and to advance the sciences accordingly.38 Alas, the admission of Tschirnhaus to the Académie had in fact

33 34 35 36

“je vous en auray la meme obligation, que si vous l’aviés fait à moy” (A III,3 N. 349, p. 604). Cf. A III,3 N. 368, specifically pp. 660–662. “Ein Philosophischer Freund” (A III,3 N. 356, p. 631). “Ein gutter Freund darauff Man sich verlaßen kann. Sie haben Mir mitt der communicatione Phosphori Eine Genereuse Freundschafft erwießen” (A III,3 N. 384, p. 686). 37 Cf. A III,3 N. 406. 38 “je pourrois fournir de temps en temps à l’Academie Royale des observations curieuses sur ces matières, et meme des Mineraux en nature” and “je tacheray d’en tirer des conclusions, et d’avancer par là les sciences” (A III,3 N. 407, p. 726).

278

Chapter 1

worsened the prospects for Leibniz himself.39 Gallois was apparently unwilling to advocate the admission of a further foreign member not resident in Paris. These setbacks do not reflect Leibniz’s public standing at this juncture, however. That Friedrich Schrader commenced his correspondence with Leibniz, on March 4, 1681, with flattering words, namely, writing that “I have observed, for a long time already, that your fame is flourishing around the globe”,40 may indeed be attributed to the young age of the correspondent. Of greater weight is the reverence shown by Detlev Clüver, a fellow of the Royal Society of London, in his first letter to Leibniz, on April 16, 1680, in which he placed the addressee among those “who try to lift human knowledge to a higher pinnacle”.41 Leibniz had, however, also to tolerate the satirical remarks about him in Johann Joachim Becher’s Närrische Weißheit und Weise Narrheit (meaning foolish wisdom or wise foolery/ folly’ish wisdom or wise folly) of 1682, in which the author made fun of him as the inventor of a stagecoach with which one might travel between Hanover and Amsterdam in six hours.42 That Leibniz had in fact contemplated the possibility of such an express coach, was probably revealed (perhaps inadvertently) to Becher by Crafft, as the latter admitted to Leibniz in a letter of June 1, 1683.43 Leibniz was also informed, on March 4, 1682, by Christoph Pfautz,44 and on August 18, by Sebastian Scheffer,45 that extracts and quotations from his letters concerning questions of meteorology, and terrestrial magnetism, had been printed in Albert Meyer’s Dissertatio mathematica de observationibus aerometricis (1681),46 and in Johann Christoph Sturm’s Epistola invitatoria ad observationes magneticae variationis … instituendas (1682),47 respectively.

39 Cf. A I,3 N. 491. 40 “famam Tuam jam diu per orbem florere animadverti” (A III,3 N. 183, p. 362). 41 “Inter eos Te collocatum esse, qui scientiam humanam ad sublimius aliquod fastigium deducere allaborant” (A III,3 N. 57, p. 184). 42 Cf. J. J. Becher, Närrische Weißheit und Weise Narrheit oder Ein Hundert so Politische alß Physicalische Mechanische und Mercantilische Conceptem und Propositionen. Frankfurt am Main, 1682, specifically p. 147. 43 Cf. A III,3 N. 473, specifically pp. 825f. 44 Cf. A III,3 N. 330, specifically p. 574. 45 Cf. A III,3 N. 387, specifically p. 697. 46 Cf. A. Meyer, Dissertatio mathematica de observationibus aerometricis hactenus institutis et imposterum instituendis, Kiel, 1681. 47 Cf. J. Chr. Sturm, Epistola invitatoria ad observationes magneticae variationis communi studio junctisque laboribus instituendas, Altdorf, 1682, and also the review in the Acta Eruditorum, (August 1682), pp. 258–260.

1676–june 1683

279

2 Mathematics The further development of Leibniz’s thought in pure mathematics during his first three years in Hanover (1677–1679) – in as far as it is documented in his correspondence  – was predicated on the following list of thematic foci: the quest for general equations for all differentiable and integrable curves, a task that developed out of the two classical problems of tangent determination and of quadrature, and which found expression, for example, in the correspondences with Oldenburg and Tschirnhaus; the determination of curves from the properties of tangents, also called the inverse tangent method (likewise found in the correspondences with Oldenburg and Tschirnhaus); the search for solution forms of equations of the fifth degree or higher, and in particular for generalized formulae (viz. Cardano’s formula; also in the Tschirnhaus correspondence); the outline of an algebraic morphology, emanating from multiplication tables of algebraic terms (likewise in the Tschirnhaus correspondence); the investigation of transcendental and, in particular, of exponential equations (for example in the correspondence with Huygens); the further extension of the method of the series development of functions and numerical magnitudes (particularly in the discussion of the results of Newton and Gregory in the correspondence with Oldenburg); the formulation of a general method for Diophantine arithmetic (for example the correspondence with Arnold Eckhard), and – last but not least – the projection of a geometry of position, or of a “characteristica geometrica”, i.e. of an axiomatized geometry founded on “characters”, as a special case of a general characteristic (in particular in the correspondences with Huygens and Tschirnhaus).48 In comparison with the outstanding importance of mathematics during Leibniz’s years in Paris (1672–1676), and in his first three years in Hanover (1677–1679), the subject had a somewhat reduced importance in his correspondence during the early 1680s. This is attributable to the fact that his correspondence with Huygens and Tschirnhaus was less voluminous and, furthermore, to the circumstance that, following the death of Oldenburg, the mathematically relevant correspondence with the Royal Society of London was interrupted. In his sole letter to Huygens in this period, on February 5, 1680, Leibniz commenced with the words “Behold an example of my method of tangents”, to which he added “I have taken the first example which appeared to me to be equally quaint and cluttered with irrationals”.49 Attached to this letter 48 Cf. A III,2, p. XXVIII. 49 “Voicy un example de ma methode des Touchantes, j’ay pris le premier qui me paraissoit egalement curieux et embarrassé d’irrationales” (A III,3 N. 22, p. 71; HO, 8, pp. 267f.).

280

Chapter 1

then, there was an explanation of his method of finding maxima and minima (“Specimem Methodi meae de Maximis et Minimis”), with the dispatched text having the following heading: “Example taken from my new method of tangents” (“Exemplum ex Nova mea Tangentium Methodo ductum”).50 In effect, this example that Leibniz would once again include in the first publication of his differential calculus – namely in his article “Nova methodus pro maximis et minimis”, of October 168451 – was to prove particularly suitable for demonstrating the superiority of the new calculus over existing methods. In February 1682, Leibniz published the article “De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus expressa”, in the recently-established journal Acta Eruditorum of Leipzig.52 Here, the so-called ‘Leibniz series’, as well as the technical term ‘transcendent’, appeared in print for the first time. Two months before the appearance of the first number of the new journal, on October 29, 1681, Leibniz had been approached by the co-editor Christoph Pfautz to contribute such a keynote article in the following words: “it will, in my judgement, be not an unworthy honor to be among the first to make a contribution to our transactions”.53 As the manuscript reached Pfautz later than planned, Leibniz’s article appeared only in the second monthly installment of the new journal. In this article Leibniz also publicly presented, for the first time, an equation with the unknown in the exponent. For the mathematics professor Pfautz, this represented such a surprise that – although the context could hardly have left any doubt – he contacted the author to make certain that xx, or x to the power of x, was in fact intended.54

50 Cf. A III,3 N. 23, pp. 73–78; HO, 8, pp. 269–271. 51 Cf. G. W. Leibniz, “Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratur, et singulare pro illis calculi genus”, Acta Eruditorum, (October 1684), pp. 467–473, and also chap. III (pp. [96]–117) in: M. Parmentier (ed., trans.), G. W. Leibniz: La naissance du calcul différentiel: 26 articles des Acta Eruditorum, Paris, 1989; N. 14 in: A. Lamarra, R. Palaia (eds., trans.), H. Schepers (Preface), Gottfried Wilhelm Leibniz: Essais scientifiques et philosophiques. Les articles publiés dans les journaux savants, 3 vols, Hildesheim, Zürich, New York, 2005; chap. 8 (pp. 51–62) in: H.-J. Heß, M.-L. Babin (eds., trans.), Gottfried Wilhelm Leibniz: Die mathematischen Zeitschriftenartikel, Hildesheim, Zürich, New York, 2011. 52 Cf. G. W. Leibniz, “De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus expressa”, Acta Eruditorum, (February 1682), pp. 41–46 (Leibniz: Parmentier, 1989, chap. I, pp. [61]–81; Leibniz: Essais Scientifiques, 2005, N. 7; Leibniz: Heß-Babin, 2011, chap. 3, pp. 9–18). 53 “erit id meo judico non indignum ut inter prima sit, quae Actis nostris pretium concilient” (A III,3 N. 289, p. 506). 54 Cf. A III,3 N. 305, p. 528.

1676–june 1683

281

Following the article (regarding a fuming liquid) in the Journal des Sçavans in 1681, referred to above,55 Leibniz wrote three articles in 1682 – on mathematics, optics and chemistry – for the Acta Eruditorum,56 and prepared a fourth (on simple interest and discount calculation), that appeared in the following year.57 His mathematical article, of February 1682, on the arithmetic quadrature of the circle was translated into English and appeared in the Philosophical Collections.58 It found the attention and interest of scholars as far away as Dublin, where St George Ashe referred to it in a paper entitled “Concerning the squaring of the circle”, which was read to the Dublin Philosophical Society in November 1684.59 Thereafter, Leibniz prepared his article on simple interest and discount calculation, which was intensely discussed with Pfautz from February 1683 and which duly appeared in the journal in October of that year.60 The fecundity of this discussion is revealed in an annotation of Leibniz, from the summer of 1683, to a note received from Pfautz, and expressed in the following words: “from which I can beautifully see that he has understood my method”.61 Consideration of the expressions, referred to here, in which the unknown, or the variable, appears in the exponent had, as in the years prior to this, particularly engaged Leibniz’s mathematical mind. He saw here, to a certain extent, the hitherto missing keystone to the completion of his infinitesimal calculus. The determination of tangents to exponential curves had not yet been satisfactorily solved and, as he wrote to Tschirnhaus on May 23, 1681, things were such that “if we had these, we would also know what quadratures 55 Cf. note 20. 56 Cf. G. W. Leibniz, “De vera proportione circuli … expressa” (note 52); “Unicum opticae, catoptricae et dioptricae principium”, Acta Eruditorum, June 1682, pp. 185–190 (Leibniz: Essais Scientifiques, 2005, N. 9; Leibniz: Heß-Babin, 2011, chap. 4, pp. 19–28). For English translations of this and 24 further articles, published between 1682 and 1712, cf. the forthcoming publication: R. T. W. Arthur et al., G. W. Leibniz: Published articles on natural nhilosophy; “Meditatio de separatione salis et aquae dulcis, novoque separationum chymicharum genere”, Acta Eruditorum, (December 1682), pp. 386–388. 57 Cf. G. W. Leibniz, “Meditatio juridico-mathematica de interusurio simplice”, Acta Eruditorum, (October 1683), pp. 425–432 (Leibniz: Essais Scientifiques, 2005, N. 11; Leibniz: Heß-Babin, 2011, chap. 5, pp. 29–38). 58 Cf. G. W. Leibniz, “The true proportion of the circle to the square”, Philosophical Collections, (April 1682), pp. 204–210. 59 Cf. K. Theodore Hoppen (ed.), Papers of the Dublin Philosophical Society 1683–1709, Dublin: The Irish Manuscripts Commission, 2008, 2 vols, specifically vol. 1, no. 122, pp. 135–146, and in particular pp. 144f.; K. Theodore Hoppen, The common scientist in the seventeenth century: A Study of the Dublin Philosophical Society 1683–1709, London, 1970. 60 Cf. note 57. 61 “eleganter unde video eum meam methodum intellexisse” (A III,3 N. 469, p. 819).

282

Chapter 1

these are, whether analytical, if this can be done, or transcendental”.62 The introduction of expressions in which the unknown, or variable, appeared in the exponent also attracted the interest of Ferguson and Tschirnhaus,63 and provided occasion for discussion between the latter and Leibniz as to whether such expressions, or curvilinear coordinates, are better suited for describing transcendental curves.64 Regarding other questions relating to the theory of curves, and the infinitesimal calculus, Leibniz’s correspondence with Tschirnhaus likewise proved to be particularly fruitful. On May 31, 1682, this correspondent referred to a procedure for the determination of points of inflexion,65 having explained a few days earlier his method of tangents to Leibniz,66 which would be applicable also for certain transcendental curves and which was published half a year later in the Acta Eruditorum.67 Tschirnhaus, in the letter of May 31, referred to a drawing showing both a “parabola cubica” (ABC), and a common or Archimedean parabola (ABD)  – overlapping and congruent from the point A to the point of inflection B, and thereafter diverging to their respective end points C and D – in the following words (which Leibniz recorded separately in an extract he made from Tschirnhaus’ letter): “You will, Sir, know that the continuation of the cubic parabola is not towards D as with the Archimedean parabola but rather to C”. And to this he added: “I have an easy method of recognizing such directly from the calculation itself in all curves”.68 Considerable attention was likewise given to a detailed discussion of Tschirnhaus’ problem of the catacaustic curve,69 as well as related problems like the diacaustic curve,70 these being curves which arise in connection with the reflection and refraction of light. Leibniz found opportunity for a summarizing representation of his most important mathematical accomplishments in two separate letters to the Jesuits François de la Chaise (in April–May 1680), and to Adam Adamandy Kochański (in July–August 1680), with whom he had 62 “Si haec haberentur, haberemus etiam quadraturas quales sunt, scilicet vel analytice, quando id fieri potest, vel transcendenter” (A III,3 N. 233, p. 428). 63 Cf. A III,3 N. 42 and N. 356, respectively. 64 Cf. A III,3 N. 368. 65 Cf. A III,3 N. 358, specifically pp. 639–641. 66 Cf. A III,3 N. 357, which was an attachment to N. 356 of May 27, 1682. 67 Cf. E. W. v. Tschirnhaus, “Nova methodus tangentes curvarum expedite determinandi”, Acta Eruditorum, (December 1682), pp. 391–393. 68 “Meinen H. ist bekand daß die continuatio parabolae cubicae AB nicht versus D wie die Parabola Archimedis sondern in C; Ich habe Einen leichten Methodum solches gleich ex ipso calculo in omnibus curvis zuerkennen”; cf. note 65, pp. 640f. 69 Cf. A III,3 N. 355 and N. 357. 70 Cf. A III,3 N. 233, N. 348, N. 356, N. 368 and N. 384.

1676–june 1683

283

contact some years before. In the letter to La Chaise, he referred, first of all, to the algebra of geometry, a ‘characteristica geometrica’ or a geometric characteristic, which included his ‘analysis situs’ or ‘geometria situs’, viz. the geometry of location, writing that: “there is in geometry itself an analysis totally different from algebra which goes directly to location”. Secondly, he referred to his differential calculus, and its capabilities, in the following words: “I have so many observations, and so many new openings in these matters, that I am convinced that I can supply the means to infinitely surpass the columns erected by Viète and Descartes”. Finally, in this letter to La Chaise, he underlined the importance of reducing problems in mechanics, and engineering, to the language of pure mathematics – and specifically of reducing machines to machine-equivalent figures for calculation purposes – in the following words: “But I would esteem all of this very little, if I did not see the means of reducing the problems of mechanics to the terms of pure mathematics, and of representing machines in calculations just as figures do”.71 In the said letter to Kochański, from July–August 1680, Leibniz reported that, during his stay in Paris, he had not only progressed “to the adyton or innermost sanctuary of analysis”, but had also surpassed the borders of Cartesian mathematics. Descartes had been stranded at the beginnings of true mathematics, which ultimately revealed “a more sublime analysis which I am wont to call transcendental”. Of course he also touched here upon his arithmetic quadrature of the circle and, in this context, “the discovery in practice of the use of [his] trigonometric series or geometry without tables”, through which geometry was in a certain sense freed from an ignominy.72 Leibniz’s extensive exchange of ideas in the early 1680s with Johann Jakob Ferguson, the Dutch mathematician and author of a much appreciated book entitled Labyrinthus algebrae (1667),73 included questions of number theory,74 71 “il y a dans la Geometrie même une analyse toute differente de l’Algebre, qui va directement à la situation … j’ay tant d’observations, et tant de nouvelles ouvertures en ces matieres, que je me persuade de pouvoir donner moyen de passer infiniment les colonnes posées par Viète et des Cartes … Mais je estimeray peu tout cecy, si je ne voyois moyen de reduire les problemes de Mechanique aux termes de la pure geometrie, et de mettre les machines en calcul tout comme les figures” (A III,3 N. 61, pp. 189–193, specifically p. 190 and p. 192). 72 “ad intima analyseos adyta penetravi … Nam pulcherrima maximeque in vita communi utilia problemata indigent Analysi quadam sublimiore, quam ego vocare soleo transcendentem … In praxeos usum autem reperi … Trigonometriam sine tabulis … Earum ope datum quodque problema Trigonometricum resolvi potest” (A III,3 N. 91, pp. 242–245, specifically p. 243). 73 Cf. J. J. Ferguson, Labyrinthus algebrae, verdeelt in vijf deelen, Den Haag (The Hague), 1667. 74 Cf. A III,3 N. 40, N. 43 and N. 385.

284

Chapter 1

the calculation of annuities,75 the solution of equations,76 the quadrature of the circle by means of a curve studied and constructed by Pierre de Fermat, James Gregory, and Guido Grandi, and later called the ‘Witch of Agnesi’ curve (after Maria Gaetana Agnesi, 1718–1799),77 the summation of the series of the reciprocal triangular numbers,78 an extreme value problem,79 Huygens’ cycloidal pendulum,80 and a curve problem similar to the example of the Leibniz’s tangent method communicated to Huygens,81 an inverse tangent problem,82 the real sum of two imaginary expressions,83 the extension of binomial development to broken exponents,84 and the solution of non-homogeneous equation systems,85 a matter which related to Leibniz’s studies of the theory of determinants,86 which in turn represent an application example of his thought concerning a ‘universal characteristic’. Regarding the latter, the basic idea was explained by Leibniz in a letter to Detlev Clüver, on May 28, 1680, in which he insisted on the superiority of his combinatorial characteristic in comparison with normal algebra.87 The use of numbers instead of letters would allow, in every calculation step, the formation law for the emerging expressions to clearly abound, with the consequence that the control of the calculation, and the avoidance of mistakes, would be facilitated. Above all, the inner structure of the solution was clearly given expression in accordance with the problem statement. In this procedure the unknowns were written larger for greater clarity. In terms of terminology, Leibniz used double indices to represent coefficients, without however adding the indexed letter. This notation, which he had already used in 1678, was now employed, for example, in the treatment of Alhazen’s problem on which he and Ferguson worked.88 75 Cf. A III,3 N. 42. 76 Cf. A III,3 N. 51, N. 54, N. 56, N. 353, N. 377, N. 459 and N. 466. 77 Cf. A III,3 N. 48, and also: C. Martini, and G. Wolfschmidt (ed.), Zwei Frauenleben für die Wissenschaft im 18. Jahrhundert, Hamburg, 2017 (Introduction, note 17). 78 Cf. A III,3 N. 48. 79 Cf. A III,3 N. 48 and N. 49. 80 Cf. A III,3 N. 48 and N. 51. 81 Cf. A III,3 N. 48. 82 Cf. A III,3 N. 363. 83 Cf. A III,3 N. 51, N. 54 and N. 55. 84 Cf. A III,3 N. 51, N. 53 and N. 55. 85 Cf. A III,3 N. 44, N. 45, N. 46 and N. 47. 86 Cf. Leibniz: Knobloch (Determinants), 1980; E. Knobloch, 2000 and 2018 (Introduction, note 18). 87 Cf. A III,3 N. 66, pp. 200–203, in particular p. 202. 88 Cf. A III,3 N. 48, N. 50, N. 51 and N. 52.

1676–june 1683

285

Likewise, Leibniz’s considerations of number systems, other than the decimal system, stood in connection with the combinatorial characteristic. In discussions with Ferguson, Leibniz had apparently elaborated on number systems to the base 2, 11 and 12.89 The dyadic, or binary, number system also found the interest of Tschirnhaus, in a letter of May 27, 1682.90 Leibniz, writing to him at the end of June 1682, expressed his expectation that many “harmoniae” would be found in the dyadic system, which were not so evident in other number systems. Thus he wrote: The Progressio bimalis (viz. Progressio dyadica) would be particularly useful for expressions of quantities in numbers, since it is the best and the simplest, and I do not doubt that many harmonies could be found there, which are not to be detected in other progressions.91 In his letter to Clüver, on May 28, 1680, Leibniz expressed himself at first only in general terms with the statement that he had noted that they did not have characters of numbers as required.92 Addition and multiplication ought to follow purely, and mechanically, from the numeral without the help of one’s memory or a multiplication table. Following this, in his reply on July 26, 1680, Clüver recalled the dyadic, or binary, system and the reduction of arithmetic figures to the simpler zeros and ones. However, he added that someone wanting to bring about the general introduction of the binary system could expect to face difficulties, or  – as he put it  – have to wash the Ethiopian white.93 Leibniz expressed his surprise at Clüver’s congenial understanding in relation to this and related questions and, at the beginning of his letter of September 10, 1680,94 he paid a compliment to the correspondent to the effect that he could 89 Cf. A III,3 N. 48, p. 137f. 90 Cf. A III,3 N. 356, p. 627 and p. 632. 91 “Die Progessio Bimalis würde sonderlich ad expressiones quantitatum in numeris nüzlich seyn, denn es prima und simplicissima [sic], und zweifle nicht daß sich darinnen viel harmoniae finden würden so in andern progressionen nicht also zu spühren” (A III,3 N. 368, pp. 655f.). 92 “notavi, nos non habere characteres numerorum quales oportet” (A III,3 N. 66, p. 202). 93 “reliquas quas habemus figuras aithmeticas ad simplices illas 0 et 1 reducendo … Verum Aethiopem forsan lavabit, qui nova quaedam hac de re … Orbi obtrudere vellet” (A III,3 N. 89, p. 238). 94 “Literae tuae mihi gratissimae fuerunt, vel ideo quod ex illis conjicere mihi videor te non parum ultra vulgus mathematicorum profecisse” and “Logistica progressionis binaria ubi nulli alii occurrunt characteres praeter 0, 1 saepicule usus sum cum fructu: neque ista usus communis sed theoriae causa adhibeatur itaque communis numerandi ratio sine magna ratione solicitanda non videtur” (A III,3 N. 106, pp. 262f.).

286

Chapter 1

see, from the very welcome letter, that he had advanced far beyond the broad mass of mathematicians. He clarified his standpoint, however, stressing the fact that, although he himself had used the progression of binary logic (where no other characters except zeros and ones occurred) with advantage, he did not conceive the binary system for general use, but merely for theoretical purposes. With the following words, from a letter to Christoph Pfautz of April 28, 1682, Leibniz rejected the call for him to give attention to a (for him) mundane problem, which had been publicly enunciated in the Acta Eruditorum, in the following words: I do not tackle any mathematical problem, unless it is either particularly elegant, particularly useful in matters mechanical or physical, or finally, shows us a new method for solving an infinity of other problems.95 Leibniz did not, however, disdain from dealing in detail with some other elementary tasks relating to the construction of a triangle in a letter, dating from the end of December 1679, which served to establish contact with the renowned Italian polyhistor Antonio Magliabechi.96 However, in doing so, he did not depart from his basic principle. He actually took such elementary tasks as the starting point for a consideration of the use of the linear analysis of their predecessors.97 In fact, Leibniz insisted that, he who chose to apply the algebraic methods of Viète and Descartes might quickly embroil himself in vast calculations, as he put it.98 In the end, he left the matter to the judgement of Magliabechi himself as to how long the analysis, which at that time was in use everywhere, had previously been lacking perfection.99 With this correspondent, however, he did not articulate the fact that he believed himself to be – with his geometrical characteristic – in possession of the toehold for the removal of this deficiency.

95 “Ego nullum problema Geometricum curo, nisi sit vel valde elegans; vel valde utile ad rem mechanicam aut physicam; vel denique novam methodum nobis ostendat ad infinita alia problemata solvenda” (A III,3 N. 345, p. 597). 96 Cf. A III,3 Supp. N. II, pp. 5–39, in particular p. 34. 97 “usum analyseos linearis veterum” (p. 34). 98 “in calculos ingentes se induere possit” (p. 34). 99 “Unde aestimandum tibi relinquo,Vir Clarissime, quam longe adhuc absit analysis quae hodie passim in usu est, a perfectione vulgo jactata” (p, 34).

1676–june 1683

3

287

Natural Philosophy and Physics

Whereas several of the mathematical investigations, from Leibniz’s first three years in Hanover (1677–1679), relate directly to questions raised, or left unsolved, by Descartes, this applies to an even greater extent for a multitude of physical writings of his from these years.100 Here it was above all the Cartesian laws of motion, and laws of refraction, which, along with Leibniz’s efforts for a further development of his Hypothesis physica nova,101 provided occasion for scientific discussion, as in the letter to Honoré Fabri of May 17, 1677.102 Already during his years in Paris, Leibniz had set himself the task of reducing mechanics to geometry and, in doing so, assigned a key role to the principle of the equality of cause and effect. These studies in natural philosophy achieved a first lasting result in his 1678 outline, entitled De corporum concursu, with the introduction of the product of mass and the square of the velocity as the measure of force.103 In letters to Philipp Lohmeier,104 François de la Chaise,105 Adam Adamandy Kochański,106 and Friedrich Schrader,107 Leibniz referred to this result, and he stressed the importance of his considerations with the remark that he would place little value on all his mathematical discoveries, if he did not see the possibility of reducing mechanics to geometry. Since the laws of motion were proved, there emerged a new sphere of activity, as he stated in the following words in his letter from the second half of April or the first half of May, 1680, to La Chaise: For, regarding the laws of motion, I have finally demonstrated them by a ‘reductio ad absurdum’, demonstrating that, if the premises that I posed were not true, perpetual motion would result. Following that, it only remains that we put experiments (or experiences) of physics in order too,

100 Cf. A III,2, p. XXVIII. 101 Cf. G. W. Leibniz, Hypothesis physica nova, Mainz, 1671 and London 1671; C. J. Gerhardt (ed.), Die philosophischen Schriften, Berlin, 1880 and Hildesheim, 1965, vol. IV, pp. 177–219. 102 Cf. A III,2 N. 42. 103 Cf. G. W. Leibniz, De corporum concursu, GWLB Hanover, manuscripts LH XXXV, 9, 23,1–22 and LH XXXVII, 5, 86–91, January 1678, published in: M. Fichant, La réforme de la dynamique, Paris, 1994, pp. 71–171. 104 Cf. A III,3 N. 1. 105 Cf. A III,3 N. 61. 106 Cf. A III,3 N. 91. 107 Cf. A III,3 N. 192.

288

Chapter 1

and so reduce them to problems of mechanics and, as a consequence, also to the terms of pure mathematics.108 It is therefore logically consistent that, in the early 1680s, we find increased attention being paid to concrete or practical science in Leibniz’s correspondence. In this effort he was not satisfied with the mere accumulation of experimental data. While he very much appreciated Robert Boyle’s “judgement and experimental industriousness”,109 as he wrote in the letter of March, or April, 1681 to Friedrich Schrader, he criticized what he saw as Boyle’s reticence in drawing conclusions. Experimental results should be ordered and structured by means of principles, and an attempt ought to be made to explain the phenomena in terms of magnitude, form and movement. Otherwise, he wrote, our natural philosophy would not be of much greater benefit in practice than the common, or scholastic, philosophy. Accordingly, the paradigm to be followed lay in the accumulation of empirical observations (like those of “Verulamius”, i.e. Francis Bacon, or Robert Boyle) and similarly of calculations (like those of Galileo and Descartes), in the organizing and carrying out a system of experiments, in refining calculations by means of experiments, and thus advancing mathematics and physics.110 During his first visit to London, Leibniz visited Boyle at Ranelagh House on Pall Mall  – the residence of Boyle’s sister, Katherine Jones, viscountess Ranelagh, with whom he lived from 1668 until 1691– on February 12, 1673, as is evident from the opening lines of a letter for the Royal Society, written the following day, in which he recalled that meeting.111 Thereafter, through his correspondence with Heinrich (or Henry) Oldenburg, the German-born secretary 108 “Car pour les regles du mouvement, je les ay enfin exactement demontrées par une reduction ad absurdum: monstrant que si celles que je pose n’estoient vrayes il y auroit un movement perpetuel. Apres cela il ne nous restera, que de mettre en ordre les experiences de physique, pour les reduire aux problemes de mecanique, et par consequent aussi aux termes de la pure geometrie” (A III,3 N. 61, p. 192). 109 “judicium et industriam experimentalem” (A III,3 N. 192, p. 373). 110 “Alioqui philosophia nostra non multa ad praxin utilior erit quam vulgata. Quodsi itaque multos in observando quidem Verulamio et Boylio, in ratiocinando autem Galilaeo et Cartesio similes haberemus; si experimenta ordine institueremus et disponeremus; si ratiocinationes experimentis inaedificando mathesin physicam magis excoleremus  …” (p. 373). 111 “Londini d. 3 [13] Feb. 1672/73. Cum heri apud Illustrissimum Boylium … commemoravi ego” (A III,1 N. 4, p. 22); cf. also A.-M. Walsh, The daughters of the first earl of Cork: Writing family, faith, politics and place, Dublin, 2020, and in particular p. [10] (The Boyle family tree, showing Katherine and Robert as the 6th and 12th of the Boyle siblings, respectively) and p. 13 (regarding the “sibling relationships and the roles they played in perhaps the most important family in seventeenth-century Ireland”); M. DiMeo, Lady Ranelagh:

1676–june 1683

289

of the Royal Society and editor of the Philosophical Transactions, Leibniz repeatedly conveyed greetings to Boyle, directed questions to him, and sought to establish contact with him. Boyle’s words too, that reached Leibniz through Oldenburg were pronounced friendly as, for example when, on April 22, 1675, this correspondent wrote of Boyle’s words of affection for Leibniz,112 or on March 4, 1677, even of enthrallment or endearment for Leibniz.113 And even after Oldenburg’s death, in September 1677, Leibniz learned that Boyle had enquired about him as, for example, from Friedrick Slare who, on July 18, 1680, referred to Boyle’s regular expressions of great respect, reverence or veneration for Leibniz.114 Indeed six years later, at the end of June 1686, Detlev Clüver could report Boyle’s continuing interest in Leibniz’s work, particularly regarding metals. However, the correspondent found himself to be totally unable to report about Leibniz’s chemical studies as he informed him in this letter.115 In his reply to Clüver, at the end of July 1686, Leibniz returned Boyle’s compliments in similar words,116 before elaborating his thoughts on Boyle’s works and characterizing his own contribution to the study of metals. In his official correspondence, Leibniz usually expressed his reverence for Boyle and tried to encourage him to make known, or to publish, his results. Thus, for example, in a letter to Henri Justel, Royal Librarian at St. James’s Palace in London under William III, on October 20, 1690, he wrote: Please do me the favor and, given the occasion, convey my reverence to the Chevalier Boyle, whom I hold in the greatest esteem, and encourage him to reveal to us those wonderful things he has previously only alluded to or completely withheld from us.117

112 113 114 115 116 117

The incomparable life of Robert Boyle’s sister, Chicago, 2021, and in particular chap. 7, pp. 163–194 (Robert Boyle moves in). “Dominus Boylius prae caeteris amplissimam sui erga Te affectus testificationem edebat” (A III,1 N. 49, p. 244). “Vale, et a Dno Boylio, qui te valde amat, plurimam salve” (A III,2 N. 20, p. 49). “Patronus Dmnus Boyle (qui saepius nominis tui mentionen facit venerabilem)” (A III,3 N. 84, p. 231). “Quid in rebus metallicis agas, Dn. Boyle saepius ex me quaesivit” and “sed nihil ipsi de studiis tuis Chymicis indicare potui, utpote mihi plane incognitis” (A III,4 N. 146, p. 279). “Celeberrimo Boylio rogo data occasione officiosissimam a me salute nunties” (A III,4 N. 148, pp. 284f.). “Faites moy la grace, si Vous en trouvés l’occasion de faire mes baisemains à M. le Chevalier Boile, que j’honnore infiniment, et exhortés le a nous donner sans reserve bien des belles choses qu’il n’a indiquées qu’à demy ou dont il n’a rien encor donné” (A I,6 N. 122, pp. 266f.).

290

Chapter 1

In Leibniz’s epistolary exchanges with other correspondents, there are indications of the topics discussed during his meeting with Boyle, on February 12, 1673. Thus, for example, Leibniz referred in a letter to Oldenburg about three weeks later, on March 8, 1673,118 to Boyle’s allusion during their meeting probably to a recent review, in the Philosophical Transactions,119 of Ralf Bohun’s work A discourse concerning the origine and properties of wind (1671).120 Again, more than twenty years later and following Boyle’s death, Leibniz recalled in the PS to a letter of October 24, 1694, to Johannes Teyler that Boyle had informed him about a vegetable emetic from the West Indies.121 It was in a similar context that the only direct correspondence between Leibniz and Boyle materialized, namely after Boyle had sent through an intermediary a sample of an Indian seed to duke Johann Friedrich of Hanover. At the end of October 1677 Leibniz then wrote a short official acknowledgment to Boyle for the present received of “some doses of a certain Indian seed, which has a great force on the memory, and which possesses without doubt certain other extraordinary virtues”.122 Whereas the sole letter Leibniz sent to Boyle, and the exchanges of greetings through intermediaries were of a cordial nature, a range of critical remarks regarding Boyle are also to be found in Leibniz’s correspondence as, for example, in the previously cited letter of March, or April, 1681 to Friedrich Schrader.123 As regards practical science, and physics in particular, the question of priority in the development of the vacuum pump proved to be a point of contention. Boyle (together with Robert Hooke) had improved the vacuum pump, which had originally been developed by Otto (von) Guericke, and equipped with this pneumatic machine, or engine, Boyle had embarked on his epoch-making experiments on the properties of air. In Leibniz’s eyes, however, Boyle had unjustly received acclamation for the development of the vacuum pump to the detriment of Guericke, with whom he himself had corresponded in 1671 and 1672.124 In fact, the discovery of the new device by Guericke had first been made widely known through an appendix in Caspar Schott’s Mechanica 118 “Locutus est mihi Dominus Boylius de quodam praedictore ventorum, qui ei menstruas suas praedictiones mittere solebat, sic satis veraces” (A III,1 N. 9, p. 41). 119 Cf. Philosophical Transactions, vol. 7, no. 90, (January 30, 1673), pp. 5147–5150. 120 Cf. R. Bohun, A discourse concerning the origine and properties of wind: With an historicall account of hurricanes, and other tempestuous winds, Oxford, 1671. 121 “Feu M. Boyle m’a dit qu’il y a une Herbe des Indes qui fait vomir sans effort” (A III,6 N. 67, p. 204). 122 “quelques doses d’une certaine semence indienne, qui a un grand pouvoir sur la memoire, et qui sans doute est douée de quelques autres vertus extraordinaires” (A III,2 N. 91, p. 252). 123 Cf. note 109 above. 124 Cf. A II,1 N. 54. N. 62, N. 75, N. 77, N. 82, N. 83, N. 101, N. 103 and N. 104.

1676–june 1683

291

hydraulico-pneumatica, published at Würzburg in 1657,125 and in advance of Boyle’s publication. The title of Schott’s appendix had left no doubt as to the priority of Guericke in this discovery: Experimentum novum Magdeburgicum, … Inventum primo Magdeburgi a Ottone Gericke urbis illius consule. The seminal publication of Boyle three years later took the form of a letter addressed to his Anglo-Irish nephew Charles Boyle, Viscount of Dungarvan, with the title New experiments physico-mechanicall, touching the spring of the air, and its effects, (made for the most part, in a new pneumatical engine).126 At the outset, Boyle acknowledged his indebtedness, as regards the pneumatic engine, to Guericke in the following words: I should immediately proceed to the mention of my Experiments … by acquainting your Lordship … with the hint I had of the engine I am to entertain you of. You may be pleased to remember … I told you of a book that I had heard of, but not perus’d, published by the ingenious Jesuit Schottus  … He related how that ingenious Gentleman Otto Gericke, Consul of Magdeburg, had lately practiced in Germany a way of emptying Glass Vessels, by sucking out the Ayr at the mouth of the Vessel, plung’d under water: in regard this Gentleman was before-hand with me in producing such considerable effects, by means of exsuction of Air, I think my self oblig’d … to acknowledge the Assistance, and Encouragement the Report of his performances hath afforded me. But as few inventions happen to be at first so compleat, as not to be either blemished with some deficiencies needful to be remedy’d, or otherwise capable of improvement: so when the Engine we have been speaking of, comes to be more attentively consider’d, there will appear two very considerable things to be desir’d in it.127 125 Cf. C. Schott, Mechanica hydraulico-pneumatica: Qua praeterquam quod aquei elementi natura, proprietas demonstratur; omnis quoque generis experimenta hydraulico-pneumatica recluduntur; et absoluta machinarum aqua et aere animandarum ratio ac methodus praescribitur: Opus bipartitum …; Accessit experimentum novum Magdeburgicum, quo vacuum alii stabilire, alii evertere conantur, Frankfurt am Main, 1657. 126 Cf. R. Boyle, New experiments physico-mechanicall, touching the spring of the air, and its effects, (made for the most part, in a new pneumatical engine) written by way of a letter to the Right Honorable Charles Lord Vicount of Dungarven, eldest son to the Earl of Corke. By the Honorable Robert Boyle Esq., Oxford, 1660; M. Hunter and E. B. Davis (eds.), The works of Robert Boyle, 14 vols. London, 1999–2000, specifically vol. 1, pp. [141]–306. Regarding Boyle’s Anglo-Irish background, cf. D. Thorburn Burns, “Robert Boyle 1627–1691”, pp. 8–16 in: M. McCartney, A. Whitaker (eds.), Physicists of Ireland: Passion and precision, Bristol and Philadelphia, 2003. 127 pp. 158f.

292

Chapter 1

Nonetheless, Leibniz claimed for Guericke the status of “inventor primus” of the vacuum pump, in his correspondence from the mid-1670s. Thus, for example, in a letter to the English physician Nehemiah Grew, in July or August 1679, he referred to the noble Guericke, the consul of Magdeburg and first inventor of the vacuum pump.128 His conviction in this matter endured into the 1690s and probably for the remainder of his life. In the draft for a planned (but never dispatched) letter to Christiaan Huygens, from the first half of October 1690, Leibniz wrote: “As regards Mr Boyle, I am astonished that everybody attributes to him the [invention of the] vacuum pump of which Mr Guericke is the artificer and which Mr Boyle simply rendered more convenient [to use]”.129 Apart from any personal antipathy towards Boyle, Leibniz saw here a manifestation of prejudice against Germany and the Germans. In another deleted and never-dispatched text passage forming part of a draft of a letter to John Wallis of March 29, 1697, Leibniz claimed that no other nation was as outstanding as the German nation in acknowledging the achievements of others, and that the result of this exemplary behavior was that the Germans themselves were often disadvantaged.130 To these words he added the statement that all recognized, or acknowledged, what an outstanding man Robert Boyle had been.131 To German correspondents Leibniz expressed very similar sentiments, as for example, in a letter to Christoph Pfautz, co-editor of the Acta Eruditorum, on March 4, 1691.132 Leibniz recalled there an unidentified letter he had written to Oldenburg – perhaps that of March 8, 1673,133 but at all events before the correspondent’s death in September 1677 – in which he had pleaded for a 128 “apud Nobilissimum Gerickium Consulem Magdeburgensem antliae evacuantis inventorem primum” (A III,3 N. 327, p. 802). 129 “A propos de M. Boyle je m’étonne que tout le monde luy attribute la machine du vuide, dont M. Gericke est l’inventeur, et que M. Boyle a seulement rendue plus commode” (A III,4 N. 282, p. 618). 130 “Caeterum non ignoras nullam gentem esse proniorem Germanis in laudationem scriptorum exterorum. Usque adeo ut aliquando suis injuram faciant” (A III,7 N. 85, variant reading p. 351). 131 “Agnoscimus omnes quantus Vir fuerit Robertus Boilius”; cf. also J. G. O’Hara, 2018 (Introduction, note 61). 132 “Memini me aliquando Oldenburgio scribere, ut Gerikio vero inventori machinae falso Boilianae honorem restitueret, sed noluit ne Boilii et Anglorum gloriae minus favisse videretur. Ego alienissimus sum a talibus postulatis, optem tamen Germanos nostros paulo curiosiores esse in suis tuendis ornandisque, nec tantum aliis cum suorum injuria deferre, ut velut Echo quaedam, solis celebrandis exteris nati videamur, ipsis illis irridentibus et malam gratiam reddentibus, quos ultra meritam extollimus” (A III,5 N. 10, p. 67). 133 Cf. A III,1 N. 9, pp. 41f.

1676–june 1683

293

rehabilitation of Guericke. The ex-patriot Oldenburg did not wish however – according to Leibniz  – to derogate the reputation of Boyle, or to slight the English in this matter, a position that deeply alienated Leibniz, as he now told the correspondent. In a letter to the medical professor in Wittenberg, Georg Franck von Franckenau, on January 6, 1694,134 Leibniz once again referred to his letter to Oldenburg, as well as the latter’s anonymous review of Guericke’s Experimenta nova (1672),135 in the Philosophical Transactions of November 28, 1672.136 In this context, Oldenburg was portrayed by Leibniz almost as a turncoat, since he had not asserted and defended Guericke’s priority in the development of the vacuum pump. This had then been subsequently elaborated, with additions and improvements, and had found new, indeed outstanding, experimental applications in the hands of Boyle, the correspondent was told. Even as regards the investigation of the physical properties of the air, like weight or density, Guericke had been, in Leibniz’s view, the leading figure and Boyle his subaltern. In his correspondence with Samuel Reyher, in 1679 and 1680, he dealt with the respective contributions of Boyle and Guericke. Thus, in a letter of September 8, 1679, to Reyher, Leibniz – referring implicitly most likely to Schott’s Technica curiosa (1664), and explicitly to Guericke and most likely to his Experimenta nova (1672) – characterized Guericke’s contribution in the following words: “I know that Guericke and many others had already observed that evacuated vessels revealed different weights for the specific gravity of the surrounding air”.137 Then, in a subsequent letter of August 20, 1680, to Reyher, he also dealt with Boyle’s contribution, with the 1661 Latin version of his New experiments in mind. Referring here specifically to the defective static barometer type, which was used by Boyle and Guericke, and which consisted of a fairly large glass bottle, held in balance by a copper weight in very light balance pans, he wrote the following: 134 “… quod amicissimum  … nostrum Henricum Oldenburgium  … reprehendissem per literas, cum de Gerickiano opera, ubi in lucum prodiit pene maligne censuisset in suis Ephemeridibus, et quid caput erat dissimulasset, Gerickum fuisse verum Machinae Aerem exantlantis inventorem, quae nonnullis tantum additionibus, compendiis, et ad nova experimenta applicationibus sane egregiis Boiliana facta erat” (A III,6 N. 1, pp. 9f.). 135 Cf. O. v. Guericke, Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio, Amsterdam, 1672, and reprint Aalen, 1962; O. von Guericke, R. Glover Foley Ames (ed., trans.), The new (so-called) Magdeburg experiments of Otto von Guericke, (International Archives for the History of Ideas, no. 137), Dordrecht, 1994. 136 Cf. Philosophical Transactions, vol. 7, no. 88, (November 18/28, 1672), pp. 5103–5105. 137 “Scio jam Gerikium aliosque multos notasse, quod vasa evacuata diversum obtineant pondus pro gravitate specifica aeris circumfusi” (A III,2 N. 341, p. 827); cf. K. Schott, Technica curiosa sive mirabilia artis libris XII comprehensa, Würzburg and Nuremberg, 1664, pp. 45 and 52; O. v. Guericke, Experimenta nova, 1672, pp. 100 and 114f. (note 135).

294

Chapter 1

Boyle however applied a column just like Guericke and others but, since that device of self-measuring statics,138 (which was [later] applied by me for other better and useful applications), did not occur to him, it became necessary to examine a glass column in the weighing scale with new weights being added or removed as often as he wanted in order to know the increment and decrement [of its weight].139 More than 16 years later, Leibniz was continuing to insist on the leading role of Guericke. Thus, in a letter to the Italian physician and medical professor Bernardino Ramazzini, in January 1697, he wrote: “This Guericke (the great promotor of this doctrine whom Boyle followed) observed long ago that serene air [in good or fair weather] was heavier or weightier”.140 In the late 1670s and early 1680s, Leibniz’s occupation with a variety of topics in practical or concrete science was often prompted by a particular correspondent. Thus, for example, the medical professor in Helmstedt, Günther Christoph Schelhammer, confided to him, in January 1681, that he was working on a book about hearing and he requested Leibniz’s view of this matter. Here the correspondent wrote: My dissertation on sound is developing into a proper tract, but I will soon conclude the effort. If therefore, most noble Sir, you would be willing to give me the pleasure of communicating your sentiments concerning your observations on sound, I would ask that you take the opportunity to do so at the first occasion.141 Leibniz seized the opportunity to elaborately explain his thoughts on acoustics in letters of February–March 1681 and January 1682, respectively.142 Following 138 emphasis, underlining by Leibniz. 139 “Boylius quidem pilam adhibebat, quemadmodum et Gerickius et alii, sed quia hoc artificium staticae Autometrae (quod et ad alia magis etiam utilia a me adhibitum est) ei in mentem non venit, coactus est pilam vitream in lance examinare novis ponderibus additis vel adem[p]tis, quoties ponderis ejus incrementum vel decrementum scire voluit” (A III,3 N. 97, p. 252); cf. R. Boyle, Nova experimenta physico-mechanica de vi aeris elastica, et ejusdem effectibus, facta maximam partem in nova machina pneumatica, Oxford, 1661, pp. 186ff., also Rotterdam, 1669. 140 “Illud Gerickius (maximus hujus doctrinae promotor quem Boilius est secutus) dudum observavit aerem serenum esse ponderosiorem” (A III,7 N. 67, p. 264). 141 “Dissertatio mea de auditu in integrum tractatulum excrescit, sed propediem finem ei imponam, si itaque, Vir Nobilissime, stat tibi sententia observationibus tuis de sono me beare, rogo ut id proxima quaque facias occasione” (A III,3 N. 153, p. 318). 142 Cf. A III,3 N. 182 and N. 311.

1676–june 1683

295

Leibniz’s communications in these letters, Schelhammer acknowledged his contribution in the section of his book De auditu (1684), that treated the propagation of sound.143 When Mariotte brought up the same topic, in letters of March–April and August 8, 1681,144 respectively, Leibniz repeated his detailed explanations for the French physicist in a letter from the second half of August.145 Before Leibniz and Mariotte, however, sound and hearing were already understood as involving the sympathetic resonance between the vibrating air and various parts of the inner ear. The work of Claude Perrault, for example, who had treated the matter in his Essais de physique ou Récueil de plusieurs traitez touchant des choses naturelles (1680),146 was referred to, and criticized, by Mariotte in his letter to Leibniz of August 8, 1681.147 The cause of sound, according to Leibniz and as outlined in his reply of the second half of August,148 lay in the vibrations of tiny air particles. By means of such oscillations, the sound was carried from the resonating body to the ear. Independently of the sound level or loudness, or the sonority, the sound was transmitted at a constant speed. Accordingly, the oscillations of a resonating body, having a given tension, were always isochronous and so the same tone pitch was produced. Alas, Leibniz failed to publish his thoughts on acoustics, which belong to the most persuasive, or compelling, parts of his work on physics.149 A planned publication, in the form of an appendix to Schelhammer’s book, failed to materialize, as did sporadic plans for a publication in the Acta Eruditorum. Thus, in a letter of April 28, 1682, to Christoph Pfautz, Leibniz refers to “certain small dissertations I have in which are explained distinctly and in mechanical terms how sound is produced, which nobody has previously achieved”.150 Leibniz was referring here to the draft of an article he presumably wrote at the beginning of 1682, and with the title “De soni generatione …; excerpta ex Epistolis G. G. L.”.151 The article never did appear in the journal and Ernst Gerland, writing more than a hundred years ago, did not rule out the possibility that Leibniz’s thought on acoustics might have been influenced by Newton’s Principia mathematica 143 Cf. G. Ch. Schelhammer, De auditu liber unus, Leiden, 1684, specifically p. 125. 144 Cf. A III,3 N. 193 and N. 262. 145 Cf. A III,3 N. 269. 146 Cf. C. Perrault, Essais de physique ou récueil de plusieurs traitez touchant des choses naturelles, 3 vols, Paris, 1680, in particular vol. 2, pp. 246–247 (Du bruit). 147 Cf. A III,3 N. 262, p. 464 (note 144). 148 Cf. A III,3 N. 269, pp. 479–482 (note 145). 149 Cf. H. Breger, A III,3, Introduction, p. XXX. 150 “dissertatiuncula quam habeo, in qua distinctissime et plane mechanice explicatur modus quo fit sonus, quod hactenus nemo praestitit” (A III,3 N. 345, pp. 596f.). 151 Cf. GWLB, Hanover, Manuscript: LH XXXVII, 1 sheet (Bl. 18–19).

296

Chapter 1

of 1687.152 However, Leibniz’s published correspondence for the early 1680s has in meantime revealed that he had developed his thoughts on acoustics independently, and in advance, of Newton. According to Leibniz’s line of thought, as outlined in his letter to Schelhammer of February–March 1681,153 the hitherto existing theories of acoustics failed to address the heart of the matter, in that they neglected the most important aspect, namely the elasticity of the air. Only in terms of this property of the air, could it be explained how pitch is propagated so exactly. Regarding the creation of sound, Leibniz explained that, while the remote cause might be a blow to a body, viz. a percussion, the true, or immediate, cause would be its restoration, or a repercussion, which would manifest itself in the form of a vibration, or an oscillation. The constancy of pitch was thus a consequence of the general principal of the isochronism of elastic vibrations, or oscillations. Leibniz explained in detail the reasons for the fact that different pitches can be transmitted in the air, and that the ear can be simultaneously in resonance with different sonorous bodies. Schelhammer objected, in his reply of April 23, 1681,154 that not every sound was a vibration, or oscillation, giving the example of a blow to a cushion. Leibniz replied, on January 23, 1682,155 that the blow could be so strong that the cushion would be ruptured. However, anything that is ruptured must have previously been in a state of tension. To produce a sound, a blow would suffice that strained the threads of the cushion, and thus generated a striving for the restitution of the original state. The argument that every break, or fracture, is preceded by elastic tension is also the fundamental idea behind the theory of the breaking, or fracture, strength of materials, which was developed jointly by Leibniz and Mariotte in their correspondence. Whereas Galileo had  – in his Discorsi e dimostrazioni matematiche (1638)156 – considered the body to be absolutely rigid, and assumed a sudden break, Mariotte supposed that the body consisted of elastic fibers, or filaments, which bend before breaking, as he first explained to Leibniz in a letter of April 28, 1678.157 Mariotte had encountered the problem 152 Cf. E. Gerland, Geschichte der Physik von den ältesten Zeiten bis zum Ausgange des achtzehnten Jahrhunderts, Munich, Berlin, Oldenbourg, 1913, in particular p. 665. 153 Cf. A III,3 N. 182. 154 Cf. A III,3 N. 206. 155 Cf. A III,3 N. 311. 156 Cf. Galileo Galilei, Discorsi e dimostrazioni matematiche, intorno a due nuove scienze attenenti alla mecanica & I movimenti locali, Leiden,1638; S. Drake (trans.), Discourses and mathematical demonstrations concerning two new sciences pertaining to mechanics and local motions, Madison (Wisconsin), 1974. 157 Cf. A III,2 N. 163.

1676–june 1683

297

of fracture strength in the course of investigations of aqueducts, or conduits, for the royal waterworks. In a letter of July 20, 1682, he communicated to Leibniz his experimental results, as well as his critique of the theory of fracture strength, as developed by Galileo in the Discorsi.158 Corresponding to his different theoretical assumptions, Galileo had obtained a proportionality factor of 1/2, whereas Mariotte held a value of 1/4 to be correct. Leibniz, who at the time did not have access to a copy of the Discorsi (due to reconstruction work at the ducal library in Hanover), believed at first that both theoretical assumptions would lead to more or less the same result, as he told the correspondent in a letter from late July, or early August, 1682.159 Mariotte could however, he thought, convince him of the truth of the opposite view. The discussion continued over several letters, between August 1682 and January 1683,160 and finally resulted in Leibniz’s demonstration, in March–April 1683,161 on the basis of Mariotte’s assumption, that the correct proportionality factor was 1/3. Mariotte, writing on June 5, 1683, accepted the value found by Leibniz, concluding his communication with the words: “I will undertake the experiment as soon as possible[, in order] to establish whether it is necessary to take a third of the thickness in place of a half”.162 This result – that was published by Leibniz, in July 1684 in the Acta Eruditorum,163 and by Mariotte in 1686, in his Traité du mouvement des eaux,164 – has gone down in the history of elasticity, and of the strength of materials, as the “Mariotte-Leibniz theory”.165 The genesis of this theory is documented in the Leibniz-Mariotte correspondence. A further theme, that was portrayed in detail by Leibniz at this juncture, was in the field of geophysics, and was concerned with the variation of magnetic declination. Johann Georg Volckamer and Georg Christoph Eimmart had observed in Nuremberg the temporal variation of the magnetic declination – a phenomenon which, although previously known, was new to them  – and had communicated their findings in letters to other scholars. When Leibniz 158 Cf. A III,3 N. 376. 159 Cf. A III,3 N. 380. 160 Cf. A III,3 N. 394, N. 400, N. 436 and N. 437. 161 Cf. A III,3 N. 456, pp. 794f. 162 “Je feray l’experience au plustost pour sçavoir s’il faut prendre le tiers de l’espesseur au lieu de la moitié” (A III,3 N. 474, p. 832). 163 Cf. G. W. Leibniz, “Demonstrationes novae des resistentia solidorum”, Acta Eruditorum, (July 1684), pp. 318–325. 164 Cf. E. Mariotte, Traité du mouvement des eaux et des autres corps fluides, Paris, 1686, in particular the extract from the original version of the Traité sent to Leibniz (A III,3 N. 437) and corresponding to Mariotte, Oeuvres, Tome II, Leiden, 1717, pp. 461–465. 165 Cf. Introduction, note 67, and I. Todhunter (K. Pearson, ed.), 1886 and 2014, p. 6; C. Truesdell, 1960, pp. 59–64 (Introduction).

298

Chapter 1

learned of this, he contacted, in the fall of 1680, Sebastian Scheffer, a member of the Academia Naturae Curiosum (or the Academia Leopoldina), living in Frankfurt, with the proposal that the Academia arrange to carry out a series of corresponding measurements, at different places throughout the German empire. Thus, Leibniz wrote, at the end of the first draft of the letter, that from such corresponding temporal and spatial measurements  – with which the Academia might provide a service to humanity – he expected decisive results in a relatively short time, viz. on the basis of observations repeated monthly over a year.166 With the help of a natural law for the spatial and temporal variations of magnetic declination, he thought that one of the most discussed practical problems of the time might be solved, namely the problem of the determination of longitude at sea, as he wrote near the end of the dispatched letter to Scheffer.167 Regarding this point in particular, Volckamer and Eimmart  – to whom Scheffer had passed on Leibniz’s proposal – reacted in a joint letter for Leibniz, in early May 1681, with a certain degree of skepticism.168 Volckamer forwarded a transcribed copy of an essay by Erasmus Bartholin, which revealed that the values for the magnetic declination, in Copenhagen and on the neighboring island Ven, varied appreciably, the changes being discontinuous and, accordingly, without apparent practical applicability. Thereupon, Leibniz presented in a further representation, included in a letter of June 20, 1681  – sent to Scheffer for forwarding to Volckamer,169 and subsequently referred to by the latter on August 22,170 as a wonderful letter – his detailed thoughts on the matter, which were supported by a profound knowledge of the relevant literature. Two essential assumptions in particular were defended by Leibniz, namely the validity of a law for the variation of magnetic declination, and his heuristic principle or law of continuity. Descartes had attributed declination to a certain randomness, in the make-up and structure of the earth, whereas Leibniz was convinced of the existence of a regularity that could be detected by relatively simple means. This rule, or law, would also satisfy the requirements of the continuity principle. Referring to various measurements, including those 166 “Quodsi iidem suas observations quovis mense repetere vellent, ubi commodum erit, atque ita unius anni colligere, nobisque communicare; ausim sperare hoc arcani hujus detectionem. Atque si veluno loco praestabit celeberrima Naturae Curiosorum societas, satis genus humanum sibi obligaret” (A III,3 N. 117, p. 279). 167 “sperarem arcanam variationis regulam inveniri posse, quod et mire utile navigantibus, et honorificentissimum Curiosis nostris futurum est” (p. 280). 168 Cf. A III,3 N. 217. 169 Cf. A III,3 N. 248. 170 Cf. Scheffer’s letter to Leibniz of August 12 (22), 1681 (A III,3 N. 271).

1676–june 1683

299

from a sea voyage, Leibniz showed that, in general, the magnetic declination only changed slowly and gradually, and accordingly was probably spatially and temporally continuous. In the year 1679 – through the encouragement of Mariotte – a further focus of geophysical investigation was added in Leibniz’s correspondence, namely meteorology. This encompassed the use of measuring instruments, like the barometer, thermometer and hygrometer, and found expression particularly in the correspondences with Philipp Lohmeier,171 and Samuel Reyher.172 In Leibniz’s correspondence with Mariotte, widespread attention was also given to the discussion of questions of hydrostatics, of water power, of water raising machines, and indeed, the previously considered discussion of the fracture strength of materials was derived from this problem area. The mutual interests of Leibniz and Mariotte came together here. From 1680, Leibniz was occupied with problems of water power, and in particular, of water lifting devices in the Harz mountains. Also at this time, Mariotte was working on his (posthumously-published) Traité du mouvement des eaux,173 which was inspired by similar projects of the French king. Mariotte provided answers, for his part,174 to questions of Leibniz,175 or he reported, of his own accord,176 about things “which could be of great value on certain occasions”.177 Matters relating to astronomy, and celestial mechanics, had only marginal importance in Leibniz’s correspondence in the late 1670s, and early 1680s. Tschirnhaus, for example, reported to Leibniz about the planetaria of Ole Christensen Rømer and of Huygens,178 and Scheffer was able to inform him about a fiery celestial appearance, which he regarded as something supernatural.179 Tschirnhaus, on the other hand, referred to Edmond Halley’s comet,180 and Pfautz and Samuel Reyher mentioned the comet of 1680.181 Pfautz requested, on October 29, 1681, Leibniz’s expert opinion about a comet 171 Cf. A III,2 N. 336. 172 Cf. A III,2 N. 333, N. 338, N. 339 and N. 341. 173 Cf. note 164. 174 Cf. A III,3 N. 62 and N. 193. 175 Cf. A III,3 N. 25. 176 Cf. A III,3 N. 365. 177 “je crois que cela pourra estre de grande utilité en quelques occasions” (A III,3 N. 131, p. 292). 178 Cf. A III,3 N. 356 and N. 399, respectively. 179 Cf. A III,3 N. 430. 180 Cf. A III,3 N. 399. 181 Cf. A III,3 N. 155 and N. 169, respectively. Regarding the comet of 1680, cf. C. Meinel (ed.), Grenzgänger zwischen Himmel und Erde: Kometen in der Frühen Neuzeit, (Kataloge und Schriften der Staatlichen Bibliothek Regensburg, vol. 1), Regensburg, 2009 and 2022 (digital

300

Chapter 1

that had been observed over several months from November 1680. Newton and Gian Domemico Cassini had – in contrast to John Flamsteed and Jean Charles Gallet  – concluded (incorrectly) that two comets were involved, and Pfautz hoped Leibniz might be able to resolve the issue with his own observations.182 The observation of two comets was based on a false assumption, or interpretation, and Leibniz – notwithstanding the fact that he had not been able to undertake observations himself – was able, in December 1681, to provide an appropriate reply to Pfautz’s question, insisting that twin comets were not involved, and referring to observations of an earlier comet, from December 1664, with perhaps explanations given by Adrien Auzout, or Johannes Hevelius, regarding that earlier comet in mind.183 In the years 1677–1679, questions from certain areas of optics concerning, for example, the theory of colors, and optical instruments such as the microscope and the telescope, were a pronounced interest in Leibniz’s correspondence, in particular with Mariotte and Huygens. This interest in optics would continue in the early 1680s. Already before the publication, in the Acta Eruditorum in June 1682, of his principle of the easiest light path under the title “Unicum opticae, catoptricae et dioptricae principium”,184 Leibniz discussed the principle in correspondence with Huygens, specically in letters from (on January 11, 1680), and to (on February 5, 1680), this correspondent.185 Then, following the publication of the article in question, objections, which were raised by Basilius Titel and Pierre Ango, were reported to Leibniz on November 18, 1682, by Christoph Pfautz, to whom he duly replied, on February 17, 1683.186 This exchange provided a further reason for him to express his views on the matter. Pierre de Fermat (1607–1665), as well as the Jesuits Ignace Gaston Pardies (1636–1673) and Pierre Ango187 – the latter in his work L’Optique (1682)188 – had formulated a principal of the shortest time and had supposed that light moved

edition), and in particular chap. 6 (Segmentierung der Diskurse: Der Komet von 1680), pp. 91–112. 182 “De Cometa nupero, uno an duplici variae sunt sententiae: quid Tibi, ex observationibus quas dubio procul domesticas propriasque habes, videatur” (A III,3 N. 289, p. 506, and annotation). 183 “Cometam eundem fuisse non geminum … Eadem quaestio eadem responsio fuit circa cometam anni ni fallor 1665. Observationes circa nuperum Cometam mihi ipsi instituere non licuit” (A III,3 N. 301, p. 525, and annotation). 184 Cf. note 56 above. 185 Cf. A III,3 N. 4 and N. 22; HO, 8, pp. 256–258 and pp. 267f., respectively. 186 Cf. A III,3 N. 419, pp. 740–742, and the non-extant reply N. 440, p. 777. 187 Cf. N. 419, p. 741, annotation. 188 Cf. P. Ango, L’Optique divisée en trois livres, Paris, 1682.

1676–june 1683

301

more slowly in a denser medium.189 However, according to Leibniz, the light followed the easiest path, or the “via facillima”, whereby a greater resistance of the medium leads to a greater velocity. After Pfautz once again referred to the issues raised, on May 8, 1683,190 Leibniz responded, on May 14, stating clearly that he did not claim priority in the formulation of the minimal principle of optics, and that both Willebrord Snel(l) van Royen (1580–1626) and Fermat had preceded him.191 Just the same he stressed that he could – by means of his differential calculus – provide a considerably shorter proof of the minimal principle than Fermat, in particular, had done and, moreover, that the demonstration of Snell no longer existed. He insisted that even the ancients had already used the same artifice in catoptrics,192 and that he was simply bringing together, or reconciling, the metaphysical principle of the shortest path with the mechanical principle of the composition of movements.193 In November 1676 – when Leibniz was on his way to Hanover for the first time – he visited the Dutch pioneer of microscopy, Antoni van Leeuwenhoek, in Delft. Leibniz’s continuing interest in Leeuwenhoek, and his work, found its expression during the years and decades that followed, in the form of numerous utterances regarding him, in letters sent to a variety of correspondents. It was only in the summer of 1715, that a direct correspondence between the two finally developed. And so, in the last fifteen months of Leibniz’s life, at least eight letters were exchanged between the two.194 However, the first report about Leibniz’s meeting with Leeuwenhoek is to be found in a letter he sent from Amsterdam, which was written shortly after the encounter (on November 28, 1676) to Henry Oldenburg in London. There he reported that he had fulfilled Oldenburg’s request for him to deliver a letter to Leeuwenhoek.195 As regards Leeuwenhoek’s microscopic observations, he expressed here his delight and hope that the curiosity of others might be awakened in this way, which in turn would be of great importance for the advancement of physical 189 Cf. A. I. Sabra, 1981, chap. V and VII (Introduction, note 86). 190 Cf. A III,3 N. 461, specifically p. 803. 191 “Demonstratio theorematis dioptrici non est tanti, ut ideo me velim nominari, nam habere jam eam Snellius et Fermatius ante me” (A III,3 N. 463, specifically pp. 806f. and annotations). 192 “Sed ego unifico compendio duarum lineolarum mei calculi officio, quod Fermatius multis paginis, Snellii enim demonstratio non extat, imo veteres eadem arte in Catoptricis jam usos ostendo” (p. 806). 193 “et hujus principia Meraphysici (de minima via) consensum cum mechanico principio compositionis motuum concilio” (pp. 806f.). 194 Cf. J. G. O’Hara (in M. Kempe, ed., 2016), and L. C. Palm, et al., 2018, specifically Letters 316–320, 322, 323, 326 (Introduction, note 95). 195 Cf. A III,5 N. II (Supplement), specifically p. 6.

302

Chapter 1

science.196 Shortly after his arrival in Hanover (in the last days of the year 1676), he reported to duke Johann Friedrich about his most important contacts in the Netherlands. These included, first and foremost Christiaan Huygens – whose opus on the pendulum clock, Horologium Oscillatorium (1673),197 he alluded to – and four others, namely Jan Hudde, Baruch de Spinoza, Theodor Cranen and of course Leeuwenhoek. Thus he wrote to the duke: In Holland I have Mr [Christiaan] Huygens de Zuylichem, the inventor of pendula, whose brother [Constantijn] is secretary of state to the Prince of Orange; likewise Mr [Jan] Hudde, Burgermaster of Amsterdam, and one of the leading mathematicians of the century, not to mention [Baruch de] Spinosa at the Hague, [Theodor] Cranen at Leiden, [Antoni van] Leeuwenhoek at Delft, and others.198 In the first draft of a letter for Jean Paul De La Roque, from the end of 1677, Leibniz reported about Leeuwenhoek in the context of microscopy, and of lens optics in particular. He stressed the value of microscopic observation for medicine, and the medical arts, referring specifically to Leeuwenhoek’s observation of animate beings, or little animals, in water interfused with pepper,199 which he most likely had learned about during their meeting in Delft, in November 1676, and which had been published in the Philosophical

196 Here he wrote the following words: “Leewenhoekii observationibus valde sum delectatus, optarimque plures alios passim eadem curiositate animari, quod magno rei Physicae fructu futurum esset”. 197 Cf. Ch. Huygens, Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae, Paris, 1673; HO, 17 (L’horloge à pendule 1656–1666), pp. 1–153 and pp. 155–236; HO, 18 (L’horloge à pendule 1666–1695), pp. 1–702. 198 “En Hollande j’ay Monsieur [Christiaan] Hugens de Zuylicom inventeur des pendules, dont le frere [Constantijn] est secretaire d’Estat du Prince d’Orange; item Mons. [Jan] Hudde Bourguemaistre d’Amsterdam un des premiers Mathematiciens du siècle, sans parler de [Baruch de] Spinosa à la Haye, [Theodor] Cranen à Leide, Lewenhoek à Delpht, et autres” (A I,2 N. 7, p. 17). 199 “Usus in eo consistit: quod lentes quo sunt minores hoc magis amplificant minusque obscurant objectum crassitie sua  … Mirae se offerent structurae rerum, magni forte ad medicinae artiumque vitae utilium perfectionem usus et species animalculorum apparebunt variae qualia nuper in aqua quae nocte super pipere stetit nasci observavit diligentissimus Leewenhoekius  … In quo industria Leewenhoekii plurimum laudanda atque imitanda est” (A III,2 N. 94, pp. 257f.).

1676–june 1683

303

Transactions in March–April 1677.200 In a copy of a further draft (which most likely mirrored the dispatched letter), Leibniz then wrote that: The use of these lenses is easy to understand, for one knows that they advantageously enlarge the object to the extent to which they are small and, although as a result they reveal but a small part, they obscure it less as a result of their own small size. That is why, if you put one in the orifice of a brass or silver plate in such a way that the eye be covered, and the object be illuminated from the other side all vis-à-vis the lens, you will be surprised by its size and form. To commence working with it, nothing is more appropriate than a flea. You will find that the majority of things of nature, up to the size of a pin, are transparent when they are fairly thin. You could see, for example, that pepper causes animalculae [larvae] to be produced in water, as Mr Leeuwenhoek, whose industry in this area deserves commendation, has shown; and you will find many other useful things for the advancement of medicine and the arts.201 Following Oldenburg’s death, in September 1677, Leeuwenhoek sent a series of reports about his microscopic investigations to the Royal Society. All in all, between September 1677 and April 1679, he sent eight such reports of which that concerning the production and nature of mammalian or human sperm, entitled “Observationes de natis e semine genitali animalculis”, deserves particular mention.202 Accordingly, Nehemiah Grew, who acted as secretary of the Society from 1677 to 1679, was able to inform Leibniz, on August 4, 1678, about 200 Cf. A. van Leeuwenhoek, “Observations … concerning little animals observed in rain- well-  and snow-water, as also in water wherein pepper had lain infused”, Philosophical Transactions, no. 133, (25 March 1677), pp. 821–831. 201 “L’usage de ces lentilles est aisé à comprendre; car l’on sçait qu’elles aggrandissent d’avantage l’object à measure qu’elles sont petites et quoyque par consequent, elles n’en decouvrent qu’une petite partie elles l’obscureissent moins à cause de leur peu d’épaisseur. C’est pourquoy si vous en mettés une dans le trou d’une lame de cuivre ou d’argent, en sorte l’oeil soit à couvert et l’object illuminé de l’autre costé tout vis à vis la lentille, vous serés surprise de sa grandeur et de sa figure. Pour commencer à s’en servir rien est si proper qu’une puce. Vous trouverés que la pluspart des choses de la nature jusqu’au bout d’une aiguille, sont transparentes, quand ells sont assez minces. Vous pourrés voir par exemple que le poivvre fait naistre des vers dans l’eau comme M. Leewenhock [sic] dont l’industrie en ces matieres merite des louanges, a observé: et vous trouverés plusieurs autres choses utiles pour l’avancement de la medicine et des arts” (A III,2 N. 94, pp. 260–262). 202 Cf. A. van Leeuwenhoek, “Observationes de natis e semine genitali animalculis”, Philosophical Transactions, no. 142, (December 1677–February 1678), pp. 1040–1043.

304

Chapter 1

Leeuwenhoek’s continuing commitment to microscopic research, and he referred in particular to the discovery of swarms of minute animate beings in water interfused for some days with pepper. All said, more than a million little animals were to be found in a single drop of the fluid.203 Three months later, on November 6, 1678, Johann Sigismund Elsholz wrote to Leibniz from Berlin, and he recalled a visit by Johann Daniel Crafft, in the previous summer, during which microscopy was discussed. Elsholz now hoped to obtain a microscope from Holland through Leibniz’s influence. Thus he wrote: While I also showed Mr Crafft at the time some microscopes, he recommended to me above all those being made at present by Mr Samuel von Müßchenbroeck in Leyden, with five or six lenses, which can be varied and inserted according to whether the bodies, which one is observing, are large or small … You would thus do me a great favor, Sir, if you were to be so good as to help me in acquiring such a microscope, with of course adequate remuneration. He also reported at the time about a new invention, consisting of a small little glass sphere and being made by a certain Leeuwenhoek in Delft, one of which I would also very much like to have.204 Evidence of Leibniz’s own interest in the spherical, or globular, microscope is found in a letter to Christian Philipp in Leipzig, on November 22, 1678. On this occasion he wrote: The first person to discover the small globular microscopes was Mr Hudde, who is at present Burgermaster of Amsterdam. He did this more than 12 years ago. Mr Leeuwenhoek has improved these, and used them 203 “Dnus Leeuwenhoeck Delphensis Naturae Indagator maxime sedulus, Nobis Transmisit repetitas Observationes Microscopicas, de certis Animalculis exquisite minutis, satis tamen vivacibus, in Aqua communi, piperis integri per aliquot dies infusi viribus impraegnata conspiciendis. Tuto dixeris, plus quam 1 [00]0 000, seu millena mille Animalium guttae uni innatare” (A III,2 N. 192, pp. 479f.). 204 “Dieweil ich auch dem H. Krafft damahls einige Microscopia sehen ließ, hat er mihr vor allen gelobet die jenige art, welche gegenwertig verfertiget werden von H. Samuel von Müßchenbroeck  … in Leyden mit 5 oder 6 Gläsern, die man verendert und einschiebet, nachdem die corpora, die man besehen will, groß oder klein sind … Mein h. Herr würde mich also höchlich obligiren, wan Er so gütig seyn, und mihr zu einem solchen Microscopio, ümb gute Bezahlung, behülfflich erscheinen wolte. Er hat zugleich noch von einer newen invention meldung gethan, welche aus einem sehr kleinen Glaß=Küglein bestünde, und von einem in Delfft namens Lewenhuch [sic] verfertiget würden: dergleichen ich dan auch gern haben möchte” (A I,2 N. 364, pp. 378f.).

1676–june 1683

305

with great success. At the moment, a great fuss is being made in France about these as a new discovery.205 From Elsholz’s letter to Leibniz, of February 8, 1679, it is evident that the correspondent was already in possession of a microscope with a single lens (“unica lenticula vitrea”), and had in mind a compound instrument with two lenses (“microscopium globularium”). And so he wrote: I thank you very much for the report received about the spherical or globular microscopes. I find Mr Thomas Bartholinus [1616–1680] … has the very same Mr Leeuwenhoek in mind, and Mr Joh. Chr. Sturm … has provided a figure of his [Leeuwenhoek’s] first kind of microscope, which is of the simplest construction consisting of a single glass lens. I already have such an instrument, and my thoughts are that, if in place of the said lens a globule made of Venetian glass were to be introduced, there would then exist a globular microscope … the best solution would be for your lordship to do me a favor and help me acquire, for good remuneration, a complete globular microscope along with its pedestal.206 Johann Georg Graevius of the University of Utrecht likewise informed Leibniz, in a letter of March 24, 1679, about Leeuwenhoek, whose activities were all that he found noteworthy in mathematics or physics, referring specifically to the extraordinary numbers of little animals, or animalcula, observed under the microscope in blood and human semen, and the communication of results to the Royal Society of London.207 Finally, on January 18, 1681, Christoph Pfautz 205 “Le premier qvi a trouué les petits microscopes globulaires est Mons. Hudde qvi est apresent Bourguemaistre d’Amsterdam. Il en a fait il y a plus de 12 ans. Mons Lewenhoek les a embellis et mis en usage avec grand succés. Maintenant on en fait grand bruit en France, comme d’une chose nouuelle” (A I,2 N. 371, pp. 385f.). 206 “dancke ich sehr wegen ertheilter nachricht von den Microscopiis globulariis. Ich finde, daß H. Thom. Bartholinus … eben desselben H. Leewenhoecks gedencket, und H. Io. Chr. Sturmius … stellet in einer Figur vor sein primum Microscopij genus, quod simplicissimae structurae est, et unica lenticula vitrea constat. Ein solches habe ich albereit, und sind meine gedancken, wan an stat selbiger lenticulae ein solcher Globulus aus Venedisch glaß hinein gesezet würde, daß es alßdan ein Microscopium globularum seyn könnte … Das fertigste Mittel wäre, wan M. h. Herr mihr diese gunst erzeigen, und ein solch ganz fertiges Microscopium globularium samt seinem Pedestall ümb gute satisfaction zu wege bringen” (A I,2 N. 403, pp. 419f.). 207 “In Physicis et Mathematicis vix quicquam memorabile hic nuperius inventum, nisi quod Delfis sit, qui mirabilia animalcula et infinita in sanguine et semine humano detexit subsidio microscopii accuratissimi, de quibus observationibus extant quaedam epistolae ad societatem Anglicam exaratae Anglice” (A I,2 N. 433, p. 448).

306

Chapter 1

reported to Leibniz about a tour he had undertaken in the previous year to the Netherlands and Holland – visiting Amsterdam, Antwerp, Brussels, Delft, Leiden and Utrecht – as part of an intended journey to England, and specifically about his meetings with Graevius in Utrecht, and Leeuwenhoek in Delft.208 Concave mirrors were yet another topic in Leibniz’s correspondence at this juncture. In letters exchanged with Tschirnhaus, Leibniz was informed about the correspondent’s progress in the manufacture of such concave mirrors,209 and he expressed his own judgement on the matter.210 Leibniz also discussed problems of optics with the indefatigable experimenter Mariotte,211 whose tract De la nature des couleurs212 he avidly awaited in August 1681.213 Leibniz’s suggestion of a possible attribution of the color of blood to refraction was convincingly rejected by Mariotte,214 without however Leibniz conceding defeat on the question.215 Mariotte, who in his letters came as a matter of course directly to the point in question, and reported briefly and concisely about new developments in science, was for Leibniz the most interesting correspondent on questions of physics at this juncture. Mariotte reported in detail about his own experimental research, as well as about books in progress. In addition to the nature of an elastic collision,216 and the mode of operation of the wedge,217 motion in a resisting medium received particular attention.218 In a letter from the first half of June, 1682, Leibniz asked Mariotte about experiments carried out by the Académie des Sciences on this topic, in the hope of obtaining support for the mathematical treatment of the process of resisted motion leading to the science of ballistics. Referring to the third and fourth days in Galileo Galilei’s Discorsi, he wrote here: It pleased me one day to consider that Galileo, on treating the descent of heavy bodies, had neglected the resistance of the air, whose effect is 208 “Itaque uno Graevio Ultrajecti salutato … Angliam petere statuimus … Ad Batavos reversi, Bruxellas et Antwerpiam excurrimus  … in Batavis Ultrajecti, Lugduni et Amsterodami praecipue exegimus … et Delphis in transitu Dno Lewenhoeck, salutatis” (A III,3 N. 155, pp. 319f.). 209 Cf. A III,3 N. 199, N. 356, and N. 455. 210 Cf. A III,3 N. 233, and also N. 123. 211 Cf. A III,3 N. 62, N. 262 and N. 341. 212 Cf. E. Mariotte, De la nature des couleurs, Paris, 1681. 213 Cf. A III,3 N. 269. 214 Cf. A III,3 N. 193. 215 Cf. note 213. 216 Cf. A III,3 N. 474. 217 Cf. A III,3 N. 365 and N. 370. 218 Cf. A III,3 N. 5, N. 24, N. 62, N. 68, N. 79 and N. 394.

1676–june 1683

307

nonetheless notable. I searched for what was the true proportion under consideration of this resistance. The consideration is very subtle and comes down to one of those problems of mathematics, which I call transcendental since they are independent of algebra. I believe nonetheless, that I found the solution on making certain physical assumptions which experience or experiment should confirm. That is the reason why, not doubting at all that your people have made, or are making, a considerable number of experiments regarding the time of descent of bodies, and regarding that which occurs if a heavy body is projected by a determined force … I entreat you, Sir, to communicate to me those experiments, and others relating to ballistics. For, I imagine that I could perhaps deduce certain things to help establish mathematically this fair science.219 4

Technology: Mining in the Harz District

Following a first preparatory stay in the fall of 1679, Leibniz commenced his activity in ore mining in the Harz mountains – which represented an important economic factor for the Welf territories – in the summer of 1680. With the construction of windmills, he aimed to tap into a new power source for the drainage of the mines. Previously, water wheels had been employed in order to operate the pumping machinery, used for draining the mines. These water wheels were powered using rainwater collected in ponds or reservoirs. Thus, the operation of the ore mines had depended on the available quantity of rainwater and, in times of drought, ore production was often considerably reduced. At first Leibniz anticipated relatively problem-free and rapid success for his plans to employ windmills, notwithstanding the protracted negotiations with the mining authority and with duke Ernst August in Hanover.220 219 “M’amusant un jour à considerer que Galilei en determinant la descente des corps pesans a negligé la resistence de l’air dont l’effect portant est notable, j’ay cherché quelle seroit la vraye proportion en adjoutant la consideration de cette resistence. Consideration qui est tres subtile, et qui revient à un de ces problemes de Geometrie, que j’appelle Transcendans, parce qu’ils sont independans de l’Algebre. Je croy pourtant d’en avoir trouvé la solution en faisant certaines suppositions physiques que l’experience doit establir. C’est pourquoy ne doutant point que vos Messieurs n’ayent fait ou fait faire un nombre considerable d’experiences touchant le temps de la descente des corps et touchant ce qui arrive, quand un corps pesant est jetté par une force determine … je vous supplie Monsieur de me communiquer ces experiences et autres qui se rapportent à la ballistique. Car je m’imagine que j’en pourray peutestre tirer quelque chose, pour determiner Geometriquement cette belle science” (A III,3 N. 370, p. 665). 220 Cf. the Introduction to A I,3.

308

Chapter 1

Thus, he wrote the following to Tschirnhaus, from near Nordhausen on May 23, 1681: “I will be occupied this summer in completing at last my windmills which I am applying in the mines”.221 In the course of events, he was absolved from this commitment only in the summer of 1685, and then without a satisfactory outcome. Fresh difficulties arose repeatedly forcing him to continually alter his plans. Thus, for example, an iron crankshaft was at first envisaged as a connection between the windmill and the field rod, that was intended to transmit the energy to the pumping machinery. Since, however, the requisite furnace was inoperative for a lengthy period, an alternative construction had to be devised, as the miller and master carpenter Hans Linsen informed him on December 12, 1680.222 This temporary arrangement then led to further repair and maintenance work.223 Only in the summer of 1682 was it possible to install the crankshaft, which weighed 13 hundredweight, as is evident from Linsen’s letter of August 2 of that year.224 Three week later, on August 24, Linsen informed him that, for the transport of an iron shaft in the hilly country, as many as 16 horses were required.225 To such extraneous influences, one can also add the prevailing weather conditions. Operations had to be suspended during the winter months. Then, on April 7, 1681, Leibniz complained to Johann Daniel Crafft about the diabolic weather conditions that were holding up operations, and thus causing him to lose time in the Harz mountains.226 In addition to such external factors, internal difficulties of Leibniz’s own designs also played a role in the delays. The transfer ratio in the cog and rung internal transmission of the windmill –namely, that between the cogs of the cogged wheel and the vertical staves of the lantern pinion – had to be altered several times in 1681–82 from its initial state in June 1680.227 Likewise, the success of a project involving power transmission by means of compressed air – referred to in letters to Linsen in September and October 1682228 – proved not to be feasible with the materials available. And so, Leibniz was to acquire engineering experience through a series of unforeseen setbacks. In addition, the lack of cooperativeness on the part of the local mining authority, and of the mining officials, added greatly 221 “Ego hac aestate occupabor in absolvendis tandem meis molendinis ventaneis, quae fodinis applico” (A III,3 N. 233, p. 428). 222 Cf. A III,3 N. 136. 223 Cf. A I,3, p. 184. 224 Cf. A III,3 N. 382. 225 Cf. A III,3 N. 391. 226 “Das böse wetter embarassirt mich sehr, und macht mich zeit aufm Harz verlieren” (A III,3 N. 198, p. 386). 227 Cf. A III,3 N. 77 and N. 78. 228 Cf. A III,3 N. 403 and N. 408.

1676–june 1683

309

to the difficulties. Thus, in an underhanded manner, the Harz project, that Leibniz had originally hoped to complete successfully in one or two summers, developed into a time-consuming preoccupation over several years. In the 42 month period, between January 1680 and June 1683, Leibniz travelled fourteen times to the Harz district, and he spent a total of 18 months there. On the occasion of one of the few palpable successes – which however soon proved to be fleeting – Leibniz told Crafft in retrospect, on March 26, 1682, that he could have ceded on a hundred occasions to the multifarious opposition forces he had to face, if he had not wanted to show that it was a core feature of his mindset (or of his “humor”) not to let up until he had carried out what he had set out to do.229 Leibniz’s unusual stubbornness here is remarkable, and it may perhaps be attributable to the fact that not just the proof of the practicality of a theoretical idea was at stake, but also his reputation at court and his future influence on the new duke. The correspondences relating to windmill construction in the early 1680s – namely those with Hans Linsen, Heinrich Schütz, Reinhart Pfeffer and Johann Hagen – include estimates of costs, design drawings, receipts concerning wages paid and smithy costs, reports of the master carpenter Linsen during Leibniz’s absences, as well as his instructions for Linsen. From these correspondences – as well as from those with duke Ernst August and with the mining office230 – certain insights can be gleaned concerning Leibniz’s plans, his visits to the mining district, and the progress of operations. Naturally, Leibniz’s commitment to his windmill venture, as well as his interest in discoveries and innovations in this area, are also reflected in a range of other correspondences. Thus, in a letter from the end of November, or early December, 1679, Leibniz informed Christiaan Huygens about his windmill project for draining the mines, and that was above all intended to replace the water wheel-powered system, that suffered especially in times of drought. He specified, for the depth at which the water lay in the mine, a value of the order of 100 mining measures of length, or “toises” – intended was probably ‘Lachter’ or ‘Berglachter’ (being about 1.8 to 2.0 meters) – and so he wrote: I plan to endeavor to achieve that wind mills be applied in the Harz mines, which belong to my sovereign, in order to expel the subterranean waters, 229 “Ich habe mich vieler addressen bedienen mußen, vmb die Sach bey vielfälltig oppositionen so weit zuebringen, hette es auch wohl 100 mahl liegen laßen, wenn ich nicht zeigen wollen, daß Mein humor seye, nicht nachzuelaßen, biß ich außgeführet, was ich angefangen” (A III,3 N. 336, p. 579). 230 Published in the volumes of the first series of the Academy edition (A I).

310

Chapter 1

which hamper the miners and which one normally removes by means of water wheels, which are powered by water from certain mountain streams, or large reservoirs. However, water is often wanting in times of drought. The depth from which the subterranean water has to be raised is sometimes up to a 100 ‘toises’, and more. I would appreciate your opinion regarding the above.231 In answer to this query, Huygens communicated his opinion in the closing paragraph of a letter of January 11, 1680. He proposed using a paternoster system, using a chain and buckets for lifting the water from the mine. Although technically possible for depths of 100 lachter, or fathoms (“toises”), Huygens thought any investment in machinery ought to match the expected return. He recalled learning, from a Scottish gentleman, about such a chain and bucket pumping system that had been successfully employed in coal mining, albeit using horse power, or horse mills, rather than water power. Thus, the correspondent wrote: For the windmills which you would like to apply for removal of the water from the mines, I believe that it is practical, and that the chain and bucket system is the best method. But the depth of 100 units of length is considerable, and it is up to you to establish if the richness of the mines can be a recompense for the cost of the machines, which as you know is considerable. I remember that a Scottish gentleman told me once that, using such chains, he had drained coal mines whose depth was not less than those you referred to. However, it appears that he only used horse mills which would operate very slowly.232

231 “J’ay dessein de faire en sorte qu’on employe des moulins à vent aux mines du Harz qui appartiennent à mon maistre, pour en puiser l’eau sousterraine, qui empeche les travailleurs, et qui s’en tire ordinairement par des moulins que l’eau venant de quelques ruisseaux et grands reservoirs fait agir. Mais l’eau manque souvent dans un temps sec. La profondeur dont il faut tirer l’eau sousterraine est quelque fois jusqu’à 100 toises et plus. Je souhaitte vostre avis là dessus” (A III,2 N. 361, p. 899 and p. 904; HO, 8, pp. 251f.). 232 “Pour les moulins à vent que vous avez envie d’emploier pour vuider l’eau des mines, je crois que cela est pratiquable, Et que la chaisne avec des seaux est le meilleur moyen. Mais la profondeur de 100 toises est bien grande et c’est à vous à examiner si la richesse des mines peut recompenser les fraix de ces machines qui comme vous sçavez coustent beacoup. Je me souviens qu’un Siegneur Escossois m’a dit autrefois qu’avec de chaines comme cela il vuidoit l’eau de ses mines de charbon, qui n’avoient pas moins de profondeur que celles dont vous parlez. Il me semble pourtant qu’il n’y emploioit que des chevaux, ce qui devoit aller bien lentement” (A III,3 N. 4, pp. 48f.; HO, 8, pp. 256–258).

1676–june 1683

311

In his reply to this, on February 5, 1680, Leibniz then elaborated on his Harz project. A special difficulty was the corrosiveness of the water in the pits, which would damage the metal components of a bucket and chain pumping system, he told the correspondent. Instead it was necessary to employ a score of pumps (having wooden cylinders), which were arranged in tiers one above the other, and which were powered by water wheels. His idea, Leibniz explained, was to avail of wind power to service and replenish the reservoirs, which otherwise might run dry in times of drought, while retaining the existing system of pumps, and tiers of pumps. There remained the difficulty that the wind supply was erratic, and he told that he had thought of an arrangement where the windmill sails might be rotated a little, in order to remain in the direction of the wind, and where the inclination of the axis of the sails might be varied according to the strength of the wind. Thus he wrote: I thank you, Sir, for what you have told me concerning the coal mines where use was made of a chain and bucket pumping system, at a depth of up to a 100 units of length. I believe that would also function in the Harz mines if there was not a particular inconvenience, namely the corrosivity of the water we want to remove from our mines, which quickly eats into the iron. That is the reason why one uses a score of pumps, one above the other. These pumps operate by means of water wheels, and my idea is simply to see if the water scarcity, in times of drought or otherwise, could be counteracted by the use of wind power, storing the water in the grand reservoirs constructed for this purpose, and using the existing pumps. But the irregular flow of the wind, which at times [also] acts with a certain violence that can damage the machines, means a remedy is required and [specifically] a method of operation that is simple, convenient and durable. I thought of arranging for the sails of the wind mill to be turned a little, with their axes inclined a little, when the wind becomes too strong, without however the cross which carries the sales changing its position.233 Regarding the expansion of Scottish coal production between 1550 and 1700, cf. chap. 5, pp. 62–72 (Coal mining), in: J. Shaw, Water power in Scotland 1550–1870, Edinburgh, 1984. 233 “Je vous remercie, Monsieur, de ce que vous me mandés touchant les mines de charbon, où l’on s’est servi des chaines à seaux jusqu’à la profondeur de 100 toises. Je croy que cela reussiroit bien aussi au Harz, s’il n’y avoit un inconvenient, qui est la corrosivité des eaux qu’on est constraint de tirer de nos mines, qui mange bien tost le fer. C’est pourquoy on s’y sert d’une vingtaine de pompes les unes sur les autres; ces pompes jouent par le moyen de moulins à eau; et mon dessein n’estant que d’essayer, si au défaut de l’eau dans un temps sec ou autrement on pourroit y employer le vent, ménageant l’eau dans les grands

312

Chapter 1

Leibniz’s associate Crafft appears to have informed him belatedly, but then frequently, about the state of the windmill enterprise. As an experienced project developer himself, Crafft realized at the outset the essence of the matter, and he stated accordingly – at the beginning of September 1680 – that, while Leibniz’s ideas were good in theory, only time could tell if they would survive the test of practice,234 and a month later, on October 3, he cautioned Leibniz that such things always prove more difficult than anticipated.235 Just the same, Crafft had reason and opportunity on several occasions to congratulate Leibniz on partial successes,236 as well as to direct his attention, at the end of January, 1681, to a reference to his project in a Leipzig gazette.237 Apart from his windmill venture in the Harz district, Noel Douceur, Mariotte and Jobst Dietrich Brandshagen, all reported to Leibniz about new water-lifting machines in Paris and Copenhagen,238 and furthermore, through the intercession of Johann Jakob Ferguson, Leibniz received, in November 1682, accurate and detailed construction drawings of a Dutch windmill.239 5

Projects: Calculating Machines

In the fields of mechanics, and engineering in general, Leibniz’s efforts in the late 1670s had met with little success, not least because of a lack of qualified assistants.240 His efforts from his base in Hanover, that were supported by Abbé Soudry’s brother (who died in the summer of 1678), Friedrich Adolph Hansen and Mariotte, to motivate the Parisian clockmaker Ollivier to complete the improved model of the four-function calculating machine – namely that which had been first presented at the Royal Society of London in 1673 – proved to be futile, so that only an appointment (or assignment to a post) in Hanover seemed to offer the prospect of further progress. Leibniz’s efforts to reservoirs faits pour cet effect, je n’ay qu’à employer les mêmes pompes déja faites. Mais le vent allant fort inégalement, et agissant quelques fois avec une violence qui pourroit endommager les machines, il s’agit d’y remedier, et de faire l’application d’une maniere simple, commode et durable. J’ay pensé de faire en sorte que les ailes du moulin se tournent un peu et s’inclinent quand le vent deviant trop fort, sans que pour cela la crois qui porte ces ailes change de place” (A III,3 N. 22, p. 72; HO, 8, p. 267f.). 234 Cf. A III,3 N. 103. 235 Cf. A III,3 N. 113. 236 Cf. A III,3 N. 306, N. 347, N. 429 and N. 472. 237 Cf. A III,3 N. 161. 238 Cf. A III,3 N. 141, N. 193 and N. 415. 239 Cf. A III,3 N. 416 and N. 417. 240 Cf. A III,2, Introduction, p. XXIX.

1676–june 1683

313

develop his calculating machine, about which he informed various correspondents in the spring of 1680,241 appear to have suffered also due to lack of time. Clüver’s admonition, on July 26, 1680,242 that the completion of the calculating machine was more important than work for the Hanoverian court proved to be of no avail, not least because of Leibniz’s commitment to his time-consuming windmill project in the Harz mountains. A further difficulty was the lack of a suitable skilled craftsman in Hanover for work on the machine. At all events Leibniz was pleased to be informed by Ferguson, on November 10, 1682, about two prospective Dutch clockmakers – brothers, then aged 23 and 21, and sons of a clockmaker – who were willing to travel to Hanover and take up employment there. Thus the correspondent wrote: I have inquired about someone with a very good knowledge of clockmaking and an inclination to go abroad, and I have finally found that two skillful youths, brothers whose father is a clockmaker and who has imparted to them a very good understanding of that trade, are intending to travel to France next summer and, on that occasion, would be willing to go to Hanover first and spend some time there. However, since they want to travel together, I believe one ought to employ both of them and thus accelerate the work, because, according to what I heard, each of them understands his art, or trade skills, equally well, the one being 23 and the other 21 years old. They are demanding, for each of them, a ducat a day and travel expenses, which appears a lot to me, and they are claiming an assurance in advance with information about the nature of their employment, their subsistence being the essence of their enthusiasm for the work.243

241 Cf. A III,3 N. 32, N. 61 and N. 66. 242 Cf. A III,3 N. 89. 243 “Ick hebbe mede naer jemand vernomen die het horologiemaecken seer wel is verstaende, genegentheijd hebbende om derwaerts te gaen, ende eijndelijck bevonden dat twee geschickte Jongelingen Gebroeders, welckers Vader een horologiemaecker is, ende die hun dat handwerck mede seer wel verstaen, van meeninge sijn toecomende somer near Vranckrijck te reijsen, ende bij dese occasie wel eerst tot Hanover souden willen comen en daer eenigen tijd blijven, doch dewijle sij te samen willen reijsen, soo gelove ick dat men hun beijde soude moeten emploijeren, ende ‘t werck soo veel verhaesten, want, volgens ‘t gene ick gehoord hebbe, souden sij beijde hun const even wel verstaen, sijnde de eene van 23 ende d’ander van 21 jaren; sij eijsschen jeder een ducaton des daegs en defroijement op de reijse, dat mij wat veel dunckt, ende pretenderen alvorens verseeckeringe ende te weten waer toe men haer soude emploijeren, als die, subsisteren connende wat moedich op hun werck sijn” (A III,3 N. 416, pp. 735f.).

314

Chapter 1

Leibniz’s English correspondents Detlev Clüver and Robert Hooke – to whom he turned to through the intercession of Theodor Haak – were the ones who emphatically enquired about progress in the construction of the calculating machine, not least because the machine appeared to be a part of a larger project for the mechanization of thought, that was predicated on an interdependency of philosophical principles and of mathematical (and scientific) results. To Haak Leibniz wrote, for example, in February, 1680, that a general script was conceivable with the help of which one might be able, for every topic, to calculate and prove just like in algebra and arithmetic. Thus he wrote: For I believe it possible to conceive a certain universal script with the help of which one can calculate in every kind of matter, and find demonstrations in the same way as in algebra and arithmetic … perhaps it is also possible to define a task of another kind, useful either for humankind or in matters relevant to the sciences.244 Recalling his visits to London in 1673 and 1676, and his meetings there with Henry Oldenburg, he then added: “I once spoke about that matter with Mr Oldenburg, who had promised me to communicate the deliberations about this matter to renowned members of your society, but I do not know if he did so”.245 Finally, regarding Robert Hooke’s desired involvement, he wrote: “I desire nonetheless that Hooke should learn these my thoughts for, by virtue of his great ingenuity, he ought to be able to adjudicate in these matters”.246 Of interest also is the fact that, at the end of 1674, Leibniz had already conceived an analog equation-solving instrument, referred to as a “Constructor, instrumentum algebraicum”.247 6

Techno-Economic Projects

In the late 1670s and early 1680s, there was no shortage of economic and technological project conceptions in Leibniz’s correspondence and new schemes 244 “Ego enim scripturam quondam universalem excogitari posse arbitror, cujus ope calculare in omni genere rerum et demonstrationes invenire possimus, perinde ac in Algebra et Arithmetica … nescio an utilus aliud generi humano, in rebus ad Scientias pertinentibus, Munus dari possit” (A III,3 N. 28, p. 83). 245 “Locutus sum olim ea de re cum Do Oldenburgio, qui mihi cum egregiis vestrae Societatis Viris ea de re Consilia communicare promiserat, quod an fecerit nescio” (pp. 83f.). 246 “Volui tamen Cogitata haec mea sciret Hookius; nam pro excellenti ingenio suo judicare de illis potest” (p. 84). 247 Cf. A III,1 N. 58, p. 272.

1676–june 1683

315

were constantly being discussed or implemented. In all, more than a fifth of Leibniz’s correspondence in mathematics, science and technology, in the thirty-month period between January 1680 and June 1683, related to two correspondents who epitomized a type of Baroque discoverer or projector, namely the merchant Martin Elers and Leibniz’s associate and friend Johann Daniel Crafft, who was a pioneer in manufacture and manufacturing in Germany.248 With Elers and Crafft Leibniz discussed a multitude of enterprises, or undertakings, intended to provide national economic benefits. Most such projects were of a kind that required the financial support of, and the granting of privileges by, a prince. Thus, the techno-economic proposals were discussed for the most part in the context of the realization chances at one or other European court. And so, we find Elers at the ducal court in Celle, at the court of the elector of Brandenburg in Berlin, and finally at the court of the Danish king in Copenhagen, busy in each instance with his efforts to convince the prince in question, alas always with the same course of events and outcome, namely initial success followed by subsequent disappointment. Correspondingly, Crafft repeatedly reported about his discussions, and negotiations, with the Saxon mercantile community – whose trade was being adversely affected by the establishment of manufactories in their territory – and with ministers, and the estates, or the broad orders of the social hierarchy of the territory.249 The difficult ambient conditions, combined with the lack of maturity of many a project, was not without effect on the cooperation of Leibniz and these two correspondents. Good agreement, mutual recommendations, and common intentions, alternated with intrigues and scheming, in which letters were tactically withheld from addressees, or regurgitated. Following a suggestion of Leibniz, both he and Crafft adopted a cryptographic script or cipher – or intentional alteration of individual alphabetic characters, intended to hamper decryption by other parties – in their letters, and which occasionally led to confusion or misunderstanding, on Crafft’s part, as a result of false encryption,250 or of vague intimation in non-encrypted text passages.251 In the mercantile policy that he and Crafft wanted to propose to the emperor, Leibniz saw a secret formula, not only for restoring Germany unscathed to an integral whole, but also for achieving happiness and for rendering his imperial majesty formidable once again. In an ‘aide-mémoire’ for Crafft, written in the second half of July 1680, Leibniz proposed that the correspondent write to Philipp Wilhelm von Hörnigk – the brother of the Imperial privy counsellor 248 Cf. W. Loibl, 1998 (Introduction, note 144). 249 Cf. A III,3 N. 306. 250 Cf. A III,3 N. 132. 251 Cf. A III,3 N. 179.

316

Chapter 1

in Vienna, Johann Moritz von Hörnigk – the following lines in which Leibniz himself was the unnamed reference person. His words were: I have entered into discussion with a person, of whose merit and good intentions I have been assured (also by others) over a long period. This person has revealed wonderful concepts to me, which are perfect for combination with my own, with the result that I now believe that the right secret has been discovered, by means of which not only Germany can be restored again to a unity, and to happiness, but also your Imperial Majesty can be rendered formidable again and, also simultaneously, your authority indissolubly connected with the common good.252 With the establishment of manufactories in the German empire, and the introduction of import barriers for French goods, wealth and tax intake would be increased and, at the same time, the power of France would be weakened. Furthermore, according to Crafft, the establishment of manufactories should be recommended to the German princes at the diplomatic conference on reunifications, meeting at Frankfurt, since all, or most, of that pertaining to the prosperity of Germany was rooted in such disprized manufactories or, in Crafft’s words, in his letter of September 2, 1681, to Leibniz: At Frankfurt, nothing would be more important for the common good of Germany than the recommendation of manufactories, but who can appreciate this, as long as one does not understand it. And all, or the most, that can contribute to the welfare of Germany is rooted in the despised manufactories.253 Of course Crafft knew from experience that those wielding power failed to realize that the greatest benefit for themselves lay in the provision of sustentation for their subjects, or in the words of his letter to Leibniz of October 3, 252 “Ich bin mit einer Person in conferenz kommen, deren merite und guthe intention mir auch andern von langer Hand bekandt; diese hat sich mit sehr herrlichen concepten herausgelaßen, die mit den meinigen so trefflich wohl zu combiniren; daß ich numehr glaube man habe das rechte arcanum ausgefunden, dadurch Teutschland nicht allein in integrum zu restituirem sondern auch glucklich und Kayserl. Mt formidable zu machen, auch deren autoritat cum bono publico, gleichsam indissolubiliter zu verknüpfen” (A III,3 N. 82, p. 225). 253 “Zue Franckf. were pro bono Germaniae höher nichtß alß die Mfren zue recommendiren, aber wer kann es, weil man es nicht verstehet, begreiffen. Vnd alles, oder das meiste so ad salutem Germaniae strecken kann, bestehet in den verachteten Manufacturen” (A III,3 N. 278, p. 492).

1676–june 1683

317

1680, that: “The essence of the matter lies in the (to us Germans still unknown) secret, namely that the rulers fail to appreciate that their greatest advantage lies in providing their subjects with sustentation”.254 Leibniz developed the same train of thought, but without an anti-French accentuation, in the draft of a letter written for Crafft, in the second half of July 1680, intended to be sent to the elector of Brandenburg. In order not to come into conflict with the foreign policy of the elector, Leibniz stressed that an embargo on French goods would not be required, since domestic goods, like silk and wool products, could be produced better and more inexpensively, with the result that, in the long term, even the export of manufactured goods would be conceivable. Thus, Leibniz, posing as Crafft, asserted the importance of what the outcome would be in, namely: That, notwithstanding the many difficulties I faced, that which I have promised here, and demonstrated completely and in practice, namely that all silk and wool products, and manufactories, in Germany, could be brought to perfection, thus enabling in this way the saving of millions annually in wages, which otherwise would go out of the country. That indeed, not just domestic products could hold their own against their foreign counterparts, but that they could also become better and more inexpensive, thus enabling in this way that foreign products could be kept out of the country without applying sanctions, indeed with the astonishing result that we could export, with advantage, our manufactured products to those places from which we otherwise import them.255 Crafft placed particular hopes in his invention of new machines for textile manufacture. He told Leibniz, in a letter of December 6, 1680, that he had wonders in hand and would teach the world a lesson, having developed 254 “eben darin steckt das bey vns Teutschen noch vnbekannte Secret, daß die herren nicht wißen, daß ihr gröster Nutze darin bestehe, wenn Sie ihren vnterthanen zue Nahrung helfen” (A III,3 N. 113, p. 275). 255 “daß ich ohngeacht vieler schwürigkeiten das jenige so ich alhier publice versprochen, vollkömlich und practice demonstriret, nehmlich das alle sidene und wullene zeüge und manufacturen in Teütschland in perfection zu machen; und dadurch millionen jahrlich an arbeitslohn so sonst ausm Lande gehen, zu ersparen. Ja daß nicht allein die einländische wahren mit den frembden zu marcke gehen und certiren, sondern auch beßer und wohlfeiler gemacht und gegeben, und daher die frembden auch ohne Verboth ausm Lande gehalten werden können, ja welches zu verwundern; daß wir sogar unsere manufacturen an die orthe da wir sie sonst hehrgehohlet mit nuzen schicken” (A III,3 N. 83, p. 229).

318

Chapter 1

a veritable philosopher’s stone.256 Crafft stressed in a letter  – composed the end of May 1681 during a meeting with Leibniz  – to the pensionary of Haarlem, Michael ten Hove, the usefulness of the new invention, namely the ribbon-loom, or mola limbolaria.257 Although the loom needed to be deployed in a purpose-built building,258 he nevertheless believed he could market the device even in Holland. Then, in a letter of January 8, 1682, Crafft requested that Leibniz approach Jan Hudde, in Amsterdam, in this matter. Thus he wrote: Progress has been made to the point that I no longer have any doubts and find that it is a matter from which a whole country could have honor and benefit: a work which a republic like Holland should value, for which reason I consider it advisable to inform Mr … Hudde without further delay, and I would welcome it if you would, Sir, be pleased to act as an intermediary in the matter.259 Crafft forwarded a fabric sample and recommended to Leibniz that he get the opinion of a braid and lace maker concerning it.260 However, he had also to confess that his three machines were idle, and needed to be replaced by a modified machine, since, contrary to all expectations, the fabric had gone out of fashion. Although this trend would surely be reversed, his circumstances did not allow him to await this development.261 Crafft and Leibniz followed with interest the efforts of Elers to persuade the duke of Celle to establish a new town near Harburg (south of Hamburg) for emigre Huguenots.262 The duke of Celle insisted on financial participation in the scheme by the duke in Hanover, who in turn insisted on the fulfillment 256 “nun miracula vnter handen, es scheinet, daß der gantzen wellt eine newe lection werde vorgeben ratione usus, ist es in hoc genere der rechte lapis philosophicus” (A III,3 N. 132, pp. 293f.). 257 This loom was known in Germany as ‘Bandmühle’, ‘Mühlstuhl’ or ‘Schnurmühle’; cf. U. Troitzsch, 1991 and R. Reith, 2000 (Introduction, note 145). 258 “Mirabile inventum est et subtilissimi ingenii artificium, quod nullum incommodum secum habet praeter hoc unicum, quod in aedificiis communibus commode exerceri non potest, sed domus proprias in eum usum extructas requirit” (A III,3 N. 232, p. 426). 259 “Eß ist so weit kommen, daß ich nun gantz nicht daran zue zweifeln habe, vnd eine Sache finde, daß ein gantzes Landt Ehr vnd Nutzen davon haben könne: Ein Werck welches eine Republique gleich Holland ist, aestimiren sollte, dannenhero ich rathsamb hallte solches ohne ferneren Verzug Herrn … Hüdde vorzuetragen, vnd were mir lieb, wenn M. h. H. alß ein tertius sich darin gebrauchen laßen wollte” (A III,3 N. 306, p. 532). 260 Cf. A III,3 N. 418, p. 740, and N. 429, p. 760. 261 “dieweilen die mode derselben wieder alles Vermuthen plötzlich gefallen; Sie wird zwar ohnfehlbar wieder kommen, aber mein Zuestand läßt mich darauf nicht wartten” (p. 760). 262 Cf. A III,3 N. 129 and N. 166.

1676–june 1683

319

of certain other conditions.263 A decision about the matter was delayed, and Elers finally had to depart without success.264 Another one of several proposals that Elers presented to the Brandenburg court likewise proved to be a failure. The Brandenburg-African company was to bring a large number of Africans into the territory,265 which the elector would then make available to farmers (against payment) as slaves or farm laborers. In addition, if the Africans were to be trained once a week in the use of fire arms, then the elector would acquire cheap and good soldiers since these were by nature hardy and strong. Thus, Elers outlined this project, on February 7, 1682, to Leibniz in the following words: In short, my suggestion was that his Electoral Highness should, through the African company that is already established in his territory and that has already successfully traded with Africa, bring black people into the country (just as the company is already buying people there and selling them to the Hispanics in America and elsewhere as slaves) and then distribute them among the farmers to be used as slaves paying annually for each of these that which they would pay annually in wages to a farm laborer. In this way they would make a profit of 12 to 16 per cent on their investment and, if the said individuals were to be trained once a week in the use of fire arms, they could if required be exploited better than European peoples in times of war, for they are by nature hardy and strong, and would furthermore increase the population of their territories, colonizing and building with advantage in various locations.266 263 Cf. A III,3 N. 160 and N. 180. 264 Cf. A III,3 N. 302. 265 The formal foundation of the Brandenburg-African Company followed an Electoral edict of March 17, 1682; cf. A III,3 N. 319, p. 559 (annotation). Regarding the Brandenburg-African Company (1682–1721), cf. H. Weiss (ed.), 2016 (Introduction, note 146). 266 “Curtz zu sagen mein vorschlag ist gewesen, Ihr Cfl. Durchl. solten durch die affericanische Comp. so in dero Landen bereits auffgerichtet und die bereit mit guten nutzen dahin gehandelt, lassen anhero bringen von den swartzen menschen (so sie die Companie alda cauffen und an die Hispanier in Amarica und ander orter vor Slaven vercauffen) und alßdan dieselbe unter seine bauren austeiln, und fur knechte gebrauchen lassen, und vor dieselbe jaarlich zalen lassen was sie sonst an einen bauwren kenecht jaerl. zalen mochten, so wurden sie von Ihrem angelegeten gelde jaerlich 12 à 16 procento rente machen connen, und wan dieselbe eins die woche in die waffen geexersiret wurde, so conten sie sich derselben im Crige wen sie wollten besser als von europeischen volckern bedienen, weiln dieselbe von natur hardi und starck weren, und wurden uber demme daerdurch Ihr lant mit volck vermeeren Ihre Lender die an unterscheetlichen orde legen mit nutzen bebauwen connen” (pp. 559f.).

320

Chapter 1

Crafft was likewise approached by Elers in the matter, and his judgement was that the project was totally impractical and that the projector could expect to experience more dishonor than honor with this proposal, a view which he communicated to Leibniz on February 24, 1682.267 Leibniz’s letter to Elers of February 17, 1682, has not been found, but it was referred to at the beginning of the correspondent’s reply, on March 1, 1682. There he related that a copy of his proposition had been taken to Vienna for presentation to the emperor. From this reply, an insight can be obtained into Leibniz’s thoughts on the matter. In the context of the foundation of the Brandenburg-African Company, Leibniz must also have suggested that the Dutch had forbidden the holding of serfs, or slaves, in the republic itself. Elers had not heard of such a total prohibition of the slave trade in the Dutch republic, but solely that slavery and serfdom were prohibited in the county itself, and the ruling that black people brought into the country should enjoy freedom. Just the same, Elers insisted that no small number of black people were being held in Holland, even among the Jews. Once again, he insisted that the black laborers – once provided with appropriate clothing, and following a period of acclimatization, would be hardier than their European counterparts. Thus he wrote in his reply to Leibniz: That the Dutch have forbidden such, I have never heard, but only that, if someone brings a negro into the county, he can no longer be held as a slave there, because they do not want that some live in serfdom but rather that all should be free there. Nonetheless, one finds there no small number, particularly among the Jews. Once they are supplied with clothes in accordance with the climate change from their country of origin, they can endure everything better than the Europeans.268 Following this, Elers recalled Crafft’s skepticism about the prospects for the project in hand, and he suggested that the latter’s views were very much at 267 “Ich befinde aber dieselben also beschaffen, daß Er von derselben mehr Schimpf alß Ehre haben muß, in deme ich dieselbe nach mein einfalle gantz impracticabel finde” (A III,3 N. 328, p. 369). 268 “Das die Hollander sulches verboten habe nimmer gehort sondern woll wan einer einen Neger daerbringet denselben nicht meer voor einen Slauen halten mag weiln sie nicht wollen das einige Leibeigenschaft sonder daselbst alles frey sein soll. Dennoch vindet man alda keine geringe anzal und zumael unter den Juden. Wen Sie mit Cleider versehen nach gelegenheit des Cliemaets daer sie gebracht werden so connen sie alles besser austehen alß die Europeer” (A III,3 N. 329, p. 572). Regarding the Dutch and Atlantic slave trade, cf. J. Postma, 1990 and 1992 (Introduction, note 146).

1676–june 1683

321

variance with Leibniz’s opinion of the matter. Thus he added: “our friend Crafft may [see] a pile of difficulties, his opinion is indeed far from that of milord”.269 Crafft was, however, to have the last word on Elers’ project involving the Africans (“wegen der Schwartzen”), in a letter to Leibniz on May 7, 1682. He was of the opinion that the demographics of Germany differed from those of North American territories like Canada, where the rural settlement of black Africans might indeed make economic sense. He also believed that Elers’ resettlement project would – like many other projects of his – in due course die a natural death. Thus he wrote: But regarding the answer to |Elers|,270 I say that if we were in the condition like that in Canada, they would also be profitable and necessary. As regards the population of Germany, we have, if we really want it, in my humble opinion, easier and cheaper means than through Africa; more about this viva voce. In the meantime, this proposal will, along with many others of |Elers|, die of its own accord.271 The trend found in the epistolary exchanges of the late 1670s – where questions arose regarding the possible application of machines, as for example in the mechanization of silk and wool manufacture – continued in the early 1680s.272 In a letter from Dresden, on January 30, 1680, Crafft referred to a woolen, or silk, manufactory, and specifically a proposal submitted to the elector of Saxony for the establishment of a workhouse and orphanage in connection with a bag cloth and stockings manufactory.273 For the duchies of Brunswick and Lüneburg, he also proposed the establishment of a bag cloth manufactory,274 and his exchange of ideas with Leibniz about the possibility of steel production in the Harz district resulted in Leibniz turning to duke Ernst August in the matter.275 269 “unser freundt Crafft mag auch ein hauffen difficolteiten, ist gaer weit von M. h. H. seine meinungh” (p. 572). 270 Name enciphered in the manuscript. 271 “Aber ratione der Antwortt an |Elers| sage ich, wenn wir in dem Zuestand, wie die zu Canada seyn, weren, weren Sie vns auch profitlich vnd nöthig, waß die population von Teutschland betrifft, darzue haben wir, wenn wir nur wollen, meines wenigen erachtenß leichtere vnd vnkostlichere Mittel, alß durch Africam, davon einmahl mundlich. Vnterdeßen wirdt dieser Vorschlag mit noch vielen anderen von |Elers| von sich selbst ersterben” (A III,3 N. 347, p. 599). 272 Cf. A III,2, Introduction, p. XXIX. 273 Cf. A III,3 N. 18, pp. 63f. 274 Cf. A III,3 N. 113, p. 275. 275 Cf. pp. 274f.

322

Chapter 1

Even greater was the diversity of the projects in which Elers was involved. During a visit to glassworks – located in the hills of the Weser Uplands – he found a process to facilitate the making of burning glasses, or lenses, as he informed Leibniz from Hanover on May 15, 1681.276 From Dresden, on July 8, 1681, he informed Leibniz about his quest for a new kind of wax bleachery,277 and from Berlin he reported, on December 30 of the same year,278 that he had informed the elector about an inventor who claimed to have a means of preventing ships from sinking. Over several months, Elers promoted an – in his words – “infallible” project, which, as he explained in his letter from Dresden, on September 2, 1681, consisted of a most profitable process involving printing with silver, gold and other metals.279 The intention here was to market a wallpaper, consisting of silk printed with gold or silver, and Elers enclosed samples with his letter to Leibniz. Crafft, for his part, as he informed Leibniz in his letter of May 7, 1682, considered this project to be both impractical and inefficient. His words were: “I have retained no sample of it, because I do not admire it in the least and consider it to be an impractical and inefficient matter”.280 Elers finally abandoned this project for lack of start capital. Although there exists no statement from Leibniz about it, the letters of Crafft and Elers leave no doubt that he had shown an interest in it, and had requested further details from the correspondents. The same applies to Elers’ work on the production of armor, or mail armor, made out of silk. When, at the end of August 1681, Leibniz remarked that armor of that kind was obtainable in England at a high price, Elers replied, on September 2,281 that his kind of armor, in which apparently a network of brass wire was incorporated, would be considerably cheaper.282 With the elector of Brandenburg, Elers did not have any success with this armor and, on December 30, 1681, he informed Leibniz that the elector had already received a similar coat of armor as a gift from king Charles XI of Sweden, and had tested the extent to which it was resistant to musket balls, or shot, by having a soldier, who was awaiting execution by gunfire, wear the armor and serve as a target. Although, the musket ball did not penetrate the armor, the proband collapsed and the shot was found to have produced a 276 Cf. A III,3 N. 224, pp. 417f. 277 Cf. A III,3 N. 257, p. 460. 278 Cf. A III,3 N. 302, p. 526. 279 “es bestehet in drucken mitt silber goldt und ander Metalen woran einen grossen provid und debiet sein wirt” (A III,3 N. 279, p. 496). 280 “Ich habe keine Probe darvon behallten, dieweil ich es im geringsten nicht aestimiret vnd vor ein impracticabile vnd vntuchtige Sache gehalten” (A III,3 N. 347, p. 599). 281 Cf. A III,3 N. 279, p. 495. 282 Cf. A III,3 N. 278, p. 490.

1676–june 1683

323

bloated, purulent and bloody wound that would have required surgery to treat, Leibniz was informed.283 Communications and discussions of projects in engineering, or technology, were not limited to the correspondences with Elers and Crafft at this juncture. On March 21, 1682, Tschirnhaus related that he had seen in Paris a recently discovered repeater clock that could be made to chime on awakening in the night. Thus he wrote: I have seen in these days a strange clock which is very convenient at night. If one awakes in the night, and does not know how often the clock has struck, one pulls the cord and the clock strikes again just as often as on the previous occasion, also the quarter hours, and as often as one wants and pulls the cord.284 Jobst Dietrich Brandshagen reported, on November 5, 1682, from Copenhagen, where preparations for a war with Sweden were underway, about certain bellicose inventions like setting ships on fire with cannonballs. He related that: One has discovered also here at last how ships can be set on fire with cannons, and it does not cost any more effort, and time, to load such a cannon with an incendiary cannonball, as with ordinary cannonballs.285 Brandshagen’s subsequent account, on May 15, 1683,286 of the components of these incendiary cannonballs interested Leibniz, as did the function of a rifled gun in which the powder was automatically transferred to the priming pan.287 Remarkable was a ballistic mortar allegedly made out of board, or pasteboard,

283 “und habe man es umb die rechte probe zu haben an einen soldaten so archebusirt zu werden verdammet solches probiret sey von der musquetenkugel getroffen ubern hauffen gefallen die kugel war zwar nicht durch den harnisch gangen, der orth aber sehr auffgeschwollen und voller eiter und bluth geworden, so man hatte mußen aufschneiden” (A III,3 N. 302, p. 526). 284 “Ein curioses Horologium habe diese tage gesehen, so in der nacht sehr commode, wenn man erwacht, und nicht weis wieviel es geschlagen ziehet man nur die chorde so schlegt die uhr gleich wieder, so viel als sie zulezt geschlagen, auch die vierthel, so offt man will und die chorde ziehet” (A III,3 N. 358, p. 641). 285 “Mann hat hier nun auch entlich erfunden wie mann die schiffe soll in den brandt stecken mit Canonen, vndt gehöret nicht mehr mühe vndt zeit dazu eine Canone mit dieser brandt kugel zuladen als wen es mit ordinaire kugeln geschicht” (A III,3 N. 415, p. 731). 286 Cf. A III,3 N. 465, p. 810. 287 Cf. A III,3 N. 415, p. 732; N. 428, p. 753; N. 465, pp. 809f.

324

Chapter 1

by Brandshagen and reported in a letter to Leibniz, on April 3, 1683.288 Because of the easy transportability, the mortar, from which nine grenades had already been fired, was superior to mortars made of metal, at least according to the correspondent. The suggestion to use the peculiar material had apparently come from Leibniz himself, who had been inspired by an article, written by Jean Bonfa S.J., in the Journal des Sçavans.289 7

Projects: The Organization of Science

Besides his personal ambition to receive recognition of the Académie des Sciences, both the draft of a letter addressed to Jean Baptiste Colbert, and one finally dispatched to Jean Gallois, in October 1682,290 reveal a particular commitment on Leibniz’s part to the organization and the advancement of science with government support. The fact, that the Académie was in a position to carry out large-scale projects, was repeatedly revealed to Leibniz through his correspondence with Mariotte. The latter not only reported continuously about regular meetings of the Académie, but also, for example (in a letter of January 25, 1683), about the journey of a group of savants to the equatorial region, in the course of which the astronomer Jean Richer’s disputed measurements of the length of the seconds pendulum in Cayenne (in French Guiana) were confirmed.291 A further group of academicians undertook journeys for the preparation of an improved map of France, which was reported by Mariotte on November 29, 1681, and furthermore to dissect samples of rare fish species, which had previously been reported by Mariotte, on December 1, 1680.292 Already in a letter of December 7, 1677, Mariotte had outlined his idea of undertaking corresponding simultaneous weather observations at different locations in Europe, writing as follows: I am continuing to make observations of winds and of the constitution of the air. I have a correspondent at Avignon and another at Dijon. If you wanted to contribute a part of your resources to the effort, I have no doubt that we could find some rule for the changes of time and the 288 Cf. A III,3 N. 450, p. 785. 289 Cf. p. 785, and: J. Bonfa, “Extrait d’une lettre du R. P. Bonfa, …, touchant une nouvelle invention de faire des pendules de carton”, Journal des Sçavans, (January 23, 1679), pp. 23f. 290 Cf. A III,3 N. 406 and N. 407, respectively. 291 Cf. A III,3 N. 297, N. 406, p. 719 (annotation) and N. 436 (Mariotte’s letter of January 25, 1683), p. 771 (annotation). 292 Cf. A III,3 N. 297, pp. 519, and N. 131, pp. 290f., respectively.

1676–june 1683

325

vicissitude of the winds  … I also read the barometer every day, and I record the observations. If you would also like to join the effort, we might be able to make a discovery by comparing our observations.293 Mariotte’s idea was immediately adopted by Leibniz, and he passed it on to some of his own correspondents in the form of a request for them to undertake similar observations themselves. Whereas Philipp Lohmeier in Lüneburg was (in early January 1680) having difficulties in acquiring the requisite instruments,294 Samuel Reyher was among those who sent weather observations (on September 8, 1680),295 which Leibniz then forwarded to Mariotte and for which he received in return (in March–April 1681), and for purposes of comparison, Mariotte’s own observations.296 Mariotte had previously sent Leibniz weather observations (in mid-January 1680),297 and he had reported in particular (on July 5, 1680) about a storm in France, and had enquired about wind conditions on the same day in Germany.298 Whereas the correspondence with Nehemiah Grew, who had relinquished his office as secretary of the Royal Society of London at the end of 1679, was interrupted in the spring of 1680, Leibniz was kept informed about the activities of the Royal Society by Theodor Haak, although not as comprehensively and regularly as by Mariotte regarding the activities of the Académie des Sciences. Leibniz was also able to maintain contact with the Academia Naturae Curiosorum (the Academia Leopoldina) in Halle, with the help of the Frankfurt physician Sebastian Scheffer. Through the intercession of Leibniz, an article about an oversized kidney from the Journal des Sçavans also appeared – in a Latin translation, and under Scheffer’s name – in the Miscellanea Curiosa Medico-Physica,299 the journal founded by the Academia Leopoldina in 1670. Leibniz had also used his contact to Scheffer to propose to the Academia a 293 “Je continue à faire les observations des vents et de la constitution de L’air. J’ay un correspondent à Avignon et un aute à Dijon. Si vous y voulez contribuer un peu de vostre soin, je ne desespere pas que nous ne pussions trouver quelque regle pour les changements du temps et pour la vicissitude des vents … j’observe aussy chaque jour le barometer et j’en escris les observations, si vous vouliez en prendre aussy la peine, nous pourrions decouvrir quelque chose en conferant nos observations” (A III,2 N. 116, p. 291). 294 Cf. A III,3 N. 1, p. 44. 295 Cf. A III,3 N. 105, pp. 260–262. 296 Cf. A III,3 N. 193, p. 374. 297 Cf. A III,3 N. 6, p. 52. 298 Cf. A III,3 N. 79, pp. 221f. 299 Cf. S. Scheffer, “De Rene Monstroso”, Miscellanea Curiosa, Decur. 1, Ann. IX/X, (1678/1679), pp. 258–261. The matter, wrongly attributed to Scheffer, had previously been reported in the Journal des Sçavans, (January 24,1678), pp. 31–36; cf. A III,3 N. 162, p. 331.

326

Chapter 1

system of corresponding terrestrial magnetic observations. This proposal in turn gave Johann Georg Volckamer reason to consult with Johann Christoph Sturm about the creation of a mathematical-magnetic association for such an undertaking, or in Volckamer’s words as quoted by Scheffer in his letter to Leibniz of August 22, 1681: Mr D. Leibniz has written a wonderful letter concerning the declination of the magnetic needle and has given me reason to confer very soon with Mr Sturm, professor of mathematics at Altorf, as to how we should proceed in this matter, as for example by means of a patent to constitute a mathematical-magnetic society, which would [then] collect exact observations everywhere in order to find out if one can arrive at an exacter science of magnetism.300 Sturm, for his part, wrote an Epistola invitatoria,301 in which the learned and the scholarly were called upon to undertake corresponding observations.302 Sturm’s appeal – following the initiating step taken by Leibniz and revealed in his correspondence – may not have had quite the desired success, yet it did find a greater resonance than similar invocations had previously achieved. With another proposal Leibniz was less successful, namely that to encourage the Academia Leopoldina to pursue utile activities. Leibniz prompted Volckamer, through Scheffer, to encourage the physicians of Nuremberg  – for the sake of science – to establish contact with the renowned craftsmen, or tradesmen, of that city, and to publish the results of such discussions. Volckamer’s reply – quoted in Scheffer’s letter to Leibniz of April 3, 1682 – was to the effect that, while the suggestion was by no means bad, no scholar would be willing to communicate his knowledge to tradesmen, especially without financial compensation or remuneration.303 Leibniz then confided to Scheffer, in his reply in mid-April, that he considered the reaction from Nuremberg to be ludicrous, writing as follows: “As to the answer from Nuremberg (but keep this between us), I could almost have laughed”.304 His vision was that 300 “Es ist H. D. Leibnitz wegen der acus magnetice declinatione ein herrlich schreiben, u. hat mich verursachet, daß ich mit Hn Sturmio, Prof. Mathematicum Altorfi ehester tagen werde conferiren, wie wir in tali negotio hin u. wider, etwan durch ein patent werden eine Societatem Mathematico-magneticam zusammen bringen, die allenthalben genaue observationem sollen einnehmen umb zu vernehmen, ob man in des Magnetis genauere Wissenschafft einkommen könt” (A III,3 N. 271, p. 483). 301 Cf. note 47 above. 302 Cf. A III,3 N. 248, N. 271, N. 284 and N. 387. 303 Cf. A III,3 N. 340, p. 585. 304 “Über die antwort von Nürnberg (haec inter nos) hätte bald lachen müßen” (A III,3 N. 342, p. 588).

1676–june 1683

327

the bookish erudition of the scholars should be annotated with countless and useful explanatory notes of the practitioners, craftsmen and tradesmen, as he explained to the correspondent: To counter such sterility, I had made the proposal regarding how the countless new and useful annotative expressions, prevalent in the population although unknown among the learned, might be used to this end.305 Shortly after the accession of the duke Ernst August, Leibniz proposed to his prince the establishment of a military academy in Hanover, or Göttingen, perhaps with the ulterior motive of assembling a circle of scholars in his own vicinity.306 As mathematics professor for the proposed academy, Leibniz had the Dutch mathematician Ferguson in mind, and perhaps also the aristocratic Tschirnhaus as its director. The latter, however, writing from Paris on May 27, 1682, and again on August 6 of that year, informed Leibniz about a plan of his own to assemble a group of scholars around him at his manor in Kieslingswalde, near Görlitz.307 Tschirnhaus aspired to a pension from the Académie des Sciences with which he hoped to pay salaries to the Danish mathematician Georg Mohr, to a tradesman, a physician as well as an individual versed in algebra, all of whom would work to bring his inventions to execution. Although, in the case of Tschirnhaus, the pension never did materialize, Leibniz surely followed his plans with interest, just as in the case of the foundation of a scientific academy in Venice by Ambrose Sarotti, the secretary of the republic of Venice, which was referred to by Friedrich Schrader in a letter of April 23, 1682, and in which he wrote: In Italy, a learned man called Sarotti is planning a new society for virtuosi. They wrote to me that it will be engaged in carrying out experiments in physics and mathematics and excerpting books.308 Sarotti had returned from a diplomatic mission to England, and he had drawn inspiration for his academy from the Royal Society and, while in London, 305 “Solcher sterilitat nun zu hülffe zu kommen habe ich den vorschlag gethan gehabt, wie man unzahlbare neue und nüzliche anmerckungen die schohn unter den leuten sind, nur daß sie den gelehrten nicht bekand, herfür geben könne” (p. 589). 306 Cf. A I,3 N. 40. 307 Cf. A III,3 N. 356, p. 630 and N. 384, pp. 686f., respectively. 308 “In Italia curiosum Virum Sarotti nomine novam Societatem Virtuosorum moliri; scribunt mihi, quae experimentis Physicis et Mathematicis faciendis ac libris excerpendis occupabitur” (A III,3 N. 344, p. 594, and annotation).

328

Chapter 1

he had organized Denis Papin’s participation in the enterprise.309 Leibniz requested from Friedrich Schrader, in a letter of July–August of the same year, any further details which the correspondent might have obtained.310 Sebastian Scheffer, replying on August 18 to a similar request, did in fact raise the prospect of soon being able to provide such further details.311 8

Alchemy and Chemistry

The relatedness of scientific knowledge and economic prosperity characterized the areas of interest in Leibniz’s correspondence with Heinrich (or Henning) Brand, Johann Daniel Crafft and Georg Hermann Schuller, during the first three years in Hanover.312 In these correspondences, issues of applied science, and in particular chemistry, came to the fore with questions arising, like about phosphorus and its usability,313 or about the healing powers of various chemical substances, or medicaments, such as wound healing or sore water, antifebrile or febrifugal medicaments, and moxibustion or moxa.314 Parallel to this, the centuries-old problem of gold extraction, or reduction, and of the improvement, or ennoblement, of metals (transmutation) continued to be the subject of ever new experimentation and speculation. White phosphorus was first discovered in 1669, or in the early 1670s, by the alchemist and pharmacist Brand in Hamburg. Leibniz himself would later publish an account of this discovery, entitled Historia inventionis phosphori (1710).315 The new substance was first scientifically studied,316 both by Johann Kunckel (von Löwenstern from 1693) and by Robert Boyle, and

309 Cf. D. Papin, “Augmenta quaedam et experimenta nova circa antliam pneumaticam, facta partim in Anglia, partim in Italia”, Acta Eruditorum, (June 1687), pp. 324–335, specifically p. 331. 310 “Rogo ut mihi de Societate philosophica quam Sarottum instituisse scribis, distinctiora referas, si quae comperisti” (A III,3 N. 381, p. 682). 311 “Vom Sarotti will bald was vernehmen” (A III,3 N. 387, p. 698). 312 Cf. A II,2, Introduction, pp. XXVIIIf. 313 Cf. in volume A III,2 the two letters to the Charles-Honoré Duc de Chevreuse (N. 80 and N. 246) and the correspondence with Brand. 314 Cf. the correspondence with J. H. Kornmann von Hornsbach (A III,2 N. 160, N. 161, N. 201 and N. 212). 315 Cf. G. W. Leibniz, “Historia inventionis phosphori”, Miscellanea Berolinensia, vol. 1, (1710), pp. 91–98 (Leibniz, Opera Omnia, II,2, pp. 102–108). 316 Cf. C. Wahl, 2013, and H. Peters, 1912 &1916, J. R. Partington, 1936, J. Golinski, 1989, and H. Kragh, 2002 (Introduction, note 176).

1676–june 1683

329

publicized in their works, entitled Phosphorus mirabilis (1678),317 and The aerial noctiluca (1680), respectively, whereby the term ‘noctiluca’ was first used by the Wittenberg professor Georg Caspar (Kaspar) Kirchmaier (Kirchmayer).318 When Leibniz visited Boyle in London, on February 12, 1673, their discussions evidently embraced a phosphorus-like substance. Seven years later, in a letter to Nehemiah Grew on March 19, 1680, Leibniz reported the visit to Hanover of an Englishman named Roger Breatridge, who claimed to have a kind of powder that would ignite spontaneously after a certain time.319 In this context then, Leibniz recalled the discussions he had with Boyle, in 1673, and the mention made of such a substance on that occasion, and he expressed his desire to learn what exactly was involved.320 About 1674, Christian Adolph Balduin (1632–1682) prepared a phosphorescent form of calcium nitrate, by mixing chalk and the spirit of nitre (nitric acid), and about which he published a tract entitled Phosphorus hermeticus.321 This development was made known to Leibniz in a discussion with Crafft, on March 12, 1677, following which Leibniz made the following note: March 1677[,] from the communication of Mr Krafft. Balduin’s phosphorus is made as follows. One takes chalk and dissolves it in spirit of nitre, as much as can be dissolved. Then, one takes the thick liquid and removes it cleanly into a retort, whereas the residue is kept isolated from the air. If one wants to carry out an experiment, one takes a little of this … and applies a flame intensely with the result that a yellow-green spot is

317 Cf. J. Kunckel, Oeffentliche Zuschrifft von dem Phosphoro mirabili und dessen leuchtenden Wunder-Pilulen, Wittenberg, 1678. 318 Cf. R. Boyle, The aerial noctiluca, or, some new phenomena, and a process of a factitious self-shining substance, London, 1680; Boyle, The works, vol. 9, pp. 265–304. Kirchmaier (Kirchmayer) attributed the discovery of phosphorus to Kunckel in his work published in 1676–77; cf. G. K. Kirchmaier, Noctiluca constans et per vices fulgurans, Wittenberg, 1676, enlarged in: “Noctiluca constans et per vices fulgurans, diutissime quaesita, nunc reperta; Dissertatione brevi praevia de luce, igne, ac perennibus lucernis. Wittenberg 1676”, in: Miscellanea Curiosa, Decur. I, Ann. VIII, (1677), pp. 219–246, and also H.-J. Kruse, 2012 (Introduction, note 176). Leibniz was first informed about Kirchmaier’s work by Oldenburg in a letter from London written on March 4, 1677 (A III, 2, N. 20, p. 49). 319 “ajebat sibi esse pulveris genus, quod definite tempore ignem concipiat” (A III,3 N. 32, p. 87). 320 “Et memini Dn. Boylium in colloquio mecum habito rei hujus mentionem facere. An vera comperta, scire velim” (p. 87). 321 Cf. C. A. Balduin, Phosphorus hermeticus, sive magnes luminaris, Frankfurt and Leipzig, 1675.

330

Chapter 1

left over, which subsequently, on being exposed to the air, attracts light to itself.322 Crafft had also become acquainted, in February or March 1676, with Brand’s phosphorus and its discoverer, and a little time later he received a sample of the new chemical substance. Then, in mid-May 1677, Crafft presented the substance at the court in Hanover, and he confided no-doubt the name of the discoverer to Leibniz. At all events – in a letter of mid-July 1677 sent to Friedrich Adolph Hansen and Henri Justel in Paris for forwarding to Jean Paul de la Roque – Leibniz informed the correspondents about Crafft, who was then in Amsterdam, characterizing him as an inquisitive person working in Holland for the sake of personal fortune and glory,323 and he gave them a detailed account of Crafft’s (or rather Brand’s) phosphorus under the heading “The phosphorus of Mr Krafft or liquor of dry earth and its composition which continually emits large beams of light”.324 Towards the end of this letter, Leibniz also informed the correspondents that Balduin had sent a sample of his phosphorus to king Charles II, writing that: “One of the friends of Mr Oldenburg sent him a [type of] phosphorus, for presentation to his majesty, which is also remarkable in that one notices through the glass several images of the sun, some greater than the others”.325 Leibniz had previously been informed in the following words by Henry Oldenburg, on March 4, 1677, about the phosphorus sent by Balduin: “Mr Balduin, a Saxon from Dresden, recently sent a gift to our king”, adding that “his phosphorus is displayed like a sun or candle, thus absorbing light in order to reemit it in the dark”.326 322 “Mart. 1677[.] Ex communicatione domini Kraft. Phosphorus Balduini wird also gemacht. Man nimmt Kreide, solvirt sie in spiritu nitri, so viel davon solviren läßt. Alsdann nimmt man den dicken liquorem, zieht ihn trocken ab in einer Retorte, und das übrig bleibende verwahrt man von der Luft. Wenn man ein Experiment machen will, so nimmt man ein wenig davon … und giebt stark Feuer, so bleibt ein gelbgrünlicher Fleck sitzen, welcher hernach, an die Luft gestellt, das Licht an sich zieht” (A III,2 N. 36, pp. 80f.). 323 “Monsieur Krafft est un curieux, qui travaille en Hollande pour sa fortune et pour sa gloire” (A III,2 N. 59, p. 191). 324 “Le Phosphore de M. Krafft ou Liqueur et Terre seiche de sa composition qui jettent continuellement de grands éclats de lumiere” (p. 191). 325 “Un des amis de Mr. Oldenburg luy envoyé un Phosphore pour presenter à sa M. B. qui a encore cela de particulier qu’on y Remarque à travers le verre plusieurs Images du Soleil les unes plus grandes que les autres” (pp. 191f.). 326 “Dnus Balduinus, Saxo Dresdensis, dono nuper misit Regi nostro … Phosphorum suum, qui soli vel candela expositus, lucem ita imbibit, ut eam in tenebris reddat” (A III,2 N. 20, p. 49).

1676–june 1683

331

In July 1678, during a visit to Hamburg, Leibniz then availed of the opportunity to call on Brand and to negotiate a contract with him for the divulgement of his secret and the perfecting of the production process. The outcome was the completion of a contract between the two that was done at Hamburg, on July 24, 1678 (new style).327 Brand had first aspired to the position of personal physician to duke Johann Friedrich, but finally settled for an appointment as ‘Medicus’ and ‘Chymicus’. He then accompanied Leibniz to Hanover, where they arrived around September 5 of that year.328 The circumstances of, and events surrounding, Brand’s employment in the service of the duke of Hanover, are reflected in his correspondence with Leibniz in 1678,329 in 1679,330 and between 1680 and 1683. In a letter of September 2, 1682,331 Brand requested the payment of the final installment of his salary from his employment in Hanover during 1678 and 1679. Notwithstanding such restitution claims, Brand was clearly referred to in Leibniz’s letters as the “inventor primus” of the new substance. In fact, this attitude on Leibniz’s part mirrored the fashion in which he referred to Otto von Guericke’s role in the development of the vacuum pump, before it was subsequently improved by Boyle. Thus, for example, in a letter of July or August 1679 to Grew – in which he also characterized Guericke as the “inventorem primum” of the vacuum pump – Leibniz referred to the “flashing phosphorus which, as you know, was first discovered by Heinrich Brand, after whom it was undeniably refined by Mr Kraft (who visited you two years ago), and [by] Mr Kunckel”.332 Robert Boyle likewise learned of the discovery of phosphorus from Crafft who visited him in London, on September 25 and October 2, 1677.333 In his tract The aerial noctiluca, presented to the Royal Society in December 1680, Boyle referred to the discovery, and his knowledge of it, in the opening prefatory address headed “To my very Learned Friend Dr. J. B.”, a reference surely to James Butler, duke of Ormond (1610–88). There he wrote:

327 “so geschehen Hamburg den 14 julij Ao 1678. Gottfried Wilhelm Leibniz[.] Heniricus Brand M. D. et philosoph.” (A III,2 N. 187, pp. 473f.). 328 Cf. A III,2, N. 190, N. 194, N. 195, and N. 200. 329 Cf. A III,2, N. 213, N. 221, N. 222, N, 232, N. 239, N. 242, N. 247, N. 249 and N. 250. 330 Cf. A III,2, N. 257, N. 260, N. 278, N, 279, N. 282, N. 290, N. 293, N. 294, N. 297, N. 304, N. 307, N. 314 and N. 317. 331 Cf. A III,3 N. 395, pp. 707f. 332 “phosphorum fulgurantem, quem ut nostis primus invenit Henricus Brand a quo Dominus Kraft (qui apud vos biennio abhinc fuit) et Dominus Kunckel, qui cum porro excoluit, profecisse non diffitentur” (A III,2 N. 327, p. 802). 333 Cf. A III,2 N. 39, p. 118.

332

Chapter 1

Having said thus much of the several sorts of artificial phosphoruses, I shall be very brief in speaking of their inventors, whereof I have but an imperfect information  … I find the first invention is by some ascribed to the above mentioned Mr. Kraft, (although I remember not, that when he was here, he plainly asserted it to himself;) by others attributed to an ancient chymist, dwelling at Hamburgh, whose name (if I mistake not) is Mr. Branc[sic], and by others again, with great confidence, asserted to a famous German chymist in the court of Saxony, called Kunckelius. But to which of these so noble an invention, as that of the two German noctilucas, is justly due, I neither am qualified nor desirous to judge; and therefore, without prejudicing any Man’s Right, I will proceed to that, which, I presume, is the chief thing you would know of me, namely, An Account of the Occasion and Steps of my own Attempt to make a Noctiluca  … After the experienced Chymist Mr. Daniel Krafft had, in a Visit that he purposely made me, shewn me and some of my Friends, both his Liquid and Consistent Phosphorus … he … confest to me at parting, that at least the principal matter of his Phosphorus’s, was somewhat that belong’d to the Body of Man.334 And, a little further on in the same preamble Boyle wrote that he had received further clues regarding the new substance from yet another visitor, who he referred to as “a learned and ingenious Stranger, (A. G. M. D. Countreyman, if I mistake not, to Mr. Krafft)”, probably a reference to Ambrose Godfrey Hanck(e)witz. By the early 1680s phosphorus was becoming internationally well-known and this was reflected in Leibniz’s correspondence. Thus, at the end of a letter of July 18, 1680, from London, Friedrich Slare referred to the various forms of phosphorus, and to the intelligence about the new substance provided by Crafft during his visit in 1677, as well as to the ongoing effort to produce it, writing specifically that there was hardly any space left for him to write about Balduin’s phosphorus, which was inferior to the preparations of Brand and Kunckel. Crafft had informed him that it was constituted of human excrement

334 Cf. note 318 above, and Boyle, The works, vol. 9, pp. 272f. Regarding James Butler, cf. P. Elmer, “Promoting medical change in Restoration Ireland: The chemical revolution and the patronage of James Butler, duke of Ormond (1610–88)”, chap. 4, in: J. Cunningham (ed.), Early Modern Ireland and the world of medicine: Practitioners, collectors and contexts. Manchester (UK), 2019. Digital accrss in December 2022 (National Library of Medicine): https://www.ncbi.nlm.nih.gov/books/NBK541883/.

1676–june 1683

333

but they had not yet been successful in producing it.335 In the same letter, Slare wrote the following words: “I remember that you once desired me to write you in English that you might the better exercise your knowledge of the Tongue”,336 and so, on February 24, 1681, the correspondent informed him that “The Phosphorus liquidus has been made here by two of us, Mr Boyle calls it the Noctiluca”,337 adding that “he has writ several observations on his, we can only make them of Urina inspissata”,338 and that “Kuncle pretends he makes it ex re Minerali Metallica et vegetabili quocunque”. Robert Hooke was likewise interested in the new substance. In a letter of July 22, 1680, sent by Hooke to Theodor Haak, to be forwarded to Leibniz, he wrote: As to the phosphoros, I understand from France that it is brought to that perfection as to Inlighten a whole Room by the splendor of it when Inclosed in a Glasse. If Dr Leibnitz knows any thing of the composition thereof I should take it as a great favour if he would please to Impart any thing concerning it.339 Leibniz, who had, assisted by Brand, produced phosphorus in Hanover, informed Tschirnhaus at the end of June 1682 about both his own (or Brand’s) process, and about that of Boyle, both of which involved heating and repeated and protracted distillation procedures starting with the requisite raw material, namely human urine. Thus he wrote to Tschirnhaus at the end of June 1682: Sir, you may make whatever arrangements you like with the phosphorus. I should, however, point out that making phosphorus is a pretty difficult exercise, and one must take care, particularly in the final steps, that the retort does not crack. Mr Boyle’s route is somewhat shorter, as I see from his description; it is lacking in something at times, and also does not give such strong phosphorus, and furthermore he is not instructive, for he does not provide an analysis of the process, nor indicate from which part of it the most powerful phosphorus comes. Without doubt, Mr Boyle 335 “Vix datur spatium ut aliquid scribam de Phosphoro Balduini, nec multum refert, cum ista Praeparatio Dmi Brand aut Kunkelii hunc superat ut sol minora sydera. Ex humanis Excrementis consistere mihi narravit Kraft. Nobis nondum successit” (A III,3 N. 84, p. 232). 336 Cf. p. 231. 337 Cf. A III,3 N. 178, p. 349. 338 i.e. from thickened or concentrated urine. 339 Cf. A III,3 N. 87, p. 235.

334

Chapter 1

came across this process because it was imperfectly communicated to him. I enclose both processes with this letter, both the way I have made it, as that of Mr Boyle.340 In the production process, a series of intermediate products were produced, namely concentrated urine (“dicken urin”), oil of urine (“oleum urinae”), a so-called “caput mortuum oleosum”, containing a hard superfluous salt and a black loose or soft material (“eine schwarze lückere materi”), and then an amber-like hard stone (“eine ganz harte materi wie ein börnstein”). The final product was characterized by its brightness and property of glowing in the dark, but the core fire-containing substance was the “caput mortuum oleosum”. Concerning his own process, Leibniz gave the following detailed account: I take urine that had been left standing for a time, about a barrel-full … I boil it until it begins to become thick, like a thick sirup, at which point one puts this thick urine into a retort, and lets the phlegm and volatile contents be completely dissipated in smoke, and when red drops begin to come, one places a receptacle in position and collects the oil of urine in this vessel. At this point, one smashes the retort into pieces and finds a residual caput mortuum oleosum, whose lower part is a superfluous hard salt and upper part a black loose or soft material which one retains. One puts the oil of urine once again into a retort, and forcefully extracts all moisture from it, and finds in the retort a black loose or soft material, [which is] very similar to that found in the previous retort. One puts these residual soft materials from the retorts together and expels the fire from it in the following manner. Take a good retort made of stone … and put in it about 24 loth [viz. 3/4 lbs or c. 0.42 kg] of the black loose or soft material, or of the caput mortuum oleosum, and place a glass receptacle in place, which has been luted or sealed, and apply an open flame, but at first mildly until the retort begins to glow, and continue the process for 16 hours, and intensely for the final 8 hours. There soon appears white 340 “hat also M. h. H. vom phosphoro nach seinem belieben zu disponieren. Nur dieses muß bemerken, daß den phosphorum zu machen eine zimlich beschwehrliche arbeit, und muß man sonderlich bey der lezten arbeit zusehen daß die retorte nicht springe. Des Mons Boyle weg ist etwas kürzer aber wie ich aus seiner beschreibung sehe, so fehlet er ihm bisweilen, gibt auch keinen so starcken phosphorum, und überdieß so ist er nicht instructif, denn er weiset nicht analysin subjecti et ex qua ejus parte potissimum veniat phosphorus. Zweifelsohne ist M. Boyle darauff gefallen, weil ihm der phosphorus imperfecte communiciret worden. Schicke hiemit beyde processus so wohl wie ich es gemacht, als wie M. Boyle” (A III,3 N. 368, p. 661).

1676–june 1683

335

smoke or clouds, which fall to the bottom like a slimy (or muddy) oil. Parts of a substance are also transferred, which attaches itself very firmly to the glass. It is an amber-like hard stone in which the best force or power is contained. In the continuing distillation process, the receptacle becomes very bright and glows in the dark. That which has been transferred is entirely luminous, but the dry parts more than the wet parts. From this one sees that the fire is contained in the caput mortuum oleosum.341 Then Leibniz came to the second, for him, inferior process, namely that of Boyle and began as follows: “The following more confused process was used by Mr Boyle. Take a considerable quantity of human urine …”.342 In the closing words of this detailed description of Boyle’s process, there is a corresponding evaluation. The superiority of his own process lay in an additional step, involving the refinement of the “caput mortuum oleosum”, to obtain a hard salt byproduct and the core soft black matter. Thus he wrote: “From this one sees that Mr Boyle left both the salt and the caput mortuum oleosum together, and therefore I am not surprised that his phosphorus was, as he admits, weaker”.343 A French translation of part of Leibniz’s communication to Tschirnhaus from 341 “Habe genommen urin so eine zeitlang gestanden etwa eine tonne … kochet es ab bis es beginnet dick zu werden, wie ein dicker sirup, alsdann thut man diesen dicken urin in eine retorte, läßet das phlegma und volatile vollends wegrauchen, und wenn rothe tropfen zu kommen beginnen, leget man einen recipienten vor und empfängt darin das oleum urinae. Alsdann schlägt man die retorte in stücken, darin findet man ein caput mortuum, deßen unter theil ist ein hartes salz, so sicher nicht dienet, das obere theil ist eine schwarze lückere materi, die hebt man auf. Das oleum urinae tut man wieder in eine retorte und ziehet alle feuchtigkeit starck davon ab, so findet man in der retorte eine schwarze lückere materie der ieztgedachten, so in voriger retorte gewesen ganz gleich. Thut sie zusammen und treibt das feuer daraus folgender maßen. Nim eine guthe steinere retorte … darein tue etwa 24 loth von der schwarzen materi oder capite mortuo oleoso, lege einen zimlichen gläsern recipienten vor, so wohl verlutiert, und treibs also in freyen feuer, doch erstlich gelinde bis die retorte wohl gluet, treibs wohl 16 stunden lang die lezten 8 Stunden aber gar starck. Es kommen bald weiße Nebel oder wolcken und sezet sich wie ein schlammigt oel zu boden. Gehet auch wohl etwas von einer materi mit über, die sich ganz hart an das glas anleget, ist wie ein börnstein, darin bestehet die beste krafft. Im werenden distillieren ist der recipient ganz hell, und leuchtet im finstern. Was übergangen, ist alles leuchtend; doch das siccum mehr als das humidum. Hieraus siehet man daß das feuer stecke in dem capite mortuo oleoso” (pp. 661f.). 342 “Folgender proceß so mehr confus ist von Mons. Boyle gebraucht worden: Nim eine zimliche menge Menschen Urin …” (p. 662); cf. also: R. Boyle, The aerial noctiluca, 1680 (note 318 above), and in particular “The Process”, pp. 105–109. 343 “Hieraus siehet man daß Mons. Boyle das sal so wohl als caput mortuum oleosum beysammen gelaßen, daher mich nicht wundert, daß sein phosphorus wie er gestehet, schwächer gewesen” (p. 662).

336

Chapter 1

the end of June 1682 was then published in July 1682 in the Proces Verbaux of the Académie des Sciences. It was referred to by Boyle at the beginning of his New experiments, and observations, made upon the icy noctiluca (1682), where he asserted the priority of his publication.344 From Tschirnhaus’ earlier letter of May 27, 1682, we learn that in Paris a secret formula for the production of phosphorus was being offered for sale by an Englishman and, from Mariotte’s still earlier letter of April 13 of that year, that various members of the Académie des Sciences were experimenting with the substance, and that “at the time someone wanted to take it with his hands and rub it into his hat and [also] to make light appear between the drapes taken from a bed”. In the event, the hat, bed and drapes all caught fire, and Mariotte added that the Académie members who “had their fingers burnt were not healed for 15 days”.345 While in Copenhagen, Jobst Dietrich Brandshagen had the opportunity to produce a large quantity of phosphorus but, when he presented the product to the king, the latter saw in the new substance a source of amusement and, to the dismay of the correspondent, he besmeared the entire consignment in the course of an evening. In his letter of mid-January 1682,346 Brandshagen also related that to enhance phosphorescence in the dark, he himself had rubbed the substance into his face, an action which resulted in severe nausea along with a feeling of having nothing under the skin and, furthermore, the following morning his whole face had an ulcerous or pyogenic appearance. Besides such playful applications, which made phosphorus most suitable for public performances, Leibniz saw an eminent theoretical importance of this novel fiery substance. As he wrote to Tschirmhaus, at the end of June 1682, he knew no better process which squared with the three universal alchemical principles – namely mercury, sulfur and salt – since the end product, or fiery substance,

344 Cf. the French translation of Leibniz’s communication: G. W. Leibniz, “L’Operation pour faire le phosphore”, Procès Verbaux des Séances de l‘Académie des Sciences, Tome IX, (4.7.1682), pp. 165–166 (A III,3 N. 368, p. 651 and pp. 662f.); R. Boyle, New experiments, and observations, made upon the icy noctiluca imparted in a letter to a friend living in the country: to which is annexed A chymical paradox, London, 1681/2 [1682], and in particular the opening “Advertisement of the publisher to the reader”. 345 cf. Tschirnhaus’ account (A III,3 N. 356, p. 625) and that of Mariotte (A III,3 N. 341, pp. 586f.). The latter’s words were as follows: “ces jours passez quelqu’un voulut prendre avec les doigts pour en frotter son chapeau et y faire paroistre de la lumiere entre les rideaux tirez d’un lit … Les autres Mrs qui ont eu les doigts bruslez n’en gueriront de 15 jours”. 346 Cf. A III,3 N. 310, pp. 540f. and also H. Kragh, 2003 (Introduction, note 176).

1676–june 1683

337

derived neither from a solid state, or a fixed salt, nor from a volatile or mercurial spirit, but rather from an intermediate oily or sulfuric liquid.347 The Académie des Sciences too was appreciative of the fact that Leibniz was willing – for the sake of supporting the advancement of Tschirnhaus – to disclose the production process for phosphorus in exchange for other scientific secrets. Thus, Mariotte wrote, on June 22, 1682, that “Our chemists are prepared to exchange their finest secrets for your phosphorus [secret]”.348 Leibniz received through Tschirnhaus two such secrets from the Académie, which were referred to as “a growing salt” (“Sel vegetans”) and “gold rendered volatile without fulmination” (“l’or rendu volatile sans fulminer”). The first of these was a salt, which was said to grow like a plant in water, and Leibniz was informed accordingly in the following words: “the first is unordinary or strange and grows no differently to a plant, if one puts some of the salt in water and lets it stand for about 8 days”.349 The experiment of an Italian, who had demonstrated a smoking or fuming liquid at the court in Celle, was described by Leibniz in a report for the Journal des Sçavans, which he sent to the editor Jean Paul de La Roque in January, or early February, 1681.350 In September 1680, it had led to a discussion with the professor of medicine in Helmstedt, namely Günther Christoph Schelhammer, who in turn had involved Georg Wolfgang Wedel, a professor in Jena.351 Schelhammer had conjectured, in a letter to Leibniz of June 14, 1680, that the smoke rising from the liquid was attributable to an inner fire in the fluid, and he seized the opportunity to ask Leibniz about phosphorus.352 Replying on September 24, 1680, Leibniz made clear that the smoking liquid had nothing in common (“nihil commune habet”) with phosphorus and he, for his part, enquired of Schelhammer about where Wedel’s description of the smoking liquid had been published.353 A multitude of chemical considerations in Leibniz’s correspondence may be categorized under the heading of the economic utilization of chemical 347 “Ich weiß keinen proceß, der auff die vulgate Chymicorum principia, sal, sulphur und mercurium beßer quadrire als die composition dieses feuers oder pyropi, den dieses feuer komt eigentlich nicht aus dem sale fixo, noch aus dem volatile oder Mercuriali, sondern aus dem medio oder oleo vel sulphure” (A III,3 N. 368, p. 662). 348 “Nos Chymistes sont prests de troquer leurs plus beaux secrets contre le vostre du Phosphore” (A III,3 N. 365, p. 649). 349 “das Erste ist curieus, und wächset nicht anders als wie Eine Plante, wen man von den Saltz in waßer gethan und es etwan 8 tage stehen leßet” (A III,3 N. 384, p. 686). 350 Cf. A III,3 N. 163. 351 Cf. A III,3 N. 109, pp. 266f. 352 Cf. A III,3 N. 71, pp. 207f. 353 Cf. A III,3 N. 110, p. 268.

338

Chapter 1

processes. Often the dividing line to the techno-economic projects is difficult to draw. Writing to Grew, on March 19, 1680, Leibniz desired to learn, for example, whether the Royal Society could produce a fluid gold paint with which clothing might be dyed.354 In the production process of ruby glass (“artificiall Rubine”), Leibniz and Robert Hooke were equally interested. In the previously-cited letter of July 22, 1680, sent by Hooke to Theodor Haak, for forwarding to Leibniz, the correspondent requested information concerning the production of both phosphorus and ruby glass. Thus he wrote: As to the phosphoros, I understand from France that it is brought to that perfection as to Inlighten a whole Room by the splendor of it when Inclosed in a Glasse. If Dr Leibnitz knows any thing of the composition thereof I should take it as a great favour if he would please to Impart any thing concerning it, or concerning the composition of the artificiall Rubine.355 In Crafft’s, and Elers’, endeavors for the perfection of pearls, the correspondents believed themselves to be in a position to report initial success at the beginning of September, 1681.356 Above all, however, it was the range of very different chemical processes for the preparation of gold and silver that, again and again, played a role in the correspondences with these two projectors. Leibniz apparently esteemed such projects less than the techno-economic processes already referred to, and he was accordingly impatient on occasions as for example in his letter to Crafft, on April 7, 1681, when he wrote: I desire very much the success of your most recent enterprise, Sir. You ought to freely report what the quantity of | silver |357 was, as of the given half ducat of | gold |;358 in that coming from me there was surely nothing, because it was resinous.359

354 Cf. A III,3 N. 32, p. 88. 355 Cf. A III,3 N. 87, p. 235. 356 Cf. A III,3 N. 278, pp. 493f. and N. 279, p. 497. 357 enciphered in the manuscript. 358 enciphered in the manuscript. 359 “Ich verlange sehr den success von m[einem] h[ohen] H[erren] lezter entreprise, m. h. H. wolle mir ohnbeschwehrt melden, aus was fur qvantität | lunam [viz. silver] |als gegeben | halb ducat an sol [viz. gold] | in der die von mir dazu kommen ist gewiß nichts gewesen, weil sie harzisch” (A III,3 N. 198, p. 386).

1676–june 1683

339

Nevertheless, there can be no doubt about Leibniz’s interest in the preparation, or separation, of gold and silver from suitable raw materials or chemical precursors. Thus we find, at the beginning of September 1681, Elers reporting about his efforts, together with the personal physician at the court in Hanover, namely Christof Pratisius, to obtain silver from cinnabar through the application of sulfur and lead.360 Crafft, Christoph de Rojas y Spinola  – the Dutch-born Bishop of the Viennese new town district (“Wiener Neustadt”) in Austria – and Leibniz himself discussed the possibility of obtaining silver from the liquation, or segregation, of Spanish copper coins, as is to be seen from Crafft’s letter to Leibniz of December 25, 1682.361 In January 1680, both Leibniz and Crafft had followed attentively the efforts of various chemists in Dresden, who were seeking to obtain gold from copper, mercury, and from silver.362 In July 1682, Elers reported the sale of a process for obtaining gold – on the basis of intelligence obtained from Leibniz – to a Berlin chemist for a sum of 8000 Taler.363 Alas, he appears not to have received the sum in question, a part of which was intended for Leibniz.364 A much larger sum, namely 20,000 Taler, was mentioned in relation to the offer of the Dutch punchcutter, and engraver, Christoff Adolphi, whom Leibniz had probably first encountered during his time as a student in Leipzig. In January 1680, Adolphi offered Crafft different chemical secrets including a process to obtain mercury from all metals except gold, and to separate sulfur and mercury. Thus he wrote the following text to Crafft, who then forwarded it to Leibniz on January 30: To begin with, I know the secret as to how to draw, within a period of eight days, mercury out of all metals except gold (that would require a longer period) by means of distillation without having a knowledge of some mercurial additives. These [are] | silver |,365 | iron |, | tin |, | copper |, | lead |, | antimony |, and are very beautiful … There is still another secret, of such rarity that I have never heard of it in my whole life, of knowing, or being told of, a liquorish measure which, in your hands, would clearly separate sulfur and mercury, and could be used as long as the dampness lasts so that, by this means, a great deal of mercury is obtained and it is 360 Cf. A III,3 N. 279, pp. 496f. 361 Cf. A III,3 N. 429, specifically pp. 756f. and p. 762. 362 Cf. A III,3 N. 2, pp. 45f. and N. 18, p. 61. 363 Cf. A III,3 N. 371, pp. 666f. 364 Cf. A III,3 N. 361, pp. 643f. 365 alchemical symbols for silver (Luna), iron (Mars), tin (Jupiter), copper (Venus), lead (Saturn) and antimony in the manuscript.

340

Chapter 1

very beautiful … There is yet a second secret promising a yearly profit of a hundred times a hundred, over and above all expenses, … so should your Honor now know someone who is prepared to pay 20,000 Taler for both secrets …, then for the rest you will have preference and be free to profit from it, should it please your Honor to be first to acquire this offering … done in all secrecy.366 Then, in early February 1680, Leibniz requested further details from Adolphi, as well as a demonstration of the truth of his propositions with, as a return service, the promise or prospect of an utmost commitment on his part.367 At the very least, Leibniz desired the communication of details to which Adolphi was privy, since, as he explained, commonly – through untrustworthy pretentiousness – valuable things never come to fruition, whereas in contrast – through honest and unreserved communication with persons known for their steadfastness – incomplete knowledge of things can sometimes be perfected and rendered useful.368 A reply from Adolphi proved not to be forthcoming. Leibniz also used contacts with his correspondents to clarify problems that arose in his reading of chemical literature, or to make inquiries about further investigations. In a letter to Sebastian Scheffer in March 1682,369 he referred to a polemical work,370 which was directed against Johann Rudolf Glauber (1604–1670), and in which the author Christoph Fahrner had referred to a 366 “Vooreerst soo weet het secreet om uijt alle metallen behalven het goud, dat soude wat langer tijt vereijschen, in den tijt van acht dagen de mercurium te trecken, ende dat doer manier van distillatie sonder eenige mercurialische additien te weeten, dese | silver |, | iron |, | tin |, | copper |, | lead |, | antimony | ende sijn seer schoon … Noch isser een naeder secret van diergelijke rariteit, mijn leven niet gehoort hebbe, te weten, een liquorisch mensurum twelch in u hand datelich sulphur ende mercurium separeert, ende kann soo lange gebruijcht worden, als de vogttigkeit duijrt, soo dat door die manier seer veel Merc. bekombt, ende is seer schoon … Noch isser een tweede secret tot winst wil toe seggen jaerlich hondert met hondert, boven alle onkosten … soo U. E. nu iemand weet die voor beijde secreten belieft te geven 20000 rth. contant … de rest wil U. E. lieber en vrij stellen om daermede profijt te doen, soo U. E. nun behagen in dese voorschlag heeft sal verlangen mit den eersten … alles in secretesse” (A III,3 N. 19, pp. 67f.). This letter was forwarded to Leibniz as an attachment to A III,3 N. 18. 367 Cf. A III,3 N. 27, pp. 81f. 368 “Nur dieses habe beyfügen wollen, daß gemeiniglich durch unvertreuligkeit und immoderate praetensionen auch guthe dinge erliegen und unnüz werden, hingegen durch aufrichtige und un-reservirte communication mit solchen Personen deren solidität bekand, bisweilen auch unvollkommene dinge perfectioniret und zu nuzen bracht werden” (p. 81). 369 Cf. A III,3 N. 339, pp. 583f. 370 Ch. Fahrner, Widerlegung oder vielmehr Warnung vor der groß prallenden Explicatio Miraculi mundi, und der betriegerischen genandten Wolfahrt Teutschlands Johann Rudolph Glaubers, Stuttgart 1656.

1676–june 1683

341

chemical process through which – ostensibly and with little effort – an appreciable quantity of silver could be obtained from lead. In January–February 1683, Leibniz asked Scheffer371 – who in his youth had worked as an assistant with Fahrner  – for information about the process in question, and Scheffer duly consulted his former mentor about the matter before replying to Leibniz, on February 27, 1683, with information about Fahrner’s indisposition but willingness to reply.372 The production of gold and silver from tin – and a passage in a work of Glauber – were at the center of a query Leibniz sent to Crafft at the end of August 1681. In connection with this query, which he was unable to answer, Crafft made a remark, in his reply on September 2, 1681, that epitomizes chemical research at the time, namely that he was from day to day becoming more and more confirmed in his conviction that all was possible, and available, in nature, and thus required only to be diligently and correctly sought. Thus, the correspondent wrote: The precipitation of | gold |373 and | silver | from | tin | has, to the best of my knowledge, not yet been found, and that which Glauber wanted to achieve though his malformed brain, I myself have never practiced, or heard that it was licensed or experimentally investigated by others. I am from day to day being strengthened in my conviction that everything is possible, and available, in nature and requires only to be assiduously sought, and dealt with, by means of the right capabilities.374 The fact, that everything appeared possible, implied also that there could be a quest for very remarkable things in nature. Thus, Crafft was persuaded by an alchemist, at the Leipzig Fair, that a non-wetting water existed in nature, as he reported to Leibniz, on November 11, 1682.375 While Leibniz’s response to this has not been found, it seems that his attitude may well have been characterized by a cautious skepticism.376 Moreover, even Crafft himself relativized, in 371 Cf. A III,3 N. 438. 372 “H. Fahrner ist kranck, so bald er die kräffte, will er mir gnügen leisten” (A III,3 N. 442, pp. 778f.). 373 alchemical symbols for gold, silver and tin in the manuscript. 374 “Die praecipitation des | gold | vnd | silver | aus dem | tin | ist meines wißens biß dato noch nicht funden, vnd waß Glauber durch sein halbkopf darin außrichten wollen, habe ich niemahl selbst practicirt, noch von andern approbirt oder experimentirt gehöret. Ich werde in meiner opinion täglich in mehr und mehr gestärket, daß alles muglich vnd in die natur gelegt, wenn darin nur fleißig gesucht, vnd durch die recta ingenia recht furgenommen wirdt” (A III,3 N. 278, p. 489). 375 “daß eine solche aqua non madefaciens manus in natura sey” (A III,3 N. 418, p. 739). 376 Cf. A III,3 N. 452.

342

Chapter 1

a letter of December 25, his search for this mysterious fluid with a degree of melancholic self-reprobation.377 In the fall of 1681, Leibniz invited the alchemist Jakob Vierort to a presentation of an alleged transmutation of his at the court in Hanover. Leibniz had made thorough enquiries in advance about Vierort contacting Herman Jansen,378 a certain Dr Stolberg,379 Crafft,380 and Heinrich Meibom.381 Crafft advised Leibniz, on September 2, 1681,382 to expose the presumed swindler by exchanging (at an appropriate moment) the alleged philosopher’s stone (which was embedded in wax) with plain wax. If then, in the aftermath, gold were to be produced by the power of the charlatan, the deception would be revealed. In the end, Leibniz demanded that the alchemist himself not be present during the performance of the transmutation. Since Vierort rejected this precondition, it is probable the planned performance, in the presence of duke Ernst August, never did take place. 9

Geology, Mineralogy and Paleontology

In Leibniz’s first years in the Harz mountains, we find the beginning of the investigations that would culminate in his posthumously-published Protogaea.383 In this period, we also find the first intimation, which was expressed to Otto Mencke on October 22, 1681, of an intended article for the Acta Eruditorum on this topic.384 As is evident from a letter of mid-October 1682 to Jean Gallois, Leibniz had arrived at results regarding the formation of minerals, which strongly deviated from the received view and which he thought might easily

377 Cf. A III,3 N. 429, pp. 758f. 378 Cf. A III,3 N. 250 and N. 256. 379 Maybe Johann Reinhard Stolberg; cf. A III,3 N. 251, p. 450. 380 Cf. A III,3 N. 266, pp. 475f. 381 Cf. A III,3 N. 287 and N. 288. 382 Cf. A III,3 N. 278, p. 491. 383 Cf. G. W. Leibniz, Ch. L. Scheidt (ed.), Summi Polyhistoris Godefridi Guilielmi Leibnitii Protogaea sive de prima facie telluris et antiquissimae historiae vestigiis in ipsis naturae monumentis dissertatio ex schedis manuscriptis viri illustris in lucem edita a Christiano Ludovico Scheidio, Göttingen, 1749; Protogaea, oder Abhandlung von der ersten Gestalt Der Erde und den Spuren der Historie in den Denkmaalen der Natur, Leipzig, 1749; G. W. Leibniz, Leibniz: Opera Omnia, 6 vols, Geneva 1768, in particular vol. 2, part 2, pp. 181–198 (preface) and 199–240; Leibniz: Cohen-Wakefield, 2008, and Leibniz: Scheid-Engelhardt-Wellmer, 2014 (Introduction, note 190). 384 Cf. A I,3, N. 437, p. 506.

1676–june 1683

343

be given a mechanical foundation, and verified accordingly. Thus he wrote to Gallois: I simply want to tell you at present that I have had occasion to make considerable observations of the physical world, and particularly as regards a knowledge of minerals. Since there are mines in the neighborhood, which are considered to be among the most extensive in Germany, I wanted to avail of the opportunity, and there I found things far removed from the common opinion regarding the origin of minerals and, nonetheless, so simple to demonstrate solely on the basis of mechanical reasoning.385 He continued by explaining that he had made important discoveries, regarding the formation of rocks and of the ore deposits found in lead and copper mines: “I have indeed found many things which I could demonstrate regarding the generation of rocks and metal mines, for example I could explain the production of the lead mine”.386 In addition, he had made unique discoveries regarding copper mines and had found an explanation for a certain wonder of nature he had come across, probably a reference to the fossilization of two fish later treated in his Protogaea.387 Thus, he continued to inform Gallois that: I also have made unique discoveries regarding copper mines, and I have found a distinctive explanation concerning a certain wonder of nature, which came into my hands. It is a stone on the surface of which nature has traced perfectly, with the features of a metallic mine, two different animals. It is easy to prove that there was no manipulation involved. I had the idea to design it exactly, and to explain the production very distinctly, in a little treatise, necessary for the understanding of my

385 “Je vous diray seulement à present, que J’ay eu occasion de faire des observations considerable en physique, et particulierement dans la connoissance des mineraux. Car il y a dans le voisinage des mines qu’on compte par my les plus considerable de l’Allemagne, j’ay voulu profiter de l’occasion; où j’ay trouvé des choses si éloignées de l’opinion commune touchant l’origine des mineraux, et cependant si aisées à demonstrer par des raisons entierement mechaniques” (A III,3 N. 407, pp. 724f.). 386 “J’ay donc trouvé bien des choses que je puis demonstrer touchant la generation des pierres, et des mines des metaux, par exemple je puis expliquer la production de la mine de plomb” (p. 725). 387 Cf. Leibniz: Opera Omnia (note 383), in particular vol. II,2, pp. 214f.; Leibniz: CohenWakefield, 2008 (note 383), see pp. 42–53 and Fig. 3 (Fish implanted on slate).

344

Chapter 1

reasoning, and which would be considerable in terms of the new consequences one might draw from it.388 In practical terms, Leibniz’s frequent journeys to the Harz mountains provided him with a welcome opportunity for geological and mineralogical studies, since he considered a scientific treatment of all matters relating to mining to be a desideratum. In a letter to Nehemiah Grew, on March 19, 1680, Leibniz posed the question as to whether amber found in the ground near the location Wunstorf (not far from Hanover) could have originated there.389 And in January and March, 1682, Ferguson replied to queries received from Leibniz about a goldmine on Sumatra.390 Already, on November 24, 1681, Leibniz had requested from the director of that mine Benjamin Olitsch – a former Saxon mining official who had joined the Dutch East India Company – information from his rich treasure trove of experience. The sentiment expressed in the closing words of this letter – viz. “I often wish to have the pleasure of receiving news from you Sir”391 – proved to be in vain. Olitsch died on Sumatra in May 1682. In his letter to Olitsch, Leibniz referred to fossilization specimens found in Mansfeld slate, which had revealed the likes of natural fish, and which he found to be of particular interest. His words to Olitsch were: “I would like to know among other things your thoughts, Sir, concerning the Mansfeld slate”, to which he added the statement: “I am inclined to believe there were natural fish there”.392 About the time Leibniz composed his letter to Olitsch, in October–November 1681, an inspector of the mint in Zellerfeld, named Becker, enquired in conversation with him about the processing procedures for various ores, on which occasion reference was also made to ores from other regions

388 “J’ay encor des decouvertes singulieres sur des mines de cuivre et j’ay trouvé l’explication distincte d’une certaine merveille de la nature, qui m’est tombée entre les mains. C’est une pierre sur la surface de la quelle la nature a tracé parfaitement bien avec des traits d’une mine metallique deux animaux differens; il est aisé de prouver, que l’artifice n’y a pas eu de part. Je me suis proposé de la faire desseigner exactement, et d’en expliquer la production tres distinctement par un petit traité, necessaire pour l’intelligence de mes raisons; et qui seroit considerable pour les consequences nouvelles qu’on en peut tirer” (note 385 above, p. 725). 389 “In pago quodam non procul ab Hanovera distante, reperta est sub terra massa succini, quod an ibi natum sit difficilis judicatio est” (A III,3 N. 32, p. 87). 390 Cf. A III,3 N. 307, pp. 535f. and N. 338, pp. 581f. 391 “wundsche offt durch guthe zeitung von M. h. H. erfreuet zu werden und verbleibe” (A III,3 N. 296, pp. 516–518, specifically p. 518). 392 “Ich verlange unter andern zu wißen was M. h. H. von dem Mansfeldischen schiefer halte, ich glaube fast es seyen naturliche fische da gewesen” (p. 517).

1676–june 1683

345

of geological or mining interest, like Muscau, near Görlitz in Saxony, or Poland and even East India.393 10 Medicine Following a meeting in Hanover, in September or early October 1681, with Heinrich Meibom, professor of Medicine in Helmstedt, Leibniz wrote the following words to the correspondent, on January 23, 1682, regarding observations of triangular vascular formations: “when I was recently on the road, I thought about the triangular vascular formations which you said you had observed”.394 Here Leibniz took an anatomical observation of the correspondent – whose exact investigation and verification with the aid of a microscope he considered to be essential – as a starting point for a lengthy theoretical consideration about the form of blood vessels. Assuming the blood vessels to be elastic and of polygonal cross section – with the best case being triangular and worst case circular – they represented what he termed a most simple hydraulic machine which, notwithstanding the irregular (or intervallic) entry (or intrusion) of the blood, guaranteed a regular extrusionary rate of flow.395 Thus, resorting to trigonal prismatic geometry to describe the shape of such blood vessels – whose cross section was represented in a drawing by a circumscribed polygon, that might range from a triangle (the best), through a multi-faceted polygon, to a circle (the worst) – he imagined a hollow triangular prism or tube to be filled with water and continually supplied through an orifice as the most simple hydraulic machine to emulate blood flow. However, the experiment entailed a mechanical problem of reconciling the intermittent, or pulsed intrusion, with the continuous extrusion of the fluid.396 And the solution of this mechanical problem did not seem to him to be at all simple.397 Immediately following this line of thought, Leibniz elaborated a further consideration in which elasticity emerges as an explanatory principle in anatomy, 393 Cf. A III,3 N. 292, pp. 507–509. 394 “Ceterum cum nuper in itinere essem, meditatus sum de triquetris capitis vasis, quae a Te observata narrabas” (A III,3 N. 312, pp. 551–555, specifically p. 552). 395 “Deprehendi autem statim tubo elastico polygono, et inprimis trigono, is enim maxime remotus est a circulari, effici posse machinam hydraulicam, quae liquorem continuo jactu extrudat, licet is non continue, sed per intervalla tantum in eam intrudatur” (p. 553). 396 “Sit enim prisma trigonum cavum, seu tubus … Ponamus hunc tubum esse aqua plenum, et in eum intrudi aquam novam per foramen … habebimus machinam hydraulicam simplicissimam ex uno scilicet tubo constantem, quae intrusione aquae licet interrupta, extrusionem tamen perpetuam seu jactam continuum efficere poterit” (pp. 553f.). 397 “Cujus mechanici problematis solutionem … non adeo facilem arbitror visum iri” (p. 554).

346

Chapter 1

while adhering to his triangular prism (or tube) model for the form of blood vessels. And the longer and fewer the sides of the circumscribed polygon were, the more flexible they would be, he wrote.398 He then proceeded to present his views on acoustics and concluded that something must exist in the hearing organ which can be homotonic, or of uniform tension or tonus, with every sonorous body. The solution was thus to be sought in anatomy.399 He encouraged Meibom, as he had done previously with Schelhammer,400 to pursue this outstanding anatomical problem of identifying the missing entity, and to inform him accordingly.401 Otherwise, Leibniz considered the main questions of acoustics to be essentially solved. New observations about kidneys and urinary tracts were reported, or discussed, in various correspondences in the early 1680s. Sebastian Scheffer had good contacts in Padua, and he forwarded on May 23, 1682,402 a report of an anatomical discovery of Domenico Marchetti, which was also reported in the Journal des Sçavans,403 and which Leibniz in turn passed on without comment to Friedrich Schrader a couple of months later.404 Likewise, Scheffer’s letter, of January 1681,405 reveals that Leibniz acted as an intermediary between Henri Justel and Scheffer himself for the publication in the Miscellanea Curiosa of a description of an extremely enlarged kidney.406 Schelhammer’s investigations in this area were initiated following his acceptance of a medical professorship in Helmstedt, about which he informed Leibniz on November 18, 1680.407 In relation to medical science, it was an anatomical investigation of the sexual organs of the mole, that became the starting point of a discussion between Schelhammer and Leibniz and that was continued over several letters, in 1680 and 1681. The overture to this discussion 398 “Posset quidem idem praestari polygono quovis, sed trigonum et simplicissimum et aptissimum esse patet, quia a circulo remotissimum, ac proinde majoribus paucioribusve laminis sive elastris ceteris paribus constare potest, quae proinde facilius curvantur. Nam omne corpus tensum quo est longius, eo flectitur facilius” (p. 554). 399 “Quod ut fiat, necesse est in organo auditus esse aliquid, quod possit cuilibet dato corpori esse homotonum, adeoque exprimere sive imitari tonum oblatum quemvis. Hoc quae sit, ab anatomia petendum est” (p. 554). 400 Cf. A III,3 N. 182 and N. 311. 401 “de quibus judicium tuum expecto, qua ratione ad partes anatomia cognitas adplicari meditations istae possint” (note 394, p. 555). 402 Cf. A III,3 N. 354, p. 608. 403 Cf. Journal des Sçavans, (June 8, 1682), p. 215. 404 Cf. A III,3 N. 381, pp. 682f. 405 Cf. A III,3 N. 162, in particular p. 331 and annotation. 406 Cf. note 299 above. 407 “non ingratum erit etiam illud cognoscere, heri professionem medicam ordinariam mihi in solenni Legatorum illustrium consessu esse collatum” (A III,3 N. 124, p. 286).

1676–june 1683

347

was a brief meeting between the two in Hanover. Following Leibniz’s first letter of June 2, 1680,408 and Schelhammer’s reply on June 14,409 the topic of discussion was extended in Leibniz’s next letter of September 24,410 and the focus moved from the anatomy of the mole (“de Talpae gen[eratione]”) to the question of sexual reproduction in general.411 In the contemporary controversy about the constituent parts of mammalian semen – in particular between the medical professor in Leiden, Johannes van Horne (or Hoorn, 1621–1670), the physician Reinier de Graaf (1641–1673) in Delft, and the Amsterdam anatomist and naturalist Jan Swammerdam (1637–1680)  – Schelhammer took the side of van Horne (1668),412 and that of Swammerdam (1672),413 in opposition to that of de Graaf (1668 and 1673).414 Thus, Schelhammer, writing to Leibniz on November 18, 1680, expressed his belief that he had identified the existence of three separate constituents of the seminal fluid, which were being continually produced in testicles, prostate or prostatic glands, and seminal vesicles, and then effused into the urethra for removal from the body.415 Then, on December 16, Leibniz expressed his skepticism, and he interjected that it should be investigated whether all three constituents were equally necessary for animal reproduction.416 The question could not, however, be answered by the correspondent, in his reply on January 10, 1681, and notwithstanding his knowledge of medical literature, and his considerable thought regarding the matter, he readily conceded that Leibniz’s objection in the matter was valid.417 408 Cf. A III,3 N. 69. 409 Cf. A III,3 N. 71. 410 Cf. A III,3 N. 110. 411 Regarding theories of sexual generation in this context, cf. C. Dobell, 1932 and 1958, C. Pinto-Correia, 1997, J. Klein, N. Takahata, 2002, and N. Lane, 2015 (Introduction, note 202). 412 Cf. J. van Horne, Suarum circa partes generationis in utroque sexu observationum prodromus ad celeberr. virum Guernerum Rolfinckium, Leiden, 1668. 413 Cf. J. Swammerdam, Miraculum naturae sive uteri muliebris fabrica, notis in D. J. van Horne prodromum illustrata, Leiden, 1672, in particular p. 11. 414 Cf. R. de Graaf, De virorum organis generationi inservientibus, de clysteribus et de usu siphonis in anatomia, Leiden and Rotterdam, 1668; Partium genitalium defensio, Leiden 1673. 415 “Quod de Talpae gen. scire desideras, illud est. Grafius unicam virilis seminis materiam agnoscit, et Cl. Hornio contradicit qui triplicem esse docuerat. Ex testibus enim, prostatis, ac vesiculis seminalibus subinde aliam atque aliam suppeditari. Hanc vindicait postea Swammerdammius  … contra Grafium. Eandemque mea observatio indubiam reddit plane, dum nihil inter se testes et vesiculas ac glandulas communicare vidi, sed singulis suos ductus esse proprios quibus seorsim unumquodque semen in uretram effundat” (note 407 above, pp. 285f. and annotations). 416 “Circa materiam seminalem triplicem illud investigandum esset, an omnis aeque necessaria sit generationi animalis” (A III,3 N. 139, p. 304). 417 “Quae de partibus seminalibus addis vera sunt” (A III,3 N. 153, p. 318).

348

Chapter 1

A veritable sensation among scholars was caused by Denis Papin’s digester, in which animal bones could be rendered soft and made edible. Papin first presented his pressure pot at the Royal Society, in May 1679, and the first publications regarding it,418 came a year or two later from Robert Boyle,419 and Papin himself,420 and reviews were published in the newly-established Acta Eruditorum.421 Mariotte informed Leibniz, on June 4, 1681, about a presentation of the digester at the Académie des Sciences.422 Leibniz had previously been informed, on July 18, 1680, by Frederick Slare who wrote the following on that occasion: I shall give you a further Account of this most excellent Invention. NB. I dined yesterday with the Author, who treated me with this Dish, and I found the Bones as good as the Flesh: 1. He uses no Chymical or Galenical Domestic or exotic Ingredient excepting clear fountain water, so that we need not feare any ill Consequence. 2. It is done in a vase clause, the constant circulation of ye most subtile parts seeme to make this deepe impression upon the Bone. 3. There is such a contrivance of the Balneum in which this vessel is contain’d that ye water included can not swell and extend itself (as is usual in common potts), for it is so comprest by a screw that keeps the Cover down that it acts with more vigour than can be imagin’d. 4. The flesh is not spoyld but eates very savary and good. I am now treating a Person in a Consumption with this dyet.

418 Cf. A III,3 N. 110, in particular the annotation p. 269. 419 Cf. R. Boyle, Experimentorum novorum physico-mechanicorum continuatio secunda. In qua experimenta varia tum in aere compresso, tum in factitio, instituta, circa ignem, animalia … cum descriptione machinarum continentur, London, 1680, in particular the Forward and pp. 218–223. 420 Cf. D. Papin, A new digester, or engine for softning bones, containing the description of its make and use in these particulars: viz. cookery, voyages at sea, confectionary, making of drinks, chymistry, and dying, London, 1681; La Manière d’amolir les os et de faire cuire toutes sortes de viands, Paris, 1682. Regarding the circulation of Papin’s device later in the century, cf. M. Storni, “Denis Papin’s digester and its eighteenth-century European circulation”, British Journal for the History of Science, vol. 54(4), (2021), pp. 443–463. 421 Cf. the reviews of Papin’s work under the headings: “A new digester, or engine for softening bones … Novus digestor aut machina pro emolliendis ossibus”, Acta Eruditorum, (April 1682), pp. 105–109; “La maniere d’amolir les os”, Acta Eruditorum, (October 1682), pp. 305–308. 422 Cf. A III,3 N. 240, p. 436.

1676–june 1683

349

5.

Many Chymical as well as Culinary matters may be improved by this Machin. If you were very desirous of such a Machin, I believe I could procure you one viz. a small one that weighs 14 or 15 pound to boyle a Fish or a small joint of meat. This is a rarity: for I know no Person that has one excepting ye Author.423 Leibniz then negotiated with Slare about the purchase of such a digester.424 During these negotiations, he aroused (presumably deliberately) the impression in Schelhammer that it was a discovery which came from France.425 Schelhammer was in fact curious to learn what was causing the softening of the bones, and he thought the invention might have useful applications in medicine.426 Friedrich Schrader saw in Papin’s steam digester an analogy to rachitis or rickets, which likewise made bones soft. However, he was more interested in the opposite problem, namely as to how one might petrify and indurate the parts of animals, and innards, so that they would retain their form and position, as he informed Leibniz on December 8, 1681, in the following words: I have recently received from Holland Papin’s French language tract on the elixation of bones, and Mr [Burchard de] Volder, professor of Cartesian philosophy in Leiden, brought me from Paris a certain kind of bone of an animal which can be carved like meat, and why should one not imitate nature here, which at times generates humors in our bodies [and] which render bones soft and flexible? … but, actually I would rather learn quite the contrary, namely how one might petrify and indurate the parts of animals, and the visceral organs, so that they retain their form and position.427 423 Cf. A III,3 N. 84, pp. 231f. 424 Cf. A III,3 N. 178 and N. 218. 425 Cf. A III,3 N. 110, p. 269. 426 “Forsan enim in medicina usum esset habiturum non contemnendum” (A III,3 N. 124, p. 286). 427 “Ich habe neulichst aus Holland erhalten des Papini tractatum de emolliendis ossibus Gallice scriptum, und hatt H. Volder Prof. Philosophiae Cartesianae in Leiden, mir os animalis cujusdam aus Paris mit gebracht welches man wie fleisch zerschneiden kan, und wie solte man die natur hierin nicht können imitiren welche zuweilen in corporibus nostris solchen humorem generiret qui ossa reddit mollia et flexilia? … aber möchte ich im gegentheil eigentlicher wißen wie man die partes animalium und viscera petrificiren und induriren könne daß sie ihre formam und situm behielten” (A III,3 N. 299, p. 522).

350

Chapter 1

The knowledge which Schrader had gained on his journeys  – about the embalming of corpses, and related matters like the induration and petrification of visceral organs – through reading, and through his own experiments,428 was duly greeted with acknowledgement by Leibniz in July–August 1682.429 Therapeutic and pharmaceutical topics were likewise not wanting in Leibniz’s correspondence at this time. Regarding the spectacular application of cinchona bark by the English physician, Sir Robert Talbot, Leibniz sought to obtain the opinions of the Royal Society,430 as well as of the personal physicians of the duke at the court in Celle, namely Heinrich Christoph Ebell and Dietrich Conerding.431 Leibniz’s question about the appropriate use of antimony preparations was answered in detail by Schrader,432 and Ferguson was able to inform him about a skin cosmetic, which Leibniz then designated as “Cosmeticum Fergusoni”.433 Scheffer used sulfur as medication against cough,434 and he concocted an “antepilepticum” (viz. an antiepileptic or epilepsy drug) from the hearts of frogs.435 The age-old conflict between physicians and apothecaries also raised its head in the early 1680s. Schelhammer complained in September 1680 that he, as a medical professor, had to leave the production of medications to the apothecaries, writing that: It is the reason why many very beautiful discoveries can never be made, for chemistry requires a very great investment and, if one is not reassured that one will be reimbursed for the medication that one prepares, who would be stupid enough to entirely waste his efforts and his money [on this].436 In this dispute Leibniz endorsed the standpoint of the physicians, writing in his reply to Schelhammer, on September 24, that: “I am surprised that the preparation of medications is forbidden in your academy, and the statutes of the 428 Cf. A III,3 N. 265, N. 299 and N. 344. 429 “Pulchrum est quod refers de viscerum induratione in duritiem saxeam” (A III,3 N. 381, p. 682). 430 Cf. A III,3 N. 32, p. 88. 431 Cf. A III,3 N. 10, N. 29 and N. 129. 432 Cf. A III,3 N. 265 and N. 344. 433 Cf. A III,3 N. 41, pp. 100f. 434 Cf. A III,3 N. 162, p. 331. 435 Cf. A III,3 N. 387, p. 697 and p. 699. 436 “c’est la raison pourquoy plusieurs tresbelles decouvertes ne se peuvent jamais faire, car la chimie demande une tres grande depence, et quand on n’est soulagé de ce qu’on peut rembourser des medicamens qu’on prepare, qui sera si fou que de perdre sa peine et son argent entierement” (A III,3 N. 109, p. 267).

1676–june 1683

351

medical faculty ought to outweigh the external apothecaries, to the advantage of the medics who prepare their own medications”.437 The Chinese method of diagnosing diseases, by pulse observation, also aroused Leibniz’s interest. In January, 1681, Scheffer answered a query from Leibniz, and he referred to a letter of November 20, 1679, which he had received from the botanist and physician, Andreas Cleyer, which contained mussels from Jakarta and from which excerpts were later published in the Miscellanea Curiosa.438 Thus Scheffer wrote: “About Dr Clayer’s method I have nothing further to report beyond that which he briefly explained in the letter to me … This Dr Clayer has already lived 18 years in New Batavia [Jakarta], and collected there many beautiful things”.439 Here “Dr Clayer’s method” refers to the diagnosis of illnesses by means of pulse observations, and which was treated by Cleyer in his publications Ad Chinarum doctrinam de pulsibus (1680),440 and Specimen medicinae Sinicae (1682).441 In a subsequent letter to Leibniz, on August 18, 1682, Scheffer once again referred to his correspondence with Cleyer, and his hope of obtaining further information from East India.442 Extracts from a letter of December 20, 1683, sent by Cleyer from Malacca to Scheffer, and referred to in a letter to Leibniz, on October 23, 1685,443 were duly published in the Miscellanea Curiosa in 1685.444 In the final letter, of December 8, 1685, that Leibniz received from Scheffer  – the correspondent died on January 20, 1686 – there is a final 437 “Miror in vestra Academia Medicis praeparatione medicamentorum interdici, et statuta facultatis medicae potius extraneis pharmacopolis, quam ipsis Medicis, qui profecto vere pharmacopoei esse debent favere” (A III,3 N. 110, p. 269). 438 Cf. Miscellanea Curiosa, Decur. 2, Ann. 4, (1685), pp. 1–8, also published (pp. 60–62) in: M. B. Valentini, Oost-Indianische Sendschreiben von allerhand raren Gewächsen, Bäumen, Jubelen, auch andern zu der Natur-Kündigung und Artzney-kunst gehörigen Raritäten … aus … in Holländischer Sprach geschriebenen Originalien in die Teutsche Mutter-Sprache übersetzet, Frankfurt a. M., 1704. 439 “Von H. Dr Clayers methodo kan nichts weiters berichten, als was er mit wenigen in meinem brief angeführt … Dießer H. Dr Clayer hat schon 18 Jahr in Neu Batavia gewohnet, u. viel schöne Sachen gesamlet” (A III,3 N. 162; cf. pp. 331f. and annotations). 440 Cf. A. Cleyer, Clavis medica ad Chinarum doctrinam de pulsibus, Frankfurt am Main, 1680, also published in: Miscellanea curiosa, Decur. II, Ann. IV, Append., (1686), pp. [1]–144. 441 Cf. A. Cleyer, Specimen medicinae Sinicae, sive, Opuscula medica ad mentem sinensium, continens I. De pulsibus libros quatuor e sinico translatos. II. Tractatus de pulsibus ab erudito Europaeo collectos, Frankfurt am Main, 1682. Regarding Cleyer and the Chinese method of pulse observation, cf. L. L. Barnes, 2005 (Introduction, note 215). 442 “Ich hoffe ehest widerumb etwas aus OstIndien zu erlangen” (A III,3 N. 387; cf. p. 698 and annotation). 443 Cf. A III,4 N. 99, p. 226. 444 Cf. Miscellanea Curiosa, Decur. 2, Ann. 4, 1685, pp. 2–7.

352

Chapter 1

reference to Cleyer’s contributions for the Miscellanea Curiosa. Thus, Sheffer wrote on that occasion: I am concerned only with matters from the play of nature, like plants, mussels and other maritime matters with which the licentiate Clayer from Malacca and New Batavia has provided me, one part of which will be treated in the coming ephemerides [viz. Miscellanea Curiosa].445 Pestilence and epidemics featured strongly in Leibniz’s correspondence. At the end of 1679, the plague afflicted Vienna and spread in the following years via Prague and Leipzig, without however reaching the territories of the principalities of Brundswick and Lüneburg. On May 24, 1680, the physician Crafft urged that Leibniz should not put off a planned journey to Dresden, and that the rumors circulating about the plague there were false, and possibly fabricated by surgeons to advance their own financial interests. Thus, Crafft wrote on this occasion: “That all is without foundation and is more a superfluous fear than truth, and that is even more the case as the surgeons like to fabricate, where they can, reports of bubonic plague outbreaks for their own profit”.446 Leibniz lingered in Saxony in the first half of July 1680. That the pestilence began spreading there at this time is evident, not only from the relief of Christof Pratisius, expressed in his letter of July 20,447 following Leibniz’s return, but also from Crafft’s communication of August 6, telling of the spread of the contagion in recent weeks. Here the correspondent wrote: “Our contagion has increased very much in recent weeks to the point that even on a single day there have been fifty deaths. We must wait and see what God has in store for us”.448 The plague had, we learn from Crafft’s letter of early September, spread almost exclusively among the common poor people, and there had

445 “Ich lege mich nur auf die Sachen wie die natur spielt, von Gewächsen, Muscheln, u. anderen Seesachen, damit mich H. Lic. Clayer aus Malacca u. Nova Batavia regaliert, deßen ein theil in künfftigen Ephemeridibus wird gedacht werden” (A III,4 N. 112; cf. p. 240 and annotation). 446 “daß alleß von keinem fundament, vnd mehr eine vberflüßige furcht, alß warheit seye, vnd das noch mehr, daß die chyrurgi vmb ihres gewinß willen bubones gerne erkunstelten, wenn Sie nur könnten” (A III,3 N. 65, p. 199). 447 Cf. A III,3 N. 86, p. 233. 448 “Vnsere contagion hatt etliche wochen her sehr zuegenommen, so gar daß in ein tag in die 50 gestorben: waß Gott weiter uber vnß verhänget, mußen wir erwartten” (A III,3 N. 93, p. 247).

1676–june 1683

353

been scarcely any cases among people who had taken precautions, and been able to care for themselves and their kin.449 The outbreak of the plague restricted considerably the movement of travelers at this juncture. Crafft was unable to travel to Berlin from Dresden, as he informed Leibniz on April 4, 1681.450 Likewise, Christoph Pfautz and Otto Mencke, who were preparing the launch of their journal Acta Eruditorum with a journey to the Netherlands and to England, beginning at the end of May or early June 1680, had – on their return journey to Saxony – to linger for some months in the town of Oldenburg, from where Pfautz informed Leibniz on January 18, 1681.451 Leibniz developed not only health care policy measures to combat the spread of the plague, for example his “Recommendations to combat the plague” (“Vorschläge gegen die Pest”452) – addressed to duke Ernst August and involving the closure of borders – but he also pursued medical deliberations on the matter. In a letter from the end of September 1680 to Crafft, he wrote: “I have had the thought that infusional medicine might be the most powerful and rapid remedy against the pestilential poison”.453 The “Medicina infusoria” might, he thought, be the most efficacious remedy against the pestilence, since he believed that it was beyond doubt that the malady resided especially in the body’s humors, and above all in the blood, since the “spiritus”, or animus, was nothing other than the most subtle of humors.454 Accordingly, the root of the evil was to be found in the blood, out of which the other humors are all brought together, or with which they communicate.455 Leibniz concluded his considerations regarding the plague by calling on Crafft to use his good rapport to the Saxon vice-chancellor, Johann David von Oppel, to thoroughly investigate the cause of the pestilence, and in particular the changes in the blood of those afflicted by the malady, before reporting the successful outcome to himself.456 449 “Im ubrigen vnsere infection belangend, so grassiret dieselbe biß dato fast allein vnter denen gemeinen armen Leuthen, vnd haben wir fast kein oder wenig exempel von Leuthen die Sich vorsehen vnd ihrer pflegen könen” (A III,3 N. 103, p. 258). 450 Cf. A III,3 N. 196, in particular pp. 378f. and p. 382. 451 Cf. A III,3 N. 155, p. 319. 452 Cf. A I,3 N. 108. 453 “Es ist mir beygefallen, ob nicht die Medicina infusoria vielleicht das kräfftigste und geschwindeste remedium gegen das pestilentialische gift seyn solte” (A III,3 N. 111, p. 270). 454 “Zweifels ohne ist das malum nicht in partibus solidis sondern in humoribus, den die spiritus sind doch nichts anders als humores subtillissimi” (p. 270). 455 “Ists nun in humoribus so ist radix mali vermuthlich in sanguine, aus welchem die andern humores alle conlatirt werden, oder doch mit ihm communiciren” (p. 270). 456 “M. h. H. kan wohl durch den H. ViceCanzler von Opel zu wegebringen daß dieses gründtlich untersuchet werde alsdann bitte mir den succes zu berichten” (p. 271).

354

Chapter 1

Less formidable was the suggestion of the resident of the elector of Mainz in Vienna, namely Johann Christoph Gudenus, who proposed onions as an amulet against the plague. He had been convinced of their effectiveness during the most recent outbreak in Vienna, and he correctly observed that the question, namely as to whether or not this vegetable acted as a preservative against the pestilence, had not been answered, but at least, he insisted, it did not do harm in any way. This line of thought is found at the end of a letter, dated August 25, 1680, which Gudenus wrote to Crafft, and which was forwarded to Leibniz in early September.457 A statement of Leibniz about this proposal has not been found. The medical profession, including studies and qualification, was a matter of special interest to Leibniz. On two occasions, the actions of academically unqualified physicians were graphically described. On the first such occasion, an individual named Scradetzky had apparently found a cure for gout, and he had worked miracles in Berlin, even curing the elector himself, according to the account of May 7, 1682, that Leibniz received from Crafft.458 As a reward, the individual in question was granted the right to import wines tariff-free, which Elers reported to Leibniz three months later, on August 22.459 Subsequently, he was named electoral councilor at the court of Saxony, only to have his appointment annulled in the following year, as Crafft reported to Leibniz from Dresden, on April 12, 1683, in the following words: The alleged gout healer is called Baron Scradetzky and he has received great credit and much money here, but his ill-fated journey to [the courts at] Berlin and Celle has brought him into such disrepute that, on his return here, his annual salary of 1000 Taler, together with his council title, were revoked, following which he departed head over heels from here, presumably fearing financial penalties.460

457 “ob es nun virtute dieser wurtzel praeservirt, oder die guthe leüthe sonst von Gott behütet worden, weiß man zwar nit, doch ist so viel daß Sie auch wenigstens nit schadet” (A III,3 N. 104, p. 260). 458 Cf. A III,3 N. 347, pp. 600f. 459 Cf. A III,3 N. 390, pp. 700–702. 460 “Der vermeinte Podagram-Curirer Baron hieße Scradetzky, hatte hier großen Credit vnd viel Geld bekommen, aber Seine vngluckliche reys auf Berlin vnd Zell, hatt ihn in solche desreputation gesetzet, daß man bey Seiner wiederkunfft die ihm gegebene jährliche bestallung von 1000 rthl. sambt dem Rathß praedicat wieder abgenommen, worauf Er uber halß vnd kopf von hier weggereyßet, vermuthlich auß furcht, man möchte im geld dergleichen thun” (A III,3 N. 452, p. 789).

1676–june 1683

355

Similar vicissitudes appear to have been experienced by another charlatan, a Roman whose departure from several courts Scheffer described, on August 18, 1682, as “malodorous”.461 Scheffer concluded his report about the medication of the empiricist in question with a note of skepticism about the value of the genre in general, writing that: “Such empiricists do at times have something, but then cannot really make proper use of it”.462 Statements of Leibniz regarding an amulet presented to the elector of Brandenburg – which was referred to by Elers on August 22, 1682463 – against pain caused by stone (kidney, ureter and urinary stone), or indeed about the question posed by Schrader464 concerning the age-old issue of the influence of the moon on the body humors, have not been found. The blacksmith’s laborer, who claimed to be able to diagnose all diseases by urine observation – and which was reported by Scheffer on May 23, 1682465 – was at all events not taken seriously by Leibniz. 461 “Ist doch von vielen höffen mit gestanck hinweg kommen” (A III,3 N. 387, pp. 697f.). 462 “Solche Empirici haben underweilen etwas, u. könnens doch nicht recht gebrauchen” (p. 698). 463 Cf. A III,3 N. 390, pp. 700f. 464 Cf. A III,3 N. 299, p. 523. 465 Cf. A III,3 N. 354, in particular p. 608 and p. 610.

Chapter 2

July 1683–1690 A [Francesco] Spoleto non contemnenda expecto  … Hortatus sum, ut mathematicum in re medica agat, quoad ejus fieri potest.1 Leibniz to Francesco Bianchini, March 18, 1690

∵ 1

Biographical Background (1683–1690)

Leibniz’s correspondence in mathematics, science and technology  – in the period between July 1683 and December 1690 – consists of almost 300 missives, or conversation records, written either by Leibniz himself (about a quarter), or by his correspondents (about three quarters), and involves in all about sixty individuals. The five most extensive correspondences  – namely, those with Christian Huygens, Johann Daniel Crafft, Ehrenfried Walter von Tschirnhaus, Hans Linsen, and Rudolf Christian von Bodenhausen – constitute roughly half of the total correspondence in terms of voluminosity in the seven and a half year period under consideration.2 Leibniz’s personal and public life between 1683 and 1690 was markedly shaped by a number of important developments. Firstly, following a ducal decree, his efforts for the improvement of the efficiency of the ore mines in the Harz mountains had to be wound up. Secondly, his acceptance of a commission to write a dynastic history of the house of Welf (Guelf or Guelph) led to extensive travel in different regions of Germany, Austria and Italy (which involved a two and a half year absence from Hanover). In the wake of his Italian journey, and towards the end of 1690, his promotion to the position of director of the ducal library in Wolfenbüttel was in the offing, an appointment that was to make him into a commuter between the neighboring towns of Hanover and Wolfenbüttel in the principality of Brunswick-Wolfenbüttel. 1 A III,4 N. 244, p. 481; Translation: From [Francesco] Spoleti I expect nothing unworthy or disdainful (viz. no mean achievements) … I encouraged him to apply mathematics in medical matters as far as this is possible. 2 Cf. H.-J. Hess and J. G. O’Hara, A III,4, Introduction, pp. [XXIII]–LXV.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_004

July 1683–1690

357

The efforts of Leibniz in the Harz Mountains for the testing of engineering techniques, processes and procedures, with the goal of improving the revenue from the mines can of course be traced back to the year 1679. By the middle of 1683, his activities in mining had involved expenses amounting to about five times his annual salary, however without a successful conclusion being in sight. Accordingly, at the end of 1683, duke Ernst August ordered the discontinuation of treasury payments for the engineering trials. Since, at this juncture, Leibniz was still very convinced of the technical feasibility of his proposals for improvement of the Harz mines, he ordered the continuation of the work for a further year at his own personal expense. However, by the spring of 1685, the point had arrived for him to concede, and to comply with the wishes of the duke for the conclusion of the test series. Leibniz’s decision in this matter was offset by the circumstance that the duke managed to awaken his interest in a project of a very different nature, namely that to research and write a history of the house of Welf. As regards the historiographical assignment, Leibniz now quickly immersed himself in the work surrounding the planned history and, in particular, of obtaining new and reliable sources. In this context he undertook exploratory journeys to the locations of the archives of the ruling branches of the house of Welf. However, it quickly became apparent that additional sources in libraries and archives in Bavaria needed to be consulted, and there in turn he found references to Italian sources. Thus, from originally smaller journeys in his own region there developed a great, almost three-year-long expedition whose main stations were Munich, Augsburg, Vienna, Venice, Rome, Florence, Bologna, Modena and Ferrara. Leibniz’s grand tour through Germany, Austria and Italy is documented, firstly, in his correspondence with his friend and associate Johann Daniel Crafft, with whom he met up in January 1688 in Graupen (now Krupka) in northern Bohemia for detailed discussions,3 secondly, in the proposals he laid before the emperor in Vienna towards the end of the same year,4 and thirdly, in a series of discussions and communications during his stay in Rome – from April to November 1689 – with Nicolas Toinard, Claudio Filippo Grimaldi, Vitale Giordani, Adrien Auzout, and Domenico Quarteroni.5 His writings and correspondence concerning China with Grimaldi – who was superior of the Jesuit mission, and president of the ‘Tribunale Mathematicum’ in Peking – deserves 3 Cf. A III,4 N. 202. 4 Cf. A III,4 N. 204, N. 205, and N. 206. 5 Cf. A III,4 N. 209–221, and also A. Robinet, G. W. Leibniz: Iter Italicum (Mars 1689–Mars 1690), Florence, 1988.

358

Chapter 2

particular mention here, as do the exchanges with the mathematics professors Giordani and Quarteroni, as well as with the numismatist Toinard and with the French expatriate in Rome Auzout. During his (presumably second) sojourn in Vienna  – at the end of April and in the first half of May 1690  – Leibniz had extensive discussions with Christian Holeysen, the son of a moneyer of Augsburg and a chemist who employed ores from the Hungarian mines.6 It had been Leibniz’s intention to visit those mines himself, but in the end he had to abandon the idea.7 Among Leibniz’s multifarious duties and occupations, during the 1680s, was the search for suitable assistants and travel companions. Here his correspondences with the apothecary Johann Christian Wachsmuth, and with the mining engineer Friedrich Heyn, deserve particular mention. The latter reported about his experience in the mines of Cornwall, and he accompanied Leibniz on the first leg of the Italian journey to Vienna. 2

Mathematics: Infinitesimal Calculus and Other Issues

Just as one might consider the period of Leibniz’s Paris sojourn (1672–1676) to be the foundational phase of Leibnizian mathematics, one may also treat the first seven years in Hanover that followed as an expansion phase. In this period the newly created infinitesimal calculus developed into a widely diversified discipline with multifarious – in particular physical – applications, notwithstanding the fact that the methodical and philosophical foundations of the discipline left many questions still unanswered. This development took place in the stillness of Leibniz’s study, and outside the public domain. Then, in the year 1684 the mature phase of the Leibnizian calculus began. At the beginning of this phase came the fundamental publications on differential and integral calculus. There then followed, in rapid succession, a series of journal articles in which physical themes were treated mathematically, and quantitatively, and the public controversy about the true measure of force brought Leibniz to prominence in learned circles. Also in connection with this dispute – in particular that with the Abbé Catelan  – stood the first mathematical competition initiated by Leibniz, namely the challenge to solve the isochrone problem, which called for the determination of the curve along which a body, descending under the influence of terrestrial gravity, reaches the datum, or base line, in the same period of time regardless of the point on the curve from which the 6 Cf. A III,4 N. 252–258. 7 Cf. A III,4 N. 251 (p. 500, annotation), and A I,5 N. 133 (p. 251), N. 134 (p. 252), N. 168 (p. 307), N. 185 (p. 325), and N. 218 (p. 379).

July 1683–1690

359

descent began. The publication of Leibniz’s solution of the problem (the isochrone curve or semi-cubic parabola), in April 1689,8 represented a landmark in the dispute with the Cartesians, and in particular with the Abbé Catelan, which had been going on for almost three years. During his years in Paris Leibniz had already provided friends and correspondents with a more or less far-reaching insight into his new methods, especially in the areas of tangent determination and of quadratures. Among his mentors, friends, and associates, Christiaan Huygens and Ehrenfried Walter von Tschirnhaus, in particular, deserve mention in this context and, among his correspondents, men like Henry Oldenburg and Jean-Paul de La Roque stand out. Leibniz’s willingness to communicate had the objectives of obtaining critical suggestions, of making his results known and, accordingly, of asserting his priority claims. This policy of keeping a limited public informed about his results proved difficult, after 1676, at the remote and secluded ducal residence in Hanover, and it was likewise difficult to maintain friendships and scholarly correspondence from there. It also became clear to Leibniz – as is evident from several drafts for the publication of his differential calculus  – that long-term reticence in relation to his most important discoveries would inevitably lead to priority disputes. The fact that the first such dispute arose with one of his last remaining Parisian associates, who was both a countryman and a friend, must then have come as a shock to both of them. In the article “Methodus  … quadraturam, aut impossibilitatem ejusdem  … determinandi”, published in the Acta eruditorum in October 1683,9 Tschirnhaus made public insufficiently understood parts of the Leibnizian quadrature method. Since Tschirnhaus failed to answer a (no longer extant) dispatch of February 1684 from Leibniz,10 seeking clarification in the matter, he decided to publish the article “De dimensionibus figurarum inveniendis”, in the Acta Eruditorum in May 1684,11 in order to assert his priority claims, and to correct a flawed assertion of Tschirnhaus. The latter, in a letter of August 31, 1684,12 then claimed 8

Cf. G. W. Leibniz, “De linea isochrona, in qua grave sine acceleratione descendit, et de controversia cum Dn. abbate D. C[atelan]”, Acta Eruditorum, (April 1689), pp. 195–198 (Leibniz: Parmentier, 1989, chap. VII, pp. [154]–165; Leibniz: Essais Scientifiques, 2005, N. 28; Leibniz: Heß-Babin, 2011, chap. 12, pp. 89–95). 9 Cf. E. W. v. Tschirnhaus, “Methodus datae figurae, rectis lineis et curva geometrica terminatae, aut quadraturam, aut impossibilitatem ejusdem quadraturae determinandi”, Acta Eruditorum, (October 1683), pp. 433–437. 10 Cf. the ‘textual witness’ (version L1) of A III,4 N. 66, p. 140. 11 Cf. G. W. Leibniz, “De dimensionibus figurarum inveniendis”, Acta Eruditorum, (May 1684), pp. 233–236 (Leibniz: Parmentier, 1989, chap. II, pp. [82]–92; Leibniz: Essais Scientifiques, 2005, N. 12; Leibniz: Heß-Babin, 2011, chap. 6, pp. 39–45). 12 Cf. A III,4 N. 67, pp. 142–144.

360

Chapter 2

that he had been completely misunderstood by Leibniz, and he believed that he had done nothing wrong in his altruistic efforts for the advancement of the common good, an exercise in which he had previously experienced Leibniz as fellow advocate. Tschirnhaus’ reply, entitled Responsio ad objectionem, in which he tried to refute the allegations of Leibniz, was first intended as an article for publication in the Acta Eruditorum, but it was eventually forwarded directly to Leibniz as an attachment to the letter of August 31, 1684.13 At this juncture, Leibniz finally decided to publish an account of the first part of his infinitesimal calculus, namely the differential calculus, in the epoch-making contribution entitled “Nova methodus de maximis et minimis”, which appeared in the Acta Eruditorum in October 1684.14 Notwithstanding conciliatory efforts on Leibniz’s part, his correspondence with Tschirnhaus was interrupted for almost a decade in the wake of this dispute. The second part of Leibniz’s analysis, namely the integral calculus, appeared with the title “De geometria recondita” in the Acta Eruditorum, almost two years later in June 1686.15 Leibniz’s continuing efforts to make his infinitesimal calculus known among colleagues can be seen in his correspondence with figures like Christiaan Huygens. As Leibniz’s mentor in mathematics during the years in Paris, Huygens had been informed about his discoveries in analysis.16 Up to his return to the Netherlands in 1681 – which led to an interruption of their correspondence – Huygens remained skeptical about the necessity, and power, of the Leibniz’s methods in comparison with his own geometrical methods.17 On January 11, 1680, he had expressed the desire to see a sample showing the power of Leibniz’s infinitesimal calculus.18 Leibniz had complied by sending, on February 5, a “Specimen Methodi meae de Maximis et Minimis”,19 with a problem calling for the determination of the tangent to a curve having a constant sum of the reciprocal distances from four given points on the axis. Huygens did not tackle this problem at once but, when (in March 1687) he came across the 13 Cf. A III,4 N. 68. 14 Cf. G. W. Leibniz, “Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratur, et singulare pro illis calculi genus”, Acta Eruditorum, (October 1684), pp. 467–473 (Leibniz: Parmentier, 1989, chap. III, pp. [96]–117; Leibniz: Essais Scientifiques, 2005, N. 14; Leibniz: Heß-Babin, 2011, chap. 8, pp. 51–62). 15 Cf. G. W. Leibniz, “De geometria recondita et analysi indivisibilium atque infinitorum”, Acta Eruditorum, (June 1686), pp. 292–300 (Leibniz: Parmentier, 1989, chap. V, pp. [126]– 143; Leibniz: Essais Scientifiques, 2005, N. 20; Leibniz: Heß-Babin, 2011, chap. 10, pp. 69–81). 16 Cf. the previously unpublished items: A III,1 N. 29 and N. 39. 17 Cf. A III,2 N. 359: HO, 8, pp. 243–245. 18 Cf. A III,3 N. 4; HO, 8, pp. 256–258. 19 Cf. A III,3 N. 23; HO, 8, pp. 269–271.

July 1683–1690

361

task again, he immediately found a suitable geometrical method to solve it,20 and so he continued to be skeptical about Leibniz’s methods. The correspondence with Huygens was revived in January 1688, with a letter written by Leibniz,21 after he had seen Huygens’ solution of the isochrone problem – which had been enunciated by Leibniz himself, in the Nouvelles de la République des Lettres in September 1687,22 – following its publication, in the same journal, in October 1687.23 Having established agreement between Huygens’ and his own solution, Leibniz sketched (without resorting to the formulism of his calculus) his own method for the determination of the curve. Leibniz also used the occasion of providing a letter of recommendation, for Johann Jakob Spener, to present Huygens with the main features of his infinitesimal calculus, and to indicate the relevant articles in the Acta Eruditorum. He concluded this letter with the following request: “I desire to have some day your judgement, the weight of which I appreciate”.24 This then served as an inducement for Huygens to write the following, on August 24, 1690: I have seen from time to time something of your new algebraic calculus in the Acta of Leipzig but, finding obscureness in it, I did not really study it in order to understand it and, furthermore, because I believed myself to be in possession of an equivalent method, be it for finding tangents to curves where the ordinary rules do not apply, or only with great difficulty, or for several other investigations.25 Accordingly, he presented another challenge for Leibniz’s calculus in the form of two problems involving the inverse tangent method, essentially the task of 20 Cf. HO, 20, pp. 500–502. 21 Cf. A III,4 N. 201, pp. 369f.; HO, 9, pp. 257–259. 22 Cf. G. W. Leibniz, “Réponse à la remarque de M. l’Abbé D. C[atelan] contenuë dans l’article I de ces Nouvelles, mois de Juin 1687 où il prétend soûtenir une loi de la nature avancée par M. Descartes”, Nouvelles de la Republique des Lettres, (September, 1687), pp. 952–956, in particular p. 956. 23 Cf. Ch. Huygens, “Solution du problème proposé par M. L[eibniz] dans les Nouvelles de la Republique des Lettres, du mois de Septembre 1687”, Nouvelles de la Republique des Lettres, (October, 1687), pp. 1110f. 24 “Je souhaite d’en avoir un jour vostre jugement, dont je sçay le poids” (A III,4 N. 267, pp. 536–538). 25 “J’ay vu de temps en temps quelque chose de Vostre nouveau calcul Algebraique dans les Actes de Leipsich, mais y trouvant de l’obscurité, je ne l’ay pas assez etudié pour l’entendre, comme aussi parce que je croiois avoir quelque methode equivalente, tant pour trouver les Tangentes des Lignes courbes où les regles ordinaires ne servent pas, ou fort difficilement, que pour plusieurs autres recherches” (A III,4 N. 271, p. 547; HO, 9, pp. 470–473).

362

Chapter 2

determining two curves having been given their respective subtangents. Thus he wrote: If your method serves here, and for other matters, as you say, you can rest very much assured about what my judgement will be, and you will very much oblige me, as well as all mathematicians, by explaining it in a special or dedicated treatise.26 Leibniz’s efforts to solve the inverse tangent problems presented by Huygens, as well as the latter’s reaction, are revealed in the continuing correspondence between the two in the year 1690.27 However, Huygens could not be convinced, at this point, of the superiority of the Leibnizian calculus, and misunderstanding and confusion about the respective solution curves employed, as well as Huygens’ aversion to the exponential equations used by Leibniz, only reinforced the correspondent’s skepticism. 3

Natural Philosophy

Whereas Leibniz’s philosophical interests can be traced back to his earliest youth, it was only at the beginning of the year 1686 that he succeeded in producing a first comprehensive conceptual design of his philosophical system, namely in the form of his Discours de metaphysique.28 This work was forwarded to the influential French philosopher Antoine Arnauld, and their correspondence is one of the most important philosophical exchanges to be found among Leibniz’s manuscript papers. About the same time, Leibniz composed an article for the Acta Eruditorum, in which he believed he could exemplify his long-standing criticism of the philosophy of Descartes on the basis of an easily recognizable mistake, namely regarding the principle of the conservation of momentum, or impulse. This was to become the starting point of a prolonged scientific dispute about whether the forces in dynamics should be characterized by the velocity, or by the square of the velocity, and about which of these entities is conserved in nature. Whereas Descartes considered the product of mass and velocity to be a key magnitude of kinetics, Leibniz 26 “Si vostre method sert icy et aux autres choses que vous dites, vous pouvez estre tres seur quel en sera mon jugement, et vous m’obligerez fort, aussi bien que tous les geometres en l’expliquant clairement et dans un traité expres” (A III,4 N. 271, pp. 548f.). 27 Cf. A III,4 N. 282, N. 291, and N. 296; HO, 9, pp. 521–527, pp. 536–540, and pp. 568–572. 28 Cf. G. W. Leibniz, Discours de métaphysique, 1686 (A VI,4 N. 306, pp. 1529–1588).

July 1683–1690

363

proposed an alternative, namely the product of the mass and the square of the velocity, whose conservation he saw as a fundamental feature of nature. His “Brevis demonstratio erroris memorabilis Cartesii”, in the Acta Eruditorum of March 1686,29 provoked – following its translation and publication in French, in the Nouvelles de la République des Lettres, in September 168630 – intense and lasting reactions from the side of the Cartesians, which were led at first by François, Abbé de Catelan.31 Finally, in April 1689, Denis Papin joined the fray with an article in the Acta Eruditorum, entitled “De gravitatis causa”.32 Leibniz then saw himself obliged to respond to Papin, in the May 1690 number of the Acta, with an article entitled “De causa gravitatis et defensio sententiae suae de veris naturae legibus contra Cartesianos”.33 This was to be the prelude then to an extensive correspondence, between Leibniz and Papin, which was initiated a little time later. However, at first, viz. until the year 1690, this conflict received only passing mention in Leibniz’s scientific correspondence, in particular with Christiaan Huygens and with Jacob Bernoulli.34 During, and following, Leibniz’s Italian journey, Rudolf Christian von Bodenhausen became for him, not just an industrious correspondent, but also an assistant and editor of his planned opus Dynamica de potentia et legibus naturae corporae. Accordingly, in their correspondence, one meets not only problems of the organization, and reorganization, of this work, but also, in respect of content, questions and definitions of core concepts such as, for example, specific gravity, mass, and homogenous magnitudes. Bodenhausen

29 Cf. G. W. Leibniz, “Brevis demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae, secundum quam volunt a Deo eandem semper quantitatem motus conservari; qua et in re mechanica abutuntur”, Acta Eruditorum, March 1686, pp. 161–163, and “A brief demonstration of a notable error of Descartes and others concerning a natural law”, in: Leibniz: Loemker, 1989 (2nd ed.), chap. 34, pp. 296–302 (Introduction, note 15). 30 Cf. G. W. Leibniz, “Demonstration courte d’une erreur considerable de M. Descartes & de quelques autres touchant une loi de la nature selon laquelle ils soutiennent que Dieu conserve tousjours dans la matière la même quantité de mouvement, de quoi ils abusent même dans la mechanique”, Nouvelles de la République des Lettres, (September 1686), pp. 996–999. 31 “Courte remarque de M. l’Abbé D. C. où l’on montre à Mr. G. G. Leibnits [sic] la paralogisme contenu dans l’objection precedente”, Nouvelles de la République des Lettres, (September 1686), pp. 999–1003. 32 Cf. D. Papin, “De gravitatis causa et proprietatibus observationes”, Acta Eruditorum, (April 1689), pp. 183–188. 33 Cf. G. W. Leibniz, “De causa gravitatis et defensio sententiae suae de veris naturae legibus contra Cartesianos”, Acta Eruditorum, (May 1690), pp. 228–239. 34 Cf. A III,4 N. 201 (p. 369) and N. 279 (p. 581), respectively.

364

Chapter 2

had already begun to prepare the fair copy,35 when, on February 20, 1690, Leibniz forwarded to him from Venice a further installment of the work in question, which included, among other things, a section containing the “manner of estimating velocities, impetus, effectus and the potentia of mobiles”, with the further information that “to this belongs then the differential calculus of which a significant specimen has so far been attached”.36 Further chapters, like one on varied accelerated and retarded motion (“ein caput De Motu varie accelerato et retardato”), were announced here. Then, on March 4, 1690, Leibniz raised once again the prospect of supplements, including a whole chapter on the application of dynamics to machines (“ein ganzes caput applicationis dynamicae ad Machinas”), which he hoped to complete during the return journey to Germany. Thus he wrote: “I will however only be able to elaborate this, together with the conclusion of the chapter ‘On the section of bodies’, on the return journey to Germany since I am too distracted here”.37 With a letter of March 11, 1690, there then followed further additions to the Dynamica, on which occasion he wrote: “I have dispatched, Sir, at the same time some supplements and, specifically, the first folio of the chapter on varied accelerated or retarded motion”.38 With a letter of March 18, 169039 – written while still in Venice – Leibniz sent Bodenhausen further parts of the Dynamica and, as an attachment,40 a revised version of an appendix containing a reprint of his article, of October 1684, on the differential calculus, namely the “Nova methodus pro maximis et minimis”. The new classification of the work included two main parts, which corresponded to his pair of systematic works on motion from the year 1671  – viz. the Theoria motus abstracti and the Theoria motus concreti, (from the Hypothesis physica nova41)  – and were to include “dynamica simplicia seu a 35 Cf. A III,4 N. 229, p. 448 and p. 450. 36 “modus aestimandi velocitates, impetus, effectus, potentias mobilium … dazu gehohret dann der calculus differentialis deßen auch ein Hieher gehoriges specimen beygefuget” (A III,4 N. 236, specifically pp. 462f.). 37 “ich werde aber solches samt dem schluß des capitis De sectione corporum erst auff der rückreise nacher Teutschland elaboriren können weilen alhier alzu distrahiret” (A III,4 N. 242, specifically pp. 473f.). 38 “Habe zugleich M. h. H. einige supplementa und in specie das erste folium des capitis De Motu varie accelerato aut retardato zugestellet” (A III,4 N. 243, pp. 478f.). 39 Cf. A III,4 N. 245, pp. 483–486. 40 Cf. A III,4 N. 246. 41 Cf. G. W. Leibniz, Hypothesis physica nova, Mainz, 1671, London, 1671, and also H. Oldenburg’s Advertisement of Leibniz’s Hypothesis physica nova, sive theoria motus concreti, una cum theoria motus abstracti (London, 1671), in: Philosophical Transactions, no. 73, (July 17, 1671), pp. 2213–2214, and Dr. [John] Wallis’s opinion concerning the Hypothesis physica nova of

July 1683–1690

365

rebus abstracta”, and “dynamica concreta”, concerned with that which touches on the system of things, as he told Bodenhausen in his letter of March 18.42 He then proceeded to present a detailed outline of the projected work, giving a breakdown according to part, section and chapter. As a result of this rearrangement, the completion of the Dynamica was considerably delayed, not least because Bodenhausen was now compelled to recopy a large portion of the work.43 Leibniz was himself also unable to complete the work, as planned, during the return leg of his Italian journey. Back in Hanover, notwithstanding his increasing commitments, he was nonetheless still hoping, on July 6, 1690, to find the time to complete the supplements, and to conclude the work on the Dynamica as a whole. Nevertheless, he had to concede, to Bodenhausen, that the arrangement of the content of the work would have to be set aside until all had been put together.44 In a letter from Bodenhausen, sent from Florence on November 11, 1690, the correspondent told of his continuing efforts for the Dynamica, and that he was looking forward to receiving further additions, including one on the construction of a thermometer conceived by Leibniz.45 4

Physics: Celestial Mechanics, Mechanics, Acoustics, Optics and Sundry Topics

Before Leibniz’s Italian journey, topics in celestial mechanics such as comets had only marginal importance in his correspondence, as for example when Christoph Pfautz referred to observations of a comet (in the summer of 1683), and of a solar eclipse (in the summer of 1684), which had been reported in the Acta Eruditorum, and in the Journal des Sçavans, respectively.46 Spurred on by the appearance of Newton’s Philosophiae naturalis principia mathematica in 1687,47 Leibniz worked intensively on the theory of planetary motion

42 43 44 45 46 47

Dr. Leibnitius … here inserted in the same tongue, wherein it was written to the publisher, in: Philosophical Transactions, no. 74, (August 14, 1671), pp. 2227–2231. “Puto totum opus dividi posse in duas partes circa dynamica simplicia seu a rebus abstracta; et dynamica concreta circa ea quae in systemate rerum contingunt” (cf. note 39, pp. 483f.). Cf. A III,4 N. 247, N. 259, and N. 262. “Es ist außer zweifel daß die einrichtung des wercks gesparet werde bis alles beysammen” (A III,4 N. 264, p. 527). “constructio Thermometri, deßen M. h. H. gedacht; erwarte also solche nebst anderen, so Ihm beliebet den Dynamicis beyzufügen” (A III,4 N. 288, p. 649). Cf. A III,4 N. 11, p. 23 and N. 70, p. 159. Cf. I. Newton, Philosophiae naturalis principia mathematica, London, 1687 (2nd ed. Cambridge, 1713; Editio ultima auctior et emendatior, Amsterdam 1714; 3rd ed. London 1726);

366

Chapter 2

during the tour of southern Germany, Austria and Italy. Shortly before his departure from Vienna, his principal contribution on this topic appeared in February 1689 in the Acta Eruditorum with the title “Tentamen de motuum coelestium causis”.48 In this article – as already in the Hypothesis physica nova of 1671 – Leibniz hypothesized a rotating ether vortex around the sun as the cause of planetary motion. The motion of planets, resulting from this vortex, he resolved into a circular motion (or “circulatio harmonica”), having a rotational velocity which was inversely proportional to the radius, and a radial motion (or “motus paracentricus”), which corresponded to the force of gravity, or centrifugal force. The combination of both components of the motion yielded the elliptical planetary motion, as well as Kepler’s first two laws. According to Leibniz, Johannes Kepler had been the first to adumbrate the true cause of gravity. After Kepler, Ismael Bouilleau and Seth Ward had derived the law of equal areas for planetary motion, with the help of mathematical constructions (circles, epicycloids etc.), but without being able to give a physical explanation for the law. With the introduction of harmonic circular motion, Leibniz considered that he himself had now succeeded in going a step further and presenting a basis for a physical explanation of all three of Kepler’s laws of planetary motion.49 Throughout his entire Italian journey, Leibniz continued his work on planetary theory, in the course of which he undertook an adaption, or revision, of his Tentamen. In Rome, where he met many members of the Accademia fisico-matematica, like Francesco Bianchini, Vitale Giordani and Domenico Quarteroni, he was able to present his ideas on planetary motion to Adrien Auzout, who encouraged a further publication on this topic. In a letter to Nicolas Toinard, in May or June 1689, shortly after that meeting, Leibniz reported about his conversations with Auzout, as well as about the planned publication, und he emphasized the simplicity of his celestial mechanics and its agreement with Kepler’s laws, writing: I have thoughts, which appear to give the true reasons for the laws of planets by simply supposing a very natural movement, common to all I. B. Cohen, A. Whitman, J. Budenz (eds., trans.), Isaac Newton: The Principia. Mathematical principles of natural philosophy: A new translation  … Preceded by a guide to Newton’s Principia, Berkeley, Los Angeles, London, 1999. 48 Cf. G. W. Leibniz, “Tentamen de motuum coelestium causis”, Acta Eruditorum, (February 1689), pp. 82–96; Translation: “An essay on the causes of celestial motions” in: D. Bertoloni Meli, 1993 and 2002, pp. 126–142; cf. also the previously cited secondary literature (Introduction, notes 73 and 74). 49 Cf. also the previously cited secondary literature (Introduction, notes 75 and 76).

July 1683–1690

367

circumsolar matter, from which the general planetary laws can be geometrically demonstrated most serendipitously, and with wondrous simplicity, … and having had the good fortune to meet Mr Auzout here, who is without doubt one of the most capable persons in the world to adjudicate in the matter, I explained to him a part of my reasoning, which appeared to give him much satisfaction, as did several beautiful theorems derived from my principles concerning the movement of the planets. He exhorted me to publish this, which I am most willing to do[.]50 Leibniz finally became a member of the Accademia Fisico-Matematica, and he composed for it his Phoranomus seu de potentia et legibus naturae, which, however, was to remain unpublished until the late twentieth century.51 Leibniz’s desire to return to Hanover via Paris, and to have discourse there, on astronomical topis in particular, proved not to be feasible because of the war with France. On the return journey he wrote to Bodenhausen on March 18, 1690, from Venice, about the need to extend his article in the Acta Eruditorum to cover matters like the inverse-square law of gravitational attraction. Thus he wrote on this occasion: “In the Tentamen de motuum coelestium causis I will need to supplement the one or the other thing such as rational argumentation a priori, as to why gravity attracts according to the inverse-square rule”.52 Following Leibniz’s return to Hanover, the theory of planetary motion continued to be referred to in his correspondence, for example in letters sent to Erhard Weigel, in September 1690,53 and to Otto Mencke in the following month.54 The appearance of his article “Tentamen de motuum coelestium causis”, however, also presented a difficulty for Leibniz in relation to 50 “J’ay des pensées qui paroissent donner les veritables raisons des loix des planets en supposant seulement un movement tres naturel commun à toute la matiere circomsolaire, d’où les loix planetaires generals se demonstrent geometriquement le plus heureusement du monde et avec une simplicité surprenante … et ayant eu la bonne fortune de rencontrer icy Mons. Auzout, qui est sans doute un des plus capables du monde pour en juger, je luy ay expliqué une partie de mes raisonnemens, dont il paroist avoir beaucoup de satisfaction aussi bien que de plusieurs beaux theorems touchant le mouvement des planetes qui naissent de mes principes. Il m’exhorte de le faire publier, et je le ferois volontiers” (A III,4 N. 209, pp. 401f.). 51 Cf. G. W. Leibniz (A. Robinet, ed.), Phoranomus seu de potentia et legibus naturae, Rome, Juillet 1689, Florence, 1991 (Introduction, note 77). 52 “In dem Tentamine De Motuum coelestium causis werde ein und anderes zu suppliren haben, als rationem a priori, cur gravia attrahantur in ratione duplicata reciproca distantiarum” (A III,4 N. 245, p. 485). 53 Cf. A III,4 N. 276, pp. 564f. 54 Cf. A III,4 N. 281, p. 587.

368

Chapter 2

ecclesiastical policy, which is reflected, for example, in his correspondence with Bodenhausen, and with Bianchini. Evident here is the circumstance that an open discussion of Copernican cosmology among scholars in Italy, in the last decade of the seventeenth century, was still problematical. Thus, at the end of February 1690, Bodenhausen had to explicitly inform Leibniz that, in an intended Italian reprint of his “Tentamen” from the Acta Eruditorum, it would be necessary to omit the names of Kepler, Galileo and Copernicus, and some further text, to avoid conflict with the Inquisition or, in the words of the correspondent, that: At the beginning of the “Tentamen de motuum coelestium causis” laudable and approving references are indeed made to Kepler, Galileo and Copernicus, but, because of the Inquisition, it will be necessary to leave out these names, and several instances of verbal expression, which might arouse suspicion in relation to the motion of the earth but which, nonetheless, will not distract from the tract and the fine discoveries.55 Again in the following month, on March 18, 1690, Leibniz turned to Francesco Bianchini – who was close to Pope Alexander VIII, and had enjoyed the pontiff’s patronage – with the request that he exert an influence on him. Here he wrote: We have a most wise pontifex who, if he had the privilege of hearing about the case for a better astronomy, would, without doubt, protect liberty, and reverse the unjust administration of justice, and the repression of certain men in these studies.56 He was, however, soon to be confronted with the fact that Bianchini could see no hope of amelioration in the matter in question. Thus, the correspondent wrote in his reply of April 7: “As regards the contentious question of astronomy

55 “im anfang des Tentaminis de Motuum Coelestium causis des Kepleri[,] Galilaei v. Copernici zwar rühmlichst v. billichst gedacht, aber wegen der Inquisition nöthig seyn wird, diese Nahmen v. etliche wenige worte, so auf den Motum terrae argwohnen machen, auszulaßen, welches doch dem Tractat v. schönen erfindungen nichts benehmen wird” (A III,4 N. 240, p. 469). 56 “Habemus pontificem sapientissimum, qui si otium haberet audiendi causam astronomiae melioris, haud dubie oppressam quorundam hominum in his studiis minus versatorum praeposteris judiciis in libertatem vindicaret” (A III,4 N. 244, p. 482).

July 1683–1690

369

with the man responsible, who could contribute much to our affairs, I despair of ever having the opportunity of touching upon this matter”.57 Celestial mechanics was also a focus in Leibniz’s revived correspondence with Christiaan Huygens. On February 8, 1690, Huygens sent Leibniz his recently published work Traité de la lumière … Discours de la cause de la pesanteur,58 together with an accompanying letter.59 Leibniz only received the book in the second half of the month of September 1690, but then he immediately embarked on intensive studies of both Huygens’ Traité and Newton’s Principia mathematica, as is to be seen from his drafted, but never dispatched, letter addressed to Huygens from the first half of October.60 His commentaries on the theories of Newton and Huygens, chronicled therein, are provided with annotating remarks regarding his own celestial mechanics. Leibniz found himself unable to endorse the views of Newton about gravity and planetary motion resulting exclusively from gravitation. In fact, he considered the supposition of an ether, for the explanation of the motion of the planets, or of the moons of Jupiter and Saturn, to be absolutely essential. His overt adherence to Cartesian vortices, in correspondence with Huygens, is indicative of an indispensable centerpiece of his planetary theory. Leibniz, in fact, assumed the existence of two vortices rotating about the sun. The first caused gravitation and terrestrial magnetism, while the second coarser vortex moved the planets. In Leibniz’s comments about Newton’s Principia mathematica, admiration and rejection went hand in hand. Thus, he found an explanation of gravity, and indeed of the law of gravity, to be wanting in Newton’s work. For the law of gravity, and for the photometric inverse-square law, Leibniz suspected analogous explanations. As regards Huygens’ explanation of gravity, he found similarities between his own conceptions of a centrifugal force, produced by the rotating ether, and Huygens’ explanation. Leibniz’s explanation of these 57 “Quod attinet ad vindicias Astronomiae apud eum virum procurandas, qui rebus nostris conferre plurimum posset; despero ansam ejus rei attingendae mihi unquam oblatum iri” (A III,4 N. 249, p. 498). 58 Cf. Ch. Huygens, Traité de la lumière  … avec un discours de la cause de la pesanteur, Leiden, 1690; HO, 19, pp. 451–547 and HO, 21, pp. 427–499: Reviews in Acta Eruditorum, (October 1690), pp. 481–487 and (November 1690), pp. 561–565; Ch. Huygens, Treatise on light: In which are explained the causes of that which occurs in reflexion & in refraction, and particularly in the strange refraction of Iceland crystal, London, 1912; Ch. Huygens, Treatise on light, Frankfurt am Main, 2020. Regarding the broader context of the publication of Huygens’ twin treatises, cf. H. Aldersey-Williams, Dutch light: Christiaan Huygens and the making of science in Europe, London, 2020, and in particular chap. 14 (Light and gravity), pp. 359–388. 59 Cf. A III,4 N. 235. 60 Cf. A III,4 N. 282 (specifically the textual witness items L3, L4 and L5); HO, 9, pp. 521–527.

370

Chapter 2

phenomena was based on the principle of equality of the active force – which was proportional to the square of the velocity – in the respective orbits of the bodies rotating around the sun. On the basis of this model, he saw a means of deriving both Kepler’s third law and the law of gravity. In his correspondence with Huygens in the final quarter of the year 1690,61 Leibniz also enquired about the correspondent’s opinion regarding Newton’s explanation of the ebb and flow of the tides, as well as of the tails of comets. Unlike Newton, Leibniz considered the tail of a comet not to be of a material nature, but rather an optical phenomenon comparable to the rainbow. Since Huygens had spoken with Newton a number of times during a visit to England in the summer of 1689, Leibniz thought it possible that he might very well have taken the opportunity of verbally articulating objections regarding the Principia mathematica to the author, and he hoped in this way to learn, at least indirectly, something about Newton’s views regarding these issues. Alas, these hopes were dashed, as Huygens communicated – in his reply on November 18, 1690  – mainly his own thoughts about the tides, and the tails of comets.62 However, he did indicate that, while he considered Newton’s explanation of ebb and flow to be partly absurd and without foundation, he did feel much more comfortable with Newton’s theory of cometary tails. The appearance of Newton’s Principia mathematica led Leibniz to pay increasing attention to other topics in physical research. Thus, during and after the grand tour to Italy, Leibniz paid renewed attention to the topic of the resistance of a medium, or of movement in a resisting medium. From these efforts emerged the article entitled “Schediasma de resistentia medii”, which appeared in the January 1689 number of the Acta Eruditorum.63 The intention of writing such an essay was by no means new. Already in the years 1683 and 1684, Leibniz’s attention was drawn to this problem when Edme Mariotte sent him accounts of his thoughts, and experimental investigations, concerning the fall of a body, taking account of the resistance of the air.64 Furthermore, François Blondel’s work L’art de jetter des bombes (of 1683)65 dealt with this topic although, in Leibniz’s view, it contained nothing which went beyond existing explanations – which had been given by Galileo and Descartes – for the motion of a projectile, and whose trajectory was supposed to be a parabola. This assessment of Blondel’s opus, he expressed in a letter to his London 61 Cf. A III,4 N. 282 (p. 617) and N. 287 (pp. 643f. and p. 646); HO, 9, pp. 532–535. 62 Cf. A III,4 N. 291, pp. 656f.; HO, 9, pp. 536–540. 63 Cf. G. W. Leibniz, “Schediasma de resistentia medii, et motu projectorum gravium in medio resistente”, Acta Eruditorum, (January 1689), pp. 38–47. 64 Cf. A III,4 N. 13, N. 41 and N. 52. 65 Cf. F. Blondel, L’art de jetter les bombes, Paris, 1683 and Den Haag (The Hague), 1685.

July 1683–1690

371

correspondent Detlef Clüver, at the end July 1686, and he hinted for the first time at an intended publication in which he would broach the issue of the resistance of the air, a matter which had been disregarded by Galileo and Torricelli. Thus he wrote on that occasion: You will have seen the book of the French mathematician Blondel on the art of throwing bombs, where almost nothing of any importance has been added over and above the demonstrations of Galileo and Descartes regarding the parabolic trajectory. It is especially so, in as far as he claims to show by experiment that the resistance of the air  – which Galileo, Torricelli, and likewise [Blondel] himself in this investigation, have neglected – will not lead to any noteworthy sensible errors, concerning which I would like to hear the sentiments of men, in your circles, who may be well versed in these matters. If that were to be the case, those demonstrations would be sufficient for practice, but if not, new ones would be necessary for subjecting the resistance of the air to calculation, concerning which matter I already have certain not insignificant [thoughts].66 Leibniz’s “Schediasma” appeared after Newton’s Principia mathematica (1687), but in advance of Huygens’ Discours de la cause de la pesanteur (1690), two works in which comparable research results were presented. The results announced by Leibniz in this article were based on a successful application of his differential calculus, although in fact he withheld the details of the mathematical elaboration. He distinguished between two forms of resistance, namely “resistentia absoluta” and “resistentia respectiva”, which were, for the same time intervals, proportional to the velocity and the square of the velocity, respectively. Here Leibniz’s theory of absolute and respective, or relative, resistances corresponded roughly to Newton’s much more elaborate treatment of this topic in Book II, Sections I and II of the Principia mathematica. Leibniz did not consider a combination of the two forms of resistance, as was done in Newton’s treatment in Book II, Section III. The corresponding

66 “Videris opinor librum Blondelii mathematici Galli de arte bombos jaciendi, ubi nihil fere magni momenti demonstrationibus Galilaei et Cartesii de motu per parabola addidit. Illud potissimum est quod contendit Experientiam ostendere resistentiam äeris quam Galilaeus, Torricellius partier atque ipse in hac disquisitione neglexerunt non satis sensibiles errores producere, de quo virorum apud vos in his rebus versatorum sententias audire velim. Id enim si verum esset sufficerent ad praxin demonstrationes illae, sin minus novis opus esset ad resistentiam äeris ad calculos revocandam, de quo jam non contemnenda habeo” (A III,4 N. 148, pp. 287f.).

372

Chapter 2

results, published by Huygens in 1690,67 had in fact been obtained by him more than twenty years earlier.68 Leibniz first learned of these results from the Discours, whereby his reception of Huygens’ thought went hand in hand with his own efforts to revise and extend the “Schediasma”, which is evident from their correspondence in November and December 1690.69 In elaborating his propositions, Leibniz made some ‘faux pas’ which, although he was able to correct them quickly, added to the difficulty of reaching an understanding with Huygens. The latter’s lack of familiarity with the infinitesimal calculus likewise contributed, in no uncertain fashion, to the communication obstacles between the two. The fruit of this epistolary exchange, at the end of 1690 and in early 1691, was the article “Additio ad schediasma de medii resistentia”, which Leibniz published in the Acta Eruditorum in April 1691.70 Related to this topic, namely of motion in resisting media, are a number of other issues, which were treated both in the never-dispatched letter to Huygens, from the first half of October 1690,71 and in the further epistolary exchanges with the same correspondent. These issues included the nature of an extended and resisting medium, the admissibility of a “dureté parfaite”, or of a perfect hardness of matter, and finally the question of the existence of atoms in a space devoid of air and matter. The kernel of Leibniz’s theory of matter is his theory of elasticity, a matter which occupies a central place in the entire corpus of Leibnizian physics. It was the basis of his theory of sound generation, and sound propagation, and of the breaking or rupture strength of materials. On the occasion of the appearance of Günther Christoph Schelhammer’s book De auditu (1684),72 Leibniz explained his understanding of sound production, sound propagation and of hearing, in a letter of May 16, 1684, sent to Friedrich Schrader.73 In this letter, he recalled that some three years earlier, in August 1681,74 he had communicated similar thoughts in French to Mariotte.75 The cause of sound, according to Leibniz, lay in the vibrations of tiny air particles. By means of such oscillations, the sound was carried from the resonating body to the ear. Independently of the sound level or loudness, or the sonority, 67 68 69 70 71 72 73 74 75

Cf. Ch. Huygens, Discours de la cause de la pesanteur, 1690, in particular pp. 168–176. Cf. HO, 19, pp. 102–119 and pp. 144–157. Cf. A III,4 N. 292 and N. 293; HO, 9, pp. 546–552 and pp. 555–559, respectively. Cf. G. W. Leibniz, “Additio ad schediasma de medii resistentia publicatum in Actis mensis Febr. 1689”, Acta Eruditorum, (April 1691), pp. 177f. Cf. A III,4 N. 282 (specifically the textual witness items L3, L4 and L5); HO, 9, pp. 521–527. Cf. G. Ch. Schelhammer, De auditu liber unus, Leiden 1684. Cf. A III,4 N. 55, specifically pp. 114–118. Cf. A III,3 N. 269, pp. 479–482. “Quam opinionem meam Clmo Mariotto perscriptam” (note 73, p. 117).

July 1683–1690

373

the sound was transmitted at a constant speed. Accordingly, the oscillations of a resonating body, having a given tension, were always isochronous and so the same tone pitch was produced. As far as the human experience of sound was concerned, Leibniz believed that there existed an organ (the “ossicula”) within the ear, which is stimulated by the vibrations, or oscillations, of the air, and so produces a corresponding sound in the ear.76 The experience of pitch was related to the frequency of the received vibrations from the tiny air particles, with relatively acute (and grave) sounds coming from relatively rapid (and slow) vibrations, respectively, of corresponding particles, with the vibrations of the smaller particles being more rapid.77 Leibniz also considered the questions, as to how this organ could be consonant with all the resonating bodies, and how the eardrum could reproduce the corresponding sounds. Here he compared the ear to a musical instrument (like a zither or a lute), in which many different strings are stretched, and which render sonorously many different sounds, and in harmony with other instruments. The elasticity of the air also played an essential role in Leibniz’s theory of heat. As in the case of acoustics, Leibniz’s occupation during the 1680s with this topic can be attributed to the appearance of a tract by one of his correspondents. When, on March 4, 1684, he learned, from a letter of Friedrich Schrader,78 of the appearance of a dissertation entitled De frigoris natura, over the defense of which the correspondent was presiding,79 he immediately expressed his interest.80 He then elaborated his view that, in the same way that metals in a furnace are liquefied, or that water over a fire evaporates, the sun takes care that – by virtue of different internal movements it produces in bodies – fluids remain in their physical condition or state of matter. Also, the effects of heat and cold in the human body could be attributed to the motion of particles. Once the flux, or the movement of these particles, reaches a certain degree, the feeling of warmth is evoked in man. If, on the other hand, the human body is debilitated and the body humors are under attack, then

76 “Et credo ossicula intra aurem contremiscentia ad aeris ingruentis vibrationes tonum in aure exprimere; eorum autem periostia eum ad commune sensorium propagare” (note 73, p. 116). 77 “Prout autem sonus est acutus aut gravis eum aut a majoribus aut a minoribus particulis exprimi[,] Minorum enim celeriores sunt vibrationes” (note 73, p. 116). 78 Cf. A III,4 N. 49. 79 Cf. F. Schrader, De frigoris natura: Respondens Justus Bernhardus Slepper, Helmstedt, 1684. 80 “Dissertationem tuam de frigore avide expecto” (note 73, p. 115).

374

Chapter 2

the human being experiences the sensation of cold.81 In relation to this, reasons were also given for the circumstance that water in a vessel, when frozen solid, expands, and might even burst its container. Leibniz attributed this to the fact that the air – being present in only small bubbles – is not in a position to make its elastic properties operative since – due to a lack of convection – it is prevented from forming larger bubbles.82 Analog processes also take place, for example, in the explosion of gunpowder, where scattered air pockets are only able to unite and form larger bubbles through the application of fire.83 Yet another example was that of a river, which was normally regulated by lumbering using large tree trunks, but which might, under certain circumstances, have the capability of sweeping away large obstacles in its path, like a bridge for example.84 In essence then, Leibniz’s theory is based on the assumption of the existence of small elastic particles which, as long as they are isolated and mutually obstructive, are not in a position to break down certain barriers. Elasticity, as an explanatory principle, was of course also at the center of the theory of the strength of materials, which was developed by Leibniz and Mariotte in the years 1682 and 1683.85 A query of Jacob Bernoulli, in a letter of December 25, 1687,86 concerning the beams of precision balances and Leibniz’s article “Demonstrationes novae de resistentia solidorum”, which had appeared in the Acta Eruditorum in July 1684,87 was only comprehensively answered by Leibniz following his Italian journey, on October 4, 1690.88 A month later, on November 5, Leibniz also informed Bodenhausen about Bernoulli’s question.89 At the center of the considerations was the quest for the form and configuration of a uniform break-proof beam. Although Leibniz considered his starting 81 “In universum dici potest solem motu intestine vario, quem in corporibus excitat, tenere fluida in statu fluiditatis, quemadmodum metalla fluunt in furnace, et aqua ebullit super igne; nec ullum apud nos esse corpus tam solidum, quin aliquis sit in eo fluiditatis gradus. Porro si fluxus ille seu motus varius partium exiguarum satis sit vehemens excitat in nobis sensum caloris; sin ita debilitetur, ut humores corporis nostri inde notabiliter afficiantur, sentitur frigus” (p. 115). 82 “Suspicor plurimun aëris compressi in aqua latere, sed in exiguas adeo partes dispersi, et sub iis suam vim Elasticam exercere non possit” (p. 115). 83 “Quemadmodum aër compressus, qui in pulvere pyrio latet, non ante agit, quam ubi accedente igne liberatur quoniam scilicet antea in partes nimis exiguas disperses erat” (p. 115). 84 “quemadmodum videmus fluvium non cum exigua frustra lignorum sed cum ingentes trabes defert, pontem rumpere” (p. 115). 85 Cf. in particular A III,3 N. 394, N. 400, N. 437, and N. 456. 86 Cf. A III,4 N. 200, pp. 364–368. 87 Cf. G. W. Leibniz, “Demonstrationes novae de resistentia solidorum”, Acta Eruditorum, (July 1684), pp. 319–325. 88 Cf. A III,4 N. 279, specifically pp. 571–580. 89 Cf. A III,4 N. 285, pp. 627f.

July 1683–1690

375

hypothesis to be uncertain, namely that the strain or extension of the carrier beam fibers is proportional to the tensioning or straining force,90 he was convinced that his “demonstrationes”91 could also be valid under different premises. In the letter to Jacob Bernoulli of October 4, 1690, the profile of a uniform fracture-resistant carrier beam, which was subjected to both its own weight and an additional load (like an attached weight), was at the center of the considerations. Leibniz had omitted this additional loading in his article of July 1684, and Bernoulli had not been able to find the solution on his own, since it depended on Leibniz’s “analysin extraordinariam”, or infinitesimal calculus, as he tried to make clear in his letter of November 5, 1690, to Bodenhausen. Galileo – he told the correspondent – had already treated the issue “de resistentibus figuris”, but in a different sense and without taking the beam’s own weight into consideration (“abstrahendo ab ipsarum pondere proprio”), which was mathematically a much simpler task or, in Leibniz’s words, “the matter becomes very easy and it is only a problem of ordinary analysis”.92 It was Leibniz’s conviction they were dealing here with a task, which simply could not be solved using ordinary analysis and which required rather the application of his infinitesimal calculus. Besides his focus on dynamics, and specifically his Dynamica, Leibniz’s interests in the 1680s also included statics, albeit to a lesser extent. A dispute with the Italian Jesuit Giovanni Francesco Vanni, in 1684 and 1685, about the static moment of a heavy body on an inclined plane,93 led Leibniz to write the article “Demonstratio geometrica regulae apud staticos receptae de momentis gravium in planis inclinatis”, which duly appeared, in November 1685, in the Acta Eruditorum.94 However, a direct correspondence between the adversaries never materialized, and the exchange of opposing arguments took place through third parties, namely Antonio Magliabechi and Otto Mencke, and Leibniz’s objections in the Acta Eruditorum remained anonymous. Leibniz’s thoughts on optics in the late 1680s were largely determined by his interest in the works of Newton and Huygens. His only significant publication 90 “quod olim in Actis Lipsiensibus posui, extensiones esse, ut vires tendentes” (note 88, p 572). 91 “de figuris aeque resistentibus demonstrationes” (note 88, p 575). 92 “auff welchem fall die sach ganz leicht, und nur ein problema ist Analyseos ordinariae” (note 89, p. 628). 93 Cf. the correspondence with Christoph Pfautz (A III,4 N. 74, N. 96, N. 97 and N. 98). 94 Cf. [G. W. Leibniz], “Demonstratio geometrica regulae apud staticos receptae de momentis gravium in planis inclinatis, nuper in dubium vocatae: et solutio casus elegantis, in Actis Novembri 1684 pag. 512. propositi, de globo duobus planis angulum rectum facientibus simul incumbente: quantum unumquodque planorum prematur, determinans”, Acta Eruditorum, (November 1685), pp. 501–505.

376

Chapter 2

during this period – the article “De lineis opticis” in the Acta Eruditorum of January 168995 – was closely connected with the articles “Tentamen de motuum coelestium causis” and “Schediasma de resistentia medii”, both of which had come into being under the influence of the recently published Principia mathematica of Newton. Shortly after Leibniz’s return to Hanover, Huygens informed him, on August 24, 1690,96 about hints Newton had given him – on the occasion of their meeting in the summer of 1689 – about a planned work on optics, as well as about new experiments on the theory of colors. The delivery of Huygens’ Traité de la lumière, in the second half of September 1690, was also a major influence on Leibniz’s thinking about optics, as is evident from his drafted (but never dispatched) letter from the first half of October.97 Leibniz was exceedingly impressed by Huygens’ presentation of his wave theory of light, and he referred in particular to the propagation of a wave represented using Huygens’ geometrical analysis, his construction of wave fronts, his derivation of the laws of reflection and refraction, and his explanation of the phenomenon of double refraction in Iceland spar on the basis of spherical wave propagation.98 In this drafted letter, intended for Huygens, he did not forget to recall the efforts of predecessors in the development of the wave theory, namely the Jesuits Ignace Gaston Pardies and Pierre Ango. While Huygens’ presentation of the laws of reflection and refraction, as well as of the phenomenon of double refraction, found Leibniz’s unconditional approval, as regards the latter phenomenon he saw in Huygens’ treatment only a description and not an explanation of the observed appearances. Such an explanation, he presumed, would simultaneously provide the key to a theory of colors. And for this reason, he expressly requested that Huygens communicate to him his understanding of the nature of colors, especially as this topic had been left out of consideration in the Traité de la lumière. Thus he wrote: The use you make of waves to explain the properties of light surprised me, and nothing is more wonderful than this facility with which this line, which touches all of the individual waves and constitutes the general wave, satisfies the laws of reflection and refraction known from 95 Cf. G. W. Leibniz, “De lineis opticis et alia; excerpta ex literis ad ***”, Acta Eruditorum, (January 1689), pp. 36–38 (Leibniz: Parmentier, 1989, chap. VI, pp. [144]–153; Leibniz: Essais Scientifiques, 2005, N. 25; Leibniz: Heß-Babin, 2011, chap. 11, pp. 83–87). 96 Cf. A III,4 N. 271, specifically p. 547; HO, 9, pp. 470–473. 97 Cf. A III,4 N. 282 (in particular the textual witness items L4 and L5); HO, 9, pp. 521–527. 98 Cf. A. I. Sabra, 1981, chap. 8 (Introduction, note 86); O. Darrigol, 2012, chap. 2, especially sect. 2.3. (Introduction, note 87); H. Aldersey-Williams, 2020, chap. 13, pp. 339–342 (note 58 above).

July 1683–1690

377

experiment. But, when I saw that the assumption of spheroidal waves serves you with the same ease for explaining the phenomena of double refraction of Iceland spar, I advanced from esteem to admiration [for your work] … Has the Iceland crystal provided any particular information regarding the nature of colors?99 Long before the appearance of the Traité de la lumière in 1690, Leibniz had been informed of Erasmus (or Rasmus) Bartholin’s discovery of double refraction in Iceland spar – published in his Experimenta crystalli islandici disdiaclastici, quibus mira et insolita refractio detegitur (1669) – and Huygens’ subsequent explanation of the phenomenon (in August 1677), in a letter received from Heinrich Siver in Hamburg, written on June 16, 1678.100 Leibniz, to all appearances, never carried out experiments himself in order to explain the phenomenon of double refraction in Iceland spar, although he may possibly have had the intention of doing so. As early as September 10, 1683, Georg Mohr had sent him (with Brandshagen as bearer) from Copenhagen a quantity of Iceland spar with the promise to send him more of this mineral. Thus, Mohr wrote on that occasion: “Because this good opportunity has presented itself, I am already sending you, Sir, the Island crystal which I have at present; I have been promised more and when I get it I will keep it for you, Sir”.101 Once again, in a letter written on December 19, 1690, he was reminded of the crystal by Johann Jacob Spener who wrote: “I have also finally obtained some of the Iceland crystal, albeit with great difficulty, and with this I have already made several interesting

99 “L’usage que vous faites des ondes pour expliquer les effects de la lumiere m’a surpris, et rien n’est plus heureux que cette facilité, avec la quelle cette ligne qui touche toutes les ondes particulieres, et compose l’onde generale satisfait aux loix de reflexion et de refraction connües par l’experience. Mais quand j’ai vû que la supposition des ondes spheroidales vous sert avec la même facilité à resoudre les phenomenes de la refraction disdiaclastique du crystal d’Island, j’ay passé de l’estime à l’admiration … Le crystal d’Islande n’a-t-il rien fourni de particulier sur les couleurs?” (A III,4 N. 282, L5, pp. 609f.). 100 Cf. A II,1 N. 179, pp. 626–629, in particular p, 628, and also Huygens’ note of August 6, 1677, entitled“Causa mirae refractionis in crystallo Islandica” (HO, 19, pp. 427–443). Regarding Bartholin’s opus, cf. R. Bartholin, Experimenta crystalli islandici disdiaclastici, quibus mira et insolita refractio detegitur, Copenhagen, 1669; E. Bartholin (T. Archibald, trans; J. Z. Buchwald and K. Moller Pedersen, Intro), Experiments on birefringent Icelandic crystal … with a facsimile of the original publication, Copenhagen: Danish National Library of Science and Medicine, 1991. 101 “terwijle dese goode gelegenheit presentert, soo sende U. E., al dat Jslands Christal soo ick tegenwordig hebbe, mijn is meer beloft, wen ick het bekoome, sal voor V. E. in bewaring houden” (A III,4 N. 23, p. 51).

378

Chapter 2

discoveries”.102 Among other things, Spener claimed to have found another, and better, method than that of Huygens for polishing the crystal, namely by employing aqua fortis (nitric acid). Optical instruments and equipment routinely attracted the attention of Leibniz and his correspondents. In correspondence with Tschirnhaus, there were already reports in the years 1681 and 1682 about the construction of concave mirrors by the correspondent.103 There is likewise evidence in Leibniz’s correspondence in the following years of Tschirnhaus’ long-standing involvement in the improvement of such mirrors. On September 4, 1683, for example, he wrote to Leibniz about the commissioning of a mirror of three lower-arm lengths diameter, and of one with a diameter of seven quarters of a lower-arm length, to be completed within four months.104 In the following letter of December 7, 1683, he then informed Leibniz about the five most important requirements for the construction of such mirrors. On that occasion he wrote: My concave mirror is exact. The finest requirements are five in number, namely[, first] that one has a material that one can produce in the form of large plates, 2nd that one can arrange a perfectly round figure in it, 3rd that it can be perfectly polished as a mirror, 4th that the figure and polished surface can not be easily altered, and therefore be conserved, 5th that it does not become too expensive. | Copper |105 has all of this [and is] better than other materials.106 His own mirror, Tschirnhaus emphasized, provided admirable results, exceeded expectations, and was unique among its kind in Germany.107 Then, two years later, he submitted an article on new optical experiments entitled “Novae quaedam experientiae opticae” to the editors of the Acta Eruditorum, a 102 “Von Cristallo Islandico habe auch entlichen wie wohl mit großer mühe einiges obtinirt, und mit selbigen, schon undterschiedene curiose inventa gefunden” (A III,4 N. 297, p. 692). 103 Cf. A III,3 N. 199, N. 233, and N. 356. 104 “hierdurch getrauete Mir Einen zu machen; der 3 Ellen im diametro, und auffs lengste (dieser ist nur 7 viertel der Ellen) innerhalb 4 Monath fertig sein solte” (A III,4 N. 21, p. 48). 105 | as alchemical symbol in the manuscript |. 106 “Mein brennspiegel ist richtig. Die fuhrnehmste requisita sind 5, nehmlich daß man eine materi habe, die man in große platten treiben könne, 2. daß man eine perfect runde figur ihr conciliiren könne, 3. daß man sie perfect als ein Spiegel poliren konne, 4. daß sie die figur und politur nicht leicht changieren kann und also wohl halten kann, 5o daß sie nicht alzu theuer falle. Dieses alles hat das | Kupfer | beßer als andere” (A III,4 N. 42, p. 92). 107 “Mein Spiegel thut admiranda effecta wie unlangst gedacht  … ist dergleichen nicht in Teuschland” (p. 92).

July 1683–1690

379

copy of which was sent by Christoph Pfautz, in September 1685, to Leibniz asking for his expert opinion.108 Pfautz desired, in particular, an explanation of an experiment described using a microscope without a lens. Tschirnhaus claimed that, by the placement of the object in proximity to the observing eye, an enlargement was achieved. In his reply, Leibniz recalled a similar observation of an object through a slit, close to the eye,109 that had once been described by Christoph Scheiner (in Oculus, 1619).110 Notwithstanding Leibniz’s positive verdict on Tschirnhaus’ investigation, the article in question never did appear in the Leipzig journal.111 In microscopy it was above all the observations of Antoni van Leeuwenhoek that continued to attract Leibniz’s attention. In the months before his Italian journey, Leibniz expressed his views about Leeuwenhoek in his philosophical correspondence with Antoine Arnauld, referring in particular to Leeuwenhoek’s Observations (or Observationes) that had been published in the Philosophical Transactions.112 In this context, Leibniz referred specifically to Leeuwenhoek’s observations of animate beings, or little animals, in water interfused with pepper, and those concerning the production and nature of mammalian or human sperm. Here he also alluded to Leeuwenhoek’s animalculist theory of preformation. According to this theory, an entire organism was pre-formed in the little animals, or animalcula, found in human or mammalian sperm, and it had only to unfold or de-convolve itself in the process of fertilization. From a philosophical point of view, the generation (and later death) of an animal represented merely a transformation from one state to another. Thus, on December 8, 1686, Leibniz wrote the following lines to Arnauld: As it is possible, according to the views of Mr Leeuwenhoek, that every generation of an animal is nothing other than a transformation of an

108 Cf. A III,4 N. 96, specifically pp. 219f. 109 Cf. A III,4 N. 98, specifically pp. 223–225. 110 Cf. Ch. Scheiner, Oculus, hoc est fundamentum opticum, Innsbruck, 1619, in particular lib. 1, pars II, cap. 2. 111 Cf. E. W. von Tschirnhaus, Novae quaedam experientiae opticae; GWLB, Hanover (Manuscript: LH XXXV 15,3 Bl./Sheet 1). 112 Cf. A. van Leeuwenhoeck “Observations  … concerning little animals observed in rain-  well- sea- and snow-water; as also in water wherein pepper had lain infused”, Philosophical Transactions, no. 133, (March 25, 1677), pp. 821–831, and “Observationes de natis e semine genitali animalculis”, Philosophical Transactions, no. 142, (December 1677–February 1678), pp. 1040–1043.

380

Chapter 2

already living animal, there is reason to believe that death too is just another transformation.113 Then, on April 30, 1687, he wrote in a further letter to Arnauld that: Experience (or experiment) favors this multitude of animate beings. One finds that there is a prodigious quantity of animals in a drop of water imbued with pepper; and one can in an instant cause the deaths of millions.114 Again, in September 1687, he wrote to Arnauld that, putting philosophy aside, from the results of experimental science alone, entire organisms appeared to be present in the form of still imperceptible little animals. His words here were: Putting reasoning aside, experiments render it quiet probable that every animal was already an organism while it was still imperceptible. And several competent men, particularly Mr Swammerdam and Mr Leeuwenhoek (whose merit is above others in these matters), have tended to this interpretation.115 Finally, on October 9, 1687, Leibniz wrote again to Arnauld about his penchant for Leeuwenhoek’s sentiments, referring in this context to a work of Jan Swammerdam from the year 1672.116 Thus he wrote: I have understood for some time that Mr Leeuwenhoek has views which are pretty close to mine, in that he maintains that even very big animals are born by a manner of transformation. I do not dare either to approve or to reject the details of his opinion, but I consider it to be most veritable in general, and another great observer and anatomist Mr Swammerdam 113 “comme il se peut que selon les sentimens de M. Leewenhoeck toute generation d’un animal, ne soit qu’une transformation d’un animal déja vivant, il y a lieu de croire aussi, que la mort n’est qu’une autre transformation” (A II,2 N. 24, p. 115). 114 “l’experience favorise cette multitude des choses animés. On trouve qu’il y a une quantité prodigieuse d’animaux dans une goutte d’eau imbue de poivre; et on en peut faire mourir des millions tout d’un coup” (A II,2 N. 42, p. 189). 115 “mettant les raisons à part les experiences rendent assez probable, que tout animal estoit déja organisé, bien qu’il fust imperceptible. Et plusieurs habiles hommes particulierement Messieurs Schwammerdam et Leewenhoek (qui valent bien d’autres en ces matieres) ont penché de ce costé là” (A II,2 N. 56, pp. 235f.). 116 Cf. J. Swammerdam, Miraculum naturae sive uteri muliebris fabrica, notis in D. J. van Horne prodromum illustrata, et tabulis … adumbrata, Leiden, 1672.

July 1683–1690

381

attests to his penchant for it. Well then, the views of these men referred to here are worth more than a lot of others in these matters.117 Electrical phenomena and terrestrial magnetism were relatively new research areas in the seventeenth century. Already in the years before 1683, declination, inclination and the strength of terrestrial magnetism were topics in the epistolary exchanges between Leibniz and his correspondents. The variation of terrestrial magnetism, as well as a project for corresponding magnetic observations,118 represented a focus in Leibniz’s correspondence with the Frankfurt physician Sebastian Scheffer. On July 21, 1684, Leibniz approached the then secretary of the Académie Royale des Sciences in Paris, Jean-Baptiste Du Hamel, with the following query: I also desire to learn if the descriptions of the mechanical arts, which were commenced by order of the Academie, have been continued, if the meridian of the observatory has been established, and if the variation of the magnetic needle has been observed along this meridian.119 Later, it was from Huygens that Leibniz most likely expected to obtain an explanation of the phenomena of magnetism and electricity. Thus, in his drafted but never dispatched letter from the first half of October 1690,120 and again in his letter of November 7, Leibniz enquired of Huygens – in connection with deliberations concerning celestial phenomena (comets and rainbows) – about the laws of terrestrial magnetism. Thus he asked: “Has one not discovered anything about the laws of the variation of the magnetic needle[?] I imagine, Sir, that you have had thoughts about the matter in question, just as about many other matters of physics”.121 117 “J’ay appris depuis quelque temps que M. Leewenhoeck a des sentimens assez approchans des miens, en ce qu’il soutient que même les plus grands animaux naissent par une maniere de transformation, je n’ose ny approuver ny rejetter le detail de son opinion, mais je la tiens tres veritable en general, et M. Swammerdam autre grand observateur et Anatomiste, temoigne assez qu’il y avoit aussi du penchant. Or les jugemens de ces Messieurs là valent ceux de bien d’autres en ces matieres” (A II,2 N. 57, pp. 254f.). 118 Cf. A III,3 N. 117, N. 248, N. 271 and N. 284. 119 “Je souhaite aussi de sçavoir, si on a continué les descriptions des Arts mecaniques qu’on avoit commencées par l’ordre de l’Academie, si le meridian de l’observatoire est établi, et si on a observé la variation de l’eguille le long de ce meridian” (A III,4 N. 62, p. 131). 120 Cf. L4 and L5 of A III,4 N. 282, specifically pp. 600f. and p. 617; HO, 9, pp. 521–527. 121 “N’a-t on rien decouvert sur les loix de la variation de l’Éguille aimantée, je m’imagine, Monsieur, que vous aurés medité là dessus, aussi bien que sur beaucoup d’autres matieres de physique” (A III,4 N. 287, pp. 644 and 646; HO, 9, pp. 532–535).

382

Chapter 2

Alas, in his reply of November 18, Huygens did not see himself in a position to give a satisfactory explanation, either for the variation of terrestrial magnetism, or for known electrical phenomena. The words of his reply were: I have had certain thoughts about the magnet, but the reason for the variation of the magnetic needle is unknown to me, and it does not follow from certain laws known to me, although there are those who want to establish these. I find the effects of amber also more difficult to explain than those of the magnetic needle, principally with regard to certain new phenomena, which I have scarcely found through my experiments.122 Huygens surely had in mind here his Traité de l’aimant, about which he had given an account to the Académie des Sciences in 1679.123 In his reply of November 24, 1690, Leibniz then alluded to Otto von Guericke’s experiment, in which electric sparking had been obtained with a ball of sulfur, to his own correspondence with Guericke, in 1671 and 1672,124 as well as to his knowledge of observations of the variation of terrestrial magnetism at sea. And so he wrote: Since you have undertaken experiments of consequence with amber, I can tell you that the late Mr Guericke has done very significant work on electric bodies. He once wrote to me about this,125 and I will look up the details. That which has led me to believe that the magnetic needle obeys a certain rule (although still unknown) was that I have seen ship log-books of long journeys where it was observed very often, and where it did not change in leaps and bounds but rather only gradually.126

122 “J’ay quelques meditations sur l’Aimant, mais la raison de la variation de l’Eguille m’est inconnue; qui ne suit pas des loix certaines que je scache, quoyqu’il en a qui en ont voulu etablir. Je trouve les effets de l’Ambre encore plus difficiles à expliquer que ceux de l’Aimant, principalement à l’egard de quelques nouveaux phenomenes que j’ay trouvez, il n’y a guere, par mes experiences” (A III,4 N. 291, p. 657; HO, 9, pp. 536–540). 123 Cf. HO, 19, pp. 574–604, and J.-B. Du Hamel, Regiae Scientiarum Academiae historia, Paris, 1701, p. 184. 124 Cf. A II,1 N. 54. N. 62, N. 75, N. 77, N. 82, N. 83, N. 101, N. 103 and N. 104. 125 Cf. Guericke’s letter to Leibniz of June 16, 1671 (A II,1 N. 62). 126 “Puisque Vous avés fait des experiences de consequence avec l’ambre, je vous diray que feu Mons. Gericke en avoit fait de fort considerable avec des corps Electriques. Il m’en écrivit un jour, et j’en chercheray le detail. Ce qui m’a fait croire que la variation de l’Éguile a quelque regle (quoyqu’ inconnue encor) c’est que j’ay vû des journaux des grands voyages où elle estoit tres souvent observée et où elle ne changeoit pas par sauts mais peu á peu” (A III,4 N. 292, p. 669; HO, 9, pp. 546–552).

July 1683–1690

383

In the wake of this, Huygens referred to his familiarity with Guericke’s Experimenta nova (1672),127 and he provided some further thoughts, concerning his own electrical experiments (carried on since 1672)128 and theories, in his final letter of the year 1690, written on December 19. There he wrote: I have the book of Mr Guericke where he reports his experiments on amber. If he has communicated others to you, I would be pleased to be privy to this knowledge. Several of mine were undertaken in the light of certain hypotheses[,] which I conceived to explain this admirable attraction and its diverse phenomena, but I still have not reached the end of this speculation.129 Worthy of mention in this connection is also Leibniz’s assessment of the relative merits of Guericke and Robert Boyle in the investigation of the nature of a vacuum. While Leibniz considered Boyle to be an outstanding experimentalist, he doubted that he had drawn hitherto unknown conclusions in his mechanical philosophy. Boyle’s air (or vacuum) pump was likewise, in Leibniz’s eyes, simply a further development of Guericke’s discovery. Thus, at the end of his drafted, but never dispatched, letter of October 1690 to Huygens, he wrote: “As regards Mr Boyle, I am disappointed that all the world attributes to him the [invention of the] vacuum pump, of which Guericke was the inventor and which Boyle at most rendered more convenient”.130 Leibniz saw a similar injustice in the case of Willebrord Snell van Royen, the Dutch discoverer of the law of refraction which was later attributed to Descartes and Kepler. But, even the latter of this pair had suffered at the hands of the former, having been denied the credit for being the first to suggest an explanation of gravity based on the centrifugal force experienced by rotating bodies. Thus, Leibniz continued:

127 Cf. O. von Guericke, Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio, Amsterdam, 1672. 128 Cf. HO, 19, pp. 607–611. 129 “J’ay le livre de Mr Guericke où il raporte ses Experiences de l’Ambre. S’il vous en a communiqué encore d’autres, je seray bien aise d’y participer. Plusieurs des mienes ont esté faites en vuë de certaines hypotheses que je me suis imaginées pour expliquer cette admirable attraction et ses divers phenomenes, mais je ne suis pas encore venu à bout de cette speculation” (A III,4 N. 296, p. 691; HO, 9, pp. 568–572). 130 “A propos de M. Boyle je m’étonne que tout le monde luy attribue la Machine du vuide, dont M. Gericke est l’inventeur, et que M. Boyle a seulement rendue plus commode tout au plus” (A III,4 N. 282, p. 618).

384

Chapter 2

I see that the same thing happened to your Snellius, the first inventor of the true law of refraction which was attributed just the same to Descartes and to Kepler, who was the first to observe that one could explain gravity by the efforts of rotating bodies to distance themselves from their center, a line of thought sequestrated since by Mr Descartes.131 5

Technology: Mining and Power Technology

As regards Leibniz’s interests in the fields of technology and engineering, the 1680s saw both a continuity, in the form of his pursuits of earlier interests, as well as a departure in the guise of the emergence of new areas of activity. The first category includes, in particular, the multifarious proposals for improvement of ore mining, and for the requisite water resources management in the Harz mountains. Already in the fall of 1679, a contract between Leibniz and the local mining authority – the Board of Mines in Clausthal – was ratified by duke Johann Friedrich.132 This was for a one-year trial of the use of windmills for draining the Dorothea Landskron colliery, an undertaking which was moved to the Catharina colliery in the spring of 1680.133 The plan was to raise the pit water from the mine by means of a pump assembly, which was attached directly to a windmill, viz. the so-called “immediate” windmill solution. In August 1680, Leibniz then presented a new arrangement in the form of a plan first devised by a Dutchman, namely the mining official Peter Hartsinck (or Hartzingk) who died in that year. This alternative plan – which Leibniz had previously rejected but now advocated – envisioned that the windmills would not be used to power the pumping machinery directly, but would rather form part of a pumped-storage system.134 The service water, being used to drive water wheels attached to the pumping machinery, was to be returned from the collecting pond, located below the prime mover, to its original storage pond above the water wheel by the use of wind power, viz. the so-called “mediate” 131 “Je voy que la même chose est arrivée à vostre Snellius, premier inventeur de la veritable loy des refractions qu’on attribute cependant à des Cartes et à Kepler, qui s’est avisé le premier qu’on pouvoit expliquer la pesanteur par l’effort que font les corps circulans de s’eloigner du centre, pensée dont M. des Cartes s’est fait honneur dépuis” (note 130, pp. 618f.). Regarding Snell van Royen and the law of refraction, cf. for example, K. Hentschel, “Das Brechungsgesetz in der Fassung von Snellius: Rekonstruktion seines Entdeckungspfades und eine Übersetzung seines lateinischen Manuskriptes sowie erganzender Dokumente”, Archive for the History of the Exact Sciences, vol. 55, (2001), pp. 297–344. 132 Cf. A I,2 N. 181. 133 Cf. A I,3 N. 35. 134 Cf. J. Gottschalk, 1982 (Introduction, note 101).

July 1683–1690

385

windmill solution. A commission then decided that, at the Catharina colliery, the direct (or “immediate”) system should continue in operation while simultaneously, at the Zellbach colliery, the indirect (or “mediate”) system should be deployed making use then of two separate windmills.135 The preferential trials of the direct system were very much drawn out due to a variety of circumstances. These included the circumstance that the employment of new pumps proved to be controversial, as did the use of control mechanisms for a steadier, or more uniform, operation of the windmill and, in addition, that a system of power transmission using compressed air was contemplated. As a result, the costs increased to over 2000 Taler by the middle of the year 1683, and on December 6 of that year, duke Ernst August ordered the suspension of payments by his court to the mining company until the efficiency of the windmills could finally be established.136 Leibniz, who previously had to contribute only a third of the costs, now agreed to the continuation of the trials for a further year entirely at his own expense.137 Two new test series – using the direct or “immediate” method – were carried out in 1684 (in the absence of Leibniz himself) at the Catharina colliery, but with only partial success, mainly as a consequence of the erratic wind supply in the mountainous environment. Because of the varying strength (and direction) of the wind, Leibniz pursued simultaneously – from the beginning of 1684 – his “mediate” or indirect project using horizontal windmill technology. In this system, the vanes of the wind turbine rotated horizontally about a vertical axis, which allowed the wind power to be better and more uniformly regulated. For the construction of such a horizontal windmill, which was considerably cheaper but also correspondingly less efficient in comparison to a conventional windmill, the duke had promised the payment of a sum of 200 Taler on January 31, 1684. This horizontal windmill operated presumably satisfactorily at the location of the lower Eschenbach pond, but not under full-load conditions. An actual practice test – with piston pumps, or an Archimedean screw system, attached to raise water – was probably never carried out. Finally, after a third test series – which was carried out at the beginning of 1685 (this time in Leibniz’s presence) at the Catharina colliery with a directly-attached windmill – failed to prove an unreserved success, the duke ordered (on April 14, 1685) the termination of the windmill trials.138

135 Cf. A I,3 N. 60. 136 Cf. A I,3 N. 216. 137 Cf. A I,4 N. 4. 138 Cf. A I,4 N. 147.

386

Chapter 2

Notwithstanding this setback, Leibniz was unable to free himself from his commitment to the Harz undertaking. In September 1685 he presented a new proposal to the duke,139 this time for the improvement of the winding machinery – used for uplifting or hoisting the ore in the mines – employing a closed-loop, or endless cable, to be powered by water wheels and to be put to the test at three pits owned by the duke in the Thurm Rosenhofer mountain range.140 Scarcely a year later, Leibniz considered the practicability and advantage of this system to have been proven, but he nonetheless accepted (at least for the time being) the termination of the test series in the light of outstanding repair and maintenance work at the pits.141 And so, at the end of the year 1686, Leibniz finally departed from the Harz mountains, where he had spent a considerable portion of the previous seven years. Almost another seven years were then to intervene, before (in 1693) the challenge to improve the Harz mining processes would once again capture his interest. Leibniz’s activity in the Harz mining district for the period from February 1684 to August 1686 – namely during the time of the final three test series with the direct or “immediate” vertical windmill technology at the Catharina colliery, as well as with the indirect or “mediate” horizontal windmill technology, and the ore-lifting techniques at the Thurm Rosenhof pit – is reflected above all in his general political and historical correspondence at this time.142 His most important correspondent in relation to his mining interests was surely Jobst Dietrich Brandshagen, who supervised the trials and experiments during his absence and recorded the financial accounting in writing on his behalf. Leibniz’s correspondence with Brandhagen (between 1677 and 1690) is spread between his general political and historical correspondence and his correspondence in mathematics, science and technology, for this period. On the other hand, reports, accounts and sundry communications sent by the master carpenter, Hans Linsen, to Leibniz, clearly belong to his correspondence in the area of engineering and technology and include, firstly, those from the summer and fall of 1683 relating to work on the direct or “immediate” windmill at the Catharina colliery,143 secondly, those relating to a probably failed effort in 1685 to secure an order or commission for the implementation of the

139 Cf. A I,4 N. 165. 140 Cf. A I,4 N. 172. 141 Cf. A I,4 N. 241. 142 Cf. volume A I,4; Leibniz’s activities in the Harz mining district have also been comprehensively documented in a supplementary volume of his general political and historical correspondence for the period from 1692 to 1696 (I, Supp.). 143 Cf. A III,4 N. 6, N. 15, N. 22, N. 30, and N. 33–36.

July 1683–1690

387

horizontal windmill technology,144 and thirdly, those for the period between November 1685 and March 1686, during which the use of a closed-loop or endless cable in the winding machinery was being investigated at the Thurm Rosenhof mine.145 For his part, Linsen was, throughout the period in question, willing and in a position to assist Leibniz in acquiring wooden models for his technical designs.146 Also, in relation to this important correspondence with Linsen, stand a range of minor correspondences and communications with tradesmen, smiths and material suppliers, which document above all financial accounts, and reveal expenditure for materials and labor.147 Leibniz’s knowledge of mining was not limited to his own practical experience in the Harz district. Contacts with persons from other mining districts, in Germany and elsewhere in Europe, frequently came to the fore. Early in 1687, for example, there developed an extended correspondence between Leibniz and the mining engineer Friedrich Heyn, who then had recently returned from England. In a letter  – from which Leibniz had an extract made  – of November 30, 1686, to the Harz resident and apothecary Johann Christian Wachsmuth,148 Heyn lauded the knowledge he had gained during his stay in England, among other things concerning Robert Boyle’s process for making phosphorus, a process for the desalination of sea water, and regarding a process, employed by Prince Rupert of the Rhine (1619–1682),149 for tempering iron or for the production of the alloy named after him (Prince Rupert’s metal). On the basis of his practical experience in English mining – ore mining in particular – and of his familiarity with English mineral ores, Heyn was in a position to introduce himself to Leibniz as a prospective assistant, on February 6, 1687.150 In this letter sent from Lüneburg, he reported about a new powerful water wheel-powered pumping machine, with rod engine-like sectional components, that had been designed by Johann Joachim Becher, and then successfully deployed and operated in the mining district of Cornwall, following Becher’s untimely death in 1682.151 The new machine – Leibniz was 144 Cf. A III,4 N. 88 and N. 89. 145 Cf. A III,4 N. 101–105, N. 109, N. 113, N. 118, N. 120, N. 122, N. 124, N. 130, N. 131, N. 133, N. 135, N. 138, and N. 139–144. 146 Cf. A III,4 N. 85, N. 89, N. 143, N. 160, N. 163, N. 166, and N. 174. 147 Cf. in particular the correspondence (in A III,4) with H. C. Heße. E. Müller, R. Pfeffer, Z. Pöhler, H. A. Moltfelt, J. Plappert, C. Wahner, and P. Zehn. 148 Cf. A III,4 N. 155. 149 Known in Germany as ‘Prinz Ruprecht von der Pfalz’. 150 Cf. A III,4 N. 159, pp. 301–303. 151 Since Becher wrote from Truro during his journey to Cornwall’ (cf. J. J. Becher, Tripus hermeticus fatidicus, pandens oracula chymica, Frankfurt, 1689, p. 6 and p. 98), this town, or the tin mines in the vicinity, may well have been the location in question.

388

Chapter 2

told – incorporated neither a standard “suck and press” pumping-system, nor a scoop water wheel system, but consisted rather of a “Taschenkunst”, or rag and chain pump, which was also known as a chain of beads or paternoster pump. This type of pump had previously been used in Hungary, and had in fact been described more than a century before by Georg Agricola.152 The novelty of the Cornish machine,153 – Leibniz was told – was that it incorporated not a single chain pump, but rather a series of stages – comparable to the sections of a “Stangenkunst”, or rod-engine transmission system – involving pumps of a kind that might operate using several pipes of different measure, both in perpendicular and inclined shafts, and at depths of up to 100 or more fathoms. The power supply could come from wind-power, water power, horse power or even manpower, Leibniz was told. Thus, Heyn gave the following account in his letter of February 6, 1687: I have spent several years in England and studied in particular the waterworks there, [and] I accordingly visited their coal, iron, lead, and especially tin, mines. In the latter type I have spent the most time, and there four years ago an extraordinary waterworks was designed by Dr Johann Joachim Becher who, however, died in London shortly afterwards, namely at the beginning of October 1682. However, the scheme was pursued after his death and only brought to completion about a year and a half ago. It provided a greater effect than any previous waterworks in Cornwall and continues to do so. The creation in question is neither a suck and press pump nor a scoop [or Persian] wheel, but rather a rag and chain pump [a chain of beads or paternoster pump] and which has previously been called the ‘Taschenkunst’ in Hungary, an account of which has been given by Georg Agricola in De Re Metallica on pages 148 to 158 of the Latin edition printed in Basel in 1657.154 It is just the same but in far greater perfection. It incorporates not a single-stage chain pump, like those previously used in Hungary, but rather a series of stages, like the sections of a ‘Stangenkunst’ [or rod-engine transmission system]. It has a most interesting movement providing a remarkable alleviation, and can be powered by wind power, horse power, water power and, if needs be, by manpower. It operates in perpendicular or inclined shafts and, depending on the mine water requirement, varying numbers of pipes of different

152 Cf. G. Agricola, De re metallica libri XII, Basel, 1556. 153 Cf. G. Hollister-Short, 1976, 1977 (Introduction, note 103). 154 As regards pagination, this edition is identical with that of 1556.

July 1683–1690

389

measure are employed and the ‘vis motiva’, or motive force, is generated accordingly; it can operate at depths of up to 100 or more fathoms.155 In a further letter of March 26, 1687 – following receipt of Leibniz’s (no longer extant) reply of February 25 – Heyn reported further, but in a more cautionary fashion, about the new machine in Cornwall.156 The perfection of the machine had taken three years, and it had involved an investment of more than 15 thousand Taler. Once fully functional, it had brought the operating company a monthly return on its investment of eleven hundred Taler, or two hundred and fifty pounds sterling. Alas, his most recent intelligence from England was that the machinery had in the meantime come to a complete standstill, as a consequence of the vein having been cut off and of a mining accident. Thus Heyn wrote on this occasion: I have to be honest and concede the point, that in such matters innumerable obstacles arise both with respect to persons and to practical matters, and that works of this kind can never be brought to a desired conclusion without an enormous effort. In this sense, the works in question produced in the past three years costs of over 15 thousand Taler before the correct way was found and, if there had not been the corresponding pressure, such wonderful works would never have reached such perfection, but would rather have been buried prematurely and in an embryonic state. It did, however, in due course provide the company, which 155 “Ich habe mich etliche jahr in England auffgehalten und absonderlich der Wasserwercke darinnen erkundiget, dahero ich ihre Kool-  Eisen-  Bley-  und fürnemlich Zinn-Minen besucht, bey welchen letztern ich die meiste Zeit zugebracht, woselbst vor nunmehro 4 jahren ein ungemein Wasserwerck durch Doct. Joh. Joachim Bechern, welcher aber kurtz drauff, als im anfange des Octobr. 1682 in London gestorben, angegeben worden, es ist aber nach seinem tode fortgesetzet und nur erst vor ungefehr anderthalb jahren zu seiner vollkommenheit gebracht worden, welches mehr effect, als iemals eine Kunst in Cornwall gethan und noch thut. Gesagte Kunst ist weder ein Suck- Press- Pump- noch Schöpffwerck sondern es ist ein werck, welches vor diesem in Ungarn die Taschenkunst genennt worden, von welcher G. Agricola De Re Metallica a pag. 148 usque ad pag. 158, in der Latein. Edition, so zu Basel 1657 gedruckt, einigen nachricht giebet. Alleine es ist daselbst in weit besserer perfection, gehet nicht una catena wie vor diesem in Ungern [sic], sondern in divisionibus von kasten zu kasten wie die Stangen-Kunst, hat eine curiöse bewegung, welche eine sonderbare erleichterung hat, kann mit wind, pferden und wasser und im nohtfall mit menschen getrieben werden, gehet perpendiculariter und oblique, nach dem die gruben sehr wasser-nöhtig seyn, nachdem werden auch dir röhren gros oder klein, wenig oder viel eingerichtet und die vis motiva wird drin nach proportion angeordnet, es kan auff 100 und mehr faden gehen” (note 150 above, p. 302). 156 Cf. A III,4 N. 165, pp. 312–315.

390

Chapter 2

had advanced the investment costs, with a monthly return of more than 1100 Taler, namely 250 pounds sterling, … Now, however, the noble works have come to a total standstill, as has been reported to me from the same location in England, due to the fact that the vein has been cut off, and as a result of a damaging and tragic mining accident which happened there.157 Heyn then offered to reveal the details of the Cornish machine to Leibniz using a model of the device, writing as follows: And so, as your humble servant, who could considerably satisfy your curiosity in the matter, I am willing to reveal to you the total structure of the works. Thereafter, with your immense knowledge and experience in such matters, you will recognize the excellence of these waterworks, the exposé of which will of course have to be done using a model.158 In addition, Heyn provided Leibniz with further information about Becher’s demise, his family situation, his legacy, and liabilities.159 He also informed him about Becher’s writings – his chemical writings in particular – and also about the satirical work, entitled Närrische Weißheit und weise Narrheit (foolish wisdom or wise foolery/ folly’ish wisdom or wise folly) of 1682, in which the author had ridiculed discoveries and projects of a range of contemporaries including Leibniz himself.160 Although not mentioned in Heyn’s letter, the work in 157 “ich mus der warheit beyfall geben und bekennen, daß in dergleichen sachen sich unzehliche hindernüsse so wol a personis, als a rebus finden und daß dergleichen werck niemals ohne grossen nachdruck zu einem gewüntschtem zweck gelangen könne; wie denn dasselbe werck diese drey jahr über, ehe der rechte weg gefunden worden, über 15 tausend rthl. gekostet, und were nicht ein solcher nachdruck gewesen, hätte solch herrliches werck niemals seine vollkommenheit erreichet, sondern were, als ein embryon, vor der zeit in seiner unvollkommenheit begraben worden. Es hat aber auch hernachmals der Company, so die unkosten geschossen, ieden monaht über 1100 rthl., nemlich 250 lbs Sterlings, wieder eingebracht. … Nunmehro aber stehet das edle Werck, wie ich aus England von demselben orte berichtet worden, gantz stille, indem sich die ader abgeschnitten und auch ein schädlicher und unglückseeliger bergfall sich daselbst ereignet” (p. 312). 158 “So meine wenigkeit dessen curiosität hierinne einige satisfaction geben könte bin ich erbötig und bereit, demselben die gantze Structur des Wercks zu eröffnen; da denn dessen ungemeine wissenschafft und experientz in dergleichen Excellentiam hujus operis erkennen wird, welches denn durch ein Modell wird geschehen müssen” (p. 313). 159 Cf. pp. 313f. 160 “Seine Närrische Weisheit und Weise Narrheit ist bekandt, da er des Herrn Hoffrahts auch erwehnet” (cf. J. J. Becher, Närrische Weißheit und weise Narrheit, Frankfurt am Main, 1682, p. 147).

July 1683–1690

391

question contained, as an appendix, an additional work entitled Dr. Bechers kurtzer doch gründlicher Bericht von Wasserwercken und Wasser=Künsten (Dr Becher’s short but thorough report on waterworks and water wheels),161 where an invention he claimed – perhaps that referred to by Heyn in his letters to Leibniz – is alluded to. This was essentially a variant of the ‘Stangenkunst’, or rod engine technology, involving a double rotary crank mechanism (“Körben” or “Kurbeln”) and an intervening double rod mechanism (“doppeln Stangen”). Regarding the long-established German ‘Stangenkunst’, or rod-engine technology, Becher explained that it was essentially a power transmission system, connecting regular or circular motions at both ends by means of an irregular or retrograde linear (viz. alternating) motion in between. It connected a prime mover (“un mobile”) – supplying wind power, water power or horse power – with a distant load (“una causa movente”) like a flour mill. Becher’s printed description was as follows: With ‘Stangenkunst’ solutions I am reminded of a movement, which I invented, namely with a double rotary crank mechanism and a double rod mechanism, where the movement of the crankshafts, at both ends of the rods, is circular, and in between the rods move irregularly with retrograde motion. This movement serves the purpose that – at a location where one has no available power source (like water, wind or horse power), and where a regular and rotary motion has to be provided there where the mobile (for example a flour mill) is to be moved (and also operated linearly), and where it occurs at times that the prime mover is not located close to the load but must be positioned rather at a distance from it – one can employ the ‘Stangenkunst’ and maintain a rotary motion.162 In Heyn’s next letter of July 1687 – following a meeting of the two in Lüneburg in late June or early July – the correspondent recalled that he had informed Leibniz during their meeting about yet another water mill near Ehrenfriedersdorf, in the Freiberg mining district of Saxony, that was likewise compared to the 161 Cf. pp. 181–203. 162 “Bey Beschluß der Stangen=Kunst erinnere ich mich einer Bewegung/ welche ich inventirt/ nemblich mit doppeln Körben und doppeln Stangen/ da die Bewegung der Körben im Anfang und Ende der Stangen circular gehet/ und in der mitte der stangen/ irregular/ nemblich motu retrogrado gehet. Diese Bewegung dienet darzu/ daß wo man keine bewegende Krafft hat/ als Wasser/ Wind oder Pferd/ welche regular und circular gehet/ und das mobile welches bewegt soll werden/ exempli gratia eine Mahl-Mühl/ auch gerade gehen muß/ und es sich bißweilen begiebet/ daß das mobile nicht bey der causa movente dicht stehen kann/ sondern eine Distance davon seyn muß: so kann man die Stangen=Kunst brauchen/ und doch eine runde Bewegung halten” (pp. 196f.).

392

Chapter 2

“Stangenkunst” or rod engine technology. The machine in question was most likely nothing other than a technically improved version of the so-called “Ehrenfriedersdorfer Radpumpe”. This was essentially a piston-pump system, and it consisted of several pump stages arranged one above the other and powered by a single prime mover. Just as with the machine of Becher’s design in Cornwall, the focus in Heyn’s account of the machine in Saxony was the mechanism which transmitted the power of a prime mover (a horse mill or water wheel) to two or three pump stages, arranged one above the other. It had been employed, he explained, at a pit which had stood still for years due to a lack of adequate pumping machinery. Here Heyn wrote: Following the time when I had the honor of seeing you here, Sir, I received from various trustworthy friends reliable reports that the waterworks in Saxony, which I referred to, provide great effects and are proving far superior to the ‘Stangenkunst’ [or rod-engine system]. These are located at Ehrenfriedersdorf near Freiberg, where a mine, which previously could not be serviced by any machine and had stood under water for many years, was made operative with the aid of such machines; it is now being powered by horse power and is to be made operable using water power, about which development you will no doubt obtain information from elsewhere.163 The piston-pumps with flap valves – just like the rag and chain or paternoster pumps – represented a conventional technology, which was, however, still capable of improvement through the reduction of friction losses, as for example by means of a leather packing, or sealing, of valve-pistons. While Heyn was convinced, and enthusiastic, about the possibilities for the use of machines like those in Cornwall or Saxony, Leibniz saw the prospects with a degree of sobriety. The modification of a machine, like that in Ehrenfriedersdorf, would in Leibniz judgement – as he outlined in his reply to Heyn of mid-July 1687 – not lead to any increase in efficiency. He then presented the following simple calculation to illustrate the point. For a mine shaft with total lifting height 163 “Ich habe nach der Zeit, als ich die Ehre gehabt denselben hier zu sehen, von unterschiedlichen glaubwürdigen Freunden sichere nachricht erhalten, daß das Wasserwerck in Sachsen, vorvon ich gedacht, grossen effect thut und die Stangen-Kunst weit übertrifft, es stehet zu Ehrich-Friedrichs-dorff üm Freyberg, woselbst eine grube, welche mit keiner Kunst hat können gewältiget werden und lange jahr unter wasser gestanden, durch desselben hülffe baubar gemacht worden, es wird anitzo mit pferden getrieben und soll mit wasser gangbar gemacht werden, worvon derselbe zweiffels ohne auch anderwerts vernehmen wird” (A III,4 N. 179, p. 331).

July 1683–1690

393

requirement of a hundred lachters (about 200 meters), and a desired delivery volume from the mine of half a hundredweight of water for each revolution of the water wheel above ground, a head (equal to the diameter of the water wheel) of some 30 feet, or 5 lachter (about 10 meters), and a volume of at least 10 hundredweights of water would be required in order to power each such rotation of the wheel. However, in reality one would require a great deal more to compensate for the considerable friction losses in the transmission mechanism. With this train of thought, Leibniz broached the fundamental problem in all such mechanical power transmission systems, namely the enormous friction losses between the parts of the mechanism. Thus, he wrote to Heyn on this occasion: As regards the waterworks which are supposed to be operational at Ehrenfriederndorff, I cannot yet change my former opinion until I am presented with better arguments or more reliable experiments. In my judgement, through changes of this kind no additional force is to be gained, but, on the contrary, he who wants to achieve this result must be able to avoid the friction losses involved. Besides which, the remaining entirety is founded on a certain equilibrium and compensation and he – who in practice has a water wheel of 30-feet diameter, and with this wants to raise water from the mine from a depth of about 100 lachter such that with every rotation of the water wheel half a hundredweight of water be delivered above ground – could achieve this result if, with every rotation of the water wheel, somewhat more than 10 hundredweight of water were directed from above against the vanes, or dropped into the buckets, of the wheel. That required over and above this is due to the friction forces that arise from the field rods above ground and the mine rods under ground, from the leather sealings which lie between the cylinders and the pistons of the pumps, and the like, and these losses often absorb more force than the principal load itself. This is my candid opinion of the matter in hand.164 164 “Wegen der waßerkunst welche zu Ehrenfriederndorff stehen soll, kan ich meine vorige meinung noch nicht andern, biß ich entweder beßere rationes oder gewißere Experimenta erfahre. Meines ermeßens ist durch dergleichen anderungen keine force zu gewinnen, sondern wer solches thun will muß die frictiones vermeiden konnen. Außer welchen das übrige alles in einen gewißen aeqvilibrio und compensation beruhet und wer am tage ein waßerradt von 30 schuhen hoch hat und damit daß waßer in der grube etwa 100 lachter hoch heben will, also daß bey ieden umbgang des waßer-rades ein halber Zentner waßer oben außgegoßen werde; der kondte es ausrichten wenn bey ieden umbgang des rades etwas mehr als zehn zentner waßer in den schauffeln herab fielen; was drüber das gehet

394

Chapter 2

In his letters to Leibniz, Heyn also reported about his professional experience in salins, or salt works, and he enquired about a salt refinery being set up near the town of Einbeck. As Heyn’s attempts to find employment at such a salt works proved unsuccessful, he opted to accompany Leibniz on his research tour as far as Vienna. By the time of Leibniz’s return from Italy, Heyn had become a mining official, a tax gatherer and inspector in Ilmenau. From Leipzig, on June 6, 1690, he sent Leibniz mineral ores in which fossilized plants were to be seen, and concerning which he wrote: “I send you enclosed several ore specimens from the same mine location and in particular I admire the organogenic shale and limestone, in which the grown trees are to be found, the likes of which I have never seen before”.165 Then, in a subsequent letter from Ilmenau, written on November 14, 1690, he expressed his pronounced interest in a forthcoming German translation of the third and fourth parts,166 which had previously not been translated, of A. A. Barba’s Arte de los metales (1640),167 and which was then being prepared by Christoph Pratisius, the personal physician of duke Ernst August in Hanover. Wachsmuth, who had brokered Heyn’s role as Leibniz’s companion on the first leg of the Italian journey,168 and who had even contemplated accompanying Leibniz himself to Italy,169 served him not only as a supplier of medication. He also provided Leibniz with important information about the Harz mining towns and their administration, as well as about learned travelers in the Harz mountains such as, for example – in a letter of July 19, 1687 – about the Swedish mining expert Eric Odelius who, while fulfilling a royal commission, was exploring the Harz district and – provided with a letter or recommendation auf die vorfallenden frictiones welche durch die feld- und grubenstangen[,] liederungen und dergleichen verursachet werden so offtmahls mehr krafft absorbiren als das principale onus selbsten. Dieß ist meine aufrichtige meinung von diesen dingen” (A III,4 N. 182, p. 336). 165 “Ich übersende hierbey etliche Ertze von selben wercke, absonderlich admirire ich die Kräuter schiefer und Kalcksteine, worinnen sich die gewachsenen bäume finden, indem ich von dergleichen vorhero niemals gesehen” (A III,4 N. 261, p. 518). 166 “Möchte wol wissen, ob das 3te und 4te theil von dem Alb. Alonso Barba durch H. D. Bradisium … übersetzt were” (A III,4 N. 289, p. 651). 167 Cf. A. A. Barba, Arte de los metales, Madrid, 1640; The first book of the art of metals … translated into English in the year 1669, London, 1670, and The second book of the art of mettals … English’d by the Right Honourable Edward [Montagu, first] earl of Sandwich [+1672], London, 1674; The art of metals … in two books, 2nd ed., London, 1674: cf. also the German translation of parts 1 and 2 of Barba’s opus by Johann Lange: Berg-Büchlein, darinnen von der Metallen und Mineralien Generalia und Ursprung, wie auch von derselben Natur und Eigenschafft … gehandelt wird, Hamburg, 1676. 168 Cf. A III,4 N. 175. 169 Cf. A III,4 N. 189.

July 1683–1690

395

from Wachsmuth – desired to meet Leibniz in Hanover on his return journey to Sweden. Thus, Wachsmuth wrote on this occasion: Yesterday I gave a stranger from Stockholm, whose name is Odehlius, a letter because he desires greatly to speak to you. He has studied medicine, and has no doubt also learned mine surveying and mine sampling and is a felicitous ore and metal enthusiast, about which he has also disputed in Paris. I made his acquaintance while in England. Otherwise he is from a genteel family and of stately means; he is en route to Stockholm where he is to become Inspector of the Royal Laboratory and, as I see from his letter, that, following the wishes of the king, he has, in the course of his inspection efforts, spent several days here in the mountains, etc. … from where he intends to attend upon your Excellency … he will be in Hanover in 8 days.170 On July 31, 1683, the Dutch mathematician Johann Jakob Ferguson reported to Leibniz about a technically interesting wind-powered water elevator, which he had seen during an inspection of the new fortifications of the town of Breda. The machines in use, the “slang-molens” or snake mills, required a strong wind and their performance was apparently equivalent to that of three “ketting-molens” or chain mills. Thus the correspondent wrote: Being in Breda for the purpose of inspection of the new fortifications there, I have seen among other things the effectiveness of many and different water mills, and on this occasion I observed a ‘slang’ or snake mill powered by the wind which, with a fair wind blowing, raised an incredibly large amount of water, indeed more than with 3 chain mills.171

170 “Gestern habe einer frembden person aus Stockholm ein Schr. mit geben an Ihr. Excellce weiln Er sehr verlanget mit Sie zu sprechen, deßen Nahme ist Odehlius[,] hat Medicinam studiret, v. hat das Mahrscheiden v. probiren wohl gelernet, ist ein treffl. Liebhaber von Ertzen v. Metallen, worvon Er auch in Paris Disputiret, habe ihn in Englandt gekennt, ist sonst von fürnehmer Familie v. Stattlichen mitteln, er wird gleich auff Stockholm gehen, und inspection über des königliche laboratorium bekommen, wie ich aus seinen Schr. ersehen, daß Er auff deß königs begehren kommen muß, hat sich hier etzl. tage in berge etc. besehen … von dar wird Er bloß Ihr. Excell. auffzuwarten … wird in 8 tagen zu Hannover sein” (A III,4 N. 183, p. 337). 171 “Tot Breda sijnde, ende de nieuwe fortification aldaer besiende, hebbe ich onder anderen gesien de effecten van veele ende verscheijde watermolens, ende bij die occasie geobserveert een slang-molen door de wint gedreven werdende, dewelcke met reedelijcke wint ongelooflijck veel waters opwerpt, ja meer dan 3 Ketting-molens” (A III,4 N. 7, p. 17).

396

Chapter 2

Leibniz then informed the correspondent, on August 25, about his horizontal windmill, and he even raised the possibility of introducing such systems to Holland, writing as follows: The windmill that I have made in the Harz mountains lifts water to a height of more than 450 feet and always turns itself into the direction of the wind, a facility which was only made possible just a little time ago, and this automatic positioning system might also be applied with the windmills used in Holland to power water pumps.172 To this Leibniz added a query,173 about the exact nature of the so-called “Slang-molen” type, and the “Ketting-molen” type, referred to by the correspondent. In his reply from Amsterdam on September 11, Ferguson compared the operation of the former to a rotating wooden spiral, or helical staircase, i.e. an Archimedean screw, and the latter to a chain elevator system, in which the water was lifted by a system of troughs attached to the chain and arranged one above the other. His words on the matter were: Under the designation ‘Slangmolen’, one understands here a wooden shaft covered over with a thin wooden barrier in the manner of a spiral or helical staircase, which on rotation forces water to rise, and a ‘Ketenmolen’ is so called because troughs are fixed on a chain, and attached one above the other, which on passing through the water carries it from below to above.174 As regards the new fortifications of the town of Breda, the correspondent was particularly interested in learning whether Leibniz’s wind mills in the Harz mountains operated effectively under moderate wind conditions. Thus he added: “And, as regards Breda, I have remarked that there a strong wind is 172 “Die Windtmühle die ich auff dem Harz machen laßen hebet das waßer mehr als 450 schuch hoch und stellet sich allezeit selbst in wind, welches schohne eine zeit hehr gar net gethan und diese selbststellung wurde bey den WindMühlen, so in Holland das waßer auß pompen gar artig zu appliciren seyn” (A III,4 N. 14, p. 30). 173 “Was M. h. H. in Hollandisch Slang-molen item Ketting-molen nennet, verstehe ich nicht” (p. 30). 174 “Door een Slangmolen verstaet man hier een houd rondom met dun houd beset op de maniere van een wentel-trap, het welck door sijn draeijen’t water naer om hooge drijft, ende een Ketenmolen word soo genoemt om dat een keten waer aen eenige over eijnde staende baderen gehecht sijn, door’t water heen van beneden naer boven altijd gevoert word, ende alsoo’t water met sich is nemende” (A III,4 N. 24, p. 57).

July 1683–1690

397

necessary, so I am very curious to learn if your mill can provide a sufficient effect when only a light wind is blowing”.175 While Leibniz’s most important innovation in mining was no doubt the exploitation of wind power, he was also very much occupied with water-powered and water-raising machines, and in this regard too, he tried to obtain information about corresponding developments, and corresponding technologies, in other European countries. Already on December 20, 1680, Noel Douceur had informed him from Paris that “His Majesty is going to spend ten thousand to construct an arm of the river Loire to Versaille”,176 and in March–April 1681 Edme Mariotte added the intelligence that: “He who raised the water up to 200 feet at St Germain takes the water on the river Seine by means of the mills which operate the pumps to raise the water up to 80 feet, and deposit it in a large reservoir”.177 Then, in July 1684, Leibniz himself requested information about relevant publications and projects of the Académie Royale des Sciences in Paris, in a letter to the secretary Jean-Baptiste Du Hamel expressing his wishes in the following words: I would also like to learn … if the machine which raises the water from the Seine at St Germain in order to have it flow to Versailles has been brought to perfection. And about that which the Englishman Mr Moreland has done, or is doing at Versailles.178 Leibniz was enquiring here specifically about the activities of Samuel Morland, who had been sent to France in early 1682 by king Charles II to gain knowledge and experience for the further improvement of English waterworks and water-lifting machines. Morland’s involvement was in the scheme  – known as the Machine of Marley – that Louis XIV had in hand, and whose installation was planned and carried out between 1681 and 1683.179 In January 1685, 175 “ende hebbe Ick tot Breda geremarqueert dat daer toe stercke wint nodich is, soo dat ick seer curieux ben te verstaen off uw Edts molen wel met sachte wind eenich effect can doen” (p. 57). 176 “Sa Majesté va despencé dix milium pour faire venir un bras de la riviere de Loire à Versaille” (A III,3 N. 141, pp. 307f.). 177 “Celuy qui a elevé de l’eau jusques à 200 pieds à St Germain prend l’eau dans la riviere de Seine par des moulins qui font jouer des pompes qui elevent l’eau jusques à 80 pieds, et la versant en un grand reservoir” (A III,3 N. 193, p. 374). 178 “Je souhaitte aussi de sçavoir … si la Machine qui eleve l’eau de la Seine à S. Germain pour la faire aller à Versailles est en sa perfection. Et ce que Mons. Moreland Anglois a fait, ou fait de bon à Versailles” (A III,4 N. 62, p. 131). 179 Cf. H. W. Dickinson, 1970, pp. 74f. (Introduction, note 107).

398

Chapter 2

Leibniz enquired once again about the scheme, this time in a letter to Claude Comiers and in the following words: “I would very much like to learn if the Academie Royale des Sciences is continuing its design for the description of the arts, and likewise about the nature of the new hydraulic machine powered by the Seine to deliver water to Versaille”.180 Alas, an answer to this letter has not been found. To the field of power technology belong certain themes from the area of transportation technology which also arose occasionally in Leibniz’s correspondence. Georg Mohr reported, for example in September 1683,181 about Nicolaas Witsen’s tract on ancient and contemporary shipbuilding – entitled Aeloude en hedendaegsche Scheeps-Bouw of 1671182 – a work that also attracted Leibniz’s interest and from which he made extracts. Likewise, in preparing his Italian journey, Leibniz established contact with a certain G[-] S[-] Schmid from Sulbeck (near the town of Einbeck) concerning the improvement of coaches and carriages. In the sole surviving item of this correspondence, dated July 17, 1687, Schmid had however to admit his inability to complete the fabrication of his “Schese rolandte”, but he did include a detailed drawing of such a carriage or coach.183 Leibniz’s vision of a stage or post coach that could travel from Hanover to Amsterdam in six hours was reported, perhaps inadvertently, by Johann Daniel Crafft,184 to Johann Joachim Becher and ridiculed by the latter in his satirical work Närrische Weißheit und weise Narrheit (1682).185 Five years later, on February 28, 1687, this gave Friedrich Meurs von Blauenstein in Dresden occasion to enquire about the validity of the scurrilous report, when he wrote the following words to Leibniz [sic]: “Please advise me if that is true which Doctor Becher wrote in his book entitled ‘weise narrheit’ of an idea you have had of a mail or post coach capable of traveling from Hanover

180 “Je voudrois bien sçavoir si l’Academie Royale des Sciences continue le dessein de la description des Arts, item en quoy consiste la nouvelle Machine Hydraulique que la Seine fait aller pour donner de l’eau à Versailles” (A III,4 N. 81, p. 197). 181 Cf. A III,4 N. 23, pp. 51f. 182 Cf. N. Witsen, Aeloude en hedendaegsche scheeps-bouw en bestier: Waer in wijtloopigh wert verhandelt de wijze van scheeps-timmeren, by Grieken en Romeynen: Scheeps-oeffeningen, strijden, tucht, straffe, wetten, en gewoonten, Amsterdam, 1671; the 2nd ed. with title: Architectura navalis et regimen nauticum: Ofte aeloude en hedendaegsche scheeps-bouw en bestier, Amsterdam, 1690. 183 Cf. A III,4 N. 181, pp. 334f. 184 Cf. A III,4 N. 29, p. 62. 185 Cf. note 160 above.

July 1683–1690

399

to Amsterdam in a period of six hours”.186 The words added to this by Meurs, namely “I know that he was a most defamatory person”,187 was for Leibniz tantamount to an answer. In his reply, on October 10, 1687, he did not allude to matter again.188 6

Ballistae – Military Engines and Engineering

Besides Leibniz’s activities in relation to power technology – reflected above all in the trials of machines and engines undertaken in the Harz mines – the ongoing controversy surrounding the cast-iron process of Noel Douceur was finally laid to rest early in 1685.189 As outlined in the previous chapter, Leibniz had – in the reign of duke Johann Friedrich and through the intercession of Mariotte – purchased a process from Douceur that allegedly rendered cast iron malleable. The process in question had an obvious military significance particularly for the improvement of the production of canons. Douceur had received half of the agreed price of 1000 livres at once, while the payment of the other half of the sum, which Mariotte retained in a fiduciary capacity, had been made dependent on a verification of the process. When Johann Friedrich’s successor, Ernst August, refused to ratify the payment of the outstanding sum, Leibniz found himself in a difficult situation in relation to Mariotte who energetically supported the claims of Douceur. In March 1682, Leibniz had finally agreed to the payment of a further 400 livres,190 so that there remained only a final outstanding payment of 100 livres. At the beginning of 1685, this last payment was finally made by the sister of the (in the meantime) deceased Mariotte,191 after the condition set by Leibniz had been fulfilled by an expert’s report.192 Authentication by Claude Comiers,193 with the assurance that he had seen and validated the experiments of Douceur for iron production, allowed Leibniz to conclude this – both for himself and the court in Hanover – inglorious affair. 186 “Mandez moy s’il est vray, ce qui le Docteur Becher escrit de vous dans son livre intitulé ‘weise narrheit’ d’un concept qui vous avez d’un chariot de Post pour le faire aller d’Hannover à Amsterdam dans le temps de six heurs” (A III,4 N. 161, p. 306). 187 “Je scay qu’il at esté une homme fort medisant” (p. 306). 188 Cf. A III,4 N. 193. 189 Cf. the correspondences with Douceur and Mariotte in A III,2 and A III,3, and Chapter 1 of the present work. 190 Cf. A III,3 N. 334. 191 Cf. A III,4 N. 83. 192 Cf. A III,4 N. 61. 193 Cf. A III,4 N. 81.

400

Chapter 2

Once in possession of the Douceur process, Leibniz could at least pride himself with the achievement in various places, such as at the Danish court. On July 6, 1683, Brandshagen reported, from Copenhagen, that he had spoken to the king about, among other matters, the iron process and had, on that occasion, read aloud to the monarch the postscript of a letter from Leibniz.194 The full technical details of this process were – on the occasion of its original communication in 1679 – kept a secret from all except duke Johann Friedrich. However, Leibniz was informed to the extent that – in a text intended for duke Ernst August, and entitled “Bedencken betreffend eine Proposition von verbeßerung der Eisen Stuck und ander Eisen-manufacturen” (Thoughts concerning a proposition for the improvement of [cast] iron and other iron manufactory processes) from June 23, 1684 – he described the Douceur roasting or annealing process in words which may be summarized in English as follows: one buries the iron piece, or other cast iron, in beechwood charcoal in such a way that it is entirely covered by the coal. The charcoal, and the iron, are hermetically sealed so that no air can reach the iron. Thereupon, fire is applied so that the surrounding charcoal becomes engulfed by the flames which, however, do not touch the core iron piece itself. The coating of glowing ash works itself into the iron which does not become molten, but is merely tempered and in this way improved. The exact wording of the text prepared by Leibniz is as follows: The foundation of the operation by which cast iron pieces can be improved, and to a great extent relieved of their brittleness, has been known to me for some time now and, in fact, it is nothing other than a cementation of the cast iron by means of occlusion using charcoal, since according to the opinion of the chemists, the alkali of charcoal absorbs or changes ferric acid, from which the iron becomes brittle. One buries namely, the piece of iron, or other cast iron, in beechwood charcoal in such a way that it is completely covered all over with this coal. The coal and iron are so joined together that no air can penetrate the agglomeration. Only then is fire applied, so that the whole becomes engulfed in flames and, although the piece is covered with the coal, yet the flame may not touch it. The coals, being hermetically sealed, are therefore not consumed or burnt to ashes, and only glow and burn by working into the iron, which is also not liquefied or smelted, but rather is only burnt through thoroughly, and thus improved.195 194 Cf. A III,4 N. 1, p. 4. 195 “Das fundament der operation dadurch gegoßene eiserne Stücke verbeßert und von ihrer sprodigkeit guthen theils befreyet werden, ist mir eine geraume Zeit hehr bekand und

July 1683–1690

401

A similar instance, comparable to the Douceur process, was the production of quality damascene steel, which had been a matter of interest at European courts since the late middle ages.196 It is therefore not surprising that the matter arose in the letters of Brandshagen and Martin Elers, sent from Copenhagen in August–September 1683 and August 1684, respectively.197 Elers also enquired, on this occasion, about a military bridge which reportedly had been tested by the duke of Celle. The correspondent claimed to have made a similar discovery himself. Military technologies were likewise the subject of Leibniz’s correspondence with Brandshagen in Denmark. On July 6, 1683, Leibniz was informed about the correspondent’s activities with the Danish artillery.198 Four years later, after Brandshagen had quit the Danish service, he reported to Leibniz, on July 23, 1687, about a meeting in Hamburg with a former lieutenant of the Danish artillery.199 The latter had revealed to him the layout of French ballistic mortars, intelligence which Brandshagen was now willing to make available to Leibniz. In the following letter, on August 27, 1687, Brandshagen enquired about a possible trial of such a mortar.200 In addition, he offered Leibniz plans, or layouts, of Danish howitzers, and of grenade or artillery shell launchers. On September 24, 1686, Friedrick Meurs von Blauenstein reported from Dresden about his investigations of iron and steel production which he had undertaken with a particular focus on military applications.201 Concerning the production of damascene blades, the same correspondent wrote the following text, on February 28, 1687, in reply to a query from Leibniz: I can give you every satisfaction regarding your request for information as to whether I can make blades just as good as damascene blades. In reply, in der that nichts anders als eine caementation des gegoßenen Eisens, so mit kohlen in occluso geschieht; da nach der Chymisten meinung das alkali der kohlen, das acidum ferri, davon das eisen spröde wird, absorbiret oder verändert. Nehmlich man begräbet das Eiserne Stück oder ander gegoßen Eisen, in büchenen kohlen, dergestalten daß es umb und umb mit diesen kohlen umgeben. Kohlen und Eisen seind mit einander wohl verschloßen, daß keine lufft dazu kann. Alsdann wird feuer gegeben, also daß die flamme herumb schlagen, und die kohlen mit dem Stück umbgeben muß, doch darff sie solche nicht berühren. Die kohlen, also verschloßen werden nicht verzehret, noch zu asche, sondern glüen nur, und arbeiten in das Eisen, welches auch nicht schmelzet, sondern nur durch-glüet, und also dadurch verbeßert wird” (A III,4 N. 57, p. 121). 196 Cf. A. Williams, 2003, sect. 1, appendix 2, pp. 14f.; A. Williams, 2012, chap. 3, pp. 36–38 (Introduction, note 116). 197 Cf. A III,4 N. 19, p. 43 and N. 65, pp. 137–139. 198 Cf. A III,4 N. 1, pp. 4f. 199 Cf. A III,4 N. 184, pp. 338f. 200 Cf. A III,4 N. 188, pp. 346f. 201 Cf. A III,4 N. 151.

402

Chapter 2

I can assure you that since your last letter I have made several, which cover every design requirement of damascene blades and which have cut iron just as good as wood.202 In listing his discoveries and innovations, Meurs also referred to a smelting furnace for the mass production of steel in Saxony, writing as follows: “I have made a large furnace for making steel in quantity at a forest location near Freiberg, to where I will be going in a few days to direct the operations”.203 However, most of his innovations referred to in this letter served exclusively military purposes, as for example, a type of light armor, halberds, grenade throwers, or copper coatings for canon muzzles. 7

Engineering Science

In the decades following Galileo Galilei’s death, his disciples in Italy were to play a leading role in the development of the science of waters.204 Leibniz’s meetings in 1689–1690, and the ensuing correspondences, with major figures of the second generation of Galileo’s disciples in Italy have therefore a special significance.205 The renowned physician Bernardino Ramazzini, for example, was also interested in problems of hydraulics and hydromechanics, and these topics were central issues in his correspondence with Leibniz in the year 1690. Their epistolary exchanges included, for example, fundamental considerations which mark the beginning of the theory of streamlines in fluid mechanics.206 The starting point here was the intelligence Leibniz received that Domenico Guglielmini – a physician, mathematician and engineer, with whom he would correspond over several years  – intended to treat fundamental questions of fluid mechanics in a tract entitled Aquarum fluentium mensura nova methodo inquisita (1690–1691).207 In addition to this, Leibniz was interested in a work 202 “je vous pouvois donner une entiere satisfaction sur la demande qui vous me faictes (à scavoir) si je peu faire des lames, aussi bonnes qui celles qu’on appellee de Damas. Pour une response: je vous peu asseurer qui [sic] depuis les vostres dernieres, j’en ay fait plusieurs, qui ont tenu toute prevue de celles de Damas, et ont coupé le fer mesme comme le bois” (A III,4 N. 161, p. 305). 203 “J’ay faict un grand fourneau pour faire de l’acier en quantité dans une forest proche de Freyberg où je iray en peu de jours pour y ordonner les manovriers” (A III,4 N. 161, p. 306). 204 Cf. C. S. Maffioli, 1994 (Introduction, note 127). 205 Cf. pp. 219–236. 206 Cf. J. G. O’Hara, 2002 (Introduction, note 127). 207 Cf. D. Guglielmini, Aquarum fluentium mensura nova methodo inquisita, 2 parts, Bologna 1690–1691: part 1 (books 1–3, 1690) and part 2 (books 4–6 with appendix, 1691).

July 1683–1690

403

planned by Ramazzini on the springs or wells of Modena,208 which duly appeared in 1691 under the title De fontium Mutinensium … scaturigine.209 In the discussions Leibniz had with Ramazzini in Modena  – between December 30, 1689, and February 2, 1690 – he had learned that his vis-à-vis wanted to experimentally investigate the flow of water around an obstacle in a stream. From discussions with Guglielmini  – whose acquaintance he had made in Bologna around December 25, 1689 – he also knew of the latter’s plans to write a tract about the laws of fluid motion in open channels. Although Galileo’s disciple Benedetto Castelli (1578–1643) had formulated one of the fundamental laws of fluid mechanics, viz. the continuity law, in his book Della misura dell’acque correnti (1628),210 several other basic questions had remained unanswered, as for example about the vertical velocity distribution in a stream. Even in the third edition of Castelli’s book of 1660, the corresponding proposition  – which postulated a linear velocity distribution increasing from the river bed to the water surface – had proved unsatisfactory. Motivated by this, Guglielmini intended to place the laws of open-channel flow on a new foundation. When, on February 25, 1690, Leibniz enquired of Ramazzini about the progress of Gugliemini’s undertaking,211 the correspondent, in his reply of April 15, 1690,212 reported instead about another planned work entitled De motu mechanico by yet another engineer of Modena, namely Giovanni Baptista Boccabadati, a friend of his whom Leibniz had also met during his stay in that city. Boccabadati had been concerned above all with the problem of flooding along the Po tributaries, the Panaro (or Scultenna) and Secchia (or Gabellus), and, during the recent inundations at the beginning of April 1690, he had undertaken observations and measurements along these rivers, about which Ramazzini reported to Leibniz in his letter of April 15. In commenting on Boccabadati’s practical experience, Leibniz, in his reply of July 16, then brought up Castelli’s theorem about the vertical velocity distribution in a stream. Leibniz doubted that an exact rule for this velocity distribution in natural waters could be given, and he posed an additional question – the answer to which would of necessity lead to a generalization of the proposition in question – namely concerning the increase of the velocity of flow downstream from a point where the channel depth suddenly increased. Leibniz’s conviction was that, at a greater 208 Cf. A III,4 N. 239, p. 467. 209 Cf. B. Ramazzini, De fontium Mutinensium admiranda scaturigine tractatus physicohydrostaticus, Modena, 1691. 210 Cf. B. Castelli, Della misura dell’ acque correnti, Rome, 1628 and Bologna, 1660 (3rd ed.). 211 Cf. A III,4 N. 239, p. 467. 212 Cf. A III,4 N. 250, pp. 499f.

404

Chapter 2

distance from such a point, the velocity increase of the stream would be negligible. As regards Boccabadati’s “Inquisitiones” he wrote: He most correctly observed that the water of a river above a certain mass (an earth wall, levee or dam), causing a bend or turn,213 was deeper than below, because any change causes delays in locations along the course, adding water above the mass and subtracting it below. It would be an interesting investigation to define by how much the speed of the river is increased with increased ‘altitude’ (stream depth). Castelli in his book Della misura dell’ acque correnti proposed a certain theorem on this matter but he stumbled over the demonstration, and to me it appears to be totally impossible to assign such a fixed rule, and if the water mass of the river increases considerably at a certain point, there will be no notable increase of velocity at a point in the river well below this point of increase.214 Following his return to Hanover, Leibniz received several reports about Boccabadati, and about the planned work of his on mechanics that was to be founded on the practical experience of the author in the floodplain, or flood zone, around Modena. Thus, Ramazzini referred, on April 15, 1690, to an interruption of Boccabadati’s work on his tract on the principles of mechanics, that was to be based entirely on restoration efforts along the Po tributaries 213 Perhaps Leibniz had in mind here a structure in the river Tiber built by the Dutch hydraulic engineer, and member of the Accademia Fisico-Mathematica Romana, Cornelis Meyer (Meijer, 1629–1701) about which Tschirnhaus had informed him in a letter from Rome on April 10, 1678; cf. A III,2 N. 154, p. 365 and pp. 383f., and the tract: C. Meyer, L’arte di restituire a Roma la tralasciata navigazione del suo Tevere, Rome, 1683. Furthermore, cf. K. van Berkel, “ ‘Cornelius Meijer inventor et fecit’: On the representation of science in late seventeenth-century Rome”, part 2 (Networks of knowledge: Commerce and the representation of nature), chap. 11, pp. 277–94, in: P. Smith, P. Findlen (eds.), Merchants and marvels: Commerce, science, and art in early modern Europe, New York and London, 2002; J. Connors, “The one-room apartment of Cornelis Meijer”, chap. 3, pp. [45]–64, in: N. Avcioğlu and A. Sherman (eds.), Artistic practices and cultural transfer in early modern Italy: Essays in honour of Deborah Howard, Farnham (UK), 2015. 214 “Rectissime observavit aquam fluminis supra moles vel aggeres, flexum imperantes, esse altiorem quam infra. Nam quicquid decursum in aliquot loco moratur, flumen ibi reddit altius, et infra ipsi subtrahit aquam. Elegantis disquisitionis foret definire, quantum rapiditas fluminis augeatur altitudine aucta. Castellus in libro de mensura aquarum theorem quoddam proposuit ea de re, sed haesit in demonstratione; et mihi omnino videtur non posse talem assignari regulam constantem; et licet aqua fluminis notabiliter crevisset, tamen si locus fluminis multum esset infra locum qui causa est incrementi non fore adeo notabile augmentum velocitatis” (A III,4 N. 266, pp. 531f.).

July 1683–1690

405

Panaro (or Scultenna) and Secchia (or Gabellus), and where large-scale flooding, and defilement of the fields, was a threat following heavy rains.215 And two years later, on March 30, 1692, Ramazzini reported about a further delay in the completion of the work.216 Alas, the work was still unpublished at the time of Boccabadati’s death in 1696. As regards Guglielmini’s forthcoming tract, Leibniz, in his letter to Ramazzini, of July 16, 1690, expressed his skepticism about whether an exact rule, to supersede Castelli’s rule, might indeed be formulated, adding the following text: “D. Guglielmini told me that he is planning a book about the same issue, and will assign a rule different from the Castellian rule. I fear the matter is too complex as to allow the assignation of any rule of this kind”.217 Finally, in the paragraph that followed, he expressed his pleasure at the prospect of the impending appearance of Ramazzini’s own tract.218 Leibniz learned about the appearance of the first part of Guglielmini’s tract from a letter of Bodenhausen of September 16, 1690.219 Replying on November 5, he immediately requested that the correspondent send him information about the most important propositions in Guglielmini’s work and their foundation.220 Then, in the first half of November, Leibniz received a review copy of the work from Otto Mencke,221 and a little time later, on November 17, he sent a first opinion about Guglielmini’s book to Bodenhausen. At the center of Leibniz’s interest was Guglielmini’s postulated parabolic velocity increase from the water surface to the river or canal bed. This “scala fallacy”, as it was later called,222 was based of the false assumption of the applicability and validity of Torricelli’s efflux law in an open stream. Whether Leibniz immediately recognized that the mistake in Guglielmini’s proposition was rooted in an 215 “D. Boccabadatus opus suum de Mechanicis Principiis intermisit, modo totus intentus ad fluminum Scultennae, et Gabelli reparationem, quae flumina ob ingentes pluvias magnam illuvionem agris nostris minantur” (A III,4 N. 250, p. 499). 216 “D. Boccabadatus totus est circa Opus suum de Conatu Mechanico, sed nova quae quotidie in hac materia illi sese produnt illius editionem remorantur” (A III,5 N. 67, p. 283). 217 “D. Guillelminus mihi dicebat librum se moliri de eodem argumento, et diversam a Castelliana regulam assignaturum. Ego re expensa vereor ut ulla hujusmodi assignari possit” (A III,4 N. 266, p. 532). 218 “Opus tuum elegantissimum de fontibus vestris procedure non dubito, idque intelligere erit perjucundum” (p. 532). 219 Cf. A III,4 N. 273, p. 558. 220 “Bitte bey müßiger zeit mir ohnbeschwehrt einige nachricht von den furnehmsten propositionibus in H. Gvillelmini tractat, und deren fundament zu geben” (note 89 above: A III,4 N. 285, p. 632). 221 Cf. A I,6, p. 284f. 222 Cf. S. Leliavsky Bey, 1951, p. 466, and J. C. I. Dooge, 1987 (Introduction, note 129).

406

Chapter 2

inadmissible application of the Torricellian law is not clear. At all events, he emphatically asserted that the velocity distribution postulated by Guglielmini could have no validity in real rivers and canals. Thus he wrote: That which D. Guglielmini writes in the first three books of Aquarum fluentium mensura cannot be valid in stream currents and other large works, as he admits himself, since the increment of velocity, which, as is well known, varies in the subduplicate ratio of the height of descent, is totally altered in the flowing and dashing of the water and cannot accordingly be applied.223 And in addition, he hinted at the relevance of considerations from his own article “Schediasma de resistentia medii” (of January 1689), for the matter in hand.224 In his anonymous review of the first part (the first three books or chapters) of Guglielmini’s Aquarum fluentium mensura nova methodo inquisita, in the Acta Eruditorum of February 1691, Leibniz desisted from any kind of criticism and restricted himself to an account of the basic tenets of the work.225 8

Projects: Economics and Administration

Leibniz’s attitude to mercantile economics, and to absolutist administration in the late seventeenth century, was predicated both upon a fundamental rationalist and idealist world outlook as upon external necessities, such as the need for a well-functioning system of payment, or an efficient coinage system. Thus, proposals for improvement of such monetary systems are to be found in Leibniz’s correspondence and collaboration with Crafft,226 and others like Christian Holeysen.227 Leibniz interests also encompassed calculations of interest and discount, of bonds and debentures in finance and commerce, as well as the evaluation of life annuities and insurance, reflected in particular 223 “Was D. Guglielmini in seinem ersten 3 büchern de Mensura aquarum currentium schreibet, kan in den ströhmen v. andern großen wercken nicht statt haben, wie er selber bekennet, den das incrementum velocitatis, welches freylich bekandter maßen in subduplicata ratione altitudinum descensus sich verhällt, wird in fließen v. hinbrütschen des waßers gäntzlich alteriret, v. kann nicht appliciret werden” (A III,4 N. 290, p. 653). 224 “man nehme denn dazu, was ich de Resistentia ambientis angewiesen” (p. 653). 225 Cf. G. W. Leibniz (anon.), “Aquarum fluentium mensura nova methodo inquisita autore Domenico Gulielmino M.D.”, Acta Eruditorum, (February 1691), pp. 72–75. 226 Cf. A III,4 N. 204. 227 Cf. A III,4 N. 254 and N. 256.

July 1683–1690

407

in his correspondence with Johann Jakob Ferguson. In an article in the Acta Eruditorum entitled “Meditatio juridico-mathematica de interusurio simplice”, in October 1683,228 he treated the problem of determining the current value of a loan repaid ahead of schedule. The difficulties Leibniz experienced following the publication of this article – including the accusation that he was an advocate of the then frowned-upon method of charging compound interest (“Anatocismus”) – can be followed in his correspondence with Christoph Pfautz,229 the editor responsible for mathematical and scientific articles in the Acta Eruditorum. Questions of cost effectiveness and economic feasibility of processes, and of undertakings and business ventures, were also taken to heart by Leibniz. Thus, for example, he excerpted passages from the papers of the metallurgist and refiner of metals, Christian Holeysen, concerning the economic efficiency of the Hungarian mines.230 He also carefully noted Crafft’s communication of a claim that gold could be made from the best iron slag.231 Without discussing the truth or validity of such gold extraction processes, Leibniz found that, because of the cost of related ingredients, such processes could simply not be cost-effective and were accordingly to be rejected. But other more legitimate processes, such as salt production,232 or the introduction of street illumination using oil as a fuel for lamps,233 were always assessed by Leibniz from the viewpoint of cost effectiveness. In addition to such considerations of cost effectiveness, there was another aspect which determined Leibniz attitude to projects and processes under consideration, namely cameralism and the cameral sciences. On the basis then of such a mercantilist-cameralist conviction, Leibniz’s interest developed in manufactories such as silk and wool manufactories,234 in iron and steel production and in the wine trade,235 in the production of armor,236 in textile

228 Cf. G. W. Leibniz, “Meditatio juridico-mathematica de interusurio simplice”, Acta Eruditorum, (October 1683), pp. 425–432. 229 Cf. A III,4 N. 11, N. 17 and N. 43. 230 Cf. A III,4 N. 251, N. 255 and N. 258. 231 Cf. A III,4 N. 202, p. 373; A III,4 N. 176, and Leibniz’s own proposal for improvement of the ore hoisting and winding machinery. 232 Cf. A III,4 N. 132, N. 155 and N. 165. 233 Cf. A III,4 N. 210, p. 405, and N. 265, p. 530. 234 Cf. A III,4 N. 19, and N. 204, pp. 376f, 383, 385f. 235 Cf. A III,4 N. 202, pp. 372f., and N. 204, pp. 383 and 386. 236 Cf. A III,4 N. 63, p. 135.

408

Chapter 2

printing,237 in the improvement of the luster of pearls,238 and in a range other economic projects. Also in the area of governmental economic planning and administration, Leibniz’s correspondence reveals a wide range of proposals he made both at state level in Hanover, as at the Imperial level in Vienna. Thus, in a memorandum intended for presentation to the emperor  – prepared in Vienna in the second half of 1688 – we find Leibniz, in the guise of Crafft, advocating the establishment of a “Bergkollegium”, an Imperial mining college or council that would establish and coordinate the occurrence of mineral and ore deposits within the empire. To this end, a laboratory was to be set up and a chamber of arts maintained, where the most important mechanical inventions and innovations would be presented. This mining institution was intended to preempt the import of ores and minerals that were already available in Germany, and to play an important role in the colonization of those regions of Hungary that had recently been freed from Turkish rule, that is after the ending of the siege of Vienna, the defeat of the Turks in 1683, and the Habsburgs’ reconquest of Hungary that followed. At the outset of his petition to the emperor, Crafft (or pseudonymously Leibniz) provided a brief account of his life,239 and studies, his travels in Europe and in the American colonies, his professional life in the service of the electors in Mainz and Saxony, and his experience over a broad spectrum of manufactories. Thus he wrote: First, I completed studies in medicine, cultivating in the process botany and chemistry, investigated in the mines the intense heat treatment of metals, pursued a vocation as a mining physician, traveled in Holland, France, England, and in the American colonies. Thereafter [I was] in the service of the elector of Mainz Johann Philipp, entrusted with commercial and manufacturing matters, glass, iron, steel, hammer works, mill works, and sheet metal works, wines, spicery, sugar, the wool and silk trade, cultivation of mulberry trees, privy to, or let in on, the secrets of chemistry and other curious matters. Following his death [I served] with the electorate of Saxony, and really demonstrated for the first time in Germany that one could fabricate with advantage foreign togs and stuff, cloths and

237 Cf. A III,4 N. 19. 238 Cf. A III,4 N. 65, pp. 138f. 239 Cf. W. Loibl, 1997 (Introduction, note 144).

July 1683–1690

409

drapery, which factory also flourished and only suffered through contagion, change of government and of private passions (or fashion).240 He then outlined his abilities in a number of areas including experience in the American colonies, offering, first and foremost, his services in the colonization of Hungary, adding: Thus I have, firstly, done much in matters of colonization, and there was not very much wanting for me to settle in America. However, Hungary is now a better and more opportune object of colonization than America itself, and the right time for this is very much at the moment, through Your Majesty’s Christian and, thanks be to God, felicitously-deployed weapons.241 Chemical substances, that were available in nature and were of interest from the viewpoint of economic utilization, included paints. In July 1687, Heyn reported about veins of iron ore which he had observed on the river Elb(e).242 Several of these veins, when mixed with crude ores, were found to be suitable as paint, providing fine umbra and brown ocher pigments. Likewise in the long letter, composed jointly by Leibniz and Crafft for the emperor in the second half of 1688, the experience gained by Crafft, and Heyn, in producing and applying paints was emphasized.243 A complete factory, or plant for the processing of mineral ores, was contemplated here in the light of ongoing building activity in Hungary, and in lower Austria, where such paint products would be particularly useful, especially for the conservation of wood and even of stone. 240 “so habe erst studia et medicinam dabey botanicam und chymiam excolirt, auff den bergwercken die tractation der metallen im großen feuer untersuchet, vocation als bergMedicus gehabt, in Holland[,] Franckreich[,] England und die Americanischen colonien gereiset, hernach von Churf. Joh. Philippo zu Maynz in commercien und Manufactursachen, glaß, Eisen, Stahl, hammer, mühl und blechwercken, weine, specerey, zucker, wollen und seidenhandel, erzeilung der maulbeerbäume, zugeschweigen der chymi und curiositaten mich gebrauchen laßen. Nach deßen todt bey ChurSachsen zuerst in Teutschland wurcklich demonstriret, daß man die fremden Zeige und tücher mit vortheil fabriciren könne, welche fabric auch floriret und nur durch contagion, veranderung der Regirung und privat passiones einen stoß gelitten” (A III,4 N. 204, p. 376). 241 “so habe 1.) in materi der Colonirung viel gethan, und hätte nicht viel gefehlet, mich in America niederzulaßen. Ungarn aber ist nun ein beßer und gelegner objectum Coloniarum als America selbsten, und eben iezo durch E. Mt so christliche als gottlob gluckliche waffen die rechte zeit dazu vorhanden” (p. 377). 242 Cf. A III,4 N. 179, p. 331. 243 Cf. W. Loibl, 1997 (Introduction, note 144), p. 379 and pp. 388f.

410

Chapter 2

A range of physical and chemical issues arose in Leibniz’s correspondence, both in the context of scientific and engineering applications and of techno-economic projects. Examples from the latter category (during the 1680s) include: dyeing of garments, production of ruby glass, perfection of pearls, retrieval and extraction of gold and silver, phosphorus production and the desalinization of sea water. Thus, for example, in Leibniz’s correspondence with Ramazzini, the desalination of seawater being pursued by an Englishman (called Nathan Lacy) living in Modena, was referred to.244 Even the topic of emissions from laboratories, and protection against such emissions, arose in Leibniz’s correspondence at this juncture. At the end of 1689, Leibniz made the acquaintance in Modena not only of the physician Ramazzini but also of the chemist Bernardino Corradi. With the approval of Ramazzini, Leibniz supported Corradi in a dispute, with a certain Giovanni Paolo Stabe de Cassina, about dangerous emissions being produced in applications (or processing) using vitriol. Leibniz’s backing took the form of a contribution to Corradi’s polemical pamphlet, directed against his opponent, entitled Raccolta … nella virtuosa gara iatro-chimica.245 Leibniz’s contribution consisted of a letter sent to both Ramazzini and Corradi,246 and was essentially an historical note about the “Historia inventae tincturae scarlatinae” – or the discovery of scarlet dye – by the Dutch innovator Cornelis Drebbel (1572–1633), Leibniz referred here specifically to Drebbel’s short tract on the nature of the weather elements, entitled in the German translation Ein kurzer Tractat von der Natur der Elementen (1608).247 9

Alchemy and Chemistry

As in the years prior to 1683, phosphorus continued to be an important topic in Leibniz’s correspondence in that year, and throughout the decade. First discovered by Heinrich (or Henning) Brand in Hamburg (in or shortly after 1669), it had become internationally known by the early 1680s, even though the production process was still being guarded as a secret by some. Thus, Brandshagen reported from Copenhagen, in July 1683, about the distrust he was experiencing there because of his reluctance to provide intelligence about his mortar 244 Cf. A III,4 N. 239. 245 Cf. B. Corradi, Raccolta di tutto quello che fin ora estato scritto nella virtuosa gara iatro-chimica tra il dott. G. P. Stabe de Cassini e Bern. Corradi, Modena, 1690. 246 Cf. A III,4 N. 230 and N. 233, respectively. 247 Cf. C. J. Drebbel, Ein kurzer Tractat von der Natur der Elementen und wie sie den Windt, Regen, Blitz und Donner verursachen und wozu sie nutzen, Leiden, 1608 and Hamburg, 1619.

July 1683–1690

411

bombs, and about phosphorus.248 Sometimes, Leibniz himself received incorrect, or inaccurate, reports from his correspondents. As regards the transfer of knowledge about phosphorus to England, for example, Heyn reported, on November 30, 1686, that intelligence about this German discovery had been communicated by Johann Joachim Becher to Robert Boyle, who then had his German laboratory assistant produce it. Boyle’s more accurate version of events, however, was that he had received the essential intelligence about the production process from Crafft, and another German informant referred to as “A. G. M. D.”249 Heyn, on the other hand, sent Leibniz the following account: As regards the material that is supposed to ignite spontaneously at a certain time, I am not sure if perhaps the phosphorus is intended. This was first discovered in Germany and was communicated to Mr Boyle esq. by Dr Becher, who then had his German laboratory assistant make it. Subsequently his German laboratory assistant at the time, Mr Bilger [surely Johann Friedrich Bilger,] … perfected the process admirably and obtained an amount in this way. His present German laboratory assistant, Mr Gottfried, is now energetically working on this  … This phosphorus is made from urine, as is perhaps known, and what he has announced about it is for the most part that which Dr Becher communicated to him and, if I am not mistaken, a certain Dr Schultze is the discoverer of the said phosphorus.250 Leibniz then corrected the text, replacing “Schultze” with the correct name of the discoverer “D. Brand”. “H. D. Becher” ought to have been J. D. Crafft. Leibniz simply noted here that it was another laboratory assistant of Boyle.251 248 Cf. A III,4 N. 1, p. 5. 249 Cf. R. Boyle, The aerial noctiluca, or, some new phenomena, and a process of a factitious self-shining substance, London, 1680; Boyle: The Works, 1999–2000, vol. 9, pp. 265–304, in particular pp. 272f. and Chapter 1 of the present work. 250 “die Materie anbelangend, so sich selbst zu einer gewissen zeit anzünden sole, weiß ich nicht ob etwann der phosphorus gemeint werde, welcher erstlich in Teutschland erfunden, dem H. Boyle Esq. durch H. D. Becher aber communiciret worden der den solchen durch seine Teutsche Laboranten  … hat excolliren lassen; wie denn dessen damaliger Teutscher laborante H. Bilger [surely Johann Friedrich Bilger] … sich darinne vortrefflich perfectioniert und viel dabey gewonnen, Sein itziger Teutscher Laborante aber H. Gottfried starck darinne anitzo arbeitet … Dieser Phosphorus nun wird aus urin, wie vielleicht bekand ist, gemacht, und was er davon raus gegeben, ist meistentheils was ihm H. D. Becher communiciret und, wo ich mich nicht irre, ist einer D. Schultze der Erfinder des gesagten Phosphorus” (A III,4 N. 155, p. 295). 251 “ist ein ander. H. Boylen laborant soll es haben” (p. 295).

412

Chapter 2

Finally, he changed “Gottfried” to “Hangwiz”, a reference to Ambrose Godfrey Hanck(e)witz. At mid-year 1687, Leibniz commissioned Brandshagen to carry out chemical experiments in Hanover including on phosphorus production.252 The latter then compiled a list of what he required to produce phosphorus.253 During Leibniz’s absence from Hanover in late April and early May 1687, the master tailor Curd Reimers had to make sure that Brandshagen was able to collect enough urine for the phosphorus production, and that he was accordingly compensated.254 On the eve of his Italian journey then – and almost twenty years after its discovery of phosphorus – Leibniz was able to pride himself on his knowledge of the discovery and of the production process. Three years later, on February 20 and March 4, 1690,255 in fulfillment of a promise made to the hereditary prince Ferdinando – the heir apparent in Florence – he sent from Venice details of the production process, as well as verses he had composed regarding this wondrous substance, to the prince’s tutor, Bodenhausen, with the following request: “Please, express my greetings to both of their royal highnesses and, given the opportunity, present to the older prince the phosphorus process together with my verses, because I promised this to his Highness”.256 Bodenhausen was subsequently able to report to Leibniz, on August 12, 1690,257 that he had recited the details of the process, and in Leibniz’s name, to the prince, who immediately joined in a disputation with him. In addition, Bodenhausen related that the prince’s younger brother, namely prince Gian Gastone, had expressed his admiration and praise for Leibniz, and for the recited verses about phosphorus. Even after 1690, Leibniz’s interest in the discovery and investigation of phosphorus continued. In 1692, in the Mémoires of the Académie des Sciences, he found an account of the history of the discovery of phosphorus from the viewpoint of Wilhelm Homberg,258 which became a subject of discussion in his letter to Simon Foucher of October 27, 1692,259 and 252 Cf. A III,4 N. 184, p. 340. 253 Cf. A III,4 N. 178, pp. 329f. 254 Cf. A III,4 N. 171. 255 Cf. A III,4 N. 236, p. 464 and N. 242, p. 477, respectively, and the annotations. 256 “Bitte  … bey denen beyden durchlauchtigsten Prinzen in gnaden zu erhalten, und da es gelegenheit gibt, dem altisten H. Prinzen, Durchlt des phosphori operationem samt meinen versen zu geben, weilen ichs ihr Durchlt versprochen gehabt” (N. 236, p. 464). 257 Cf. A III,4 N. 270, p. 543. 258 Cf. A III,5 N. 98 (p. 367), N. 113 (pp. 419f.) and N. 127 (p. 477), and also: L. M. Principe, The transmutations of chymistry: Wilhelm Homberg and the Académie Royale des Sciences, Chicago and London, 2020. 259 Cf. A II,2 N. 185, pp. 609f.

July 1683–1690

413

in that to Bodenhausen of January 23, 1693.260 Alas, his own Historia inventionis phosphori only appeared in the year 1710.261 The properties of afterglow, or phosphorescence and ignitability, were in the seventeenth century the principal reason for investigating phosphorus. However, other methods of encapsulating fire and combustion also attracted the interest of Leibniz and his correspondents. Thus, for example, Leibniz recorded – in the memo of a conversation with Christoph Pratisius between 1683 and 1687262 – a means of distilling without fire which the conversation partner had learned from a carbonarius or charburner. To this was added a further application, namely that of preserving heat over an extended period during a journey. Saltpeter was – as the main ingredient of gunpowder – also of great interest at that time, whereby the focus was on improved processes for its manufacture, rather than the investigation of its chemical properties. Thus, in a letter from Copenhagen on August 1, 1684, Elers referred to a hypothetical process, by which one might be able to establish a perpetual saltpeter works at low cost, and providing a high weekly production without having to leach and concentrate in ditches, or trenches, in the usual fashion.263 In January 1688, Leibniz also noted – after his conversation with Crafft in Graupen264 – the damming opinion of his conversation partner about a suggestion for the improvement of saltpeter production using a vault or dome, in which the product might appear on rocks following blasting, without the need for leaching and concentrating. The range of chemical issues that were subjects of discussion in Leibniz’s correspondence included processes for obtaining precious metals, and in particular gold. On August 1, 1684, Elers reported from Copenhagen about the trial of a chemical process – communicated by Leibniz himself – for the reduction of gold powder in aqua fortis or nitric acid.265 Regarding the course of the trials, we learn that, at the outset, the correspondent could have sworn that the actual outcome would be six times the anticipated one. However, it transpired that – after the preparation had been left standing for a certain period – all of the product was consumed once again. A repeat of the trial with fresh acid

260 Cf. A III,5 N. 127, p. 477. 261 Cf. G. W. Leibniz, “Historia inventionis phosphori”, Miscellanea Berolinensia, Berlin, 1710, pp. 91–96; Leibniz: Opera Omnia, 1768, vol. II,2, pp. 102–108. 262 Cf. A III,4 N. 196. 263 Cf. A III,4 N. 63, pp. 133–135. 264 Cf. A III,4 N. 202, p. 372. 265 Cf. A III,4 N. 63, pp. 134f.

414

Chapter 2

also fell short of expectations, which had accordingly shattered the correspondent’s belief in the process, indeed “for the remainder of his life”.266 In his discussion with Crafft in Graupen in January 1688, Leibniz learned details about the technique of gold panning in rivers. The notes Leibniz made on that occasion included the following: Not far from Regensburg there are gold panners267 who wash gold from the sand of the Danube. They need for this a sieve (or strainer) on which the gold sludge hangs. [Going] to Bruchsal via Speyer there was also one [such gold panner]. One is of the opinion that a man can earn a Taler a day [with this].268 A few years earlier, Leibniz had received from the Académie Royale des Sciences – through Tschirnhaus, and in exchange for the communication of the phosphorus process  – a description of two other processes, which were referred to as “l’or rendu volatile sans fulminer” (gold rendered volatile without exploding) and “un sel vegetant” (a herbal salt),269 respectively. After Tschirnhaus had given Leibniz an account of these processes, when they met in October 1682, he included written transcripts with his letter of September 4, 1683.270 However, having displaced these copies, Leibniz had to request them again at the end of a letter to Jean-Baptiste Du Hamel, on July 21, 1684, in the following words: I was promised the communication of certain other nice curiosities of which I do not despair. It is true that Mr Tschirnhaus brought me those concerning gold rendered volatile without exploding, and a herbal salt. However, regrettably, the paper has been lost and I ask you, Sir, to obtain it once more, together with certain other curiosities which one will consider appropriate for communication to me.271 266 “so das ich nun geresolviert mich zeit lebens hierinnen nichts mehr zu glauben” (p. 135). 267 underlining by Leibniz. 268 “Nicht weit von Regenspurg sind goldwäscher so aus dem Donausand gold waschen. Sie brauchen hährine sibe, da sich der goldschlich anhenget. Zu Bruchsal uber Speyer war auch einer. Man meint ein mann konne des tages 1 thl. verdienen” (A III,4 N. 202, p. 372). 269 Cf. A III,3 N. 384, p. 686 and p. 691. 270 Cf. A III,4 N. 21, p. 49. 271 “On m’avoit promis la communication de quelques autres belles curiosités, dont je ne desespere pas; il est vray que Mons. Tschirnhaus m’apporta la composition de l’or rendu volatile sans fulminer, et d’un sel vegetant. Mais par malheur le papier s’en est perdu, et je vous supplie Monsieur de l’obtenir derechef avec quelques autres curiosités dont on trouvera à propos de me faire part” (A III,4 N. 62, p. 132).

July 1683–1690

415

Then  – in the postscript to a letter of October 17, 1684, to Tschirnhaus  – he repeated the request once again for the renewed communication of the processes, in particular of the “auri volatilisatio”, or gold rendered volatile process, originally given in exchange for his communication of the phosphorus process.272 Often such processes were treated as secrets, as for example a melting process for changing the color of lead to that of bronze (“pour rendre le plomb en couleur de bronze à la fonte”) that Douceur had promised him in January, and again on August 6, 1683.273 From Venice Christof Pratisius reported, on October 26, 1685, about several hundred Italian alchemists, all of whom were occupied with the investigation of a certain cinnabar process. Thus, he wrote that: “There are several hundred alchemists all working for the same goal, namely to find something in the cementation of silver with cinnabar”.274 After Leibniz learned that Bodenhausen wanted to join this effort, he wrote to him in August 1690 approving the study of the chemical process in question, which involved a remarkable chemical reaction or “transplantatio”. He had also been informed about an adulteration of the process, done by falsifying the cinnabar using lead oxide, and the possible use of cinnabar of antimony. And so he wrote the following to Bodenhausen: The cinnabar process would indeed be worth investigating, although it is fantastic, so to speak, that a ‘transplantatio’ occurs. A person has reassured me that, if the cinnabar be adulterated with red lead (lead oxide), like in the form it is commonly sold by apothecaries, there would be an argument … that one could also try using cinnabar of antimony.275 A central concern in Bodenhausen’s chemical experiments was the study and investigation of mercury. In this connection he reported to Leibniz, on 272 “Si quando vacat, quaeso ut mihi processus illos mihi pro phosphoro a Parisiensibus communicatos denuo mittas, in quibus erat auri volatilisatio; scripsi enim me schedas perdidisse” (A III,4 N. 71, p. 167). 273 Cf. A III,3 N. 434, and III,4 N. 9 (pp. 18f.) and N. 13. 274 “alchimisten sindt ettliche hundert, die aber alle in diesem eintzigen laboriren, nemblich in cimento lunae cum Cinnabrio, waß darinn zu finden” (A III,4 N. 100, p. 229). 275 “Der Cinoberproceß wäre wohl untersuchens werth den gleichwohl wunderlich daß gleichsam eine transplantatio geschicht. Es hat mich einer versichert, wenn der Zinober mit Menge [=Mennige] verfalschet wie er gemeiniglich in apotheken verkaufft wird, gebe er ein argumentum … man köndte auch Cinnabarin antimonii probiren” (A III,4 N. 272, pp. 551f.). Regarding cinnabar of antimony, cf. W. R. Newman, L. M. Principe, 2002, chap. 2, p. 104, note 34 (Introduction, note 182).

416

Chapter 2

September 16, 1690,276 about his work on the writings of the alchemist Geber (i.e. Jabir ibn Hayyan, fl. c.721–c.815) and in particular about a work which he referred to as “the small little book of the Summae of Geber”, or “das kleine büchlein der Summae Geberi”.277 In his reply of November 5, 1690, Leibniz advised the correspondent to record his experiments in writing in the form of a diary for the benefit of science, writing as follows: “I beg you, Sir, to diligently record your chemical operations in the form of a diary. It must be possible to obtain useful consequences from this, relating to the cause of things”.278 In addition, Leibniz could report the establishment, by the court, of a chemical laboratory in Hanover under the direction of Pratisius.279 Although Leibniz was impressed by the alchemist Geber and considered his writings to be well-founded, he had certain doubts about the correctness of Geber’s results, which he expressed as follows in this letter to Bodenhausen: “I have read again the Summam perfectionis of Geber. One can see that the author had experience and was also deeply contemplative, yet one does not know where one is with him in his main work”.280 Then, as an instance of this contrariness or inconsistency, Leibniz cited the chapter on the sublimation of mercury, writing that: In the chapter ‘De Sublimatione Mercurii’ he actually says one ought to sublime it from talc … a little later however he says it would be better to sublime it from fitting substances … it appears indeed that he is aiming at common (or crude) quicksilver, if one is to trust his own words.281

276 Cf. A III,4 N. 273, pp. 556f. 277 Cf. Geber, C. Horn (ed.), Chymia sive traditio summae perfectionis et investigatio magisterii, Leiden, 1668. 278 “Bitte M. h. H. wolle belieben seine Chymicas operationes per modum diarii fleißig zu zeichnen. Maßen nuzliche conseqvenzen circa causas rerum daraus zu machen” (A III,4 N. 285, p. 631). 279 “Ihre Durchlt haben alhier nunmehr ein laboratorium auffrichten laßen, welches H. D. Pratisius zu drigiren hat” (p. 631). 280 “Gebri Summam perfectionis habe wieder gelesen. Man siehet wohl daß der Autor Experienz gehabt, auch eines tieffen Nachsinnens, doch weiß man nicht im hauptwerck wie man mit ihm dran ist” (p. 632). 281 “Im Cap. De Sublimatione Mercurii sagt er zwar man sole ihn a Talco sublimiren … bald aber darauff sagt er es wäre beßer daß man ihn a convenientibus sublimire … Es scheinet wohl daß er auff Mercurium vulgi gehet, wenn man seinen eignen worthen trauen soll” (p. 632).

July 1683–1690

417

Being unable to undertake such experiments himself, Leibniz hoped to obtain clarification of important questions from those of Bodenhausen. As regards Geber, he was willing to keep an open mind, notwithstanding his predominating skepticism. Even the clarification of a specific point in this complex matter could amount to a breakthrough, he told the correspondent in the following words: I do not doubt, Sir, that you will have certain experiments, that will make what Geber says credible for him, and serve as an indication (or as evidence), considering that I have not come sufficiently far in these matters and therefore do not know if they can be attributed to Geber; at the same time I do not want to either reject or contradict him. But I have to admit that hitherto the arguments against him appear to be stronger. It would be a great [achievement] if one could simply find something fruitful regarding some specific matter here.282 Bodenhausen then reported to Leibniz, on November 11, 1690, that one of his princely students – presumably the hereditary prince Ferdinando – was adept at doing chemical experiments and, a few days before, had produced mercury in his chambers from the regulus of antimony  – i.e. the metallic antimony reduced from its ore  – without any mercurial addition, an experiment that Bodenhausen himself also hoped to attempt. Accordingly, the correspondent wrote on this occasion: He made as well mercury (| Mercurium |283) a few days ago from the regulus of antimony (| Antimonium |) in his room without any mercurial (| Mercurium |) addition. When I subsequently asked him to communicate his secret, he promised to do so. I will therefore make every effort to obtain the secret and try it myself.284 282 “Ich zweifle nicht M.h.H. werde einige Experimenta haben, so ihm dasjenige was Geber saget glaublich machen und pro clave dienen gleich wie ich in diesen dingen nicht weit gnugsam kommen, und also nicht weiß ob dem Geber allerdings zutrauen, also will ihn gleichwohl auch nicht verwerfen noch wiedersprechen. Nur mus bekennen das bishehr die rationes in contrarium stärcker geschienen. Es wäre ein großes wenn man auch nur aliqvid particulare cum fructu in diesen finden köndte” (p. 632). 283 alchemical symbols between | |. 284 “gleichwie Er vor wenig tagen den | Mercurium | aus dem regulo | Antimonii | in seiner kammer ohne allen | Mercurialischen | zusatz gemacht. Darauff als ich gebeten, mir solches secret zu communiciren, hat Er mir es versprochen; werde mich also bemühen solches zu erhalten, v. selbst versuchen” (A III,4 N. 288, p. 648).

418

Chapter 2

Leibniz regularly used his contacts with correspondents, associates and friends to obtain new information about known chemical processes. On June 26, 1689, he obtained intelligence from Crafft about the efforts of Johann Elias Rothmaler in Vienna to demonstrate a transmutation of metals, a demonstration which – it was claimed – the whole world ought to heed as a proof of the veracity of the transmutation of metals, at least according to Crafft’s report.285 Leibniz, for his part, wrote the following skeptical comment between the lines of Crafft’s text in which he expressed his suspicion that the claim would not hold up: “vereor ne sit stantiarismus”. On another occasion, in August 1689 and April 1690, Crafft likewise reported about a process286 – which had been named after a certain count Lobkowitz – for the transmutation of silver into gold and silver, using, among other substances, mercury. Yet another example was the separation process of Christian Holeysen. The latter resided in Vienna, between 1688 and 1692, in order to present to the emperor his purported process for an improved yield of gold from auriferous silver. At the end of April, or in the first half of May, 1690, Leibniz was able to make detailed excerpts from Holeysen’s submissions to the emperor,287 and to carry on conversations with him which he recorded in writing.288 Besides the possible production, or extraction, of gold and silver by means of the chemical transmutation of metals, Leibniz was especially interested in an improvement in the processing of ores – referred to as the “maturation” of metals – not just for obtaining new knowledge, but also for greater economic benefit, as he explained to the mining official Johann Christian Orschall in a letter from Hanover in August 1687. Regarding the process as such he wrote: As regards the maturation of metals, I have always had the standpoint that one understands by this [method] such an improvement of the ores, by means of which more can be obtained than through the common sampling [method].289

285 “auf daß die gantze Welt sehen sole, daß die transmutation der metallen warhafftig … seye” (A III,4 N. 210, pp. 405f.). 286 Cf. A III,4 N. 215 (pp. 419f.) and N. 248 (pp. 493f.). 287 Cf. A III,4 N. 253, pp. 504–506. 288 Cf. A III,4 N. 254–258. 289 “Was die Maturation der Metallen betrifft, so habe ich allezeit dafür gehalten, man verstehe dadurch eine solche verbeßerung der Erze, vermittelst deren ein mehrers darauß zu erhalten, als durch die gemeine Proben” (A III,4 N. 187, p. 343).

July 1683–1690

10

419

Geology, Mineralogy and Paleontology

Having accepted the commission as court historian, Leibniz began to extend his project to write a history of the House of Welf, and to include prehistory. His long-standing interest in the natural history of regions  – like the Harz district – accordingly led him to include Earth history or the geological history of the Welf territories. In relation to the genesis of this work – which was designated Protogaea,290 in Leibniz’s summary report for the Acta Eruditorum in January 1693291 – that was originally conceived as the prelude to the history of the Welfs, and was largely founded on his knowledge of the Harz mountain range, there exists a report in the form of an extract from a letter of January 1687, which he sent to the clergyman Barthold Meier whom he probably met while on a visit to the Harz mountains in late October or early November 1685.292 This report was concerned with the “Baumannshöhle”, a cave near the small town of Rübeland, which Leibniz had inspected during that visit in the fall of 1685.293 In addition, there are some scattered reports in Leibniz’s correspondence (between 1683 and 1690) about interesting prehistorical finds.294 Thus, at the end of a letter to Georg Mohr in the second half of July 1683, Leibniz wrote that he had discovered fish fossils in shale, and that he suspected that the fish had lived in water before being petrified. On that occasion he wrote: I have here some shale stones in which nature has laid complete figures of fish with copper streaks such that copper can really be smelted from

290 Cf. G. W. Leibniz, Chr. L. Scheidt (ed.), Summi Polyhistoris Godefridi Guilielmi Leibnitii Protogaea sive de prima facie telluris et antiquissimae historiae vestigiis in ipsis naturae monumentis dissertatio ex schedis manuscriptis viri illustris in lucem edita a Christiano Ludovico Scheidio, Göttingen, 1749; Protogaea, oder Abhandlung von der ersten Gestalt der Erde und den Spuren der Historie in den Denkmaalen der Natur, Leipzig, 1749; Leibniz, Opera Omnia, 6 vols, Geneva 1768, in particular, vol. 2, part 2, pp. 181–198 (preface) and pp. 199–240; Leibniz: Ch. L. Scheid, and W. von Engelhardt, F.-W. Wellmer (trans., eds.), 2014; Leibniz: Cohen-Wakefield, 2008; (Introduction, note 190). 291 Cf. G. W. Leibniz, “Protogaea. Autore G. G. L.”, Acta Eruditorum, (January 1693), pp. 40–42. 292 Cf. A III,4 N. 157, pp. 299f. 293 Cf. note 290 above, and in particular G. W. Leibniz, Chr. L. Scheidt (ed.), Protogaea, 1749, pp. 67–69, and Leibniz: Cohen-Wakefield, 2008, chap. XXXVII, pp. 108–113. cf. also: J. Mattes, 2022, pp. 60–62 (Introduction, note 191). 294 Cf. A III,4 N. 3, N. 148, and N. 284.

420

Chapter 2

it. I would almost suspect that, water being there, such fish were petrified to stone.295 Likewise, in his letter to Du Hamel on July 21, 1684, Leibniz reported about his recent studies and views regarding Earth history, and in particular about the formation of rocks and minerals (mineralogenesis),296 which were at variance with those of Agricola, Descartes and Nicolas Steno (Niels Stensen).297 Thus, he informed the correspondent that: “I have studied a little the mines of which our country abounds, and I have views that are totally at odds with those of Agricola, Descartes and Mons. Stensen”.298 The same line of thought is found in a letter he wrote to Detlev Clüver at the end of July 1686. Concerning the formation of metals Georg Agricola had supposed – in De ortu et causis subterraneorum (1546)299 – that mineral veins had come into existence, after groundwater had permeated the rocks and been boiled by subterranean heat to attain a certain denseness, thus forming metal ore deposits. Leibniz attributed the process of the subterranean formation of minerals by fire to spirits trapped in the mines, and he insisted he could reproduce the process in experiments. Thus, he wrote in this letter to Clüver: I have observed things not only regarding the generation of metals … but also about the origin of those spirits which are hidden in minerals, and I am bolstered in the view that minerals are formed not from water, as it appeared to Agricola and others, but rather that the state in which they are found comes from a certain active embedded fire. I could certainly demonstrate this in experiments at many locations.300 295 “Ich habe alhier einige schiefer-steine darinn die natur vollkommene figuren von Fischen mit Kupfer-strichen eingeleget, also daß wahrhaftig Kupfer daraus zu schmelzen. Dorfte fast suspiciren, daß das wasser darinn solche fisch gewesen zu Steine geworden” (A III,4 N. 3, p. 13). 296 Regarding mineralogenesis, cf. J. E. H. Smith, 2011, pp. 228f., and regarding Leibniz’s geological research in the Harz mountains, cf. H.-J. Waschkies, 1999 (Introduction, note 191). 297 Cf. N. Stensen, De solido intra solidum naturaliter contento dissertationis prodromus, Florence, 1669, and Leiden, 1679. Regarding Stensen’s biography and papers, cf. T. Kardel, P. Maquet (eds., trans.), 2013 and 2018, and regarding Leibniz’s connection with Stensen, cf. A. Vibeke Vad, 2002, and M. Lærke, 2018 (Introduction, note 191). 298 “J’ay étudié un peu les mines dont nostre pays abonde, et j’ay des sentimens tout à fait differens de ceux d’Agricola, de des Cartes, et de Mons. Stenonis” (A III,4 N. 62, p. 131). 299 Cf. G. Agricola, De ortu et causis subterraneorum libri V, Basel, 1546, in particular lib. III. 300 “Ego quaedam non tam circa generationem metallorum … quam circa larvarum illarum quibus in mineris obteguntur originem observavi et in ea confirmor sententia, pleraque non tam aquam ut Agricolae et aliis visum est, quam per actualem quondam ignem

July 1683–1690

421

Descartes had disputed Agricola’s hypothesis that groundwater was the source of the subterranean fluids from which minerals form, and he suggested instead that they form from molten rock.301 Leibniz considered Descartes’ account to be particularly meager, and off the mark, the author having had no experience in the mines, and being beguiled by written sources, or in the words of his letter to Clüver at the end of July 1686: “That which Descartes has said about matters concerning metals and minerals is particularly meager, and not to the point, and I think he was beguiled by the authority of written sources, because he had never gone near a mine location himself”.302 Finally, on June 6, 1690, Friedrich Heyn sent Leibniz samples of mineral ores from the Ilmenau mines, specifically of shale and limestone, in which fossilized plants were to be seen, together with the following text: “I enclose herewith several ores from the same mine location; I admire in particular the herbal shale and limestone, in which the natural trees are to be found, the likes of which I had not seen before”.303 11

Biology and Medicine

Leibniz’s idea, expressed in his letter to Huygens on November 24, 1690, of using a vacuum extractor, or pneumatic press, to remove things from bodies was no doubt indicative of future technical applications for which the time had not yet come. This idea was formulated as follows: “Previously I had the intention of trying to see if, by means of a vacuum, one might be able to draw something from a body, among other things by attaching filters to it, since that would be a type of press (or pump) more subtle and more uniform than the ordinary”.304

fusionis, in eum quo reperiuntur statum devenisse. Multis certe locis id contigisse possum demonstrare experimentis” (A III,4 N. 148, p. 285). 301 Cf. R. Descartes, Principia philosophiae, Amsterdam, 1644, in particular pars IV, cap. 45ff. 302 “Quae Cartesius dixit de rebus metallicis et mineralibus, mire jejuna, et a rebus ipsis aliena sunt, et puto scriptorium autoritate deceptum fuisse, quia ipse loca fodinarum nunquam adierat” (note 301, p. 285). 303 “Ich übersende hierbey etliche Ertze von selben wercke, absonderlich admirire ich die Kräuter schiefer und Kalcksteine, worinnen sich die gewachsenen bäume finden, indem ich von dergleichen vorhero niemals gesehen” (A III,4 N. 261, p. 518). 304 “J’avois eu autres fois la vue d’essayer si par le moyen du vuide on ne pourroit tirer quelque chose des corps, entre autres y joignant des filtres, puisque ce seroit une espece de presse plus subtile et plus uniforme que l’ordinaire” (A III,4 N. 292, pp. 659–669, specifically p. 668; HO, 9, pp. 546–552).

422

Chapter 2

The various “instrumenta et experimenta pneumatica”, on the other hand, which were topics of discussion in Leibniz’s interlocution with the Marburg physician and Cartesian Johann Jakob Waldschmidt, on November 6, 1687, were not of a technical, but rather of a botanical or zoological, nature. Two particular experiments were discussed. In the first the leaves of a plant were inserted into a vacuum flask while the roots remained above the flask, outside in the fresh air, and then, in the second experiment, vice versa.305 When the vacuum pump was put into operation, water and vital spirit (or sap) were drawn from the roots through the meatus to the leaves, but not with the inverse or reverse experimental arrangement.306 Waldschmidt attributed this effect to the presence of valves in the vessels of the plants, through which liquids flow, whereas Leibniz supposed that not just valves, but also inflected fibers, were operative, these being the essence of the acumen, or perspicacity, of those parts of the plant to which the sap tends.307 The second experiment, which was discussed by Leibniz and Waldschmidt, involved introducing a small fine tube into the vein of a dog, and then pumping air into this tube. The outcome was the immediate death of the animal, because the blood was suddenly pumped through the veins to the heart, and the blood circulation accordingly blocked.308 This conversation also touched on a bell mouth (speaking tube), or acoustic horn, which had been discovered, or developed, by Waldschmidt. Concerning this Leibniz wrote: “He has a speaking trumpet through which one may not speak loudly but can in fact be heard at a distance of half a German mile (I think, a quarter of a mile)”.309 Among the medical topics discussed in Leibniz’s correspondence in the years leading up to 1690, therapeutic and pharmaceutical themes were the main focus. In the correspondences with Heyn, and particularly Wachsmuth, a multiplicity of medicinal products are referred to. Besides medicaments – like Peru balsam syrup, smelling salts (“Schlagbalsam”), sweet almond oil, white candied sugar – which Leibniz obtained from Wachsmuth, other products like 305 “Das erste, daß er eine plantam genommen, also daß die Wurzel oben in freier Luft, und die Blätter in dem Vacuo; item contra” (A III,4 N. 198, p. 362). 306 “Auf die erste Weise hat sich das Wasser oder Sp. v., wenn man zu pumpen angefangen, durch die meatus a radice hinein nach den Blättern gezogen; auf die andere Weise hat es sich nicht wollen thun lassen” (p. 362). 307 “Hr Waldschmidt inferiert valvulas darauf, ich inferire nicht sowohl valvulas als fibras omnes ad instar acuminum in aristis in illas partes ad quas succus tendit flexas” (p. 362). 308 “wenn man einem Hunde in die venam einen kleinen subtilen tubulum hineinsticht, und dann stark darein bläst, so bleibt der Hund gleich todt; weil dadurch auf einmal das Blut ex venis nach dem Herzen getrieben, und die circulation gestopft wird” (p. 362). 309 “Er hat eine redende Trompete dadurch man eben nicht stark reden darf, und kann doch auf eine halbe teutsche Meile gehöret werden. (Ego puto, eine Viertelmeile.)” (p. 362).

July 1683–1690

423

medication against dysentery and the pest, Armenian bole, or white Armenian bole,310 also deserve mention. Herbal remedies too were popular like, for example, an emetic from America, which was referred to as a “plant from America to make vomiting easier”.311 In a letter to Bodenhausen, on January 13, 1690, Leibniz tried to get information about a herbal remedy against podagra, or gout, which the Jesuit missionary Claudio Filippo Grimaldi had brought from China, and which was to be found in the garden of the grand duke in Florence. Here he wrote: I request, my dear Baron, that you have the plant in the grand ducal garden – which father Grimaldi brought from China claiming its infallible and rapid action against gout – shown to you, that you also inquire about how it is to be applied, and that you communicate to me a short description of the plant and its purported effect.312 Bodenhausen then reported, on January 28, that he too had been promised this cure for gout (“curam podagrae”),313 and that he intended to investigate the Chinese plant in question. However, almost half a year later, on July 6, Leibniz had to remind the correspondent, requesting details once again of the Chinese plant against gout to be found in the grand ducal garden.314 It was also Bodenhausen who, on September 16, 1690, drew Leibniz’s attention to a panacea against chronic diseases, being claimed by Samuel Ledel from Görlitz,315 and that had been treated by him in the medical journal Miscellanea Curiosa in 1688.316 Then, in a note drafted for his reply of November 5, 1690, to Bodenhausen’s letter of September 16, with the heading “Pro responso ad D. Baronis de Bodenhausen literas 16 7br 1690”, Leibniz wrote that the author had noted that it was a panacea, “which was presented in the form of a pill or tablet that, when given as a two- or three-grain dose, completely suppressed 310 Cf. A III,4 N. 159, p. 303. 311 “Planta aus America so vomitus ohne beschwerung macht” (A III,4 N. 155, p. 296). 312 “Ersuche auch M.h.H. Baron in Ihr. Durchlaucht des Großherzogs Garten sich die plantam zeigen zulaßen, so der P. Grimaldi aus China gebracht, und deren unfehlbare schleunige wurckung [sic] gegen das podagra rühmet auch sich zu erkundigen wie sie gebraucht werden solle, und mir eine kleine beschreibung von der planta und deren vorgegebenen würckung [sic] mittheilen” (A III,4 N. 227, p. 443). 313 Cf. A III,4 N. 234, p. 458. 314 viz. the “plantae chinensis Antipodagricae so in des grosherzogs garten davon particularia verlange” (A III,4 N. 264, p. 528). 315 Cf. A III,4 N. 273, p. 557. 316 Cf. S. Ledel, “De curiosis vere curiosis”, Miscellanea Curiosa, Decur. II, Ann. VII, (1688), pp. 84–86, in particular observatio 42.

424

Chapter 2

all chronic and exasperating diseases317”.318 He himself had, in the meantime, tried to obtain further details about this alleged universal remedy by asking Pratisius to write to a well-known “medicus” in Görlitz on the matter.319 The fact that Leibniz, and his correspondents, were always interested in remedies, and therapies, can be seen from a passage in a letter of December 7, 1683, from Tschirnhaus, in which a method for preventing and treating women’s breast diseases, including breast cancer, was highlighted. Breastfeeding women were often found to have painful breast diseases, and breast ulcers, which, if not treated, might often lead to malignant diseases like breast cancer. A common resort for such patients was a painful operation at the hands of a barber-surgeon,320 which the correspondent now sought to replace with milder treatment methods. Thus, he wrote to Leibniz: Women when they have children often have great pains and ulcers on the breast which then have to be lanced by the barber and are accordingly very painfully treated. If however such steps are not taken on time, even cancer, or a similar corrosive disease, can develop. I have, following my principles, not only arranged – in the case of those who invariably get this when they have children – that they do not get the likes of it again, but also that women – who have had it – have their breasts so treated that they are amazed in view of the pains which they would otherwise have to endure.321 Two years before embarking on his grand tour of Austria and Italy, on October 26, 1685, Leibniz received a damming report by Pratisius, from Venice, about the situation regarding medical practice and practitioners there. Thus, the correspondent wrote: “Good medicine has, as far as practice is concerned, degenerated here to the extent that Venice would do well, as was done in Rome 317 underlining by Leibniz. 318 “quae in forma pilulari exhibita et ad gr[anum] II vel III pro dosi data radicitus tollat omnes morbos Chronicos et desperatos” (underlining by Leibniz; A III,4 N. 285, p. 626). 319 Cf. A III,4 N. 285, p. 631. 320 Cf. M. Fishbein (1957) and McCallump (2008), pp. 36f. (Introduction, note 216). 321 “Die Damen wenn sie Kinder bekommen so kriegen sie vielmahls große schmerzen und ulcera an den brüsten, welche durch den Barbier hernach aufgeschnitten und also sehr schmerzhafft curirt werden, wenn man aber nicht bey zeiten dazu thut so wird gar Krebs oder dergleichen Corrosivisch malum darauß. Ich habe nach meinen principiis nicht allein verursachet, daß die es stets gehabt, wenn sie Kinder bekomen, nicht mehr hinfuhro dergleichen bekommen, sondern auch das Damen die es gehabt, ihre brust curiret, daß sie sich verwundert in betrachtung der schmerzen, die sie sonst ausstehen müssen” (A III,4 N. 42, p. 91).

July 1683–1690

425

in the past,322 to expel all these ruffians”.323 Pratisius expressed similar sentiments regarding the decadence of the pharmaceutical system,324 and of the methods of treatment, including the insinuation that the “methodus medendi” there could be learned in a quarter of an hour.325 Leibniz’s Italian journey then provided him then with a welcome opportunity for oral discourse on medical subjects with Italian physicians and scientists. At the end of 1689, he made the acquaintance in Modena of the renowned physician Bernardino Ramazzini, who was a pioneer of modern industrial medicine. Whereas, as indicated above, in Leibniz’s exchange of ideas with Ramazzini, matters from the fields of engineering and technology were foremost, he was particularly impressed in the case of two other medici by their mathematical abilities. Thus, he wrote the following to Huygens, on July 25, 1690, concerning Domenico Guglielmini and Francesco Spoleti: “I have met two medics well versed in mathematics for whom I have great expectations, Mr Guglielmini at Bologna and Mr Spoleti at Padua”.326 In the draft for this letter, he added words to the effect that both were good mathematicians (“tous deux bons Mathematiciens”). In this context, Leibniz advocated treating medicine as an exact science, and he pleaded for its mathematization. Likewise, we read in a letter he sent from Venice sent to Francesco Bianchini, on March 18, 1690, the following: “From Spoleti I do not expect anything disdainful … I encouraged him to apply mathematics to ‘res medica’ which he is capable of doing”.327 Leibniz’s vision of medicine rooted in calculus  – essentially an appropriate and precise form of expression in the process of reasoning  – was even more pronounced in another letter he sent from Venice to Bodenhausen, on February 20, 1690. There he wrote on that occasion: [May it be that] God wanted that medicinalia and the like should exist both concretely and potentially. Nonetheless, it is certain that these 322 Perhaps a reference to J. de Laet (ed.) C(ajus)/G(aius), Plinius Secundus, Historia naturalis libri XXXVII, Leiden, 1635, in particular liber XXIX, chap. 5, sect. 11; cf. J. Hardouin (ed.), C(ajus)/G(aius), Plinius Secundus, Historiae naturalis libri XXXVII in usum Delphini, 5 vols, Paris, 1685. 323 “Die gute Medicin ist, was praxin anlanget, hier so weit gekommen, daß Venedig wohl thäte, wie vor diesem zu Rom, daß sie die kerls alle verjagten” (A III,4 N. 100, p. 228). 324 “pharmaceutica ist hier relegirt” (p. 228). 325 “vnnd kan man den method. Medendi in einer viertel stunde lernen” (p. 228). 326 “J’ay trouvé deux Medecins, bien versés dans les Mathematiques dont je me promets quelque chose[,] M. Guillelmini à Bologne et M. Spoleti à Padoue” (A III,4 N. 267, p. 533 and p. 566; HO, 9, pp. 448–452). 327 “A Spoleto non contemnenda expecto … hortatus sum, ut mathematicum in re medica agat, quoad ejus fieri potest” (A III,4 N. 244, p. 481).

426

Chapter 2

things, in as far as they are subject to reason, can also be reduced to calculation. For, indeed, calculus is nothing other than a most appropriate and compendious expression of reasoning (or of rational thought).328 328 “Wolte Gott daß Medicinalia und dergleichen concreta so wohl in potestate wären. Gleichwohl ist gewiß, daß auch diese dinge, in so weit sie rationi unterworfen, auch in calculum zu bringen. Denn calculus nichts anders als aptissima et compendiosissima ratiocinationum expressio” (A III,4 N. 236, p. 462).

Chapter 3

1691–1693 j’aime mieux un Leewenhoek qui me dit ce qu’il voit, qu’un Cartesien qui me dit ce qu’il pense.1 Leibniz to Christiaan Huygens, March 2, 1691

⸪ 1

Biographical Background (1691–1693)

Leibniz’s correspondence in mathematics, science and technology for the years 1691–1693, consisting of more than 200 often lengthy letters written both by Leibniz himself (about one third) and by his correspondents and third parties (about two thirds), involved a total of about 30 individuals.2 The five most voluminous correspondences – those with Rudolf Christian von Bodenhausen, Johann Daniel Crafft, Johann Sebastian Haes, Christiaan Huygens and Denis Papin – constitute more than half of the total correspondence in mathematics, science and technology in this triennium. Particularly important for Leibniz (even though the number of letters at this juncture was not great) were his correspondences with Johann Bernoulli, Domenico Guglielmini, Guillaume François de L’Hospital, Isaac Newton, Christoph Pfautz, Bernardino Ramazzini, Ehrenfried Walther von Tschirnhaus and Johann Georg Volckamer. The most important biographical events for Leibniz in the early 1690s were his appointment as director of the library in Wolfenbüttel, on January 14, 1691,3 the appearance in May 1693 of his monumental work on sources for international law viz. the Codex juris gentium diplomaticus,4 the coming into being, and the taking shape, of his history of the House of Welf (Guelf or Guelph), 1 A III,5 N. 9, pp. 62f.; Translation: I prefer a Leewenhoek who tells me what he sees to a Cartesian who tells me what he thinks. 2 Cf. H.-J. Hess and J. G. O’Hara, A III,5, Introduction, pp. [XXI]–LXVIII. 3 Cf. A I,6 N. 17. 4 Cf. G. W. Leibniz (ed.), Codex juris gentium diplomaticus, in quo tabulae authenticae actorum publicorum, tractatuum, aliarumque rerum majoris momenti per Europam gestarum … continentur, Hanover, 1693, and also the reviews in: Acta Eruditorum, (August 1693), pp. 370–380 and Histoire des Ouvrages des Savans, (December 1693), pp. 177–182.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_005

428

Chapter 3

particularly in the light of the Hanoverian dynasty’s procurement of electoral status in 1692, his efforts to bring about a reunion of the Christian churches, and, last but not least, the revival of his interest in the ore mines in the Harz mountains. Leibniz’s involvement in writing the history of the Welf dynasty led, in addition to his duties as librarian, to numerous local journeys, for example to Hildesheim, Celle and Brunswick. Economic projects, conceived together with Crafft, made a journey to Hamburg necessary in the second half of September 1693 and, at the end of the same year, there followed a new phase of regular visits to the Harz mining district. This restless period for Leibniz led to the frequent neglect of his correspondence, with the result that incoming letters were sometimes left unattended to in Hanover, and so could not be punctually answered. It also occurred at times that Leibniz did not have the requisite materials at a variety of locations for replying in detail to letters, which meant that only tentative or incomplete replies were possible.5 The completion of Leibniz’s Codex juris gentium diplomaticus, which contained records and charters relating to treaties and records of international legal agreements, from the 12th to the 15th centuries, as well as efforts to find documents for a planned follow-up volume, are reflected in his correspondence from 1693. Leibniz hoped for support in obtaining material from among his circle of acquaintances, which included diplomats, librarians, scholars, and even scientists like Huygens. His antennal senses, or feelers, reached out to Holland, England, and Italy in the quest for interesting documents for the planned supplementary edition. Leibniz entertained, in particular, the hope of obtaining material from Dutch and English sources through Huygens’ mediation. He hoped that with the help of Huygens’ brother Constantijn – secretary to stadholder-king William III – to achieve the cooperation of English scholars in locating relevant documents from English archival sources and, at the end of a letter of April 20, 1691, he addressed the issue directly.6 Although skeptical, Huygens did write to his brother, as he informed Leibniz at the end of his reply two weeks later.7 However, the initiative was to prove unsuccessful. With a letter of March 20, 1693, Leibniz sent a printed copy of the title page with an announcement of the Codex to Huygens, with the following text near the end:

5 Cf. for example, A III,5 N. 33, N. 98, N. 162 and N. 178. 6 Cf. A III,5 N. 17, p. 103; HO, 10, pp. 83–85. 7 Cf. A III,5 N. 21, p. 113; HO, 10, pp. 93–94.

1691–1693

429

Behold something of a completely different nature, which I am attaching here. I have examined a quantity of curious documents, relating to history and public affairs, of which I am publishing a miscellany or anthology. The [volume] with the oldest [texts], before the year 1500, will appear this springtime in a folio volume. But for the modern [texts], particularly from our century, I still desire a lot of things.8 Huygens, although impressed by Leibniz’s project, was not prepared to collaborate in the undertaking, and he even expressed his regret that Leibniz should be sacrificing his time for it, near the end of his reply, on September 17, 1693. Here the correspondent wrote: I should not forget to say a word regarding your Codex Juris Gentium, a project about which you desired to inform me. That is a grand work indeed which you have in hand, Sir, and it will be of use to a lot of people and I would like to play a greater part than I can in serving you and providing you with material. But the little attachment and liking I have for such political airs and graces, per queste canzoni politiche,9 to use the words with which pater Paolo [Sarpi] referred to them, keeps me away from anything relating to them, and it even causes me pain that a spirit like yours should be spending time on them.10 Notwithstanding Huygens’ skepticism, Leibniz did not abandon the hope of obtaining material from Dutch and English sources through his mediation. Thus he wrote near the end of his reply, on October 11, 1693: It must nevertheless be admitted that also in matters of law, of morals and of politics, one can have discoveries and exact reasoning … I would 8

“Voicy quelque chose de tout autre nature, que je joins icy. J’ay eu en main quantité de pieces curieuses qui servent à l’Histoire et aux affaires, dont je feray imprimer le recueil. Celuy des plus anciennes, avant l’an 1500, paroistra ce printemps dans un volume in fol. Mais pour les modernes, particulierement de nostre siècle[,] je souhaitterois encor bien des choses” (A III,5 N. 140, p. 525; HO, 10, pp. 425–432). 9 underling by Huygens. 10 “Je ne dois pas oublier de vous dire un mot touchant vostre Codex Juris Gentium, dont vous m’avez voulu communiquer le projet. C’est là un grand ouvrage que vous entreprenez Monsieur, qui sera utile à bien des gens, et je voudrois estre plus propre que je ne suis à vous y servir en vous fournissant de la matiere. Mais le peu d’attachement et d’estime que j’ay per queste canzoni politiche, comme le P. Paolo [Sarpi] les appelloit, me tient hors de commerce pour tout ce qui les regarde, et je souffre mesme avec peine qu’un esprit comme le Vostre y emploie du temps” (A III,5 N. 185, p. 636; HO, 10, pp. 509–512).

430

Chapter 3

be very pleased to receive one day your judgement on the preface to my diplomatic code. I have informed you about my project because I believed that perhaps one of your friends in Holland might be able to provide me with some item of interest, of which there are without doubt some which would prove honorable for your Republic.11 Through the intermediation of Henri Justel, the Royal Librarian in London, Leibniz eventually made contact with the English scholar Thomas Smith, who was to give him the support he desired in his historical research.12 In Italy, Leibniz hoped to avail of the multifarious contacts of Antonio Magliabechi – the custodian of the grand ducal library in Florence  – in order to obtain material for the continuation of his Codex, and here Bodenhausen acted as intermediary.13 In Germany, Leibniz approached, among others, the librarian in Kassel, Johann Sebastian Haes, to obtain material for the second volume of his Codex, alas, also in this case, without success.14 Much of what was discussed in Leibniz’s correspondence in the years 1691– 1693 was connected with his planned ‘opus historicum’. Thus, the naturalhistorical development of the earth was a central theme of an extensive correspondence with the French scientist, traveler, cartographer and orientalist, Melchisédech Thévenot, until his death in 1692.15 Here the groundwork was laid for the first part of the Welf history, namely his posthumously published Protogaea. Thereafter, Leibniz worked on the following part that was to be concerned with the barbarian migrations. In this context, the protolanguage on which all later languages were based, and the origin of human beings, were central research topics for him. He used comparative linguistics here as a means to shed light on the interrelationship of languages, and thus on the relatedness and origin of peoples. Thus, for example, in a letter sent on June 3, 1692, to Henri Justel for presentation to Edmond Halley, Leibniz – referring to the opus Orbis eruditi literatura (1689) by Edward Bernard,16 the Savilian professor of astronomy at Oxford – wrote the following: “I opt to follow Bernard the man of 11 “Il faut cependant avouer, qu’encor en matiere de droit, de morale et de Politique on pourroit faire des decouvertes et des raisonnenens exacts … Je seray bien aise de voir un jour vôtre jugement sur la preface de mon Code diplomatique. Je Vous avois communiqué mon project parce que j’ay crû que peutestre quelque un de vos amis en Hollande me pourroit fournir quelque piece curieuse, dont il y en auroit sans doute qui seroient honorables à vôtre Republique” (A III,5 N. 191, specifically pp. 650f.; HO, 10, pp. 538–543). 12 Cf. A III,5, p. LVII. 13 Cf. A III,5 N. 144, p. 536, and N. 201, p. 669. 14 Cf. A III,5 N. 149 and N. 190. 15 Cf. A I,7 N. 173. 16 Cf. E. Bernard, Orbis eruditi literatura à charactere Samaritico deducta, Oxford, 1689.

1691–1693

431

the incomparable doctrine, the ‘Harmonica Linguarum et Literarum’, the opus on languages and letters … that investigation will be of great use in identifying the origins of nations”.17 2

Infinitesimal Calculus and Other Mathematics

The triennium in question represents one of the most productive phases for Leibniz’s mathematics in all of his years in Hanover. Whereas, in the wake of his discovery of the infinitesimal calculus in Paris between 1672 and 1676, he had remained irresolute over years about when and how to best inform the public about his new mathematical methods, there followed on the first series of articles in the Acta Eruditorum on the differential and integral calculus – in October 1684,18 and June 1686,19 respectively – a period of reticence lasting a number of years, primarily a consequence of his research tour to Austria and Italy. The few journal articles that did appear arose not so much from the spontaneity of mathematical creativity, but rather from a sense of necessity not to publish results too late. Thus, Leibniz’s articles about movement in a resisting medium, in January 1689,20 and about the foundation of celestial motions, in February 1689,21 have to be seen in connection with the appearance of Newton’s Principia mathematica in 1687, whereas the publication of his isochrone solution, in April 1689,22 represented a conclusion – for the time being at least – of the dispute with the Cartesians (in particular with the Abbé Catelan) which had been going on for almost three years. The curve in question (the isochrone 17 “Bernardum incomparabilis doctrinae virum opto persequi Harmonica Linguarum et Literarum  … Multum ea disquisitio proderit ad noscendas nationum origines” (A III,5 N. 80, pp. 314f.). 18 Cf. G. W. Leibniz, “Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratur, et singulare pro illis calculi genus”, Acta Eruditorum, (October 1684), pp. 467–473 (Leibniz: Parmentier, 1989, chap. 3, pp. [96]–117; Leibniz: Essais Scientifiques, 2005, N. 14; Leibniz: Heß-Babin, 2011, chap. 8, pp. 51–62). 19 Cf. G. W. Leibniz, “De geometria recondita et analysi indivisibilium atque infinitorum”, Acta Eruditorum, (June 1686), pp. 292–300 (Leibniz: Parmentier, 1989, chap. 5, pp. [126]– 143; Leibniz: Essais Scientifiques, 2005, N. 20; Leibniz: Heß-Babin, 2011, chap. 10, pp. 69–81). 20 Cf. G. W. Leibniz, “Schediasma de resistentia medii, et motu projectorum gravium in medio resistente”, Acta Eruditorum, (January 1689), pp. 38–47. 21 Cf. G. W. Leibniz, “Tentamen de motuum coelestium causis”, Acta Eruditorum, (February 1689), pp. 82–96. 22 Cf. G. W. Leibniz, “De linea isochrona, in qua grave sine acceleratione descendit, et de controversia cum Dn. abbate D. C[atelan]”, Acta Eruditorum, (April 1689), pp. 195–198 (Leibniz: Parmentier, 1989, chap. 7, pp. [154]–165; Leibniz: Essais Scientifiques, 2005, N. 28; Leibniz: Heß-Babin, 2011, chap. 12, pp. 89–95).

432

Chapter 3

or semi-cubic parabola) was the desired solution to the first mathematical contest, or challenge question, which had been conceived to demonstrate the superiority of the Leibnizian infinitesimal calculus. Leibniz had challenged Catelan to determine the curve along which a body, under the influence of terrestrial gravity, approaches the earth’s surface at a constant speed. A related question was the problem of finding the paracentric isochrone, or the curve along which a body, again under the influence of terrestrial gravity, veers away from a given point at a constant speed. The latter problem, although enunciated by Leibniz himself, was however not seriously tackled at this juncture.23 Further mathematical contests were to follow. Jacob Bernoulli, who (besides Leibniz and Huygens) had solved the isochrone problem, combined his solution with a retaliation challenge question addressed to the creator of the differential calculus, namely to mathematically determine the form of the catenary, that is to find the curve described by a non-extensile catena, or chain, suspended at its extremities from two points having the same elevation and under the influence of terrestrial gravity.24 Leibniz, who immediately solved the hanging chain problem for himself, set the turn of the year 1690–1691 as a deadline for all mathematicians wanting to join the contest to submit their solutions.25 In early December 1690, Jacob Bernoulli’s younger, but estranged, brother Johann sent, as first, his solution to the editors of the Acta Eruditorum,26 as Leibniz learned from a letter sent by Christoph Pfautz, on February 14, 1691.27 Huygens, after some hesitation, forwarded his solution,28 through Leibniz, to the journal editors in Leipzig.29 Tschirnhaus alone, although explicitly approached by Leibniz, failed to respond to the challenge. Thus, Leibniz was only able to present two solutions (in addition to his own) of the catenary problem, which were published in the June 1691 number of the Acta Eruditorum. The initiator of the 23 Cf. A III,5 N. 12, p. 75, and N. 138, p. 509. 24 Cf. Jac. Bernoulli, “Analysis problematis antehac propositi, de inventione lineae descensus a corpore gravi percurrendae uniformiter, sic ut temporibus aequalibus aequales altitudines emetiatur; et alterius cujusdam problematis propositio”, Acta Eruditorum, (May 1690), pp. 217–219. 25 Cf. G. W. Leibniz, “Ad ea, quae vir clarissimus J. B., mense Majo nupero in his Actis publicavit, responsio”, Acta Eruditorum, (July 1690), pp. 358–360 (Leibniz: Parmentier, 1989, chap. 8, pp. [166]–172; Leibniz: Essais Scientifiques, 2005, N. 30; Leibniz: Heß-Babin, 2011, chap. 13, pp. 97–101). 26 Cf. Joh. Bernoulli, “Solutio problematis funicularii”, Acta Eruditorum, (June 1691), pp. 274–276. 27 Cf. A III,5 N. 7, p. 52. 28 Cf. Ch. Huygens, “Solutio ejusdem [i.e. funicularii] problematis”, Acta Eruditorum, (June 1691), pp. 281–282. 29 Cf. A III,5 N. 21, p. 112; HO, 10, pp. 93f.

1691–1693

433

competition, Jacob Bernoulli, published his solution,30 in an article that immediately followed Leibniz’s solution.31 Leibniz’s correspondence with Bodenhausen and Huygens provides interesting background information about this contest, as for example about Leibniz’s sense of pride regarding his own solution,32 about his attempts to make this solution comprehensible for Bodenhausen,33 about his ambition to make the contest known in Italy, the homeland of Galileo Galilei who had been one of the first to tackle this problem albeit without success,34 or about Huygens’ suspicions that Leibniz might have been prematurely privy to Johann Bernoulli’s solution, or even that Leibniz und Johann might have had common artifices at their disposal, which had been denied to himself.35 Another year was to pass before a further contest aroused mathematical passions again. Since Leibniz had, through the intercession of his friend and associate Bodenhausen in Florence, fervently tried to demonstrate to Vincenzo Viviani – a disciple and biographer of Galileo – and his compatriots the superiority of the differential calculus over the simple geometrical methods of contemporary Italian mathematicians, a retaliation move became inevitable. Viviani had secretly prepared the ‘Florentine problem’ (as it was later to be designated), and it was circulated in the form of a pamphlet, dated April 4, 1692. This problem, with the title Aenigma geometricum de miro opificio testudinis quadrabilis hemisphaericae,36 called for the cutting out of four windows from a hemisphere, such that the remaining surface area would be squareable. Leibniz received the pamphlet through the Florentine envoy in Vienna, on May 27, 1692. He solved the problem on the same day and sent his solution with a letter to the Florentine hereditary prince Ferdinand, on May 29, 1692.37 At the same time, he had the single-page problem enunciation,38 together 30 Cf. Jac. Bernoulli, “Specimen alterum calculi differentialis … una cum additamento quodam ad problema funicularium, aliisque”, Acta Eruditorum, (June 1691), pp. 282–290. 31 Cf. G. W. Leibniz, “De linea in quam flexibile se pondere proprio curvat, ejusque usu insigni ad inveniendas quotcumque medias proportionales et logarithmos”, Acta Eruditorum, (June 1691), pp. 277–281 (Leibniz: Parmentier, 1989, chap. 10, pp. [186]–199; Leibniz: Essais Scientifiques, 2005, N. 34; Leibniz: Heß-Babin, 2011, chap. 15, pp. 115–124). 32 Cf. A III,5 N. 24, pp. 117f., and N. 33, pp. 150–154. 33 Cf. A III,5 N. 34, pp. 154f. 34 Cf. A III,5 N. 12, p. 77, and N. 24, pp. 117f. 35 Cf. A III,5 N. 13, pp. 86f. (HO, 10, pp. 55–58), N. 21, p. 112 (HO, 10, pp. 93f.), N. 36, pp. 157f. and pp. 160–163 (HO, 10, pp. 127–134), and N. 37, pp. 165f. (HO, 10, pp. 139–143). 36 V. Viviani (anon.), Aenigma geometricum de miro opificio testudinis quadrabilis hemisphaericae a D. Pio Lisci Pusillo [i.e. Viviani] Geometra propositum, Florence, 1692. 37 Cf. A I,8 N. 154. 38 Cf. Acta Eruditorum, (June 1692), pp. 274f.

434

Chapter 3

with his solution,39 printed in the June number of the Acta Eruditorum. Jacob Bernoulli’s solution appeared in the same journal two months later.40 Then, on July 12, 1692, Bodenhausen forwarded to Leibniz the solution of L’Hospital, with the heading “Solutiones problematis de Templo Hemisphaerico”,41 having discovered it, and partially transcribed it, at the Florentine court. However, L’Hospital’s solution  – that had been achieved in cooperation with Johann Bernoulli  – remained unpublished at the time. After Huygens had seen Viviani’s solution in the latter’s tract Formazione e misura di tutti i cieli,42 he too solved the problem,43 but he hesitated and then reneged on his intention to forward it to Leibniz. Jacob Bernoulli, for his part, pointed out a mistake in Leibniz’s solution, in a letter he sent to Otto Mencke in July 1692,44 following which Leibniz published an “Additio” in January 1693.45 Yet another mathematical problem frequently mentioned in Leibniz’s correspondence at this juncture was the so-called “Bernoulli problem”, formulated by the younger Bernoulli brother, Johann, in the Acta Eruditorum in May 1693.46 The call here was for the determination of the curve, whose axis intercept from the origin to the intersection with the tangent (“resecta”) has a constant proportion, or ratio (m/n), to the length of the tangent. Bernouli revealed at the outset that for m/n = 1, the curve is a circle, and that for a rational ratio (m/n) the curve in question would be geometrical, whereas for an irrational ratio it would be transcendental. In the course of the year 1693, the older brother

39 Cf. G. W. Leibniz, “Constructio testitudinis quadrabilis hemisphericae”, Acta Eruditorum, (June 1692), pp. 275–279 (Leibniz: Essais Scientifiques, 2005, N. 42b; Leibniz: Heß-Babin, 2011, chap. 21, pp. 161–168). 40 Cf. Jac. Bernoulli, “Aenigmatis Florentini solutiones varie infinitae”, Acta Eruditorum, (August 1692), pp. 370f. 41 Cf. A III,5 N. 92, pp. 348–350. 42 Cf. V. Viviani, Formazione, e misura di tutti i cieli: con la struttura, e quadratura efatta dell’intero, e delle parti di un nuovo cielo admirabile, e di uno degli antichi delle volte regolari degli architetti, curiosa esercitazione matematica di V. V., ultimo scolare del Galileo, Florence, 1692. 43 Cf. HO, 10, N. 2771 (“27 octobre 1692”), pp. 336–338. 44 Cf. A III,5 N. 138, p. 508, and annotation. 45 Cf. G. W. Leibniz, “Additio … ad solutionem problematis”, Acta Eruditorum, (January 1693), p. 42. 46 Joh. Bernoulli, “Solutio problematis Cartesio propositi a Dn. de Beaune”, Acta Eruditorum, (May 1693), pp. 234f.

1691–1693

435

Jacob Bernoulli,47 Leibniz,48 L’Hospital,49 and Huygens published, or communicated, their solutions of the Bernoulli problem. Huygens communicated his solution of the problem  – at which he had arrived in consultation with L’Hospital  – to Leibniz, on September 17, 1693. This problem  – the solution of which had posed difficulties for Huygens – led to an admission on his part that his previous skepticism about the power of Leibniz’s calculus was possibly unfounded. It now appeared to him that it might be possibly superior to his own much appreciated geometrical methods. And so he wrote in this letter: I increasingly admire the beauty of the geometry, in the new progress being made in it every day and where you have had such a large part, Sir, there where it has only been possible through your wonderful calculus.50 Being at present but moderately versed in it and for that still not understanding anything of ddx, I would very much like to learn if you have been confronted with considerable problems where it has to be employed, for which reason I might have the desire to study it.51 With reference to the text he had underlined in this passage, Leibniz wrote a commentary at the end of Huygens’ letter which began with the words: I am delighted to see that by your solution of the problem of Mr Bernoulli, that [with] your ordinary penetration, you have now discovered that there is much of beauty in the differential calculus, from which you have desired to take the trouble to enter into it.52 47 Cf. Jac. Bernoulli, “Solutio problematis fraterni”, Acta Eruditorum, (June 1693), pp. 255f. (incorrect pagination). 48 Cf. G. W. Leibniz, “Ad problema Majo nupero in his Actis p. 235 propositum”, Acta Eruditorum, (July 1693), p. 313 (Leibniz: Essais Scientifiques, 2005, N. 56; Leibniz: Heß-Babin, 2011, chap. 26, pp. 191f.). 49 Cf. G. F. A. de L’Hospital, “Solution du problème que Monsr de Beaune proposa autrefois à Mr. Descartes”, Journal des Sçavans, (September 1, 1692), pp. 598f. 50 underlining by Leibniz. 51 “J’admire de plus en plus la beauté de la geometrie, dans ces nouveaux progres qu’on y fait tous les jou[rs], où vous avez si grande part Monsieur, quand ce ne seroit que par vostre merveilleux calcul. M’y voilà mainte[na]nt mediocrement versé, sinon que je n’entens encore rien aux ddx, et je voudrois bien scavoir si vous avez [re]ncontré de problemes considerables où il faille les emploier, afin que cela me donne envie de les etudier” (A III,5 N. 185, pp. 634f.; HO, 10, pp. 509–512). 52 “Je suis ravi de voir par vostre solution du probleme de M. Bernoulli, que vostre penetration ordinaire, vous a maintenant fait decouvrir ce qu’il y a de plus beau dans le calcul differentiel, dés que vous avés voulu prendre la peine d’y entrer” (p. 635).

436

Chapter 3

This long-awaited moment of recognition of the value of his new calculus, from his mentor of the Parisian years (1672–1676), was a source of joy for Leibniz, and he reciprocated with praise both for a new curve of Huygens – previously only communicated in encrypted or enciphered form – namely a limiting curve of a tautochrone, or isocrone double pendulum (analogous to the cycloid as limiting curve of a simple tautochrone or isochrone pendulum), and for his treatment of the involute of the catenary viz. the tractoria or tractrix. First and foremost, however, he relished the recognition of his differential calculus, both in Huygens’ letter of September 17, and then publicly in the Acta Eruditorum in the following month.53 Thus Leibniz wrote the following in his reply to Huygens on October 11: All that which I promised myself in producing the new calculus, which you, Sir, are beginning to find convenient, was to open a path where people having a greater penetration than me could find something of importance. And now I am damned to keep my solemn promise since you have found it good to avail of it and to pay me the honor of declaring this publicly. I am enraptured to see that, in your solution of the problem of Mr Bernoulli, you have remarked that there is more of beauty in our differential calculus, as well as that you have desired to take the trouble to enter into it.54 Besides the three public contests, a wide variety of topics appears in Leibniz’s mathematical publications, and correspondence, in the period from 1691 to 1693. Out of this diversity, some characteristic or exemplary topics deserve particular notice.55 The first example concerns one of the central questions that had led to the discovery of the differential calculus during his years in Paris, namely quadrature methods, involving the determination of an area under a given curve (quadrature), of the arc length (rectification), as well as of the connection between these, that is between quadrature and rectification. In 53 Cf. Ch. Huygens, “De problemate Bernoulliano”, Acta Eruditorum, (October 1693), pp. 475f. 54 “Tout ce que je m’estois proposé en produisant le nouveau calcul que vous commencés, Monsieur de trouver commode, a esté d’ouvrir un chemin où des personnes plus penetrantes que moy pourroient trouver quelque chose d’importance. Et maintenant voti damnatus sum, depuis que vous trouvés bon de vous en servir et c’est me faire beaucoup d’honneur que de le declarer publiquement. Je suis ravi de voir par vostre solution du probleme de M. Bernoulli, que vous avés remarqué ce qu’il y a de plus beau dans nostre calcul differentiel, aussitost que vous avés voulu prendre la peine d’y entrer” (A III,5 N. 191, pp. 645f.; HO, 10, pp. 538–543). 55 Cf. A III,5, pp. XXV–XXXI.

1691–1693

437

the triennium in question, these issues were discussed in Leibniz’s correspondences with Huygens, Tschirnhaus, L’Hospital and Newton.56 Another example relates to the inverse tangent method by which, from the properties of tangents or subtangents, the corresponding curves could be determined.57 Leibniz considered this to be his most important mathematical discovery of his years in Hanover. However, in his publications in the early 1690s, this inverse tangent method had not yet become an autonomous topic, nor did Leibniz reveal related general solution procedures. A proposed exchange of methods with Nicolas Fatio de Duillier, under the aegis of Huygens, failed to materialize when Leibniz decided to forego the interexchange. Nonetheless, Leibniz felt obliged to communicate a summary account of the basics of his inverse tangent method, on October 5, 1691.58 For mathematical tasks derived from the physical world in particular, the value of the inverse tangent method is evident, as for example in the determination of curves like the catenary, or of envelopes from the properties of their tangents or subtangents. The final example concerns the (plane) curve representation methods  – discussed in Leibniz’s correspondence with Huygens among others – which were of great importance for his mathematical thought and understanding.59 From the multitude of special curves treated in Leibniz correspondence in the early 1690s, those having real-world applications deserve particular mention here, like for example, the Archimedean spiral, the catenary, and auxiliary or related curves. In the discussion of the catenary problem, Leibniz pointed out, for example, the connection with the loxodrome or rhumb-line curve – that is the line cutting all meridians at the same angle and that which is followed by a ship sailing in a fixed direction – in his correspondence with Huygens.60 Notwithstanding Huygens’ words of praise for the differential calculus, in his letter of September 17, 1693, Leibniz’s relationship with his former mentor was complex, and at times strained. In conclusion then, this relationship will be reconnoitered here by taking a closer look at three specific mathematical issues in their correspondence in the early 1690s. These were their discussions, and disputes, about the so-called ‘Leibniz series’ for the arithmetic quadrature of the circle, the solutions of the catenary problem, and the proposed exchange of inverse-tangent methods between Leibniz and Huygens’ collaborator at the time, the Swiss mathematician Nicolas Fatio de Duillier. 56 57 58 59 60

Cf. pp. XXVf. Cf. pp. XXVIf. Cf. A III,5 N. 41, pp. 181–189 (HO, 10, pp. 197–202). Cf. A III,5, pp. XXVIII–XXXI. Cf. A III,5 N. 29, pp. 135f. (HO, 10, pp. 109–112) and N. 39, pp. 175–178 (HO, 10, pp. 156–162).

438

Chapter 3

The review of Huygens’ twin tracts on light and gravity of 1690 in the Acta Eruditorum, in October and November 1690,61 produced the first turbulence in the resumed correspondence between Huygens and Leibniz. In a letter of October 9 of that year, Huygens had expressed displeasure at the failure of the journal editors to provide a review of his book.62 Further contention was brewing in Leibniz’s reading of the work. In his Discours de la cause de la pesanteur, Huygens had introduced the infinite series a + 1/3 a3 + 1/5 a5 + 1/7 a7 + … for the quadrature of the hyperbola,63 and commented on the similarity with the ‘Leibniz series’ for the arithmetic quadrature of the circle, which had been published in the Acta Eruditorum in February 1682, viz. a – 1/3 a3 + 1/5 a5 – 1/7 a7 + …. Writing to Huygens on November 7, 1690,64 Leibniz remarked that Huygens’ series likewise resulted from considerations of his on movement in resisting media published in the Acta Eruditorum in January 1689. He had, he told the correspondent, even employed it in a then unpublished manuscript of 1676 entitled “De quadratura arithmetica”.65 Huygens, as we learn from his reply of November 18, 1690, was unable to comprehend the derivation of the quadrature of the hyperbola from Leibniz’s series.66 He rejected having had any previous knowledge of Leibniz’s 1676 paper which, he suggested, Leibniz ought to have published. Leibniz answered in haste, on November 24,67 to counter any suspicion of conceitedness on his part in the implication of his previous letter that Huygens had somehow derived his series from his paper on movement in resisting media. Then, with the publication of the eagerly awaited review of Huygens’ book, a further difficulty arose. The reviewer, Leibniz explained in the same letter, had likewise confused the two series, but he denied any hand in this misrepresentation.68

61 Cf. the review of Ch. Huygens, Traité de la lumière  … Discours de la cause de la pesanteur, Leiden, 1690, in: Acta Euditorum, (October 1690), pp. 481–487, and (November 1690), pp. 561–565. 62 Cf. A III,4 N. 280, p. 586; HO, 9, pp. 496–499. 63 Cf. Ch. Huygens, Discours de la cause de la pesanteur, 1690, p. 174. 64 Cf. A III,4 N. 287, pp. 644f. and p. 647; HO, 9, pp. 532–535. 65 Cf. G. W. Leibniz (E. Knobloch, ed.), De quadratura arithmetica circuli ellipseos et hyperbolae cujus corollarium est trigonometria sine tabulis (Abhandlungen der Akademie der Wissenschaften in Göttingen, mathematisch-physikalische Klasse, 3rd series, no. 43), Göttingen, 1993. 66 Cf. A III,4 N. 291, p. 657; HO, 9, pp. 536–540. 67 Cf. A III,4 N. 292, pp. 659–669; HO, 9, pp. 546–552. 68 Cf. pp. 667f., and also the reviews of the twin tracts in the Acta Eruditorum in October (pp. 481–487) and November (pp. 561–565) 1690, in particular p. 564 (regarding the infinite series).

1691–1693

439

When Huygens wrote again on December 19, 1690, he still had not seen the review but he requested that Leibniz take steps to have the reported error corrected.69 He was overwhelmed by what he interpreted as an excuse, or apology, on the part of Leibniz. However, in his reply, on February 6, 1691, Leibniz expressed astonishment at the suspicion behind Huygens’ suggestion that he had provided an excuse or apology.70 There was, in his view, nothing to be excused, since he had no part whatsoever in the misrepresentation of the facts of the case. However, knowing Huygens as well as he did, he was prepared to exonerate him. As an alibi he could present a letter of November 7, 1690, from Otto Mencke, editor of the Acta Eruditorum, from which he first learned of the review, and which was then already in print. Besides, Leibniz suggested, their applications of the series were so different as to rule out any suspicion of plagiarism. Huygens, writing on February 23, 1691, then clarified his intentions in alluding to an excuse, or apology, from Leibniz.71 Such an apology was of course superfluous as he never had the faintest suspicion of Leibniz’s involvement in the affair. Finally, on March 2, 1691, Leibniz announced that he had written to the editors of the Acta Eruditorum to correct the error and clarify the issue,72 and – with the appearance of Leibniz’s note on the matter in the April number of the journal73 – this particular dispute was finally laid to rest. During their four years together in Paris, Leibniz had provided Huygens with a preview of his methods in the area of analysis. However, Huygens was then skeptical, and he continued to be so later (at least until 1693) concerning the power and superiority of Leibniz’s analytical methods over his own geometrical methods. This is particularly evident in their discussion of the catenary problem in 1690 and 1691. It was in fact Huygens who suggested (on October 9, 1690) the mathematical description of the catenary as a test for the power of Leibniz’s calculus.74 As outlined above, this problem had been posed by Jacob Bernoulli in the Acta Eruditorum (in May 1690) as a challenge to Leibniz, and he had reacted in the July number by setting the term of a year within which other mathematicians might also submit their solutions. Huygens then communicated to Leibniz (in his letter of October 9) an encoded solution of the problem, and he requested the same in return. Replying on October 13, 1690, Leibniz announced that he had obtained close agreement with the results 69 70 71 72 73

Cf. A III,4 N. 296, p. 690; HO, 9, pp. 568–572. Cf. A III,5 N. 6, pp. 38–51; HO, 10, pp. 9–16. Cf. A III,5 N. 8, pp. 53–58; HO, 10, pp. 17–22. Cf. A III,5 N. 9, pp. 58–64, in particular pp. 58f.; HO, 10, pp. 49–52. Cf. G. W. Leibniz, “Additio ad schediasma de medii resistentia publicatum in Actis mensis Febr. 1689”, Acta Eruditorum, (April 1691), pp. 177f. 74 Cf. A III,4 N. 280, pp. 585f.; HO, 9, pp. 496–499.

440

Chapter 3

expressed in Huygens’ anagram, the only difference being an opposite sign in one of his equations.75 He had determined a number of features and properties of the curve, of its surface of revolution, and of the area between the curve and its axis. On the November 18, 1690, Huygens replied that the difference in sign observed by Leibniz appeared to indicate a difference of approach and, once again, he requested an enciphered solution from Leibniz.76 The latter, however, failed to comply with this request, and so the matter rested until early in the new year. On February 23, 1691, Huygens then urged Leibniz to conclude his work on the catenary so that the results might be communicated to the journal.77 In his view, the task did not appear to be particularly difficult, unless Leibniz was expecting more than he had obtained himself. On March 2, 1691, Leibniz announced to Huygens that Johann Bernoulli had likewise found a solution, whereas their mutual rival Tschirnhaus had failed to respond to the challenge.78 Bernoulli, Leibniz believed, might have profited from his calculus, since this, or an equivalent method, would surely be required for the solution of the problem – a remark that conveyed to Huygens the impression that Leibniz had some knowledge of Bernoulli’s solution in advance of the submission of his own. Once again, on March 26, 1691, Huygens demanded that they exchange their results, in encoded form, in advance of submission to the journal editors.79 He included a revised version of his own anagram, which he suggested might also be offered to Bernoulli in exchange for his. Ignoring Huygens request, Leibniz replied on April 20, 1691, announcing that the editors of the Acta Eruditorum had written to him.80 Bernoulli had already submitted his solution, and he had informed the editors that a solution from Huygens would also be forthcoming. He considered that there was no need to send Bernoulli the encoded solution, and he thought that they ought to submit their respective solutions as quickly as possible as the deadline set had in the meantime passed. And, he pledged Huygens confidentially. In a letter of April 21, 1691, which crossed with that of Leibniz of April 20, Huygens sent a correction to his encoded solution, and he stressed for the last time the desirability of exchanging results in this form.81 He also announced that he was taking the precaution of sending his 75 76 77 78 79 80 81

Cf. A III,4 N. 283, p. 622; HO, 9, pp. 516–520. Cf. A III,4 N. 291, pp. 655f.; HO, 9, pp. 536–540. Cf. A III,5 N. 8, p. 57; HO, 10, pp. 17–22. Cf. A III,5 N. 9, pp. 61f.; HO, 10, pp. 49–52. Cf. A III,5 N. 13, pp. 86f.; HO, 10, pp. 55–58. Cf. A III,5 N. 17, pp. 97–100 and p. 102; HO, 10, pp. 83–85. Cf. A III,5 N. 18, p. 104; HO, 10, pp. 86–88.

1691–1693

441

solution to an unnamed friend. This recipient was in fact Henri Basnage de Beauval, the editor of the Histoire des Ouvrages des Scavans. Finally, on 5 May, 1691, without having received the requested encoded solution, Huygens sent Leibniz his full solution, sealed and ready for forwarding to Leipzig.82 Three weeks later, on May 27, Leibniz announced to Huygens that he had submitted both their solutions.83 A pause of nearly two months now ensued before Leibniz wrote again, on July 24, 1691, announcing that he had seen the three solutions printed in the June number of the Acta Eruditorum.84 Although he had not found time to make a full comparison, his first examination had revealed good agreement in the heart of the matter. He was looking to Bernoulli to make an exact comparison of the three solutions and, since the latter had employed his calculus, he expected a share in the glory of his success too. He then presented Huygens with the detailed results of his own first survey, which was in fact a preview of his paper “De solutionibus problematis catenarii”, in the Acta Eruditorum of September 1691.85 The catenary is mathematically similar to the graph of the hyperbolic cosine, and so Leibniz could announce that both he and Bernoulli had related the problem to the quadrature of the hyperbola. Both of them had given the tangents, the length, or rectification, of the curve, as well as its center of gravity. He himself had provided the center of gravity of the space generated by the rotation of the catenary. All three of them had given tangents and the rectification of the curve. Bernoulli and Huygens had surpassed himself in considering the evolute of the catenary. Leibniz then singled out Bernoulli for particular praise. He had done extremely well; two or three years earlier he had been far from entertaining any expectations of such results. Bernoulli’s success had come of course through his adoption of Leibniz’s own calculus. Nonetheless, Leibniz found Bernoulli’s constructions quite different from his own. Whereas Bernoulli has been content to assume the quadrature of the hyperbola, or the rectification of the parabola, he himself had reduced the whole to logarithms which he considered a great simplification. A further issue was the relation of the catenary to loxodrome, or rhombic lines, i.e. those on the surface of a sphere making equal oblique angles with the meridians, which was of practical importance in marine navigation. Leibniz 82 83 84 85

Cf. A III,5 N. 21, p. 112; HO, 10, pp. 93–94. Cf. A III,5 N. 22, p. 114; HO, 10, pp. 99–100. Cf. A III,5 N. 29, pp. 132–135; HO, 10, pp. 109–112. Cf. G. W. Leibniz, “De solutionibus problematis catenarii vel funicularis in Actis Junii A. 1691 aliisque a Dn. I. B. propositis”, Acta Eruditorum, (September 1691), pp. 435–439 (Leibniz: Parmentier, 1989, chap. 11, pp. [200]–209; Leibniz: Essais Scientifiques, 2005, N. 35; Leibniz: Heß-Babin, 2011, chap. 16, pp. 125–133).

442

Chapter 3

referred Huygens to a paper of his in the Acta Eruditorum of April 1691, entitled “Quadratura arithmetica communis sectionum conicarum … cum usu speciali ad lineam rhomborum nauticam”,86 in which he had treated such loxodrome or rhombic curves, giving results that he had worked out perhaps 15 years earlier in Paris. His interest in this topic had been revived through the investigation of the catenary. Leibniz also recalled that Bernoulli had treated the loxodrome curve in another paper in the Acta Eruditorum of June 1691, entitled “Specimen alterum calculi differentialis”.87 On that occasion Jacob Bernoulli – not Johann as Leibniz seemed to think – had failed to observe that the loxodrome curve is related to the quadrature of the hyperbola, or to logarithms, or to the catenary. Shortly after receiving Leibniz’s communication of July 24, 1691, Huygens obtained the June number of the Acta Eruditorum, containing the three solutions of the catenary problem and the additional paper of Jacob Bernoulli. Huygens’ first reaction to the outcome of the competition was favorable, as we learn from a letter of September 1, 1691.88 He too had found good agreement between all three solutions. If Leibniz had obtained more results than himself, it must indeed be due to the potentiality of the new calculus. For his own part, he had only found those results he had set out to find, and had not sought the additional results provided by Leibniz and Johann Bernoulli. Huygens added that he had made his discoveries very early on, but he had hitherto been unable to relate the catenary to the quadrature of the hyperbola. He had in effect failed using his own methods and thought that, since Johann Bernoulli had also employed Leibniz’s calculus, this must have been central to their success. He therefore requested a short explanation from Leibniz. Shortly after dispatching this letter of September 1, Huygens discovered the means of reducing the construction of the catenary to the quadrature of the hyperbola, which he then communicated in a follow-up letter of September 4.89 However, the complementary tone of the previous letter was now replaced by one of reproach, or rebuke. In a postscript, he presented his thoughts on remarks in Johann Bernoulli’s paper relating to the construction 86 Cf. G. W. Leibniz, “Quadratura arithmetica communis sectionum conicarum quae centrum habent, indeque ducta trigonometria canonica ad quantamcumque in numeris exactitudinem a tabularum necessitate liberata: cum usu speciali ad lineam rhomborum nauticam, aptatumque illi planisphaerium”, Acta Eruditorum, (April 1691), pp. 178–182 (Leibniz: Parmentier, 1989, chap. 9, pp. [173]–185; Leibniz: Essais Scientifiques, 2005, N. 32; Leibniz: Heß-Babin, 2011, chap. 14, pp. 103–113). 87 Cf. Jac. Bernoulli, “Specimen alterum calculi differentialis … una cum additamento quodam ad problema funicularium, aliisque”, Acta Eruditorum, (June 1691), pp. 282–290. 88 Cf. A III,5 N. 36, pp. 158f. and pp. 160–163; HO, 10, pp. 127–134. 89 Cf. A III,5 N. 37, pp. 165–169; HO, 10, pp. 139–143.

1691–1693

443

of the catenary based on the quadrature of the hyperbola, and the rectification of the parabola. Huygens suggested that Bernoulli’s paper – having been sent to Leipzig in December 1690 – could very well have been communicated to Leibniz, a suspicion which was reinforced by his reading of a statement in Bernoulli’s published paper. Although Leibniz had given him an assurance of having had no prior knowledge of Bernoulli’s construction, Huygens considered it possible that he might at least have been privy to the fact that Bernoulli had a construction based on the quadrature of the hyperbola. Furthermore, a remark in Leibniz’s letter of October 13, 1690, suggested to him that Leibniz did not have the construction in question at that point. Leibniz, he suggested, might have avoided this trouble if he had sent his results in encoded form – in advance of publication – as he had been called upon to do a number of times. Replying on September 21, 1691, Leibniz first greeted the agreement found by Huygens between the three solutions, and he readily admitted never having contemplated the evolute of the catenary.90 He then addressed Huygens’ rebuke. The correspondent, Leibniz suggested, having established the reduction of the catenary to the quadrature of the hyperbola, had rightly supposed that they had obtained their results in a similar way. However, his suspicion had gone too far and had now produced a quarrel, or dispute, between them. He offered an assurance that the editors of the Acta Eruditorum had handled Bernoulli’s paper with confidentiality, not even informing him that this solution was founded on the quadrature of the hyperbola. Leibniz insisted, however, that he had an alibi, who could provide proof of his independent discovery. His alibi took the form of a letter sent to a friend in Florence – intended was of course Rudolf Christian von Bodenhausen – in late 1690, with the latter replying, on January 19, 1691, acknowledging the intelligence.91 As regards Huygens’ calls for him to send an encoded solution, he had been unable to comply and had considered it unnecessary. Furthermore, Leibniz thought that Huygens had distorted the sense of Johann Bernoulli’s statement in the published paper. Originally Bernoulli had understood the turn of the year 1690–1691 to be the deadline, after which the solutions, having been submitted by all parties, might be exchanged. He himself had been surprised to learn, on seeing the printed papers, that Bernoulli had reduced the problem to the quadrature of the hyperbola. Although he had no knowledge of how Bernoulli had arrived at this, he suspected that he had benefited from the new calculus. A further possibility was that the investigation of the loxodrome, or rhombic curve, might have suggested to Bernoulli the construction of the catenary. 90 Cf. A III,5 N. 39, pp. 171–179; HO, 10, pp. 156–162. 91 Cf. A III,5 N. 3, p. 27.

444

Chapter 3

Developing ideas of Willibrord Snel, Leibniz himself had demonstrated, in his April 1691 article “Quadratura arithmetica communis sectionum conicarum  … cum usu speciali ad lineam rhomborum nauticam”, that lines can be constructed as a sum of secants of arcs, and that this sum corresponds to the quadrature of the hyperbola. Jacob Bernoulli had treated the loxodrome curve in his June 1691 article “Specimen alterum calculi differentialis”, and had added a supplement on the catenary (“Additamento quodam ad problema Funicularium”). Huygens too, Leibniz recalled, in his solution had referred to the quadrature of a curve depending on the sum of secants of arcs, which he had obtained from tables. Leibniz now inquired about this matter, but he was careful to stress that his own approach had been different. In the same letter, Leibniz hit back at Huygens by suggesting that, firstly, since the correspondent had reduced the catenary to the sum of secants of arcs, and secondly, since he himself had reduced this sum to logarithms in his paper of April 1691, Huygens should have been able to understand the connection between the catenary and the quadrature of the hyperbola. Leibniz also stressed here a number of points arising from the investigation of the catenary – which supported the superiority of his calculus  – such as exponential expressions or logarithms, and their application to the catenary, and to the transformation of quadratures to those of hyperbola and circle. When Huygens replied – after a delay of almost two months, on November 16, 1691 – the tone of his letter was again conciliatory.92 He desired to learn how the new calculus had served Leibniz in obtaining the quadrature of the hyperbola from the catenary. He urged Leibniz to publish this example of the power of the calculus, and he promised that – if he himself were to find something different in his method – he would be willing to publish it too. As regards the doubts expressed in his previous letter, he was now entirely satisfied with Leibniz’s explanation. At first he had been taken aback by the words ‘quarrel’ or ‘dispute’, and the suggestion that he had distorted the sense of Bernoulli’s words. He had, he insisted, acted in good faith and the slight doubt that remained was of too little importance to warrant the use of such expressions in dealing with it. In the meantime, he had examined the work of Willebrord Snel Tiphys Batavus (1624),93 which had provided the inspiration for Leibniz’s approach to the loxodrome, and seen how Snel had demonstrated that longitudes could be obtained as a sum of secants. Following a method given by James Gregory – in

92 Cf. A III,5 N. 46, pp. 196–200; HO, 10, pp. 182–191. 93 Cf. W. Snellius, Tiphys Batavus, sive histiodromice, de navium cursibus et re navali, Leiden, 1624.

1691–1693

445

his Exercitationes geometricae (1668)94 – he himself had found the construction of the catenary and, in his view, more simply than by Leibniz’s analysis of the loxodrome, which he had not understood at the time of publication. Drawing on a paper commenced in October–November 1690,95 he communicated his method of finding the sum of secants to comply with Leibniz’s request. Once again, he urged Leibniz to make his analysis of curves available, even if the methods, such as the reduction of quadratures to those of circle and hyperbola, had yet to be perfected. The third issue, on which contention between Leibniz and Huygens arose, concerned Leibniz’s “methodus tangentium inversa”  – a cornerstone of his calculus, by which the construction of tangents was related to the finding of quadratures – and a rival method used by Nicholas Fatio de Duillier, the young Swiss mathematician who collaborated both with Huygens and Newton. In resuming their interrupted correspondence, on July 25, 1690, Leibniz sought to outline for Huygens the advantages of his calculus,96 referring to his fundamental papers in the Acta Eruditorum, which had appeared in the decade since their earlier correspondence. Taking the example of the cycloid, he attempted to show how the properties of transcendental curves might be simply described. This led Huygens to formulate, in his reply of August 24, 1690, two examples to test Leibniz’s “methodus tangentium inversa”.97 In late September and October 1690, Leibniz worked on a paper in which he attempted to solve these problems, employing exponential equations for the solution of the second problem in particular. In a series of drafts for an intended letter, Leibniz struggled to obtain the best means of communicating his results to Huygens.98 Though not yet perfected, Leibniz considered his method adequate for the solution of the problems proposed, depending only on the quadrature of the hyperbola, or logarithms. On reception of a further letter of October 9, 1690, from Huygens,99 Leibniz laid this intended letter aside, and he composed a reply, on October 13, in which he communicated his equation for the second of the inverse tangent problems, namely a transcendental exponential equation that could also be expressed as a differential equation.100 In a follow-up letter of November 7,

94 Cf. J. Gregory, Exercitationes geometricae, London, 1668, in particular pp. 14–17. 95 Cf. HO, 10, pp. 192–194. 96 Cf. A III,4 N. 267, pp. 534f. and pp. 536–538; HO, 9, pp. 448–452. 97 Cf. A III,4 N. 271, pp. 547–549; HO, 9, pp. 470–473. 98 Cf. A III,4 N. 282, pp. 588ff.; HO, 9, pp. 521–527. 99 Cf. A III,4 N. 280, pp. 584–586; HO, 9, pp. 496–499. 100 Cf. A III,4 N. 283, pp. 620f.; HO, 9, pp. 516–520.

446

Chapter 3

he provided further elaboration of this result.101 Notwithstanding Leibniz’s efforts, the entire question of transcendental equations still seemed obscure to Huygens, as is clear from his reply of November 18.102 In two subsequent letters from Leibniz, on November 24,103 and on December 5,104 respectively, further discussion of the two inverse tangent problems is to be found. It now became apparent that Leibniz and Huygens were following different conventions regarding signs in the subtangents, leading to quite different solutions. Then, on December 19, Huygens admitted a certain admiration for Leibniz’s solution.105 However, he remained skeptical that a universal rule might exist, and he recalled an inverse tangent rule, communicated to him in 1687 by Fatio de Duillier, that he had not yet been properly investigated. The discussion of the inverse tangent problems continued in early 1691. On February 6, Leibniz maintained that he had provided the solution of Huygens’ problems, not as a sign of the perfection of his method but rather of its utility.106 He considered his exponential expressions to be the most perfect method of representing transcendental curves, since they provided a finite equation containing only ordinary magnitudes in the exponents, and to be at all events superior to serial, or differential, forms of expression. Leibniz also enquired about Fatio’s inverse tangent rule alluded to by Huygens. From the latter’s reply on February 23, 1691, Leibniz learned that Fatio was then staying at The Hague.107 Huygens explained that – although he had meanwhile examined Fatio’s communication of 1687 – Fatio himself had in the meantime further developed the method, and had succeeded in finding the two curves corresponding to the two subtangents proposed by Huygens to Leibniz. However, Fatio was as yet unable to handle cases involving roots, and that contained unknowns, and more than a single term. Leibniz’s interest in Fatio’s method was now awakened. On March 2, 1691, he disclosed that the little he had seen of Fatio’s work had impressed him.108 As Fatio had found Huygens’ curves, he had most likely developed short cuts in his calculus. Leibniz then proposed that, if Fatio were to disclose his method for the solution of Huygens’ problems, he for his part would send examples of his method applied to cases where Fatio had encountered difficulties. Then, on 101 Cf. A III,4 N. 287, pp. 641–643 and 645f.; HO, 9, pp. 532–535. 102 Cf. A III,4 N. 291, pp. 654f.; HO, 9, pp. 536–540. 103 Cf. A III,4 N. 292, pp. 665–667; HO, 9, pp. 546–552. 104 Cf. A III,4 N. 293, pp. 670–675; HO, 9, pp. 555–559. 105 Cf. A III,4 N. 296, pp. 682–690; HO, 9, pp. 568–572. 106 Cf. A III,5 N. 6, in particular pp. 44–47; HO, 10, pp. 9–16. 107 Cf. A III,5 N. 8, in particular pp. 56f.; HO, 10, pp. 17–22. 108 Cf. A III,5 N. 9, pp. 59–62; HO, 10, pp. 49–52.

1691–1693

447

March 26, Huygens announced that he had proposed the exchange of methods to Fatio.109 However, the latter had reservations, and still hoped to master the outstanding difficulties with roots, and he was accordingly reluctant to send Leibniz what would be a rather lengthy treatise on the subject. On April 21, 1691, Huygens then announced the intensification of his cooperation with Fatio.110 The latter had confided his inverse tangent method to him, and they were developing the method further from day to day. It remained to be seen, Huygens wrote, if Fatio would find the means of handling composite roots in the subtangent, in which area Leibniz had made such progress. By early May, Fatio was beginning to see the exchange of papers with Leibniz as a worthwhile proposition. On the fifth of that month, Huygens explained that Fatio had encountered unexpected difficulties in applying his method to cases of subtangents having composite roots, and therefore had agreed to the proposed exchange.111 He gave an undertaking that Fatio’s method would be dispatched at once on receipt of Leibniz’s method. On May 27, Leibniz agreed to the exchange and promised to send his paper as soon as his official duties allowed.112 The correspondence between Huygens and Leibniz in the summer of 1691, was in fact dominated by discussion of the catenary solutions. However, a reminder by Huygens at the end of a letter of September 1,113 of the agreement made with Fatio, led Leibniz to suggest, near the end of his reply on September 21,114 a mutual acquaintance  – namely the theologian Gerhard Meier in Bremen – as an intermediary to receive their respective contributions. Leibniz then composed the paper entitled “A Method by which the construction of innumerable lines from a given property of a tangent, or the equation between abscissa and ordinate from the given value of the subtangent, is shown”,115 which was sent on October 5 to Meier, who duly confirmed its receipt on October 10.116 On November 16, Huygens wrote that he had been expecting Leibniz’s method for some time, and that he was now grieved that Leibniz was taking precautions as if he might not keep his word.117 He rejected out of hand the idea of exchanging the papers through Meier, and he called 109 Cf. A III,5 N. 13, pp. 83–86; HO, 10, pp. 55–58. 110 Cf. A III,5 N. 18, in particular p. 104; HO, 10, pp. 86–88. 111 Cf. A III,5 N. 21, pp. 111f.; HO, 10, pp. 93f. 112 Cf. A III,5 N. 22, p. 114; HO, 10, pp. 99f. 113 Cf. A III,5 N. 36, in particular p. 164; HO, 10, pp. 127–134. 114 Cf. A III,5 N. 39, in particular p. 178; HO, 10, pp. 156–162. 115 “Methodus, qua innumerarum Linearum Constructio ex data proprietate Tangentium seu aequatio inter Abscissam et Ordinatam ex dato valore Subtangentialis, exhibetur” (A III,5 N. 41, pp. 181–189; HO, 10, pp. 197–202). 116 Cf. A I,7 N. 196 and N. 199, respectively. 117 Cf. A III,5 N. 46, in particular p. 201; HO, 10, pp. 182–191.

448

Chapter 3

on Leibniz to fulfill his side of the agreement by sending the paper directly to him. Four days later then, on November 20, Meier forwarded Leibniz’s paper to Huygens.118 In this work, following an introductory treatment of the fundamentals of analysis, Leibniz turned his attention to the “methodus tangentium inversa”, and he stressed the ease with which the problem of inverse tangents could be reduced to quadratures. This was followed by an introduction to his infinitesimal calculus. The renowned Fatio, he explained, had failed in the application of his method when irrationals enter the equation of the subtangent, recalling in particular the example of the subtangent proposed by Huygens. A discussion of the nature of infinitesimals was then followed by an explanation of the terminology of the differential calculus. This calculus, Leibniz asserted, would be the key to the representation of transcendental curves by finite equations. Taking the cycloid as an example, he obtained the tangent to this curve, and he asserted that all the properties of the cycloid could be obtained analytically from such a calculation. Turning to the example given by Huygens, he obtained the general value of the subtangent, and the differential equation allowing the conversion of the problem of inverse tangents to quadratures. This was followed by further illustrations of this reduction to the quadratures of the circle and hyperbola. In December 1691 Huygens devoted himself to the study of the inverse tangent method of Leibniz, and he wrote a paper with the title “Methodus Leibnitii”.119 On December 18, he provided Fatio with a report on Leibniz’s “Methodus”,120 before replying to Leibniz on January 1, 1692.121 Huygens’ judgement on the merits of Leibniz’s paper was harsh. To begin with, he confessed a lack of familiarity with Leibniz’s calculus, and he admitted that he had wrestled with the paper before getting to the bottom of the matter. His conviction was that – in reducing the inverse tangent problem to quadratures – Leibniz’s method failed to provide the expected advantages. Testing the method on known curves, by assuming only a knowledge of their tangents, he found himself always confronted with impossible quadratures. The method failed to reveal whether a curve examined was geometrical or not, and whether or not it required quadratures, such as that of the hyperbola, for its construction. One would not achieve anything, if one was not able to obtain quadratures when possible, or at least know when they were impossible. All this, combined with 118 Cf. A III,5 N. 52, pp. 232f.; HO, 10, pp. 196–197. 119 Cf. HO, 20, pp. 542–546. 120 Cf. HO, 10, pp. 209–212. 121 Cf. A III,5 N. 52, pp. 232–236; HO, 10, pp. 221–225.

1691–1693

449

Leibniz’s assertion that this was the best method at his disposal, led Huygens to suggest that only a small sample of the method had been communicated. In the case of Fatio’s method, this would not be possible, for the method was such that to reveal a part would be tantamount to revealing the whole. Leibniz ought therefore, he suggested, to resolve to send the principal part of his method. Replying on January 8, 1692, Leibniz began the letter by having recourse to a metaphor of an evil spirit (“quelque esprit malin”), to which Huygens later added the words “little devil” (“petit demon”), who constantly managed to cause contention between then.122 Leibniz maintained that he chose to laugh at the malice of this demon. He expressed the hope that Huygens had not passed on his paper to Fatio, as he now desired to cancel the agreement made. Although, under the circumstances, Huygens would have the advantage of being privy to both methods, the damage would be limited. He would let it up to Huygens’ discretion to decide whether he should send something in exchange, but at all events he preferred not to be under obligation to others, and to be the subject of complaint. He remained convinced that he had fulfilled his part of the agreement, for he could say in good faith that to resolve the problem he needed only the means explained in his paper, namely the reduction of the problem to a self-evident quadrature, without resorting to a particular method of quadratures. He readily admitted that his method had its limitations, but he had understood that the same applied for Fatio’s method. As regards Huygens’ claim that it would be unjust to reveal all of Fatio’s method in exchange for only a part of his, Leibniz suggested that the constituent part in question might possibly be of greater value than Fatio’s method in its entirety. His own method succeeded, he suggested, in a multitude of cases including those involving transcendental quantities, where neither Fatio’s method, nor any other given up to that time, had succeeded. His infinitesimal calculus, Leibniz was convinced, was superior to that of Archimedes, in the same way that the geometry of Viete and Descartes had superseded that of Euclid and Apollonius. On February 4, 1692, Huygens then confirmed that he had not shown Leibniz’s paper to Fatio.123 However, he continued to insist that Leibniz had provided only a part of his method, finding it applicable only in cases where the inverse tangent problem had been reduced to the quadrature of the circle, or to that of the hyperbola. A further defect of Leibniz’s method – as Huygens saw it – was that it frequently related the problem to impossible quadratures, even though the curve considered might be simply geometrical. Nevertheless, 122 Cf. A III,5 N. 53, in particular pp. 236–239; HO, 10, pp. 225–230. 123 Cf. A III,5 N. 59, in particular pp. 252f.; HO, 10, pp. 238–240.

450

Chapter 3

he offered to communicate some discovery of his, if there was something Leibniz might care to have, in order not to be under obligation to him. Just as Leibniz believed he would be unlikely to profit much from an insight into Fatio’s method, the latter, for his part, appeared not to greatly desire Leibniz’s method either. Fatio claimed to be able to find the equation of the curve in a multitude of cases, from the given property of the tangent with composite incommensurables, and he insisted that he had successfully completed the task for the subtangent given by Leibniz, without having had recourse to quadratures. Finally, Huygens himself had doubts about Leibniz’s claims concerning the power of his calculus, in particular in investigations relating to the cycloid. The dispute was finally laid to rest in the Spring of 1692. Complying with the desire of Fatio,124 Huygens wrote to Leibniz (on March 15) that Fatio desired that he should reveal his method to Leibniz should he still be interested.125 The offer was politely declined by Leibniz on April 11, 1692.126 This survey of the correspondence of Leibniz and Huygens between 1690 and 1692, particularly in relation to the three mathematical issues, or disputes, considered, appears to support Leibniz’s assertion later in life – for example his remark to Nicolas Remond on March 14, 1714127 – that Huygens at first threw scorn on his infinitesimal calculus before finally acknowledging its superiority shortly before his death (viz. in 1693). More generally, in the unfolding correspondence in the early 1690s, we find that human character traits are revealed which represent important aspects of their respective personalities. It seems evident that, in elaboration and discussion of their respective systems (and particularly in mathematics), comradeship and rivalry, friendship and suspicion, unanimity and dissension, magnanimity and vanity, mutual affinity and antagonism, charm and strangeness, entered the personal relationship of Leibniz to his former mentor of the Parisian years.128 3

Natural Philosophy and Dynamics

Leibniz’s interest in the fundamental questions of natural philosophy  – and, in particular, in his most important discovery in the area of mechanics, namely the determination of the physical quantity that is conserved in 124 Cf. HO, 10, p. 259. 125 Cf. A III,5 N. 65, p. 277 and p. 280; HO, 10, pp. 268–270. 126 Cf. A III,5 N. 69, in particular p. 290; HO, 10, pp. 283–286. 127 Cf. Leibniz: Loemker, 1989 (Introduction, note 15), in particular chap. 68, p. 656. 128 Cf. O’Hara, 1996 (Introduction, note 27).

1691–1693

451

all mechanical changes (i.e. vis viva) – was indeed very much alive following his return to Hanover in 1690. The factors that contributed to this continuing interest included the unfinished state of his Dynamica de potentia et legibus naturae corporae, the appearance of Huygens’ Discours de la cause de la pesanteur (jointly with, or as an appendix to the Traité de la lumiere), and especially his correspondence with Papin that came about through the mediation of Johann Sebastian Haes. Newton’s Principia mathematica too continued to be an influence and, last but not least, the idea of his French correspondents Paul Pellisson-Fontanier and Simon Foucher of realizing a contrasting juxtaposition of the Cartesian and Leibnizian convictions, for the purpose of disquisition by “habiles Geometres”,129 resulted in a continued striving on Leibniz’s part for more succinct and comprehensible explanations of his most important propositions. The history of Leibniz’s principal work on dynamics begins in the year 1689, and it is documented primarily in his correspondence with Bodenhausen. However, at the beginning of 1691, central parts of the Dynamica were still missing, like the conclusion of the chapter on impact, and topics like the “problema staticum generale”, string tension, the construction of the thermometer, and finally an entire section about machines. Thus, on January 19, 1691, Bodenhausen wrote the following text about the lack of progress towards completion of the work: If I only had the end of the section on the collision of bodies, then I could have all of the tract or opus up to Miscellaneous ready, and order the figures with their numbers and engrave them in copper. In the meantime you could, Sir, replace, step by step and at your leisure, the promised supplements, like for instance the general problem of statics, likewise on the tension of strings or chords, the construction of the thermometer etc. [NB] but (that which I have omitted [namely]) the 4th section on machines (as you instructed me in your last table or index of sections and chapters, which order I am following) must come before Miscellaneous, and I wanted to gain time because of the many drawings or figures.130 129 Cf. A I,7 N. 110, p. 194. 130 “Hätte ich nur das ende sectionis De concursu corporum, so könte ich schon den gantzen Tractat oder Opus ante Miscellanea fertig halten v. die figuren mit ihren Zahlen ordiniren v. ins kupffer bringen. Unterdeßen k̈onnte M. h. H. mählich v. mählich die supplementa promissa, np. Problema staticum generale, item de tensione chordarum, constructione thermometri etc. mit guter weile ersetzen. [NB] Sed (quod omiseram) Sectio 4ta de Machinis (wie Er mir in Seiner letzten tabula oder indice sectionum et capitum geordnet, welcher ordnung ich folge) muß denen Miscellaneis vorgehen, v. wolte ich gerne wegen

452

Chapter 3

And, on June 23, 1691, Bodenhausen expressed himself quite indignantly regarding his impression of Leibniz’s inactivity here, and he announced that he was placing all his hopes in an early conclusion of the time-consuming “opus historicum” that seemed to be keeping Leibniz from higher-order thought, and from discoveries concerning the advancement of the sciences, viz. “inventis circa augmentum scientiarum”. Here Bodenhausen was in fact expressing very similar sentiments to those of Christiaan Huygens, who – for example in his letter of September 17, 1693 – expressed his regret that Leibniz was sacrificing his time for the realization of the Codex juris gentium opus.131 Bodenhausen’s exact words were: NB. From the opus on dynamics the end of the chapter on the collision of bodies is still missing, the same applies for the whole of the 5th section on machines; the same for the Preface etc. I wish that the Opus historicum could soon be brought to a happy conclusion, so that you can achieve in profundity, Sir, that which others cannot do, and it is a sin that your time for higher-order thoughts, and for discoveries concerning the progress of the sciences, is being wasted with such tedious and unnecessary matters.132 However, Bodenhausen’s judgement, namely that Leibniz had been preoccupied for months with historical research and had, accordingly, been inactive in the field of natural philosophy and dynamics, was premature. Leibniz had in fact written to him just one day earlier, informing him that he had communicated to Antonio Alberti (alias Amable de Tourreil) in Rome his thoughts about the nature of bodies, as well as about the overestimation of their physical extension, and that he had requested that Alberti pass on the text in question to their mutual friend Bodenhausen.133 Alberti, for his part, had independently turned to Bodenhausen with the request that he should try to motivate Leibniz der vielen figuren Zeit gewinnen” (A III,5 N. 3, p. 31; marginal emphasis here [“NB”] added by Bodenhausen). 131 Cf. A III,5 N. 185, p. 636; HO, 10, pp. 509–512. 132 “NB. Es mangelt annoch am Opere Dynamico das ende capitis De concursu corporum; item tota sectio 5a de Machinis; Item Praefatio etc. Wünsche, daß das Opus historicum ehest zu glücklichem ende gerathe, damit M. h. H. in altioribus das praestire, was andere nicht können, v. ist eine sünde, daß man mit solchen mühsamen v. unnöthigen sachen Ihm die Zeit zu höhern gedancken v. inventis circa augmentum scientiarum benimmet” (A III,5 N. 25, p. 127). 133 “Ich habe Herrn Alberti zu Rom auff begehren einige rationes communicirt, warumb nuda extensio naturam materiae nicht mache, und gebethen er mochte es doch M. h. H. communiciren” (A III,5 N. 24, p. 119).

1691–1693

453

to explain the cause of gravity. At the same time he had expressed the desire to learn the publication date of Leibniz’s Dynamica. And so, on December 1, 1691, Bodenhausen could inform Leibniz that: Mr Antonio Alberti has written to me recently from Rome and asked, Sir, to what extent your Dynamica was complete and in the press; I answered him however that the work was on hold for now due to many new ideas and related tracts arising, until you, Sir, have completed your ‘opus historicum’, and have more time and leisure to complete the work.134 To this Bodenhausen added that he would request Alberti to forward to him Leibniz’s demonstrations about the nature of matter.135 The aforementioned letter, which Leibniz sent to Alberti, was in fact published in the Journal des Sçavans of June 18, 1691.136 Also, in a letter to Paul Pellisson-Fontanier, from the second half of July, 1691, Leibniz developed his fundamental thoughts about force (“force”, “l’effort”, “conatus”) as the most important property of bodies,137 and he further expanded these formulations in a subsequent letter of November 19 (or 29), 1691, to include concepts like active and passive force.138 In the course of this initiative, he also sent important documents from his disputes in the 1680s with the Abbé Catelan and Nicolas Malebranche to France. He likewise referred to his discussion at that time with Antoine Arnauld and, accordingly, Pellisson initiated contacts with members of the Académie des Sciences.139 And so, at the turn of the year 1691–1692, Leibniz saw himself obliged to compose a written summary of his central thoughts on dynamics. This was perhaps also the reason why Leibniz asked the completely perplexed and irritated Bodenhausen, in a no longer extant letter of December 23, 1691 – referred to in the correspondent’s reply of January 12, 1692140 – to forward 134 “H. Antonio Alberti hat mir unlängsten von Rom geschrieben, v. gefraget, wie weit M. h. H. Dynamica nunmehr im druck verfertiget; ich habe ihm aber geantwortet, daß das werck wegen vieler newen gedancken v. zufallenden tractaten annoch ruhen müße, biß M. h. H. mit Seinem Opere Historico fertig, v. mehr zeit v. ruhe habe solches zu vollenden” (A III,5 N. 49, p. 210). 135 “Ich werde denselben ersuchen umb M. h. Hn demonstrationes circa naturam materiae, so er mir nicht communiciret” (p. 210). 136 Cf. A III,5 N. 24, p. 119, and the “Extrait d’une lettre … sur la question, si l’essence du corps consiste dans l’étendue”, Journal des Sçavans, (June 18, 1691), pp. 259–262. 137 Cf. A I,6 N. 99. 138 Cf. A I,7 N. 110. 139 Cf. A I,7 N. 120. 140 Cf. A III,5 N. 55, pp. 245f.

454

Chapter 3

his fair copy of the Dynamica to Hanover. In a subsequent letter of February 25, 1692, he was able to conciliate the correspondent with the explanation that he needed the manuscript only to refresh his memory of the content. His words here were: “As regards the manuscript on dynamics, I only asked for my fair copy of it so that I can complete it, because I have to a great extent lost my trains of thought concerning it”.141 In the meantime he had sent a newly composed text, whose title was Essay de dynamique, or Élémens de dynamique,142 with a letter of January 18, 1692, to Pellisson, but not without emphatically pointing out the difference to his projected Dynamica in the following words: A lot of other things come into my Dynamica, either to explain the whole à priori, or in order to show the use and the application to the solution of particular cases, but I have only taken that which appears to me to be more easy and convenient in design, to explain the general principle of the conservation of the absolute force.143 To this he added his wish that his essay be examined by Nicolas Malebranche in person.144 Unfortunately, this initiative on Leibniz’s part led to no more than a mere reading of the Essay de dynamique before the Académie des Sciences on July 28, 1692, by Philippe de La Hire, and to the production of transcripts. A public discussion about it, or even the requested transmission of a copy to Malebranche, never materialized. This envisaged copy, had it been forwarded on time, might well have been an influence on Malebranche’s tract Des loix de la communication des mouvemens, which appeared in the summer of 1692.145 Immediately after receiving this tract, Leibniz made notes on Malebranche’s

141 “Was betrifft das Manuscriptum dynamicum, so verlange ich mein exemplar nur darumb, damit ichs konne absolviren, den ich habe die ideen alzu sehr davon verlohren” (A III,5 N. 64, p. 276). 142 Cf. A. Foucher de Careil, Œuvres de Leibniz, publiées pour la première fois d’après les manuscrits originaux, avec notes et introductions, 7 vols, Paris, 1859–75 [= Leibniz: Œuvres de Leibniz], in particular vol. 1, 1859, pp. 470–483, and 1867 (2nd ed.), pp. 651–667; P. Costabel, Leibniz et la dynamique, Paris, 1960, pp. 97–106; P. Costabel (R. E. W. Maddison, trans.), Leibniz and dynamics: The texts of 1692, London, 1973. 143 “Il entre bien d’autre choses dans ma Dynamique, tant pour expliquer le tout à priori, que pour en monstrer l’usage et l’application à la solution des cas particuliers, mais je n’en ay pris, que ce qui me paroist plus aisé, et convenable au dessein, d’expliquer le principe general de la conservation de la force absolue” (A I,7 N. 129, p. 247; cf. annotation). 144 “Je voudrois que cet Essay pût estre examiné par le R. P. Malebranche luy même” (p. 247). 145 Cf. N. Malebranche (anon.), Des loix de la communication des mouvemens, Paris, 1692.

1691–1693

455

text,146 and  – through the intercession of Daniel Larroque147 – had them delivered to Malebranche. The latter replied to Leibniz directly with a letter of December 8, 1692,148 that was dispatched together with L’Hospital’s first letter to Leibniz of December 14, and which was written in the hand of an amanuensis.149 Apparently, under the influence of Malebranche’s tract, Leibniz undertook a further revision of the Essay de dynamique at the end of 1692.150 On July 12, 1692, Bodenhausen was able to report the dispatch to Venice of his fair copy of the Dynamica,151 and Leibniz confirmed its delivery in Hanover on October 5, 1692.152 Once he had perused the work, he realized that he would require more time than he then had in order to complete the opus. For his part, Bodenhausen believed he could accelerate the completion of the work in this way by forwarding his clean copy,153 yet Leibniz politely declined in a letter of July 22, 1693, since for him the overriding problem was the lack of time to proceed with the work.154 Already in the spring of 1692, Leibniz had undertaken a second attempt to gain the backing of French scholars for his Descartes critique, and the establishment of dynamics on a new foundation. On May 6, 1692, he sent a paper to Pellisson about the resultant of forces acting in different directions,155 intending it as a contribution for the Journal des Sçavans, and with the title “Règle générale de la composition des mouvemens par M. d. L.”156 However, 146 Cf. C. I. Gerhardt (ed.), Die philosophischen Schriften von Gottfried Wilhelm Leibniz, Berlin, 7 vols, 1875–1890; Hildesheim, Zürich, New York, 1961–62, and in particular vol. 1, pp. 346–349. 147 Cf. A I,8, p. 549. 148 Cf. note 146, in particular vol. 1, pp. 343–346. 149 Cf. A III,5 N. 120. Virtually all of L’Hospital’s letters to Leibniz were written in Paris and signed “Le M. De Lhospital” by the correspondent’s wife, namely the mathematician Marie-Charlotte de Romilley de la Chesnelaye, marquise de L’Hospital. The letters written in the hand of Charlotte de L’Hospital were those dated: February 24, 1693 (III, 5 N. 133); June 15, 1693 (III,5 N. 161); November 30, 1694 (III,6 N. 79); March 2, 1695 (III,6 N. 97); April 25, 1695 (III,6 N. 110); May 27, 1695 (III,6 N. 120); July 8, 1695 (III,6 N. 141); September 3, 1695 (III,6 N. 158); December 1, 1695 (III,6 N. 177); March 19, 1696 (III,6 N. 217); July 20, 1696 (III,7 N. 6); November 23, 1696 (III,7 N. 50); March 17, 1697 (III,7 N. 81); June 13, 1697 (III,7 N. 105); September 30, 1697 (III,7 N. 143); December 26, 1698 (III,7 N. 250); February 9, 1699 (III,8 N. 12); July 13, 1699 (III,8 N. 56), and June 9, 1701 (III,8 N. 267). 150 Cf. note 146, vol. 6, pp. 215–231. 151 Cf. A III,5 N. 91, pp. 342f. 152 Cf. A III,5 N. 108, p. 400. 153 Cf. A III,5 N. 125, p. 468, and N. 144, p. 536. 154 Cf. A III,5 N. 171, p. 599. 155 Cf. A I,7 N. 157. 156 Cf. the extant copy by G. F. Des Billettes: chap. 3 in Leibniz: Costabel, 1960 and 1973 (note 142 above).

456

Chapter 3

when Pellisson died on February 7, 1693, Leibniz’s text had still not appeared in print. L’Hospital’s communication of June 15, 1693,157 about the determination of tangents to focal curves, resulted in Leibniz undertaking in great haste a revision of his “Règle générale”, which he hurriedly sent, on July 23, 1693, to Paris,158 since he had reason to fear antecedence by a publication of L’Hospital on the same topic, as is evident from a letter of L’Hospital to Johann Bernoulli of September 21, 1693.159 Finally he had success, and, in the September 1693 number of the Journal des Sçavans, there appeared his contribution “Règle générale sur la composition des mouvemens”, and in addition two application examples.160 The Essay de dynamique, on the other hand, was to remain unpublished during Leibniz’s lifetime. Leibniz had already corresponded with Simon Foucher before his research tour to Austria and Italy and, on his return, he strove to revive this epistolary exchange. For this purpose he sent several letters to Paris. To his letter of March 23, 1691, to Christophe Brosseau161 – to which the aforementioned extract from his letter to Alberti was attached  – he finally received a reply from Foucher, which was dated May 30.162 When, in the following letter of December 31, Foucher reported that “Mr [Melchisédech] Thevenot is displeased that you have not imparted anything of your mechanics which you have left in Florence”,163 Leibniz felt obliged, in January 1692, to report in detail about the state of his Dynamica, which had been left in the hands of Bodenhausen in Florence for edition and publication. Although in an advanced state, and wanting only a wrap-up contribution from himself, he was confronted with the dilemma that his renewed consideration of the subject constantly led to a mêlée of new thoughts, for which he did not have the leisure to sort out. Thus he wrote to Foucher: The reason why I left my draft of a new science of dynamics in Florence, is that there was a friend there, who took it upon himself to arrange it and to prepare a fair copy, and even to publish it. And its publication only 157 Cf. A III,5 N. 161. 158 Cf. A III,5 N. 173, p. 610 and annotations. 159 Cf. Naturforschende Gesellschaft in Basel (ed.), Der Briefwechsel von Johann Bernoulli, Basel, 1955ff., in particular vol. 1, pp. 188–190, and specifically p. 190. 160 Cf. G. W. Leibniz, “Règle générale de la composition des mouvemens”, Journal des Sçavans, (September 7, 1693), pp. 417–419. 161 Cf. A I,6 N. 228. 162 Cf. A II,2 N. 114. 163 “Mr Thevenot est fasché de ce que vous ne nous avez pas fait part de vostre Mechanique que vous avez laisse à Florence” (A II,2 N. 132, p. 475).

1691–1693

457

depends on me because, the fair copy having been produced, I only need to send the conclusion. But every time I contemplate the matter, I have an abundance of new thoughts regarding it, for which I do not have the leisure to sort out.164 This passage  – along with other parts of the letter relating to philosophical axioms – appeared in the Journal des Sçavans of June 2, 1692,165 and in this way a public discussion with Leibniz about philosophical assumptions was initiated by Foucher that continued until August 1693.166 In addition, Foucher helped Leibniz to reestablish contact with Jean Gallois, and he convinced the latter to send Leibniz the numbers of the Mémoires of the Académie des Sciences that had hitherto been published, and for which Leibniz expressed his gratitude in a letter to Gallois, on December 8, 1692.167 Gallois even offered Leibniz the option of publishing his works in the Mémoires, and he in turn reacted by recommending the printing of his Essay de dynamique that had been sent to Pellisson. Following the latter’s death, Foucher regularly informed Leibniz about the whereabouts of the first version of this Essay, which he himself was yet to see half a year later. To begin with, it had remained among the papers in the sealed estate of Melchisédech Thévenot (who died on October 29, 1692), and then (in July 1693) it was in the hands of Pierre Varignon for appraisal. Towards the end of the triennium under consideration, the correspondence between Leibniz and Foucher  – in which, among other things, Leibniz’s Hypothesis physica nova of 1671, infinite divisibility and effective infinity were discussed  – suffered more and more from the public dispute between the two philosophers in the Journal des Sçavans, and finally it was interrupted for two years. Leibniz’s acquaintance with Denis Papin can be traced back to their time together in Paris, where Papin had served (from 1673 to 1675) as an assistant of Huygens, at the laboratory of the Académie des Sciences.168 A correspondence between Leibniz and Papin – his junior by one year – did, however, not 164 “La raison qui me fit laisser à Florence mon brouillon d’une nouvelle science de la Dynamique, est qu’il y eut un amy, qui se chargea de le debrouiller et de le mettre au net, et même de le faire publier. Et il ne tient qu’à moy qu’il paroisse, puisqu’il est mis au net, je n’ay qu’à y envoyer la fin. Mais toutes les fois que J’y pense, il me vient une foule de nouveautés là dessus, que je n’ay pas le loisir de digerer” (A II,2 N. 137, p. 494). 165 Cf. G. W. Leibniz, “Extrait d‘une lettre de M. de Leibniz à M. Foucher, Chanoine de Dijon, sur quelques axiomes de philosophie”, Journal des Sçavans, (June 2, 1692), pp. 247–249. 166 Cf. A II,2 N. 166, N. 185, N. 212, N. 219, N. 225, N. 226, N. 230 and N. 234. 167 Cf. A III,5 N. 118, pp. 443f. 168 Cf. A III,5 N. 56, p. 247.

458

Chapter 3

develop at first. Since Papin’s views on natural philosophy had been shaped by Descartes’ philosophical thought – a judgement that was likewise articulated by Huygens, in his letter to Leibniz of July 11, 1692, with the words “It is from those who[,] like Descartes[,] hold that the essence of a body consists solely in its extension”169 – it was inevitable that Leibniz would encounter Papin’s opposition to his assault on Cartesianism launched with the publication of his article “Brevis demonstratio erroris memorabilis Cartesii”, in March 1686.170 Papin’s rejoinder, entitled “De gravitatis causa et proportionibus observationes”,171 only appeared, however, after an interval of three years, in April 1689, when he had taken up a mathematical professorship and settled in Marburg. Papin’s defense of the natural philosophy of Descartes was directed not only against Leibniz, but also against Johann Christoph Sturm and Jacob Bernoulli, among others. Papin’s central argument rested on the assumption that the cause of gravity (“potentia”) is an ether vortex, which acts on a body with infinite velocity (at least in comparison the velocity of the body itself). Since this action at any instant occurs by virtue of an equal number of equally strong blows to the body, it is proportional to the elapsed time (and accordingly to the velocity attained by the body), and it is not proportional, for instance, to the traversed distance (and accordingly to the square of the attained velocity). The same proportionalities applied also for the resistance (“resistentia”) encountered by bodies in motion. Leibniz, following his return to Germany from Italy, encountered Papin’s article in the course of working through the Acta Eruditorum, and he composed at once (probably in Augsburg) his response, with the title “De causa gravitatis et defensio sententiae suae de veris naturae legibus contra Cartesianos”, which he dispatched from Vienna at the end of April 1690 to Otto Mencke in Leipzig, and which duly appeared in the May number of the journal.172 A not very flattering characterization of Papin – as a person who had not embraced

169 “Il est de ceux qui veulent avec des Cartes que l’essence des corps consiste dans la seule etendue” (A III,5 N. 90, specifically p. 338; HO, 10, pp. 296–304). 170 Cf. G. W. Leibniz “Brevis demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae, secundum quam volunt a Deo eandem semper quantitatem motus conservari; qua et in re mechanica abutuntur”, Acta Eruditorum, (March 1686), pp. 161–163, and “A brief demonstration of a notable error of Descartes and others concerning a natural law”, in: Leibniz: Loemker, 1989 (2nd ed.), chap. 34, pp. 296–302 (Introduction, note 15). 171 Cf. D. Papin, “De gravitatis causa et proprietatibus observationes”, Acta Eruditorum, (April 1689), pp. 183–188. 172 Cf. G. W. Leibniz, “De causa gravitatis et defensio sententiae suae de veris naturae legibus contra Cartesianos”, Acta Eruditorum, (May 1690), pp. 228–239.

1691–1693

459

his viewpoint, and who had gravely erred in his explanation of gravity173 – was at the center of this first communication to the editor of the Acta in the wake of the long Italian journey. Following a general rejection of Papin’s arguments, which included references to proofs from his own projected Dynamica, Leibniz turned, under the twelfth and final heading of his “De causa gravitatis”, to the attacks of Papin against himself. He accordingly defined force (“vis”), or indirectly an unequal force (“vim inaequalem”), in the following words: “And therefore I define that an unequal force exists in a place where, in the event of substitution [of the body] in another place, there ensues a mechanical perpetual motion”.174 From this, Leibniz concluded that the force is conserved in the bodies considered. However, it follows of necessity from his definition, that the forces are proportional to the product of weight and height (under the influence of terrestrial gravity). Otherwise  – as he demonstrated by means of a thought experiment – the possibility of a “motus perpetuus mechanicus” would arise, which was of course considered to be absurd.175 The condition for the validity of this conclusion on Leibniz’s part is – logically considered – the complete substitutability of the bodies incorporated in the definition of force and  – physically considered  – the complete transferability, or transmission, of the force between bodies. In conclusion, Leibniz attempted to provide proof that the source of the error on the side of the Cartesians lay in the circumstance, that many philosophers considered the total movement in the world to be a perpetual, and an inalterable or invariable magnitude. Papin’s reply followed this time after five months,176 even though it first appeared in print only in the January 1691 number of the Acta Eruditorum, with the title “Mechanicorum de viribus motricibus sententia”.177 This time Papin changed his argumentation strategy in that he consciously adapted it to that of his antagonist. First of all, he gave his definition of force (“potentia” or “vis”) as follows: “Of two bodies in motion, that one has more ‘potentia’, which is able to produce a greater effect; if neither of the two be so disposed, those bodies have 173 Leibniz justified his response to Papin with the following words: “da er doch mein argument gar nicht eingenommen und auch in explicatione gravitatis sehr geirret” (cf. A I,5 N. 329, p. 572). 174 “Itaque vim inaequalem habere hoc loco definiam, quorum unum si surrogare liceret in alterius locum, oriri posset motus perpetuus mechanicus” (note 172, p. 234; [emphasis in italics by Leibniz]). 175 Cf. G. Freudenthal, 1999–2002 (Introduction, note 50). 176 Cf. A I,6 N. 135. 177 Cf. D. Papin, “Mechanicorum de viribus motricibus sententia, asserta a D. Papino adversus Cl. G. G. L[eibniz] objectiones”, Acta Eruditorum, (January 1691), pp. 6–13.

460

Chapter 3

equal forces”.178 Additionally, he remarked that the effect would be measured neither by the distance covered, nor by the duration of the motion, but rather exclusively by the resistance to be overcome. On the basis of these preconditions, he then refuted Leibniz’s thought experiment, whereby he denied above all the possibility of a complete transferability, or transmission, of the force. In this very assumption he saw the source of Leibniz’s error. Leibniz now also allowed himself more time, sending his next contribution only in August, 1691, evidence for the existence of which is provided by Mencke’s reply, of August 24, to Leibniz’s no longer extant letter of August 16.179 The article in question on the laws of nature and the true estimation of moving forces, set against that of the Cartesians, was entitled, accordingly, “De legibus naturae et vera aestimatione virium motricium contra Cartesianos”, and it appeared in the journal one month later.180 A week before this mailing to Mencke, Leibniz had dispatched his first (non-extant) letter to Haes, in the form of an attachment to a letter addressed to Friedrich Lucae of August 9.181 Leibniz hoped to obtain information from Papin’s confidant Haes about the activities of his opponent, and perhaps even to initiate a direct correspondence, as is apparent from his flattering characterization of him in the following words from the letter to Lucae: “The inventions and excellent thoughts of the ingenious Mr Papin have been known to me for many years already. I believe I have already met him once in Paris when he was working with Mr Huygens”.182 In the article “De legibus naturae”, Leibniz attempted above all to refute Papin’s argument regarding the non-transferability, or non-transmissibility, of the total force of a body in that he declared the pure-thought assumption of such a transfer from one place to another (“unum in alterius locum substitui”) to be sufficient. He considered himself not to be obliged to offer the means of realizing such a transfer, or substitution (“modum actu183 efficiendi hanc substitutionem”). He also believed that, in the event that “causa” and “effectus” were not equivalent, the wisdom of the Creator would be derogated. The proof – demanded by Papin – of the complete transfer, or transmission, of force 178 “Duorum corporum in motu illud habet plus potentiae, quod potest plus effectus producere: si vero neutrum sit ejusmodi, illa corpora habent vires aequales” (p. 7). 179 Cf. A I,7 N. 169. 180 Cf. G. W. Leibniz, “De legibus naturae et vera aestimatione virium motricium contra Cartesianos. Responsio ad rationes a Dn. P. mense Januarii proximo in Actis hisce p. 6 propositas”, Acta Eruditorum, (September 1691), pp. 439–447. 181 Cf. A I,6 N. 348, cf. p. 595. 182 “Ingeniosissimi Papini inventa et meditationes egregiae mihi a multis jam annis fuere notae. Credo me ipsum jam olim vidisse Parisiis cum apud Dn. Hugenium ageret” (p. 595). 183 emphasis by Leibniz.

1691–1693

461

from a body of greater mass to one of lesser mass, he provided once again by means of a thought experiment. He also formally defended the possible existence of a body having perfect or total hardness that had been denied by Papin. The issue for Leibniz was not that such perfect hardness might actually exist in the real world, and for him it would suffice that it be conceivable without contradictions. In addition, the deviation from the condition of perfect hardness could be assumed to be arbitrarily small. Subsequently, Leibniz offered new arguments to support his views: he measured the quantity of effect (“quantitas effectus”) not by (or by means of) gradational or incomplete entities (“entibus modalibus sive incompletis”), but rather by substantial or absolutely real (“substantiis seu realibus absolutis”) entities. Equal forces would then exist, if an equal number of elastic springs, each having the same resilience or tension force and being in the same state of stress, were to be traversed, or overcome. Only the real measure of the forces (“realis virium mensura”) would fulfill the transferability, or transmission, requirement of the laws of nature and of the science of estimating in general (“Scientia aestimandi in universum”). Following a further letter from Leibniz to Haes, at the end of November 1691,184 the stage was finally set for a direct correspondence with Papin. Haes’ reply (of January 31, 1692),185 had as an enclosure the first letter (of January 23, 1692) from Papin to Leibniz,186 together with an addendum,187 in which Papin articulated his reply to Leibniz’s “De legibus naturae”. With this step, the dispute – which had thitherto been conducted publicly in the Acta Eruditorum – was relocated to the private correspondence between Leibniz and Papin.188 This was much to the satisfaction or pleasure of the editor of the journal, Otto Mencke, who expressed his desire to publish a summary account of the outcome once the dispute had been resolved. Thus, he wrote the following lines to Leibniz, on April 16, 1692: “That you, Sir, will otherwise debate the controversy with him in private is most welcome to me, for indeed it is best that, once you reach an agreement, a short account of it be included in the Acta”.189 184 Cf. A III,5 N. 48. 185 Cf. A III,5 N. 58. 186 Cf. A III,5 N. 56, pp. 246f. 187 Cf. A III,5 N. 57, pp. 247–251. 188 Cf. E. Gerland, Leibnizens und Huygens’ Briefwechsel mit Papin nebst der Biographie Papin’s, Berlin, 1881 and Wiesbaden, 1966; L. de la Saussaye, A. Péan, L. de Belenet, La vie et les oeuvrages de Denis Papin, vols. 7–8 (Correspondence), Blois, 1893–1894. 189 “Daß sonst M. h. Herr seine controvers mit ihm privatim debattiret, ist mir sehr lieb; dan es freylich am besten, daß wan Sie sich verglichen, eine kurtze relation davon ad Acta gebracht werde” (A I,7 N. 381, p. 668).

462

Chapter 3

In the first phase of the correspondence between Leibniz and Papin (January to December 1692), sixteen letters were exchanged between the adversaries in the dispute. This correspondence included a piece giving a synopsis of the controversy about the true measure of moving force, which was written by Papin in late October, or early November, for the Acta Eruditorum with the title “Synopsis controversiae circa legitimam virium motricium aestimationem excerpta a D. Papin”. It was forwarded to Leibniz who added more than fifty marginal annotations and commentaries.190 In November, Leibniz also composed three drafts for a piece of his own, likewise intended for the Acta Eruditorum, either before or after receiving Papin’s “Synopsis controversiae”.191 Leibniz probably failed either to return Papin’s piece to Leipzig, or to dispatch his own piece to Mencke or Papin.192 Subsequently, the correspondence was interrupted for a period of two and a half years, until the summer of 1695. There was but a single communication in this period from Papin,193 which was forwarded with Haes’ letter of May 11, 1693, to Leibniz.194 4

Physics: Celestial and Terrestrial Mechanics

During his tour of Austria and Italy, Leibniz had studiously and copiously worked on the theory of planetary motion. While in Vienna, he composed his main article on this topic, namely his probe or test piece on the causes of celestial motions, entitled “Tentamen de motuum coelestium causis”,195 and subsequently, in the course of the Italian journey, he came to the conclusion that a revision of the text was essential. Following his return, the theory of planetary motions was again and again a topic in his correspondence with Huygens. Leibniz understood his treatment of the matter as an alternative portrayal to the explanations given in Newton’s Principia mathematica (1687),196 and in Huygens’ Discours de la cause de la pesanteur (1690). The kernel of Leibniz’s theory was an ether vortex rotating about the sun and causing the movement of the planets. This movement could be resolved into two 190 Cf. A III,5 N. 114, pp. 422–433. 191 Cf. A III,5 N. 116, pp. 435–441. 192 Cf. annotation, p. 435. 193 Cf. A III,5 N. 150, pp. 552f. 194 Cf. A III,5 N. 149, pp. 549–552. 195 Cf. G. W. Leibniz, “Tentamen de motuum coelestium causis”, Acta Eruditorum, (February 1689), pp. 82–96; “An essay on the causes of celestial motions” in: D. Bertoloni Meli, 1993 and 2002, pp. 126–142 (Introduction, note 74). 196 Cf. Bertoloni Meli, 1993 and 2002 (Introduction, note 73).

1691–1693

463

components, namely a circular motion (“circulatio harmonica”), and a radial motion (“motus paracentricus”) of the celestial body and, through a combination of these components, both the elliptical planetary orbits and the first two laws of Kepler were obtained. Leibniz held the view that – through the introduction of the harmonic circular motion – he had succeeded for the first time in establishing a physical explanation of Kepler’s laws of planetary motion. However, he was unable to embrace Newton’s conception of gravity, and of planetary motions, produced exclusively by gravitation. He preferred rather to presuppose the existence of an ether, and of Cartesian vortices. At the same time he found similarities between his own conception of the centrifugal force, arising from a rotating ether, and Huygens’ explanation of the law of gravity. Terrestrial gravity should, according to Leibniz, have the same cause as the attraction between the planets, and between massive bodies, namely rotating ether vortices. His understanding of gravity also led him to the supposition of rays of attraction, which he conceived as analogous to light rays and whose inverse square law was the analog of the photometric inverse square law. Thus, he wrote to Huygens on April 11, 1692: “I believe that also according to this manner of explaining gravity, by the centrifugal force of a very subtle fluid, one can conceive [it] as rays of gravitation”.197 His vortex theory also allowed Leibniz to explain further phenomena, like the round or spherical form of the terrestrial globe and of water drops, respectively, as well as the parallelism of the earth’s axis and those of the other planets of the solar system. For Huygens, on the other hand, Leibniz’s theory was inapprehensible, and so, in his reply of July 11, 1692, he wrote: If you approve of my explanation of gravity, I do not see how you could understand that such a movement of ambient matter can cause the roundness of water drops, and the gravitational attraction of lead towards the earth, or of the planets to the sun … I also fail to see how the cause I have given for gravity might coincide with the attraction which you attribute to rays coming from the center.198 197 “Je crois qu’encor selon cette maniere d’expliquer la pesanteur, par la force centrifuge d’un fluide tres subtil, on peut concevoir comme des rayons d’attraction” (A III,5 N. 69, specifically p. 288; HO, 10, pp. 283–286). 198 “Si vous approuvez mon Explication de la Pesanteur, je ne vois pas comment vous pouvez comprendre qu’un semblable movement Materiae ambientis puisse causer et la rondeur des goutes d’eau, et la Pesanteur du plomb vers la Terre, ou des Planetes vers le soleil … Je ne vois pas non plus comment la cause que je donne de la Pesanteur, puisse coincider avec l’attraction que vous concevez par des rayons emanants du centre” (A III,5 N. 90, specifically p. 336; HO, 10, pp. 296–304).

464

Chapter 3

Neither the published “Tentamen”, nor Leibniz’s explanations in his letters, could convince Huygens of the confirmability of Leibniz’s theory. Although Huygens continued to be more than skeptical, Leibniz resolutely continued his efforts to show an equivalence, or agreement, between their rival systems. He firmly believed that the very different conceptions could be harmonized, and he expressly included the Newtonian position here, when he wrote the following to Huygens, on September 26, 1692: “It is necessary to examine which explanation is the best, or if one can reconcile them. The same can be said about Mr. Newton’s explanation of ellipses”.199 Huygens, however, upheld his rejection of Leibniz’s understanding of things. Notwithstanding some concededly positive aspects of the vortex theory, he expressed his conviction of the superiority of his own theory, in his letter of January 12, 1693.200 Whereas, with Leibniz’s vortex theory, certain phenomena – as, for example, the fact that the planets all rotated in the same direction – were easy to explain, with others – like the constant eccentricity of the planetary orbits, the acceleration and deceleration of celestial bodies along their orbital paths, or the movement of comets through rotating vortices – explanation proved more difficult. Although Leibniz conceded these difficulties, in his letter of March 20, 1693, he upheld the possibility of bringing the competing systems into mutual agreement.201 Towards Newton he had likewise been expressly conciliatory, when he wrote the following, three days earlier, in the opening letter of their direct correspondence: To the illustrious Mr Isaac Newton … Wonderful is that which you have discovered to produce Keplerian ellipses, by simply supposing attraction or gravitation and trajectory, although I tend to the belief that all this is achieved or guided by the motion of an ambient fluid, analogous to gravity and magnetism around us; nothing of this however detracts from the dignity and verity of your discovery.202 199 “Il faudra examiner quelle explication est la meilleure, ou si on les peut concilier. Le même se peut dire à l’egard de l’explication de Mons. Neuton des Ellipses” (A III,5 N. 106, specifically p. 389; HO, 10, pp. 316–321). 200 Cf. A III,5 N. 123, specifically pp. 456–458; HO, 10, pp. 383–389. 201 Cf. A III,5 N. 140, specifically pp. 515–517; HO, 10, pp. 425–432. 202 “Illustri Viro Isaaco Neutono  … Mirificum est quod invenisti Ellipses Keplerianas prodire, si tantummodo attractio sive gravitatio et trajectio in planeta concipiantur, tametsi enim eo inclinem, ut credam haec omnia fluidi ambientis motu sive effici sive regi, analogia gravitatis et magnetismi apud nos; nihil tamen ea res dignitati et veritati inventi tui detraxerit” (A III,5 N. 139, pp. 512–514, in particular p. 513); cf. H. W. Turnbull et al. (eds), The Correspondence of Isaac Newton, 7 vols, Cambridge, 1959–1977, and in particular vol. 3, 1961, pp. 257f. with facsimile.

1691–1693

465

Closely connected with the theory of planetary motion were questions regarding sun spots, referred to in correspondence with Augustinus Vaget (Vagetius),203 who had presided over the examination of a dissertation entitled Dissertatio de maculis in sole visis (1693),204 and also questions about the nature and motion of comets in the solar system. These matters were treated in letters for Edmond Halley (on June 3, 1692),205 from Erhard Weigel (on February 18, 1693),206 to Vagetius (on October 7, 1693),207 and from Newton (on October 26, 1693).208 Leibniz considered in particular the observed tails of comets to be purely optical phenomena, whereas others accorded them a material character. Another astronomical topic discussed was Huygens’ work on parhelia, or mock suns, from 1670.209 On March 2, 1691, Leibniz directed the following query, together with an exhortation for the publication of Huygens’ tract on dioptrics, writing: “I remember that you have formerly treated the cause of parhelia, I hope that you will include an illustration in your Dioptrica and that you will [soon] give us this longed-for work after so many delays”.210 In his reply, on March 26, Huygens simply announced that: “The demonstration of parhelia will be in my Dioptrica, on which I will be working this summer”.211 Alas, Huygens’ Dioptrica was only published posthumously in 1703.212 The shape of the earth was a further topic considered in Leibniz’s correspondence with Huygens in the early 1690s. At the center of attention here was Leibniz’s critical assessment of the value of a book, published in the year 203 Cf. A III,5 N. 129 (p. 486), N. 135 (p. 501), and N. 181 (p. 621). 204 Cf. A. Vagetius, M. E. Ettmüller, De maculis in sole visis disseret praeses M. Augustinus Vagetius, [et] respondens Michael Ernestus Ettmüllerus, Wittenberg, 1693. 205 Cf. A III,5 N. 80, p. 314. 206 Cf. A III,5 N. 132, p. 493. 207 Cf. A III,5 N. 189, pp. 641f. 208 Cf. A III,5 N. 194, pp. 655–658, in particular p. 657; Newton: Correspondence, vol. 3, 1961, pp. 285f. 209 Cf. Ch. Huygens, “An account of the observations, made by the Philosophical Academy at Paris … together with a discours … concerning the cause … of parelia’s or mock-suns”, Philosophical Transactions, (June 20, 1670), pp. 1065–1074, and also: HO, 6, p. 162 and HO, 7, p. 11 and p. 41. 210 “Je me souviens, que vous avés traité autres fois de la cause des parelies, j’espere que vous en mettrés la demonstration dans vostre dioptrique, et que vous nous donnerés après tant de delais cet ouvrage si desiré” (A III,5 N. 9, specifically p. 62; HO, 10, pp. 49–52). 211 “La demonstration des Parelies sera dans ma dioptrique, à la quelle je vay travailler cet Esté” (A III,5 N. 13, specifically p. 88; HO, 10, pp. 55–58). 212 Cf. Ch. Huygens (B. de Volder, B. Fullenius eds.), Opuscula postuma, quae continent Dioptricam, Leiden, 1703. Regarding coronae and parhelia, cf. “De coronis et parheliis”, HO, 17, pp. 351–362; “Traité des couronnes et des parhélies”, HO, 17, pp. 364–445; HO, 17, Appendices I–XV, pp. 446–516.

466

Chapter 3

1691 by Johann Caspar Eisenschmidt, with the title Diatribe de figura telluris elliptico-sphaeroide,213 in which the author postulated an elliptical-spheroidal shape of the earth. Unlike Newton and Huygens, however, he assumed the earth to have an excess of mass at the poles rather than at the equator. On January 8, 1692,214 and again on February 19, 1692,215 Leibniz sought Huygens’ opinion about the matter. Although he had only read a short account of the work in the Acta Eruditorum,216 Huygens likewise doubted the correctness of Eisenschmidt’s conclusion, a view he expressed in his reply of March 15, 1692. Here he wrote: It seems to me that he is building on a very insecure foundation, knowing the different measures that have been made of the terrestrial globe. For one knows how divided among themselves the observers are who have worked in the same clime. One observes furthermore that Jupiter is elliptical in the sense of Mr Newton and me, and reason will have it so, whereas there is nothing in favor of an elliptic figure in Mr Eysenschmid[’s work].217 Huygens thus attached considerable doubt to the hypothesis of Eisenschmidt, but he reserved nonetheless a final judgement in the matter until reliable results of the then ongoing longitude determinations became available. Through the clocks, which he had developed for these measurements, Huygens was himself directly involved in this effort. On July 11, 1692, he finally reported that he had – having at last read Eisenschmidt’s Diatribe – compiled a list with several objections. Notwithstanding these, however, he was left with a good impression of the work in question, it appearing to him to be scholarly and well-written.218 During his grand tour of Austria and Italy Leibniz also gave attention to the question of the movement of a body in a resisting medium. Almost simultaneously with the “Tentamen”, he composed the essay, or schediasm, on the resistance of a medium and on the motion of heavy projectiles in a resisting 213 Cf. J. C. Eisenschmidt, Diatribe de figura telluris elliptico-sphaeroide, Straßburg, 1691. 214 Cf. A III,5 N. 53, specifically p. 242; HO, 10, pp. 225–230. 215 Cf. A III,5 N. 63, specifically p. 270; HO, 10, pp. 260–263. 216 Cf. Acta Eruditorum, July 1691, pp. 315f. 217 “Il me semble qu’il bastit sur un fondement fort peu seur, savoir les differentes mesures qui ont esté faites du globe Terrestre. Car on sçait combien different entre eux les observateurs qui ont travaillé sous le mesme Climat. On observe d’ailleurs que Jupiter est Elliptique dans le sens de Mr Newton et de moy, et la raison le veut, au lieu qu’il n’y en a point pour la figure Elliptique de Mr Eysenschmid” (A III,5 N. 65, specifically p. 278; HO, 10, pp. 268–270). 218 “Il paroit docte au reste et ecrit bien” (A III,5 N. 90, specifically p. 337; HO, 10, pp. 296–304).

1691–1693

467

medium, with the title “Schediasma de resistentia medii, et motu projectorum gravium in medio resistente”.219 Both of these works represent alternative proposals to the views of Newton presented in his Principia mathematica of 1687. Through his efforts – undertaken in his correspondence at the end of 1690 and in early 1691 – to make his results understandable for Huygens, it became evident to Leibniz that he needed to revise the “Schediasma” and correct mistakes in it. This was done in the article “Additio ad Schediasma de medii resistentia”, in the Acta Eruditorum in April 1691,220 and to which he referred in a letter to Huygens on July 24, 1691.221 Already on February 23 of that year, Huygens had come to realize that Leibniz had adopted a different definition of resistance to his, and that of Newton, and so he wrote on that occasion: “It is evident that you take the effect of the resistance for the resistance itself. But to Mr Newton and to me the resistance is the pressure of the medium against the surface of a body”.222 A considerable part of Huygens’ comprehension difficulties was in fact rooted in this different understanding of “resistentia”. Leibniz, in his reply of March 2, maintained that he had sufficiently explained his position, but did not underestimate the danger of such misunderstandings. Thus he wrote: I had believed myself to be able to estimate the resistance by its immediate effect, that is to say by the reduction of the velocity of the body that senses it, and I have expressed myself very much in the above sense throughout my discourse, but I do accept that it demands attention.223 5

Physics: Optics

Leibniz’s thoughts on optics at this juncture were likewise influenced by the works of Huygens and Newton. From the autumn of 1690, he occupied himself with Huygens’ recently published Traité de la lumière. An intended detailed 219 Cf. G. W. Leibniz, “Schediasma de resistentia medii, et motu projectorum gravium in medio resistente”, Acta Eruditorum, (January 1689), pp. 38–47. 220 Cf. G. W. Leibniz, “Additio ad schediasma de resistentia medii publicatum in Actis mensis Febr. 1689”, Acta Eruditorum, (April 1691), pp. 177f. 221 Cf. A III,5 N. 29, specifically p. 135; HO, 10, pp. 109–112. 222 “il est evident que vous prenez l’effect de la resistence pour la resistence mesme. Mais à Mr Newton et à moy la resistence est la pression du milieu contre la surface d’un corps” (A III,5 N. 8, specifically pp. 54f.; HO, 10, pp. 17–22). 223 “J’avois crû de pouvoir estimer la resistence par son effect prochain, c’est à dire par la diminution de la vistesse du corps, qui la sent, et je m’estoit assés expliqué là dessus dans tout mon discours, mais j’advouë qu’il demande de l’attention” (A III,5 N. 9, specifically p. 59; HO, 10, pp. 49–52).

468

Chapter 3

discussion he put off again and again,224 and so, on March 26, 1691, Huygens had to remind him of his treatise on optics in the following the words: “You will also tell me some day how you find my explanations of refraction and of Iceland spar, about which I have not heard a word from you until now”.225 Only after more than a year had elapsed, on April 11, 1692, did Leibniz finally express his views regarding Huygens’ wave theory of refraction, and double refraction, in the following words: I believe I have indicated more than once that your recent treatises have given me infinite pleasure. This explanation of Iceland Spar is like a proof of the correctness of your reasoning on light; there was but a single circumstance about which you had not yet provided satisfaction, but maybe it has been explained in the meantime.226 Leibniz was thinking here of the phenomenon of the polarization of light that Huygens had observed but not explained. Huygens’ explanation of colors, which Leibniz found wanting in the Traité, also interested him very much. Already on August 24, 1690, Huygens had informed him about intimations made by Newton, during a meeting they had in the summer of 1689, concerning a planned work of his on optics, as well as about new experiments on the theory of colors.227 Thereupon, Leibniz requested further information, first of all from Huygens, on January 8, 1692,228 then from Halley, on June 3, 1692,229 and finally from Newton himself, on March 17, 1693, when he wrote: Huygens has indicated to me that you communicated to him certain new phenomena of colors. I desire very much that it be possible to deduce the explanation of those colors, called fixed colors, from appearances, or that

224 Cf. A III,4 N. 282, pp. 597–600, and pp. 609f.; HO, 9, pp. 521–527. 225 “Vous me direz aussi quelque jour comment vous trouvez mes Explications de la Refraction et du Cristal d’Islande, de quoy jusqu’icy je n’ay pas appris la moindre chose” (A III,5 N. 13, specifically p. 88; HO, 10, pp. 55–58). 226 “Je crois d’avoir marqué plus d’une fois, que vos derniers traités m’ont plû infiniment. Cette explication du Crystal d’Islande est comme une épreuve de la justesse de vos raisonnemens sur la lumiere, il y avoit une seule circonstance sur laquelle Vous ne Vous aviés pas encor satisfait, mais peutestre, qu’elle aura esté éclaircie depuis” (A III,5 N. 69, specifically pp. 287f.; HO, 10, pp. 283–286). 227 Cf. A III,4 N. 271, specifically p. 547; HO, 9, pp. 470–473. 228 Cf. A III,5 N. 53, specifically p. 242; HO,10, pp. 225–230. 229 Cf. A III,5 N. 80, p. 314.

1691–1693

469

the means of producing them by refractions can be shown, such that all of a certain surface shows a specific color.230 While Newton confirmed Huygens report, in his reply of October 26, 1693, he was not prepared to reveal his results. Even his intended work on optics was put in a long-term context, not least in order to avoid controversy, or in his words: I think I have discovered the certain explanation of the phenomena of colors, both apparent (as they are called) and fixed but I desist from publishing a book, lest the ignorant (or unliterate) direct disputes or controversy towards me.231 Leibniz was most impressed by the power and capability of Huygens’ wave theory of light, especially by the derivation of the law of refraction it facilitated. In this, he thought, Huygens had outclassed his predecessors, namely the Jesuits Ignace Gaston Pardies and Pierre Ango, as he explained in a letter to Tschirnhaus, on January 30, 1693, in the following words: As regards the theory of light, the Huygenian waves are nothing other than a certain means of considering pressure … I liked very much that in this way the sine law of refraction is so beautifully derived. The good pater Pardies, or following him pater Ango in his Dioptrica, were hardly successful at all.232 For all that, a theory of light lacking an explanation of colors remained for Leibniz incomplete. And so he continued: I desire to see the fixed colors properly explained, at least from an evident hypothesis. Namely, one takes as known the colors produced by a (water) 230 “Significavit mihi Hugenius, nescio quae nova phaenomena colorum sibi a Te communicate. Ego valde optem ut ratio colorum quos fixos vocant, ex apparentibus deduci possit, seu ut ostendatur ratio efficiendi per refractiones, ut tota aliqua superficies certum colorem ostendat” (A III,5 N. 139, p. 514). 231 “Colorum phaenomena tam apparentium ut loquuntur quam fixorum rationes certissimas me invenisse puto sed a libris edendis manum abstineo ne mihi lites ab imperitis intententur et controversiae” (A III,5 N. 194, p. 657). 232 “Was die theoriam Luminis betrifft, so seind die undae Hugenianae nichts anders als ein gewißer modus pressionem considerandi … Mir hat sehr gefallen, daß dadurch die lex refractionis so artlich herauß komt secundum sinus. Der guthe Pater Pardies, oder auß ihm der P. Ango in seiner dioptica, haben schlecht bestanden” (A III,5 N. 130, p. 488).

470

Chapter 3

drop or a prism, and, leaving aside their final cause, asks further how with their help consistent and constant colors can be obtained.233 In a letter to Bodenhausen, on July 22, 1693, Leibniz praised the work Dioptrica nova, which had been published in 1692 by the Dublin physicist William Molyneux.234 Thus, he wrote on that occasion: Mr Molineux has published a work Dioptrica in the English language containing much that is good as regards both practice and theory. He avails very much there of my thoughts concerning a universal principle of the direction of rays common to optics, catoptrics and dioptrics.235 In Dioptrica nova,236 which was the first treatise in English on dioptrics, the author had presented parts of Leibniz’s article “Unicum opticae, catoptricae et dioptricae principium” (1682),237 in an English translation, and had given Leibniz priority for the formulation of Fermat’s principle, which of course clearly preceded it in time. Pierre de Fermat’s mature thinking on optics,238 which dated from the late 1650s, had been communicated in his correspondence and in his works Synthesis ad refractiones and Analysis ad refractiones of 1662.239 Leibniz, in his 1682 article, had suggested that light follows the path of least resistance, in contrast to Fermat’s principle of least time. Leibniz’s 233 “Ich wündschte die colores fixos recht erclaret zu sehen; ad minimum ex hypothesi apparentium. Nehmlich man nehme vor bekand an die farben, die ein tropfen oder das prisma gibt, deren endtliche ursach dahinstellend, und frage weiter, wie mit deren hulff beständige durchgehende farben zu wege zubringen” (p. 488). 234 Regarding Molyneux, cf. Simms (P. H. Kelly, ed.), 1982 and J. G. O’Hara, 2004 (Introduction, note 90). 235 “M. Molineux hat eine Dioptricam in Englischer Sprach herausgeben, darinn viel guthes quoad praxin et theoriam. Er approbiret darinn sehr meine gedancken de principio universali directionis radiorum opticae catoptricae et dioptricae communi” (A III,5 N. 171, p. 602). 236 Cf. W. Molyneux, Dioptrica nova: A Treatise of Dioptricks, in two parts. Wherein the various effects and appearances of spherick glasses, both convex and concave, single and combined, in telescopes and microscopes, together with their usefulness in many concerns of human life, are explained, London, 1692. 237 Cf. G. W. Leibniz, “Unicum opticae, catoptricae et dioptricae principium”, Acta Eruditorum, (June 1682), pp. 185–190 (Leibniz: Essais Scientifiques, 2005, N. 9; Leibniz: Heß-Babin, 2011, chap. 4, pp. 19–28). 238 Cf. Sabra, 1981, chap. 8, and Darignol, 2012, chap. 2, especially sect. 2.3 (Introduction, notes 86 and 87). 239 Cf. P. de Fermat, Analysis ad refractiones and Synthesis ad refractiones (1662) in: P. de Tannery et al. (eds.), Oeuvres de Fermat, Paris, 4 vols and suppl., 1891–1912, in particular vol. 1, pp. 170–172 and pp. 173–179, respectively.

1691–1693

471

interpretation was also that preferred by William Molyneux in his Dioptrica nova. Molyneux’s treatise likewise contributed to Huygens’ resumption of his work on dioptrics in the spring of 1692.240 The latter undertook a detailed examination and critique, which was later published with the title “Ex Dioptrica nova Guilielmi Molyneux. Edita 1692”.241 While Huygens expressed approval of the work in general, Leibniz, for his part, was flattered by Molyneux’s use of his 1682 article and, in his correspondence and writings, he referred to Dioptrica nova as an excellent work on a number of occasions.242 It was, first and foremost, to the third part of his posthumously-published Dioptrica, viz. “Des telescopes et des microscopes”, that Huygens’ attention was now directed. Optical instruments, and devices, had also been the subject of Leibniz’s correspondence with Tschirnhaus over a period of more than ten years.243 In contrast to Huygens’ theoretical studies, practice was the priority for Tschirnhaus in his efforts for the perfection of optics, as he made clear in a letter to Leibniz on January 13, 1693.244 Tschirnhaus believed he possessed special abilities in the construction of telescopes and he wrote accordingly: “I have an immense knowledge about how to build telescopes so that they, although unbelievably large, can be made very accurate”.245 In microscopy too great advances had been made and so he added: As far as microscopy is concerned I have noted that just as we can make telescopes so that, unboundedly [and] increasingly, we discover distant objects, it can likewise happen that with these microscopes we unboundedly discover more and more things at close range.246 In both areas, Tschirnhaus succeeded in considerably improving the illumination of the instruments. Similarly with concave mirrors, Tschirnhaus’ long-standing commitment led to substantial progress towards perfection. 240 Cf. A III,5 N. 90, specifically p. 336 and annotation; HO, 10, pp. 296–304, and also p. 276 and pp. 279–281. 241 Cf. HO, 13,2 pp. 826–844. 242 Cf. J. G. O’Hara, 2001 (Introduction, note 93). 243 Cf. A III,3 and III,4 (and Chapters 1 and 2 of the present work). 244 “Sonsten bin gleichfals in diesen intent die Opticam zu perficiren nicht so wohl was die Theorie anlangt als die praxin” (A III,5 N. 124, p. 464). 245 “Die Telescopia zubereiten weiß ungemeine sachen, daß ob Sie schon von unglaublicher größe, dennoch gantz accurat können fabricirt werden” (p. 464). 246 “Was die Microscopia betrifft habe angemerckt daß wie wir Telescopia können machen so indefinite, mehr und mehr die entfernten sachen entdecken; so könne es gleichfals mitt diesen Microscopiis geschehen: daß wir indefinite, immer mehr und mehr die nahen sachen entdecken” (p. 464).

472

Chapter 3

Finally, Tschirnhaus raised the prospect of a breakthrough through his work on his optical instruments, and possibly resulting in a sensation, comparable perhaps to Galileo Galilei’s Sidereus nuncius.247 Thus he continued: “Now, however, I have very remarkable things in hand. Should they succeed, the world will experience a new Sidereus nuncius but, as future [developments] have not yet been perfected, I cannot promise anything for sure”.248 Leibniz emphatically supported Tschirnhaus’ practice-related optical investigations. Accordingly, he wrote to the correspondent on January 30, 1693: That which you promise, Sir, regarding telescopes and microscopes, are very remarkable things, and I emphatically urge you, yourself, in the light of the very great utility that is to be expected, to continue the effort. What could be a better conception than to give microscopes simultaneously magnification, a light weight, and a larger field of view. I appreciate this much more than a new Sidereus nuncius, although the likes of such would be both laudable and important.249 The fact that the resolution capabilities of such optical instruments would inevitably reach their limits was certainly evident to Leibniz. However, the objective was to approach these limits as closely as possible. And so he continued: It appears in the meantime, that these instruments are by their nature subject to limitations since in the last analysis the dust particles in the air would become all too visible and obscure the objects. Still, if we could approach these boundaries in as far as it is possible, that would in itself be sufficient.250 247 Cf. G. Galilei, Sidereus nuncius magna, longeque admirabilia spectacula pandens, Venice, 1610; A. van Helden (trans., ed.), Galileo Galilei: Sidereus nuncius or The sidereal messenger, 2nd ed., Chicago and London, 1989 and 2015. 248 “Ietzo aber habe gantz sonderbahre sachen unterhanden; wo die wohl reuissiren, so wird die weld einen newen Nuntium sydereum zuerlangen haben, aber da futuris so noch nicht perficirt kan nichts gewieses versprechen” (note 244 above, p. 465). 249 “Was M. h. H. circa Telescopia und Microscopia verspricht sind trefliche sachen, so zu treiben ich wegen des großen daher erwartenden Nuzens Sie selbst höchlich ersuche. Was mag beßeres erdacht werden, als den Microscopiis zugleich Vergroßerung, liecht, und ein grosers feld zu geben. Ich schäze dieß hoher als einen neuen Nuntium sidereum, wiewohl auch solcher so rühmlich als wichtig seyn würde” (A III,5 N. 130, p. 488). 250 “Es scheinet inzwischen daß dieße instrumenta von der natur daher begrenzet, weil endtlich die staübgen in der lufft alzu sichtbar werden und die objecta bedecken wurden. Doch wenn wir nur noch so weit es thunlich uns diesen grenzen nahern köndten, wäre es schohn gnug” (p. 488).

1691–1693

473

In the years following his Italian journey, Leibniz retained his interest in the microscopic observations of Antoni van Leeuwenhoek, and he referred to him again and again in his correspondence. Leibniz’s meeting with the microscopist Marcello Malpighi in Italy, likewise proved to have had a special influence on him. On July 25, 1690, for example, he reported to Huygens as follows about his encounters with mathematicians and physicists in Italy: I met Mr [Adrien] Auzout in Rome, Mr [Vincenzo] Viviani in Florence, father Estienne de Angelis [Stefano degli Angeli] in Padoue and Mr Malpighi in Bologna, who are almost the only ones with whom one can talk about that which goes beyond the ordinary in mathematics and physics.251 Writing to Huygens, on March 2, 1691, Leibniz drew a dividing line between philosophical thought and practical, or observational, science. Distancing himself from the Cartesian world view, he introduced the observer Leeuwenhoek as the preferential antipole to a contemplative Cartesian. Here he wrote: Is there not anyone at present who has philosophical meditations regarding medicine? The late M. Crane [Theodor Craanen] would have been right for this. The Cartesians are too prejudiced as regards their own hypotheses; I prefer a Leeuwenhoek who tells me what he sees to a Cartesian who tells me what he thinks.252 To this sentiment he added, however, that it behooved one, in the final analysis, to bring together the philosophical and the observational approaches, or in his words: “It is nonetheless necessary to join reason with observations”.253 In a letter to Melchisedech Thévenot, on September 3, 1691, Leibniz referred to the auspicious work of the microscopists Malpighi and Leeuwenhoek, alluding in particular to the latter’s vast collection of instruments in the following words: “It is a pity that there are so few people who can promise something 251 “J’ay trouvé Monsieur [Adrien] Auzout à Rome, Mons. [Vincenzo] Viviani à Florence; le pere Estienne de Angelis [Stefano degli Angeli] à Padoue et M. Malpighi à Boulogne; qui sont presque les seuls avec les quels on puisse parler de ce qui passe l’ordinaire en mathematiques et en physique” (A III,4 N. 267, p. 533). 252 “N’y a-t-il personne à present qui medite en philosophe sur la medecine? Feu M. Crane [Theodor Craanen] y estoit proper, mais Messieurs les Cartesiens sont trop prevenus de leur hypotheses; j’aime mieux un Leewenhoek qui me dit ce qu’il voit, qu’un Cartesien qui me dit ce qu’il pense” (A III,5 N. 9, pp. 62f.). 253 “Il est pourtant necessaire de joindre le raisonnement aux observations” (p. 63).

474

Chapter 3

good, like Mr Malpighi and Mr Leeuwenhoek who has almost as many microscopes as objects [of observation]”.254 Again and again, Leibniz recalled his meeting with Leeuwenhoek in Delft, in November 1676, and he extended greeting to him through travelers. At the end of a letter to Friedrich Simon Löffler on May 15, 1693, for example, he wrote: “You will visit Leeuwenhoek in Delft and [so please] convey my greetings to him. He once allowed me to see his famous microscope exhibition which I advise you not to miss out on”.255 6

Engineering Science: Hydromechanics and Mechanics of Fluids

When Leibniz met Bernardino Ramazzini in Modena – during his stay there from the end of December 1689 to early February 1690 – he encouraged the Italian physician to continue his scientific and engineering investigations alongside his medical research. This entailed, above all, the study of the motion of mercury in a Torricellean tube (or mercury barometer), and the investigation of the springs of Modena. Besides his physical experiments with a barometer, Ramazzini undertook an investigation in which he correlated barometric pressure with the health and the subjective well-being of people. In Leibniz’s correspondence with Ramazzini,256 we find (in the year 1691) the beginnings of an effort that would culminate in the publication of Ramazzini’s barometric diary – Ephemerides barometricae Mutinensis anni 1694 – that was first published in Modena in 1695.257 In a letter of May 4, 1691, Ramazzini recalled that Leibniz had suggested (while in Modena) the measurement of temperatures at various depths in the springs or wells of the town.258 Then, 254 “C’est dommage qu’il y a si peu de personnes qui promettent quelque chose de bon, comme M. Malpighi et Mons. Leewenhoeck qui a presque autant de Microscopes que d’Objets” (A I,7 N. 173, p. 354). 255 “Loewenhoekium Delphis adibis, et a me salutabis ignoto. Licuit mihi olim ejus favore videre praeclara microscopia spectacula; quae, ne negligas, hortor” (A I,9 N. 462, p. 686). 256 Cf. P. Di Pietro, Carteggio fra Ramazzini e Leibniz, Atti e memorie della deputazione di storia patria per le antiche provincie Modenesi, ser. IX, vol. IV–V, (1964–1965), pp. 141–174; Bernardini Ramazzini, Epistolario, pubblicato in occasione del CCL anniversario della morte, a cura di Pericle di Pietro, Modena, 1964. 257 Cf. B. Ramazzini, Ephemerides barometricae Mutinenses anni M. DC. XCIV. Una cum disquisitione causae ascensus, ac descensus mercurii in Torricelliana fistula juxta diversarum aeris statum. His accessere epistolae Jo. Bapt. Boccabadati et Frc. Torti, Modena,1695; 2nd ed. in: R. J. Camerarius, Ephemerides meteorologicae Tubingenses, ab anno seculi nonagesimo primo ad quartum Rudolphi Jacobi Camerarii, Augsburg, 1696. 258 “optabam enim, ut Tu praesens suaseras, aliquot experimenta capere de horum Puteorum temperie secundum variam altitudinem” (A III,5 N. 20, p. 109).

1691–1693

475

when in October 1690, a borehole was drilled it became possible for Ramazzini to undertake the temperature, and air-pressure, measurements advocated by Leibniz. Ramazzini devoted an in-depth investigation, and study, to the water supply system of Modena. The results he published in a physical-hydrostatic tract (of 1691) on the bubbling fountains of Modena  – with the title De fontium Mutinensium admiranda scaturigine tractatus physico-hydrostaticus – a work that was also to influence the development of Leibniz’s ideas on earth history, and which appeared in his posthumously-published Protogaea in 1749.259 In his tract, Ramazzini described the surface and geological structure of the ground, the level and movement of the ground water, artesian aquifers and the erection of artesian wells – or wells from which water flows under natural pressure without pumping – as well as measures for the prevention of contamination and pollution. Furthermore, the work contains recordings of ground temperatures at various depths down to 80 feet, representing measurements that were probably the first of their kind to be undertaken in Europe. The springs of Modena represented an inexhaustible source of pure water that was also suitable for medical applications. Investigating the spring source, and the water yield, of these springs belonged likewise to the goals Ramazzini had set himself. In his view, the ocean, or the open sea, was the origin and source of all waters. By means of various channels, the water reached the hidden water reservoirs in the mountains. Then, it was distilled by virtue of the great heat there, and it finally arrived at Modena and surroundings having passed through various sand layers. Leibniz was informed during and after his stay in Modena about Ramazzini’s investigations, as well as about the coming into being and development of the aforementioned tract De fontium Mutinensium … scaturigine. On April 15, 1690, Ramazzini admitted his intital lack of progress following Leibniz’s departure in the following text: “Following your departure I did not contemplate anything of consequence in relation to my opus De fontium Mutinensium, nor have I attempted any experiment regarding the ascent of water in the ‘tubus intermedius’”.260 Three months later, on July 16, Leibniz then encouraged the correspondent, and he urged him to maintain his efforts in the following words:

259 Cf. B. Ramazzini, De fontium Mutinensium admiranda scaturigine tractatus physicohydrostaticus, Modena, 1691. Regarding its impotance for earth historiography, cf. C. Hodoba-Eric, 2020 (Introduction, note 128). 260 “Post discessum tuum nihil amplius circa opus meum De Fontib. Mutin. meditatus sum, neque ullum experimentum de aquae ascensu in Tubo intermedio pertentavi” (A III,4 N. 250, p. 499).

476

Chapter 3

“I do not doubt that your most elegant work treating your springs or wells will duly appear, about which it will be a pleasure to be informed”.261 Then, following publication of the work, Ramazzini returned once again to the physical experiment – referred to by Leibniz in his letter of February 15 (25), 1690 – that was clearly of special interest to him. Thus, writing on March 30, 1692, the Italian correspondent referred to an experimental arrangement that showed different water levels in two glass tubes, while water flowed out of an intermediate tube.262 In addition, following Leibniz’s advice, he had included in his tractatus physico-hydrostaticus a table,263 showing the variations of the thermometric and barometric levels in the subterranean wells of Modena, and he now informed Leibniz accordingly.264 In these hydrodynamic experiments  – that were intended to substantiate Ramazzini’s explanatory model for the springs of Modena – we find possibly the first measurements of hydraulic grade lines, or lines showing the variation of piezometric head along a streamline.265 Following his return from Italy, on July 25, 1690, Leibniz reported to Huygens about meetings with two other Italian physicians, also well-versed in mathematics, namely Domenico Guglielmini and Francesco Spoleti.266 Of the two, it was the former who was soon to emerge as one of his most important correspondents in Italy.267 The academically qualified physician Guglielmini was particularly interested in problems of hydraulics and hydromechanics. In his tract Aquarum fluentium mensura nova method inquisita (1690–1691),268 he treated fundamental questions of the mechanics of fluids in open-channel flow in canals and flumes. According to Guglielmini, the laws of fluid flow in open channels were to be explained exclusively in terms of the base slope of the channel, the inclination of the water surface and the pressure of the water (with the upper layers of the stream exercising pressure on the lower layers). 261 “Opus tuum elegantissimum de fontibus vestris procedere non dubito, idque intelligere erit perjucundum” (A III,4 N. 266, p. 532). 262 “experimentum quod ostendit inaequalem elevationem aquae in duabus vitreis fistulis dum e fistula intermedia aqua effluit” (A III,5 N. 67, p. 283). 263 Cf. B. Ramazzini, 1691 (note 259 above), p. 16. Only a short extract of Leibniz’s letter of February 15 (25), 1692, is extant (cf. A III,5 N. 62, p. 267). 264 “Tabellam adjeci ex tuo consilio, ut pateret, quid in Thermometro ad varias altitudines aestivo tempore dimisso efficeret vis frigoris, et in Barometro Aeris gravitas” (note 262, p. 283). 265 Cf. C. S. Maffioli, 1994 (Introduction, note 127), p. 214. 266 Cf. A III,4 N. 267, specifically p. 533 and p. 536; HO, 9, pp. 448–452. 267 Cf. C. S. Maffioli, 1994 (Introduction, note 127), pp. 220–222. 268 Cf. D. Guglielmini, Aquarum fluentium mensura nova methodo inquisita, 2 parts, Bologna 1690–1691; part 1 (books 1–3, 1690) and part 2 (books 4–6 with Appendix, 1691).

1691–1693

477

Gravitation and resistance, or friction forces, were left out of consideration entirely. And, in mathematical terms, Guglielmini’s theory was restricted to considerations regarding proportions of homogeneous magnitudes. In Italy, hydromechanics was a firmly established academic subject by the 1690s. It was regularly taught at the universities in the Po Valley, and in particular at Bologna. In hydromechanics and hydraulics, the practical-empirical tradition of Renaissance technology and the scientific-mathematical tradition of Galileo Galilei, Benedetto Castelli and Evangelista Torricelli came together. Guglielmini, a disciple of Marcello Malpighi and Geminiano Montanari, became ‘Inspector general of territorial waters’, and professor of mathematics in Bologna. Leibniz, following conversations he had with Guglielmini in Bologna between December 22 and 30, 1689, was aware of the Italian’s plans to write a tract about water flow in open channels, in order to establish the laws of fluid flow on a new basis. Back in Hanover, he then received a review copy of the first part (containing the first three of a total of six books, or chapters) of the Aquarum fluentium mensura as an enclosure to a letter from Mencke of November 7, 1690.269 His review of the work appeared anonymously in the February 1691 number the Acta Eruditorum.270 At the center of Leibniz’s interest was the parabolic velocity increase from the water surface to the bottom of the channel, that had been postulated by Guglielmini on the basis of Torricelli’s efflux law. Leibniz did not question here the validity, or applicability, of the Torricellian theorem for water flowing in open channels. He merely established that the velocity distribution postulated by Guglielmini would not be applicable in real rivers and canals. After reading this review, but before he had seen the tract itself, Denis Papin wrote a critique of Guglielmini’s opus, which duly appeared (in May 1691) in the Acta Eruditorum, with the title “Observationes quaedam circa materias ad hydraulicam spectantes”.271 In Leibniz’s anonymous review of Guglielmini’s work,272 Papin had encountered Guglielmini’s fundamental theorem (Proposition 2 of Book 2) concerning the velocity in an inclined watercourse, according to which, the velocity of water flowing through an arbitrary section of the channel is equal to the efflux velocity from an orifice, having the area of this section, in a cistern under a pressure head equal to the difference in elevation between the channel commencement and the section in question. 269 Cf. A I,6 N. 135. 270 Cf. G. W. Leibniz (anon.), Review of Aquarum fluentium mensura nova methodo inquisita Autore Dominico Gulielmino M.D., Acta Eruditorum, (February 1691), pp. 72–75. 271 Cf. D. Papin, “Observationes quaedam circa materias ad hydraulicam spectantes, mensi februario hujus anni insertas”, Acta Eruditorum, (May 1691), pp. 208–213. 272 Cf. p. 74 (note 270).

478

Chapter 3

For Papin, this represented a contradiction of his own view, which he had presented in the context of an investigation of the so-called ‘Wurtemberg siphon’, viz. his article “Examen siphonis Wurtemburgici” published in May of the previous year.273 There he had maintained that the quantity of fluid flowing out of an inclined water pipe, or duct, was only half of the effluent through an orifice (having the same cross-sectional area as the pipe cross section) in the bottom of an open container, and under a pressure head equal to the difference of elevation between the upper and lower openings of the inclined pipe.274 Leibniz informed Magliabechi, in a letter of August 23, 1691, about Papin’s “Observationes”, and he suggested a reply by Guglielmini.275 For his response to Papin’s criticism, Guglielmini then chose the form of an open letter addressed to Leibniz, and dated December 24, 1691.276 A short time later, Guglielmini composed a second open letter (dated February 16, 1692), this time addressed to Magliabechi. In this, he treated the movement of fluids in siphons in response to Papin’s “Examen siphonis Wurtemburgici”. Both of these open letters appeared in print (in March 1692) under the title Epistolae duae hydrostaticae.277 And, in the same year, both works of Guglielmini – the Aquarum fluentium mensura and the Epistolae duae hydrostaticae – were reprinted by Gaudenzio Roberti, the publisher of the Giornale de’ Letterati, in his collection Miscellanea Italica physico-mathematica.278 This reprint was to contribute greatly to the dissemination of Guglielmini’s writings and thought. The dispute between Guglielmini and Papin was mainly concerned with the question – referred to above – of the efflux velocity from a pipe, or duct, in the side wall, and from an orifice in the bottom, of a container, respectively. By means of a special construction, Guglielmini was able to alter Papin’s experiment in such a way that both the efflux from the pipe, and that from the orifice in the container’s bottom, were subject to the same pressure head.279 From this it followed (at least theoretically) that the efflux velocity must be equal in both cases. In addition, Guglielmini discussed (in the Epistola addressed to Leibniz) the other objections raised by Papin against his conceptions. Of particular significance here is Guglielmini’s rejection of Papin’s view that Galileo’s laws of 273 Cf. D. Papin, “Examen siphonis Wurtemburgici in vertice effluentis”, Acta Eruditorum, (May 1690), pp. 223–228. 274 Cf. pp. 208f., Tab. V. fig. 1 (note 271), and A III,5 N. 50, p. 214 (fig.1 and annotation). 275 Cf. A I,7 N. 168, p. 346. 276 Reprinted as A III,5 N. 50, pp. 211–231. 277 Cf. D. Guglielmini, Epistolae duae hydrostaticae, Bologna, 1692. 278 Cf. G. Roberti (ed.), Miscellanea Italica physico-mathematica, Bologna, 1692. 279 Cf. p. 214, fig.1 and annotation (note 277).

1691–1693

479

free-fall have no validity in fluid mechanics. A further objection of Papin was directed against the view that, for water flow along an inclined channel, the velocity in the upper layers of the stream would be influenced, or affected, by the movement in the lower layers. In order to refute this objection, Guglielmini developed a (albeit rudimentary) model of a fluid, consisting of small globules, or beads, with which analogies and differences in the motion of solid and fluid bodies could be illustrated.280 In the spring of 1692, Leibniz received copies of the Epistolae duae hydrostaticae both from Magliabechi and from Otto Mencke. His (once again) anonymous review then appeared in the September number of the Acta Eruditorum.281 There the reviewer summarized the arguments of Guglielmini, but otherwise acted diplomatically and desisted from making any judgement about the correctness of the respective views of Guglielmini and Papin. Taking this neutral stance between the adversaries in the dispute, he simply expressed the hope that this contest might contribute to scientific progress. Two months later, Leibniz likewise reviewed the second part of Guglielmini’s Aquarum fluentium mensura – containing the final three of the six books, or chapters, plus an Appendix – in the Acta Eruditorum.282 Leibniz sent copies of Guglielmini’s Epistolae duae hydrostaticae, and of the second part of his Aquarum fluentium mensura, on May 11 and on August 4, 1692, respectively, to Papin,283 who duly acknowledged the favors in letters of July 6 and of August 13, respectively.284 Furthermore, in his letter of August 13, Papin acknowledged Leibniz’s offer to send him a copy of Benedetto Castelli’s (1578–1643) seminal work Della misura dell’ acque correnti (3rd edition 1660).285 However, he declined this offer on the grounds that he was not in position at that time to pursue scientific questions in detail. Thus, he wrote: “I also have not seen the book of the abbot Castelli, but I will await nevertheless a more appropriate time to avail of your obliging offer to send it to me”.286 Then, on October 19, 1692, Papin actually excused himself for his inactivity on the grounds of family commitments, and obligations, in the following words: “You 280 Cf. p. 229, fig. 4 and annotation (note 277). 281 Cf. G. W. Leibniz (anon.), Review of D. Guglielmini’s Epistolae duae hydrostaticae (1692), Acta Eruditorum, (September 1692), pp. 431–435. 282 Cf. G. W. Leibniz (anon.), Review of part II of D. Guglielmini’s Aquarum fluentium mensura (1691), Acta Eruditorum, (November 1692), pp. 510–514. 283 Cf. A III,5 N. 75, p. 300, and N. 95, p. 355. 284 Cf. A III,5 N. 88, p. 331 and N. 96, p. 359. 285 Cf. B. Castelli, Della misura dell’ acque correnti, Rome, 1628; 3rd ed. Bologna, 1660. 286 “Je n’ay point aussi veu le livre dell’ Abbate Castelli, Mais J’attendray pourtant un temps plus proper pour profiter de l’offre obligeante que Vous me faittes de me communiquer” (A III,5 N. 96, p. 359).

480

Chapter 3

will not believe this perhaps but in my present condition I need to contemplate with great diligence my domestic affairs and to attend to the subsistence of my family”.287 Papin’s response to Guglielmini’s Epistolae duae hydrostaticae appeared only in the year 1695, and in the form of a bilingual open letter on the measure of flowing waters, which was addressed to Huygens, and entitled Lettre, touchant la mesure des eaux courantes and Epistola de fluentium aquarum mensura, respectively, as part of his bilingual miscellany with the respective titles Recueil de diverses pieces touchant quelques nouvelles machines and Fasciculus dissertationum de novis quibusdam machinis.288 Here Papin repeated his objections in greater detail than in his article “Observationes quaedam” of 1691. In doing so he desisted from using mathematical, physical, or engineering proofs, and he restricted himself to the consideration of analogies, or differences, between solid bodies and fluids. In this way, he believed that he had refuted, or made superfluous, the objections of Guglielmini.289 Finally, the dispute between Guglielmini and Papin from the early 1690s was to have an aftermath, or sequel, in the second half of the decade, which will be summarized here in conclusion. Papin’s Recueil was reviewed (probably by Leibniz) in the August 1695 number of the Acta Eruditorum, and thus became known to Guglielmini.290 However, on June 22, 1696, when Guglielmini commenced his correspondence with Leibniz,291 he still did not have Papin’s work to hand and, accordingly, did not feel obliged to provide a response, or a rejoinder. However, he did request Leibniz’s help in acquiring a copy of the work. A month later, Papin had two copies of his Recueil sent to Leibniz, one of which although forwarded by Leibniz never did reach its intended addressee in Italy. Leibniz subsequently sent handwritten extracts from the

287 “Vous ne croyiez peut estre pas, que dans l’etat où Je suis J’ay besoins de penser avec une tres grande application à mes affaires domestiques et à faire subsister ma famille” (A III,5 N. 111, pp. 411f.). 288 Cf. D. Papin, “Lettre, touchant la mesure des eaux courantes contra Mons. Dominique Guilielmini médecin et mathématicien à Boulogne, à Monsieur Christien Hugens Seigneur de Zulichem”, Recueil de diverses pieces touchant quelques nouvelles machines. Et autres subjets philosophiques, Kassel, 1695, pp. 66–94; D. Papin, “Epistola de fluentium aquarum mensura ad perillustrem virum D. D. Christianum Hugenium”, Fasciculus dissertationum de novis quibusdam machinis atque aliis argumentis philosophicis, Marburg, 1695, pp. 68–93. 289 Cf. p. 73 (Lettre). 290 Cf. G. W. Leibniz (anon.), Review of D. Papin, Fasciculus dissertationum de novis quibusdam machinis, Acta Eruditorum, (August 1695), pp. 376–382. 291 Cf. A III,6 N. 242, pp. 793f.

1691–1693

481

work to Guglielmini.292 For his rejoinder, Guglielmini once again chose the form of two open letters, which were addressed to Leibniz and Magliabechi, respectively. However, the intended publication in the Acta Eruditorum was refused in view of its length. The publication of Guglielmini’s letter of June 5, 1697, to Leibniz,293 to which they had so long aspired, was finally procured by Leibniz himself but only thirteen years later (in 1710) in the first volume of the Miscellanea Berolinensia, thus bringing the dispute to a conclusion in the year of Guglielmini’s death.294 This letter of June 5, 1697, was concerned with, among other things, Guglielmini’s postulated parabolic velocity increase with depth – that is from the water surface to the canal bed – on the basis of Torricelli’s efflux law, with the applicability of Torricelli’s theorem generally to open-channel water flow (over both horizontal and inclined canal beds), as well as with the general validity of Galileo’s laws of falling bodies in fluvial mechanics. According to Guglielmini’s first tract Aquarum fluentium mensura nova methodo inquisita (1690–1691), the laws of fluid flow were to be explained exclusively by the fall (or head) of the channel, by the slope, or inclination, of the water surface, and by the pressure of the water. Neither gravitation nor resistance forces were taken into account. However, this abstract mathematical approach could not automatically be applied to conditions prevailing in real rivers and canals. Whereas his original tract was of a theoretical and abstract nature, Guglielmini published six years later (in 1697) a physical-mathematical tract on fluvial flows, which was entitled Della natura de’ fiumi trattato fisico-matematico, and which was to be of fundamental importance for the mechanics of fluids.295 The forthcoming publication of this tract was announced by Guglielmini in a letter to Leibniz, on June 22, 1696, with references being made to the author’s and Papin’s earlier works. Guglielmini’s position was, in his words as expressed in this letter: That I hope … to elucidate in this something that has remained arcane or obscure regarding the motion of waters taking into account the resistance. For that which formerly Mr Papin was not willing to understand,

292 Cf. A III,7 N. 64, p. 255. 293 Cf. A III,7 N. 100, specifically the annotation p. 403. 294 Cf. D. Guglielmini, “Epistola Dominici Guilielmini ad praesidem, de aquarum fluentium mensura, qua respondet epistolae D. Papini ad Hugenium”, Miscellanea Berolinensia, (1710), pp. 188–196. Reproduced as: A III,7 N. 100, pp. 403–412. 295 Cf. D. Guglielmini, Della natura de’ fiumi trattato fisico-matematico, Bologna, 1697.

482

Chapter 3

that which I had made into a mathematical abstraction of fluids in my demonstrations, it is [now] possible to include all in its value.296 In a letter to Guglielmini, on January 7, 1697, Leibniz delighted in the prospect of new knowledge emerging in the context of Guglielmini’s fluvial mechanics, including (for example) about the nature of curl, or vorticity flows. Thus he wrote: You will have initiated a mathematical investigation of fluvial flow, for the benefit of mankind, from which there is hope that the vital fluid flow of the microcosmos, and of the curl fluid flows inside our circles and vortices, will have been illustrated by you.297 Guglielmini himself referred to his Trattato near the end of his letter of June 5, 1697, to Leibniz in the following words: If D. Papin wanted more, he could see if chapter 4 of my tract meets his approval, [namely that] on fluvial flows in which I have treated this matter in detail, and have shown both by physical and mathematical reasoning why flowing waters over inclined planes grow thinner [viz. are attenuated] at the start of the flow, and in similar fashion elsewhere, which [considerations] depict exquisitely the state of the present controversy.298 That Leibniz also experienced this sentence as addressed to him, is evident from the fact that his own copy of the Trattato contains markings in his hand, including in the fourth chapter referred to here. And so, with the appearance in 1697 of Guglielmini’s main work  – namely, Della natura de’ fiumi trattato 296 “ch’io spero  … dilucidare in esso qualche cosa che restasse oscura sopra il moto delle acque considerato colla tarra delle resistenze; gia che il Sre Papini non vuol capire, ch’io nelle mie dimostrazioni facio una matematica astrazione dalle mede; né è possibile il considerarle tutte nel suo valore” (A III,6 N. 242, p. 794). 297 “Coepisti a mathematica in fluminum cursus inquisitione, populis utilissima, inde spes est vitalia microcosmi fluenta, liquoresque intra nos gyros vorticesque exercentes a Te illustratum iri” (A III,7 N. 64, p. 257). 298 “Si plura cupia[t] D. Papinus, videat, si lubet cap. 4 mei Tractatus de natura fluminium in quo de hac materia egi latius, et rationem ostendi tum Physicam tum Mathematicam, cur aquae fluentes per plana inclinata gracilescant in sui fluxus initio, aliaque his similia, quae ad praesentis controversiae statum summopere faciunt” (A III,7 N. 100, specifically p. 411 and annotation).

1691–1693

483

fisico-mathematico – the academic dispute with Papin about the fundamentals of fluid mechanics had to a great extent lost its importance. 7

Projects: Calculating Machines and Cryptography

Two machines, about which Leibniz reported in his correspondence with Bodenhausen and Huygens, deserve particular mention. In the summer of 1691, Leibniz possibly intensified his efforts to have the construction of the so-called ‘older model’ of his four-function calculating machine completed. However, he was perhaps inspired to consider these machines because of a recommendation to the Tuscan hereditary prince Ferdinand he was contemplating. At all events, at the end of a letter to Bodenhausen, on June 22, 1691, he wrote: Please, given the opportunity, convey to the noble prince my humble and abiding devotion. I have the idea of having my calculating machine, which was elaborated and executed a long time ago, brought to completion. Arnauld, Huygens und Thevenot, who have seen it long ago in Paris, have reminded me several times about it.299 That the study of mathematical curves produced by movement would also require an apparatus, or machine, to draw them was obvious, and this aspect was likewise discussed in detail by Leibniz both in a published article, entitled “Supplementum geometriae dimensoriae” of September 1693,300 and also in a letter to Huygens of October 11, 1693.301 A central theme in Leibniz’s correspondence with the court archivist in Kassel, Johann Sebastian Haes, was the cryptograph (or cipher code) developed by the correspondent and printed in a limited edition in book form, with

299 “Bitte denen Durchleuchtigsten Prinzen meine unterthanigste bestandige devotion bey gelegenheit zu bezeugen. Ich bin bedacht meine Arithmetische Machinam so vorlangst elaboriret, und auch exequiret, ins feine bringen zu laßen, Arnaldus [i.e. Antoine Arnauld], Hugenius und Thevenot, so sie vor alters zu Paris gesehen, haben mich etlich mahl daran erinnern laßen” (A III,5 N. 24, specifically p. 119 and annotation). 300 Cf. G. W. Leibniz, “Supplementum geometriae dimensoriae, seu generalissima omnium tetragonismorum effectio per motum: similiterque multiplex constructio lineae ex data tangentium conditione”, Acta Eruditorum, (September 1693), pp. 385–392 (Leibniz: Parmentier, 1989, chap. 5, pp. [247]–267; Leibniz: Essais Scientifiques, 2005, N. 60; Leibniz: Heß-Babin, 2011, chap. 30, pp. 207–220). 301 Cf. A III,5 N. 191, specifically pp. 646–648; HO, 10, pp. 538–543.

484

Chapter 3

the title Steganographie nouvelle (1693).302 The author included one copy of the work (which had a dedication to elector Ernst August of Hanover) with a letter dispatched to Leibniz on May 4, 1693,303 and he requested that it be passed on to Franz Ernst von Platen, the prime minister in Hanover. The story of the coming into being of this work, as well as of its renunciatory reception at the Hanoverian court, is documented in Leibniz’s correspondence with Haes from its commencement in July 1691. Steganography (and steganology) represented a medium for the concealment of information, and with the help of which a secret message could be hidden in an unsuspicious text. In the foreword to his Steganographie nouvelle, Haes stated that his cipher code could be particularly useful in diplomatic communications, being easy to write but difficult to decipher for the uninitiated. The author provided an historical summary of the development of cryptography, and he referred to pioneers, like Johannes Trithemius (or Johann Trittenheim, 1462–1516) – perhaps the first theoretician in the field – and Gustavus Selenus (alias Augustus the Younger, duke of Brunswick-Lüneburg-Wolfenbüttel, 1579–1666), who was author of a work entitled Cryptomenytices et cryptographiae libri IX (1624),304 and the German Jesuits Athanasius Kircher (1602–1680) and Caspar Schott (1608–1666). Leibniz, who was honored with an anonymous acknowledgment in the ‘Avertissement’ of the Steganographie nouvelle, had first made the acquaintance of Haes when he visited the natural history collection of the landgraviate library in Kassel, at the beginning of November 1687, on which occasion various projects were discussed. That these included the projected stenographic tract is evident from Haes’ first letter to Leibniz, on July 30, 1691, where he referred to a certain treatise on steganography and copology (or deliberate deception). His words here were: It is true, Sir, that I do not know exactly if it is to the description of the planetary machine in our library, or to the treatise on steganography and 302 J. S. Haes, Steganographie nouvelle, où cet art fort imparfait jusques icy, a eté mis dans une plus grande perfection; de sorte que presentement il comprend à la fois, tous les avantages, qu’on a toujours souhaité d’y voir ensemble. Composé à fin de servir d’essay et de projet pour un ouvrage plus ample et plus achevé, si celuy a le bonheur de trouver de l’approbation; et dedié … à S. A. S. Msgr. le Landgrave de Hesse, Prince de Herschfeld etc etc son tres bon et tres genereux Maitre par S. B. E. S., Kassel, 1693. 303 Cf. A III,5 N. 146, pp. 538f., specifically p. 538, annotation. 304 Cf. Herzog August II. von Braunschweig-Lüneburg (Pseud. Gustavus Selenus), Cryptomenytices et cryptographiae libri novem. In quibus et planissima Steganographiae a Johanne Trithemio … magice et aenigmatice olim conscriptae, enodatio traditur, Lüneburg, 1624.

1691–1693

485

copology, or to a new method to sense the alloying of metals by water, or to some other work you are referring to, because I cannot recall any longer the discourse which I had the honor to carry on with you, when I had the pleasure of the learned conversation with you.305 Subsequently Haes’ interest was concentrated on the Steganographie nouvelle, the completion of which was drawn out into the year 1693. He praised, again and again, the advantages of his cipher code without however revealing any details.306 When, at the end of 1692, the tract had taken on a concrete form, Haes was finally willing to provide Leibniz with an insight into his system of encryption, which involved giving a different sense to individual letters, or words, with the help of tables. Thus, he wrote on December 11, 1692: I make use of four types of character, which are all free of suspicion, although very ingenious and very convenient. I also employ six alphabetical, numerical and combinatorial tables, and by means of the sixth I show a method for the steganology … I have just not simply given instructions for the steganographies of letters, but also for those of complete words, that is to say there where a single character represents a word, and all of that simply, imperviously and without suspicion.307 Putting the final touches to the work, however, proved to be most tedious, since the author wanted – for security reasons – to leave gaps in the text (to be filled in by hand) and to send encoding examples separately and, likewise, only in handwritten form. Finally, on May 4, 1693, Haes sent his Steganographie nouvelle, together with an accompanying letter for Leibniz,308 and a letter for prime minister von Platen, as well as a separate package with additional tables and handwritten supplements to Hanover. The copy of the work in question, 305 “Il est vray Monsieur que Je ne sçay pas precisemt si c’est à la description de la Machine Planetaire de nôtre Bibliotheque, ou au traité Steganographique et copologique, ou à la nouvelle maniere d’eprouver par l’eau l’alliage des metaux, ou à quelqu’autre escrit, que Vous Vous attendiés, parce que Je ne me souviens plus des discours que J’ay eû l’honneur de Vous tenir, lorsque J’avois celuy de vôtre docte entretien” (A III,5 N. 32, p. 142). 306 Cf. for example, A III,5 N. 47, p. 204. 307 “Je m’y sers de quatre sortes de caracteres, qui sont tous sans soupçon, quoique fort ingenieux et fort commodes. J’y employe aussi six tables alphabetiques numerales combinatoires, et par le moyen de la sixieme Je montre une methode pour la steganologie … Je n’y donne pas seulemt des Instructions pour des steganographies de lettres mais aussi pour celles des mots entiers, c. à d. où un seul caractere signifie un mot, et tout cela, facilemt, impenetrablemt et sans soupçon” (A III,5 N. 119, p. 445). 308 Cf. A III,5 N. 146, pp. 538f.

486

Chapter 3

which is now preserved at the ducal library in Wolfenbüttel,309 together with numerous marginal entries by the author, consists of  – in addition to the previously mentioned ‘Avertissement’ – thirteen chapters, as well as a handwritten ‘Addition’. In the course of the correspondence with Leibniz, Haes provided further annotations, examples, and supplements to his opus. The appropriateness of the cipher code was made clear by the author’s choice of examples, which were derived from contemporary military conflicts. In the Steganographie nouvelle, reference is made to the siege (in 1691) of the town Montmélian, in the form of a letter of the duke of Savoy (Victor Amadeus II) sent to Carlo Girolamo del Carretto, the Marchese di Bagnasco.310 In relation to this letter, further examples of encoding, using the cipher, were sent to Leibniz on July 1, 1693.311 Leibniz, for his part, had at first hesitated to pass on the copy of the Steganographie nouvelle he had received, together with the supplements, to prime minister von Platen, as he informed the correspondent on June 1,312 since the author’s dedication of the work to elector Ernst August had met with a mixed response in Hanover.313 Finally, on the insistence of the correspondent, Leibniz acceded to his wishes and forwarded the material to the court. At first Haes was confident of receiving recognition, and even reward, from the elector, or as he wrote on June 11 to Leibniz: “I hope that the firm confidence which I have in the generosity of ‘His Electoral Highness’ will not have deceived me”.314 However, when a decision of the Hanoverian court in his favor proved not to be forthcoming, he made no secret of his disappointment in a letter of June 30, writing that: “I should not deny also that the dilatoriness of this affair is aggrieving, and tormenting me”.315 Yet another letter to von Platen, which was attached to a letter to Leibniz of July 31,316 proved to be of no avail. In his final letter of the year 1693 (on October 8), Haes expressed to Leibniz his great disappointment at the outcome, notwithstanding which, however, he remained convinced of the merits of his cipher code. His words of conclusion about the affair were: 309 namely at the Ducal Library (Herzog August Bibliothek), Wolfenbüttel (shelf mark: Fb 246). 310 Cf. chap. 5, 6 and 7. 311 Cf. A III,5 N. 157, specifically facsimiles pp. 503f. 312 Cf. A III,5 N. 158, p. 565, annotation. 313 Cf. A III,5 N. 149, pp. 549–552. 314 “J’espére que la ferme confidence que J’ay en la generosité de S. A. E. ne me trompera pas” (A III,5 N. 160, p. 572). 315 “Je ne sçaurois nier aussi que le retardement de cette affaire m’afflige, et me tourmente” (A III,5 N. 166, p. 590). 316 Cf. A III,5 N. 177, specifically p. 616, annotation.

1691–1693

487

The disaster which has struck this treatise at your court will never break my patience, because I have the hope that it would be better received if I had the honor to present it myself to ‘His Electoral Highness’ which is what I hope to find the means of doing, with the help of God.317 8

Projects: Experiments with Submersible Vessels

Leibniz received intelligence, in the years 1691 and 1692, concerning Papin’s Hessian pump – the “Rotatilis suctor et pressor Hassiacus” – and, in particular, regarding its employment in the development of a submersible vessel in Kassel,318 for example in a letter from Haes (on June 11, 1692), who reported about the trial of such a vessel in the presence of landgrave Karl.319 The centrifugal pump had first been developed by a tradesman in Stuttgart, and had been made public in a work of Salomon Reisel, entitled Sipho Würtembergicus, sive sipho inversus cruribus aequialtis fluens et refluens, in 1684.320 Papin had studied this innovation intensively while in London, and then (from 1688) in Marburg. Half a year after Papin first gave an account of this work – in the context of his article “Rotatilis suctor et pressor Hassiacus”, in the Acta Eruditorum (in June 1689)321 – Reisel’s book Sipho Wurtembergicus per majora experimenta firmatus (1690) was published,322 and subsequently reviewed in the March 1690 number of the Acta Eruditorum.323 Papin then responded with an account of his investigation, entitled “Examen siphonis Wurtemburgici”, in the

317 “Le desastre qui est arrivé à ce traité en vôtre Cour ne rompra jamais ma patience, parce que j’espere qu’il sera mieux receû quand j’auray l’honneur de la presenter moy méme à S. A. E. ce qui j’espere trouver moyen d’effectuer, s’il plait à Dieu” (A III,5 N. 190, p. 644). 318 Cf. F. Tönsmann, 2009, pp. 89–104 (Introduction, note 141). 319 Cf. A III,5 N. 83, pp. 323f. 320 Cf. S. Reisel, Sipho Würtembergicus sive sipho inversus cruribus aequialtis fluens et refluens hactenus inauditus, Stuttgart, 1684 (2nd ed., 1690), and the copy in Miscellanea Curiosa, decur. II, ann. III, (1684), appendix, pp. 461–472; D. Papin, “Description of a siphon performing the same things as the sipho Wurtembergicus”, Philosophical Transactions, vol. XV, no. 167, (November 1684), p. 847, and in Nouvelles de la Republique des Lettres, vol. 3, (1685), p. 537. 321 Cf. D. Papin, “Rotatilis suctor et pressor Hassiacus, in Serenissima Aula Cassellana demonstratus et detectus”, Acta Erdutitorum, (June 1689), pp. 317–322. 322 Cf. S. Reisel, Sipho Wurtembergicus per majora experimenta firmatus, in vertice effluens, correctus et detectus, Stuttgart, 1689. 323 Cf. anon, “Salomonis Reiselii … Sipho Wurtembergicus per majora experimenta firmatus, in vertice effluens, correctus et detectus”, Acta Erdutitorum, (March 1690), pp. 142–147.

488

Chapter 3

May 1690 number of the journal.324 Finally, after an interval of five years, Papin published his concluding study of the centrifugal pump under the title Antlia Hassiaca locupletata and Description de la pompe de Hesse, respectively, in his bilingual collection Fasciculus dissertationum and Recueil de diverses pieces (1695), respectively.325 The suck and press pump, developed by Reisel and Papin, was powered by the uniform movement of a human hand, and operated with the fluid (water or air) entering the machine in the direction of the axis, and escaping in a tangential direction.326 It now became a central element in Papin’s trials of a submersible vessel – his “navis urinatoria” – on the river Fulda, in 1691 and 1692. According to the accounts given by Robert Boyle,327 and Balthasar Monconys (1611–1665),328 about the experiments of Cornelis Drebbel (1572–1633) with a submersible vessel on the Thames in about 1620, the requisite air exchange, or renewal, had been achieved by chemical (or alchemical) means using drops of a quintessence. Papin’s trials of his submersible vessel then gave Leibniz occasion to recall, once again, the methods Drebbel was thought to have employed, more than seventy years earlier. A correspondent in Marburg, Hermann Peikenkamp, who informed Leibniz about Papin’s efforts, also recalled the use of a quintessence in Drebbel’s submersible vessel  – in a letter of August 3, 1692  – in the following words: “[In comparison] with the skilful invention [in the art of engineering] of Drebbel, this is not the same or similar; in particular the quintessence, by means of which fresh air replaced foul air, is missing here”.329 Whether or not the air renewal took place by the use of tubing, or hoses, connecting the submerged vessel with the atmosphere – as in the case of Papin’s

324 Cf. D. Papin, “Examen siphonis Wurtemburgici in vertice effluentis”, Acta Eruditorum, (May 1690), pp. 223–228. 325 Cf. D. Papin, Description de la pompe de Hesse, pp. 1–17 in: Recueil de diverses pieces touchant quelques nouvelles machines, Kassel, 1695; Antlia Hassiaca locupletata, pp. 1–17 in: Fasciculus dissertationum de novis quibusdam machinis atque aliis argumentis philosophicis, Marburg, 1695. 326 Cf. E. Gerland, 1881 and 1966, pp. 37–41 (Introduction, note 142). 327 Cf. the Latin translation known to Leibniz: R. Boyle, Nova experimenta physico-mechanica de vi aeris elastica, Oxford, 1661, pp. 248–250. 328 Cf. B. de Monconys, Journal des voyages, 3 vols, Lyon, 1665–1666 and Paris, 1677, specifically vol. 2, 1666, p. 33 and pp. 40f. 329 “Mit des kunsterfahrenen Drebels invention ist hierin nicht alles gleich oder gemein, sonderlich würde das quintum esse, wormit er frischer lufft bedörftige gäste erquikket, alhier fehlen” (A III,5 N. 94, p. 352).

1691–1693

489

“navis urinatoria”330 – was considered in a further letter from Peikenkamp, on October 12, 1692. In addition, in this letter, the correspondent attributed a dubious role to Boyle in the matter, through his sequestering of first-hand accounts of the undertaking. Thus he wrote that: Not only did C. Drebbel’s ship sink but it could also be moved under |water331|. If two tubes for air intake and air extraction extended to above the |water| surface, there would have been no need to suppose that pumps were used for this purpose. Without doubt the deceased [individuals,] Sir [Kenelm] Digby and Boyle[,] seized the primary report332 about this.333 In a letter Leibniz wrote to Papin, almost three years later in the first half of August 1695, he expressed the view that burning spirit of wine might well have been the quintessence in question. Even if this spirit of wine had not been a substitute for fresh air, it might indeed have had a beneficial effect. Here he wrote that: I will confide to you, Sir, that which I conjecture to have been the quintessence of the air of the famous Drebbel. It was apparently the spirit of wine that he combusted. For there is no liquor which approaches the advantage of the nature of air. And perhaps the vapor it produces serves to correct the air rendered foul by respiration … I do imagine that that alone would not be sufficient for very long without an input of air from outside. Maybe, nonetheless, this means might not be without benefit.334 330 Cf. D. Papin, “Navis urinatoriae serenissimi principis jussu constructae descriptio”, pp. 126–137 in: Fasciculus dissertationum de novis quibusdam machinis atque aliis argumentis philosophicis, Marburg, 1695; “Description du batteau plongeant”, pp. 127–143 in: Recueil de diverses pieces touchant quelques nouvelles machines. Et autres subjets philosophiques, Kassel, 1695. 331 Alchemical symbols in manuscript. 332 Cf. L. E. Harris, 1961, chap. 14, in particular p. 173 (Introduction, note 143). 333 “C. Drebbels Schiff sanke nicht nur, sondern liese sich, unter |wasser|, fort bringen. Wann daran 2 tubi, zur lufteinnehm. u. au[s]treibung, über das |wasser| herausgiengen, waren keine pumpen, wegen selbiger, nöthig zu praesumieren. Ohn zweifel haben die Seelige, Graf Digby und Boyle den nächsten bericht davon eingezogen” (A III,5 N. 110, p. 409). 334 “Je vous diray, Monsieur, ce que je conjecture avoir esté la quinte essence de l’air du fameux Drebbel. C’estoit apparement l’esprit de vin qu’il faisoit brûler. Car il n’y a point de liqueur qui approache d’avantage de la nature de l’air. Et peutestre que la vapeur qu’il donne sert à corriger l’air gasté par la respiration  … Je m’imagine bien que cela seule ne suffiroit pas long temps sans un air nouveau de dehors. Peutestre cependant que ce moyen ne laisseroit pas d’aider” (A III,6 N. 155, p. 480).

490

Chapter 3

In this connection, Leibniz recalled that he had discussed while in London Drebbel’s submarine passage across the Thames, both with Boyle (presumably on February 12, 1673) and with Drebbel’s daughter Katharina, together with her husband Johann S. Kiefler (or Kuffeler). However, he had not been able to ascertain from them whether or not fresh air had been supplied to the vessel, he told Papin: I believe Mr Boyle told me previously, just like the daughter of Drebbel whom I met in London along with her husband Mr Kiefler, that the boat of Drebbel made a pretty long crossing across the Thames. But they did not say distinctly if he took in air from outside.335 Papin of course attached little credibility to a procedure for air exchange, or renewal, achieved by chemical means and, in the construction of his underwater vessel, he employed, first a ventilator pump, and then the centrifugal pump to achieve an efficient intake of fresh air and, likewise, for the expulsion of the foul, or exhaust, air. This air exchange through hosepipes, or hosepipe tubing, between the submerged vessel and the water surface was crucial for the boat occupants, in supplying both the human respiratory system, and a lamp flame for illumination. To build, and set up, the submersible vessel (the “navis urinatoria”), Papin travelled from Marburg to Kassel in June 1691. And so the Kassel resident Haes was able to report regularly to Leibniz about Papin’s activities there. In its first design, the boat consisted of a rectangular parallelepiped box made of tinplate, with a hull made of wood and iron guide rails. In a letter to Huygens, on August 16 of that year, Papin spoke of: “A parallelepiped-shaped boat made of tinplate whose height is 5 ¾ feet, length 5 ½ [feet] and breadth 2 ½[feet]. The vessel is entirely constructed with iron and with wood, both outside and inside”.336 In addition, the vessel was provided with lockable openings in the floor and roof that were, however, not to be opened simultaneously. The upper hatch served the purpose of entry and exit, before and after immersion, respectively, whereas the bottom hatch provided an opening for sculling, or for grabbing 335 “Je crois que M. Boyle m’a conté autres fois aussi bien que la fille de Drebbel que j’ay vüe à Londres avec M. Kiefler son mari, que le bateux de Drebbel a fait un assez grand chemin entre deux eaux dans la Tamise. Mais ils n’ont point parlé distinctement s’il attiroit l’air externe” (pp. 480f.). 336 “vaisseau de fer blanc parallellipipede dont la hauteur … est de 5¾ pieds: la longueur … 5½ et la largeur … 2½. ce vaisseau est tout fortifié de fer et de bois dehors et dedans” (HO, 10, pp. 119–124, specifically pp. 119f.).

1691–1693

491

objects, while submersed. A hole was bored in the roof of the vessel, and a cylinder was soldered in there. At the outlet of this cylinder, a leather tube – that was reinforced on the inside with spiral springs – was fixed. By means of this tube, or hose – at whose upper end a piece of light wood was attached to act as a buoy on the water surface – the vessel was to maintain contact with the atmosphere while submerged. The lower end of the cylinder was located inside the vessel, and it was placed within an additional cylinder which, in turn, was provided with a downward-opening valve. Through an up and down movement of this second cylinder, air would be drawn into the interior of the vessel. According to Archimedes’ principle, the weight of the immersed boat (with its machinery and occupants) should be equal to that of the displaced volume of water. To make the vessel sink, recesses in the floor were filled with lead. To measure the depth, a barometer was installed in the interior of the submersible vessel. In order that the bottom hatch could be opened, the pressure inside the vessel had to be equal to the sum of the air pressure and the hydraulic thrust, in order to prevent the intrusion of water from below into the interior. In addition to a barometer, a compass was supplied to aid navigation. On July 30, 1691, Leibniz was informed about the progress being made in the construction of this vessel, both by Friedrich Lucae,337 and by Haes, who wrote: “Mr Papin has been occupied here for several weeks carrying out an experiment by which he will, in my judgement, surpass, if successful as I hope, the famous Drebbel”.338 However, when, in mid-August, the boat was being launched, it was considerably damaged in an accident, concerning which Haes sent a detailed report to Leibniz, on November 19. A crane – which was employed to help lower the vessel onto the river – failed to hold its load, and the vessel crashed into the water and sank. Haes reported about the incident as follows: All of this has apparently made Mr Papin more defiant not just with regard to the basic principle of the invention, which he will no doubt support and demonstrate very well again, and which he has even communicated to Mr Huygens of Zulichem, but with regard to the force of the machine.339 337 Cf. A I,6 N. 341. 338 “Mr Papin est occupé icy depuis quelques semaines à faire une experience, en quoy il surpassera, si elle reüssit bien, comme J’espere le fameux Drebelius, à mon jugement” (A III,5 N. 32, pp. 142f.). 339 “Tout cecy donna apparemment de la defiance à Mr Papin, non pour le fondement de l’invention, qu’il soutient et demontre sans doute encore fort bien, et qu’il a méme communiqué à Mr Huguens de Zulichem, mais de la force de la Machine” (A III,5 N. 47, p. 203).

492

Figure 1

Chapter 3

Papin’s submersible vessel (1691) Source: Denis Papin to Christiaan Huygens, August 26, 1691 (Huygens, Oeuvres Complètes, vol. 10, p. 120)

As Haes reported to Leibniz, Papin had sent, about a week after the accident on August 26, a detailed report (dated “de Marbourg ce 16e Aoust 1691”) about his submersible vessel, and its demise, to Huygens. In this communication, he also dealt with the utilization of his invention in the following words: “This [crashed] boat could never serve for real applications, but simply for some experiments of whose outcomes, it appears to me, one can be just as certain as if one had actually seen them”.340 Papin likewise informed Huygens, in the same letter, about his design of a new, improved bathyscaphe. In the spring of 1692, Papin was once again able, with the support of landgrave Karl, to travel to Kassel to undertake fresh experiments with the new submersible vessel. The new boat was – according to the account sent to Huygens on August 26, 1691 – of oval shape and made of wood. In the cabin, or machine room (with measurements: 6.5 feet height, 5 feet width and 3 feet depth), three persons could be accommodated. There was no longer an opening, and hatch, in the floor of the vessel. Instead there were openings at the sides, that were sealed with leather and intended for the operation of oars. The centrifugal pump was now employed in combination with a hose, or tubing, reaching to the water surface for the supply of fresh air. The removal of foul, or exhaust, air was achieved by means of a separate hose. In order to submerge the vessel, water was let in using a faucet or tap, and collected in receptacles. The rise of 340 “ce batteau ne pourroit jamais server à des usages reels; mais seulement pour quelques experiences dont il me semble qu’on peut se tenir aussi seur que si on les avoit veues” (HO, 10, pp. 119–124, specifically p. 122).

1691–1693

493

the submarine vehicle from a depth below the water surface was achieved by pumping the water in the receptacles out of the vessel. The depth of the vessel under water was to be determined using a manometer. Again on this occasion, Haes could inform Leibniz about the progress of Papin’s efforts. Thus, on May 1, 1692, the correspondent reported: “That he is at present very much occupied with the perfection of his new machine for travelling under water, of which we hope to see very soon some wonderful experimental trials”.341 Then, in a further letter of May 22, Haes praised especially the superiority of the method of air exchange and renewal, in comparison with Drebbel’s procedure, writing that: Mr Papin … is here at present in order to carry out [–] before the departure of ‘His Highness the Landgrave’ [–] an experiment of the nature of that of Drebbel, but different nonetheless to that adopted by Drebbel who, as related by Monconys, used a tincture by means of which those in the submerged vessel were relieved of the discomfort of the impure or respired air, and such that Mr Papin can have fresh air at every instant and expel the foul air. Accordingly, using Drebbel’s method it is uncertain if one could remain for very long under water, and with illumination, whereas, on the contrary, the invention of Mr Papin will suffice for as long a journey as one wishes, and for whatever period of time one would like to stay under water.342 Finally, on June 11, 1692, Haes was able to report about a successful demonstration of the submersible vessel in the presence of landgrave Karl, and he used the occasion to give a detailed description of the form of the new ship, the air exchange system, the method of submergence and reemergence, the illumination of the machine room, and the instruments to be used for navigation. Concerning the form of the boat, Haes told Leibniz that: “His vessel was 341 “qi’il soit maintenant fort occupé à la perfection de sa nouvelle Machine pour aller sous l’eau, dont nous esperons bien tôt de voir quelques heureuses experiences” (A III,5 N. 74, p. 299). 342 “Mr Papin … se trouvant presentemt icy pour faire avant le depart de S. A. Monseigr Le Landgrave une experience de la nature de celle de Drebel, differente pourtant en ce que Drebel, comme en parle Monconis, se servoit d’une teinture par la quelle ceux qui étoient au vaisseau sous l’eau se pouvoient garantir de l’incommodité d’un air infecté d’haleine, et que Mr Papin en peut avoir à tout moment du frais et chasser l’infecté. Ainsi selon la maniere de Drebel il est incertain si l’on aura pû demeurer fort long tems sous l’eau, et avec de la lumiere; où au contraire l’invention de Mr Papin suffira pour un si long voyage qu’on voudra, et pour quelque tems qu’on ait envie de demeurer sous l’eau” (A III,5 N. 78, p. 309).

494

Chapter 3

of an oval shape, made of wood, closed below and opened above where those entering are able to close the hatch from inside. There are two oars at the sides which can be swirled in every sense”.343 As regards the supply of fresh air, and the expulsion of foul air – by means of the Hessian pump and two hoses or tubes connecting the submerged vessel with the atmosphere – the correspondent added: Above there are two flexible tubes of which the openings are held upright at the water surface using cork and piping. The air is drawn in and expelled through these, thus providing forced-air ventilation by means of the suck and press Hessian pump.344 As for the tubing connecting the vessel to the atmosphere, Haes reported that security measures had been taken to prevent the entry of water by the use of valves: “The tubes which extend to the surface of the water also have, for greater security, valves close to the vessel which constantly allow the entry and removal of air but which in case of an accident prevent the intrusion of water”.345 The procedures both for sub-aqua descent by means of bolts or faucet-like devices, which allowed water to enter containers or ballast tanks (referred to as “pails” or “buckets”) inside the vessel, and for ascent by means of a special pump to expel the water from these receptacles, were explained in detail by the correspondent as follows: One makes the vessel descend and ascend through the employment of certain internal receptacles and of a very fine pump joined to them. The method of applying them is as follows. Once the vessel has been submerged in the water at a depth of two or three fingerbreadths from the surface by means of added weights, one allows the entry of water employing a bolt or pin pushed to the outside and which can be closed again. One receives this intruding water in a pail with which one pours 343 “Son Vaisseau étoit d’une figure ovale, de bois, fermé au dessous, ouvert au dessus, où ceux qui y entrent peuvent fermer le trou par en dedans. Il a deux rames à costés, qui se peuvent remuer en tout sens” (A III,5 N. 83, p. 323). 344 “Il y a en haut 2 tuyeaux pliant, dont les bouts sont soutenûs droits à la surface de l’eau avec du liege et du jonc. L’air y est attiré et chassé, et par consequent renouvellé par le suctor et pressor Hassiacus” (p. 323). 345 “Les tuyeaux qui vont à la surface de l’eau ont aussi pour plus de seurté pres du vaisseau des Epistomes, qui permettent toujours l’entrée et la sortie à l’air, mais qui en cas d’accident ne la permettent pas à l’eau qui y voudroit entrer” (p. 324).

1691–1693

495

it into the receptacles attached to the pump and which can hold 3 or 4 such pail-fulls of water, which we call buckets, and which can cause the subsidence of the entire vessel by a large or little amount, rapidly or slowly in accordance with observation. When one wants to reemerge again, one has only to expel the water from the entire vessel by means of the pump which causes the boat on feeling lightened or alleviated to ascend at once, with the pump expelling the water without allowing it to reenter.346 Finally, provision had been made for the illumination of the vessel’s interior where also instruments for sub-aqua navigation, viz. a mercury barometer for depth measurement, and a compass, were to be found. Thus, the correspondent continued: There is as well in a place within the vessel some mercury in a recurved [u-shaped] tube, which passes through the middle of the vessel and which goes to the outside in a much more prolonged vase by means of which, being in the water outside of the vessel, the mercury found in it is pressed a little or a lot as one descends under water, while it rises correspondingly in the tube which is within the vessel, revealing to those in the vessel the extent to which they are close to or below the surface. One can have a candle on the inside, as Mr Papin did, and also make little panes with very clear and strong glass; the compass is also necessary for [recording] the direction [or course] of the journey.347 346 “On fait décendre et monter le vaisseau par le moyen de certains vases qu’il y a dedans et d’une tres bonne pompe à la quelle ils sont appliqués. La maniere de s’en servir est cellecy. Quand le vaisseau est dans l’eau jusqu’à deux ou 3 doigts pres de sa surface par le moyen des poids qu’on a mîs dedans on fait entrer de L’eau, par une Cheville qui se pousse en dehors et qu’on peut refermer, on reçoit cet eau, qu’on fait entrer, dans un seau avec quoi on la verse dans les vases appliqués à la pompe, et qui peuvent contenir 3 ou 4 de ces seaux que nous nommons Eymer, ce qui peut faire enfoncer le Grand vaisseau beaucoup ou peu, viste ou lentemt comme il est visible. Quand on le veut faire remonter on ne fait que chasser l’eau hors du grand vaisseau, par la pompe, ce qui fait que le vaisseau se sentant allegerî remonte d’abord, la pompe chassant L’eau, sans luy permettre de rentrer” (pp. 323f.). 347 “Il y a de méme dans un endroit du vaisseau du Mercure dans un tuyeau recourbé qui passe au travers du vaisseau, et qui entre au dehors dans un vase beaucoup plus ample qui estant dans l’eau hors du vaisseau, le mercure qui s’y trouve se presse peu ou beaucoup, suivant le peu ou beaucoup qu’on decend sous L’eau, et montant ainsi de méme dans le tuyeau qui est au dedans du vaisseau, fait voir à ceux qui sont dedans, de combien ils sont prés ou audessous de la surfâce. On peut avoir de la chandelle en dedans, comme

496

Chapter 3

This report was complemented by a further letter from Haes of October 23, 1692, in which the principal innovations of Papin were accentuated. In contrast to the first design of the previous year – that had been conceived solely for the purpose of salvaging objects, and carrying out tasks under water – the new design envisaged journeys under water and attacks on hostile vessels. Haes once again highlighted the Hessian centrifugal pump combined with tubing for air exchange, as well as the water receptacles fitted with pumps as important improvements, writing as follows: The two machines which he had on board were the Hesse pump (viz. the suctor et pressor hassiacus) for the continuous supply of fresh air and for the removal of air rendered foul through inhalation and exhalation, and also a receptacle in which one can collect water as required inside the machine or vessel, and then pump it out again by means of an excellent pump which was applied in this vessel for water excretion.348 The two hoses or tubes, he added, had likewise been improved in comparison with the design of the first vessel, and they had been provided with valves to prevent the intrusion of water at the openings. Independently of Haes’ accounts of the two submersible vessels developed by Papin, Leibniz received an independent report from Hermann Peikenkamp. The latter related, on October 12, that he had been informed by a certain Monsieur Heppe, a military engineer and senior artillery colonel, about the overall state of submarine diving.349 Johann Philipp Heppe’s account of events was in good agreement with that of Haes in all essential points. 9

Techno-Economic Projects

In the area of mercantile economics, topics in Leibniz’s correspondence like improvement of the system of coinage,350 and of the wine and brandy trade,351 Mr Papin en a eû, et faire aussi de petits vitres avec du verre fort clair et fort épais; la bussole est aussi necessaire pour la direction de la marche” (p. 324). 348 “les deux Machines qu’il y avoit dedans etoient le suctor et pressor hassiacus pour y attire toujours de nouvel air et pour en chasser l’infecté par la haleine, et puis un vaisseau dans lequel on pouvoit faire entrer de l’eau à souhait du dedans de la Machine ou du batteau, et puis l’en rechasser aussi par le moyen d’une excellente pompe, qui étoit appliquée à ce vaisseau pour l’eau” (A III,5 N. 112, p. 413). 349 Namely by “Herren Ingenieur und ObristLieut. über die Artillerie Mons. Heppe” and about “den gantzen Zustand der waßertaucherey”, respectively (A III,5 N. 110, pp. 408f.). 350 Cf. A I,6 N. 294 and N. 332. 351 Cf. A III,5 N. 11, N. 192 and N. 193.

1691–1693

497

the economic development of kiln technology for ore and glass smelting,352 the increasing of agricultural production by the use of manures,353 the possibility of silk production through the growing of mulberry trees, and the rearing of silkworms,354 have no doubt a special significance. Likewise of importance was the discussion (or at least passing mention) that emerged, or continued, regarding metal refinement or ennoblement for gold, silver and lead production, regarding pearl cleansing procedures,355 and about retort manufacture,356 salt production,357 oil production processes,358 and much more besides. These processes, or process improvements, do not however have the importance they had in earlier years, a sentiment reflected in the following remarks made by Crafft, on March 5, 1691, about the futility of entrepreneurial involvement in manufactories without princely or baronial participation: I have nothing to do with manufactories this time, and see that it is pure madness, that a private person should of his own accord exert himself to help multiply and nourish the subjects of a monarch. If our princes, be it France, Holland or England, do not want to exert themselves and contribute to this end, which they are not doing and will not do, all will indeed remain as it was.359 Political economy, and the application of mathematics to economical-political matters, was yet another interest of Leibniz in the early 1690s and later. The work of William Petty (1623–1687), in particular, had attracted his interest at this time. Thus, in a letter to Ludwig Justus Sinold (alias von Schütz), on October 20, 1690, Leibniz wrote: “I long for  … all that which the chevalier Monsieur Petty has written about”.360 And, three months later, on January 23, 1691, he wrote the following lines to Henri Justel:

352 Cf. A III,5 N. 11, N. 42, N. 86, N. 103 and N. 110. 353 Cf. A III,5 N. 187. 354 Cf. A III,5 N. 127, N. 144, N. 162, N. 170, N. 186 and N. 201. 355 Cf. A III,5 N. 2 and N. 68. 356 Cf. for example, A III,5 N. 167 and N. 175. 357 Cf. A III,5 N. 86. 358 Cf. A III,5 N. 4. 359 “Mitt Manufacturen habe dießmahl nichts zu thun, vnd sehe daß es eine Lautere thorheit ist, daß ein privatus proprio motu sich bemühet, den Herren vntherthanen zu vermehren, vnd zu ernehren. Wenn vnsere Fürsten sich nicht gleich Franck., Holl- vnd Engeland, selbst bemühen vnd darauf spendiren wollen, wie Sie denn nicht thun noch thun werden, so wird auch wohl beym alten bleiben” (A III,5 N. 11, p. 72). 360 “Je souhaitterois … tout ce qu’a ecrit Mons le Chevalier Petty” (A I,6 N. 121, p. 263).

498

Chapter 3

As you are quite familiar with Paris and London, you could be the most competent judge of the process which Mr Petty has brought into being between these two great cities, and I would certainly like to learn which you believe has the greater population.361 Leibniz was referring here to Petty’s Deux essays d’arithmetique politique, touchant les villes de Londres et Paris (1686).362 In the years that followed, Leibniz referred a number of times to Petty’s work in his correspondence, for example, on February 11, 1697, when he wrote to Thomas Burnett of Kemney that: “I strongly approved formerly the thoughts of the late Mr Petty who demonstrated the application of mathematics to economical-political matters”.363 In a memorandum attached to a letter to Johann Theodor Jablonski, on March 19, 1701, Leibniz, referring to the pastor und preceptor in Breslau, Caspar Neumann, wrote: “Mr Neumann from Breslau (who has made good theological-political suggestions such as proposing observations of the kind like the English bills of mortality, etc.) should also interest us”.364 And, writing to Christian Titius, on April 12, 1702, he referred once again to Neumann, recalling in this connection the seminal work of Petty. Here he wrote: I learned once that your renowned Mr Neumann contemplated collecting empirical theological-political observations from baptismal and mortality registers and other records of this kind … this process might also include something of the nature of political arithmetic, a specimen of which was provided by the Englishman William Petty.365

361 “Comme vous connoissés bien Paris et Londres vous pourrés estre le judge le plus competent du process que Mons Petty a fait naistre entre ces deux grandes villes, et je voudrois bien sçavoir où vous croyés qu’il y a plus du monde” (A I,6 N. 185, p. 354). 362 Cf. W. Petty, Deux essays d’arithmetique politique, touchant les villes de Londres et Paris, London, 1686; Two essays in political arithmetick, concerning the people, housing, hospitals &c. of London and Paris, London, 1687, and also T. McCormick, 2009, p. 319 (Introduction, note 151). 363 “j’ay fort approuvés autres fois les pensées de feu Mons. Petty qui faisoit voir l’application des Mathematiques aux matieres œconomico-politiques” (A I,13 N. 330, p. 551). 364 “H. Neumann zu Breßlau (so guthe Theologic[o]-Politische Vorschlage gethan, wie observationes auf art der Engl. bils of mortality zu machen etc.) solte uns auch wohl anstehen” (A I,19 N. 268 and N. 269, specifically p. 517). 365 “Accepi aliquando celeberrimum Neumannum apud vos cogitare de observationibus Empiricis Theologico-politicis ex catalogis baptismalibus[,] emortualibus aliisque id genus colligendis  … Versatur intus etiam quodam Arithmeticae politicae genus, cujus specimen dedit Guilielmus Pettius Anglus” (A I,21 N. 121, p. 169).

1691–1693

10

499

Projects: The Organization of Science

In addition to demanding large-scale undertakings like the history of the Welfs (or Guelphs), Leibniz was also involved in – or at least expressed an interest in – a range of smaller plans and projects of an administrative, or economic, nature during the early 1690s. These included matters in the scientific field like the establishment, or the promotion, of academies and societies, as well as of institutions like the ‘Collegium Imperiale Historicum’ in Vienna,366 the ‘Kunst- Rechnungs- liebende Societät’ in Hamburg,367 or a projected ‘Societas Germana’ that might be independent of the grace and favor of a sovereign.368 The organization, and the institutions, of science in England was also a long-standing interest of Leibniz that continued after 1690. Following his return from Italy, he had resumed his correspondence with Henri Justel on October 20, 1690.369 Through this channel, he received, between 1691 and 1693,370 information about English scientists, as well as about the Royal Society of London, including, for example, the appointment of Robert Southwell as the Society’s president, and that of Edmond Halley as its secretary, as well as about the latter’s planned research journey in the Atlantic, during which the variation of the magnetic needle was to be investigated. After Leibniz had learned from Justel, in a letter dated “le 25 mars 92”,371 that Halley was prepared to correspond with him, he undertook the first step to initiate this correspondence. His letter of June 3, 1692, was forwarded by Justel to the prospective correspondent.372 However, Halley’s answer failed to materialize, and there was to be an interval of eleven years until the correspondence between the two did eventually develop, in July 1703. From Justel and Halley – as this letter of June 3, 1692 reveals – Leibniz hoped, above all, for information about the literary estate and manuscript inheritance of Robert Boyle, and the scientific treasures this was thought to contain. More detailed information about recent English advances in the fields of science and technology was also requested. Thus, Leibniz was interested in a sea-water desalination process of the English physician (and Modena resident) Nathan Lacy, in an English mining engineer called Kirckby (or Kirkby), who was involved in mining in the Ore Mountains (the ‘Erzgebirge’) in Saxony, and in the extraction 366 Cf. A III,5 N. 10. 367 Cf. A III,5 N. 81, N. 163 and N. 176. 368 Cf. A III,5 N. 165. 369 Cf. A I,6 N. 122. 370 Cf. the volumes A I,7, I,8, and I,9. 371 Cf. A I,7 N. 350, p. 624. 372 Cf. A III,5 N. 80, pp. 312–315.

500

Chapter 3

produce from a recently discovered silver mine in Wales. Leibniz likewise enquired about English mathematicians, and scientists, he had previously been acquainted with, like John Collins (1625–1683), John Pell (1610–1685), Robert Hooke, Christopher Wren, John Wallis, and of course Newton, whose reaction to the objections to his Principia mathematica – as formulated by Huygens in the Discours de la cause de la pesanteur – was of particular interest. Likewise of interest to Leibniz, at this juncture, was the theory of the relationship of languages and alphabets developed by the astronomy professor Edward Bernard. 11 Medicine In the field of medicine, Bernardino Ramazzini emerged as Leibniz’s most important correspondent following his Italian journey.373 Like many important physicians of the time, Ramazzini belonged to the iatrochemists (or chemical physicians), and so the diagnostic and therapeutic teachings of the chemiatric school are reflected in his works.374 Leibniz’s meeting with Ramazzini in Modena during his stay there – from the end of December 1689 to early February 1690  – may surely be counted among the most important events of Ramazzini’s life, since (until then) the fifty seven year old medical professor, and renowned physician, had essentially been limited to his sphere of influence, within his immediate north Italian environment. In the course of their conversations, Leibniz encouraged Ramazzini to intensify his observations, not only in the medical field, but also in areas of science and technology, and to work towards their publication. These efforts soon began to bear fruit when (already in 1690) Ramazzini published his first epidemiological work. At short intervals there then appeared several further works which were to make Ramazzini known far beyond the borders and shores of Italy, especially in the fields of epidemiology, and occupational or industrial medicine. Leibniz actively supported the dissemination of Ramazzini’s writings, and he significantly contributed to his success and fame north of the Alps. Through the use of thermometer, barometer and hygrometer, it became possible at the end of the seventeenth century to establish a relationship between illnesses, or diseases, and the prevailing weather conditions. In addition, statistical investigations were gaining a foothold in medicine. Accordingly, mortality, morbidity and population development could be quantitatively recorded for the first time. Demography, or the statistical study of population, in turn 373 Cf. for example, R. B. Añón, 2014 (Introduction, note 223). 374 Cf. for example, B. Cavarra, 2011 (Introduction, note 227).

1691–1693

501

contributed to progress in medicine. Increasingly, prevention became a principal task for the physician. The causes of diseases were sought and found in almost all areas that affected the lives of people as, for example, in weather and occupational conditions, and in the living environment. Parallel to general preventative measures, physicians began to pay particular attention to the causes, and the circumstances of the occurrence of epidemics. In the history of epidemiology in the seventeenth century, Ramazzini stands out following in the footsteps of Thomas Sydenham, who died at the end of 1689. He emerged (like Sydenham) as an epidemiologist of the Hippocratic ilk. Sydenham, who coined the concept and term ‘Constitutio’ – for the epidemic constitution of a year or season – was the first to strive for the annual publication of such “constitutiones epidemicae”. Ramazzini continued these efforts and published such “Constitutiones” for the years 1690 to 1694, which appeared in three installments. The epidemic constitutions for the years 1690,375 and 1691,376 – which were dedicated to Magliabecchi and Leibniz, respectively – appeared separately, whereas those for the years 1692 to 1694 were published together in 1694.377 All five annual constitutions eventually appeared in a single collection almost twenty years later.378 In these works, Ramazzini described all epidemic diseases that had occurred in the region around Modena in the respective year. They contained exact information, and data, about symptoms and the progression of diseases, about applied therapeutics, as well as about assessments of their effectiveness. Ramazzini also analyzed the weather in the respective years, with regard to possible weather and climatic influences on the occurrence of diseases. He even took account of the welfare of useful, or crop, plants like wheat or vine, as well as of the health of farm animals, and of livestock. He observed which section of the population, and in what manner, was affected by a particular epidemic, and he tried to find an appropriate explanation. In the Emilia-Romagna region of northern Italy, there occurred, in the years 1690 to 1694, in particular malaria and typhoid epidemics. Thus, the extreme precipitation in the year 1690, that caused flooding along the Po tributaries  – as Ramazzini reported 375 Cf. B. Ramazzini, De constitutione anni 1690 ac de rurali epidemia, quae Mutinensi agri et vicinarum regionum colonos graviter afflixit, dissertatio, Modena, 1690; reprinted in: Miscellanea Curiosa, Decur. II, Ann. IX, (1691), Append., pp. [15]–56. 376 Cf. B. Ramazzini, De constitutione anni 1691, Modena, 1692; reprinted in: Miscellanea Curiosa, Decur. II, Ann. X, (1692), pp. 79–114. 377 Cf. B. Ramazzini, De constitutionibus annorum M.DC.XCII., XCIII., et XCIV., in Mutinensi civitate, et illius ditione, dissertatio, Modena, 1695. 378 Cf. B. Ramazzini, Constitutionum epidemicarum Mutinensium annorum quinque, Padua, 1714.

502

Chapter 3

to Leibniz, on April 15 of that year, with the words “these rivers are causing great contamination of our lands due to the enormous precipitation”379 – led to a malaria epidemic which primarily affected the rural population. In his epidemic ‘constitutio’ for the year in question, Ramazzini described the course of this epidemic in detail in relation to the individual seasons. He also described attending ills, like cereal or wheat rust and animal diseases. In contrast, the following year (1691) was dry and warm. In that year, a malaria epidemic affected primarily the poorer urban population, whereas the rural population largely escaped this contagion. In the years 1692 to 1694, notwithstanding very different weather and climatic circumstances, typhoid afflictions dominated Ramazzini’s attention. He held the view that the transmission of these infectious diseases occurred through the air, and that the south wind had brought the pestilence from Africa to Italy. On the other hand, an obvious source of danger, arising from the war-time deployment of troops in the region, was seen as innocuous by Ramazzini. Since his “Constitutiones” were very successful, and seminal, in the area of epidemiology, Leibniz was able to persuade Johann Georg Volckamer  – the president of the Academia Leopoldina  – to reprint Ramazzini’s report for the year 1690, as an appendix to the Miscellanea Curiosa for the year 1691. The second installment of the “Constitutiones” likewise appeared in the German journal, and these publications helped make Ramazzini well-known north of the Alps. Again on Leibniz’s recommendation, the Academia Leopoldina accepted Ramazzini as its 201st member in November 1693. Leibniz considered Ramazzini’s epidemiological works to be particularly important, and he repeatedly recommended them to familiar and well-established physicians, suggesting that they write similar works for other regions and time intervals. A case in point here was Leibniz’s letter to Paul Pellisson-Fontanier of December 1, 1692.380 Such efforts were often successful, with the result that similar medical ephemerides were subsequently published in other parts of Europe. In Leibniz’s correspondence in the early 1690s, several instances of Ramazzini’s epidemiological considerations are to be found. In the accompanying letter (of May 4, 1691) to the consignment of his De constitutione anni 1690 ac de rurali epidemia, Ramazzini described the plight of the Modenese region at that time. The economic decline, as a consequence of the climatic and epidemic situation in the previous two years, had been aggravated by the threat of war, and a possible French intervention. Thus, he wrote on that 379 “quae flumina ob ingentes pluvias magnam illuvionem agris nostris minantur” (A III,4 N. 250, p. 499). 380 Cf. A I,8 N. 112, pp. 199f.

1691–1693

503

occasion: “To these [afflictions] are added the commotion of war, for there is fear that the neighboring duke [Fernando Carlo IV] of Mantua may bring in the French … thus we are facing a triple threshing flail”.381 The difficulties, and shortages, that had arisen in the provision supply of the Italian and allied Bavarian troops deployed near Modena, were sketched by Ramazzini in a later letter of March 30, 1692. He also suspected a connection between the shortages and epidemics of those years, on the one hand, and phenomena like malformation and mortality of infants, on the other hand. Here, anatomical, physiological, pathological and demographic aspects were combined in Ramazzini’s considerations. Specifically, he related the details of a case, where a German woman at a camp at Spilamberto near Sassuolo, south of Modena, had given birth to stillborn deformed female twins, which were conjoined at their breasts and abdomens, but were otherwise of normal proportions. Thus, Ramazzini wrote: At the beginning of the month of March in a camp at a place called Spilamberto not far from Sassuolo, a German woman suffered a monstrous birth, delivering female twins conjoined at their breasts and abdomens, but otherwise of normal proportions and very elegantly formed. Scarcely were they born, they were found to be dead.382 The remains of these stillborn twins were presented to the ducal authorities in Modena, where a post-mortem examination was carried out. Ramazzini explained that the unnamed pathologist, who dissected the remains, discovered that the twins had but a single, or shared, heart, a single stomach, and a single liver. Otherwise, each individual had its own intestines, and internal organs, including a bladder, kidneys, spleen etc.383 Finally, the remains were handed over to Ramazzini himself for anointment and conservation among

381 “His adduntur bellici motus; timor enim est, ne Dux Mantuanus [Fernando Carlo IV] nobis conterminus Gallos accersat; … sic jam nobis triplex flagellum imminet” (A III,5 N. 20, p. 109). 382 “Sub initium Mensis Martii mulier Teutonica in Castro quodam quod Spilimbertum dicitur, non valde distans a Saxolo foetum monstruosum peperit, binas scilicet faemellas pectore, et ventre ad invicem connexas, caeterum justae erant magnitudinis, ac valde elegantes; vix editae mortuae sunt” (A III,5 N. 67, p. 284). 383 “Medicus illius Oppidi monstruosum hunc partum Mutinam detulit, ac Sermo Duci dono dedit; refert idem Medicus qui illum dissecuit, se unicum Cor, unicum Stomachum, unicum Jecur observasse, in reliquis unamquamque sua habuisse Intestina, Vesicam, Renes, Lienem etc.” (p. 284).

504

Chapter 3

other cimelia.384 Ramazzini added that he had learned of the ominous occurrence of a similar monstrous birth in Bologna, and he posed a rhetorical question as to what these occurrences did in fact portend.385 Ramazzini was aware of the important role that Leibniz had to play in his scientific life. His esteem for Leibniz was reflected not only in the dedication of his work De constitutione anni 1691 apud Mutinenses, but also in his words of gratitude regarding the reprint of his De constitutione anni 1690, in the Miscellanea Curiosa, at the beginning of the aforementioned letter of March 30, 1692. Here he wrote: “From your letter I learned of my indebtedness to you … in as much as you recommended that they add my dissertation to your Miscellanea”.386 That this reprint resulted from a suggestion of Leibniz, is also evident from the fact that, when he revived his correspondence with Johann Georg Volckamer, on July 26, 1691, this was his primary concern.387 Already in the years 1681 and 1682, Leibniz had carried on a correspondence with Volckamer in which ideas were exchanged about corresponding terrestrial magnetic observations. During Leibniz’s sojourn in Nuremberg  – from December 31, 1687, to January 6, 1688 – he and the correspondent had met and conversed, as is evident from the opening words of his letter to Volckamer from the summer of 1691.388 Immediately after this, Leibniz presented his principal request to the president of the Academia Naturae Curiosorum (the Leopoldina). First, he told of his meeting with the learned Ramazzini in Modena, and of his exhortations that the Italian commit his results to print.389 Then, he explained how he had recently received Ramazzini’s De constitutione anni 1690, a work that he prized so much, in the following words: I recently received a booklet sent to me not of great bulk but nevertheless, in my opinion, weighty in terms of content, and very neatly written, in which natural history is included, and specifically, ephemerides or a diary for the year 1690 expounding the condition of the air, health and diseases of the region of ‘Longobardia’ (Lombardy) in which these were 384 “Serenmus Dux noster … faetum hunc mihi tradidit ad pollincturam, ut postmodum in Aulae Cimelio reponatur” (p. 284). 385 “Eodem tempore monstrum simile Bononiae natum accepi  … ecquid ex his portentis hariolabimur?” (p. 284). 386 “Me Tibi Debitorem ex Epistola tua accepi … adeo commendasti ut Dissertationem meam Miscellaneis suis adjacerint” (p. 282). 387 Cf. A III,5 N. 30, pp. 136–139. 388 “Jam triennium et amplius elapsum est, ex quo memini Noribergae me conspectu ac colloquio tuo gratissimo frui” (p. 137). 389 “Forte autem accidit, ut Mutinae notitia mihi nasceretur cum Medico illius orae doctissimo Bernardo Ramazzino, quem hortatus sum, ut observata sua literis mandaret” (p. 137).

1691–1693

505

recorded, and where the widely spread symptoms from overt causes are eruditely deduced and the resulting fates of the field crops and animals illustrated.390 And, above all, he added that Ramazzini had committed to continuing his medical ephemerides, throughout his remaining years and as long as his powers should permit.391 Leibniz hoped that the Academia Leopoldina might follow the Italian example, and he emphatically pointed out the importance and necessity of collecting medical statistics in Germany also. The Academia Leopoldina should use its influence to promote such undertakings, and to collect the results of such inquiries from all over the empire. On November 2, 1691, Leibniz thanked Volckamer for reprinting Ramazzini’s De constitutione anni 1690, and he expressed the hope that, through Volckamer’s influence, similar undertakings might be successful in Germany. Thus, he wrote on that occasion: “I am much indebted to you that you have accepted my plan or rather wish, however it is, in your illustrious Ephemerides. I hope also that above all by your authority and exhortation the fruit of this will come to serve the state or the common good”.392 As an exemplary case, Leibniz was able to announce that the personal physician of the elector Ernst August of Hanover, Christoph Pratisius, had promised to soon publish medical observations. A further topic from the field of epidemiology, which occupied both Leibniz and Volckamer, was the medical treatment of dysentery. On January 15, 1691, Henri Justel had reported from London about a mysterious plant root called Ipecacuanha, and which had recently been used in France as a remedy in the treatment of dysentery.393 Leibniz, in turn, informed Volckamer about this, on August 25, 1691, in the following words: “The renowned Henri Justel, now librarian of king William of Great Britain, has written to me that a newly-discovered

390 “Is ergo nuper ad me misit libellum non magnae molis, gravem tamen rebus, meo judico, et scriptum pereleganter, quo historiam naturalem, et ut ita dicam, Ephemerides anni 1690 complectitur, exponitque statum aeris sanitatisque et morborum ejus Longobardiae tractus in quo ipse versatur, et symptomata late vagata erudite deducit ex publicis causis, conspirantibus frugum atque animalium fatis illustrat” (p. 137). 391 “et quod caput est, in omnes annos sequentes dum vita viresque permittent, idem promittit” (p. 137). 392 “Multum Tibi debeo, quod qualecunque consilium vel potius votum meum in vestras illas praeclaras Ephemerides admisisti. Spero etiam fructum ejus aliquem ad Rempublicam perventurum tua in primis autoritate atque exhortatione” (A III,5 N. 44, p. 193). 393 Cf. A I,6 N. 175, p. 337.

506

Chapter 3

root has been used recently in France against dysentery”.394 Since the root in question had found use as a medicament with the French army, Leibniz hoped that this rhubarb-like plant might soon be employed by the allied forces also. Volckamer was pleased about the intelligence regarding the new remedy, and he, for his part, recommended the treatment of dysentery with vegetable or herbal remedies (like sorrel, or common or garden sorrel), the recipe for which he was happy to communicate to Leibniz.395 Ramazzini’s teaching assignment for theoretical medicine included the area of occupational, or industrial, medicine, as well as the treatment of occupational and environmental diseases, like lung diseases.396 In the course of his investigation of the water springs of Modena, Ramazzini also investigated the working conditions of laborers in the well pits and shafts. He thus, for example, reported to Leibniz, on May 4, 1691, about a particular operation in the following words: This well pit was constructed in the month of October and, since by virtue of the season it then quickly became sweltering, the workers were compelled to interrupt the work because of the excessive increase of vapors from which they were being suffocated.397 On such occasions, Ramazzini did not hesitate to descend himself into the shafts, in order not to have to rely on accounts of third parties. The knowledge he gained in the course of these investigations is to be found in his surely most important, and most renowned, work that, alas, was only to appear almost a decade later, namely his tract on the diseases of workers and tradesmen, with the title De morbis artificum diatriba (1700).398 394 “Celeberrimus Vir Henricus Justellus Regis Magnae Britannicae Guilielmi nunc Bibliothecarius ad me scripserat, in Gallia nuper radicem repertam praesentanei usus contra dysenteriam” (A III,5 N. 35, pp. 156f.). 395 Cf. A III,5 N. 38, p. 170. 396 Cf., for example, P. D. Blanc, 2012 (Introduction, note 225). 397 “Fons iste extructus est Octobris mense, et cum tunc temporis constitutio praeter morem aestuosa esset, opus intermittere coacti sunt Putearii ob nimium Vaporum ascensum, a quibus suffocabantur” (A III,5 N. 20, p. 109). 398 Cf. B. Ramazzini, De morbis artificum diatriba, Modena, 1700; B. Ramazzini, W. C. Wright (trans., ed.), Diseases of Workers, Chicago, 1940; B. Ramazzini, W. C. Wright, G. Rosen (trans., eds.), Diseases of workers, New York, London, [c.1964] (Introduction, note 224).

Chapter 4

1694–June 1696 Nostre science est mathematique, et n’a pas besoin icy de ces suppositions ou hypotheses philosophiques, bienque bonnes d’ailleurs.1 Leibniz to Denis Papin, November 17, 1695

⸪ 1

Biographical Background (1694–June 1696)

Leibniz’s correspondence in mathematics, science and technology in the thirty month period between January 1694 and June 1696, consisting of 247 items written both by Leibniz himself (110) and by (or together with) his correspondents (137), involved a total of about 30 individuals.2 Of these correspondences, those with Johann Bernoulli, Rudolf Christian von Bodenhausen, Christiaan Huygens, Guillaume François de L’Hospital, Denis Papin, and Augustinus Vagetius, were the most voluminous, representing more than half of his total correspondence in mathematics, science and technology in this period. Particularly important for Leibniz were his correspondences with Jacob and Johann Bernoulli, Huygens, L’Hospital, Isaac Newton, and John Wallis, even though only a single letter was exchanged with each of the latter two in this period. In the two and a half year period under consideration, three very different events cast a characteristic light on the circumstances of Leibniz’s life. The first (in chronological order) was his attempt to move to the Berlin court by obtaining the position left vacant there by the death of Samuel von Pufendorf, on October 24, 1694. The second event was the appearance of the first volume of the Opera mathematica of John Wallis, in the preface to which the impression was given that Leibniz already had had access to the Newtonian fluxional calculus in 1676. The third event was his (long aspired to) privy-council appointment as minister of justice, on July 12, 1696. The first event signaled Leibniz’s 1 A III,6 N. 172, p. 537; Translation: Our science is mathematics and has no need here for these philosophical suppositions or hypotheses, although good elsewhere. 2 Cf. H.-J. Hess and J. G. O’Hara, A III,6, Introduction, pp. [XXIII]–LXXV.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_006

508

Chapter 4

discontent with his personal and professional situation in Hanover and, in particular, his being overburdened with the dynastic history project. The second event documented the growing willingness of English mathematicians to claim Newton’s priority in the development of the infinitesimal calculus, and to counteract the influence of the Leibnizian form of the calculus. Finally, Leibniz’s promotion at the Hanoverian court indicates that his commitment to promoting the interests of the elector Ernst August had, to a certain degree, found recognition at court. However, with the death of the sovereign one and half years later, Leibniz’s situation was destined to change once again. Leibniz continued to live the life of a traveler, and commuter, in the early and mid-1690s. He made more than two dozen journeys out of Hanover to Wolfenbüttel  – sometimes combined with visits to the nearby town of Brunswick and to the Harz mountains – in the thirty month period under consideration. These visits to Wolfenbüttel were undertaken not just in his capacity as director of the ducal library there, and in connection with the dynastic history he had been commissioned to write, but also in the context of his fostering relations with the princes at the two other Brunswick-Lüneburg courts, namely in Wolfenbüttel and Celle. On the other hand, his journey to Holland in November 1694 – with a stopover in Münster on the outward leg, and a detour to Arnstein and Kassel on the return stretch  – was undertaken without the knowledge of his superiors, and was out of the ordinary. The main purpose of this journey was to support his associate Johann Daniel Crafft, in the context of perhaps the most important economic project at this juncture, namely the formation of a company for the production, and marketing, of brandy conceived by the two entrepreneurs as part of a trade war with France. Leibniz’s primary obligation in the service of the house of BrunswickLüneburg at this juncture was, however, the authoring of a history of the Welf (or Guelph) dynasty, from its origins in the middle ages to his own day. In addition, as historian and jurist, he was entrusted with a range of further administrative tasks, such as the defense (in printed form) of the recently attained electoral status within the Holy Roman Empire, with the consolidation of the claim of the electress of Hanover to the English throne, with the directorship, and reorganization, of the library in Wolfenbüttel, and with a range of additional demands on his legal expertise. Accompanying these official duties, there was a range of further activities which arose through his own initiative, such as the promotion of academies and learned societies, or the pursuit of church reunion and of Protestant reunion. In as far as these activities are reflected in Leibniz’s correspondence in mathematics, science and technology, particular notice must be taken of the extensive acquisition of archival

1694–June 1696

509

material for the planned dynastic history, which went hand in hand with the preparation of a supplementary volume, or Mantissa, to his Codex juris gentium diplomaticus, published in 1693. In his correspondence with Bodenhausen, Leibniz sought support in motivating the dilatory Magliabechi to expedite the dispatch of desired manuscripts from Tuscan sources. On October 15, 1694, the “Investitura Senensis” at least was sent to Hanover.3 Queries in connection with Leibniz’s research on the early representatives of the house of Este were also sent through Bodenhausen to the historian Cosimo Della Rena.4 These probably remained unanswered, and so Leibniz could  – on the occasion of the transmission of his Lettera su la connessione delle serme case di Brunsvic e d’Este5 to Bernardino Ramazzini6 – hardly desist from complaining about the lack of support from the Italians for his research on the line of Este, which was of central importance for his history of the House of Welf. 2

Infinitesimal Calculus and Other Mathematics

In the years between 1694 and 1696, Leibniz’s mathematical renown reached its zenith. At the same time the Bernoulli brothers, Jacob and Johann, were on a par with him in terms of their mathematical prowess and, as regards the number and volume of their publications, they even surpassed him. Guillaume François de L’Hospital too – benefiting from Johann Bernoulli’s initiation and instruction in the new infinitesimal calculus, and his continuing support in the preparation of publications – emerged as a formidable propagator of the new methods. In 1696 L’Hospital published the first textbook on differential calculus with the title Analyse des infiniment petits pour l’intelligence des lignes courbes,7 having previously enjoyed the acclamation of Leibniz, on June 24, 1695, in the following words: For you, Sir, [since] you are at the flower of your age, and [as] the pinnacle we have reached in mathematics represents only the outset for you, 3 Cf. A III,6 N. 21, p. 60. 4 Cf. A III,6 N. 19, p. 55. 5 Cf. G. W. Leibniz [anon.], Lettre sur la connexion des maisons de Brunsvic et d’Este, Hanover, 1695; Lettera su la connessione delle Serme case di Brunsvic e d’Este, Hanover, 1695. 6 Cf. A III,6 N. 184, pp. 576f. 7 Cf. G. F. A. de L’Hospital, Analyse des infiniment petits pour l’intelligence des lignes courbes, Paris, 1696, and also the reviews in Journal des Sçavans, (September 1696), pp. 424–428, and in Acta Eruditorum, (March 1697), pp. 137–139.

510

Chapter 4

it is easy to imagine the progress one can expect from your extraordinary brilliance.8 As regards Leibniz himself, at this juncture all the mathematicians (referred to above) continued to show reverence to him, acknowledging him without reservation as an imaginative discoverer and doyen of modern mathematics. Even Huygens, in his last years, came to the conviction that the Leibnizian calculus might be superior to his own geometrical methods in many respects – even though he considered this new method to be markedly artificial – and he did not hesitate to acknowledge his change of mind both in private correspondence and in publications.9 An indication of the pinnacle that Leibniz’s activities in this area had reached is the frequency of the mathematical journal articles published by him, mainly in the Acta Eruditorum, but also in the Journal des Sçavans and in the Giornale de’ Letterati. Whereas, in the year 1690, he produced but a single journal article, and in the following year only three, between 1692 and 1695 his output rose to at least four per year. Following the publication of two journal articles in 1696, his output once again declined from 1697 to an average of just one mathematical article per year. Thematically considered, the solution of the famous Galilean catenary problem resulted in the greatest number of his mathematical articles. Of the mathematical problems treated in Leibniz’s correspondence in mathematics, science and technology, between 1691 and 1693, one still remained to be solved in 1694, namely that concerning the “isochrona paracentrica”. This was in fact an extension of the first challenge question posed by Leibniz in 1687,10 namely to determine that curve along which a body under the influence of terrestrial gravity approaches the earth’s surface at a constant velocity (viz. the isochrone). Leibniz had published his solution of the isochrone

8

“Pour vous, Monsieur, comme vous estes dans la fleur de vostre aage, et que le plus haut point où nous sommes arrivés en Geometrie, ne fait que vos commencemens, il est aisé de juger, quels progrés on doit attendre de vos lumieres extraordinaires” (A III,6 N. 135, p. 417). 9 Cf. A III,5 N. 185, specifically pp. 634f. (HO, 10, pp. 509–512); Ch. Huygens, “De problemate Bernoulliano”, Acta Eruditorum, (October 1693), pp. 475f., and Chapter 3 (notes 51–53) of the present work. 10 Cf. G. W. Leibniz, “Réponse à la remarque de M. l’Abbé D. C[atelan] contenuë dans l’article I de ces Nouvelles, mois de Juin 1687 où il prétend soûtenir une loi de la nature avancée par M. Descartes”, Nouvelles de la Republique des Lettres, September (1687), pp. 952–956, specifically p. 956.

1694–June 1696

511

problem,11 after the appearance of Huygens’ solution,12 but before that (viz. the semi-cubical parabola) of Jacob Bernoulli.13 He combined his solution with a further challenge question, namely to find the curve under the modified condition that the body, still under the influence of terrestrial gravity, should veer away from a given point at a constant velocity. The problem was to remain unsolved for a few years,14 and Jacob Bernoulli was to be the first to publish a solution of Leibniz’s problem in the Acta Eruditorum in June 1694,15 with an addition following a quarter of a year later.16 In the month of August of that year, Leibniz presented his own solution in the same journal.17 Two months after that, there followed Johann Bernoulli’s solution.18 Huygens – to whom Leibniz had forwarded, on July 27,19 the solution of Jacob Bernoulli – identified, in his reply of August 24,20 some shortcomings, but he was happy merely to give passing mention of these in his article in the Acta Eruditorum, in

11 Cf. G. W. Leibniz, “De linea isochrona, in qua grave sine acceleratione descendit, et de controversia cum Dn. abbate D. C. [i.e. Catelan]”, Acta Eruditorum, (April 1689), pp. 195–198 (Leibniz: Parmentier,1989, chap. 7, pp. [154]–165; Leibniz: Essais Scientifiques, 2005, N. 28; Leibniz: Heß-Babin, 2011, chap. 12, pp. 89–95). 12 Cf. Ch. Huygens, “Solution du problème proposé par M. L[eibniz] dans les Nouvelles de la Republique des Lettres, du mois de Septembre 1687”, Nouvelles de la Republique des Lettres, (October 1687), pp. 1110f. 13 Cf. Jac. Bernoulli, “Analysis problematis antehac propositi, de inventione lineae descensus a corpore gravi percurrendae uniformiter, sic ut temporibus aequalibus aequales altitudines emetiatur; et alterius cujusdam problematis propositio”, Acta Eruditorum, (May 1690), pp. 217–219. 14 Cf. Leibniz’s remark in a letter to Bodenhausen from March 23, 1691 (A III,5 N. 12, p. 75). 15 Cf. Jac. Bernoulli, “Solutio problematis Leibnitiani de curva accessus et recessus aequabilis a puncto dato mediante rectificatione curvae elasticae”, Acta Eruditorum, (June 1694), pp. 276–280. 16 Cf. Jac. Bernoulli, “Constructio curvae accessus et recessus aequabilis”, Acta Eruditorum, (September 1694), pp. 336–338 [416–418]. 17 Cf. G. W. Leibniz, “Constructio propria problematis de curva isochrona paracentrica. Ubi et generaliora quaedam de natura, et calculo differentiali osculorum, et de constructione linearum transcendentium, una maxime geometrica, altera mechanica quidem, sed generalissima. Accessit modus reddendi inventiones transcendentium linearum universales, ut quemvis casum comprehendant, et transeant per punctum datum”, Acta Eruditorum, (August 1694), pp. 364–375 (Leibniz: Parmentier, 1989, chap. 17, pp. [282]–305; Leibniz: Essais Scientifiques, 2005, N. 67; Leibniz: Heß-Babin, 2011, chap. 33, pp. 239–257). 18 Cf. Joh. Bernoulli, “Constructio facilis curvae accessus aequabilis a puncto dato per rectificationum curvae algebraicae”, Acta Eruditorum, (October 1694), pp. 394–399 [474–479]. 19 Cf. A III,6 N. 49, pp. 141–143; HO, 10, pp. 659–662. 20 Cf. A III,6 N. 54, pp. 159f. and p. 164; HO, 10, pp. 664–672.

512

Chapter 4

September 1694.21 Finally, L’Hospital was unable to cope with the problem of the “isochrona paracentrica”, and so he failed to provide a solution.22 Whereas the series of mathematical task assignments, or challenge questions, did not fade away entirely after 1693  – as is evidenced for instance by Jacob Bernoulli’s inverse tangent problem in the Acta Eruditorum of October 169423 – they no longer had the intensity, or consistency, of previous years. In April 1695, for example, Leibniz commented on the drawbridge problem of Joseph Sauveur  – viz. to find the curve along which a counterweight continually keeps a drawbridge in balance – which had already been solved by L’Hospital in the late summer of 1692, but whose special solution (namely, the “limaçon”,24 or snail of Pascal) first appeared in print only in February 1695.25 In that number of the Acta Eruditorum, there also appeared the solution of Jacob Bernoulli,26 and his brother Johann’s generalized conceptual formulation.27 Subsequently, Leibniz turned his attention to other mathematical questions, and only in mid-1696 was he enthused by the very beautiful (or in his words “auß der maßen schönen”) task setting of Johann Bernoulli in the Acta Eruditorum, of June 1696,28 namely the brachistochrone problem, or the task of determining the curve of fastest descent of a body under the influence of terrestrial gravity between a certain point and a lower point which is not directly below the first. Having been informed about the task formulation by Johann Bernoulli, on June 19,29 Leibniz communicated at once (on June 26) his solution (namely, a cycloid) to Bernoulli.30 Johann reciprocated by sending Leibniz, with a letter of July 31, 1696,31 two solution procedures, one utilizing 21 Cf. Ch. Huygens, “Constructio universalis problematis a clarissimo viro, Joh. Bernoullio, superiori anno mense Majo propositi”, Acta Eruditorum, (September 1694), pp. 338–339 [418–419]. 22 Cf. A III,5 N. 120, p. 449, and N. 133, pp. 495f. 23 Cf. Jac. Bernoulli, “De methodo tangentium inversa”, Acta Eruditorum, (October 1694), pp. 391–394 [471–474]. 24 Cf. A III,6 N. 95 (pp. 288–290), N. 120 (p. 377), N. 135 (p. 415), and the annotations to these letters. 25 Cf. G. F. A. de L’Hospital, “Solutio problematis physico mathematici ab erudito quodam geometra propositi”, Acta Eruditorum, (February 1695), pp. 56–59. 26 Cf. Jac. Bernoulli, “Solutiones superioris problematis”, Acta Eruditorum, (February 1695), pp. 65f. 27 Cf. Joh. Bernoulli, “Animadversio in praecendentem solutionem Illustris. D. Marchionis Hospitalii”, Acta Eruditorum, (February 1695), pp. 59–65. 28 Cf. A III,6 N. 244, p. 805, and Joh. Bernoulli, “Supplementum defectus geometriae Cartesianae circa inventionem locorum”, Acta Eruditorum, (June 1696), pp. 264–269. 29 Cf. A III,6 N. 241, pp. 790f. 30 Cf. A III,6 N. 243, in particular pp. 799–803. 31 Cf. A III,7 N. 14, pp. 49–55.

1694–June 1696

513

the law of refraction of light, and another direct method that was however to remain unpublished. Johann had to resort to a printed flysheet to remind mathematicians of his challenge question, after the original deadline set (the end of the year 1696) had passed.32 And so, in the May 1697 number of the Acta Eruditorum, there appeared, in addition to the contributions of Leibniz,33 and of Tschirnhaus,34 the solutions of Johann Bernoulli,35 of his brother Jacob,36 of L’Hospital,37 and of Newton.38 In his contribution, Leibniz prefaced his discussion of the brachistochrone problem with words in which he characterized the problem as the (provisional) summit of the public mathematical challenges, and he stressed the value and importance of such scientific contests. Moreover, Jacob Bernoulli added two new challenge questions to the communication of his solution, one of which was the famous isoperimetric problem that called for proof that the closed plane curve, which for a given arc length encloses the greatest possible area, is a circle. In fact, variational and extremal task assignments relating to this isoperimetric problem had already been addressed earlier in Leibniz correspondence, for example with Johann Bernoulli in the summer months of 1695.39 32 Cf. facsimile in: H. H. Goldstine and D. Speiser (eds.), Die Streitschriften von Jacob und Johann Bernoulli, Basel 1991, in particular p. 260. 33 Cf. G. W. Leibniz, “Communicatio suae pariter, duarumque alienarum ad edendum sibi primum a Dn. Jo. Bernoullio, deinde a Dn. Marchione Hospitalio communicatarum solutionum problematis curvae celerrimi descensus a Dn. Jo Bernoullio geometris publice propositi, una cum solutione sua problematis alterius ab eodem postea propositi”, Acta Eruditorum, (May 1697), pp. 201–206 (Leibniz: Parmentier, 1989, chap. 21, pp. [345]–358; Leibniz: Essais Scientifiques, 2005, N. 84; Leibniz: Heß-Babin, 2011, chap. 40, pp. 297–307). 34 Cf. E. W. von Tschirnhaus, “De methodo universalia theoremata eruendi, quae curvarum naturas simplicissime exprimunt; de problemate item Bernoulliano”, Acta Eruditorum, (May 1697), pp. 220–223. 35 Cf. Joh. Bernoulli, “Curvatura radii in diaphanis non uniformibus, solutioque problematis … de invenienda linea brachystochrona … et de curva synchrona seu radiorum unda construenda”, Acta Eruditorum, (May 1697), pp. 206–211. 36 Cf. Jac. Bernoulli, “Solutio problematum fraternorum, peculiari programmate cal. Jan. 1697 Groningae, nec non Actorum Lips. mense Jun. & Dec. 1696, & Feb. 1697 propositorum: una cum propositione reciproca aliorum”, Acta Eruditorum, (May 1697), pp. 211–216. 37 Cf. G. F. de l’Hospital, “Solutio problematis de linea celerrimi descensus”, and “Solutio problematis publice propositi a Dn. Joh. Bernoullio”, Acta Eruditorum, (May 1697), pp. 217f. and pp. 218–220, respectively. 38 Cf. I. Newton, “Epistola missa ad praenobilem virum D. Carolum Mountague Armigerum, Scaccarii Regii apud Anglos cancellarium, & societatis regiae prasidem, in qua solvuntur duo problemata Mathematica à Johanne Barnoullo Mathematico celeberrimo proposita”, Acta Eruditorum, (May 1697), pp. 223f., and also Philosophical Transactions, vol. 19, no. 224, (January 1697), pp. 384–389. 39 Cf. A III,6 N. 113 (p. 355), N. 133 (pp. 402f.) and N. 137 (p. 427).

514

Chapter 4

The challenge questions, referred to here, were by no means the only mathematical issues that got Leibniz’s attention between 1694 and 1696, and, in fact, they were not even the dominant issues in his mathematical correspondence. At the center of interest for him was still the new analysis, within which the development of a not insignificant number of sub-disciplines became increasingly apparent. These included, as was previously the case, especially the theory of differential equations, integration theory, differential geometry, and the theory of series. To these were now added fundamental questions of his ‘scientia infiniti’. In comparison, Leibniz’s other areas of mathematical interest  – such as algebra, elementary geometry, his ‘analysis situs’, number theory and Diophantine arithmetic  – proved to be of lesser importance in these years. A discussion of dyadic, or binary, mathematics – that had not been treated in Leibniz’s mathematical and scientific correspondence for more than a decade – continued to be wanting in the period from 1694 to 1696. However, from the spring of 1696, this topic came to the fore in Leibniz’s general political and historical correspondence with duke Rudolf August of Wolfenbüttel, as for example the exposé of the binary number system given in an attachment to a letter of May 18, 1696, he sent to the prince.40 The interest of Leibniz and his correspondents in diverse aspects of the ‘inverse tangent method’ (as it was commonly called at the time) – namely, to determine curves from the properties of their tangents – was evident in his mathematical and scientific correspondence after 1690. A point of culmination was reached then, with the publication of an article of August 23, 1694, entitled “Considerations sur la difference entre l’analyse ordinaire et le nouveau calcul des transcendants”, in the Journal des Sçavans, in which Leibniz skillfully summarized the essence of the method in question.41 A number of other mathematical topics came to the fore between 1694 and 1696.42 These included the typological classification of differential equations, whereby Leibniz had the greatest success with first-order explicit differential equations. For the solution of differential equations of second (or higher) order, which were often considered with respect to curvature and inflection-point behaviors, he had to continue to resort to substitutions, variable separation and power series development, without being able to arrive at a typological classification. Other topics within the sub-discipline of analysis, included the 40 Cf. A I,12 N. 67. 41 Cf. G. W. Leibniz, “Considerations sur la difference qu’il y a entre l’analyse ordinaire et le nouveau calcul des transcendentes”, Journal des Sçavans, (23 August 1694), pp. 666–671 (Leibniz: Essais Scientifiques, 2005, N. 66; Leibniz: Heß-Babin, 2011, chap. 32, pp. 233–237). 42 Cf. A III,6, pp. XXVII–XXX.

1694–June 1696

515

attribution of differential equations to pure quadratures (integrals), and  – within the theory of integration, which had occupied Leibniz in the twenty or so years since his Paris sojourn – the transformation of complicated integrals into integrals of known geometrical interpretation, or the representation of basic integrals to which almost all other integrals might be reduced using appropriate substitutions. In the area later to be known as differential geometry, Leibniz’s correspondence with the Bernoulli brothers was of greatest significance as regards increase of knowledge. While (in the early and mid-1690s) the Bernoullis stood out by virtue of their investigations of the curvature behavior of curves, Leibniz directed his attention to the study of the properties of arrays, or families, of curves. Finally, in the area of (non-numerical) series theory, there was an important mathematical innovation in the guise of the so-called ‘Bernoulli series’, both in the Acta Eruditorum,43 and in Leibniz’s correspondence.44 In the year 1694 we find Leibniz’s first announcements of a planned work about a ‘scientia infiniti’. Over a longer period he had stressed the necessity of an explanation of the elements of this higher geometry, for example in a letter to Augustinus Vagetius on January 6, 1694, when he wrote: I see that all has not yet been given for direct reasoning concerning infinity. And of course I once thought about the adumbration of certain elements of a ‘scientia infiniti’ (which is nothing other a higher form of general mathematics).45 Then, in a no longer extant letter of either February 24, or March 7, 1694 (new style) – i.e. either that of February 14 or of February 25 (old style) – he confided in Otto Mencke about his plan to incorporate contributions of other mathematicians into the work, as is evident from Mencke’s reply of March 17. There the editor of the Acta Eruditorum recommended that Leibniz include a resumé of

43 Cf. Joh. Bernoulli, “Additamentum effectionis omnium quadraturarum et rectificationum curvarum per seriem quandam generalissimam”, Acta Eruditorum, (November 1694), pp. 437–441 [517–521], and also G. Ferraro, The rise and development of the theory of series up to the early 1820s, (Series: Sources and Studies in the History of Mathematics and Physical Sciences), New York, 2008, in particular chap. 3, pp. 45–52 (The Bernoulli series and Leibniz’s analogy). 44 Cf. A III,6 N. 55 (p. 172), N. 81 (pp. 243f.) and N. 163 (p. 509). 45 “Video nondum omnibus datum esse recte ratiocinari de infinito. Et certe mecum aliquando cogitavi de Scientia infiniti (quae nihil aliud est, quam Mathesis Generalis sublimior), elementis quibusdam adumbranda” (A III,6 N. 2, p. 14).

516

Chapter 4

his planned work in order to achieve the participation of other mathematicians, expressing himself as follows: Should my honorable-patron decide to present an idea of the intended work about a ‘scientia infiniti’ in the Acta [Eruditorum], other mathematicians would presumably feel encouraged to make their contributions.46 A few weeks later, on March 31, Leibniz also reported to Johann Bernoulli (who was likewise a correspondent of Mencke) about his desire to write a work about the principles of higher mathematics (with the possible title “Scientia infiniti”) in the following words: I once contemplated that I could somehow complete these studies by writing a little book, which I thought it would be not inappropriate to call ‘scientia infiniti’, in which the principles of higher mathematics would be presented.47 There then followed (in relatively close succession) references to the planned work in letters Leibniz sent to several additional correspondents, including Erhard Weigel on May 20,48 Huygens on June 22,49 Johann Andreas Schmidt on August 13,50 L’Hospital on August 16,51 and Adam Adamandy Kochański on August 20,52 whereas, on the other hand, he failed to act on the suggestion of Mencke to include an outline of his conception of the work in the Acta Eruditorum. That which can be gleaned about the content of the work is relatively vague and general. It was to contain a theory of quantities, which should make fundamentally clear the different nature of finite quantities (algebra) and infinite quantities (infinitesimal calculus). Similarly, the important research results of leading mathematicians in the field of the new analysis were to be presented, as is evidenced by the invitations sent in 1694 to the Johann Bernoulli, and 46 “Wan mein Hochg. Patron in denen Actis eine ideam des vorhabenden wercks de Scientia Infiniti entwerfen wollte, würden vermuthlich andere Mathematici aufgemuntert werden, das ihrige beyzutragen” (A I,10 N. 183, p. 304). 47 “Cogitavi aliquando me utcunque absolvere his studiis, conscripto libello quem Scientiam infiniti non incommode inscribi posse putem, in quo superioris matheseos principia traderentur” (A III,6 N. 12, p. 37). 48 Cf. A III,6 N. 36, p. 95. 49 Cf. A III,6 N. 45, specifically p. 125; HO, 10, pp. 639–646. 50 Cf. A I,10 N. 339, pp. 499f. 51 Cf. A III,6 N. 52, p. 151 and N. 79, p. 238. 52 Cf. A I,10 N. 346, p. 513.

1694–June 1696

517

to his brother Jacob (including the words “and I expect your views and those of your outstanding brother”53), to Huygens and L’Hospital.54 Leibniz even wanted to have Newton participate in his work, as can be seen from his letter to Huygens of June 22, where he wrote: Your exhortation has reaffirmed me in the plan I have to present a certain treatise that will explain the fundamentals and the applications of the calculus of sums and differences, and certain connected matters. I will add to it, in the form of an appendix, the beautiful thoughts and discoveries of certain mathematicians, who have decided to avail of it, if they should have the goodness to send them to me. I hope that the Marquis de l’Hospital would like to do us this favor[,] if you should consider it appropriate to approach him in the matter. The Bernoulli brothers might do so as well. If I find something from the contributions of Mr Newton inserted in the Algebra of Mr Wallis, which provides us with the means of progress, I will profit by doing justice to him. But may I take leave to implore you yourself to favor me with that which you consider appropriate.55 At this juncture, the so-called priority dispute already had a long prehistory, and was destined to continue until Leibniz’s death and beyond.56 By 1694 the controversy had gone on for over a decade, having arisen primarily from the circumstance that neither Leibniz nor Newton had been informed early on about the achievements of the other in the area of infinitesimal analysis. The English mathematicians knew almost nothing until 1684 about Leibniz’s method, in particular about the date of its discovery and the chronology of its elaboration. Leibniz, for his part, had been informed by letters from the secretary of the Royal Society about certain results, and during his second London visit in 1676 he had access to Newton’s manuscript De analysi per aequationes numero 53 “et Tuam, et Fratris Tui viri eximii sententiam expecto” (A III,6 N. 12, p. 37). 54 Cf. A III,6 N. 84, p. 250. 55 “Vostre exhortation me confirme dans le dessein que j’ay de donner quelque Traité qui explique les fondemens et les usages du Calcul des sommes et des differences; et quelques matieres connexes. J’y adjouteray par maniere d’appendice les belles pensées et découvertes de quelques Geometres, qui ont bien voulu s’en servir, s’ils veulent avoir la bonté de me les envoyer. J’espere que M. le Marquis de l’Hospital voudra bien nous faire cette faveur si vous jugés apropos de le luy proposer. Messieurs Bernoulli freres, en pourront faire autant. Si je trouve quelque chose dans les productions de M. Neuton inserées dans l’Algebra de M. Wallis, qui nous donne moyen d’avancer, j’en profiteray en luy rendant justice. Mais oserois-je bien vous supplier vous même de me favoriser de ce que vous jugerés apropos” (note 49 above, p. 125). 56 Cf. Introduction to A III,1 and A III,6, pp. LVIff.

518

Chapter 4

terminorum infinitas of 1669, but, until 1693, he had no knowledge either of the method of fluxions, or of the chronology of its development. The result was that both sides could rightfully consider themselves to be the founder of infinitesimal mathematics, and – in as far as not just the results but also the methods were comparable – believe that the other side could have borrowed from them. Of particular significance in relation to the smoldering priority dispute was the role played by Nicolas Fatio de Duillier. The latter – following a year-long cooperation with Huygens – lived in London from 1687 where he developed his own inverse tangent calculus,57 and had gained the trust of Newton, by 1689 at the latest. There followed a second period of residence in Holland lasting more than a year, during which time he again had regular contact with Huygens,58 and to whom he subsequently wrote from London, on December 28, 1691, the following words: It is true, as Mr Leibnitz says, that there are several means to resolve this problem. To me it appears from that which I have been able to see until now, regarding which I learned from papers written many years ago, that Mr Newton is without doubt the original author of the differential calculus, and that he comprehended it just as perfectly, or more so, than Mr Leibnitz [who] failed to understand it again and the latter did not even have the thought itself, which did not come to him at all, as it appears, but only on the occasion of [receiving] that which Mr Newton wrote to him on this subject.59 And, suggesting that Newton shared his view, Fatio continued, with a reference to Newton’s Principia mathematica, writing as follows: (See Sir, if you please, page 253 of the book of Mr Newton). Also, I can only feel rather disappointed that Mr Leibnitz failed to note anything in 57 Cf. N. Fatio de Duillier à Christiaan Huygens (1687), HO, 22, pp. 126–151, being a reply to Huygens’ letter of July 11, 1687 (HO, 9, p. 90). 58 Cf. A III,5 N. 8, specifically pp. 56f. (HO, 10, pp. 17–22), N. 13, pp. 83–86 (HO, 10, pp. 55–58), and N. 18, specifically p. 104 (HO, 10, pp. 86–88). 59 “il est vrai comme le dit Monsieur Leibnitz qu’il y a plusieurs manieres de resoudre ce probleme. Il me paroit par tout ce que j’ai pû voir jusques ici, en quoi je comprens de papiers ecrits depuis bien des années, que Monsieur Newton est sans difficulté le premier Auteur du calculus differentialis, et qu’il le connoissoit autant ou plus parfaitement que Monsieur Leibnitz ne le connoit encore, avant que ce dernier n’en eut eu seulement la pensée, qui même ne lui est venue à ce qu’il semble qu’à l’occasion de ce que Monsieur Newton lui ecrivit sur ce sujet” (HO, 10, pp. 213–215, specifically p. 214).

1694–June 1696

519

the Acta of Leipzig. The latest disclosures which I have had concerning this matter have come solely from a couple of words which Mr Newton addressed to me; and I was surprised, having been up to then so close to having the same ideas, that they could have escaped my knowledge over such a long time.60 Leibniz learned nothing at the time about the views of Fatio. All in all then, the view had arisen among several English mathematicians that Newton had discovered the infinitesimal calculus much earlier, which at the time was flourishing on the continent and was being attributed to Leibniz, and furthermore, that the Leibnizian method could only be a redraft with a different notation of the Newtonian fluxional calculus. This seemed all the more plausible, since Leibniz had gained an insight – during his second London visit in 1676 – into Newton’s papers,61 and, furthermore, had received two detailed letters with Newton’s results, namely the so-called ‘epistola prior’, viz. Newton’s letter to Oldenburg for Leibniz and Tschirnhaus of June 23, 1676,62 and the so-called ‘epistola posterior’, viz. Newton’s letter to Oldenburg for Leibniz of November 3, 1676.63 To achieve public acceptance both for this view, and for the achievements of the English mathematicians, evidence on Newton’s behalf needed to be promptly published. This concerned, on the one hand, Newton’s still unpublished fluxional calculus and, on the other hand, all communications of the results of the English mathematicians, that had been sent to Leibniz. Wallis was the first who resolutely attempted to implement this plan in the context of his Opera mathematica.64 However, since Newton was unwilling to give his unrestricted approval to the effort, Wallis had to be satisfied at first with extracts from the relevant material.

60 “(Voiez Monsieur s’il Vous plait la page 253 du livre de Monsieur Newton). Aussi je ne puis assez m’étonner que Mr. Leibnitz n’en marque rien dans les Acta Lipsiensia. Les dernieres ouvertures que J’ai eues sur cette matiere me sont venues de deux mots seulement que m’a dits Mr. Newton; et j’ai été surprise qu’aiant été jusque là si prez d’avoir les mêmes choses elles eussent pû echapper pendant si longtemps à ma connoissance” (p. 214). 61 Cf. Leibniz’s excerpts from mathematical paper at the Royal Society dated October 18– 29, 1676; “Leibniz: Auszüge aus mathematischen Papieren der Royal Society [18.–29. Oktober 1676]”; A III,1 N. 98, pp. 663–681. 62 Cf. A III,1 N. 88,5, pp. 533–554; H. W. Turnbull et al. (eds), The Correspondence of Isaac Newton, vol. 2, (1960), pp. 20–47. 63 Cf. A III,2 N. 38, pp. 83–116; H. W. Turnbull et al. (eds), The Correspondence of Isaac Newton, vol. 2, (1960), pp. 110–129. 64 Cf. J. Wallis, Opera mathematica, 3 vols, Oxford, 1693–1699 (vol. 1, 1695; vol. 2, 1693; vol. 3, 1699).

520

Chapter 4

Leibniz first learned from Huygens of the intended publication of Newton’s method of fluxions, in a letter of January 12, 1693, but he failed to react to the intelligence.65 He was then informed directly by Newton himself, in a letter of October 26, 1693,66 about the publication of extracts from the two ‘epistolae’ of 1676, and the solution (or divestiture) of an anagram there in the context of the revised Latin version of Wallis’ Algebra.67 Again in this case, there was no reaction forthcoming on Leibniz’s part. Huygens received the Opera volume in question, which appeared at the beginning of September 1693, from the author, and he informed Leibniz accordingly, on May 29, 1694, in the following words: Mr Wallis has sent me the new Latin edition of his grand work de Algebra that has been supplemented with something new regarding the series of Mr Newton, where there are differential equations totally resembling yours except for the characters (notation).68 Since Leibniz did not possess a copy of the work, he asked Huygens, in the PS to a letter of June 22, to copy for him those parts of Wallis’ opus containing Newton’s new findings relating to the inverse-tangent method.69 It was also in this letter to Huygens that he articulated a proposal to include appropriate contributions of Newton – as they appeared in Wallis’ Opera mathematica – in his planned ‘Scientia infiniti’, in order to do justice to his rival. Thus he wrote: “If I find something in the texts produced by Mr Newton and included in the Algebra of Mr Wallis, which gives us the means for advancement, I will profit from this in rendering him justice”.70 On August 24, 1694, Huygens was able to send him a relevant extract,71 which he had received from David Gregory. In the opening paragraph of his reply to Huygens, on September 14, Leibniz then remarked:

65 Cf. A III,5 N. 123, specifically pp. 460f.; HO, 10, pp. 383–389. 66 Cf. A III,5 N. 194, pp. 655–657. 67 Cf. J. Wallis, De Algebra Tractatus, in J. Wallis, Opera Mathematica (note 64 above), vol. 2, 1693, pp. 1–482, and in particular the article on the method of fluxions in cap. XCV. 68 “Mr Wallis m’a envoié la nouvelle edition Latine de son grand ouvrage de Algebra augmenté de quelque chose de nouveau des series de M. Newton, où il y a des Equations differentielles qui ressemblent tout à fait aux vostres horsmis les characteres” (A III,6 N. 38, specifically p. 102; HO, 10, pp. 609–615). 69 Cf. A III,6 N. 45, and in particular the PS, p. 132; HO, 10, pp. 639–646. 70 “Si je trouve quelque chose dans les productions de M. Neuton inserées dans l’Algebra de M. Wallis, qui nous donne moyen d’avancer, j’en profiteray en luy rendant justice” (III,6 N. 45, p. 125). 71 Cf. A III,6 p. LIX, and N. 54, specifically p. 161; HO, 10, pp. 664–672.

1694–June 1696

521

I see that his calculus agrees with mine, but I think that the consideration of differences and sums, is more appropriate to illuminate the spirit … it appears to me that Mr Wallis speaks rather coldly of Mr Newton … I am discontented not to have found new insights there which I had anticipated for the inverse of tangents.72 This was in fact Leibniz’s one and only (and immediately communicated) known reaction to volume 2 of Wallis’ Opera mathematica. Essentially, while expressing his disappointment that only one of the two procedures for the solution of differential equations, namely the formal power-series method, had been published, he passed over any questions of a chronological, or temporal, priority and a possible interdependence of Newton’s and his own infinitesimal methods, although he did acknowledge the alleged similarity of the two methods. However, he misjudged (or suppressed) the totally new situation, where he could henceforth no longer assume two fundamentally different versions of the infinitesimal calculus, and with the inevitable questions of priority and plagiarism arising from this.73 The next volume of Wallis’ Opera appeared in mid-April 1695, and, on November 23 of that year, Otto Mencke sent a copy (presumably of the two volumes that had appeared) to Leibniz,74 who significantly proposed including a short announcement, or advertisement, rather than a full review of the work in the Acta Eruditorum, as is evident from Mencke’s letter of February 13, 1696.75 Before this, in the second half of January or early February, Mencke had forwarded to Leibniz the invoice,76 for a number of books he had purchased for him including Wallis’ Opera. In the “Ad lectorem praefatio” to the first volume, Wallis had once again treated the infinitesimal calculus of Newton and Leibniz, with the intention of giving the impression that Newton’s calculus of fluxions had already been made known to Leibniz in the aforementioned letters of Newton, or, in words of Wallis’ published text, in the “two letters of

72 “Je voy que son calcul s’accorde avec le mien, mais je pense que la consideration des differences et des sommes, est plus propre à éclairer l’esprit … Il me semble que M. Wallis parle assez froidement de M. Newton … je suis faché de n’y point trouver les nouvelles Lumieres que je me promettois pour l’inverse des Tangentes” (A III,6 N. 56, specifically p. 176; HO, 10, pp. 675–683). 73 Cf. A III,6, p. LIX. 74 Cf. A I,12 N. 121, p. 146. 75 Cf. A I,12 N. 278, p. 423. 76 Cf. A I,12 N. 263, p. 395.

522

Chapter 4

Newton of June 13 and August 24, 1676, given to Oldenburg for communication to Leibniz where he had explained this method to Leibniz”.77 Contrary to Leibniz’s proposal, Mencke insisted on a detailed review of Wallis’ Opera in the Acta Eruditorum, preferably also providing a little history of English mathematical literature or, in his words, “a little mathematical-literary history in England”.78 Since Leibniz failed to submit his review text in the months that followed, Mencke felt justified in sending him a reminder. At last, on June 30, 1696, Mencke was able to express his thanks for Leibniz’s review, but not without mentioning that Newton had given him a present of Wallis’ Opera.79 At the same time, he offered (in vain) his services as an intermediary in transmitting messages to Newton – who in the meantime had exchanged his scholarly activities for a state appointment as master of the mint – as he wanted to express his gratitude for Newton’s generosity. In his (once again anonymous) review, in June 1696,80 Leibniz followed essentially the same strategy as in the statement to Huygens, referred to above, namely that of not alluding to questions of priority and independence of the infinitesimal methods, but rather of prioritizing his criticism of the fact that Wallis had (indeed for lack of knowledge) paid too little tribute to the achievements of the continental mathematicians, in comparison with their English counterparts. This view of Wallis as an English nationalist – with the affectation of attributing all to his own nation – is also reflected in a passage (deleted before dispatch) from a letter Leibniz sent to Thomas Burnett of Kemney half a year earlier, on December 2, 1695, which reads: I am very satisfied with Mr Newton, but not to the same extent with Mr Wallis who has treated me somewhat cold-bloodedly in his most recent Latin works by means of a pleasant preciosity or affectation of attributing all to his own nation, sed sibi plaudit ipse domi (but he is applauding himself at home).81 77 “ex binis Newtoni literis  … Junii 13 et Augusti 24 1676, ad Oldenburgium datis, cum Leibnitio tum communicandis  … ubi methodum hanc Leibnitio exponit” (Wallis, Opera Mathematica, vol. 1, viz. J. Wallis, Opera mathematica, volumen primum e Theatro Sheldoniano, Oxford, 1695, praefatio); cf. also N. Guicciardini, 2012, pp. 3–17, and in particular p. 16, note 44 (Introduction, note 31). 78 “eine kleine Historia Literaria Matheseos in Anglia” (A I,12 N. 278, p. 423). 79 Cf. A I,12 N. 428, p. 668. 80 Cf. G. W. Leibniz [anon.], Review of Wallis: Opera mathematica, vol. 1 (Oxford, 1695) and vol. 2 (Oxford, 1693), Acta Eruditorum, (June 1696), pp. 249–259. 81 “Je suis fort satisfait de M. Newton, mais non pas tant de M. Wallis, qui me traite un peu froidement dans ses dernieres oeuvres latines par une plaisante affectation de tout attribuer à sa nation, sed sibi plaudit ipse domi” (A I,12 N. 136, p. 181). Regarding the Latin

1694–June 1696

523

That Wallis would not accept Leibniz’s view was foreseeable, and thus it was no surprise that Wallis complained about this review in the opening letter of his correspondence with Leibniz, on December 11, 1696.82 In the mid-1690s, Leibniz was also criticized for the first time for alleged deficiencies in the epistemological foundations of his infinitesimal calculus. The Dutch physician Bernard Nieuwentijt published two books, in the years 1694,83 and 1695,84 respectively, in which he accused Leibniz of inconsistencies, and lack of principles, in his calculus. Since the author had his books forwarded directly to Leibniz, and seemed authentic as regards the vein of his criticism, Leibniz thought he could lay the matter to rest with an equable reply in the Acta Eruditorum.85 However, in this assumption he was mistaken. The central objections of Nieuwentijt, which were also directed against Pierre de Fermat and others, were outlined by Leibniz in letters to L’Hospital, Huygens and Johann Bernoulli in late June and early July, 1695.86 These objections were, in Leibniz’s view, aimed at the very definition of a mathematical magnitude. Thus, the “infinite parvum” was for Nieuwentijt a nonentity, or “nothing”. Accordingly, two magnitudes were only equal if their difference was zero. If Leibnizian dx differentials were equal, then the dy differentials were also. The higher differentials were all equal to zero. Finally, Leibnizian calculus was considered to be not applicable to exponential equations. Leibniz countered Nieuwentijt’s criticism with the simple ascertainment that practical experience, or experiment, had confirmed the results obtained with his mathematical magnitudes. Thus, for example, in a letter to Detlev Clüver a year later, at the end of June or early July, 1696, he wrote:

82 83 84 85 86

text here, cf. the aphorism of Horace “Populus me sibilat, at mihi plaudo ipse domi” (for example in: E. Gowers, Horace satires book I, Cambridge, 2012, specifically I, lines 66f., p. 32) and the translation “the people hiss me: but I applaud myself at home” (cf. for example, M. N. Powell, Performing authorship in eighteenth-century English periodicals, Plymouth, and Lanham, Maryland, 2012, p. 107). Cf. A III,7 N. 55, pp. 206f. Cf. B. Nieuwentijt, Considerationes circa analyseos ad quantitates infinite parvas applicatae principia, et calculi differentialis usum in resolvendis problematibus geometricis, Amsterdam, 1694. Cf. B. Nieuwentijt, Analysis infinitorum, seu curvilineorum proprietates ex polygonorum natura deductae, Amsterdam, 1695. Cf. G. W. Leibniz [anon.], Review of B. Nieuwentijt, Considerationes circa analyseos ad quantitates infinite parvas applicatae principia (1694), Acta Eruditorum, (June 1695), pp. 272–273. Cf. A III,6 N. 135, pp. 415f., and N. 136, pp. 421f. (HO, 10, pp. 714–718), and N. 137, pp. 430f.

524

Chapter 4

I do not believe at all that the differential calculus, in the manner in which we make use of it, produces useless equations like the one of Mr Nieuwentiit who did not make use of it as he should. All that which we find by our methods is justified as well by experience [or experiments] just like the rest of mathematics.87 In his contribution for the Acta Eruditorum, in July 1695,88 he also dealt with the details of the difficulties raised by Nieuwentijt. And in the following month he even appended Addenda,89 in order to demonstrate the comparability of higher-order differentials with those of first order. Johann Bernoulli too publicly rejected the objections of Nieuwentijt.90 Notwithstanding all this, the Dutchman was not willing to concede. Through Otto Mencke’s letter of April 18, 1696,91 Leibniz learned that Nieuwentijt had prepared a detailed rejoinder for the Acta Eruditorum, from which however Mencke was prepared to publish only an extract. Thereupon, the author decided to publish his Considerationes secundae circa calculi differentialis principia et Responsio ad … G. G. Leibnitium as a book, which appeared at Amsterdam in 1696,92 and was then reviewed by Martin Knorr(e) in the Acta Eruditorum, in March 1697.93 Finally, a peripheral aspect of analysis, that touched however on fundamental questions and had implications for the entire field of mathematics, namely regarding notation, deserves mention here. Thus, in the years between 1694 and 1696 we find Leibniz heeding emerging nuances in the designation of

87 “je ne crois point que le Calcul differential, de la maniere que nous nous en servons, aille à des equations vaines, comme celuy de Mons. Nieuwentiit, qui ne s’en estoit point servi comme il faut. Tout ce que nous trouvons par nos methods est justifié encor par les experiences autant que le reste de la Geometrie” (A III,6 N. 247, p. 810). 88 Cf. G. W. Leibniz, “Responsio ad nonnullas difficultates a Dn. Bernardo Nieuwentijt circa methodum differentialem seu infinitesimalem motas”, Acta Eruditorum, (July 1695), pp. 310–316 (Leibniz: Parmentier, 1989, chap. 19, pp. [316]–334; Leibniz: Essais Scientifiques, 2005, N. 73; Leibniz: Heß-Babin, 2011, chap. 36, pp. 271–282). 89 Cf. G. W. Leibniz, “Addenda ad Dn. G. G. L. Schediasma proximo mensi Julio p. 310 et seqq. insertum”, Acta Eruditorum, (August 1695), pp. 369–372 (Leibniz: Parmentier, 1989, chap. 19, pp. [335]–337; Leibniz: Essais Scientifiques, 2005, N. 74; Leibniz: Heß-Babin, 2011, chap. 37, pp. 283–286). 90 Cf. Joh. Bernoulli, “Demonstratio analytica et synthetica suae constructionis curvae Beaunianae”, Acta Eruditorum, (February 1696), pp. [82]–85. 91 Cf. A I,12 N. 353, pp. 554f. 92 Cf. B. Nieuwentijt, Considerationes secundae circa calculi differentialis principia; et responsio ad virum nobilissimun G. G. Leibnitium, Amsterdam, 1696. 93 M. Knorr(e) [anon.], Review of B. Nieuwentijt, Considerationes secundae (1696), Acta Eruditorum, (March 1697), pp. 124f.

1694–June 1696

525

differential and integral symbols, and presenting correspondents like Johann Bernoulli with suggestions for the improvement and unification of notation.94 3

Dynamics and Natural Philosophy

In the April 1695 number of the Acta Eruditorum, Leibniz’s article “Specimen dynamicum pro admirandis naturae legibus” was published.95 It represented a renewed attempt on his part to circumvent the completion of the final version of his envisaged major opus Dynamica, which had been left in the hands of Bodenhausen in Florence since 1689. Leibniz had already referred on several occasions to this more than 200-page long projected work, which was, alas, destined to remain unfinished at the time of his death. The result was that not only his French followers, but also his German friends in Otto Mencke’s circle, continued to remind him ever more distinctly of the commitment he had given. Just as French scholars had to be satisfied with surrogate contributions in the Journal des Sçavans, their German counterparts had to make do with the “Specimen dynamicum”, in the Acta Eruditorum, the second part of which, although promised for the following month, never did in fact appear. Starting with a scrutiny of the concept of movement, Leibniz arrived at that of force, or “vis”, whereby he distinguished, on the one hand, between a metaphysical “vis primitiva” and a physical “vis derivativa”, respectively, and on the other hand, between a (differential or virtual) “vis mortua” and an (integral or real) “vis viva”, respectively.96 For forces associated with corporeal or substantial states, total and partial forces, respectively, were to be considered separately and, furthermore, in the case of the latter, the “vis respectiva” (internal force), and “vis directiva” (outward-operating or outward-manifesting force), respectively, were to be regarded separately. Leibniz duly arrived at a central conclusion of the work, according to which, from the connection of metaphysical

94 Cf. A III,6 N. 101, p. 313 and N. 214, p. 711. 95 Cf. G. W. Leibniz, “Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis, et ad suas causas revocandis”, Acta Eruditorum, (April 1695), pp. 145–157, and also: H. G. Dosch, G. W. Most, E. Rudolph (eds.), Gottfried Wilhelm Leibniz  – Specimen dynamicum (Lateinisch  – Deutsch [Latin  – German]), Hamburg, 1982; R. Ariew, D. Garber, G. W. Leibniz: Philosophical Essays, Indianapolis, Cambridge, 1989, in particular Part 1 (Basic Works), chap. 16, pp. 117–138 (A specimen of dynamics toward uncovering and reducing to their causes astonishing laws of nature concerning the forces of bodies and their actions on one another). 96 Cf. A III,6, pp. XXXIVf.

526

Chapter 4

laws and the laws of extended (or physical) bodies, the actual, systematic laws of motion arise and namely in such a fashion: That every change is effectuated by degrees and every action is [accompanied] by a reaction, that a new force is only produced through the detriment of its predecessor, that a separating body is decelerated by its counterpart remaining behind, with no gain or loss in the effect other than that contained in the cause.97 However, this connection was not to be misunderstood to imply that Leibniz wanted to explain physical phenomena using metaphysical laws. In fact, it simply implied that physical laws have their foundations not in themselves, but rather in metaphysical principles. Finally, Leibniz differentiated between “causae efficientes” and “causae finales”, whereby the latter are not accessible to humans in the same manner as the former. Nonetheless, they could certainly be employed with success in particular cases in physics, as in the case of extremal principles like, for example, in optics. As first important consequence from the systematic laws of movement, Leibniz cited the true quantification of forces – as the product of mass and the square of velocity – for the example of movement under the influence of terrestrial gravity. To the context of the establishment of the laws of dynamics on a metaphysical foundation – and, following from this, the partly a priori and partly a posteriori derivations of the true measure of force – belongs also the treatment of dynamics by Leibniz in his correspondences with Johann Bernoulli (on the occasion of the appearance of the “Specimen dynamicum”), with Denis Papin (on the occasion of the appearance of the latter’s Fasciculus dissertationum and Recueil de diverses pieces, respectively),98 with L’Hospital (on the occasion of the appearance of Leibniz’s philosophical article “Systême nouveau de la nature et de la communication des substances”),99 and, last but not least, with Jacob Bernoulli. The rekindled correspondence with Papin had a long and grief-stricken history, in the course of which ever increasing similarities to a legal battle being 97 “ut omnis mutatio fiat per gradus, et omnis actio sit cum reactio, et nova vis non prodeat sine detrimento prioris, adeoque semper abripiens retardetur ab abrepto, nec plus minusve potentiae in effectu quam in causa contineatur” (cf. p. 152; note 95 above). 98 Cf. D. Papin, Fasciculus dissertationum de novis quibusdam machinis atque aliis argumentis philosophicis, Marburg, 1695; Recueil de diverses pieces touchant quelques nouvelles machines. Et autres subjets philosophiques, Kassel, 1695. 99 Cf. G. W. Leibniz, “Système nouveau de la nature et de la communication des substances, aussi bien que de l’union qu’il y a entre l’âme et le corps”, Journal des Sçavans, (June 27 and July 4, 1695), pp. 294–306.

1694–June 1696

527

imposed on Papin had become apparent. Whereas Papin was, by and large, willing to let the scholarly public decide in the matter of the competing concepts of force, Leibniz tried again and again to convince him of the falsehood of his stated positions. And so, in this matter, they could see eye to eye, neither regarding the terminology, and the theory underlying this, nor regarding the physical phenomena and their interpretation. Thus, Papin had a fundamentally different understanding to Leibniz of the concepts of “effectus” and “vis”, and he interpreted most dynamic processes by resorting to very rapid percussions in an almost massless ether. Accordingly, his argumentation – concerning events taking place over the moment of time under consideration – led again and again to what was later to become known as ‘momentum’, or ‘impulse’, while he insisted above all on the conservation of this quantity. Leibniz, on the other hand, understood “effectus” to represent an ascent or descent, under the influence of terrestrial gravity, or a spring tension or spring force, having in mind what was later to be known as ‘energy’, and he, for his part, insisted on the conservation of that quantity. However, since he had no clear conception of the physical processes involved in occurrences like the force transmission from a falling body to other bodies, or that arising in the event of two bodies being impacted at the same instant by a third body, or in the tensioning or straining (or the relaxation or relief) of a spring, he was unable to convince Papin either by means of his thought experiments, or by drawing a theoretical distinction between a differential “vis mortua” and an integral “vis viva”. And so, with his argument “Mon sentiment est fondé en raisons et en experiences” – expressed in his letter of November 17, 1695100 – he was to come to grief and encounter outright failure in his efforts to convince Papin on both of these explanatory grounds, namely of reason and experiment (or practical experience), notwithstanding (in relation to the former) his formalization efforts using, and improving, syllogism chains – to which he first resorted in his letter of April 19, 1696 – were to prove to be of no avail.101 In relation to the latter, viz. physical experiment or engineering practice, Leibniz thought he could reduce the controversy to a simple consideration in the letter of November 17, 1695. Thus, he believed that the controversy could be reduced to a consideration of two identical bodies having the same simple velocity and whose joint force would be double that of either of the bodies on its own. In the same way, four such identical bodies would have quadruple of the force of any one of the bodies on its own. Now, however, an individual body having double the velocity in question could impart this simple velocity not to two, but rather to four, other 100 Cf. A III,6 N. 172, pp. 532–543, specifically p. 533. 101 Cf. A III,6 N. 225, pp. 744–747, and also, for example, pp. 66–72 (Improving the syllogism), in: G. MacDonald Ross, Past Masters: Leibniz, Oxford, 1984.

528

Chapter 4

identical bodies. Therefore, one of the bodies on its own, having a twofold velocity value, would have quadruple the force of another one of the identical bodies, having merely the simple velocity, which for Leibniz was that which was to be demonstrated. And, furthermore, for him, an estimation of the force as the product of magnitude (or mass) and velocity, i.e. the quantity of movement, had to be incorrect, and the error involved would be very considerable in practice, he insisted. Accordingly, he wrote in his copy of the dispatched letter, of November 17, the following passage which was marked with a line in the margin: Finally, I would add that one could reduce our controversy to a most simple consideration by simply taking care that two identical bodies having the same velocity are simply the twofold of one of the two and, as a result, they also have the twofold force; and similarly four such bodies have quadruple the force, and one, which can produce exactly this fourfold force on consuming its own, also has quadruple the force. So a body with double the velocity can give the simple velocity not just to two but rather to four bodies similar to it in magnitude, hence a simple body having double the velocity has the fourfold force of that of a simple body with a simple velocity. Which is that which was required to be shown. This illustrates the extent to which one deceives oneself by estimating the force as the product of the velocity and the magnitude, or by that which one calls the quantity of movement. This is even considerable in practice.102 In his reply, on December 9, Papin rejected outright Leibniz’s proposition insisting that he was convinced that it could never be proved, and that Leibniz was merely repeating that which he had proposed at the beginning of the dispute. Accordingly, quoting from Leibniz’s letter of November 17, he wrote: I deny absolutely … that [quote] a body having a double velocity could give the simple velocity not just to two but to four bodies which are equal to it in 102 “En fin j’adjouteray qu’on peut reduire nostre controverse à une consideration fort simple en prenant seulement garde que deux corps pareils et d’une meme vistesse sont precisement le double de l’un de deux et par consequent, ils sont aussi de double force; et de meme quatre tels corps sont de force quadruple, et ce qui peut produire justement cette force quadruple en consumant la sienne, est aussi de force quadruple. Or un corps de vistesse double peut donner la vistesse simple non seulement à deux mais à quatre corps qui luy sont pareils en grandeur, donc un corps simple de vistesse double est de force quadruple de celle d’un corps simple de vistesse simple. Ce qu’il falloit demonstrer. Cela fait voir combien on s’est trompé en estimant la force par le produit de la vistesse et de la grandeur, ou par ce qu’on appelle la quantité de mouvement. Ce qui est meme considerable en practique” (note 100, pp. 539f.).

1694–June 1696

529

magnitude [off-quote] and I am very convinced that you will never prove this proposition. The example which you specify does not prove anything other than that which you have been saying since the commencement of the dispute.103

Figure 2 Papin’s mechanical thought experiment Source: Denis Papin to Leibniz, December 9, 1695 (A III,6, p. 561)

Papin found that Leibniz had proposed two instances here that could be illustrated by the following experimental arrangement: bodies (weighing 1000 and 2000 pounds, respectively) were placed in turn at the circumference of a horizontal wheel (AA), whose vertical axis and shaft passed through a cylindrical drum (D) below. A rope wound around the drum, and passing over a pulley (C), was connected to a weight, or load (B), which on falling caused the wheel (AA) above to rotate. According to Papin, Leibniz was proposing that the body B, in the first experiment, on descending two feet below would give a load of 1000 pounds above a sufficient velocity to complete four rotations in a minute of time and, in the second experiment, on descending just one foot below would give a load of 2000 pounds above a sufficient velocity to complete two rotations in a minute of time. From this, Leibniz had claimed to prove that the force, communicated to the load of 1000 pounds in the first instance, was double that communicated to the load of 2000 pounds in the second instance, 103 “Je nie absolument … qu’ un corps de vitesse double peut donner la vitesse simple non seulement à deux mais à quatre corps qui luy sont pareils en grandeur [quotation (note 100, p. 540) in italics] et Je suis tres persuadé que Vous ne prouverez jamais cette Proposition. L’exemple que Vous alleguez ne prouve rien plus que ce que Vous avez dit dez le commencement de la dispute” (A III,6 N. 179, p. 561).

530

Chapter 4

because the body B had descended through double the vertical distance in the first case. And so he continued: For you are proposing [the following] two cases: the first is that a body of a thousand pounds be placed at the circumference of the horizontal wheel AA, and that the body B (by means of the cord BCD which passes over the pulley C and is wrapped around the shaft of the wheel AA) should be capable, on descending two feet, to give our body of a thousand pounds the velocity to complete four rotations in one minute; the second case should be that, on placing a body of two thousand pounds at the circumference of the said wheel AA, it will allow that the weight B descends one foot to give this body of two thousand pounds the velocity to complete two rotations in one minute; and from that you claim to prove that the force communicated to the thousand pounds in the first case is double the force communicated to the two thousand pounds in the second case since, in the first case, it is necessary that the weight B descends through double the height.104 To this Papin replied that he judged the two experiments to be the same, in the sense that the impact on the falling weight B would be the same in both cases. His words here were: To this I reply, Sir, the same as I did to your first objection through which the dispute began: for, taking account of the blows which the body B should receive in the one or other case, I find all to be equivalent, because the said weight B in the first case ought to traverse two feet in just as little time as it would require to pass through a single foot in the second case.105 104 “Car Vous ŷ proposez deux cas: Le premier est qu’un corps de mil livres soit posé à la circumference de la roue horizontale AA: et que le poids B (par le moien de la corde BCD qui passe sur la poulie C et est entortillée autour de l’arbre de la roue AA) soit capable, en descendant de deux pieds, de donner à nostre corps de mil livres la vitesse de faire quatre tours en une minute: Le second cas doibt estre qu’en mettant un corps de deux mil livres sur la circumference de la dte roue AA il suffira que le poids B descende d’un pied pour donner à ce corps de deux mil livres la vitesse de faire deux tours en une minute: et de là Vous pretendez prouver que la force communiquée aux mil livres du premier cas est double de la force communiquée aux deux mil livres du second cas: parce que pour le premier cas il a fallu que le poids B descendist d’une double hauteur” (p. 561). 105 “A cela Je respons, Monsieur, de mesme que J’ay fait à vostre premiere objection par où a commencé la dispute: car en prenant garde aux coups que le corps B doibt recevoir dans l’un et l’autre cas Je les trouve tous pareils: parce que le dte poids B dans le premier cas

531

1694–June 1696

Writing on January 1, 1696, Leibniz insisted that Papin had misconstrued his argument, and that he had never considered a weight descending from two different heights, but rather from the same height in both experiments, in order not to be seen to be begging the question, or to be supposing that which in question. His words of reply were: As regards the body of a thousand or two thousand pounds placed on the circumference of a wheel, you have not formulated the argument as I expected it, for I did not consider weights descending from different heights, but I wish to take simply the same height for the different cases, in order not to suppose that which is in question.106 Leibniz then continued, and reformulated the problem in his sense, namely as one an engineer might be confronted with.

Figure 3 Leibniz’s engineering thought experiment Source: Leibniz to Denis Papin, January 1, 1696 (A III,6, p. 596) doibt parcourir deux pieds en aussi peu de temps qu’il luy en faudra pour parcourir un pied dans le second cas” (p. 561). 106 “A l’egard du corps de mille ou de deux mille livres, posé sur la circonferance de une roue, Vous n’avés point formé l’argument comme je l’entendois, car je ne me suis point servi de poids descendus de differentes hauteurs, mais je veux prendre seulement une même hauteur pour les differens cas, pour ne pas supposer ce qui est en question” (A III,6 N. 190, p. 596).

532

Chapter 4

An undershot vertical water wheel (M), in a stream (LM) below, powered the horizontal wheel (N) above, by means of the intervening cog-wheel and lantern-pinion mechanism, causing the weight, or load, P on the circumference of N to rotate at a velocity V. According to Leibniz, in order to double the velocity V of the weight P by doubling the size of the wheel N, it would be necessary to quadruple the cross section of the stream – with the depth of the current and the slope remaining constant – and, likewise, to enlarge the radial vanes of the wheel M – extended parallel to the wheel’s axis – by a factor of four. Alternatively, the same effect could also be achieved by quadrupling the specific gravity of the fluid, while keeping the current and the area of the vanes constant. Accordingly, Papin’s thought experiment would ultimately lead to a four-fold force increase. Thus, Leibniz continued: Well then, behold how one might render the matter intelligible in my sense. Let LM be the current of a stream which turns the vertical water wheel M, [and] which makes the weight or load P, attached at the circumference of the horizontal wheel N, move with a velocity V. I say that to double the velocity V of the weight P, by doubling the horizontal wheel, it is not sufficient to double the current, but rather it is necessary to quadruple it, so to speak. That is to say, maintaining the same depth and slope of the current, it is necessary for it to have four times the size, [which is] also possible by making vanes of the wheel M four times as long, understanding their length to be measured [between lines] parallel to the axis of this wheel. Or otherwise, keeping the vanes and the depth of the current constant, a fluid would be required whose specific gravity is four times that of the previous fluid, with all the rest being left unaltered. And by this multiplication of the size, or of the specific gravity, one would have exactly the fourfold [value] of the force, even according to you.107 107 “Voicy donc comme on pourroit rendre la chose intelligible en mon sens. Soit LM le courant d’un ruisseau, qui tourne la roue verticale M, la quelle fasse aller avec une vistesse V le poids P attaché à la circomference de la roue horizontale N. Je dis que pour doubler la vistesse V du poids P en doublant la roue horizontale, il ne suffira pas de doubler le courant, mais il le faut quadrupler, pour dire ainsi. C’est à dire laissant la meme profondeur et pante du courrant, il faut l’avoir quatre fois plus large; en prennant aussi quatre fois plus longues les ailes de la roue M, entendant leur longueur parallele à l’axe de cette roue. Ou bien gardant les ailes et la grandeur du courant, il faudroit un fluide dont la gravité specifique fut quadruplé du fluide precedent et tout le reste egal. Et par cette multiplication de la largueur ou de la gravité specifique, on auroit justement le quadruple de la force encor selon vous” (pp. 596f.).

1694–June 1696

533

According to Leibniz, an engineer who claimed to be able to drive a load of 2000 pounds, in place of one of a 1000 pounds, at a velocity of a half of V (in place of V) using a horizontal wheel having a diameter of half that of N (in place of N), would be deceiving either himself, or the public, by maintaining that the same force was being supplied in both cases. To drive the load of 2000 pounds at a velocity of half of V, a current having a magnitude of merely half of that required to drive the load of 1000 pounds at a velocity V was required, a matter which, he insisted, could be demonstrated in advance, either from a consideration of the force of gravity acting on the water, or by modelling the water using balls or globules. At all events, he hoped that Papin could at least accept that, with identical depths and inclinations of the currents considered, the forces would vary as the magnitudes. His focus on finding differences, in terms of such magnitudes, had the intention of not having to have to resort to disputed measures like that of force. Thus he continued: But if an engineer proposed, in place of a weight of a thousand pounds, a weight of two thousand pounds, and wanted to give it just half the velocity of V, employing a wheel whose diameter was but half of that of the wheel N, I say that this engineer was deceiving himself, or deceiving us, in asserting that he is providing us in that way with the same force. For, to give the half of the velocity of V to 2000 pounds, he only needs the half of the breadth of that very stream, which gives the velocity of V to the load of a thousand pounds. This is a matter which one could demonstrate in advance of the experiment, either by the weight of the water, or by making use of globules in place of water. Well then, I imagine that you would agree with me at least that, with the inclination and the depths of the currents being the same, their forces are as their magnitudes. And you see that I only wanted to seek the difference in terms of magnitude in order not to apply a disputed measure … I have taken care to make use of principles we share in common, in order to establish conclusions which we do not.108 108 “Mais si un ingenieur au lieu du poids de mille livres proposoit un poids de deux mille livres, et lui vouloit donner seulement la moitié de la vistesse V en se servant d’une roue dont le diametre ne seroit que la moitié de celui de la roue N, Je dis que cet Ingenieur se trompe ou nous trompe, en soûtenant qu’il nous fournit par là la meme force. Car pour donner à 2000 livres la moitié de la vistesse V, il n’a besoin que de la moitié de la largeur du meme courant, qui donnoit au poids de mille livres la vistesse V. Ce qu’on pourra demonstrer avant l’experience, soit par la pesanteur de l’eau, soit en se servant des globules au lieu de l’eau. Or je m’imagine que vous m’accorderés au moins que le penchant et la profondeur des courans étant les memes, leur forces sont comme les largeurs. Et vous

534

Chapter 4

On January 15, 1696, there followed Papin’s rejoinder. While accepting the legitimacy of Leibniz’s representation (alongside his own) of the force supplied to drive the weights on the horizontal wheel, he could see no advantage in this. In a reference to Leibniz’s “Brevis demonstratio”, of March 1686,109 he claimed that Leibniz was once again presenting, albeit in disguised form, his original arguments of almost ten years earlier, in which he had attempted to show that (according to the Cartesian interpretation) levers of double and single length would impart double and single velocity values, respectively, to two bodies under consideration, which was nonetheless impossible. In his consideration of wheels of different diameters, Leibniz had now revived his earlier argumentation, since wheels represented a type of lever which would (as had previously been the case) be of no avail. Accordingly, Papin wrote: As regards the body of two thousand pounds placed at the circumference of a horizontal wheel I admit, Sir, that the argument can be formulated as you have done just as well as [in the way] I have done [it]; but you will profit no more from one manner than from the other; for it is as usual only your first argument that you have somewhat disguised. You have tried a long time ago to prove that, with a lever of double length, one could, according to our interpretation, give a velocity of 2 to body 1, while with a simple length, one gives a velocity of 1 to body 2, which is nonetheless impossible … You have not been able to arrive at your objective; accordingly there is no sign that you might gain anything from the wheels of different diameters, which you are employing at present, since one knows that the wheels are types of levers … You thus see, Sir, that regardless of which side one turns this argument to, one always reverts to questions that have already been examined.110 voyés que je n’ai voulu chercher la difference que dans la largueur pour ne pas appuyer sur une mesure disputée … j’ay eu soin de me servir des principes qui nous sont communs, pour établir des conclusions qui ne le sont point” (p. 597). 109 G. W. Leibniz, “Brevis demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae, secundum quam volunt a Deo eandem semper quantitatem motus conservari; qua et in re mechanica abutuntur”, Acta Eruditorum, (March 1686), pp. 161–163, and “A brief demonstration of a notable error of Descartes and others concerning a natural law”, in: Leibniz: Loemker, 1989 (2nd ed.), chap. 34, pp. 296–302 (Introduction, note 15). 110 “A l’égard du corps de deux mille livres posé sur la circumference d’une roue horizontale J’avoue, Monsieur, que l’argument se pouvoit former comme Vous avez fait aussi bien que comme J’avois fait: mais Vous ne gaignerez pas plus d’une façon que de l’autre: car ce n’est tousjours qu’un de vos premiers arguments que Vous avez un peu deguisé. Vous avez il ŷ a long temps taché de prouver qu’avec une double longueur de levier on devroit, selon nous, donner vitesse 2 au corps 1 quand avec une longueur simple on donne vitesse

1694–June 1696

535

Finally, on February 3, Leibniz wiped the slate clean on the discussion of the horizontal wheel drive. He had believed that in their consideration and discussion of the weight carried by a horizontal wheel, as in case of two bodies impacted at the same instant by a third body, Papin had laid aside his Cartesian philosophical attitude, and deigned to restrict himself to proofs based on sensible matter and capable of experimental proof. However, the correspondent’s renewed retrenchment in his former positions had ended his hope of a resolution of their dispute. Leibniz’s concluding words in this episode of the dispute were: When you called on me to prove that a body could produce double the quantity of its movement, and I spoke of heavy weights on the horizontal wheel, and of the stream, just like [the question of] two bodies impacted simultaneously by a third, I had reason to believe that you had stooped to [the realm of] sensible proofs or to means capable of experimental verification, and I attest to having been comfortable with this. But as you have taken refuge once again in your entrenched position, from which you had appeared to have briefly departed, you have deprived us of the means to resolve the case.111 Johann Bernoulli began, in his letter of June 18, 1695, his discourse on Leibniz’s “Specimen dynamicum” with praise for the definitions given of the fundamental concepts of dynamics, in particular those for “vis mortua” and “vis viva”, for which he immediately suspected parallels to the infinitesimal calculus.112 The Leibnizian “aestimatio virium” he chose however not to follow, at least at first. As a counter-example, he introduced the penetration depths of two equal bodies that encounter a homogeneous resisting medium, but with different 1 au corps 2 ce qui neantmoins est impossible … Vous n’avez pu parvenir à vostre but: ainsi il n’ŷ a point d’apparence que Vous puissiez rien gaigner par les roues de differents diametres que Vous emploiez à present: puisqu’on sçayt que les roues sont des especes de leviers … Vous voyez donc, Monsieur, que de quelque costé qu’on tourne cet argument on retombe tousjours dans des quaestions qui ont desjà esté examinées” (A III,6 N. 196, p. 615). 111 “Lorsque vous me demandâtes de prouver, qu’un corps peut produire le double de la quantité de son mouvement, et que je parlay du grand poids sur la roue horizontale, et du courant: item de deux corps choqués à la fois par un troisieme; j’avois sujet de croire que vous etiés condescendu dans les preuves sensibles ou dans les moyens que l’experience peut verifier: et je temoignay d’en estre bien aise. Mais comme vous vous estés retiré dans vostre retranchement, dont vous sembliés estre sorti tant soit peu, vous nous ostés le moyen de vuider le procès” (A III,6 N. 201, p. 642). 112 Cf. A III,6 N. 133, pp. 408–410.

536

Chapter 4

velocities. The depths of penetration into the medium would not be proportional to the square of the velocities, but rather to the simple initial velocities. Leibniz replied, on July 4, that not every arbitrary effect could be drawn on for the estimation of forces, but only those in which the force, which is taken in or absorbed, could also be given back or emitted once again, as in the case of tensioned springs, or of ascended or attained heights of fall in the sphere of terrestrial gravity.113 In the letters that followed, Leibniz persistently refused to go into the details of Bernoulli’s counter-example. Instead, on August 8, he instructed Bernoulli in detail in the general “ars aestimandi”, which postulated homogeneity, substitutability and additivity.114 Finally, a point was reached, in Leibniz’s letter of January 2, 1696, where he was at last prepared to introduce the special problems of “resistentia medii”, as the reason for the non-applicability of Bernoulli’s experiment.115 However, by the time of Bernoulli’s reply of January 28, 1696, the correspondent had read,116 both Papin’s Fasciculus dissertationum, and his Recueil de diverses pieces,117 and the correspondence then took a completely different turn. Following his study, and contemplation, of Leibniz’s conflict with Papin, Bernoulli had come to the conclusion that Leibniz’s conception was the only tenable one, and that Papin was simply seeking subterfuges in order not to have to concede. He provided additional evidence for Leibniz’s definition of force, in order to help corner Papin, and he cautioned Leibniz urging him to reexamine the implications of his new measure of force for the center-of-gravity principles, and for respective, or relative, resistance (“resistentia respectiva”). Leibniz had in fact previously believed that he could refute Papin using the example, or thought experiment, of an oblique or slanting impact of bodies that was now being proposed by Bernoulli. However, he had consciously desisted from playing this trump card, as he confided, on February 7, 1696, in the following words to Bernoulli, seeing the correspondent henceforth as an ally in the dispute with Papin: But, as I see you in our camp, I will communicate with pleasure my principle of demonstrating a priori the true estimation of forces having

113 Cf. A III,6 N. 137, pp. 428–430. 114 Cf. A III,6 N. 154, pp. 468–473. 115 Cf. A III,6 N. 191, pp. 599–602, specifically p. 601. 116 Cf. A III,6 N. 199, p. 627. 117 Cf. D. Papin, Fasciculus dissertationum and Recueil de diverses pieces, 1695 (note 98 above).

1694–June 1696

537

indicated several times that I have it in readiness, but which until now I have not yet produced.118 Further on in this letter, he conceded that, notwithstanding the extended dispute with the Cartesians, he had long been aware that analytical mechanics was founded conjointly on two conservation laws, of which the second – namely that which specified the velocity rather than the square of the velocity, or the conservation of the quantity of progress (“conservatio quantitatis progressus”) – differed from the conservation law of Descartes only in that the directions of the velocities were being taken into account.119 Thus, he wrote: I show not just how to conserve the same absolute force, or the quantity of action in the world, but also how to conserve the same directive force, or the same quantity of progress with respect to the same parts, but with the calculation of the progress in the parts being derived from the velocity of the mass, not the square of the velocity.120 Accordingly, the second of Leibniz’s two conservation laws agreed with Descartes’ rule, as he thought he should once again emphasize in his letter to Johann Bernoulli, on March 18, 1696. Regarding the determination of the laws of motion, on the basis of his two conservation laws he alluded to: The means of determining the laws of motion by the combination of these two laws, of absolute force conservation and of directive force conservation … which [latter] rule … corresponds to the Cartesian rule of the conservation of the quantity of motion.121

118 “Sed quoniam Te in nostris castris video, lubenter communicabo principium meum a priori demonstrandae verae aestimationis Virium quod mihi in promtu esse aliquoties indicavi, nondum tamen hactenus produxi” (A III,6 N. 202, p. 648). 119 Cf. G. W. Leibniz, Dynamica de potentia et legibus naturae corporae, 1689, pars 2, sect. 2, cap. 2, prop. 12A; A III,5 N. 61 (February 1692), p. 265; the conclusion of G. W. Leibniz, “Regle generale de la composition des mouvemens”, Journal des Sçavans, (September 7, 1693), pp. 417–419; A III,6, p. XXXVIII. 120 “demonstro non tantum eandem conservari vim absolutam seu quantitatem actionis in mundo, sed etiam conservari eandem vim directivam eandemque quantitatem directionis ad easdem partes seu eandem quantitatem progressus, sed progressu in partibus computato ducta celeritate in molem, non quadrato celeritatis” (note 118, p. 651). 121 “quemadmodum … ex conjunctis his duabus legibus: conservatae vis absolutae, et conservatae directionis, determinari Leges motuuum … quae regula … coincidit cum regula conservandae quantitatis motus Cartesiana” (A III,6 N. 214, p. 709).

538

Chapter 4

Then, in the further course of the correspondence with Johann Bernoulli, topics like the laws of impact of bodies, compound and conjoint movement, the resistance of a medium, center-of-gravity principles, and statements concerning centers of oscillation and percussion (“certrum oscillationis” and “certrum percussionis”), respectively, were interpreted anew, on the basis of the two conservation laws. In addition, Bernoulli pursued pertinaciously the question of the origin of gravity (viz. ether percussion), as did Leibniz regarding the possibilities of formal and a priori (viz. “formaliter” and “virtualiter”, respectively) proof or reasoning in dynamics. Even the course of the Leibniz-Papin correspondence was occasionally commented on, in the continuing correspondence with Johann Bernoulli. Already, on October 4, 1690, Leibniz had requested the opinion of Johann’s brother Jacob, about the dispute with the Cartesians, when he wrote: “I wish to learn your views concerning my demonstration against the Cartesians [based on] a measure of forces different from that of quantity of motion”.122 On December 12, 1695, Leibniz then sent Jacob a (relatively short) instruction in the most important basic principles of his dynamics,123 having received a letter from him, of October 19, from which it was evident that he had not been convinced by the explanations given in the “Specimen dynamicum”.124 However, because Jacob introduced the elasticity of the air even in Leibniz’s example of the tensioning of springs placed horizontally in a plane, and because he felt insufficiently informed about the ongoing treatment of this matter in Leibniz’s correspondence with his brother Johann, Leibniz was unable to convince him (at least at first) of the correctness of his force concept. L’Hospital likewise had great difficulty with Leibniz’s concept of force. In particular, it appeared to him, as he made clear in a letter of December 1, 1695, that the “quantité de mouvement” and the “force” lay in close proximity to each other. On this occasion the correspondent wrote: “But, just in the same way as one might agree that the same quantity of movement would not be conserved in nature, it would not follow at all that the quantity of force would be any different”.125 This incomprehension on L’Hospital’s part provided Leibniz with the welcome opportunity – in his reply of January 25, 1696 – of presenting to him, as 122 “Sententiam tuam nosse velim circa meam demonstrationem contra Cartesianos de aestimatione virium a quantitate motus diversa” (A III,4 N. 279, p. 581). 123 Cf. A III,6 N. 181, pp. 573f. 124 Cf. A III,6 N. 168, p. 520. 125 “Mais quand même on accorderoit que la même quantité de movement ne se conserveroit pas dans la nature, il ne s’ensuivroit pas que la quantité de la force en fust differente” (A III,6 N. 177, p. 555).

1694–June 1696

539

convincingly as possible, the main features of his dynamics. Here he stressed, on several occasions, that his concept of force did not need to be proved by experience, or experiment, since it could be derived solely from the principle of the equality of cause and effect. Likewise of interest is Leibniz’s allusion to the circumstance that the difference between quantity of movement and quantity of progress (“quantité de mouvement” and “quantité de progrès”) lay solely in the directionality of the velocities. Thus, for example, he wrote on this occasion: When there are several bodies the movement of that one, which moves in the opposite sense to the direction in which one estimates the progress, should not be added except with the minus sign, that is to say this quantity of movement should be subtracted, its progress being the negative [value] of the quantity of its movement.126 Alas, in the letters that followed, L’Hospital failed to respond to Leibniz’s efforts to persuade him. 4

Physics: Celestial Mechanics, Gravitation

In several correspondences (between 1694 and 1696), Leibniz expressed his views about the cause of gravity, which he attributed to a physical fluid in motion, or an ether. Thus, for example on November 17, 1695, he wrote to Papin that he considered “the rapidity of movement of the percussing fluid, which causes gravity, to be incomparably larger than that of the ponderous body”.127 In the same letter Leibniz compared his explanation of the cause of gravity to his understanding of that given by Papin. For him the force of gravity experienced by an ascending heavy body did not come from space, or elevation, but rather from physical percussion effects, or blows, it received. On the other hand, Papin’s explanation was based on the effect of a resisting, insensible fluid. Leibniz for his part rejected such an insensible fluid, and a possible explanation of gravity on the basis of philosophical suppositions (or hypotheses), rather than mathematics. Thus he wrote: 126 “quand il y en a plusieurs corps, le mouvemens de celuy qui va en sens contraire au costé vers le quel on estime le progrés, ne doit estre adjouté qu’avec le signe de moins, c’est à dire cette quantité de mouvement doit estre soustraite; son progress estant le negative de la quantité de son mouvement” (A III,6 N. 197, p. 622). 127 “la rapidité du movement du fluide percutiant, qui fait la pesanteur, soit incomparablement plus grande que celle du corps pesant” (A III,6 N. 172, p. 535).

540

Chapter 4

I profess that the resistance that a heavy body encounters on ascending does not come from the space or the height, but from the percussions [or blows] which it receives … It appears that you believed, but it is necessary that you should prove it, Sir, that the heavy body which ascends, always receives or produces on each blow an effect precisely equal with respect to an insensible fluid which resists it, and which causes gravity … As for me, I have no need to concern myself here with that going on in the insensible matter to which you have taken refuge, and which is perhaps the cause of gravity and of the spring. Our science is mathematics, and has no need here of these philosophical suppositions or hypotheses, although good elsewhere.128 Writing to Johann Sebastian Haes, on February 3, 1696, Leibniz spoke of the ether as the source of gravity,129 whereas in a letter of July 4, 1695, to Johann Bernoulli, he referred to a gravity whose cause he attributed to an ambient fluid.130 And likewise, in a subsequent letter to Johann’s brother Jacob in the spring of 1696, he referred to a certain gravitational material whose motion was the cause of gravity.131 However, the most important discussions about gravity, or gravitation, at this juncture, are to be found in Leibniz’s correspondence with the Newton confidant Fatio de Duillier, and with Huygens. Leibniz’s renewed interest in gravitation was provoked by Fatio’s letter for him of April 9, 1694, which was sent through the Hanoverian representative in London, Wilhelm de Beyrie. Fatio had presented his tract De la cause de la pesanteur, from the years 1688–1690, to the Royal Society of London, and he had discussed the matter in person, both with Newton and Huygens, before approaching Leibniz in written form. In this letter, Fatio emphasized his adherence to Newton’s theory of gravitation, and he endorsed his universal declaration of mutual attraction, and of the inverse-square law, in the following words:

128 “J’avoue que la resistence que le corps pesant rencontre en montant, ne vient pas de l’espace ou de la hauteur, mais des percussions qu’il reçoit  … ll semble que vous avez crû, mais il s’agit que vous prouviés, Monsieur, que le corps pesant qui monte, reçoit ou produit tousjours à chaque coup un effect precisement egal à l’egard du fluide insensible qui luy resiste, et qui fait la gravité … Pour moy, je n’ay point besoin de me soucier icy de ce qui se passe dans la matiere insensible où vous vous sauvés, et qui est peut estre cause de la pesanteur et du ressort. Nostre science est mathematique, et n’a pas besoin icy de ces suppositions ou hypotheses philosophiques, bienque bonnes d’ailleurs” (pp. 536f.). 129 “l’ether auteur de la gravité” (A III,6 N. 200, pp. 638f.). 130 “gravitas, cujus causam esse ab abiente non nego” (A III,6 N. 137, p. 428). 131 “materia gravifica … quod motu suo est causa gravitatis” (A III,6 N. 235, p. 772).

1694–June 1696

541

Mr Newton persists in his belief that all the parts of terrestrial bodies attract each other, notwithstanding that which Mr Huygens has said on page 159 of his treatise on gravity.132 I am, Sir, of the same sentiment as Mr Newton and I have indicated to both of these illustrious philosophers that there can be a mechanical cause of gravity,133 which confirms not just this mutual attraction but also the diminution of gravity in the inverse proportion to the square of the distance.134 And this cause is universal for the sun, the moon and all the stars, and neither the length of time may destroy it, nor can the movement of the celestial bodies inhibit the effect.135 For Newton, and Fatio, the universe consisted for the most part of empty space, for otherwise the celestial bodies would be exposed to a large resistance from the particles of an ether, and would accordingly be decelerated. With reference to various passages in the ‘Addition’ to Huygens’ Discours de la cause de la pesanteur, Fatio elaborated Newton’s criticism. Regarding the cause of gravity he wrote: Mr Newton is again undecided between these two sentiments. The first that the cause of gravity be inherent in matter by an immediate law of the Creator136 of the universe: and the other that gravity be produced by the mechanical cause which I have found,137 which brings about that all

132 Cf. Ch. Huygens, Traité de la lumière … avec un discours de la cause de la pesanteur, Leiden, 1690 (HO, 19, pp. 451–547 and HO, 21 pp. 427–499), and also Huygens’ letter of February 7, 1690, to Fatio (HO, 9, pp. 357–360). 133 “qu’il y a … la Pesanteur”: text passage underlined by Leibniz in the manuscript. 134 “la diminution … la distance”: text passage underlined by Leibniz in the manuscript. 135 “Monsieur Newton persiste à croire que toute les parties des corps terrestres s’attirent les unes les autres, nonobstant ce que Monsieur Hugens dit à la page 159e de son Traitté de la Pesanteur. Je suis Monsieur de même sentiment que Monsieur Newton et j’ai fait voir à l’un et à l’autre de ces illustres Philosophes qu’il y pouvoit avoir une cause mechanique de la Pesanteur, qui rende raison non seulement de cette attraction mutuelle, mais encore de la diminution de la Pesanteur dans la proportion reciproque du Quarré de la distance. Et cette cause est universelle pour le Soleil, la Lune et tous les Astres, et la longuer du tems ne peut la détruire, ni le movement des corps celestes n’en peut empêcher l’effect” (A III,6 N. 14, specifically p. 45; cf. also: Fatio de Duillier to De Beyrie, HO, 10, pp. 605–608). 136 “cause de la pesanteur … du Createur” (cause … the Creator): text passage underlined by Leibniz in the manuscript. 137 “la cause Mechanique … trouvée” (mechanical cause … found): text passage underlined by Leibniz in the manuscript.

542

Chapter 4

parts of matter mutually attract each other, except those which produce gravity itself,138 and the others which could be less coarse than these.139 Fatio rejected both Huygens’ hypothesis of matter in motion to explain the gravitation of the planets in the solar system, as well as his interpretation of gravity as a centrifugal force. He then proceeded to elaborate his own mechanical explanation of gravity. In addition to terrestrial matter, which was constituted of the smallest homogeneous particles, there existed everywhere in the universe an almost infinitely thin form of matter. The particles of this thin matter, which were subject to high-speed rectilinear motion in all directions, were the cause of gravity. Whereas Fatio enjoyed the approval of Newton, drawn-out investigations were required to rebut the objections of Huygens. The essence of these objections was that, as a consequence of Fatio’s theory, the matter surrounding the earth would become increasingly dense. Notwithstanding this, and confident of victory, Fatio wrote the following in his letter to Leibniz: “But this objection fulminates entirely when one examines it with exactitude; and it is that of which Mr Huygens is at present convinced”.140 In Leibniz’s reply of May 18, 1694, which was sent to De Beyrie for forwarding to Fatio, he showed an open mind regarding Newton’s interpretation of gravity, but he stressed the necessity of a mechanical explanation of gravity, or gravitation, as an inherent property of matter. He himself was undecided, and he alluded to his public dispute with Papin in the Acta Eruditorum from April 1689.141 Thus he wrote: “As regards gravity or attraction in general, I have indicated previously in a dispute which I had with Mr Papin that I was still in [a state of] suspense regarding the cause of gravity”.142 The competing theories to explain gravitation assumed physical processes based on the effects of circular motion (Huygens), and of rectilinear motion 138 “excepté … la Pesanteur même” (except those … gravity itself): text passage underlined by Leibniz in the manuscript. 139 “Monsr Newton est encore indeterminé entre ces deux sentimens. Le premier que la cause de la pesanteur soit inherent dans la matière par une Loi immediate du Createur de l’Univers: et l’autre que la Pesanteur soit produite par la cause Mechanique que j’en ai trouvée, qui fait que toutes les parties de la matière s’attirent mutuellement, excepté celles qui produisent la Pesanteur même, et les autres qui pourroient étre moins grossieres que celles ci” (A III,6 N. 14, specifically p. 46; HO, 10, pp. 605–608, and note 135 above). 140 “Mais cette objection s’evanouit entirement quand on l’examine avec exactitude: et c’est de quoi Mr Hugens est à present persuadé” (p. 48). 141 Cf. the introductory annotation to A III,5 N. 56, p. 246, and Chapter 2 of the present work. 142 “Quant à la pesanteur ou attraction en general, j’ay temoigné autre fois dans une dispute que j’avois avec M. Papin que j’estois encor en suspens sur la cause de la pesanteur” (A III,6 N. 34, p. 85).

1694–June 1696

543

(Newton), respectively. In the case of circular motion, centrifugal force was able to provide a sufficient explanation of gravitation, but an inverse-square law (analogous to the photometric inverse-square law) could not be derived from it. Thus, Leibniz continued: And, notwithstanding that which Mr Huygens has said in this regard, [namely] that employing centrifugal force would be extremely beautiful and plausible, I have adjudicated that in the event that one is unable to provide an explanation of the diminution following the inverse square law of the distances, proved (it appears to me) by the stars, it would be necessary to have recourse to a cause similar to light, which observes this inverse square rule.143 This was followed by a report about Leibniz’s own efforts to find an explanation for gravity, and indeed both on the basis of a circular-motion hypothesis, as of one assuming rectilinear motion. Regarding the first approach (circular motion) he could state: “I have contemplated the one and the other, and I have conceived a mode of circular motion, which does not lack plausibility with centrifugal force yielding this law of gravity”.144 He then described in greater detail his second approach (based on rectilinear motion), elaborating his “explosion” theory of gravitation, and comparing it to an incendiary process, in which coarse matter, having been enriched with fine matter at a periphery, is attracted to rarefied matter at the center of attraction, or in a flame. As a consequence of the ensuing explosion, or ignition, and the accompanying rarefaction, the fine matter is expelled to the periphery again, where it serves for alimentation of the coarse material there and accordingly for the continuation of the cycle, or process. Thus he continued: Nevertheless, I have also contemplated a rectilinear movement by conceiving a continual explosion in bodies which attract others, which bring into being an attraction to effectuate an interexchange; for the explosion of a dense and tenuous matter will bring about the attraction of the rare 143 “et quoyque ce que M. Hugens en dit, en employant la force centrifuge soit extremement beau et plausible, j’avois jugé qu’en cas qu’on ne puisse point expliquer par là la diminution en raison reciproque des quarrés des distances, verifiée (ce semble) par les astres, il faudroit avoir recours à une cause semblable à la lumiere, qui observe cette raison reciproque” (p. 85). 144 “J’avois medité sur l’un et sur l’autre, et j’avois conçu une maniere de movement circulaire, qui ne manque pas de plausibilité dont la force centrifuge donneroit cette loy de la pesanteur” (p. 85).

544

Chapter 4

and coarse matter which is on the periphery (supposing space not to be empty); [this is] approximately like the explosion observed in fire which is accompanied by the attraction of air (although it enters for other reasons). And the coarse matter (not entirely but in comparison with the rare matter) being attracted to the center, will be fractured and rendered rare rather like the manner in which fire consumes and dissipates that which it attracts while in exchange the rare and dense matter which is close to the center, being strewn towards the circumference, becomes rare in turn, and serves for the nourishment of the course bodies, in order to maintain this beautiful circulation of nature.145 Such an explosion would be comparable to the movement of light, and accordingly, the inverse-square law, analogous to the photometric inverse-square law, would also be valid, or as he formulated the process in this letter: “Now, this explosion imitating the laws of light (which is maybe also nothing other than such an explosion) causes an attraction which would obey the inverse-square law of distances”.146 Finally, he expressed the view that nature might indeed opt for a combination of circular and rectilinear motion, its style being to seek the optimal minimum-redundancy solution, and so he wrote: “Maybe also the circular and linear motions might contribute to the same effect, it being the style of nature to be abundant without being superfluous in terms of the means it employs to achieve its goals”.147

145 “Cependant j’avois pensé encor à un mouvement rectilineaire, en concevant une explosion continuelle dans les corps qui attirent les autres, qui feroit naistre une attraction pour faire echange; car l’explosion d’une matiere dense et deliée, feroit naistre l’attraction de la matiere rare et grossiere qui est à l’entour (pourveu qu’on suppose l’espace occupé); à peu pres comme l’explosion qui se remarque dans le feu est accompagnée de l’attraction de l’air (quoyqu’il y entrent d’autres causes). Et la matiere grossiere (non pas tout à fait, mais en comparaison de la déliée) estant attirée vers le centre, seroit brisée et rendue deliée à peu pres comme le feu consume et dissipe ce qu’il a attire pendant qu’en echange la matiere déliée et dense qui est proche du centre, estant dispersée vers la circumference, deviendroit rare à son tour, et serviroit à la nourriture des corps grossiers, pour entretenir cette belle circulation de la nature” (p. 85). 146 “Or cette explosion imitant les loix de la lumiere (qui peut estre encor n’est autre chose elle même qu’une telle explosion) feroit une attraction, qui observeroit la raison reciproque de quarrés des distances” (p. 85). 147 “Peut estre encor que le mouvement circulaire et rectilineaire concourent à un mesme effect, le stile de la nature estant d’estre abondante sans superfluité dans les moyens qu’elle employe pour ses fins” (p. 85).

1694–June 1696

545

Huygens was informed by Leibniz, on May 6, 1694, about Fatio’s letter of April 9, 1694.148 In this letter of May 6, Leibniz elaborated once again his “explosion” theory of gravitation as follows: I already imagined previously that there could be a type of explosion or recession149 [or] rejection of a very delicate type of matter and as a result more solid, or if you like more dense, which would as a consequence constrain the more rare and more coarse parts to approach each other. And to retain this movement I imagined that the finer more delicate matter being removed from the center would form part of the nutriment of the coarse body, and that the coarse matter arriving near the center of attraction would be ripped in return, and as a result rendered fine, rather like how the fire is nourished by the attraction of matter and particularly of air.150 In the context of this emission theory, he told the correspondent that he had succeeded in deriving the inverse-square law of gravity, or gravitation. He was however, still contemplating how he might arrive at the same result on the basis of the (to him) seemingly very plausible interpretation of the force of gravity as a centrifugal force. In his reply, on May 29, Huygens then characterized Fatio’s theory, which in essence accorded with that of Pierre Varignon, as a chimera.151 Against Huygens’ objection, namely that a consequence would be a concentration of the ether-like matter above the earth’s surface, Fatio had countered with the argument that the concentration of this material would not lead to any appreciable increase of mass. As regards Leibniz’s “explosion” theory, Huygens was likewise very skeptical, and he found Leibniz to be begging the question in his consideration of gravity. Thus he wrote here: “There would be a greater appearance [of truth] in your thinking about the immutation of 148 Cf. note 135 above. 149 underlining by Leibniz. 150 “je m’estois imaginé déja autres fois, qu’il y pourroit avoir une espece d’explosion ou recessus rejection d’une matiere tres menue et par consequent plus solide, ou si vous voulés plus dense, qui obligeroit par consequent celle qui est plus rare et plus grossiere de s’approcher. Et pour entretenir ce movement je m’imaginois, que la matiere menue estant eloignée du centre entroit dans la nourriture des corps grossiers; et que la matiere grossiere arrive vers le centre de l’attraction estoit brisée en echange, et par consequent rendue menue, à peu pres comme le feu se nourrit par l’attraction de la matiere et particulierement de l’air” (A III,6 N. 26, specifically pp. 71f.; HO, 10, pp. 600–605). 151 Cf. A III,6 N. 38, specifically p. 104 (HO, 10, pp. 609–615), and also P. Varignon, Nouvelles conjectures sur la pesanteur, Paris, 1690, which was reviewed in the Acta Eruditorum, (June 1691), pp. 299–301.

546

Chapter 4

particles, and in the comparison with the attraction of the air by fire, if it were not the case that one explains this attraction by presupposing gravity”.152 In his next letter to Huygens, on June 22, 1694, Leibniz defended, and further elaborated, his notion of an “explosion” theory. The ether particles that produce light, magnetism and gravity might contain a compacted fine matter, since they themselves were still relatively large. This compressed matter would be expelled as soon as the bodies were shattered on impacting the sun, or a similar body. Yet another conception of the explosion process involved the effects of a fine material – comparable to an infinite number of little air guns enshrined within the coarser matter  – that produced light, magnetism and gravity. The spring of the coarse material would be attributable to the effects of the fine material it contained. And so he wrote: One could afresh append the explosion as if it were that of an infinite number of little air guns. For one cannot say at all that the bodies which cause light, gravity and magnetism are also coarse, in comparison with those which make their peculiar spring, and thus they inclose a compacted matter; but when they arrive at the sun, or towards the center of other bodies which cause emissions (whose interior could approach that of the sun), the grand movement which is operative there, in shattering and disassembling them, would deliver the matter which was compressed there. It appears effectively that it is from that material that the fire acts.153 To counteract a possible concentration of the fine ether-like matter around the earth, and other bodies subject to gravitation  – and to meet Huygens’ objection – Leibniz conceived a dissipation of such matter in a fashion similar to the activity of sunspots, or in his words:

152 “Il y auroit plus d’apparence dans vostre pensée de l’immutation des corpuscules, et dans la comparaison de l’attraction de l’air par le feu, si ce n’estoit pas en supposant la pesanteur qu’on explique cette attraction” (pp. 104f.). 153 “On peut encor adjouter l’explosion comme seroit celle d’une infinite d’arquebuses à vent. Car ne pourroit on point dire que les corps qui font la lumiere[,] la pesanteur et le magnetism, sont encor grossiers en comparaison de ceux qui feroient leur proper ressort, et qu’ainsi ils enferment une matiere comprimée; mais quand ils arrivent au soleil, ou vers le centre des autres corps, qui font emission (dont l’interieur pourroit repondre au soleil) le grand movement qui s’y exerce, les brisant et les défaisant, delivreroit la matiere qui y estoit comprimée. Il semble effectivement que c’est de cette maniere que le feu agit” (A III,6 N. 45, specifically p. 130; HO, 10, pp. 639–646).

1694–June 1696

547

It is true that all the ethereal matter which tends towards the earth or towards some other body, without penetrating it, cannot return. For that which does not penetrate, will, being resilient, meet other matter arriving after it. Accordingly these materials should shroud each other and accumulate together around the body, but perhaps the mass formed in this way is dissipated again just like sun spots.154 Huygens continued to adhere to his objections against Fatio’s theory of gravitation. In his letter to Leibniz of August 24, 1694, he adamantly disputed Fatio’s claims to the contrary, in the following words: I believe I have communicated to you previously the solution which Mr Fatio claimed to give to that which I objected against his theory of gravitation, and with which I was not at all satisfied. That is why I am disappointed that he should have indicated the contrary to you. I do not see that one has again provided a considerable difficulty against the cause which I have explained in my Discours, and one would give me pleasure by presenting such to me on finding it.155 Furthermore, Leibniz’s repeated call for Huygens to derive an inverse-square law from his theory of gravitation failed to impress him. Right up to his death, he was convinced of the correctness, and completeness, of his own theory. However, Leibniz’s attitude towards Huygens remained conciliatory. He henceforth characterized the different theories about gravity, or gravitation, as being essentially equivalent, and he attributed the different opinions that had emerged mainly to different linguistic usage by the adversaries. Thus, for example, on September 14, 1694, he wrote: I do consider that all the hypotheses are equivalent, and when I assign certain movements to certain bodies, I do not have, nor could I have, any 154 “Il est vray que toute matiere etheree qui tend vers la terre ou vers quelque autre corps sans percer n’en sçauroit revenir. Car celle qui ne perce point, rejaillissant, rencontrera d’autre matiere qui y arrive apres elle. Ainsi ces matieres se doivent brouiller ensemble, et s’amasser à l’entour du corps, mais peut estre, que la masse qui s’en forme est dissipée derechef à peu près comme les taches du soleil” (p. 130). 155 “Je crois vous avoir communiqué cy devant la solution que Mr Fatio pretendoit donner à ce que j’objectois contre sa Theorie de la Pesanteur, et que je n’en estois nullement satisfait. C’est pourquoy je m’etonne qu’il vous ait mandé le contraire. Je ne vois pas qu’on ait encore apporté de difficulté considerable contre la cause que j’explique dans mon Discours, et l’on me fera plaisir de me les proposer lorsqu’on en rencontrera” (A III,6 N. 54, specifically p. 162; HO, 10, pp. 664–672; cf. also note 20 above).

548

Chapter 4

other reason than the simplicity of the hypothesis[,] believing that one can take the most simple one (all things considered) for the veritable one.156 Likewise, as regards explanations of planetary motions and the tails of comets, Leibniz tried to harmonize (at least partially) the theories of Newton with his own perceptions. These astronomical topics are found in his correspondences at this time with Detlev Clüver, Fatio, Huygens and Augustinus Vagetius. In this matter, Leibniz emphasized, again and again, to his correspondents his commitment to a vortex theory of planetary motion, and his opposition to the theory of Newton that was based exclusively on gravitation. At the same time, he adopted a conciliatory position (at least at first) in his letter to Vagetius of January 6, 1694, where he wrote: The motions of the planets, which I account for by harmonic circulation with gravity, Newton[,] for all his great acumen[,] shows can be explained solely on the basis of a trajectory and gravity. Which is true if every single planet be observed on its own.157 The observed phenomenon that all planets of the solar system, and all satellites of a planet, rotate in almost the same plane and in the same direction of rotation, could for Leibniz only be explained using an ether-vortex model. Thus, he continued in this letter to Vagetius: “But unless you introduce vortices, or a ‘fluidum deferens’ [viz. a transporting fluid], the cause will not be clear why all planets of the same sun, or all satellites of the same planet are carried in almost the same plane and in the same direction”.158 Thus, he skillfully concluded that: “For this reason I imagine the incorporation of the transporting fluid in the trajectory which is splendidly achieved by means of the harmonic circulation itself. It is also not possible to explain the gravity [the gravitational pull] itself

156 “Je tiens donc que toutes les hypotheses sont equivalents, et lors que j’assigne certains mouvemens à certains corps, je n’en ay ny puis avoir d’autre raison que la simplicité de l’Hypothese croyant qu’on peut tenir la plus simple (tout consideré) pour la veritable” (A III,6 N. 56, specifically p. 183; HO, 10, pp. 675–683). 157 “Motus planetarum, quos ego Circulatione Harmonica efficio cum gravitate, Neutonus pro maximo acumine suo ostendit ex sola Trajectione et Gravitate posse explicari. Quod verum est si unusquisque planeta per se spectetur” (A III,6 N. 2, p. 13). 158 “sed nisi vortices adhibeas, seu fluidum deferens[,] causa non apparet cur omnes planetae ejusdem solis, aut omnes satellites ejusdem planetae in eodem fere plano et ad easdem partes ferantur” (p. 13).

1694–June 1696

549

of the planets without [such] fluid motion”.159 And in addition there was, as he explained in the following words, a further reason for his ether-vortex, namely the analogy to the phenomenon of terrestrial, or planetary, magnetism in the guise of a magnetic rotation, or curl: “There is in addition a certain magnetic direction similar in planets, stones [viz. magnetic minerals like lodestone] and even vortices, that is a movement recurrent on itself, or in recurrent patterns, which on our earth gives the magnetic direction”.160 With this, Leibniz’s position appeared to be sufficiently consolidated, and he continued with the statement that “Newton’s argument against vortices in the theory of planetary motion does not appear to efface my position”.161 Even for the paths of comets, it seemed to him that the ether did not present obstacles, since the rare ether-vortex scarcely impeded the trajectory of a comet, or as he wrote: “Hence the path of comets is not notably disturbed by the vortex, since the matter of a vortex is extremely rare [and] its effect only follows after persistent and repetitive impacts”.162 However, as regards the tails of comets, the views of Leibniz and Newton were irreconcilable. Newton allowed the tails a material character, whereas for Leibniz they were simply optical phenomena, as he explained to Vagetius.163 The theory of planetary motion was also an important topic in Leibniz’s correspondence with Huygens, where the exchange of views relating to the Discours de la pesanteur (1690) continued. Just as with the explanation of the theory of gravitation, Leibniz adhered to his notion of an ether-vortex circulating around the sun, whereas Huygens saw centrifugal force as being decisive. However, this force was also included by Leibniz in his considerations when writing to Huygens, on May 6, 1694. There he wrote: But as your explanation based on centrifugal force also appears to me to be very plausible, I find myself suspended between these two sentiments. The inverse-square proportion of distances comes naturally and 159 “Itaque conjugendum arbitror Trajectioni fluidum deferens, quod ipsum Circulatione Harmonica egregie praestatur. Gravitas quoque ipsa planetarum non nisi per motum fluidi explicari potest” (p. 13). 160 “Accedit directio quaedam Magnetica similis in planetis, testis et ipsa vortices, id est motus in se redeuntis, qualis in terra nostra directionem Magneticam facit” (p. 13). 161 “Argumentum Neutoni contra vortices mihi stringere non videtur” (p. 13). 162 “Trajectio Cometarum a vortice ideo non turbatur notabiliter, quia tenuissima est vorticis materia, quae non nisi diuturnis ac repetitis impressionibus effectum suum consequitur” (p. 13). 163 “Caudas cometarum esse emissions reales nondum mihi Neutonus persuadere potuit, potius Phaenomena crediderim” (p. 14).

550

Chapter 4

easily from rectilinear emission used for the imitation of light rays; I have nevertheless also contemplated an explanation using centrifugal force.164 Here, it appeared to Leibniz to be certainly possible to bring the two possible causes under consideration into harmony, and so he continued: And possibly nature joins these two causes together, as I have a certain inclination to believe with respect to the movement of the planets, or perhaps the trajectory as such and the circulation of a transporting ether are conciliatory, and effectively conciliated, all in nature being accommodative.165 Once again, Leibniz introduced here the corresponding motion of the planets of the solar system, and the analogy between the supposed ether-vortex and magnetism, as arguments against the Newtonian gravitational theory of planetary motion. A day later, on May 7, 1694, Leibniz addressed the same theme in a letter to Clüver, whereby he enquired here especially about the cause of those phenomena of celestial mechanics which he believed he could easily explain with his vortex theory, and he referred among other things to the action of a terrella, or a small magnetized model ball, representing the earth. Thus he wrote: What do you say Sir regarding the physical sentiments of Mr Newton? He holds that there is a great amount of empty space in nature, that the bodies mutually attract each other, that there is no transporting fluid in relation to the planets, but how does it come about then that several planets or satellites of the same system are always found in the same plane almost, and that all rotate in the same direction? How do we maintain the analogy that exists between the magnetic bodies and the terrella, the terrella and the earth, the earth and the sun[?].166 164 “Mais cependant vostre explication par la force Centrifugue me paroissant aussi tres plausible, je me trouve comme suspendu entre ces deux sentimens. La proportion reciproque des quarrés des distances vient naturellement et aisement de l’emission rectilineaire à l’imitation des rayons de lumiere; j’avois pourtant pensé encor à quelque explication par la force centrifuge” (A III,6 N. 26, specifically p. 72; HO, 10, pp. 600–605). 165 “Et peutestre que la nature, …, joint ces deux causes ensemble; comme j’ay quelque penchant de le croire à l’egard du movement des planets, ou peutestre la trajection propre et la circulation d’un ether deferant, sont concilliables, et concilliés effectivement, tout s’accomodant dans la nature” (p. 72). 166 “Que dites vous Monsieur des sentimens physiques de Mons. Neuton? Il tient qu’il y a beaucoup de vuide dans la nature, que les corps s’attirent mutuellement, qu’il n’y a point

1694–June 1696

551

Continuing this line of thought, he then alleged that Newton could only resort to chance in his explanatory model, writing that: “It is therefore necessary that all these analogies exist by accident without there being analogous causes”.167 And, as an argument against Newton’s explanation of comet-tail appearances as real or material emissions, he objected that the fact, that the tails were observed to be confined to the plane of motion of the comet around the sun, contradicted such a material interpretation. On this issue he wrote: However, when I consider among other matters that these tails are to be found in the common plane of the sun and of both the line of movement and of the comet, it appears to me that they ought to be emphases or effects of a certain refraction. For, if they were real emissions, why should they be confined to this plane?168 Fatio, for his part, had his mind made up on this issue. Thus, he wrote in his letter of April 9, 1694: “It is indisputable that the tails of comets are real emissions, and it is only necessary to construct some of their orbits in order to see that these emissions169 are always situated in the plane of movement of the comets”.170 Leibniz then reacted, in his reply of May 18, with the counter argument that there was a greater plausibility that: These tails are always in the plane of movement of the comet; this appears to me to be more favorable to the opinion of those who believe them to be emphatic, all the more as the sun being always in the same plane with the trajectory line of the comet, these emphases or phenomena should

167 168

169 170

de fluide deferant à l’egard des planets, mais d’où vient donc, que plusieurs planets ou satellites d’un meme systeme se trouvent tousjours dans le meme plan à peu prés, et tournent tous d’un même sens? Comment maintenir l’analogie qu’il y a entre les corps magnetiques et la terrelle; la terrelle et la terre, la terre et le soleil[?]” (A III,6 N. 27, p. 75). “Il faut donc que toutes ces analogies arrivent comme par hazard et sans qu’il y ait de l’analogie entre les causes” (p. 75). “Cependant quand je considere entre autres choses que ces queues se trouvent dans le plan commun du soleil et de la ligne du movement et de la Comete, il me semble qu’elles doivent estre des Emphases, ou Effects d’une certaine refraction. Car si c’estoient des emissions reelles, pourquoy se borneroient elles à ce plan?” (p. 75). “these emissions … movement of the comets” (“ces emissions … movement des Cometes”): text passage underlined by Leibniz in the manuscript. “Il est indubitable que les queues des Cometes sont des emissions reelles, et il ne faut que construire quelques uns de leurs Orbes pour voir que ces emissions sont toujours situées dans le plan du movement des Comets” (A III,6 N. 14, specifically p. 47; HO, 10, pp. 605–608); cf. also note 135 above.

552

Chapter 4

not fail to land there, whereas nothing can constrain the real emissions to confine themselves to the common plane of the [trajectory] line and of the sun.171 Here he likewise defended his vortex theory of planetary motion against Fatio presenting the same evidence as in the letters to Huygens and Clüver cited above. 5

Physics: Optics

Leibniz’s thoughts on optics in the years between 1694 and 1696 were determined by the works of Newton and Huygens, and in particular by the latter’s Traité de la lumière of 1690.172 On the other hand, Leibniz hoped for more precise information about Newton’s experiments from his correspondence with Fatio de Duillier. It was therefore welcome that Fatio addressed the topic in his letter of April 9, 1694, in the following words: “There are very strong reasons, drawn from the properties of light and colors, which persuade us that the rays of light consist of corpuscles which actually come to us from the sun and the stars”.173 And so, Leibniz could enquire, in his reply of May 18, about an explanation of colors. Here he referred to the hypothesis formulated by Edme Mariotte – in his De la nature des couleurs (1681)174 – which was in opposition to the view held by Newton, namely that light rays do not possess any primitive constant colors but rather that their colors change, for example following refraction. Here Leibniz wrote:

171 “ces queues soyent tousjours dans le plan du movement de la Comete, cela me paroist plustost favorable à l’opinion de ceux qui les croyent emphatiques, d’autant que le soleil estant tousjours dans le même plan avec la ligne de trajection de la Comete, ces emphases ou phenomenes ne sçauroient manquer d’y tomber, au lieu que rien n’oblige les emissions reelles de ce borner au plan commun de la ligne et du soleil” (A III,6 N. 34, pp. 86f.). 172 Cf. Ch. Huygens, Traité de la lumière … avec un discours de la cause de la pesanteur, Leiden, 1690, and also note 132 above. 173 “Il y a des raisons tres fortes, tirées des proprietez de la Lumiere et des couleurs, qui Nous persuadent que les raions de Lumiere sont des corpuscules qui viennent actuellement du Soleil et des Etoiles jusques à Nous” (A III,6 N. 14, specifically p. 45; HO, 10, pp. 605–608, and note 135 above). 174 Cf. E. Mariotte, Essays de physique, ou memoires pour servir à la science des choses naturelles. I. De la vegetation des plantes. II. De la nature de l’air. III. Du chaud et du froid. IV. De la nature des couleurs, Paris, 1679–1681.

1694–June 1696

553

And as regards light, the great difficulty in my opinion is to explain colors, above all those called fixed. I am inclined to believe that they are of the nature of apparent colors, although the late Mons. Mariotte believed the contrary. I would like to know the sentiment of Mr Fatio, and even that of Mr Newton on this point and on the arguments of Mons. Mariotte, partly opposed to Mr Newton, above all that while allowing a difference of refrangibility, he denied nonetheless that color can only appear through a separation of primitive colored rays, believing he could prove that the same ray changes color by refraction.175 Alas, a reply by Fatio to the questions that had been raised never materialized. Leibniz reported to Huygens, on May 6, 1694, about Fatio’s letter of April 9, but not without making his own skeptical position clear in the following words: I learned from Mons. Fatio, through one of his friends,176 that Mr Newton and himself are again more inclined to believe that light consists of bodies which actually come to us from the sun, and that it is in this way that they explain the different refrangibilities of the rays, and the colors, just as if there had been primitive bodies, which always retain their colors, and which came materially from the sun to us. The matter is not impossible; nevertheless it appears difficult to me that, by the sole means of these little particles which the sun fires off, according to them, one could explain the laws of refraction.177

175 “Et quant à la lumiere la grande difficulté à mon avis est de rendre raison des couleurs, sur tout de celles, qu’on appelle fixes. J’ay du penchant à croire, qu’elles sont de la nature des couleurs apparentes, quoyque feu M. Mariotte ait crû le contraire. Je souhaiteray de sçavoir le sentiment de M. Fatio, et meme celuy de M. Newton sur ce point et sur les raisonnemens de M. Mariotte opposes en partie à M. Newton sur tout lorsqu’en accordant la differente refrangibilité, il nie pourtant, que la couleur ne paroist que par une separation des rayons colorés primitifs, croyant de pouvoir prouver que le même rayon change de couleur par la refraction” (A III,6 N. 34, p. 86). 176 Namely Wilhelm de Beyrie. 177 “J’ay appris de Mons. Fatio par un de ses amis, que Mons. Neuton et luy sont plus portés encor à croire que la lumiere consiste en des corps qui viennent actuellement du soleil jusqu’à nous, et que c’est par là qu’ils expliquent la differente refrangibilité des rayons, et les couleurs, comme s’il y avoit des corps primitifs, qui gardoient tousjours leur couleur, et qui venoient materiellement du soleil jusqu’à nous. La chose n’est pas impossible, cependant il me paroist difficile, que par le seul moyen de ces petites fleches que le soleil décoche selon eux, on puisse rendre raison des loix de la refraction” (A III,6 N. 26, specifically p. 71; HO, 10, pp. 600–605).

554

Chapter 4

Likewise, Huygens  – who had discussions with Newton (in the summer of 1689) and with Fatio (between June 1690 and September 1691) – was an opponent of the Newtonian corpuscular theory. For him, the very great (but finite) velocity of light – that had been demonstrated by Ole Christensen Rømer in his article “Demonstration touchant le movement de la lumière” of 1676178 – was an important argument against this theory, as he made clear to Leibniz in his letter of May 29, 1694, in the following words: Regarding the hypothesis for light which Mr Newton and Mr Fatio believe possible, I maintain that if light consists of the particles which really come from the sun to us, and similarly from all the stars, and from objects we can see, it is a necessity that this matter be extremely rare, and that vacuum occupies incomparably more space than it, in order that it be not impeded in its course coming to the eye from an infinity of different sides. But being so rare, that is to say being composed of particles very far apart from each other, how can one explain the extreme velocity of light, which has been proved by the demonstration of Mr Romer[?].179 Huygens had already confronted Fatio with the latter objection, alas without success. A further touchstone for Newton’s theory, Huygens saw in the explanation of refraction and, in particular, of double refraction. Thus he continued: “I do not see any more than you that, with their hypothesis, they could explain the cause of refraction, and also less so that of Iceland spar which serves me as an Experimentum Crucis, as Verulamius [i.e. Francis Bacon] called it”.180 And, regarding the explanation of colors given by Newton in his article “A letter …

178 Cf. O. Rømer, “Demonstration touchant le mouvement de la lumiere”, Journal des Sçavans, (December 7, 1676), pp. 276–279. 179 “Quant à l’hypothese pour la Lumiere que Messrs Newton et Fatio croient possible, je remarque que si la lumiere consiste en des corpuscles qui vienent actuellement du soleil jusqu’à nous, et de mesme de toutes les Etoiles, et des objects que nous voions, il faut de necessité que cette matiere soit extremement rare, et que le vuide occupe incomparablement plus de place qu’elle, à fin qu’elle ne soit pas empeschée dans son cours en venant vers l’oeil d’une infinite de costez differents. Mais estant si rare, c’est à dire composée de particules si fort separées, comment est ce qu’on peut expliquer l’extreme vitesse de la lumiere, qui est prouvée par la demonstration de M. Romer[?]” (A III,6 N. 38, specifically pp. 103f.; HO, 10, pp. 609–615). 180 “je ne vois pas, non plus que vous, que dans leur hypothese ils puissant expliquer la cause de la refraction, et encore moins celle du Cristal d’Islande, qui me sert d’Experimentum Crucis, comme l’appele Verulamius” (p. 104).

1694–June 1696

555

containing his new theory about light and colors” (1672),181 Huygens’ view was that neither Newton’s, nor his own, investigations had brought sufficient clarity, or as he wrote: The experiments carried out by Mr Newton on the different refraction of colored rays are beautiful and curious, but they do not explain at all what the color in these rays is, and it is in this matter that I myself am also not completely satisfied to the present moment.182 Leibniz had in the past repeatedly attempted to obtain more detailed information about the optical experiments of Newton.183 Now, on July 9, 1694, he reminded Huygens once again in the following words about his desire to learn about these: “I once requested that you inform me about that which Mr Newton communicated to you regarding colors, if you are allowed to do so. I take the liberty of reminding you here”.184 After these efforts had been to no avail, and in the wake of Huygens’ death, on July 8, 1695, he turned once again directly to Newton himself. On a slip of paper, dated December 16, 1695, which was intended for Newton, and with which Leibniz attempted to revive their correspondence – which had been in abeyance for a year and a half – the call for Newton to publish his research concerning colors as soon as possible occupied a central position. The note that Leibniz included with a letter sent to Burnett of Kemney, probably at the end of January 1696,185 for forwarding to Newton, had the following content: It is requested here that the celebrated Isaac Newton publish among other magnificent discoveries above all those regarding the nature and causes of colors[, in relation to which] he has observed and meditated over many years. Nor do I doubt that through his profound ingenuity 181 Cf. I. Newton, “A letter of Mr. Isaac Newton, containing his new theory about light and colors”, Philosophical Transactions, vol. 6, no. 80, (19 Februar 1671 / 29 Februar 1672), pp. 3075–3087, and also P. Fara, 2015 (Introduction, note 89). 182 “Les Experiences qu’a fait M. Newton de la differente refraction des raions colorez sont belles et curieuses, mais il n’explique pas ce que c’est la couleur dans ces raions, et c’est en quoy je ne me suis pas pleinement satisfait non plus jusqu’à present” (A III,6 N. 38, specifically p. 104; HO, 10, pp. 609–615). 183 Cf. for example, A III,4 N. 282, p. 600 and p. 610 (HO, 9, pp. 521–527), and A III,5 N. 53, specifically p. 242 (HO, 10, pp. 225–230). 184 “Je vous ay supplié un jour de me faire part de ce que M. Neuton vous a communiqué sur les couleurs, si cela vous est permis. Je prends la liberté de vous en faire ressouvenir” (A III,6 N. 48, specifically p. 140; HO, 10, pp. 649–651). 185 Cf. A I,12 N. 248, p. 366 (annotation).

556

Chapter 4

much light will have been shed here[,] that his reasoning should provide ascertainment both of fixed colors and also in the case of those which are called apparent.186 Whether or not Leibniz’s note reached the addressee is unknown. A reply probably never materialized, and Leibniz had to wait almost a decade for the publication of Newton’s seminal work Opticks, or Optice.187 Prior to Huygens’ demise, Leibniz had likewise hoped to obtain valuable clues from his investigation of Iceland spar about the nature of colors, as well as an explanation of the polarization of light in the context of the wave theory.188 All in all, Leibniz was highly impressed by the effectiveness, and capability, of Huygens’ wave theory of light. In this, Leibniz thought, Huygens had far surpassed his predecessors, like the two Jesuits Ignace Gaston Pardies and Pierre Ango, and of course Robert Hooke. In his appreciation of Huygens’ achievements in optics, Leibniz had occasion to recall his own publication “Unicum opticae, catoptricae et dioptricae principium” (1682).189 The reason for this was the consignment to Huygens, on May 6, 1694, of a copy of a dissertation, over which Martin Knorr(e) had presided, entitled Dissertatio dioptrica de refractione luminis (1693).190 Thus, he wrote on this occasion: Behold a discourse on refraction by an eminent professor at Wittenberg who has adopted the task in his theses of explaining your doctrine published in the book on light. He cites me too as a reformer of the hypothesis of Mons. Descartes, and I have in fact formerly said something about 186 “Vir celeberrimus Isaacus Newtonus rogatur, ut inter alia praeclara inventa, inprimis ea quae de colorum natura et causis a multis annis observavit et meditatus est, publicare maturet. Neque enim dubito a profundissimo ejus ingenio magnam hic lucem accensum iri ut fixis quoque coloribus suae rationes exemplo eorum quos apparentes vocant assignentur” (A III,6 N. 183, pp. 575f.). 187 Cf. I. Newton, Opticks: or a treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures (viz. Enumeratio linearum tertii ordinis and Tractatus de quadratura curvarum), London, 1704; I. Newton, S. Clarke. (ed.), Optice: sive de reflexionibus, refractionibus, inflexionibus et coloribus lucis libri tres, London, 1706; I. B. Cohen, E. Whittaker, D. H. D. Roller (eds.) and A. Einstein (Foreword), Sir Isaac Newton: Opticks or a treatise of the reflexions, refractions, inflexions & colours of light: Based on the fourth edition London, 1730, New York, 1952. 188 Cf. A III,6 N. 45 and N. 56. 189 Cf. G. W. Leibniz, “Unicum opticae, catoptricae et dioptricae principium”, Acta Eruditorum, (June 1682), pp. 185–190 (Leibniz: Essais Scientifiques, 2005, N. 9; Leibniz: Heß-Babin, 2011, chap. 4, pp. 19–28). 190 Cf. M. Knorre [Praes.], J. J. Hartmann [Resp.], Dissertatio dioptrica de refractione luminis, Wittenberg 1693.

1694–June 1696

557

this in the Acta of Leipzig, but your hypothesis appears to me to be much more plausible.191 However, Huygens’ reaction was one of disappointment that Knorr had failed to appreciate the significance of his Traité de la lumière, placing his wave theory of light on a par with those of his predecessors Robert Hooke – given in Micrographica (1665)192 – and Pardies, who had laid the foundation for Ango’s work L’Optique (1682).193 In his reply, on May 29, Huygens saw the essential leap forward on his own part, in comparison with his predecessors, in the explanation of the phenomenon of double refraction, and so he wrote: I thank you for the thesis of the professor of Wittenberg and I am pleased to see the approval for my theory, although he has been somewhat unjust to me in saying that my explanation of refraction is basically the same as those of Hooke and Pardies, and only differs from them as regards the manner of explanation. For all is rooted in this manner, and these authors would have been quite frustrated in explaining the bizarrenesses of Iceland spar.194 For Leibniz, on the other hand, Huygens’ explanation of wave propagation was the essential innovation. His criticism of Ango  – which he had previously expressed in his (never dispatched) letter for Huygens from the first half of October, 1690,195 and in a communication, on January 30, 1693,196 to Tschirnhaus – was now finally articulated in his letter to Huygens, on June 22, 1694, where he wrote: 191 “Voicy un discours de la Refraction d’un sçavant professeur à Witenberg, qui s’est attaché à expliquer dans ses theses vostre doctrine publiée dans le livre de la lumiere. Il me cite aussi comme reformateur de l’hypothese de M. des Cartes, et j’avois dit quelque chose en effect, dans les Actes de Leipzig d’autres fois, qui s’y rapporte, mais vostre Hypothese me paroist bien plus plausible” (A III,6 N. 26, specifically pp. 71f.; HO, 10, pp. 600–605). 192 Cf. R. Hooke, Micrographia: Or some physiological descriptions of minute bodies made by magnifying glasses. With observations and inquiries thereupon, London, 1665. 193 Cf. P. Ango, L’Optique divisée en trois livres, Paris, 1682. 194 “Je vous rends graces de la These du Professeur de Wittenberg et je suis bien aise de voir ma Theorie approuvée, quoyqu’il me fasse un peu tort de dire que mon Explication de la refraction est dans le fond la mesme que celle de Hoocke et de Pardies, et n’en differe qu’en la maniere d’expliquer. Car tout consiste dans cette maniere, et ces autheurs auroient esté bien empeschez à rendre raison des bizarreries du Cristal d’Islande” (A III,6 N. 38, specifically p. 103; HO, 10, pp. 609–615). 195 Cf. A III,4 N. 282, p. 597, pp. 599f. and pp, 609f.; HO, 9, pp. 521–527. 196 Cf. A III,5 N. 130, p. 488.

558

Chapter 4

Assuredly Mr Hooke and Father Pardies would not have had the guide railings to arrive at the explanation of the laws of refraction through the thoughts, which they had about waves. The essence lies in the manner of which you avail yourself in considering every point of the ray, like irradiance, and in composing a general wave from all these auxiliary waves. If Mr Knorr had consulted me I would have told him my sentiment regarding the above. Father Ango, who was only acquainted with this through that which he had found in the papers of Father Pardies, having tried in vain to explain the law of sines, finally fabricated a pure paralogism, clad as a demonstration, in order to get out of the affair.197 In Leibniz’s view, all of Huygens’ predecessors had failed to explain either the refraction of light, or the phenomenon of double refraction. Notwithstanding the progress that had been made, Leibniz continued to be interested in new works appearing in the field of optics. When, for example, he learned from a review, in the Journal des Sçavans,198 of the appearance of Nicolaas Hartsoeker’s Essay de dioptrique (1694),199 his main interest proved to be the explanation of the law of refraction given there, as he explained to L’Hospital on March 18, 1695. Thus he wrote in this regard: Since Mr Hartsoeker claims to explain refraction in particular, I would like to know if he explains the law of sines by a just method and one different to that of Mr Huygens. What he does is not to explain the fixed colors, but how they come from certain tinctures, according to the report in the Journal des Sçavans.200

197 “Asseurement M. Hook et le P. Pardies n’avoient garde d’arriver à l’Explication des loix de la refraction par les pensées, qu’ils avoient sur les ondulations. Tout consiste dans la maniere dont vous vous estes avisé de considerer chaque point du rayon, comme rayonnant, et de composer une onde generale de toutes ces ondes auxiliaires. Si M. Knorr m’avoit consulté je luy aurois dit mon sentiment là dessus. Le P. Ango qui ne sçavoit de cela que ce qu’il avoit pû trouver dans les papiers du P. Pardies, apres avoir bien süé inutilement pour rendre raison de la loy des sinus, a enfin fabriqué un pur paralogisme habillé en demonstration, pour se tirer d’affaire” (A III,6 N. 45, specifically pp. 128f.; HO, 10, pp. 639–646). 198 Cf. Journal des Sçavans, (February 7, 1695), pp. 95–103. 199 Cf. N. Hartsoeker, Essay de dioptrique, Paris, 1694. 200 “Puisque M. Hartsoecker pretend particulierement d’expliquer la refraction, je souhaitterois de sçavoir s’il explique la loy des sinus par une methode juste et differente de celle de M. Hugens. Ce n’est pas expliquer les couleurs fixes, que de les faire venir de certaines teintures, comme il fait selon le rapport du Journal des Sçavans” (A III,6 N. 102, p. 318).

1694–June 1696

559

Leibniz likewise continued to encourage the publication of new research results like, for example, when Clüver announced, on June 14, 1694, a new study of his about refraction, and diffraction, of light.201 In his reply, Leibniz announced his favorable judgement on the project, but at the same time he stressed the urgency involved in the effort in the following words: “It would be something wonderful if you could explain the diffusion of rays in a new way and easily intelligible. And above all if you could account for colors both apparent and fixed. And I ask you in the name of the public to produce your thoughts soon”.202 For Huygens, who had resumed work on his dioptrics in the spring of 1692,203 Leibniz surely had greater expectations than for Clüver when he asked him in a letter of September 14, 1694: “Can we expect to soon have your Dioptrica? I hope to find there explanations of emphatic meteors following that pattern which we have seen from you in former times”.204 Alas, Huygens work on dioptrics was destined to appear only posthumously, in his Opuscula postuma of 1703.205 In microscopy, the work of Antoni van Leeuwenhoek continued to attract Leibniz’s interest in the period under consideration. A particular wish of his was to persuade Leeuwenhoek to publish some of his research results in the Acta Eruditorum of Leipzig. Alas, his efforts were to be of no avail, as is evident from a letter of February 26, 1695, from Johann August Haberstroh in Leiden. This correspondent then proposed the anatomy professor Govart Bidloo as an alternative to Leeuwenhoek, who had declined Leibniz’s offer. Haberstroh’s words here were: Because you wrote, Sir, in your last letter that you would welcome it, if Mr Leeuwenhoek were to let his interesting results concerning the construction of human body parts be published in the Acta Eruditorum of Leipzig, to which however he was not willing to consent. I for my part, have taken the liberty of speaking with the professor of anatomy here 201 Cf. A III,6 N. 43, p. 119. 202 “Ca seroit quelque chose de bien beau si vous pouviés expliquer la diffusion des rayons d’une maniere nouvelle et bien intelligible. Et sur tout si vous pouviés rendre raison des couleurs tant apparentes que fixes. Et je vous supplie au nom du public de produire bientost vos pensées” (A III,6 N. 128, p. 391). 203 Cf. A III,5 N. 90. 204 “N’aurons nous pas bien tost vostre Dioptrique? J’espere d’y trouver des explications des Meteors emphatiques suivant cette echantillon qu’on a vû de vous autres fois” (A III,6 N. 56, p. 184). 205 Cf. Ch. Huygens (B. de Volder, B. Fullen, eds.), Opuscula postuma, quae continent dioptricam. Commentarios de vitris figurandis. Dissertationem de corona et parheliis. Tractatum de motu, de vi centrifuga. Descriptionem automati planetarii, Leiden, 1703.

560

Chapter 4

Mr Bidloo. Should you feel, Sir, not uninclined to make this man the same offer which you made to Mr Leeuwenhoek, you need only inform me by letter.206 However, in a letter of December 6 (or 16), 1695, to Haberstroh, Leibniz appears to have had a clear preference for Leeuwenhoek, and he made a further attempt to try to convince him to submit his research results to the Acta Eruditorum, as is apparent from Haberstroh’s reply from Leiden on January 29, 1696.207 In the course of the year 1695, Leeuwenhoek’s Arcana naturae detecta – in which he documented his numerous discoveries – was published in Delft.208 The work contained the following dedication: “Dedicatio Illustri & Magnifico Viro Do Antonio Magliabechi”. In a letter from Florence, on October 22, 1695, Magliabechi then informed Leibniz about the new publication in the following words: “Signore Leeuwenhoek has sent me along with one of his most courteous letters the first printed pages of his forthcoming Opera”.209 And, in the draft of a letter, at the end of October 1695, for the physician Justus Schrader in Amsterdam, Leibniz stressed the importance of the observer and experimentalist in the art of medicine, referring specifically to the Dutch biologist and microscopist Jan Schwammerdam (1637–1680), as well as to Leeuwenhoek of course. On this occasion he wrote: I add that thoughts are seldom productive if they are not combined with experiments … and I would acquiesce in the view that if we had a hundred Schwammerdams or Leeuwenhoeks, we would without doubt know the structure of bodies better.210 206 “Weil mein Patron in dero letzten geschrieben hatten, wie Sie wohl gerne sehen, daß der H. Loevenhoeuk seine curieuse sachen, waß Er circa constructionem partium humanarum gefunden hätte, wollte in die Acta Eruditorum Lipsiensia inseriren laßen, Er sich aber nicht dazu verstehen wollte, so habe ich vor mir mitt hiesigen Professore Anatomiae; Hn Biedtlau … geredet. … Sollte also etwa Mon Patron nicht ungeneigt seyn, diesem Manne eben dieselben offerten antragen zu laßen, die Sie dem H. Leuvenhoeuk offerirten, könten Sie mir eß nur schreiben” (A I,11 N. 197, pp. 284f.). 207 Cf. A I,12 N. 242, p. 359. 208 Cf. A. van Leeuwenhoek, Arcana naturae detecta, Delft, 1695; Arcana naturae, ope & beneficio exquisitissimorum microscopiorum. Detecta, variisque experimenta demonstrata, una cum discursu & ulteriori dilucidatione, Leiden 1696. 209 “Il Sig. Leeuwenhoek, con una sua cortesissima Lettera, mi hà mandati i primi fogli stampati, della seguente sua Opera” (A I,11 N. 514, p. 752, and annotation). 210 “Addo et raro meditationes prodesse, quae non experimentis conjunguntur … atque adeo centum Schwammerdammios aut Leewenhoekios haberemus, melius haud dubie nosceremus corporum structuras” (A I,11 N. 521, p. 768).

1694–June 1696

561

Tschirnhaus’ commitment to optics, and in particular to the perfection of concave mirrors and convex lenses, or burning glasses, extended back to the early 1680s, and continued to manifest itself in his correspondence with Leibniz in the 1690s. Following a renewed avowal of his commitment to optics as his overriding field of activity, he explained to Leibniz, on February 27, 1694, about a new machine he had developed for the manufacture of glass convex lenses of up to two feet diameter, and having a performance superior to the mirrors he had previously made. Here he wrote: I have a machine which someone will not easily be able to discover, and if anyone came across this idea, he would not have the convenience that I have here in the country, [for] in towns it does not work as well. There [in the country] one can make optical lenses of unbelievable size and of such perfection as that of the smallest glass that was ever cut and polished. Perspective glasses of unbelievable length can be prepared in this way which were [not previously possible] for anybody … I have already made glasses with a diameter of 2 Rhineland (Rhenish) feet; these provide admirable effects, of greater excellence than all mirrors that have been made up to the present day.211 In his most recent work, Tschirnhaus had been able to produce, within seconds, glass spheres or beads from the ashes of paper and vegetable matter, or from molten porcelain, talc or asbestos. And so he continued: Thus I have recently transmuted a book of paper in a short time into 18 beautiful transparent glass balls, a double sheet giving a glass ball of the size drawn here (o) … and thus all the ashes from the vegetables give a glass, without a single addition: porcelain, talc, asbestos melt in just a few seconds to complete glass balls.212 211 “Ich habe eine Machine die nicht leicht iemand erfinden wird, und wan iemand drauff kähme; so hatt Er nicht bald die Commodität so ahhie auff dem lande habe, in städten gehets nicht so wohl an; da kan lentes Opticas von unglaublicher größe, und so vollkommen verfertigen; als iemahls das kleinste glaß geschlieffen und poliret worden. Perspective gläßer von unglaublicher länge können hiedurch bereitet werden, welches keinen Menschen möglich … Ich habe bereits gläßer gemacht, die in Diametro 2 pedes Rhynlandicos haben: diese praestiren Admiranda Effecta, viel vortrefflicher, als alle Spiegel so bieshero gemacht” (A III,6 N. 10, pp. 29f.). 212 “so habe unlängst Ein buch papier in kurtzer zeit zu 18 Schönen durchsichtigen glaßkugeln transmutirt, ein bogen giebt eine glaßkugel so groß o als hier gezeichnet … so giebt alle asche auß den Vegetabilien gleich ein glaß, ohne einzigen zusatz: Porcellan, Talck, Asbest schmeltzen in wenigen seconden zeit zu vollkommen glaßkugeln” (p. 30).

562

Chapter 4

The area of application for such burning glasses was to be in chemistry. Thus, Tschirnhaus maintained here that with such a burning glass it would be possible to burn a fleck, or black spot, in wood located under water. And it could render molten many materials like pitch, sulfur, colophony (rosin resin); it even reduced metals to a glass form, and gold to ruby glass.213 Particularly interesting as regards the state of technology at the time was Tschirnhaus’ listing of the four main advantages of convex lenses, in comparison to concave mirrors, namely that they were highly effective, while not being as heavy, and as large, as their specular counterparts and therefore easily transportable – he related that he had even taken one with him on the mail, or post, coach to Vienna – and, in addition, the refracted rays travelled below, or underneath, the lens and could be aimed at fluids and powders of all kinds, and lastly, their polish, or glaze, which in mirrors was difficult to restore, was enduring. His exact words here were: Such a glass has [the following] 3 or 4 great advantages over a mirror: 1) that they are of great effect 2) are not so heavy and large, and accordingly easy to transport, as I was able [to show and] take one with me on the post coach to Vienna; 3[)] the rays following refraction pass below, which can then also be considerable with fluids, powders and which has been done in all kinds of trials, that are not possible with mirrors 4) the polish or glaze is enduring whereas with mirrors it must be arduously restored then and there.214 Although Tschirnhaus had found a series of noble buyers for his burning glasses, this did not cover his expenditure and, therefore, he sought to offer his lenses to a wider public in Holland. However, his real intention was to establish a fund for the advancement of the sciences out of the proceeds from the sale of his optical products. Leibniz lauded Tschirnhaus’ idea in no uncertain fashion, but as regards its realization, he remained skeptical. In the Fall of 1694, Leibniz and Tschirnhaus met up twice in Hanover. During his stay Tschirnhaus 213 “Unter dem waßer brennt es gleich einen Schwartzen fleck ins holtz[,] viele materien schmeltzet es, als Schwefel pech kolofonium: die Metalla reducirt es in ein glaß; Gold in ein Rubin glaß etc.” (p. 30). 214 “Ein solch glaß hatt 3 oder 4 große vortheil vor Spiegel: 1) daß Sie größere effecta thun 2) nicht so Schweer und groß, und also leicht fortzubringen, wie dan eines auff der post nach Wien mitt Mir genommen; zum 3ten so gehen die strahlen per refractionem unterwarts, welches considerabel dan also können auff fluida, pulveres allerhand tentamina geschehen, so in Spiegeln nicht möglich 4) so ist die Politur beständig, so in Spiegeln, dan und wan mit mühe wieder muß renovirt werden” (p. 31).

1694–June 1696

563

also demonstrated his burning glasses at the court in Hanover,215 in the hope of finding purchasers, not only for a burning glass but also for a large concave mirror (with a diameter of an ‘Elle’, or two feet or more), as is evident from a later letter he wrote to Leibniz, on October 22. On that occasion he wrote: As regards the large concave mirrors having a diameter of an ‘Elle’, it would be a great favor for me if one such instrument could be installed at Hanover and that as quickly as possible. NB. You could carry out all tests even in winter (for it operates under conditions of great cold) which would then be all the more wonderful. Please be so good as to send me a message soon about this.216 Likewise in Amsterdam, Tschirnhaus offered concave mirrors for sale. From Crafft’s letter of December 30, 1694, Leibniz learned about the following detail of Tschirnhaus’ business relationship with Ameldonck Block (or Bloeck): “|Tschirn.|217 owes him 2000 Taler, which he also wanted to contribute[,]218 if only the |mirrors| were sold”.219 From Huygens’ final letter to Leibniz, on December 27, 1694, we learn of Tschirnhaus’ visit, and about his inability to demonstrate a burning glass on that occasion due to unfavorable weather conditions. Thus Huygens wrote: Unfortunately, because of the clouded conditions, I was unable to see the effect of the burning glass of about 14 inches which he brought me. It is an advantage of these glasses that they burn from top to bottom, since the material that one exposes to them can be placed on coals which augments the force of the fire. But without this I cannot believe that these glasses, should they be of two feet [diameter], such as the ones he claims to have, could equal the force of a concave mirror of 3 feet [diameter],

215 Cf. A I,10, N. 67, p. 82. 216 “Was die großen Brennspiegel so in diametro einer Ellen groß anlangt, geschehe mir ein großer gefallen wen einen von solchen zu Hanover wohl anbringen köndte und daß so bald als möglich. NB Sie köndten auch im winter alle proben thun (den in der grösten kälte gehets an) welches also desto wunderbahrer fallen würde. Sie sein so gutt und ertheilen mir bald nachricht hiervon” (A III,6 N. 65, p. 201). 217 encoded in manuscript. 218 Namely, as an investment in the company for the production of brandy. 219 “|Tschirn.| ist ihm 2000 rthl schuldig, welche Er auch mit beyschießen wollte, wann die |spigel| nur an den Mann weren” (A III,6 N. 87, p. 264).

564

Chapter 4

which we had at the ‘Academie’ in Paris [and] which could melt nails of iron in a short time.220 Huygens, for his part, had a preference for the fabrication of concave mirrors from glass, with a diameter of up to 4 feet, having a coating on the back side and a small plane mirror near the focal point, in order to direct the rays to the combustible material. In his intended reply, written on July 1, 1695, a week before Huygens’ death, Leibniz wished to inform him, that a large mirror of Tschirnhaus was to be seen in Amsterdam and also about the production of convex mirrors in Nuremberg. Thus he wrote the following: An exemplar of the large mirror of Mr Tschirnhaus is at Amsterdam, so that you could see the experiment whenever you would like. That which you say, Sir, about the concave mirrors made out of glass which someone has made at The Hague appears to me to be significant. Just the same it is difficult in the ordinary way to make them with the sheeting or lamination on the back side. Convex mirrors of glass are being made at Nuremberg which have a certain composition at the back which takes the place of the foil. I have heard from several people who have tried in vain to learn about them.221 On June 18, 1695, Johann Bernoulli had sent Leibniz (from Basel) the following premature report of Huygens’ death: “I learn this very hour from a letter of D. Hospital that the noble Huygens has passed away, ‘heu!’ [expression of dismay or pain]. So much sorrow, should it be true, surrounds me”.222 In his reply, 220 “le Malheur voulut, qu’ à cause du temps couvert je ne pus voir l’effet du verre brulant qu’il m’apporta d’environ 14 pouces. C’est un avantage de ces verres de bruler de haut en bas, parce que la matiere qu’on y expose se peut placer sur un charbon qui augmente la force du feu. Mais sans cela je ne scaurois croire que ses verres, quand ils seroient de 2 pieds, comme il dit en avoir, puissant egaler la force du miroir concave de 3 pieds, que nous avions à l’Academie à Paris, qui faisoit degouter les clous de fer en peu de temps” (A III,6 N. 86, specifically p. 260; HO, 10, pp. 696–699). 221 “Un exemplaire du grand miroir de M. Tchirnhaus est à Amsterdam, de sorte que vous en porriés voir l’experience quand vous voudriés. Ce que vous dites, Monsieur, des miroirs concaves de verre, que quelcun fait à la Haye me paroist considerable. Il est difficile cependant pour l’ordinaire d’en faire avec de la feuille derriere. On fait des mirroirs convexes de verre à Nurenberg, qui ont une certaine composition derriere qui tient lieu de feuille. J’ay ouy dire à plusieurs qu’ils ont taché en vain de l’apprendre” (A III,6 N. 136, specifically p. 419; HO, 10, pp. 714–718). 222 “Audio hac ipsa hora, ex literis D. Hospitalii, Nob. Hugenium obiisse, heu! Quantus dolor, si verum esset, me circumdaret” (A III,6 N. 133, p. 410).

1694–June 1696

565

on July 4, Leibniz expressed his grief (but also his doubts about the report), writing that: “I was greatly perturbed by what you write about the reported death of the incomparable Huygens. As I received nothing, I hope it is an error”.223 Finally, in his letter of August 8, 1695, Leibniz himself could inform Bernoulli about the passing of his former mentor (of his Paris years) with the words: “That the incomparable Huygens has passed away, you have without doubt learned [already]”.224 6

Power Technology and Mining

It was in the autumn of 1678 that Leibniz submitted his first proposal for the improvement of mining in the Harz mountains to duke Johann Friedrich in Hanover.225 Leibniz’s involvement in mining had continued until August 1685, when duke (and prospective elector) Ernst August ordered the cessation of his activities in the mines against Leibniz’s clearly formulated wishes. Nonetheless, by the middle of 1687 at the latest, Leibniz had come to terms with the fact that his involvement in mining in the Harz mountains was not desired. However, six years later, a proposal made by the moneyers Johann Jacob Jenisch and Rudolf Bornemann to increase the production of ore mining – by employing a small number of horses to power the winding machinery – led to a revival of Leibniz’s interest in the ore mines.226 When he learned of this proposed undertaking, at the end of March 1693, the authorization procedure was already at an advanced stage. Accordingly, he immediately approached both the chamber in Hanover,227 and his sovereign Ernst August,228 who ultimately had to grant approval for the proposed venture, claiming his own priority in the matter.229 Since the means of realizing a profit increase had not been clearly presented by Jenisch and Bornemann, Leibniz feared that his own idea of weight compensation, using an endless rope or cable, might actually be applied in the enterprise. In the summer of 1693, Leibniz finally succeeded in convincing Ernst 223 “Perturbasti me mirifice dum nuntiatam Tibi incomparabilis Hugenii mortem scribis. Cum nihil ad me pervenerit, erratum spero” (A III,6 N. 137, p. 430). 224 “Incomparabilem Hugenium obiisse, haud dubie intellexisti” (A III,6 N. 154, p. 473; cf. annotation). 225 Cf. A I,2 N. 73, pp. 83ff. 226 Cf. A I,Supp., N. 228 (November 23, 1692), N. 230 and N. 231 (January 29, 1693), N. 237 (April 22, 1693), N. 250 (November 27, 1693) and N. 251 (December 16, 1693). 227 Cf. A I,Supp., N. 6. 228 Cf. A I,Supp., N. 7. 229 Cf. for example, A I,4, N. 165ff.

566

Chapter 4

August that his work on the history of the Welfs (or Guelphs) would not be retarded by a revival of the Harz project, since he would be able to delegate the execution and supervision to others. Thus, the trial of Leibniz’s proposals at his own expense received short-term approval, until the end of the year 1693.230 And, the application of his rivals was accordingly put on hold. For the execution of the skilled manual work, Leibniz was able to obtain the services of Hans Linsen and fellow tradesmen and, for supervision and materials procurement, Balthasar Ernst Reimers was engaged as his managing agent and, as a skilled pitman, the senior mining official from Clausthal, Daniel Flach, was to be present at operation trials of the winding machinery. Details of the allocated pit, as of its nature and condition, along with the difficulties encountered in the trials are revealed in Leibniz’s extensive general political and administrative correspondence relating to his mining involvement in the years 1693–1696.231 As might have been expected in light of the ill-fated series of trials of Leibniz’s proposals for the improvement of engineering methods in the mines, which had been carried out during the first half of the previous decade, he once again greatly underestimated the operability and requisite time span for his undertaking. And so, at the end of 1693, he found himself trudging through a second mammoth task – in addition to the ‘opus historicum’  – whose end was not in sight and which would earn him more disappointment than recognition. A further result was that – because of the lack of the requisite leisure  – the continuation, or completion, of his other scientific plans and activities had inevitably to be put off to an even later date in the future. The years between 1693 and 1696 then marked Leibniz’s second period of activity in the Harz mining district. The improvement of the mine-dewatering pumps, and an increase in the efficiency of the winding machinery for hoisting ore, were at the center of his interest at this point. He contemplated the possibility of replacing both horse mills (“Gaipeltreiben”) and the overshot reversible water wheel (“Kehrrad”) as power sources. He hoped to achieve his goals by using a rod-engine power transmission system, from a remote water wheel to the pithead, and not just for operating the pumping machinery alone, as had previously been done, but also for the winding or hoisting machinery. In order for such a combined system to function properly, the overall power requirement needed to be significantly reduced, and Leibniz thought of achieving this, on the one hand, by employing an endless (or closed-circle) winding cable or chain. In addition, he conceived a tugging or towage mechanism 230 Cf. A I,Supp., N. 244. 231 Cf. A I,Supp., N. 1 (March 19, 1693) – N. 282 (March 14, 1696).

1694–June 1696

567

(“Geschleppe”) having a switchable pinion gear mechanism that would transform the above ground alternating linear motion, firstly, into the vertical alternating linear motion of the pump, or piston rods, by means a standard cross-shaped lever system (a ‘Kunstkreuz’), located at the pithead, and secondly, into the circular motion of the winding machinery, by means of a capstan or roller drive also located at the pithead. Thus, in theory at least, the objective would be achieved of powering both the pumping machinery (vertical alternating linear motion) and the winding machinery (circular motion) using a single vertical water wheel with its rod-engine transmission system. The completion and testing of the requisite machines proved to be very protracted, however. Only in February 1694 was Leibniz able to connect – for test purposes – the tugging system powered by the rod-engine transmission line with the capstan, or roller drive, of the winding machinery at the pithead. The complementary tugging system was connected, via a linkage mechanism, with the transmission line at a point about halfway between the water wheel and the pithead. The system proved to be functional at first and was demonstrated on February 18, 1694 – in Leibniz’s presence – to the mining officials. On the occasion of that demonstration, some 4 tons of ore were hoisted in an hour before the machinery came to a standstill.232 In the course of later hoisting trials, further dysfunctionalities were experienced and there ensued contention and conflict with the Mining Office in Clausthal which, in turn, was reported to the Chamber in Hanover.233 Leibniz delegated the supervision of the trials at the pits to Reimers, during his absence, whereas the juror Zacharias Pöhler emerged as his main opponent, or adversary, in the undertaking. On April 16, 1694, Leibniz reported to Crafft about damage to the rod-engine system, and about the opposition and obstruction being experienced from the jurors, and engineering officials, on location. His words to Crafft were: Balthasar [Ernst Reimers] … has told me almost laughable things about the objections that they will bring forth; after their ‘by hook or by crook’ strategy had gone amiss they did not know what they should come up with and the jurors and engineers were in desperation in that they were having to fear that this undertaking would be forced upon them. For this reason they have now conceived the strategy of presenting what they find wanting in this long rod-engine transmission system (which we attach 232 Cf. “Diarium von B. E. Reimers über die Versuche mit der neuen Treibkunst vom 2. (12.) Februar bis 14. (24.) April 1694” (A I,Supp., N. 148, pp. 225–239). 233 Cf. A I,Supp., N. 144, N. 145, N. 265 and N. 267.

568

Chapter 4

alternately to our machinery), and particularly at this time of year because the water wheels, which rotate rapidly as a consequence of the spring floods, need repairing, and such is made attributable to our machinery and its attachments; one can deal with this politely however. For, a certain so-called long linkage or oscillating rod on their transmission system had previously been split and one can in fact see the old fissures in it and one has therefore a complete proof that they have joined them together and continue to use them and it is just that very drawing [exertion] of the rod, which with time stretches the joints and which actually has taken place – indeed a noteworthy fact – at that part of the long rod-engine transmission line which lies beyond our linkage point.234 Leibniz also prepared the following sketch of the damaged rod-engine transmission line.235

Figure 4

Leibniz’s sketch of a damaged rod-engine transmission line Source: Leibniz to Johann Daniel Crafft, April 16, 1694 (A III,6, p. 51)

234 “Balthasar [Ernst Reimers] … hat mir fast lacherliche dinge von den objectionibus die sie auf die bahne bringen warden, erzehlet, nach dem das Brechen numehr auß sey, wüsten sie nicht waß sie solten vorbringen und waren die Geschwornen und Kunstleute au desespoir, daß sie besorgen müsten, es werde ihn dieß werck aufgebürdet werden; daher sie ietzo dieses stratagema erdacht, daß sie vorgeben was ihren bey den langen Künsten (die wir an unser werck wechsels weise anhangen) fehlsahm, und zumahl bei dieser Zeit des Jahrs, da die Künste der fluthen wegen starck gehen, repariert werden müsten solches sey von unsern werck und deßen [anhengung] hergerühret. Man kann sie aber gar artig überweisen. Den eine gewiße so genante große schwinge so an ihre kunst gebrochen ist schohn vohrher gespalten gewesen und kann man den alten riß eigentlich daran sehen und hat deßwegen vollkommen beweiß, sie haben sie wieder zusammen getrieben und brauchen sie noch und eben daß jenige Ziehen des gestengs welches sich in den fügen mit der zeit recket, ist auch geschehen quod notandum, an dem theil der langen feldkunst, da sie bey unsern treibwerk schon vorbey” (A III,6 N. 17, pp. 50f.). 235 Cf. p. 51.

1694–June 1696

569

In the drawing, the water wheel is located at point A and the pithead is at D. AC represents the rod-engine transmission line and B the point where the towage system for the winding machinery is connected to it. Since the damage had occurred in the section BC – which was separated from the main transmission system and beyond the point where the additional towage system was attached – Leibniz rejected completely any blame on his part. Thus he wrote: Let A be the water wheel, AC the rod engine, B the place where the rod engine is attached to the prime mover, C there where the rod engine transmits into the pit D; if now the inconveniences in their rod transmission system had only been found between A and B, one could say that they came from our towage system attached near B, but since however they are also to be found between B and C, it is thus indeed impossible that the root of the evil lies in our towage system, since BC does not [push and] pull on our machinery.236 Crafft kept Leibniz informed und up-to-date about the matter, for example in his letter of May 20, 1694. The rival party had in the meantime conceded that Leibniz’s combined system could function under certain favorable conditions as, for example, when the residual water level in the mine was low. However, in the event of the water quantity in the pit being considerable, the entire power of the prime mover would have to be deployed for the pumps alone. Thus, Crafft informed Leibniz that: There are files with records of recent events which have arrived from Clausthal and which were passed on to me. As regards the machine, there are the following special details: Balthasar [Ernst Reimers] (who was also summoned for this) has been questioned about the errors referred to by privy councilor L[eibniz] in his letter. After he disclosed these, they were responded to by [Zacharias] Pöhler with the alleged claim that the wheel had really become mutable [or alterable] through the [added] machine, which he wants to verify. This was also the answer he gave regarding the rod engine which Balthasar considers to have been previously damaged. 236 “Gesetzt A sey daß wasser Radt[,] AC die feldkunst[,] B der orth da die feldkunst in unsern treibwerk angehenget, C da die kunst in die Grube D hinein schiebet, wen nun die ungelegenheiten bey ihren gestäng sich allein befunden zwischen A und B so konte man [sagen] sie käme von unserm bey B angehengten werk her, weil sichs aber auch zwischen B und C befindet, so ist es Ja alda unmüglich daß es von unserm werk her komme, weiln BC an unsern werck nicht ziehet” (p. 51).

570

Chapter 4

Because of the water, however, and the reason why the machine cannot be used now, he presents the following arguments: previously, when the machine [or undershot vertical water wheel] had been powered with 9 inches of water, there had been little water in the pits, and so the [pumping and winding] machinery had been able to operate. However, now that there was much residual water in the pits, the water wheels would have enough to do to pump this out and it would be impossible to power the winding machinery at the same time. If, however, one did have enough water for the [pumping and winding] machinery, and wanted to supply more for this purpose, then the trenches, which would be too shallow, could not cope with the amount of water, and so on (etc.).237 According to Crafft’s report, the senior mining official Otto Arthur von Ditfurdt had attempted to reconcile the rival factions by pointing out that – in the event of a continuation of the trials – one of the parties would in the end have to bear the costs. Even the Chamber president, and privy counsellor, Albrecht Philipp von dem Bussche had advocated the suspension of the trials. Thus, Crafft wrote the following to Leibniz: The opinion of the gentleman v[on dem] B[ussche] is that you, Sir, should not oppose the matter very strongly in the event that the outcome should be that the machine proves not to be of any use. It would therefore be [in this event] no disgrace for you Sir … he also additionally gave to a certain

237 “Es sind vom Claßthall acta, so jüngst vorgefallen, eingeloffen, welche mir communicirt worden. Waß die Machine belanget, so sind davon diese specialia: Balthasar [Ernst Reimers] (welcher auch darzu beruffen gewesen) ist befraget worden, waß die Irthümer weren, deren HoffR. L[eibniz] in seinen schreiben gedächte: Nach dem Er solche eröfnet, sind selbige von [Zacharias] Pöhler beantworttet, mit vermeinter Behaubtung, daß das Rad würcklich durch die Machine wandelbahr worden, willß beweisen; dergl. antwortt hatt Er auch wegen der Stange, so Balthasar vor altschädig hellt, gegeben. Wegen des waßers aber, und warumb die Machine nun nicht gebrauchet werden könne, gibt Er folgende rationes: Vor diesem, da die Machine mit 9 Zoll waßer getrieben worden, weren wenig waßer in den gruben gewesen, hette also die Machine gehen können, Nun aber in den gruben viel waßer were, hetten die kunste genug zu thun, daßelbe zu heben, vnd were vnmüglich die Machine zuegleich zu treiben. Wenn man aber schon waßer genug hette, vnd mehr drauf laßen wollte, so könnten die graben, welche zu flach weren, das waßer nicht ertragen etc.” (A III,6 N. 37, p. 98).

1694–June 1696

571

degree an assurance that he would do his best in order that the expenses incurred be restituted, etc., etc.238 Even Crafft himself could not exclude the possibility that the juror Pöhler might indeed be vindicated in the end, adding that: “According to my limited understanding, I do apprehend the reply of Pöhler regarding the great amount of water in the pits and it may be that he is right on this matter. You, Sir, can judge the arguments better than I can”.239 And so, after the situation for Leibniz’s efforts to improve the ore-hoisting methods had considerably deteriorated, he reverted to the mine pumping machinery, and in the knowledge that his idea could only be successful in the long term, if he were to succeed in constructing energy-saving pumps. Instead of using leather obturator rings, he wanted to provide the pump cylinders with valves in order that the previously existing friction losses might be reduced. The fabrication of the pumps was once again entrusted to Reimers, who then kept Leibniz informed about the progress of the work in hand.240 In September 1694, the new pump was ready for use, but the testing and trials were further drawn out into the year 1695, in particular because of lack of cooperation on the part of the mining office, and of the mining officials. Reimers’ letter from early February 1695,241 in which he reported about the preparation of the trial operation, contains the final report about Leibniz’s efforts at this time for the improvement of the pumping machinery. 7 Engineering Leibniz continued to work on the improvement of pumps in the time that followed, and engineering applications outside of mining were also contemplated. Crafft, for example, in a letter from Amsterdam on June 14, 1695, professed his interest in a type of pump with a four-sided (or rectangular) section that had been referred to by Leibniz in a no-longer extant letter of May 1695. Thus, the 238 “H. GR. v. B. judicium were dieses, M. h. H. solte sich so gar sehr nicht wiedersezzen, auf den fall es dahin außschlagen solte, daß die Machine nicht zugebrauchen. Es were M. h. H. darumb keine Schand … Gebe darneben auch etlicher Maßen zu verstehen, sein bestes darbey zu thun, daß die expensen restituirt werden möchten etc. etc.” (p. 99). 239 “Nach meinen wenigen verstande apprehendire ich des Pöhlers andtwortt wegen des vielen waßers in den gruben, vnd kann wohl sein, daß Er darin recht habe. M. h. H. wird die rationes beßer alß ich zu judiciren wißen” (p. 99). 240 Cf. A I,Supp., N. 177ff. 241 Cf. A I,Supp., N. 202.

572

Chapter 4

correspondent wrote: “In the [matter of the] envisaged new four-sided pump, Sir, you should show no hesitation; I consider it to be a great invention and there would be much to be gained with it here at these locations”.242 Crafft had read the description of such a pump with pyramidal form in the Journal des Sçavans of the year 1679,243 and he now hoped to obtain further information from Leibniz about the matter, as is to be seen from his letter of February 23, 1696, where he wrote: “In the Journal des Sçavans I have found such a description but it is pyramidal, while yours, Sir, is to my knowledge uniformly wide; I would like to learn if this [design] has been found to be better”.244 Crafft claimed that he and his Dutch partners were planning flour mills for use by bakers in Amsterdam, and in other towns in Holland, which would be powered by water mills rather than windmills. And thus, he continued: Our intention is to make flour mills with it for the bakers and to seek a privilege for it in this province, but only for a certain number in order not to arouse envy among the windmillers, 3 in this town and one in each of the other large towns in Holland. We imagine that from each mill an annual profit of 4000 florins will be produced, so as soon as it has been put into execution, I will arrange things, Sir, so that you will also have one.245 The new pumps  – which were also to be employed for pumping water into elevated reservoirs, and which in turn would serve as a reserve supply for the watermills – were intended to overcome above all the unreliability of the traditional fluvial water mills. In his reply, on March 2, Leibniz then generally 242 “In dem vorgehabten newen viereckigten pumpen spahre M. h. H. keinen fleiß, ich achte es vor eine große invention, vnd were in diesen orthen viel damit zu gewinnen” (A III,6 N. 131, p. 396). 243 Cf. Anon, “Extrait d’une letter écrite a l’Auteur du Journal touchant les bascules, pour faire travailler les personnes invalides, & touchant une nouvelle manière de piston”, Journal des Sçavans, (June 26, 1679), pp. 208–211. 244 “Im Journal des Sçavans habe ich eine dergleichen description gefunden, aber Sie ist piramidal, aber M. h. H. seine ist meines behaltens, gleich weit, möchte wißen ob solches beßer befunden” (A III,6 N. 204, p. 662). 245 “Wir haben damit vor Mahlmühlen vor die Backer dardurch zu machen, vnd ein privilegium in dieser provintz darüber zu suchen, nur auf ein gewiße zahl, vmb den WindtMüllern keine jalousie zu verursachen, 3 in dieser Statt vnd in den ubrigen großen Stätten von Holland eine. Wir bilden uns ein, daß aus ieder Mühl jährlich 4000 fl. profit kommen sollen, So es hienaußgeführet werden kann, will ich es dahin richten, daß M. h. H. auch eine davon haben solle” (pp. 662f.).

1694–June 1696

573

elaborated the mode of operation of such flour mills, which could be powered by wind, water or horse power. Even four-sided (or rectangular) pumps could be employed, he maintained, having established himself the advantages of pumps of this kind by means of a cross-sectional experimental study, with a pump assembly having quadrangular dimensions of 8-inch width, 4-foot length and a 3½-foot piston stroke length. And so he wrote: As regards the mill systems where the wind raises the water to a height, from where it then falls on a wheel, it depends on how one would like to have the assurance that the bakers will find this means of grinding more to their liking. In an emergency the water can also be lifted into the reservoir using horses and therefore the flour can be ground either using horse mills or water mills. It is yet another method of lifting water without pumps and scoop or bucket elevators which in my opinion is superior to others and can be felicitously applied in such mill systems. Still, as long as one is prepared to accept not being on a par [with the other methods] in using this facility, then the four-sided pumps are adequate. I have tested one (in pure water), where the pump dimensions were 8 inches width, 4 feet height and the stroke had at least 3½ feet. They require no handling or attendance, but are enduring.246 Crafft also reported from Amsterdam, on April 22, 1695, and again on February 23, 1696, about engineering projects for desalination and salt extraction from seawater, including one on the basis of a chemical precipitation process.247 Leibniz, although skeptical regarding the prospects for such projects in general in the Dutch climate, did nonetheless express an interest in the latter method. Thus, he wrote in his reply on March 2, 1696: 246 “Bey den Muhlenwercken, da der wind daß waßer in die hohe bringen, und solches dann auffs Radt fallen soll, kömt es darauff an wie man versichert seyn möge, daß den beckern diese art zu mahlen mehr angenehm. Es kan auch im nothfall das waßer von pferden in das Reservoir geschaffet werden, und also das mehl mit Roß=, so guth als Waßermuhlen gemahlen werden. Es ist noch eine andere art das waßer zu heben ohne pompen und schopfwerck so meines ermeßens andern vorgehet, und bey solchen Muhlwercken trefflich zu appliciren. Doch wenn man es bey dieser gelegenheit nicht eben gemeinmachen will, sind die 4eckten pompen zulänglich gnug. Ich habe es (doch in reinen waßer[)] mit einer probiret, da der stiefel 8 zoll weit, und 4 schuch hoch, und der hub wenigstens 3½ schuch halt. Sie erfordern keine bedienung, sondern sind beständig” (A III,6 N. 207, p. 666). 247 Cf. A III,6 N. 109, pp. 336f. and N. 204, pp. 661f.

574

Chapter 4

As regards the salt mine I doubt if the benefit will be so considerable in Holland, since the sun prepares it in warm lands without costs. Nonetheless, the concentration by precipitation would be something special. I have some old manuscript deeds from which can be seen that an individual at the beginning of this century planned something like this in Halle, yet I cannot find the outcome of this. And it must be applied more than a little; still I believe that one could without brine and salina [viz. a concentrating house] enrich and concentrate the sole [viz. a solution in which water is saturated with natural salt].248 8

Engineering: Ballistae, Military Engines

As was to be expected in a time of war, military technology enjoyed particularly high esteem, and it was no wonder that following the death in 1694 of Johann Balthasar Lauterbach  – the professor at the military academy in Wolfenbüttel  – Leibniz had a special interest in the appointment of a successor. And so he proposed the Dutchman Johannes Teyler – the author of a work entitled Architectura militaris (1679)249 – as Lauterbach’s successor. To Huygens he wrote on May 6, 1694: I have thought about a certain learned man, resident as I believe in Holland, but whose name I am unable to recall at the moment, who published some years ago a little book in 4o, where he begins to explain the principles of fortification in a very ingenious manner and by a unique method of calculation making an estimation of the quantity of the defense [fire power] beginning with the following consideration …

248 “Das Salzwerck betr. zweifle ob der Nuz so considerabel in Holland, weilen es die Sonne in Warmen landen ohne kosten bereitet. Gleichwohl wäre die concentratio per praecipitationem etwas sonderlichs. Ich habe einige alte Acta Manuscripta, daraus zu sehen, daß einer im anfang dieses seculi dergleichen etwas zu Halle vorgehabt, doch kann den ausgang darinn nicht finden. Und muß nicht wenig anstehen doch glaube daß man ohne Söhle und Leckwerck die Söhle anreichern und das guthe concentriren köndte” (A III,6 N. 207, pp. 666f.). 249 Cf. J. Teyler, Architectura militaris, Amsterdam, [1679]; 2nd ed. Rotterdam, 1697.

1694–June 1696

Figure 5

575

Leibniz’s drawing illustrating Johannes Teyler’s method of calculating the quantity of fire power in a fortification array Source: Leibniz to Christiaan Huygens, May 6, 1694 (A III,6, p. 73)

… that the line AB although larger than BC is not able to provide more fire power than BC, if the fusillades should be parallel to DE. I have been told that the author of this little book was Dutch, or from the vicinity but that he had been an engineer in Brandenburg.250 In mid-May, 1694, Leibniz then composed a commendatory letter regarding Teyler, for Lorenz Hertel in Wolfenbüttel, which emphasized the engineer’s theoretical and practical experience in the following words: Mr Tailer [sic] … has been described to me as an excellent mathematician and engineer, as one having very extraordinary penetration, being the author of a little tract concerning fortification which he has had printed. I have as well received the intelligence, from persons who have had very close dealings with him, that he is no less experienced in practice, having 250 “J’avois songé à un sçavant homme qui demeure comme je crois en Hollande, mais dont je ne sçaurois maintenant trouver le nom, qui a publié il y a quelques années un petit livre in 4o, où il commence d’expliquer les principes de la fortification d’une maniere tres ingenieuse et par un calcul singulier en faisant l’estime de la quantité de la defense commençant par cette consideration … que la ligne AB quoyque plus grande que BC ne sçauroit donner plus de feu que BC, si les tirades doivent estre paralleles à DE. On m’avoit dit que l’auteur de ce petit livre estoit Hollandois ou du voisinage mais qu’il avoit esté ingenieur de Brandebourg” (A III,6 N. 26, specifically p. 73; HO, 10, pp. 600–605).

576

Chapter 4

been involved in many besiegements and battles, and has accordingly good abilities for teaching and the winning over of the minds of the youth.251 Although his efforts to attract Teyler to the Wolfenbüttel Academy proved to be in vain, Leibniz continued to be interested in the Teyler’s Architectura militaris. Thus, for example, he wrote near the end of his letter of October 24, 1694, to the author himself: I will be very pleased to learn whether or not you have continued [to develop] your thoughts on military architecture, which appeared to me to be beautiful and unique, although I only saw them [in your tract] in passing, not having been able to find them bookshops.252 A further instance of Leibniz’s interest in military technology is seen in the form of the report he received from Crafft about an intended (but never performed) demonstration of a repeating firearm in Holland. The gun in question – it was claimed – could fire four shots from a single barrel in a minute, or 240 in an hour. According to the report, a compatriot of Crafft had prepared a demonstration of the firearm in question at Rijswijk, seeking to impress the elector of Bavaria who was passing through. The potentate in question did inspect the arsenal in Delft but – not least due to his inebriated condition – passed through the nearby town of Rijswijk without stopping. Thus Crafft reported to Leibniz, in early January 1695, that: A high German, they say, a Saxon has carried out a trial for the elector of Bavaria [viz. Maximilian II Emanuel] in his chamber in which 4 shots were fired in a minute from a single barrel, which in an hour amounts to 240 shots. With his teeth he bit off the extremity of the cartridge before inserting it in the barrel, and in this way the barrel drew the cartridge to itself and at the same time brought the powder to the touch-pan, with the 251 “H. Tailer  … wird mir als ein treflicher Mathematicus und Ingenieur beschrieben, daß er von ganz ungemeiner penetration sey, gibt ein kleines tractatlein so er von der fortification in druck geben, ich habe aber von Leuten so genaue Kundschafft mit ihm haben Verstanden, daß er nicht weniger in praxi geübet, bey vielen belägerungen und schlachten gewesen, und dabey schohne gaben zu unterweisen, und die gemüther der jugend zu gewinnen habe” (A III,6 N. 31, p. 80). 252 “Je seray bien aise d’apprendre, si vous n’avés point continué vos meditations sur l’Architecture militaire, qui m’ont paru belles et singulieres, quoyque je ne les aye vues qu’en passant ne les ayant point trouvé chez les libraires” (A III,6 N. 67, p. 204).

1694–June 1696

577

result that nothing was required other than to pull back the musket cock. And, because several had doubts that the musket balls could have force, since they had not been rammed down securely on the powder with a ramrod, the elector ordered that he should set up planks at Rijswijk to serve as targets for the trial of whether the musket balls would in fact penetrate them. He was to inspect the arsenal in Delft, and so he wanted to observe this trial in passing. The good fellow had the planks set up at his own expense, and the elector also came to Delft but, [being incapacitated after] having had such a good drink, passed through Rijswijk without observing the trial.253 The inventor in question then carried out his trial in Amsterdam charging for entry to the performance. However, his original plan had been – following a successful trial – to serve the elector by fabricating 10,000 exemplars of this firearm, each costing a Reichstaler, and in addition, upgrading all muskets, guns and cannons in order to incorporate his invention. Thus, Crafft continued his report: The honest fellow then presented, out of necessity, his trial in Amsterdam charging money for entry. He presented himself as a ‘Senior Lieutenant’, but had made the musket barrel himself, and it had been made in a very interesting way. He would have offered the elector to charge a Reichstaler for each exemplar, provided he ordered 10,000 and, in addition, to accordingly upgrade all muskets, guns and cannons with his innovation.254 253 “Ein hochteutscher, wie Sie vermeinten, Ein Sachß hette dem Churf. von Bayern [Maximilian II. Emanuel] in seinem gemach die Probe gethan in einer minute auß einem rohr 4 schüße zu tun, welches in einer Stunde betragen 240 Schüße, Er hette mit den zähnen das eußerste von der Patron abgebißen, vnd dieselbe ins rohr gestecket, so hette daß rohr die Patron an sich gezogen vnd zugleich daß pulver auf die zündpfanne gebracht, also daß weiter nichts, alß den Haanen aufzuziehen, von nöthen. Vnd weilen etliche den scrupel machte[n], daß die kugeln, weilen Sie mit dem ladestecken nicht hienein getrieben, keine force haben möchten, alß habe der Chfurst befohlen Er sollte zu Reyßwyck Plancken aufrichten laßen, vmb an denselben die Proben zu nehmen, ob die kugeln auch penetriren würden. Er werde daß Magacin zu Delft besehen, so wollte Er en passant diese Prob anschawen. Die Plancken hatt der gute Mann auf seinen costen richten laßen, der Chf. ist auch nach Delft, hatt aber einen so guten trunck gethan, daß Er [an] Reyßwyck vorbey gangen vnd diese Prob nicht angesehen” (A III,6 N. 88, pp. 267f.). 254 “Der Ehrliche habe darauf auß Noth. seine Proben in Amsterdam vor geld sehen laßen. Er habe sich vor einen Obr.Leuten. außgeben, hatte aber das rohr selbst gemachet, vnd were sehr curieus gemacht gewesen. Er hette dem Churf. offerirt, wofern er 10/m Stuck machen laßen wollte, so von iedem 1 rth. nehmen, Es nicht allein an alle musqueten vnd rohr, sondern auch an die Stucke applicirt werden” (p. 268).

578

Chapter 4

A role model of a military expert, which emerged in England, Germany and Holland, during the seventeenth and eighteenth centuries  – and which was paradoxically characterized by the foundering of such projects – is exemplified here in this report sent to Leibniz at the beginning of 1695.255 9

Projects: Mathematical Instruments and Calculating Machines

In the years between 1694 and 1696, calculating machines came to the fore again, and they were referred to more frequently in Leibniz’s correspondence in these years than at any time in the previous two decades. An important reason for this was no doubt the completion in 1694 of Leibniz’s own so-called ‘older’ model of his four-function calculating machine. The elation in his accounts of the device served to motivate his correspondents to recall their own knowledge in the field. The great variety of models discussed in this context also clearly illustrates the extent to which the completion of such mathematical devices reflected the spirit of the time. When the landgrave Carl of Hesse-Cassel (Karl von Hessen-Kassel) expressed his interest in the mode of operation of a machine, which he had received from his brother, Leibniz was enticed to provide a detailed report, in a letter sent to Johann Sebastian Haes on April 8, 1695, about the recent history of mathematical calculating machines.256 In fact, the letters Haes sent to Leibniz, on March 28 and May 23, 1695,257 and Leibniz’s corresponding letters sent on April 8 and at the end of May or early June of that year,258 are of special significance here. These communications contained reports about the improvement of the Pascaline  – the calculator of Blaise Pascal – by the Parisian watchmaker René Grillet,259 about variants of Samuel Morland’s machine type,260 that used slide rules and Napierian logarithms and that was to be seen in the guise of an exemplar in possession of Landgrave Karl,261 about a little machine which Haes had made more than ten years earlier and which had previously been made known to 255 Cf. S. Droste, Offensive engines: Die prekäre Expertise militärischer Projectemacher (1650– 1800), Stuttgart, 2022. 256 Cf. A III,6 N. 108, pp. 329–333. 257 Cf. A III,6 N. 105 and N. 118. 258 Cf. A III,6 N. 108 and N. 124. 259 Cf. A III,6 N. 108, p. 331 and N. 124, p. 383. 260 Attached to A III,6 N. 108 was a calculating instrument and a copy of S. Morland, The description and use of two arithmetick instruments, London, 1673; cf. also H. W. Dickinson, 1970, pp. 28–33, and plates I–VII (Introduction, note 134). 261 Cf. A III,6 N. 105, pp. 326 and N. 108, pp. 329–333.

1694–June 1696

579

Leibniz,262 about yet another little machine of Charles Cotterell,263 and about the calculating cylinders of Caspar Schott,264 and of Pierre Petit.265 An adding machine of Haes from the year 1695, and a gearless machine conceived by Tschirnhaus, were surely independent developments. Concerning the former, Haes wrote on May 23, 1695: I have had constructed for ‘His Highness the Landgrave’ another arithmetic machine much more perfect than those for addition and subtraction of Mr Morland, adapted for all sorts of coinage and types of accounting used in Germany.266 Tschirnhaus too, on hearing of the completion of Leibniz’s ‘older’ machine, reported about his own very different device on February 27, 1694, writing as follows: I learn with great pleasure that your arithmetic machine is reaching greater perfection and this will indeed be good enough when it reaches 12 cipher positions, for in practice it is not easy to find the likes of it. I have also had the idea for such a machine, but have not yet fully realized this; it is however totally different from that [viz. yours], for with this [viz. mine] there are no wheels; the whole [the entire machine] is also based on a completely different foundation.267 Leibniz’s calculating machine already had its own history at this juncture. Following early designs, dating from his time in Mainz and before his sojourn in Paris (1672–1676), he had presented a wooden three-place demonstration model to the Royal Society on the occasion of his first London visit in 1673.

262 Cf. A III,6 N. 118, p. 368. 263 Cf. A III,6 N. 108, p. 331. 264 Cf. p. 368 (note 262). 265 Cf. p. 330 (note 263). 266 “J’ay fait construire pour S. A. S. une autre machine arithmetique plus parfaite de beaucoup que celles pour l’addition et la soustraction de Mr Morland, accommodée à toutes sortes de monoyes et d’especes de contes usités en Allemagne” (p. 368; note 262). 267 “Höhre sehr gerne daß Dero Machina Aritmetica zu größer perfection kombt, und wird wohl Schon genung sein, wan solche bies auff 12 Zieffern kommet, dan in praxi nicht leicht dergleichen exempel vorkommen; Ich bin auch auff eine dergleichen Machinam gefallen, habe aber solche noch nicht gäntzlich acheviret, ist aber in totum diversa ab hac; dan bey dieser keine rotae; gehet auch alles aus einen andern fondement” (A III,6 N. 10, p. 25).

580

Chapter 4

Following this presentation, on February 1, 1673, Oldenburg wrote the following lines to him on February 9: The knight Mr Moreland, of whom the knight Mr Moray268 spoke to you yesterday, and who is the inventor of an arithmetic machine, having spoken to me today about yours, has said that he is prepared to show you his tomorrow at eleven o’clock in the morning, wishing also to see yours alongside his. I am offering you my services to accompany you there at that hour in the garden of Whitehall where he has some rooms and where his said instrument is lodged, if it pleases you to take the trouble to call on me at home, and to bring your instrument along with us.269 Subsequently, an improved version of the machine made of metal, with six entry and twelve result positions (powers of ten), came into being in Paris and it was presented to the Académie des Sciences in 1675. An entry of January 9, 1675, in the Procès-verbaux of the Académie contains the following text: On the same day Monsieur Limnits [sic] presented his calculating machine for carrying out the rules of arithmetic with great ease, of which he will give a description to be entered in the minutes of the meeting. Monsieur de Limnist [sic] will give his cost estimate and he will take the trouble to obtain the craftsman and will pay him so that the machine succeeds.270

268 Namely Robert Moray; cf. A. Robertson, H. W. Meikle (ed.), The life of Sir Robert Moray: Soldier, statesman and man of science (1608–1673), London, 1922 and 2018 (Forgotten Books’ Classic Reprint). 269 “Mons. Le Chevalier Moreland, dont vous parla hier Mons le Chevalier Moray, et qui est l’inventeur d’une machine Arithmetique, m’ayant parlé de la vostre aujourdhuy, a dit qu’il est prest de vous monstrer la sienne demain sur les onze heurs du matin, desirant aussi de voir la vostre, afin de les conferer ensemble. C’est donc, Mons., pour vous offrir mon service de vous accompagner sur cete heure lá [sic] dans le jardin de Whitehal, oú il a quelques chambres, et oú son dit Instrument est logé, s’il vous plait de prendre la peine m’appeller chez moy, et faire porter vostre machine avec nous” (A III,1 N. 3; cf. pp. 20f., and annotation). 270 “Le mesme jour Monsieur Limnits [sic] a fait voir sa machine numérique, pour faire les règles d’Arithmetique avec beaucoup de facilité, dont il donnera la description pour mettre dans le Registre. Monsieur de Limnist [sic] fera son devis et il aura soin de faire venir l’ouvrier. On en fera marché avec luy, et on le payera pourvu que la machine réussisse” (A III,1 N. 43, p. 180).

1694–June 1696

581

However, the final version of this first metallic model still remained to be presented at the time of Leibniz’s departure from Paris in 1676. Accordingly, he attempted in the years that followed to entice the Parisian clockmaker Ollivier, who had been entrusted with the construction of the machine, to come to Hanover and the clockmaker did possibly arrive in Hanover at the end of 1679, or in early 1680, although the matter remains in doubt.271 When the model was finally completed, in the mid-1680s, Leibniz commissioned a larger machine with eight entry and twelve results positions. The work on this so-called ‘older’ machine was finally brought to a conclusion, by the Hanover clockmaker Georg Heinrich Kölbing, following a construction period of almost ten years. A first reference to the completion of the machine may be found in a letter (from which only an extract is extant) to L’Hospital of August 16, 1694,272 and in the correspondent’s reply of November 30. In fact, L’Hospital immediately reacted to Leibniz’s communication concerning the completion of the work on the first exemplar by commissioning a duplicate of the machine, in return for appropriate remuneration. Thus, L’Hospital wrote in this context: I am very pleased that your arithmetic machine has finally been completed, and that it operates in the manner you describe. Do the means exist to make a duplicate? and to have it then sent to Paris. If you would like to take the trouble, and if it can be done easily, you would give me true pleasure. I would send the money required to the envoy, if you were to have the goodness to inform me. The same craftsman who constructed yours could also make this one, and I would like very much for him to employ all his time and to take all trouble necessary in order that it be brought to perfection.273 Throughout the period under consideration (1694–1696), L’Hospital continued to remind Leibniz about this order.274 In a letter of October 13, 1695, to Rudolf Christian von Bodenhausen, Leibniz also referred to the completion of 271 Cf. A III,3, p. 264, and annotation. 272 Cf. A III,6 N. 52, p. 151. 273 “Je suis fort aise que vôtre machine arithmetique soit enfin executée, et qu’elle reussisse de la maniere que vous me marquez. N’y auroit il point moyen d’en faire une semblable? et de la faire ensuitte venir à Paris. Si vous vouliez bien y donner vos soins, et que cela se pût aisement, vous me feriez un vrai plaisir. Je donnerois à Mr L’envoyé l’argent qui seroit necessaire et que vous auriez la bonté de me marquer. Le même ouvrier qui a executé la vôtre pouvoit faire encore celleci, et je voudrois bien qu’il y employât tout le temps et qu’il y prit toute la peine requise pour qu’elle fût dans la perfection” (A III,6 N. 79, p. 237). 274 Cf. A III,6 N. 97 (p. 298), N. 141 (p. 438), N. 158 (p. 488) and N. 217 (p. 714).

582

Chapter 4

the machine almost a year earlier.275 And, as in the case of L’Hospital, Leibniz was flattered and obliging when Bodenhausen requested further details of the machine, no doubt with the intention of enticing the duke of Tuscany to order a duplicate.276 Yet another indication from the year 1694 is found in Leibniz’s letter to the French numismatist Nicolas Toinard, on October 14 (or 24), 1694, where he wrote: “I have finally completed the construction of my arithmetic machine, such that one can multiply numbers with it whose product can have up to twelve ciphers. It requires care and expense to achieve results”.277 Furthermore, there can be little doubt that Crafft was able to give Huygens an account of Leibniz’s calculating machine from his perspective, as we learn from Huygens’ letter of December 27, 1694, where the correspondent recalled in particular the Pascaline calculator, which had been designed and built by Blaise Pascal fifty years earlier. Here Huygens wrote: Mr Crafft told me that you have completed your arithmetic machine, which should be a remarkable device,278 and whose execution will no doubt have cost you much effort, since that which Mr Pascal made solely for additions greatly exploited and strained his mind, according to what his friends told me. One could have made it in an incomparably simpler and more convenient form, which I do not think was the same as yours. I ask you to advise me how many ciphers, and by how many, it can multiply [or can be multiplied], and if it has achieved the perfection you desire without being subject to deficiencies and flaws.279 The machine was likewise presented to visitors in Hanover, as for example on the occasion of a passing visit by Tschirnhaus in September, or October, 1694, and which is recorded in Leibniz’s letter to Jacob Bernoulli from the spring of 275 Cf. A III,6 N. 166, pp. 515f. 276 Cf. A III,6 N. 180, p. 563 and N. 187, p. 580. 277 “J’ai fait enfin executer ma machine aithmétique en grand, en sorte qu’on’y peut multiplier, des nombres dont le produit va jusqu à douze chiffres. Il a fallu des soins et des frais pour en venir à bout” (A I,10 N. 414, p. 606). 278 Subordinate clause in italics underlined by Leibniz. 279 “Mr Craft m’a dit que vous aviez achevé vostre machine arithmetique, qui doit estre une piece merveilleuse, et dont l’execution sans doute vous aura couté bien de la peine, puis que celle qu’avoit fait Mr Paschal seulement pour les additions, luy avoit grandement usé et gasté l’esprit, à ce que ses amis m’ont dit. On pouvoit la faire incomparablement plus simple et plus commode, ce que je ne crois pas estre de mesme de la vostre. Je vous prie de me mander combien de chiffres et par combien elle peut multiplier, et si elle est dans la perfection que vous souhaitez, sans estre sujette à manquer ni à se detraquer” (A III,6 N. 86, specifically p. 261; HO, 10, pp. 696–699).

1694–June 1696

583

1696, albeit with the caveat that only a part of the machine was complete on that occasion. Here Leibniz wrote: “Thus it is the first large absolute machine which previously, although still under construction, D. Tschirnhaus saw while passing through here two years ago, carrying out sample calculations for himself in that part which was complete”.280 There is also evidence of a presentation of the machine for Thomas Burnett of Kemney, which took place in Hanover in April 1695, and which was referred to in Leibniz’s final letter addressed to Huygens, on July 1, 1695. On that occasion he wrote: Mr Burnet, a Scottish gentleman and relative of the bishop of Salisbury [Gilbert Burnet] has seen my arithmetic machine here, completely finished, and the examples which I carried out in his presence, which surprised him. The products can go to 12 figures and the multiplicand has 8 figures. I could now make further exemplars as long as I have the craftsman (clockmaker) to hand.281 At about the same time as the completion of the first “exemplar”,282 work began on the second or so-called ‘younger’ machine which offered, for the same number of entry positions, sixteen result positions.283 Thus, in his letter to Bodenhausen of December 23, 1695, Leibniz wrote: My arithmetic machine is of about the size of a writing console which one takes with one on a journey and with it one can, once it is set up, multiply numbers, which are so large that the multiplicand can have no more than 8 ciphers, and the product no more than 12 ciphers. One may turn a wheel only as often as there are ciphers in the multiplicator, and the different products of particular multiplications of each and every rotation add themselves together, and one must not therefore calculate anything oneself. One can divide if the dividend does not have more than 280 “Ita prima Machina magna absoluta est, quam adhuc sub incude positam dominus de Tschirnhaus ante biennium huc transiens vidit, experimentaque sumta sunt coram ipso, in ea parte, quae erat perfecta” (A III,6 N. 235, p. 770). 281 “Monsieur Burnet gentilhomme Ecossois parent de Mons. l’Eveque de Salisbury a vû icy ma Machine Arithmetique entierement achevée, et des exemples que j’ay faits en sa presence, qui l’ont surpris. Les produits peuvent aller à 12 figures, et le multiplicandus est de 8 figures. J’en puis faire encor d’autres exemplaires maintenant pendant que j’ay l’ouvrier à la main” (A III,6 N. 136, specifically p. 422, and annotations; HO, 10, pp. 714–718). 282 Cf. A III,6 N. 166, pp. 515f. 283 Cf. A III,6 N. 187, p. 580, and N. 235, pp. 770f.

584

Chapter 4

12 [ciphers], and the divisor not more than 8 ciphers, and one may turn a wheel only so often as there are to be ciphers in the quotient. One also does not have to estimate, but the particular quotient determines itself every time, and it also shows the remainder itself. The size of the machine is also so designed that place is left for up to 4 extra positions, in order to be able to reach a product of multiplication of 16 ciphers, without making the machine greater for this reason.284 10

Projects: Submersibles, Diving Vessels and Navigation

After Leibniz’s correspondence with Denis Papin had once again been revived through the appearance of the correspondent’s bilingual work Fasciculus dissertationum and Recueil de diverses pieces in 1695,285 respectively, questions were discussed relating to Papin’s submersible or diving vessel – to which a chapter of the work had been dedicated286 – and, in particular, regarding the method of air renewal within the boat. Previously, Haes had raised the issue of the quintessence, allegedly used by Cornelis Drebbel more than seventy years earlier,287 and concerning the composition of which Leibniz had long tried to gain an insight. However, as regards the possible effect of such a quintessence both Leibniz and Papin were decidedly skeptical. To this correspondent, Leibniz wrote in the first half of August 1695 that he conjectured that the 284 “Meine Machina Arithmetica ist etwa von der große einer Schreibe lade, so man auf Reisen bey sich fuhret und damit kan man wie sie schohn fertig, zahlen multipliciren, die so groß daß der multiplicandus nicht über 8 zipfern, und der productus nicht uber 12 zipfern habe. Man darff nur ein radt so offt umbdrehen als zipfern seyn im multiplicatore, und die diversa producta multiplicationum particularium einer ieden umbdrehung addiren sich von selbsten zusammen, und darff man also nichts das geringste dabey rechnen. Dividiren kan man wenn der dividendus nicht uber 12, und der divisor nicht über 8 zipfern hat, und darff nur ein radt so offt umbdrehen, als zipfern im quotienta seyn sollen. Man darff auch nicht rathen, sondern der quotiens particularis determiniret sich iedesmahl selbst, und das residuum zeiget sich auch selbsten. Die große der Machina ist also bewand, daß plaz gelaßen noch zu 4 stellen, umb bis auff ein productum multiplicationis von 16 zipfern kommen zu können, ohne daß die Machina deswegen größer” (N. 187, p. 580). 285 Cf. note 98 above. 286 Cf. D. Papin, “Navis urinatoriae Serenissimi Principis jussu constructae descriptio”, pp. 126–137 in: Fasciculus dissertationum de novis quibusdam machinis atque aliis argumentis philosophicis, Marburg, 1695; D. Papin, “Description du Batteau plongeant”, pp. 127–143 in: Recueil de diverses pieces touchant quelques nouvelles machines. Et autres subjets philosophiques, Kassel, 1695. 287 Cf. A III,5 N. 78, p. 309.

1694–June 1696

585

substance used might have been the spirit of wine, viz. an aqua vitae prepared by distilling wine. Here he wrote: I tell you, Sir, that which I conjecture to have been the quintessence of the air of the famous Drebbel. It was apparently the spirit of wine that he burnt. For there is no [other] liquor which approaches the advantage of the nature of air. And perhaps the vapor it produces serves to correct the exhalation breathed out in respiration. It is something which nobody can judge better than you. However, I do think that that alone would not suffice for very long without fresh air from the outside. Maybe, however, this means did provide assistance. I believe that Mr Boyle once told me, just like the daughter of Drebbel [viz. Catharina Drebbel] whom I met in London along with her husband Mr Kiefler [viz. Johann Sibertus Kuffeler], that Drebbel’s boat completed a rather long passage across the Thames. But they did not say distinctly if he drew in air from the outside.288 A further more general question, which Leibniz posed in this context, concerned the possible use of spirit of wine as a fuel to power a two-stroke piston engine – with a combustion or rarefaction stroke followed by a compression or condensation stroke – similar to the use of water vapor from water held over a lamp flame. Thus he wrote: As regards the spirit of wine, I would very much like to know if you have tried to use as a substitute vapor from water held over a lamp flame to raise a piston. It appears to be very rarefiable but I do not know if it would return so easily to the liquid state by means of the cold.289

288 “je vous diray, Monsieur, ce que je conjecture avoir esté la quinte essence de l’air du fameux Drebbel. C’estoit apparemment l’esprit de vin qu’il faisoit brûler. Car il n’y a point de liqueur qui approche d’avantage de la nature de l’air. Et peutestre que la vapeur qu’il donne sert à corriger l’air gasté par la respiration. C’est de quoy personne peut mieux juger que vous. Je m’imagine bien que cela seul ne suffiroit pas long temps sans un air nouveau de dehors. Peutestre cependant que ce moyen ne laisseroit pas d’aider. Je crois que M. Boyle m’a conté autres fois aussi bien que la fille [Catharina] de Drebbel que J’ay vüe à Londres avec M. Kiefler [Johann Sibertus Kuffeler] son mari, que le bateau de Drebbel a fait un assez grand chemin entre deux eaux dans la Tamise. Mais ils n’ont point parlé distinctement s’il attiroit l’air externe” (A III,6 N. 155, pp. 480f.). 289 “A propos de l’esprit de vin, je voudrois bien sçavoir si vous l’avés essayé au lieu de l’eau sur la lampe pour elever le piston. Il paroist plus rarifiable mais je ne sçay s’il retourne si aisément en liquer par le froid” (p. 481).

586

Chapter 4

Papin replied, on September 1, that the flame producing the fumes of the spirit of wine, as well as all other flames aboard the submerged vessel, would only further pollute the air within the submersible. In this regard he wrote: As regards the quintessence of the air of the famous Drebbel, I am very convinced that it did not come from burning the spirit of wine, because experiment shows that the flame of the spirit of wine does not correct the foul air but, on the contrary, it pollutes it more and more just like the other flames.290 And to this he added: Your conjectures regarding the spirit of wine rarefied by heat are absolutely conform with certain experiments that I have undertaken; and it would not be advantageous to avail of it for the uses, of which I speak in my tract, because it would cost too much.291 In a further letter, from early October, 1695, Papin dealt in more detail with the use of a spirit of wine lamp in a submarine, or diving vessel. Once the connection with the outside atmosphere was removed the flame would be extinguished, just as if it were an oil lamp, and this would add to the pollution of the air within the vessel. On this occasion the correspondent wrote: The reason why I said that the spirit of wine fouls the air is that if one places a lamp burning the spirit of wine in a [submersible] vessel and cuts off contact with the outside air, this flame will soon be extinguished just the same as if it had been oil that one was burning. It appears to me to be something which can only be attributed to the corruption of the air enclosed in the vessel and rendered incapable of contributing any further to maintaining the flame.292 290 “Pour ce qui est de la quintessence de l’air du fameux Drebbel, Je suis fort persuadé que ce ne sçauroit estre l’esprit de vin en bruslant: car l’experience fait voir que la flame de l’esprit de vin ne corrige point l’air gasté; mais qu’au contraire elle le gaste de plus en plus aussi bien que les autres flames” (A III,6 N. 156, p. 482). 291 “Vos conjectures sur l’esprit de vin qu’on rarefie par la chaleur sont absolument conforme à quelques experiences que J’en ay faittes: et il ne seroit pas avantageux de s’en server pour les usages dont Je parle dans mon traitté parce qu’il couteroit trop” (p. 482). 292 “La raison qui me fait dire que l’esprit de vin gaste l’air c’est que si on met une lampe d’esprit de vin allumée dans un vaisseau et qu’on ferme la communication avec l’air exterieur, cette flame s’esteint bien tost de mesme que si c’estoit de l’huyle qu’on bruslast:

1694–June 1696

587

As regards the possible use of a cycle of rarefaction and condensation of spirit of wine, rather than water vapor, as part of a piston engine, Papin admitted that his experimental investigation of the idea had never attained the necessary precision to allow a judgement on the matter. However, he was skeptical as to whether the cylinder and piston would be impermeable as they were generally found not be completely impervious to the water that was used as a seal over the piston. Concerning this matter Papin wrote: As regards the proportion that exists between the force of rarefaction of this spirit and that of water, my experiments have never been developed to such precision and this would be very difficult because the pistons always let a little of the water, which one places on top to prevent the air from entering, to pass.293 In connection with seafaring, and the demands of navigation, stood the development of sea-worthy and precise clocks. Leibniz had been active in this area in his younger years, evidence for which is provided by the text “An Extract of a Letter of the Learned Dr. Gothofredus Guil. Leibnitz, concerning the Principle of exactness in the portable Watches of his invention”, which was part of his letter for Jean-Paul de La Roque of mid-March 1675.294 Huygens’ efforts in this area in the early 1690s met no doubt with Leibniz’s approval. After the correspondent had reported the completion of a new clock at the end of his article “De problemate Bernoulliano” of October 1693,295 he addressed the matter once again in a letter to Leibniz of May 29, 1694, in the following words: As regards this clock, I tell you in passing that it works as desired, and that it will be of great utility, because being just as precise as a pendulum clock of 3-foot length, with which I have observed it to agree over a period of 5 or 6 days without differing by a second, it could endure the

ce qui ne se peut, ce me semble, attribuer qu’à corruption de l’air enfermé dans le vaisseau et rendu incapable de plus contribuer à entretenir la flame” (A III,6 N. 164, p. 511). 293 “pour ce qui est de la proportion qu’il ŷ a entre la force de la rarefaction de cet esprit et celle de l’eau, mes experiences n’ont jamais esté poussées jusques à tant de precision et cela seroit bien difficile à cause que les pistons laissent tousjours passer quelque peu de l’eau qu’on met dessus pour empescher l’air d’entrer” (p. 511). 294 Cf. A III,1 N. 45, in particular version g, pp. 193–201. 295 Cf. Ch. Huygens, “De problemate Bernoulliano”, Acta Eruditorum, (October 1693), pp. 475f.

588

Chapter 4

movement of the vessel without difficulty, and it would also have other considerable advantages.296 Navigation, and in particular the method of steering and maneuvering a sailing ship, was also the subject of a public dispute between Huygens and Bernard Renau d’Eliçagaray, and concerning which Leibniz’s opinion was requested. Renau’s anonymously published book, with the title De la théorie de la manoeuvre des vaisseaux (1689),297 was criticized by Huygens in his article “Remarque … sur le livre de la manoeuvre des vaisseaux” (1693).298 Renau duly replied with a Reponse … à la remarque de M. Huguens (1694),299 which was countered by Huygens in a Replique … à la reponse de Mr. Renau, and to which Renau in turn provided a Reponse … à la replique de M. Huguens (1694).300 On May 29, 1694, Huygens had requested Leibniz’s judgement for inclusion in his Replique … à la reponse.301 As Leibniz had not seen Huygens’ Remarque, and had only vague memories of his study of Renau’s book, he desisted from giving a definitive judgement and presented only a single point of criticism – namely the author’s failure to take the center of gravity of the ship into consideration – in his letter to Huygens of June 22. He welcomed the practical nature of Renau’s work, and he recalled that the author had cited a work of Anne Hilarion de Contentin, Comte de Tourville, entitled Exercice en général de toutes les manoeuvres qui se font à la mer (1693).302 Thus Leibniz wrote on this occasion: When I formerly considered this theory, it appeared to me to be a little superficial, and I did not manage to work through it. But I have in mind doing so one of these days. I recall now that he neglected among other 296 “Pour ce qui est de cette horloge je vous diray en passant qu’elle reussit à souhait, et qu’elle sera de grande utilité, parce qu’estant aussi juste qu’une à pendule de 3 pieds, avec la quelle je la vois s’accorder pendant 5 ou 6 jours sans differer d’une seconde, elle pourra souffrir le movement du vaisseau sans peine, et aura encore d’autres avantages considerables” (A III,6 N. 38, specifically p. 101; HO, 10, pp. 609–615). 297 Cf. B. Renau d’Eliçagaray, De la theorie de la manoeuvre des vaisseaux, Paris, 1689. 298 Cf. Ch. Huygens, “Remarque … sur le livre de la manoeuvre des vaisseaux”, Bibliothèque Universelle et Historique, (September 1693), pp. 195–203, and also the extract in Journal des Sçavans, (May 9, 1695), pp. 311–318, and HO, 10, p. 478, p. 525, and annotations. 299 Cf. B. Renau d’Eliçagaray, Reponse  … à la remarque de M. Huguens, sur le livre de la manœuvre des vaisseaux, Paris, 1694, and also the partial reprint in Journal des Sçavans, (May 16 and 23, 1695), pp. 329–337 and pp. 355–363, respectively. 300 Cf. B. Renau d’Eliçagaray, Replique de M. Huguens à la reponse de M. Renau, … et La reponse de M. Renau à la replique de M. Huguens, Paris 1694. 301 Cf. A III,6 N. 38, specifically p. 103; HO, 10, pp. 609–615. 302 Cf. A.-H. de Cotentin de Tourville, Exercice en général de toutes les manoeuvres qui se font à la mer, Au Hâvre de Grâce, 1693.

1694–June 1696

589

things the center of gravity of the vessel which ought not to be neglected, it appears to me, especially in relation to leeway, since the impressions of the shock of bodies operate diversely according to the situation of the center of gravity. There were many other matters which enthralled me. The best of it is that it is based on practice and I would like to have seen the book of Monsieur Tourville on maneuvering which he cites.303 Then, in his letter of August 24, Huygens underlined his highly critical standpoint once again in the following words: It is not the little errors, or omissions, which appear in this work printed at the Express command of the king,304 as it says on the title page, and examined by the ‘Monsieurs’ of the Academie des Sciences, but rather a capital error which overturns the whole.305 Even after L’Hospital had sent Leibniz the documents relating to this dispute, he restricted himself, in writing to this correspondent, to rather general comments concerning issues of force, speed and leeway, or windward drift, of a vessel like on June 24, 1695, when he wrote: It appears also to me that Monsieur Renaud uses the term ‘Force’ a little differently to the ordinary [sense of the term] and, as that leads to the creation of equivocations, I would be obliged to read his book with care some day to uncover its sense and to find out in what it founders.306 303 “Lors que je considerois autres fois cette theorie, elle me paroissoit un peu superficielle, et je n’achevay pas de la parcourir. Mais j’y penseray un de ces jours. Je me souviens maintenant, qu’il negligeoit entre autres choses le centre de gravité du vaisseau le quel ne deuvroit pas estre negligé ce me semble sur tout pour la derive, puisque les impressions du choc des corps opérent diversement selon la situation de ce centre. Il y avoit bien d’autres choses qui m’arrestoient. Le meilleur y est ce qu’il y a de la practique et je voudrois avoir vû le livre de la manoeuvre de M. de Tourville qu’il cite” (A III,6 N. 45, specifically p. 128; HO, 10, pp. 639–646). 304 underlining by Leibniz. 305 “Ce ne sont pas de petites bevues, ou omissions, qui se rencontrent dans cet ouvrage imprimé de l’Expres commandement du Roy, comme il y a au titre, et examiné par Mrs de l’Academie des Sciences; mais une erreur capitale qui renverse le tout” (A III,6 N. 54, specifically p. 161; HO, 10, pp. 664–672). 306 “Il semble aussi à moy que M. Renaud prend le terme de la Force un peu autrement qu’à l’ordinaire et comme cela fait naistre des equivocations, je seray obligé de lire un jour son livre avec application, pour dechifrer son sens, et pour trouver en quoy il aura manqué” (A III,6 N. 135, p. 415).

590

Chapter 4

And then, on September 30, 1695, he added the following: I believe I have pointed out to you in a previous letter that it appears to me that the leeway ought to change when the speed of the vessel is different, whereas, on the contrary, the rule of Monsieur Renaud makes it always the same.307 Nevertheless, Leibniz thought that he could obtain the correct rule for leeway, or drift, and believed that the time he should invest in the study of Renau’s book would be rewarded and would give him occasion to show the power of his own dynamics. Thus he continued: It has been some time since I took the trouble to examine the matter more exactly, and I believe myself to be in a position to give the true rule. I also have the intention of considering some day the rest of the Theorie du Manoeuvre. For the matter is pulchritudinous and would give me occasion to demonstrate the application of my dynamics.308 11

Projects: Economics and Trade

As regards his interest in economics and trade advancement, and in particular in the improvement of the economic footing of his principality, Leibniz did not find any great sphere of activity in the years between 1693 and 1696. Whether it was that he lacked the necessary time for lobbying due to other obligations, or that, in such times of war, his superiors (or the sovereign) were forced to give attention more to short-term foreign-policy matters, rather than long-term advances on the home front, the outcome was that most of the projects proposed went unheeded by his superiors at this juncture. Although he was informed by his correspondents about a range of different projects, he failed in several instances – for example, regarding salt works, linen drapery or wallpaper manufacture – to advance beyond the reception, or intake, of intelligence or, at best, could only offer encouragement to others as, for example, regarding 307 “Je crois de vous avoir mandé dans une precedente qu’il me semble que la derive doit changer lorsque la vistesse du vaiseau est differente; au lieu que la regle de Mons. Renaud la fait tousjours la même” (A III,6 N. 163, p. 507). 308 “Il y a quelque temps que je pris la peine d’examiner la chose plus exactement, et je crois d’en pouvoir donner la regle veritable. Je me propose aussi de considerer un jour le reste de la Theorie du Manoeuvre. Car la matiere est belle et me donne occasion de faire voir l’application de mes dynamiques” (p. 507).

1694–June 1696

591

glass working for optical equipment, or porcelain manufacture. In end effect, apart from his renewed activities in mining in the Harz region, there was but a single undertaking in the economic field in which he was seriously involved in this period, namely that for the production of brandy from native sugar. This project was also motivated in part by his obligations towards his old, and in the meanwhile luckless, associate and one-time friend, Johann Daniel Crafft. In the course of the ‘War of the Grand Alliance’ (1688–1697), the helplessness of the German empire in the face of the conquest-oriented French king caused Leibniz to reflect very early on possible counter-measures on the economic front. To this end, a trade war seemed to be an option and, by a favorable coincidence, Crafft learned in the fall of 1693 of a projected brandy manufactory in the town of Münden, and he immediately got involved himself in the enterprise. In the same vein, Crafft had been able to inform Leibniz, on October 19 of that year, about a new ferment that had been developed in Hamburg.309 Since the greatest part of the brandy and cognac consumed in Germany was imported from France, it seemed that considerable economic damage might be inflicted on the enemy through the domestic production of such distillates. Unlike the French brandy production from wine, sugar solutions (syrup or treacle) were to be employed in the contemplated German scheme. After Crafft had reconnoitered the processes used for such distillates in Holland, he and Leibniz signed a contract for the formation of a company, whose aim was the production of brandy, or of a brandy substitute. According to the contract, a quarter of the proceeds of the company was to be used for pious or charitable purposes. A final stipulation was that the company, so formed, should be limited to the two signatories to the agreement. This restrictive clause in the contract – that was done at Hanover, on May 14 (new style), 1694310 – would in the end prove to be ominous for Crafft. Since Leibniz was not yet convinced of the profitability of the production process, he ordered, on the one hand, further trials to be carried out, with among other things the goal of producing vinegar from the residue of the distillation process, which was referred to in Crafft’s letter of August 8, 1694,311 while, on the other hand, he carried on detailed negotiations with a merchant in Hamburg named Danneberg about the process he employed.312 There was also contention between the parties to the contract regarding the location 309 Cf. A III,5 N. 192, p. 652. 310 “Vnd solle ohne approbation deßen, so hier bedungen, niemand in die Compagnie genommen werden. Geschehen Hannover den 4ten May 1694” (A III,6 N. 29, p. 78). 311 Cf. A III,6 N. 51, p. 148. 312 Cf. Gottfried Wilhelm Leibniz Library, Hanover; Manuscript: LBr. 501, fols 251–252.

592

Chapter 4

of the production facility. Thus, while Crafft advocated England as the place of production, Leibniz favored Holland, as is to be seen from a passage in Crafft’s letter of early October. There the correspondent wrote: “I know, and do indeed understand, that I should already be in Holland, albeit with the consolation that in actual fact the seat of the company has to be in England, but the systematic preparations have to be undertaken in Holland”.313 And so it was agreed to undertake the initial preparations in Holland, to where both of them travelled at the beginning of November 1694. In Amsterdam they wrote, during the second half of November, a series of memoranda intended for the Stadhouder (or head of state of the Dutch republic), and king, William III, for his diplomat George Stepney, and for the general field marshal of the forces of the States-General and governor of Mastricht, duke Johann Adolf of Holstein-Sonderburg-Plön.314 Of the two letters, which were written by Leibniz and Crafft and addressed to William III, only that of November 18, 1694, was actually dispatched.315 It was included as an attachment to a letter, dictated by Leibniz and written by Crafft, to Stepney on the same day.316 It was, however, never presented to the addressee, as is evident from Stepney’s letter to Leibniz of March 4, 1695. Stepney reported that he had handed Crafft’s latter to Charles Talbot, the duke of Shrewsbury and secretary of state, who was not willing to pass it on, since Crafft had not been prepared to disclose the details of his secret process, or in the words of the diplomat: “He wanted so much to so safeguard the secret that one was not able to establish what he wanted and, as we are not the kind of people who are prone to amusement by mysteries, the matter has remained there for lack of lucency”.317 In the letter in question, addressed to William III, Leibniz and Crafft argued that part of the strength of France lay in trade in foodstuffs and merchandising, on which its neighbors were dependent, or in their words: One of the greatest sources of French power is commerce in commodities or merchandise, which it supplies and of which it appears one has 313 “ich weiß vnd begreiffe gar wohl, daß ich schon in Holland sein solte, wiewohl mich dieses noch consolirt, daß der sedes negotii eigentlich in Engelland, sein muß, Aber die grundliche praeparatoria in Holland gemacht werden müße” (A III,6 N. 62, p. 192). 314 Cf. A III,6 N. 72–77. 315 Cf. A III,6 N. 72, pp. 213–215. 316 Cf. A III,6 N. 73, pp. 215f. 317 “il a tant voulu menager le secret qu’on n’a pas pû devenir ce qu’il vouloit, et comme nous ne sommes pas des gens à nous laisser amuser par des mysteres, l’affaire en est demeurée là faute d’éclaircissement” (A I,11 N. 208, p. 309).

1694–June 1696

593

difficulties in emulating, a circumstance which puts it in a position to have the world in its debt, and to discommode its neighbors with their own money.318 Leibniz and Crafft explained that their research had now revealed a method of circumventing this French trade monopoly, namely by enabling the English, together with their allies, to obtain the requisite products in great quantity, and of high quality and at a low price. This situation would in due course lead to irreversible damage to French foreign trade. Furthermore, such a trade war might even be legitimately continued in times of peace, which would inflict long-term damage and be tantamount to the destruction of a French province. And so they continued: Thus exact research that has been done on part of this matter has revealed the means of surpassing some of the most important French merchandise products, and of obtaining them in an equally great quantity and perfection at a lower price, by means that are at the disposal of the English and their allies. And that at as low a price as possible in order to ruin entirely this trade of France and to really close the door to it, in such a way that it could not be restored in times peace which also, with such an enemy, could otherwise only have been achieved in a padded or limited form. It is a desire of reason that one should conduct this kind of war, which is allowed in time of peace, and which would inflict an amount of damage comparable to the ruination of a province.319 Such damage would of course affect only the adversaries of England and Holland, and would promote commerce through the provision of the requisite raw materials, give increased turnover, and serve to increase the wealth and 318 “Une des sources considerables de la puissance de la France est le commerce des denrées ou marchandises, qu’elle fournit, dont il semble qu’on a de la peine à se passer, ce qui l’a mise en estat de mettre le monde en contribution, et d’incommoder ses voisins par leur propre argent” (A III,6 N. 72, p. 214). 319 “Or les exactes recherches qu’on a faites sur une partie de ces matieres, ont fait connoistre la maniere de se passer de quelques unes des plus importantes marchandises de France, et de les obtenir en aussi grande quantité et perfection pour le moins, par des moyens qui sont dans le pouvoir des Anglois et de leur amis. Et cela à aussi bon marche qu’il faut, pour ruiner entierement ce commerce de la France et pour luy fermer tellement la porte, qu’il ne puisse pas mêmes se remettre apres la paix, la quelle aussi bien avec un tel ennemi ne sera jamais que fourrée; la raison voulant, qu’on luy fasse tousjours cette espece de guerre, qui est permise en temps de paix, et qui luy feroit autant de mal que la ruine d’une province” (p. 214).

594

Chapter 4

power of the allies, promoting navigation and plantations, which might see expansion even in south America, or as they explained: This would only damage enemies and the ill-disposed. For England and Holland would attract this commerce by providing the materials and contributing to the very considerable sales and distribution. And the utility would go much further than one thought and could with the grace of God have very considerable consequences, both in this matter as on other points which arise consecutively, which [in turn] serve to increase the richness and the power of the good alliance, to promote navigation and the plantations, and to extend them even in south America.320 And, finally, the bottom line was that France would be mortified or humiliated while William and his allies would be the beneficiaries.321 For the realization of such projects, a company should be formed, and provided with prohibitive privileges to exclude any French influence. Thus, they wrote: For the realization of such projects, it is necessary that a rather substantial company be formed and provided with monopolist privileges, prohibitively directed against those who might, through its disruptions, advance to its detriment and favorize the merchandise of France.322 In effect, Leibniz and Crafft were requesting a Royal privilege for the protection of participating entrepreneurs, and they were willing to particularize the details together with a minister to be appointed by the king. Thus they added that: It is necessary, and suffices in the expectation of the privileges being formally solicited, that we obtain the Royal prerogative of Your Majesty for the assurance and encouragement of entrepreneurs and of those who 320 “Cela ne nuira qu’aux ennemis et mal intentionnés. Car l’Angleterre et la Hollande s’attireront ce commerce en fournissant les materiaux et concourant au debit qui est tres considerable. Et l’utilité va plus loin qu’on ne pense, et pourra avoir des suites tres grandes avec l’aide de Dieu, tant en cela, qu’en d’autres points, aux quels on passera consecutivement, qui serviront à augmenter les richesses et la puissance du bon parti, à faire fleurir la navigation et les plantations, et à les étendre dans l’Amerique même meridionale” (p. 214). 321 “en fin en un mot, à mortifier la France et à avantager les amis et alliés de Vostre Majesté” (p. 214). 322 “Pour venir à l’execution de ces Projets, il est necessaire, qu’il se forme une compagnie assez considerable munie de privileges prohibitifs, contre ceux qui pourroient aller sur ses brisées à son prejudice, et favoriser les marchandises de France” (p. 214).

1694–June 1696

595

wish to participate and we only ask for his agreement and his protection, in accordance with law and reason, being willing to particularize the details with a minister of Your Majesty, who wanted to deal with this request, and who could impart His volition.323 Finally, their submission contained the following call for a portion of the company’s profits to be set aside for the promotion of pious or charitable causes, and for the practical arts, under the guidance of the applicants: We declare that, in accordance with the fundamental tenets of the company, a determined portion of the profit (if God gives it his blessing) will be assigned to pious causes, for the advancement of piety and of the arts, with the applicants determining only the direction.324 On December 26, 1694, following Leibniz’s return to Hanover, Crafft was able to report from Amsterdam for the last time about a general acceptance of the project.325 Thereafter, there followed a succession of bad news reports, and evil tidings, in relation to the project. At first, as reported in Crafft’s letter of December 30, 1694, there arose contractual difficulties, then the need for a better ferment emerged, and finally there was a desire for the establishment of smaller subsidiary companies, all of which contributed to delays.326 In due course, a disappointed Leibniz had to abandon all hope of a successful conclusion of the undertaking, and he wrote off the advance payments he had made, the sole consolation for him being that his lost investment had been in the service of the commonweal, or, as he formulated the idea in his letter to Crafft of July 5, 1695, “in as much as I esteem not private gain but rather the common utility”.327 323 “il est besoin, et suffit qu’en attendant les privileges, qu’on solicitera dans les formes, nous obtenions la parole Royale de Vostre Majesté pour l’asseurance et encouragement des entreprenneurs et de ceux qui s’y voudront joindre et nous ne demandons son agrément et sa protection, qu’en tant que de droit et de raison; estant prests à particulariser les choses au Ministre de Vostre Majesté, qui a bien voulu se charger de cette requeste, et qui pourra apprendre Sa volonté” (p. 215). 324 “nous declarons que suivant les conditions fondamentales de la compagnie une portion déterminée du profit (si Dieu y donne sa benediction), sera destinée aux causes pieuses, pour l’avancement de la pieté et des arts; les proposans ne s’y reservans que la direction” (p. 215). 325 Cf. A III,6 N. 83, pp. 247–249. 326 Cf. A III,6 N. 87, pp. 263f. 327 “Immaßen ich nicht den privat Nuz, sondern nur utiltatem publicam achte” (A III,6 N. 138, p. 434).

596

Chapter 4

After an extended period of silence, Crafft finally acquiesced on February 23, 1696, to Leibniz’s decision, and he listed economic factors that had made the death of the undertaking inevitable. In particular, he suggested that sugar and syrup prices were only low enough in America to enable a profitable production of brandy from this raw material.328 Notwithstanding the setbacks, the imaginative and relentless Crafft proposed a new project that he had encountered in connection with his fight against gout, namely the removal of the fusel oils from fruit and corn liquor by means of distillation with quicklime. He accordingly characterized his recently conceived project as follows: So this is the project which I have, on the 1/11th of this month,329 most happily discovered in order to take the stench out of the fruit-syrup brandy [project], this being an enterprise with which every day almost a hundred percent profit can be achieved.330 However, Leibniz’s reaction, in his reply on March 2, was cool, noncommittal, and even recriminatory, as the following sentiment expressed at the beginning of the letter reveals: “It would indeed be preferable for me, if I did not have to sense the [character] deficit in a good friend, that his word is not trustworthy, and that he spites me with [the illusion of] a hundred percent profit”.331 And, specifically regarding the fruit brandy project, he added the following words to this: “As regards the fruit brandy, it is good if it is reliable. It is best not to say that one has the likes of it”.332 Thereafter, Crafft’s economic survival became increasingly difficult and, in April 1697, he died ill and poverty-stricken in Amsterdam.

328 Cf. A III,6 N. 204, pp. 660f. 329 Namely February 11, 1696. 330 “so ist dieß daß werck; den 1/11ten dieses habe ich dem fruchtbrandtewein den Stanck zu nehmen, felicissime außgefunden, welches eine Sach, womit alle tage fast Cento pro Cento zu gewinnen” (N. 204, p. 661). 331 “Lieber wäre mirs aber freylich, wenn ich an einen guthen freund den mangel nicht verspuhrte, daß auf seine parole nicht zu bauen, und er mir damit umb cento pro 100 abschlägt” (A III,6 N. 207, p. 666). 332 “Wegen des fruchtbrandteweins, ist schöhn wenn es sicher. Am besten ist nicht zu sagen, daß man dergleichen habe” (p. 666).

1694–June 1696

12

597

Projects: The Organization of Science and Education

In the 1690s Leibniz upheld his life-long ambition, firstly, to establish and advance societies, colleges and institutions, for the collection, advancement and resourcing of knowledge and practical skills, and secondly, to improve and extend existing institutions in order to serve the “bonum commune”, or the commonweal, in both theory and practice. The nature of his engagement, or commitment, included the conception of plans and memoranda to support the initiatives of kindred spirits, and even the exertion of influence in the filling of vacancies and appointments. The spectrum of institutions and associations considered was quite broad. It included, on the one hand, renowned and established academies (like the Academia Leopoldina, the Académie des Sciences, and the Royal Society of London), universities (like Gießen, Helmstedt and Wittenberg), military academies (like that in Wolfenbüttel), grammar schools (like that in Göttingen) and, on the other hand, scholarly coteries (like the ‘Kunst- Rechnungs- liebende Gesellschaft’ in Hamburg and the ‘Collège de curieux’ in Kassel). Thus, when on January 31, 1695, Leibniz was informed by Haes,333 that the landgrave Charles or Karl of Hesse-Cassel wanted to establish such a ‘Collège de curieux’ in his principality – in which Papin was to be one of the first members – he was prompted to provide a detailed representation on the matter, which he included with his reply of March 6 to Haes for presentation to the landgrave.334 From the extant penultimate version of this reply, it can be seen that Leibniz was sending a proposal for the establishment of an Academy of Sciences and Arts (an “Akademie der Wissenschaften und Künste”). Haes could then inform Leibniz, on March 28, of the admiration and gratitude of the landgrave for this proposal.335 However, the foundation of this academy – the ‘Collegium Illustre Carolinum’ – was to be delayed until the year 1709. The projects of Leibniz’s former mathematics professor (at the University of Jena in the summer of 1663) Erhard Weigel, like his ‘Collegium artis consultorum’, and his school and pedagogical reform efforts, deserve special attention here. In this regard, Leibniz wrote the following lines to Huldreich von Eyben in June 1693: [Prof.] Weigel wrote to me several months ago, and he also sent certain new ‘Opuscula’[or, odds and ends] dealing with the improvement 333 Cf. A III,6 N. 92, p. 278. 334 Cf. A III,6 N. 100, pp. 303–307. 335 Cf. A III,6 N. 105, pp. 326f.

598

Chapter 4

of studies, in which I find many beautiful thoughts, although the difficulties are commonly hidden in the mode of execution because help is wanting.336 While the attachments – the “odds and ends” referred to here – to a letter sent by Weigel to Leibniz, on February 18, 1693,337 have not been identified, the text of the letter to Von Eyben as well as other letters of Leibniz, in particular those to Wilhelm Ernst Tentzel of June 29, 1693,338 and to Tschirnhaus at the end of June 1693,339 leave no doubt that they contained proposals for the improvement of the organization of science. Among these suggestions was surely Weigel’s project for a ‘Collegium artis consultorum’, referred to in his letter to Leibniz of April 26, 1694.340 This project provided occasion for Leibniz to think once again about scientific institutions that would not be dependent on the grace, and monetary, support of princes. The issue of such a ‘Collegium’ was likewise addressed not only in Leibniz’s correspondence with Tschirnhaus, but also in the first letter of November 29, 1694, which he received from the physician Alexander Christian Gakenholz.341 By 1693 Weigel’s renewed commitment to pedagogy had already persisted for more than a decade. In fact, the year 1681 had marked the beginning of a creative period dominated by pedagogy in Weigel’s life to which a series of corresponding publications bear witness.342 He approached not only the Imperial Diet (the ‘Reichstag’) in Regensburg (in 1683), but also princes willing 336 “H. Weigelius hatte mir vor ethlichen monathen  … geschrieben, auch einige Neue Opuscula zugeschickt, welche zu verbeßerung der studiorum gehen; in welchen ich viel herrliche gedancken finde, ob schohn die schwührigkeit gemeiniglich in modo exeqvendi stecket, die weilen es an hülffe fehlet” (A I,9 N. 329, pp. 500f.). 337 Cf. A III,5 N. 132, pp. 492–494. 338 Cf. A I,9 N. 320, pp. 485f. 339 Cf. A III,5 N. 165, pp. 488f. 340 Cf. A III,6 N. 24, p. 68. 341 Cf. A III,6 N. 78, p. 230. 342 Cf. the following 4 works by E. Weigel: Kurtze Relation von dem nunmehr zur Prob gebrachten mathematischen Vorschlag, betreffend die Kunst- und Tugend-Information, Jena, 1684; Wegweiser zu der Unterweisungs-Kunst nicht nur des Verstandes; sondern auch des Willens, Jena, 1688; Von der Nothwendigkeit der Angewehnung dessen, was man in gerechter Maß und Weiß zu thun hat über das, daß man die Wissenschafft davon gelernet hat. Samt einer Kurtzen Relation, wie weit es mit der angestellten Kunst und Tugend- Schul bißher gekommen sey. Dabey die ins gemein so operos und schwer getriebene Sprachen mit pur lauter erbarer Lust, dazu die Kinder von Natur geneigt, in steten reden, lesen, schreiben, singen, rechnen, messen, mahlen, reiten, höfflich gehen und sich wenden, auff und aus Papier Figuren machen, und dergleichen, auff das leichteste geübet werden, Jena, 1691; Paedagogiae mathematicae ad praxim pietatis, fundamenta et principia, 2 parts, Coburg, 1694.

1694–June 1696

599

to invest in his schemes, and he campaigned for support in realizing his school reform enterprise. In the year 1683, he started a private school project in his own house. Based on this experience, and following the completion of the necessary building measures, there followed a public school project in 1690. An outstanding aspect of Weigel’s ‘School of Virtue’ (‘Kunst- und Tugendschule’) was the range of teaching materials he developed himself. At the core of his method of teaching was the activity concept. Thus, the children were taught in such a way that they remained active as much as possible during the learning process. In this context Weigel developed a so-called “Schreibregel”, or writing rule, that availed of a mechanical instrument he had designed. This was used in elementary instruction for the training of the motor function in learning to write, and it allowed the simultaneous execution of scribal movements by a large number of children. In addition to this writing rule, there was a so-called “Leseregel”, or reading rule, for school starters, and for teaching arithmetic, a corresponding learning aid was made available. A special attraction of Weigel’s private school was the “Schwebeclaß”, or floating class, which was intended to enable the scholars to accompany their memory exercises with swaying movements. It consisted of desks mounted on a floor plate, or platform, made of wooden planks. The platform was suspended by means of strong ropes, which were attached to iron hooks, and it was constantly maintained in a horizontal position parallel to the ground. In this way, a pleasant tranquility in the midst of movement was achieved, and the rhythmic movements of the individual children were combined with the common movement of the entire class. The syllabus of instruction combined rhythmics and calculation, reading and swinging, on the “Schwebeclaß” platform. Weigel’s dynamic instruction retained, by and large, the traditional syllabus, but it shifted the emphasis more towards mathematics and science. The vernacular was introduced as a full-fledged medium of instruction. Weigel chose not to curtail the amount of material that had to be learned, but rather the time that had previously been required. Weigel’s commitment to pedagogy and learning was reflected in his correspondence with Leibniz. Thus, in his letter of April 26, 1694, he elaborated his school reform plans with the following words: In the meantime the school-correction [project] is, thank God, taking shape, because I have found a means by which there are no additional expenses for the public, and which also requires no new preceptors, in that the existing teachers can with a special advantage be initiated [in these methods] to such a degree that they can instruct the youth over many years in the principles of mathematics, which contributes very much to the advancement of [knowledge of] Latin, and indeed with

600

Chapter 4

interest and joy, yet without the constraint of the so-called floating class, which I apply only in my private school for the small number of little children, and outside normal school hours, in which unadulterated series, but also for them pleasant mathematics, are used with delightfulness, so that they can remain in the school without revulsion the whole day, except for sleeping and meal times, in both summer and winter. However, in the public schools, where a 100 to 200 children have to be taught together in a single classroom, other caring means are required, which are a source of great pleasure for everybody. May God give his grace and blessing, so that most schools around here may be set up accordingly. I will not be idle if God continues with wonderment to give me as hitherto life and strength (in that I as a septuagenarian feel much fresher and healthier than I was in my youth, [or] have been up to my 50th year, and am now feeling younger every day).343 In his reply, on May 20, 1694, Leibniz strongly praised Weigel’s efforts and he announced his continuing support for these in political circles, or in his words: I express my sincere thanks both for everything else and for the details communicated regarding the progress of the educational efforts which surpass everything else. May God give his blessing to it … I have spoken about it in the presence of genteel (or courtly) ministers adding my praise and applause.344 343 “Interea gehet die Schul-Correction Gott lob wohl von statten, weil ich einen modum erfunden, daß Sie dem publico keine neue Vnkosten macht, auch keine neue Praeceptores erfodert, in dem die alten mit einem sonderlichen Vorth[eil] in 4 Wochen so weit darinnen informiret werden können, daß Sie viel Jahr in principiis mathematicis, die zur beföderung des Lateins trefflich viel contribuiren, die Jugend informieren können, vnd zwar mit Lust vnd Freuden, doch ohne Schwang der so genannten Schwebeclaß, welche ich nur in meiner privat Schul vor die wenigen kleinen kinder adhibirt, vnd nach den gewöhnlichen Schul-Stunden, darinnen lauter seria doch auch ihnen angenehme mathematica getrieben werden, zur Ergötzligkeit gebraucht, damit sie ohne Ekl den gantzen Tag ausser Schlaf vnd Tisch-Zeit, Sommer vnd Winter in der Schul bleiben können. In publicis Scholis aber, da 100 bis 200 Kinder in einer Stuben auff einmahl zu informiren sind, werden andere liebreiche Mittel gebraucht, darüber iederman ein groß vergnügen hat. Gibt Gott Gnad v. Seegen, daß hie herum die meisten Schulen also eingerichtet; werde ich nicht ermangeln, wenn mir Gott das Leben v. die Kräffte ferner wie bisher zur verwunderung verleihen (in dem ich septuagenarius viel frischer vnd gesunder alß in der jugend, bis zum 50sten Jahr gewesen, worden bin vnd noch alß alle Tage verjünget werde)” (note 340 above, p. 68). 344 “Bedancke mich hochlich sowohl wegen alles übrigen, als wegen communicirter particularitäten des progressus der Educations-arbeit so alles übertrifft, Gott gebe dazu seinen

1694–June 1696

13

601

Medicine and Res Medica

A pronounced interest in anatomy, and specifically in new anatomical insights, on Leibniz’s part was once again apparent between 1694 and 1696. In the early months of the year 1695, for example, the surgeon Jacques M. B. Bouquet accompanied prince Maximilian Wilhelm of Hanover on a tour to Italy. On March 3, Bouquet reported to Leibniz from Padua that his conversation partners there would only converse about anatomy and medicines.345 While in Padua, Bouquet had assisted a dissector with the postmortem examinations of a series of corpses. Two of these autopsies Bouquet thought particularly worthy of mention. In the first case, in carrying out the postmortem examination of a corpse, they had found the spleen split in two, with one part in the breast area and the other in the abdomen. In the second case, they appeared to be confronted with a corpse having two livers, and which were separated from each other. One liver was found in the normal location and had normal proportions. On the other hand, the second liver was discovered within the coverings of the diaphragm. According to Bouquet’s report, it had the size of two fists and weighed about two to three pounds. Furthermore, it had an approximately round figure and a small lobe. Below this second liver passed the vena cava, which led to the remaining veins and numerous arteries. Thus the correspondent wrote: It was among a quantity of bodies or corpses which we dissected at the hospital or at the anatomical theater that we found one that had one half of the spleen in the breast area and the other half in the abdomen. The other [corpse] was that of someone who had two livers separated from each other, one of normal proportions and in the normal location and the other within the coverings of the diaphragm being the size of two fists, weighing about two to three pounds and having a quasi-circular shape and a small lobe. Below this passed the vena cava sending out throughout the body a quantity of veins to receive the blood of the arteries which were present in very large numbers. That was what I observed and which I am able to affirm having aided the anatomical dissector myself in the dissection of these two corpses.346 seegen … ich habe bey vornehmen Ministris davon mit ruhm und applausu erwehnet” (A III,6 N. 36, pp. 95f.). 345 “on ne parle apresent à Padouë (au moins ceux avec quy Je converse) que d’anathomie et de medecines” (A III,6 N. 99, p. 301). 346 “c’est qu’entre quantité de corps ou cadavres que nous avons ouvert à l’ospital ou au Theatre anathomique nous en avons Trouvé un quy avoit la moitié de la Rate dans la poitrine et

602

Chapter 4

After Leibniz had requested further details (in a non-extant letter), Bouquet addressed the two autopsies once again in his next letter of June 11, 1695, in the following words: “Here is the response to that which you requested regarding the anatomical observations which I told you about in my previous [letter]”.347 First of all, he explained the circumstances of the investigation of the corpse with the two livers. Together with the dissector, he had examined an organ between the membranes of the diaphragm that was at first construed as the heart. However, through further investigation, similarities with a liver were established. The form and substance of the organ, the path of the vena cava, as well as the distribution of the veins and arteries throughout the whole body, indicated that the organ was indeed a liver. In addition, the gallbladder, and the gallbladder passage to the intestines, were found to be missing. Thus he wrote: The one with two livers was an unknown person who had died at the hospital in Padua according to what the medics at this hospital told me. I would have liked to carry out some further research on his body but I did not have the time having been engaged to aide the anatomical dissector to prepare the parts which were to serve for public lectures so that this dissector, who is a medic of the hospital, and myself could not do anything other than examine that part found within the coverings of the diaphragm and which the medic at first considered to be the heart that had descended into the abdomen. We only recognized it as being the liver or, more precisely, we named it as such only after having opened the membrane within which it had been enclosed and having considered the similarity it had with the liver. [It was determined] both by its shape and construction as by its substance[,] the passage of the vena cava and the respective distributions of the veins and arteries throughout the body [sic]. It is true that there was neither a gallbladder vesicle nor a biliary tract going to the intestines.348 l’autre moitié dans l’abdomen, l’autre est d’un autre quy avoit deux foy separé[,] un de la grandeur ordinaire et dans le lieux ordinaire et l’autre entre les Tuniques du diaphragme de la grosseur de deux poin[gs] et du pois d’environ deux à Trois livre aiant la figure quasy Ronde et une petite lobe, par dessous laquelle passoit la véne cave envoiant dans Tout son corp quantité de venes pour Recevoir le sancq des arteres quy y estoient en Tres grand nombres, voila ce que J’ay vuë et que Je puis affirmer ayant moy mesme aydé l’inciseur anathomique à la dissection de ces deux corps” (p. 302). 347 “Voicy la Responsse à ce que vous me demandés Touchant les obsservations anathomiques dont Je vous parloit dans ma precedente” (A III,6 N. 130, p. 394). 348 “Celuy des deux foy est un Incognu quy est venu mourir à l’ospital de Padoue à ce que m’en ont dict les medecins de cest ospital, J’auroit souhaité faire quelqu’autre Recherche dans son corp mais Je n’en avoit pas le Tans m’estant Engagé à ayder l’inciseur anatomique

1694–June 1696

603

Bouquet then elaborated on the special circumstances of the other autopsy. There they had been confronted with the corpse of a crippled or maimed man, a school master who had never been able to walk. As a result of his illnesses, and the circumstances of his disability, the organs of the lower abdomen were swollen or overblown, pressed together and pushed upwards. The circumstances of the man’s life also provided an explanation for his split spleen. A part of the oversized organ had in fact been pressed into the chest or breast area by an extension of the diaphragm. Thus, the correspondent continued: The one with the spleen was a local school master who had been subject to several indispositions not at all caused by the derangement of these internal organs but which was rather the cause that these innards were displaced (my explanation). This man had been a cripple who had never been able to walk. For a long time he had illnesses which had given him obstructions throughout the lower abdomen and which had tumefied or bloated all of the continuous parts, such that this man having all of the parts of the lower abdomen strongly pressed together [–] both as a result of their size as by virtue of the situation of the man who was always seated [–] which pressed upwards the innards of the lower abdomen and the spleen, which [in turn] had an extraordinary size, length and rigidity, and pushed continually against the diaphragm, and stretched insensibly its membranes causing an intrusion into the poitrine or chest region following an elongation of the diaphragm which appeared as a small sac or bag into which half of the spleen had entered.349 à preparer les parties quy devoient servir aux lecons publiques de sorte que cest Inciseur quy est un medecin de l’ospital et moy ne pume faire autre chose que d’examiner ceste partie quy se Trouvoit entre les membranes du diaphragme et que le medecin prit d’abord pour le coeur decendu dans l’abdomen, nous ne le Reconume pour foy ou pour mieux dire nous ne le nomame ainsy qu’apres avoir ouvert la membrane dans laquelle Il Estoit Envelopé et avoir conssideré la similitude qu’il avoit avec le foy. Tant par sa figure et construction que par sa substance[,] le passage de la véne cave et la distributions des vénes et des arteres dans Tout ce corp [sic]. Il est vray qu’il n’y avoit ny vesicule du fiel ny conduit bilaire alant aux Intestins” (p. 394). 349 “Celuy de la Rate estoit un mestre d’escolle du lieux mesme lequel avoit esté sujet à plusieurs Indispositions non point causé par le derangement de ce viscere mais quy estoient la cause que ce viscere estoit sortis de sa place (Je m’esplique). C’est homme estoit un cul de Jate quy n’avoit Jamais marché. Il avoit euë depuis lontans des ventre et quy en avoient Tumefié Toute les parties contenuë maladies quy luy avoient lessé des obstructions dans Tout le bas, de sorte que cest homme ayant Toutes les parties du bas ventre fort comprimé Tant par leurs grosseurs que par la situation de cest homme quy estant Toujour assis poussoit ver en haut Touts les visceres du bas ventre et la Rate quy estoit d’une grosseur[,] longeur et dureté extraordinaire poussant continuellement contre le diaphragme dilatoit

604

Chapter 4

For Bouquet, these deformities represented a grotesqueness of nature, from which no new insights could be expected into the normal functions, and functioning, of the organs involved. Thus he commented: “That is all I can tell you, Sir; I do not believe that this observation can greatly serve for understanding the use of the spleen; in the first place I regard it as a game of nature”.350 Leibniz himself regularly received communications from correspondents regarding the plague, and other epidemics, as for example, on March 29, 1695, from Augustinus Vagetius in Wittenberg, who on that occasion referred to the crawling expansion of the plague, and the epidemic disease which was spreading throughout Germany.351 However, in the field of epidemiology, Bernardino Ramazzini continued to be Leibniz’s most important correspondent. Ramazzini – urged on particularly by Leibniz himself – had published his Constitutiones epidemicae (or medical ephemerides) for the years 1690 to 1694, in which he described the epidemic diseases that occurred in the region around Modena. Thereafter, in the years that followed, Leibniz repeatedly recommended to physicians he knew that they carry out and publish similar medical compilations for other regions. Thus, on January 6, 1694, he sent such a request to the renowned physician Georg Franck von Franckenau in Wittenberg, but not without lauding Ramazzini’s achievements at the outset. Here he wrote: “And this relates to the medical history annual a specimen of which has been given by the renowned Modenese physician Bernardino Ramazzini”.352 Then he continued as follows: And I see nothing that would be more appropriate for the Leopoldine Society than the establishment of [a system of] ephemerides, the more so if the same were to be undertaken elsewhere throughout Germany. Rather short accounts would suffice in the form of letters published at the end of the year from respected physicians in various regions and it would not be necessary that they be treated exactly in the form of Ramazzini unless someone was to be independently inclined to do so … and I rejoice Inssenssiblement ses membranes et se fesoit un entré dans la poitrine par un alongement du diaphragme quy paroissoit come un petit sacq dans lequel la moitié de la Rate estoit entré” (pp. 394f.). 350 “Voila monsieur ce que Je vous En peut dire, Je ne croit pas que ceste observation serve Beaucoup à faire cognoitre l’usage de la Rate; pour la premiere Je la Regarde comme un Jeux de la nature” (p. 395). 351 “de peste hic grassante … cum morbus epidemius per majorem Germaniae partem serpat” (A III,6 N. 106, p. 327). 352 “Et huc pertinent Historia Medica Annalis cujus specimina dedit Bernardus Ramazzinus Medicus apud Mutinenses Clarissimus” (A III,6 N. 1, p. 11).

1694–June 1696

605

that you may acquiesce with me in attempting to establish this organization. Nor do I doubt that by your authority and example it might even be all the more possible to arouse the interest of renowned physicians throughout Europe.353 As things transpired, Franck von Franckenau was certainly prepared to support this call, and indeed to pass it on to medical colleagues in Wittenberg, Dresden, Torgau, Leipzig, Zerbst, Halle, Magdeburg and Berlin, as is evident from his reply almost half a year later, on June 22, 1694.354 However, for his own part, Franck von Franckenau failed to provide a compilation of the type envisioned. The direct correspondence between Leibniz and Ramazzini was very much in abeyance between 1694 and 1696. Only a single letter, which Leibniz sent on December 16, 1695, with collegial greetings extended to friends and acquaintances in Italy, is extant.355 Attached to this letter was a copy of Leibniz’s tract about the recently discovered medicinal plant from South America (viz. ‘Ipecacuanha’), which was entitled Relatio … de novo antidysenterico Americano (1696). The healing effect of ‘Ipecacuanha’ had been previously described by the Dutch physician and naturalist, Willem Piso, in his Historia naturali Brasiliae of 1648,356 but it had subsequently fallen into oblivion. Leibniz had learned about this plant for the first time from a letter of April 8, 1695, which he received from Christophe Brosseau in Paris.357 His Relatio was then conceived as a communication to the Academia Naturae Curiosorum (or Acadenia Leopoldina). In addition, Leibniz arranged for the Relatio to be published as an

353 “Nec quicquam video quod aptius quadret in Societatis Leopoldinae institutum, et Ephemeridium nomen; praesertim si passim idem ageretur per Germaniam, sufficerent breviculae Annotationes in Epistolae modum sub exitum anni publicandae a diversarum regionum medicis egregiis nec opus est ut justi tractatus denture ad Ramazzini modum nisi quis sponte eo inclinet … et gaudeo Te mihi assentiri in probando hoc instituto. Nec dubito quin tua autoritate atque exemplo excitari possit, quicquid est per Europam praeclarorum Medicorum” (pp. 11f.). 354 Cf. A III,6 N. 46, p. 134. 355 Cf. A III,6 N. 184, pp. 576f. 356 Cf. W. Piso (J. de Laet, ed.), De medicina Brasiliensi libri quatuor, in: Historia naturalis Brasiliae, auspicio et beneficio Illustriss. I. Mauritii Com. Nassau illius provinciae et maris summi praefecti adornata. In qua non tantum plantae et animalia, sed et indigenarum morbi, ingenia et mores describuntur et iconibus supra quingentas illustrantur, Leiden and Amsterdam, 1648. 357 Cf. A I,11 N. 265, p. 383 (annotation).

606

Chapter 4

appendix to Martin Lister’s Sex exercitationes medicinales de quibusdam morbis chronicis (1696).358 Leibniz also reported to Bodenhausen about the new “Antidysentericum Americanum” in a letter of December 23, 1695, in the following terms: Because the felicitous antidysenteric herb from America was communicated to me, I have had it printed for the common good in a report to the Leopoldine Society, the Academia Naturae Curiosorum, and I have had it attached by the bookseller-publisher to the Englishman Martin Lister’s unorthodox tract on certain special diseases  … The remedy is a root called Ipecacuanha found in Peru and Brazil which was already described by Piso in Historia naturali Brasiliae together with its effect but it was [subsequently] neglected. Now the effect is found to be even more felicitous than Piso thought.359 Besides being a remedy against dysentery, Leibniz envisioned further possible therapeutic applications, and he added that: “If the intestines or innards have not been corrupted by gangrene or otherwise, the remedy heals infallibly. I do not doubt that it must also have other felicitous applications, also for other diseases”.360 In addition to Bodenhausen, the issue of the new antidysenteric plant from America was broached in Leibniz’s correspondence with Johann Bernoulli in the first half of the year 1696. Thus, in the PS to a letter of February 7, he elaborated the circumstances of the rediscovery of the new “emetica sine violentia”, and he requested information about similar emetics, which had been recently introduced in the Netherlands, like the “Cortex Peruviana” (or “Cortex 358 Cf. G. W. Leibniz, Relatio ad inclytam Societatem Leopoldinam Naturae Curiosorum, De novo antidysenterico Americano, Hanover and Wolfenbüttel, 1696; M. Lister, Sex exercitationes medicinales de quibusdam morbis chronicis … Accessit G. G. L. Relatio … de novo antidysenterico, Frankfurt and Leipzig, 1696; Miscellanea Curiosa, Decur. III, Ann. III, Appendix; A. M. Roos, 2011 (Introduction, note 217). 359 “Weilen mir aus Franckreich umbstandtlich das trefliche Antidysentericum Americanum communiciret worden, so habe ichs per Bono publico in einer Relation ad Societatem Leopoldinam Naturae Curiosorum drucken, und den buchhändler bey des Martini Listeri Angli tractatu recusa de morbis quibusdam specialibus anhefften laßen … Das Remedium ist eine Radix nahmens Ipecacuanha so in Peru und Brasilien fallet, und Piso bereits in Historia naturali Brasiliae mit samt dem Effect beschrieben aber es ist negligiret worden, iezo findet sich der Effect noch treflicher als Piso vermeinet” (A III,6 N. 187, p. 579). 360 “Wenn die intestina oder interna nicht per gangraenam oder sonst gar corrumpiret, heilet dieses remedium ohnfehlbar. Ich zweifle nicht es müße noch trefliche andere usus auch in andern morbis haben” (pp. 579f.).

1694–June 1696

607

Peruvianus”) and the “Herba Paraguay”. Furthermore, he expressed his wish that the intelligence be imparted to Johann’s brother, namely Hieronymus Bernoulli, who had been educated and trained as an apothecary. Thus he wrote: I have recently taken the trouble to publish a report sent to me from France about a new and admirable antidysenteric plant which a certain merchant brought from Spain and which by Royal order was tested with innumerable successes. I do not doubt that you will have learned about it since you have been consorting with France for a long time. But indeed as that which has now been discovered is nothing other than a remedy which was already described by Piso in his Historia naturali Brasiliaei, and as these secrets were previously published and have now reappeared, I have taken the trouble to publish them for our use. I believe this remedy had fallen into oblivion until now and that it has a value not only [as a remedy] against dysentery. Piso called it Ipecacuanha. I ask that you inquire as to whether it is already on sale in Holland, in which case I am also seeking to buy a quantity of genuine and quality Cortex Peruviana and, in the same way, of the Herba Paraguay, which was already celebrated 20 years ago among the Spaniards and the English and which I hear is now gradually being introduced in Holland. The virtue of this is that it is an emetic without violent or harmful side effects. Regarding this, I request that you consult with your brother [Hieronymus].361 Thereupon, Bernoulli made enquiries about the plant conferring with, among others, the medical professor in Groningen Theodorus van Essen, whereby the two medicinal plants from south America  – the “Herba Paraguay” and the “Cortex Peruvianus” – were also considered, and referred to, in the PS to Bernoulli’s letter of March 3 to Leibniz. There the correspondent wrote: 361 “Curavi nuper edi relationem ex Gallia mihi missam de novo illo et admirabili Antidysenterico; quod Mercator quidam ex Hispania attulit, et jussu Regis innumeris successibus comprobatum est. Non dubito quia Tibi in Gallia versanti dudum innotuerit. Sed quoniam nunc compertum est nihil aliud esse quam Remedium jam a Pisone descriptum in Historia naturali Brasiliaei, et quae antea velut arcana premebantur, jam emanavere, in usum nostrorum edi curavi. Credo hoc remedium plus adhuc habere in recessu, nec ad solas dysenterias valere. Apud Pisonem vocatur Ipecacuanha. Rogo ut inquires an in Batavis jam sit venale, quo casu, et ipsius, et corticis Peruviani genuini atque selecti nonnihil mihi redimi peterem quemadmodum et herbae Paraguay, quam jam ante 20 annos apud Hispanos et Anglos celebratam audio nunc in Batavis paulatim introduci. Virtus ejus est, ut sit emetica sine violentia. De his rogo ut Dominus frater tuus cogitare velit” (A III,6 N. 202, pp. 653f.).

608

Chapter 4

Regarding the antidysenteric plant Ipecacuanha, it was known previously neither to me nor also to our recently-appointed new professor of practical medicine, a medic very experienced elsewhere whom I expressly consulted regarding this matter. The Herba Paraguay he said is already sufficiently well-known. The Cortex Peruviana will also be purchasable where you are. My brother wrote about all this [in a letter] to Amsterdam, [sent] to a certain renowned apothecary (druggist) there; but until now he has not received a reply.362 Then, a little later, on March 13, Bernoulli forwarded to Leibniz the report of the “renowned apothecary” from Amsterdam, referred to in his letter of March 3, about ‘Ipecacuanha’ and further medicinal plants with the following note: The hand-written response, which my brother [Hieronymus] received yesterday from Amsterdam, I am transmitting without delay to you, not knowing what I should do otherwise for your convenience. Perhaps you did not realize that that which you seek was so valuable, especially the Ipecacuanha root. I desire to know the means of preparing it and in what form it should be taken.363 Leibniz then reacted, on the March 18, by forwarding a copy of his Relatio, as well as a set of notes about medicinal cortices or barks. Furthermore, he enquired about possible sources of supply and about the usage of ‘Ipecacuanha’ in the Netherlands. Cinchona, or Peruvian bark, was obtainable in Hanover, although not of best quality, he told the correspondent. And he even placed an immediate order for a supply of the Peruvian bark, to which he added a query about the Paraguayan plant. Thus, he wrote on this occasion: I express my thanks to you for communicating that which your brother [Hieronymus] learned from Holland about the plants from overseas 362 “De mirabili antidysenterico Ipecacuanha nunquam antehac innotuit mihi, neque etiam novo nostro Practices Professori mecum vocato, Medico alias experientissimo, quem super hac re expresse interrogavi. Herbam Paraguay jam satis notam dicit. Cortex Peruviana etiam apud vos venalis erit. Frater meus scripsit de omnibus Amstelodamum, celebri cuidam pharmacopolae (Droguiste); sed responsum hactenus nondum accepit” (A III,6 N. 208, p. 676). 363 “En responsum autographum, quod Frater heri Amstelodamo accepit, et quod sine mora Tibi transmitto, ut sciam quid porro faciendum pro commodis Tuis. Forte non putabas adeo pretiosa esse quae petis, praesertim radicem Ipecacuanhae. Scire gestirem modum eam praeparandi et sub qua forma assumatur” (A III,6 N. 210, p. 678).

1694–June 1696

609

which I referred to. I would be most grateful for three pounds of the best Peruvian bark if it should be to hand … I will make sure to reimburse the costs at once. I think it is possible to obtain Ipecacuanha from France at a much lower price. I will inquire about it nonetheless. Regarding the Paraguayan herb remedy, I desire that we get to know its most accurate use and effectiveness.364 This order Bernoulli was able to fulfill a month later, on April 17. As for ‘Ipecacuanha’, Leibniz was informed about suppliers and the purchase price in Amsterdam. As regards this medicinal plant, as well as the “Herba Paraguay”, Bournoulli could announce that he had obtained supplies for Leibniz, but he wanted to obtain additional information elsewhere about the application and use. Information from van Essen, concerning dosage and the shortfall of the “Herba Paraguay” as an effective nauseant or emetic, was also communicated to Leibniz on this occasion. Thus Bernoulli wrote: I thank you for the communication of the description of the antidysenteric plant. Last week I obtained for you three pounds of the Peruvian bark. Please inform me about how I can best send them to you. At present the apothecary in Amsterdam is offering Ipecacuanha albeit at a price of 80 to 90 Dutch florins per long vial or ampulla. Concerning the use of this as well as of the Paraguayan herb, and the means of obtaining them, he told him [i.e. Hieronymus Bernoulli] nothing for release to the public. I will see that I nevertheless learn about this from elsewhere. Our professor of practical medicine maintains that he has made use of the Paraguayan herb at his own risk taking it in a sufficiently large dosage but he perceived absolutely nothing of an emetic effect, nor did it have any other, or only a minimal, effect.365 364 “Gratias ago quod communicas quae Dn. frater tuus ex Batavis didicat de exoticis quorum mentionem feceram. Ternae librae optimi Corticis Peruviani mihi erunt gratissimae, ut sit ad manus … Pretium statim reddi curabo. Ipecacuanham puto multo minore pretio ex Gallia obtineri posse, inquiram tamen. De Herba Paraguay cura quaeso ut circa usum efficaciamque accuratiora discamus” (A III,6 N. 214, pp. 710f.). 365 “Gratias ago pro communicatione descriptionis antidysenterici. Praeterita septimana accepi pro Te tres libras corticis Peruvianae, indica viam qua illas optime Tibi transmittere possim. Nunc Pharmacopola Amstelodamensis offert Ipecacuanham pro longe viliori pretio nempe 80 a 90 flor. Holl. De usu ejus ut et herbae Paraguay, et modo obtinendi, nihil sibi innotescere dicit: curabo tamen ut id aliunde discam. Noster Professor Medicinae Practicae asseverat se in se ipso periculum fecisse herbae Paraguay assumendo illam satis magna dosi, sed se nihil plane virtutis emeticae persensisse, nec etiam alium vel minimum effectum habuisse” (A III,6 N. 224, pp. 740f.).

610

Chapter 4

Finally, in his letter to Bernoulli of May 25, 1696, Leibniz dealt with the ineffectiveness of the “Herba Paraguay” and addressed in this context the problem of adulteration of medication, or medicinal remedies, in the following words: “The Paraguayan herb, which in the case of your friend produced no result, I suspect was not authentic. And that matter especially deters one from the use of such remedies”.366 Leibniz’s involvement in discussion of pharmacology, and pharmacological advances, was surely only derived in part from an academic interest in advances in medical science. His commitment was likewise influenced by his own health and therapy requirements and, in fact, in the years 1693 to 1695 he was often indisposed. Thus, for example, he wrote the following on May 12, 1693 to Otto Grote, the Chamber president in Hanover: “I would be very pleased if my health, which I have seen deteriorate, were to provide me with some salutary experience for the achievement of all that I have planned for the bygone history of the Serene [Guelphic] House”.367 As this pronouncement indicates, a subjectively-felt pressure of work, or overwork, in connection with the history project in particular, may have contributed to his illness pattern at this juncture.368 On October 24, 1694, we find him enquiring in the PS to a letter to Johannes Teyler about a medicinal potion – which was supposed to be obtainable in Amsterdam – that might serve as an emetic. Here he wrote: The late Mr Boyle told me that there was a herb from the Indies which helps one to vomit without effort. Now I am told that there is a house in Amsterdam where one can find a beverage which produces a similar effect. I ask you to obtain information and to tell me your view of the matter.369 Also, in a no longer extant letter to Bodenhausen, Leibniz had complained about health problems. And so, in his reply of November 17, 1694, the correspondent commented and attributed Leibniz’s indisposition to a lifetime of 366 “Herbam Paraguay quae apud amicum tuum nihil effecit, suspicor genuinam non fuisse. Eaque res imprimis deterret a talibus redimendis” (A III,6 N. 229, p. 760). 367 “Je seray trop heureux si ma santé que je voy diminuer me fournit de quoy achiever tout ce que j’ay projetté pour L’Histoire passé de la Sme Maison” (A I,9 N. 31, p. 37). 368 Cf. A III,6, p. LVf. For a modern interpretation of Leibniz’s clinical picture at this time, cf. E. Görlich, 1987, pp. 110ff. (Introduction, note 218). 369 “Feu M. Boyle m’a dit qu’il y a une Herbe des Indes qui fait vomir sans effort. Maintenant on m’a conté, qu’il y a une maison à Amsterdam où l’on peut trouver un brevage, qui fait un semblable effect. Je vous supplie de vous en informer, et de m’en dire vostre sentiment” (A III,6 N. 67, pp. 204f.).

1694–June 1696

611

overwork, writing that: “It is no wonder, Sir, that you have fallen into such an indisposition, which must come about as a result of such application, however necessary, from your youth to the present day”.370 Bodenhausen recommended to Leibniz resting himself, observing a diet and getting more exercise, or as he put it: You should, at least temporarily until your health is restored, moderate your work commitment and observe a certain diet, without which all medication is worthless, and the illness becomes incurable. I therefore wanted to advise that you indulge neither in reading nor in writing and meditation for longer than half an hour at a time (indeed less depending on your condition), but instead that you walk up and down (but without reaching a state of fatigue) or procure vomiting in the company of a good friend.371 In Bodenhausen’s letter of May 26, 1695, we find the correspondent assuming that Leibniz was suffering from a biliousness that was revealed though external inflammation (phlogosis), painful urination, or in the effects of medical drinks. For Bodenhausen it was clear: That his indisposition is totally different from what one had thought previously, in that the preeminence of bile or gall fluid is to be recognized, not only from phlogosis, inflammation around the diaphragm, bitterness of the external urethral or urinary orifice (viz. the meatus urethrae externus), uric acid, but also from the medicinal drinks (from which, no less than from the presumed disorders, there are indications according to the rule) like lemon juice; therefore (in my judgement) neither the fixed liquid remedies, nor the volatile or erratic diuretics, are be recommended, but rather those acids which do not act too strongly.372 370 “Es ist kein wunder, daß M. h. H. in solche indisposition gefallen, so nohtwendig aus gar zu vieler application von jugend auf biß anhero entstehen müßen” (A III,6 N. 71, p. 209). 371 “Er wolle doch auf eine zeit zum wenigsten, biß Er Seiner gesundheit versichert, Seine application moderiren v. eine gewiße  … diaet halten, ohne welche alle medicamente umbsonst, v. die kranckheit incurabel wird. Wollte also rathen, daß Er nicht weder mit lesen, noch mit schreiben v. meditiren über eine halbe stunde (ja auch weniger pro statu virium) auf einmahl zubringe, sondern solche mit auf v. abspatzieren (sed sine defatigatione) oder mit einem guten freunde abbreche” (pp. 209f.). 372 “daß Seine indisposition gantz anders als man zuvor gemeynet, in dem das praedominium bilis gewiß, nicht allein ex phlogosi circa diaphragma, amarite in ore, urina amariore, sondern auch aus den juvantibus (a quibus non minus quam a nocentibus sumendae sunt indicationes juxta regulam) als dem Citronensaft zu erkennen; wären also (nach

612

Chapter 4

Bodenhausen recalled here a well-known case he was familiar with, in which drops of vitriol had been successfully employed against an infectious dysentery epidemic in Italy. He recommended, among other things, the intake of this remedy in the following terms: Thus, I wanted non-authoritatively to recommend the use of such most weak acids  … as for example the aromatic ammonia spirit (spirit of ammonia) … or also (and more frequently) the driblet of vitriol … I add: the |Vitriol|373 from the Hungarian mines … would be incomparably better … I therefore suggest meanwhile this plain [vitriol] driblet as a ‘euporistum’ [household remedy].374 Considering Leibniz’s symptoms, Bodenhausen recommended in addition taking a vitriolic emetic under the supervision of a physician. His words here were: I only wanted to recommend one more thing, namely, because you, Sir, are experiencing excessive bile or gall fluid in the mouth [viz. bile reflux], breast and urine, taking[–]with the advice of and in the presence of a physician[–]a moderate emetic just once with the dose not being so great and determined by your complection. The vitriolic vomitive agents are not as rough as their antimonial counterparts which severely attack those of us who are short-winded. You, Sir, would experience a great relief and chilling.375 In addition, Bodenhausen described the mode of operation of the emetic and he advised caution at the same time, suggesting that Leibniz “take care in this not to chill [his] breast during prolonged treatment and [that he] should not

meinem erachten) weder die praecipitantia fixa, noch die volatilia urinosa, sondern nur dergleichen acida zu rathen, welche nicht zu starck agiren” (A III,6 N. 119, pp. 369f.). 373 deciphered or decrypted words, or alchemical symbols, between vertical bars. 374 “Wolte also unmaßgeblich rathen zu solchen mitioribus acidis  … als v. g. spiritus salis dulcis … oder auch (v. frequentius) zu gebrauchen den rorem Vitrioli … Addo: das |Vitriol| aus den Ungarischen bergwercken  … wäre es ohne vergleichung beßer  … Schlage also unterdeßen diesen bloßen rorem als ein euporistum vor” (pp. 370f.). 375 “Eines nur wolte ich noch rathen; nemblich, daß weil M. h. H. bilis excessum im munde, brust v. urin verspühret, Er cum consilio Medici eoque praesente ein moderates vomitiv einnehme vor einmahl, deßen dosis nicht zu groß sondern nach Seiner complexion gerichtet; die |Vitr[iol]|lischen vomitiva sind nicht so grob als die |Antimon|iata, welche uns engbrüstige … hart angreiffen … M. h. H. würde eine große erleichterung v. kühlung empfinden” (p. 371).

1694–June 1696

613

try to block perspiration in such an operation”.376 Above all, he warned that Leibniz should not delay the treatment, and that he ought to avoid every form of exertion. Leibniz’s reaction to Bodenhausen’s proposals is to be found in his letter of June 24, 1695. As far as the acidic and vitriolic remedies were concerned, he was not uninclined to try them out. As regards the application of the emetic suggested by Bodenhausen, he was hesitant and wanted to think the matter over first. Thus he wrote: As regards the forethought regarding my health, I am most grateful. And because you advocate, Sir, the mineral acids, I am all the more inclined to try out the acidulants once more. And I could thereafter continue with the driblets of vitriol. I know that some use the spirit of vitriol (viz. spiritus vitrioli or diluted sulfuric acid) but with just a little in much water. With the procurement of vomiting, I wish to think it over. It should indeed be good, provided it does not cause me any inconvenience. Yet, maybe I will consider it, please God, in the autumn.377 Leibniz also regularly received reports about the health problems, and conditions, of his correspondents, or indeed queries regarding medication and medicinal products as, for example, on April 16, 1696, from Johann Sebastian Haes regarding an appetizing tincture or lotion (“la teinture aperitive du Dr [Gottfried] Moebius”) and a volatile striated spirit of iron (“spiritum Martis volatile striatum, du Dr [Friedrich] Hoffman [senior]”), respectively.378 Johann Daniel Crafft complained again and again about his gout pains, and he sought the right medication to relieve his suffering, as for example, on September 20, 1694, when he wrote: “Medicaments from quicklime through the spirit of wine

376 “Hüte sich dabey die brust bey währender operation zu erkälten, v. verhindere den schweiß nicht bey solcher operation” (p. 371). 377 “Wegen der vorsorge vor meine gesundheit bin höchlich verbunden. Und weil M. h. H. auf die acida mineralia stimmet, so bin ich umb soviel mehr geneigt, es noch einst mit den acidulis zu versuchen. Und kondte hernach mit rore |Vitriol|li etwas continuiren[.] ich weiß daß einige so gahr den Sp. |Vitriol|li gebrauchet, aber wenig in viel waßer. Mit procuratione vomitus will mich noch ein wenig bedencken solte freilich guth seyn, wenn es mir nicht etwas ungelegenheit machte. Doch werde vielleicht gegen den herbst wils gott darauff bedacht seyn” (A III,6 N. 134, p. 411). 378 Cf. A III,6 N. 223, p. 728.

614

Chapter 4

are, it appears to me, very well known and, as I recall, Farner wrote about them in his [opus]379 Truz Podagra”.380 Against the illness of Crafft’s wife, Dorothea, a similar product, viz. Schroeder’s spirit – named after the German Paracelsian Johann Schröder – prepared with quicklime (“Spiritus calcis vivae Schröderi”), was to provide relief. Thus he added that: “The indisposition of my wife continues and is getting worse from day to day; I believe Schroeder’s spirit prepared with quicklime would be good for her, both inwardly and outwardly”.381 Leibniz’s deliberations on the medical profession, on medical progress, on medicine as an empirical science, and on the application of mathematics in medicine were further topics in his correspondence at this juncture. Thus, he wrote to Huygens on June 22, 1694: Thanks be to God that our studies have allowed us to advance considerably in medicine. But until now this science has been almost entirely empirical. It is true that empiricism in itself would be of very great value, if one would commit oneself to carefully observe, and even to carefully apply such observations that have already been made, but since medicine has attained a professional status, those who make it a profession only do so in a perfunctory manner, and only to the extent necessary for saving appearances, knowing well that few people are capable of judging that which they do.382 Leibniz even envisaged here a religious order of friars, like the Capuchins, embracing medicine as a charitable endeavor, as he explained in the following 379 Cf. Christoph Fahrner’s two letters to Jonas Zipffell, published (pp. 64–83) in: J. Zipffell, Podagrischer Triumph, das ist kurtzer doch gründlicher Bericht vom Griess/ Sand/ Stein/ und Podagra, Altenburg, 1659. 380 “Medicamenta ex Calce viva per Sp. Vini werden, wie mich duncket, darinne sehr gerühmet, vnd hatt meins behaltens Farner in seinen Truz Podagra davon geschrieben” (A III,6 N. 58, p. 187). 381 “Meine Fraw continuiret nicht nur in ihr Vnpäßlichkeit, sondern wird täglich schlimmer, ich glaube  sp. v. cum calce viva solle ihr auch gut sein, inner- vnd außerlich” (p. 188). 382 “Plût à Dieu, que nos études servissent à nous faire advancer considerablement dans la Medecine. Mais jusqu’icy cette science est presque entierement Empirique. Il est vray que l’Empirie même seroit de grand usage, si on s’attachoit à bien observer, et même à bien employer tant d’observations déja faites, mais comme la Medecine est devenue un Mestier, ceux qui en font profession ne la font que par maniere d’acquit, et autant qu’il faut pour sauver les apparences; sçachant bien que peu de gens sont capable de juger de ce qu’ils font” (A III,6 N. 45, specifically pp. 124f.; HO, 10, pp. 639–646).

1694–June 1696

615

words: “I would like that some religious order, like that of the Capuchins for example, would attach itself to medicine as a charitable principle. Such a well-regulated order could take it very far”.383 Huygens for his part, in his letter of August 24, signaled assent to Leibniz’s perceptions, but he did not enter further into a discussion of them, writing summarily that: “Your reflections on the state and the advancement of medicine are very good, and that which you propose does not seem at all impractical”.384 The mathematician Johann Bernoulli, who had studied medicine and was author of two works entitled Dissertatio chymico-physica de effervescentia et fermanttatione (1690),385 and Dissertatio inauguralis physico-anatomica de motu musculorum (1694),386 was admonished by Leibniz on July 4, 1694  – particularly with reference to the latter dissertation – to continue and maintain his commitment to medicine. Here Leibniz wrote: “I wish furthermore that you will also save some time for the contemplation of medicine which stands in need of your ingenuity, and that you will see with what acclaim your work regarding muscles has been received”.387 More than a year later, Leibniz once again referred to this proposal in a letter to Johann’s brother, Jacob Bernoulli, on December 12, 1695, writing as follows: And also that you commit if possible to contemplate attentively the organization of medicine … And so I also exhorted your renowned brother that he gradually direct his intellect to this, not as if I wished to establish a medical clinic … but rather what I thought that summer was that, with his ingenuity, it would be possible for him to initiate something not unfamiliar but great in ‘res medica’, in matters medical.388 383 “Je voudrois que quelque ordre religieux, tel que celuy des Capucins par exemple, se fut attaché à la Medecine par un principe de charité. Un tel ordre bien reglé la pourroit porter bien loin” (p. 125). 384 “Vos reflexions sur l’etat et sur l’avancement de la medicine sont fort bonnes, et ce que vous proposez ne paroit pas tout à fait inpracticable” (A III,6 N. 54, specifically p. 161; HO, 10, pp. 664–672). 385 Cf. Joh. Bernoulli, Dissertatio chymico-physica de effervescentia et fermentatione nova hypothesi fundata, Basel, 1690. 386 Cf. Joh. Bernoulli, Dissertatio inauguralis physico-anatomica de motu musculorum, Basel, 1694. 387 “Optarim autem, ut nonnihil temporis etiam Medicinae meditandae conserves quae vel maxime indiget ingenio Tuo, et vides quo applausu tua de musculis fuerint accepta” (A III,6 N. 137, p. 432). 388 “Atque utinam inciperent quibus licet, de Medicina constituenda cogitare attentius  … Itaque etiam Clmum Fratrem tuum hortatus sum, ut subinde huc animum verteret, non quasi Clinicum fieri velim Medicum … sed quod putem ea aetate, eoque ingenio, posse ab ipso in re Medica non hospite aliquid magni proficisci” (A III,6 N. 181, p. 570).

616

Chapter 4

In his reply, on March 14, 1696, Jacob then emphasized in particular the possibilities, and the benefits, of applying mathematics in medicine, citing his brother’s Dissertatio  … de motu musculorum as an example. Thus, he wrote here: I do not doubt that if someone wanted to apply mathematics to medicine, he could advance ‘res medica’ to an enormous extent. However, motivated by this opinion, I emerged as the first inspiration for my brother, motivating him to embrace and above all to undertake this study, and again and again I encouraged him to apply here the principles of science, which he had learned from me … then, being discouraged by the foreseeable difficulty, he first produced something on the tightening and the movement of muscles; notwithstanding how modest a contribution it was, he made sufficiently clear what a medic could do with the help of mathematics.389 389 “Non dubito, quod si quis principia Mathematica ad Medicinam applicare vellet, is rem Medicam, immane quantum promovere possit. Hac nempe opinione motus, Auctor primum extiti Fratri, ut hoc studium amplecteretur, et quam primum illud salutare inceperat, identidem illum stimulavi, ut principia Scientiae, quam a me didicerat, huc applicaret: … praevisa enim difficultate absterritus, vix de Fermentatione et de Motu musculorum quaedam dedit: quantillum autem istud est, satis ostendit, quid Medicus Mathesi adjutus possit” (A III,6 N. 211, p. 679).

Chapter 5

July 1696–1698 quand on a la cause d’un effect expliquable par des choses sensibles; pour quoy recourir à des suppositions peu certaines avec les Cartesiens et autres?1 Leibniz to Denis Papin, December 12, 1697

⸪ 1

Biographical Background (July 1696–1698)

Leibniz’s correspondence in mathematics, science and technology in the thirty-month period between July 1696 and December 1698, consisting of 253 communications written both by Leibniz himself (108) and by (or together with) his correspondents (145), involved a total of some 35 individuals; of these 21 were existing correspondents while 14 were newcomers.2 In the wake of the death of Christiaan Huygens in July 1695,3 the period under consideration also witnessed the passing of two other most prolific correspondents, namely Rudolf Christian von Bodenhausen and Johann Daniel Crafft. The correspondences with Johann Bernoulli and Denis Papin then became the most voluminous, and together they amount to more than half of the total of Leibniz’s correspondence in mathematics, science and technology in this period. From 1696, Leibniz’s duties at court, as well as his own historical, political and philosophical undertakings, increasingly commanded his attention.4 Two dates were of particular significance. On August 13, 1696, he was informed about his appointment as privy counselor of justice, and on February 2, 1698, his sovereign, the elector Ernst August of Hanover died following a partial transfer of governmental business to his successor Georg Ludwig – the later British monarch George I – in the previous year. The new sovereign increasingly put pressure 1 A III,7 N. 163, p. 658; Translation: When one has found the cause of an effect that is explicable on the basis of sensible matter, why revert to the suppositions of little certitude of the Cartesians and others? 2 Cf. J. G. O’Hara, Ch. Wahl, A III,7, introduction, pp. [XXIII]–LXXXIII. 3 Cf. Leibniz’s epicedium, or elegy, for Huygens (A III,7 N. 62, pp. 246f.). 4 Cf. for example, A III,7 N. 62, pp. 243–247 and N. 114, pp. 472f.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_007

618

Chapter 5

on Leibniz to bring to a conclusion his principal commission, namely to write a history of the Welf (or Guelph) dynasty. Leibniz’s promotion, in the summer of 1696, already implied an increased commitment to more rapid progress on the dynastic history project.5 And so, at this juncture, Leibniz became increasingly involved in questions of dynastic succession, and of ecclesiastical policy. In the summer of 1697, tsar Peter of Russia travelled though Brandenburg, an event that induced Leibniz to prepare a memorandum. Further fruits of this period of activity were the publication of his Novissima Sinica (1697),6 and of the editions Accessiones historicae (1698),7 and Mantissa codicis juris gentium diplomatici (1700).8 These activities were sometimes also reflected in his mathematical and scientific correspondences, as, for example, in letters to John Wallis and Richard Bentley in October 1697, where he advocated a reconciliation of the Protestant churches and a Protestant mission to China.9 The broad spectrum of his activities also had implications for his health and ability to concentrate and calculate. Thus, on December 14, 1696, he wrote the following to Guillaume François de L’Hospital: For myself, I find above all that calculations cause a feeling of uneasiness or discomfort, nonetheless they are rather unsubstantial. My spirit, being overwhelmed with other matters, does not submit itself to the volition which is necessary, something which makes me twitch nervously all the time and, when I would like to direct my attention toward something, I find myself incommoded by a kind of hot flush.10

5 6

Cf. A I,13, p. XLVII. Cf. G. W. Leibniz, Novissima Sinica: Historiam nostri temporis illustratura, in quibus de Christianismo publica nunc primum autoritate propagato missa in Europam relatio exhibetur, deque favore scientiarum Europaearum ac moribus gentis & ipsius praesertim monarchae, tum & de bello Sinensium cum Moscis ac pace constituta, multa hactenus ignora explicantur [, Hanover], 1697; 2. ed., [with supplement:] Accessione partis posterioris aucta. [vol. 2 entitled] Icon regia monarchae Sinarum nunc regnantis. Ex Gallico versa, [Hanover] 1699. 7 Cf. G. W. Leibniz (ed.), Accessiones historicae quibus potissimum continentur scriptores rerum Germanicarum, 2 parts, Leipzig and Hanover, 1698, and Hanover, 1700 (reprint). 8 Cf. G. W. Leibniz (ed.), Mantissa codicis juris gentium diplomatici, 2 parts, Hanover, 1700. 9 Cf. A III,7 N. 147, pp. 588–590. 10 “Pour moy je trouve sur tout que les calculs m’incommodent, quand meme ils sont assez petits. Mon esprit rempli d’autres choses ne s’assujettit pas à l’intention qui est necessaire ce qui me fait broncher à tous momens et lorsque je veux apporter de l’attention, je me trouve incommodé par une maniere de chaleur qui s’excite” (A III,7 N. 56, p. 213).

July 1696–1698

619

For assistance with his inchoate, or contemplated, projects, he continually sought research assistants or associates. Thus, he longed for the support of talented mathematicians for the realization of his planned opus ‘Scientia infiniti’, or for the advancement of his ‘Analysis situs’, as he informed L’Hospital (on October 18, 1697) and Bodenhausen (on December 6, 1697), respectively.11 Here he had in mind established scholars like Jacques Ozanam but, as he expressed himself in the letter to L’Hospital, most of all “young people who one could inspire [to undertake] something of consequence, in order to devolve a part of the effort among them, also giving them part of the honor and gain as is only just or fair”.12 This quest for a younger collaborator finally resulted in the initiation (in the summer of 1697) of one of Leibniz’s most voluminous correspondences, namely that with Rudolf Christian Wagner, whose curriculum vitae – that was sent to Leibniz from the ‘Academia Julia’, namely the University of Helmstedt – is dated July 18, 1697.13 2

Mathematics: The Brachistochrone and Isoperimetric Problems

As regards mathematics, the 78 months between 1690 and June 1696 had marked a most fruitful period for Leibniz, during which he proposed and solved problems of his own, as well as working on problems proposed by others. This activity had been reflected in his correspondence with a number of mathematicians, and it resulted in several publications in each of those years. In the thirty-month period that followed (from July 1696), it was above all in his correspondence with Johann Bernoulli (with a volume of about 60 letters) that mathematical questions were discussed. In this correspondence with Bernoulli, an important mathematical issue at this juncture was the continuing and widespread interest in the brachistochrone problem, or the task of determining the curve of fastest descent of a body under the influence of terrestrial gravity between a certain point and a lower point not directly below the first. The solution of the problem, or the curve of fastest descent in question, was found to be a segment of a cycloid. On June 19, 1696, Bernoulli communicated the brachistochrone problem to Leibniz, and it was also made public in the

11 Cf. A III,7 N. 149, pp. 601f., and N. 162, p. 654. 12 “des jeunes gens, qu’on puisse animer à quelque chose de consequence, pour se décharger sur eux d’une partie de la peine; en leur faisant part aussi de l’honneur et de l’avantage comme il est bien juste” (note 10, pp. 213f.). 13 “In Acad. Julia VIII. Id. Juli MDCXCVII” (A III,7 N. 119, pp. 491–495; cf. p. 491, annotation).

620

Chapter 5

same month in the Acta Eruditorum.14 The underlined text,15 with the enunciation of the problem, in the letter to Leibniz reads: “For two given points in a vertical plane A and B, determine the path AMB, along which a moving body M, starting at point A and descending under its own gravitational weight, will arrive in the shortest time at point B”.16 Bernoulli likewise informed Leibniz, in this letter, that he had forwarded the problem to France (namely to Pierre Varignon), and to England (to John Wallis).17 A week later, on June 26, Leibniz communicated a differential equation for the solution curve, referred to as the “Tachystoptata”, without however recognizing that it was a cycloid.18 Leibniz shared Bernoulli’s excitement about the problem, and he joined the effort to make it known through correspondence, and in journal articles. Bernoulli himself had a flysheet about the problem printed with the title Acutissimis qui toto orbe florent mathematicis.19 A six-month deadline was announced at first but it was subsequently extended to Easter 1697, in order to enable scholars from Italy and France to participate in the competition to solve this brachistochrone problem.20 Already in June 1696, on the 27th and the 28th of the month, respectively, Leibniz had communicated the problem to Florence, namely to Magliabecchi,21 and to Bodenhausen,22 respectively, with the intention of having it announced in the Giornale de’ Letterati. Leibniz’s proposal to make the problem known in Florence, and in Pisa, was implemented by Bodenhausen in the form of a flysheet announcing it, and which he distributed in the circles around Vincenzo Viviani and Alessandro Marchetti, also with the ulterior motive of piquing the followers of Galileo, or in the words of Bodenhausen’s letter to Leibniz of August 11(?), 1696, it was “the problem which, by virtue of its simplicity, is particularly elegant and has much concealed in the background, and the

14 Cf. Joh. Bernoulli, “Supplementum defectus geometriae Cartesianae circa inventionem locorum”, Acta Eruditorum, (June 1696), pp. 264–269, in particular p. 269. 15 Underlining surely by Bernoulli (cf. A III,6 N. 241, p. 783). 16 “Datis in plano verticali duobus punctis A et B, assignare viam AMB, per quam mobile M a puncto A moveri incipiens et propria gravitate descendens brevissimo tempore perveniat ad punctum B” (p. 790). 17 Cf. p. 790, annotation. 18 Cf. A III,6 N. 243, pp. 799–803. 19 Cf. Joh. Bernoulli, Acutissimis qui toto orbe florent mathematicis, Groningen, 1697. 20 Cf. A III,7 N. 29, p. 110. 21 Cf. A I,12 N. 423, pp. 658f. 22 Cf. A III,6 N. 244, pp. 805f.

July 1696–1698

621

stipulated condition of the shortest time should indeed cause continual perspiration among our Galileans”.23 On his own initiative, Bodenhausen also passed the problem on to the Tuscan prince Giovanni Gastone, as he confided to Leibniz in his letter of November 24, 1696.24 However, his draft for an announcement of the problem in the Giornale de’ Letterati was superseded by a communication sent by Leibniz himself (in September 1696) to Bernardino Ramazzini,25 and which duly appeared in the same month in the Giornale de’ Letterati.26 Bodenhausen provided Leibniz with detailed information about the reaction in Italy. To his disappointment, he had to report that the Italians attributed their unwillingness to tackle the problem not to any inability to solve it, but rather to other preoccupations. Bodenhausen himself, notwithstanding some knowledge of the differential calculus, had no luck in solving the problem, or, as he expressed himself in his letter to Leibniz of November 24, 1696: “I am a jackass, like the others, indeed even more so, because I am unable to avail of the light of analysis, and I am unable to deal with this problem in Zetes’27 fundamental notions of the curve by means of the tangent”.28 In the Netherlands the brachistochrone problem was disseminated through Johann Bernoulli’s flysheet. In addition, Bernoulli prompted the publication of a note on the problem in the Rotterdam journal Histoire des Ouvrages des Savans.29 His efforts met with a mixed response. Johannes Makreel – a friend of the critic of the differential calculus Bernard Nieuwentijt – had, as Bernoulli informed Leibniz on March 2, 1697, referred to the problem remarking “that this was good for the Germans, but the Dutch would not be replying to it”.30 23 “das Problema so wegen seiner apparenten simplicität überaus schön, hat viel in recessu, v. die conditio brevissimi temporis solte unsere Galileisten wohl ewig schwitzen machen” (A III,7 N. 20, p. 82). 24 Cf. A III,7 N. 51, p. 188. 25 Cf. A III,7 N. 32, pp. 119f. 26 Cf. G. W. Leibniz, “Nuovo teorema intorno al movimento de’ gravi, con un problema nuovo da risolversi”, Giornale de’ Letterati, (September 1696), pp. 225–226. 27 viz. the Argonaut Zetes in Greek mythology; cf. for example, M. J. Stewart, “People, places & things: Zetes”, Greek mythology: From the Iliad to the fall of the last tyrant, (Original content copyright 1996–2005 Michael Stewart; viewed online in December 2022: http://message netcommresearch.com/myths/ppt/Zetes_1.html). 28 “Ich bin ein Esel, wie die andern, ja noch vielmehr, weil ich mich des lichtes der analysis nicht zu bedienen weiß, v. kan in diesem problemate in zetesi elementi curvae per tangentem nicht zurecht kommen” (note 24 above, p. 188). 29 Cf. B. de Bauval, “Extraits de diverses Lettres”, Histoire des Ouvrages des Savans, (February 1697), pp. 283–285. 30 “que cela étoit bon pour les allemands, mais que les Hollandois n’y repondroient pas” (A III,7 N. 74, p. 310).

622

Chapter 5

Apparently inspired by Makreel’s profession as a financial agent and broker,31 Johann Bernoulli promised him 100 guilders for the solution of the problem.32 Leibniz, in a letter to Bernoulli of March 5, compared Makreel to the fox in a fable who declared pears beyond his reach to be bitter,33 and in his reply of March 23, the correspondent likewise alluded to the comparison of Makreel to the fox in the fable, which he had also heard from a certain friend.34 In the letter of March 5, Leibniz reflected on who indeed might be a contender to solve the brachistochrone problem. Christiaan Huygens – had he still been alive – would, he thought, not have rested until he had found the solution. The only mathematicians from whom a solution might reasonably be expected were L’Hospital, Johann’s brother Jacob Bernoulli, and also Newton. An afterthought was given to Johannes (or Jan) Hudde (1628–1704)  – the ‘burgemeester’ (or mayor) of Amsterdam – but who would, in view of his age, most likely no longer be a contender, he thought.35 Johann Bernoulli, as he reported to Leibniz on March 30, received a further reaction from a professor in Harderwijk, namely Gerard Wijnen, who considered the problem to be not at all difficult, whereas his explanations had revealed his lack of understanding.36 The sole contribution with a solution to the problem from the Netherlands came (anonymously) from the son of Salomon Dierquens  – the court president in Den Haag – namely from Nicolaas Dierquens.37 This was indeed based on the differential calculus but it was, alas, flawed.38 In France, Leibniz publicized the problem in the Journal des Sçavans in November 1696.39 Already in May of that year, it had been forwarded by Pierre Varignon to L’Hospital, and to some others,40 and L’Hospital duly presented it 31 Cf. A III,7 N. 82, pp. 334f. 32 Cf. p. 310 (note 30). 33 “vel vulpem imitantur quae pyra cum attingere non posset acerba esse dicebat” (A III,7 N. 75, p. 313). 34 “cujus equidem fabulae etiam mentionem fecerat amicus meus cum mihi egregium Mackrelii responsum perscriberet” (A III,7 N. 82, p. 335); cf. also Joh. Bernoulli, Briefwechsel, vol. 1, p. 349. 35 “Certe si Hugenius viveret et valeret, vix quiesceret nisi problemate tuo solutio. Nunc nemo est, a quo solutionem facile expectem nisi a Domino Marchione Hospitalio aut a Domino Fratre Tuo, aut a Domino Neutono; quibus adderem Dominum Huddenium Consulem Amstelodamensem nisi dudum has meditationes seposuisse” (note 33, p. 314). 36 Cf. A III,7 N. 86, pp. 355f. 37 Cf. p. 354 and p. 356. 38 Cf. Joh. Bernoulli, Briefwechsel, vol. 1, p. 348. 39 Cf. G. W. Leibniz, “Extrait d’une letre de M. de Leibniz sur son hypothese de philosofie, et sur le problême curieux qu’un de ses amis propose aux matematiciens”, Journal des Sçavans, (November 19, 1696), pp. 707–713, specifically pp. 710f. 40 Cf. Joh. Bernoulli, Briefwechsel, vol. 2, p. 95.

July 1696–1698

623

to the Académie des Sciences.41 Through L’Hospital, Bernoulli received a solution attempt by the Parisian mathematician Joseph Sauveur, which he then forwarded to Leibniz as an attachment to his letter of January 29, 1697.42 The mistakes in this attempt, which followed from a false application of the differential calculus, were contentiously analyzed in the on-going correspondence between Leibniz, L’Hospital and Johann Bernoulli.43 Leibniz decided that the infinitesimal calculus needed to be better communicated, and he ascertained how easily those, who like Sauveur were not sufficiently initiated in the infinitesimal methods, might – in dealing with the infinite and infinitely small – entangle themselves in contradictions.44 L’Hospital found himself confronted with a dearth of competent mathematicians in France – or, in the words of his letter of March 17, 1697, “we have here hardly any mathematicians capable of advancing your principles” – following which assessment, he expressed the hope that his textbook on the differential calculus, namely the Analyse des infiniment petits (1696),45 might indeed provide relief.46 However, he saw himself confronted with obstinate followers of the established methods, and he thus concluded the letter with the words: “I believe that my book will put some of them in that frame of mind, where they pertinaciously adhere to the view that one can attain everything with the ancient methods”.47 As Bernoulli explained to Leibniz, on August 24, 1697, Varignon too had complained about certain old-style mathematicians, who would do anything and everything to depreciate the differential calculus, whereby Bernoulli suspected that in particular the Abbé (François) de Catelan, Philippe de La Hire, Michel Rolle, and some other more obscure persons not worth mentioning, were the ones intended, and so he added the statement: “As for those he [Varignon] calls old-style mathematicians, he is without doubt looking at Catelan, de La Hire, Rolle and other more obscure names who do not deserve to be mentioned”.48 41 42 43 44 45

Cf. Joh. Bernoulli, Briefwechsel, vol. 2, p. 330. Cf. A III,7 N. 68, and the attachment N. 69, pp. 269–275. Cf. A III,7 N. 72, N. 74, N. 81, and Joh. Bernoulli, Briefwechsel, vol. 1, pp. 338–342. Cf. A III,7 N. 72, p. 292. Cf. G. F. A. de L’Hospital, Analyse des infiniment petits pour l’intelligence des lignes courbes, Paris, 1696, and also the reviews in Journal des Sçavans, (September 1696), pp. 424–428, and in Acta Eruditorum, (March 1697), pp. 137–139. 46 “nous n’avons ici gueres de geometres capables de pousser vos principes” (A III,7 N. 81, p. 332). 47 “Je crois que mon livre en mettra quelques uns dans ce train là quoi qu’il y en ait encore d’assez opiniatres pour pretendre que l’on peut tout faire par les methods anciennes” (pp. 332f.). 48 “Quos hic vocat mathematicos styli veteris, haud dubie collimat in Catelanum, de la Hire, Roolium aliosque obscuri nominis qui nominari non merentur” (A III,7 N. 134, p. 561).

624

Chapter 5

From Basnage de Beauval, Bernoulli learned that La Hire had arrived by three different routes each time at the same incorrect solution of the brachistochrone problem, namely a semicubical parabola, as he informed Leibniz in a letter of June 17, 1697.49 L’Hospital’s solution of the problem  – which was presented to the Académie des Sciences on April 20, 1697 – then proved to be an important victory over the opponents of the infinitesimal calculus. In his letter of August 24 to Leibniz, Johann Bernoulli could accordingly include the following extract, from a letter (of August 6) which he had received from Varignon, regarding L’Hospital’s success and the blow dealt to his opponents: “It is however true that in the wake of the solution which Monsieur le Marquis de l’Hospital gave to your problem regarding the line of fastest descent,50 they do not speak as much or as loud as beforehand”.51 Leibniz was then happy to pass on this report to others, for example to Otto Mencke and to Etienne Chauvin at the end of August, or in early September, of that year.52 The brachistochrone problem first reached England in the form of a communication from Johann Bernoulli to John Wallis in the summer of 1696.53 In addition, Bernoulli sent two copies of his flysheet to Wallis and Newton, respectively, in January 1697. The brachistochrone problem was in fact the only mathematical contest, in Leibniz’s ambit, in which Newton participated. It provoked a plagiarism allegation from the side of Fatio de Duillier, and initiated thereby a new phase of the priority dispute. In the light of this, English reactions to the brachistochrone problem, as well as those in Leibniz’s circle to Newton’s solution, have a particular significance. Already in March 1697, Bernoulli received from Basnage de Beauval an anonymous solution to the problem from England – without details of the exact approach taken – which had appeared two months before in the Philosophical Transactions.54 Bernoulli sent a copy to Leibniz on March 30, and he correctly 49 Cf. A III,7 N. 106, p. 446. 50 regarding … descent: Text in italics represents underlining by Leibniz in the manuscript, which also contains a series of additional remarks in his hand. 51 “Il est pourtant vray que depuis la solution que M. le Marquis de l’Hospital a donnée de vôtre probléme De Linea Celerrimi Descensus, ils ne parlent plus tant ni si haut qu’auparavant” (note 48, p. 561); cf. also Joh. Bernoulli, Briefwechsel, vol. 2, pp. 122–124. 52 Cf. A I,14 N. 263, p. 439, and N. 279, pp. 473f., respectively. 53 Cf. A III,6 N. 241, p. 790, annotation. 54 Cf. I. Newton [anon.], “Epistola missa ad prænobilem virum D. Carolum Mountague Armigerum, Scaccarii Regii apud Anglos cancellarium, & societatis regiae prasidem, in qua solvuntur duo problemata Mathematica a Johanne Barnoullo [sic] mathematico celeberrimo proposita”, Philosophical Transactions, vol. 19, no. 224, (January 1697), pp. 384–389; extract in the Acta Eruditorum, (May 1697), pp. 223f.; T. D. Whiteside (ed.), The mathematical papers, 8 vols, Cambridge, 1967–1981, in particular, vol. 8, pp. 5f.

July 1696–1698

625

concluded that Newton was the author of the solution in question.55 The author of the piece had acknowledged that he had received two flysheets with the problem, and Bernoulli considered Newton to be more familiar with recent developments in infinitesimal calculus than the other recipient, namely Wallis. A letter, sent to Basnage de Beauval, reveals that Bernoulli even believed that Wallis had died.56 The fact that Newton needed only a single day to solve the problem – as he had indicated in presenting his solution – proved to be a cause for sneering on Beauval’s part but, for Leibniz, it was a welcome proof of the effectiveness of the infinitesimal calculus since, as he told Bernoulli on April 25, for someone who was in command of the method, a day was more than enough whereas, for those not versed in the method, a period of years would not suffice. That Newton had partly studied the differential calculus, and partly an analogous method, was the view that Leibniz presented to Bernoulli, when he wrote the following text in this letter: It is sufficiently clear that Newton intently contemplated partly ours and partly an analogous method … you will see Newton derived his solution following your problem [announcement] from the same source as mine, but used however an unnecessary indirect route.57 Words of a similar tenor, namely that only those had been able to solve the problem, who had used the differential calculus, are to be found in a letter of May 7, which Leibniz sent to Etienne Chauvin,58 and which was then partly reproduced in the Nouveau Journal des Sçavans,59 and in his own contribution regarding the brachistochrone problem in the Acta Eruditorum, in May 1697.60 However, the latter article did not take Newton’s solution into account, since Leibniz had already sent his own contribution to Otto Mencke before he 55 Cf. A III,7 N. 86, p. 354, annotation. 56 Cf. Joh. Bernoulli, Briefwechsel, vol. 1, p. 430. 57 “Newtonum enim partim nostra, partim nostris Analoga meditatum esse intento studio, satis constat … videris Newtonum suam secundi Tui Problematis solutionem ex eodem mecum fonte derivasse, sed circuitu tamen non necessario usum esse” (A III,7 N. 92, p. 380, and p. 381). 58 Cf. A I,14 N. 91, p. 155. 59 Cf. G. W. Leibniz (anon.), “Nouvelles litteraires”, Nouveau Journal des Sçavans, (May–June, 1697), pp. 292f. 60 Cf. G. W. Leibniz, “Communicatio suae pariter, duarumque alienarum ad edendum sibi primum a Dn. Jo. Bernoullio, deinde a Dn. Marchione Hospitalio communicatarum solutionum problematis curvae celerrimi descensus”, Acta Eruditorum, (May 1697), pp. 201–205 (Leibniz: Parmentier, 1989, chap. 21, pp. [345]–358; Leibniz: Essais Scientifiques, 2005, N. 84; Leibniz: Heß-Babin, 2011, chap. 40, pp. 297–307).

626

Chapter 5

received that of Newton. The fact that he did not send a subsequent amendment to the journal editor was indeed a conscious decision on his part, which he justified, in his letter to Bernoulli, on April 25, 1697, with the behavior of his English rivals who, without waiting for the deadline to pass, had published the solution of the problem, and had not even sufficiently acknowledged the services of Bernoulli himself.61 In May 1697, Thomas Burnett of Kemney confirmed Leibniz’s supposition that Newton was indeed the author of the solution in question, and Leibniz, for his part, instructed the correspondent, on May 28, to convey his esteem to Newton. In addition, Leibniz emphasized that it was not he, who had sent Newton the brachistochrone problem, but rather Johann Bernoulli. He himself, on receiving the problem from Bernoulli, had solved it as rapidly as Newton had, namely while travelling on a coach from Hanover to Wolfenbüttel, and then later at his lodgings. Thus he wrote to Burnett of Kemney: When he proposed this problem to me, I found its solution and perhaps in as little time as Mr Newton, for I did it in the coach going from Hanover to Wolfenbüttel and, as soon as I arrived at my lodging house, I successfully applied the method which I had conceived for arriving at a solution.62 Later, following the allegations made against Leibniz by Fatio de Duillier in his solution published in 1699, which included the allegations of plagiarism of Newton, he wrote to Wallis that Bernoulli had sent the flysheet to Newton without his knowledge and, furthermore, that it was not his style to provoke men of merit with problems in this fashion.63 In fact, Leibniz had mentioned the brachistochrone problem neither to Wallis nor to Tschirnhaus. However, he did recommend, on November 28, 1698, that Bernoulli, his brother, and others, send further problems to Newton for the sake of the advancement of science.64 And Bernoulli, in a contribution in the Histoire des Ouvrages des

61 Cf. A III,7 N. 92, p. 379. 62 “Quand il me proposa ce problem, j’en donnay la solution et peutestre en aussi peu de temps que Mons. Newton, car je le fis en carosse allant d’Hanover à Wolfenbuttel et aussitost que je vins[sic] dans l’hauberge j’executay avec success la methode que j’avois imaginée pour y arriver” (A I,14 N. 132, p. 220). 63 Cf. A III,8 N. 64, p. 194. 64 “Problema[ta] Dno Fratri vel aliis proposita vellem et Dno Newtono communicari curasses, pro incremento scientiae” (A III,7 N. 244, p. 947).

July 1696–1698

627

Savans of June 1697, availed of the opportunity of Newton’s solution to provide a eulogy of its author.65 The only correct solutions then of the brachistochrone problem, which reached Mencke before the deadline had elapsed, came from Johann Bernoulli,66 his brother Jacob,67 L’Hospital,68 and Newton.69 Johann Bernoulli had already sent his solution to Leibniz on July 31, 1696, with the request that he forward it on time to Mencke.70 Leibniz complied with this request, but he also persuaded Johann to keep one of his two solution approaches secret. The first approach, which he characterized as indirect, established an analogy to the problem of finding the path of a ray of light in homogeneous media. This allowed him to embrace a general hypothetical connection between path and velocity in place of Galileo’s law of falling bodies. From the law of refraction, as it applied to the infinitely small, Bernoulli derived his differential equation. In his second, or direct solution approach, as he called it, he compared infinitely small sections of the curve of different curvatures, but with a common circle of curvature center, and he derived from this an equation for the curvature radius. In addition, he showed, by a synthetic proof, that the cycloid was the only possible solution. Leibniz saw potential in Bernoulli’s direct approach and persuaded him to publish, neither this nor the synthetic proof. For the same reason, Leibniz also declined to publish his own solution, or in the words of his letter of September 2 to Bernoulli: “I will be done with my solution in a few words”.71 Bernoulli’s brother Jacob sent his solution directly to Mencke, as he informed Leibniz on February 6, 1697.72 L’Hospital first sent, on February 25, a solution attempt to Johann Bernoulli, who forwarded it to Leibniz on March 5.73 He then 65 Cf. Joh. Bernoulli, “Lettre de Mr. Bernoulli à l’auteur”, Histoire des Ouvrages des Savans, (June 1697), pp. 452–467. 66 Cf. Joh. Bernoulli, “Curvatura radii in diaphanis non uniformibus, solutioque problematis … de invenienda linea Brachystochrona … et de curva synchrona seu radiorum unda construenda”, Acta Eruditorum, (May 1697), pp. 206–211. 67 Cf. Jac. Bernoulli, “Solutio problematum fraternorum, peculiari programmate cal. Jan. 1697 Groningae, nec non Actorum Lips. mense Jun. & Dec. 1696, & Feb. 1697 propositorum: una cum propositione reciproca aliorum”, Acta Eruditorum, (May 1697), pp. 211–216. 68 Cf. G. F. de l’Hospital, “Solutio problematis de linea celerrimi descensus”, and “Solutio problematis publice propositi a Dn. Joh. Bernoullio”, Acta Eruditorum, (May 1697), pp. 217f. and pp. 218–220, respectively. 69 Cf. I. Newton, “Epistola missa ad prænobilem virum D. Carolum Mountague”, and in particular the extract in the Acta Eruditorum, (May 1697), pp. 223f. (note 54 above). 70 Cf. A III,7 N. 14, with attachment N. 15, pp. 58–68. 71 “Ego mea solutione paucis verbis defungar” (A III,7 N. 29, p. 110). 72 Cf. A III,7 N. 71, pp. 278f. 73 Cf. A III,7 N. 76, p. 316, annotation.

628

Chapter 5

returned it to L’Hospital on March 8.74 The latter then sent (on March 17) his final solution to Leibniz for forwarding to Leipzig.75 In his own contribution, or introduction to the four solutions being published, Leibniz – having withheld his own solution  – was only able to comment on the competition, describing that which he considered novel in this kind of extremum problem.76 And, through his intensive occupation with the brachistochrone problem, it had become clear to him how far his analysis was still removed from perfection. From Tschirnhaus, who rejected the differential calculus, no solution of the brachistochrone problem was to be expected from the outset, especially in view of the fact that he had previously failed to provide a solution to the catenary problem although he had been publicly invited to do so.77 This earlier invitation to solve the catenary problem had been a reaction to Tschirnhaus’ announcement of a new method of his own and, in the time that followed, the Bernoulli brothers had reacted very critically to further announcements,78 which were published in Tschirnhaus’ programmatic article “Nova et singularis geometriae promotio” of November 1695.79 In the context of the brachistochrone problem, this skepticism continued. Thus, for example, Johann Bernoulli wrote the following lines to Leibniz on August 25, 1696: “I do not think D. Tschirnhaus will provide anything whatsoever here, just as he did not provide anything very much regarding the catenary problem, because perhaps he considers his participation here not to be of value”.80 Particularly acrimonious were the words of Johann Bernoulli in a letter of January 29, 1697, to Leibniz, in which he compared Tschirnhaus to an alchemist who touted his secrets with pompous words without ever producing anything. Here Bernoulli wrote: 74 Cf. A III,7 N. 78, p. 321, annotation. 75 Cf. A III,7 N. 81, p. 331, annotation. 76 Cf. G. W. Leibniz, “Communicatio suae  … solutionum problematis curvae celerrimi descensus” (note 60 above). 77 Cf. G. W. Leibniz, “Ad ea, quae vir clarissimus J. B., mense Majo nupero in his Actis publicavit, responsio”, Acta Eruditorum, (July 1690), pp. 358–360 (Leibniz: Parmentier, 1989, chap. 8, pp. [166]–172; Leibniz: Essais Scientifiques, 2005, N. 30; Leibniz: Heß-Babin, 2011, chap. 13, pp. 97–101), specifically p. 360 and A III,5, p. XXII. 78 Cf. Jac. Bernoulli, “Observatiuncula ad ea, quae nupero mense Novembri de dimensionibus curvarum publicata leguntur authore D.T.”, Acta Eruditorum, (June 1696), pp. 260f.; Joh. Bernoulli, “Supplementum defectus geometriae Cartesianae circa inventionem locorum”, Acta Eruditorum, (June 1696), pp. 264–269, in particular pp. pp. 267f. 79 Cf. E. W. von Tschirnhaus, “Nova et singularis geometriae promotio”, Acta Eruditorum, (November 1695), pp. 489–493. 80 “Non puto Dn. Tschirnhausium hic quicquam praestiturum, cum nequidem in catenaria aliquid praestiterit, quia forsan sua applicatione haec non digna censet” (A III,7 N. 27, p. 100).

July 1696–1698

629

I have read and re-read the outline of D. Tschirnhaus, but I profess that he has satisfied none of our objections; he says very much while saying nothing; he affects I do not know what obscurity by which he has enough to do to cloak his errors, and at the same time he bolsters his mysteries in pompous words as alchemists are accustomed to do over and over again, yet he produces nothing at any time.81 Leibniz’s criticism was also in evidence in the drafts of his letters,82 whereas his dispatched texts, like that sent to Jacob Bernoulli at the beginning of April 1697, were more diplomatic.83 Tschirnhaus’ article “De methodo universalia theoremata eruendi” of May 1697, which Mencke had placed among the solutions of the brachistochrone problem,84 provoked further criticism in Leibniz correspondence with Johann Bernoulli and L’Hospital.85 In his article of May 1697, Tschirnhaus only briefly mentioned the problem. He presented the cycloid as the solution, but he left open the question as to whether he had solved the problem himself. Both Bernoulli and Leibniz suspected that he had most likely learned the solution from Mencke, during the Leipzig Spring Fair of 1697. Leibniz only infrequently had the possibility of consulting the Philosophical Transactions, and Johann Bernoulli apparently did not receive the February 1697 number with a consignment from Hans Sloane, which he referred to in his letter to Leibniz on May 25, 1697.86 And so, Leibniz was only belatedly informed by John Wallis, in a letter of September 8, 1699, about yet another anonymously-published English solution of the brachistochrone problem, namely that of David Gregory, in that February number of the Philosophical Transactions. The respective contributions of Newton and Gregory appeared in fact in the Philosophical Transactions in the months of January and February,

81 “Legi et relegi schediasma Dn. D. T. sed, fateor, nulli ex nostris objectionibus satisfacit, multa dicit sed nihil dicit, affectat nescio quam obscuritatem qua errores suos palliare satagit, et simul sua mysteria pomposis verbis ut alchymistae solent usque et usque promittit, nihil tamen unquam producit” (A III,7 N. 68, p. 267). 82 Cf. A III,7 N. 62, pp. 232–238, and N. 192, pp. 770–773. 83 Cf. A III,7 N. 88, p. 363. 84 Cf. E. W. von Tschirnhaus, “De methodo universalia theoremata eruendi, quae curvarum naturas simplicissime exprimunt; de problemate item Bernoulliano”, Acta Eruditorum, (May 1697), pp. 220–223. 85 Cf. A III,7 N. 102 (pp. 423–426), N. 106 (p. 446), N. 143 (pp. 579f.) and N. 149 (pp. 602 and 607f.). 86 Cf. A III,7 N. 98, p. 392.

630

Chapter 5

1697.87 Wallis’ words in his letter of September 8, 1699, were: “I had certainly perceived that this curve was found by our Newton, but also by David Gregory around the same time … which was done in the Philosophical Transactions”.88 In conclusion, it may be recalled that the brachistochrone problem was a mathematical problem rooted in the physical world, and that the considerations concerning it were subject to physical influences. Thus, for example, in connection with the solution of this problem, Leibniz and Johann Bernoulli discussed orthogonal trajectories,89 or specifically a family of curves in a plane that intersects a given family of curves at right angles. Methods for the determination of orthogonal trajectories had already been developed in 1694 by Leibniz and Bernoulli.90 An important influence here came from physics, and in particular from ‘Huygens Construction’ in the theory of light propagation, in which the light waves were shown to be orthogonal to the rays.91 In connection with the presentation of his solution of the brachistochrone problem, Jacob Bernoulli challenged his brother Johann to solve other mathematical problems, among which was the isoperimetric problem.92 For the correct solution, he offered his younger sibling a prize of 50 Taler, which would have amounted to about a third of Johann’s ‘accidental annual income’  – referred to as “emolumenta academica quae vocant accidentia” – or a tenth of his yearly regular income, or “salarium fixum”, of 1250 florins or “500 talerorum imperialium”.93 Jacob’s problem was a generalization of the classical isoperimetric problem, which calls for the determination of the plane figure of the largest possible area whose boundary has a specified length. He asked Leibniz, on February 6, 1697, to help make the problem known in France and Italy, writing the following: “If it would please you to take the trouble so that that, which I have otherwise proposed in the Acta Eruditorum, might become known in France and Italy, I should be under an obligation to you for the favor”.94 87 Cf. I. Newton, “Epistola missa ad prænobilem virum D. Carolum Mountague” (note 54 above), and D. Gregory, “De ratione temporis quo grave labitur per rectam data duo puncta conjungentem”, Philosophical Transactions, vol. 19, no. 225, (February 1697), pp. 424f. 88 “Noveram quidem hanc Curvam a Newtono nostro fuisse repertam; sed et a D. Davide Gregorio, sub idem tempus … quod factum est in Transactionibus Philosophicis” (A III,8 N. 72, p. 221). 89 Cf. A III,7. p. XLIVf., and N. 15, N. 27, N. 29 and N. 43. 90 Cf. A III,6. N. 55, pp. 173–175, and N. 81, p. 245. 91 Cf. p. 17 in: Ch. Huygens, Traité de la lumière … avec un discours de la cause de la pesanteur, Leiden, 1690; HO, 19, pp. 451–547 and HO, 21 pp. 427–499. 92 Cf. Jac. Bernoulli, “Solutio problematum fraternorum” (note 67 above), p. 214. 93 Cf. A III,7 N. 68, p. 268. 94 “Quod si placeat insuper curare, ut quae vicissim in Actis propositurus sum, in Gallia quoque et Italia innotescant, beneficio me obstringes” (A III,7 N. 71, p. 279).

July 1696–1698

631

However, replying at the beginning of April, Leibniz recalled that the brachistochrone problem had shown that nothing was to be expected from France (with the exception of L’Hospital), and from Italy, and so – unlike in the case of the brachistochrone problem – he did nothing to help circulate the isoperimetric problem. His exact words in this matter were: “I will be glad to take the trouble so that your problem also becomes known in France and Italy, although (with the exception of the Marquis de l’Hospital), there is nothing we can hope for from the French and much less from the Italians”.95 In the PS to a letter to Johann Bernoulli two months later, on June 7, he urged the correspondent to tackle the problem, but he insisted that the prize money was necessary, since the problem lacked elegance and usefulness and, at best, might help advance the art of invention or discovery, viz. the ars inveniendi. Here he wrote: I wanted that you immediately accept because your brother is proposing a new problem and setting a deadline and a prize [for its solution]. He thought of what he suggests doing, because the problem which he proposes is not in itself elegant, nor does it appear to have utility, except that it might perhaps advance the ars inveniendi.96 The Bernoulli brothers were to remain the only ones to seriously tackle the isoperimetric problem. Already on June 17, 1697, Johann could announce his solution of the problem in a letter to Leibniz.97 However, Jacob had not specified the procedure for adjudicating, and awarding the prize. Since no agreement was reached in the matter, the conflict was drawn out over a number of years, and it manifested itself in polemics, mainly in the Journal des Sçavans. It represented a further escalation in the brooding conflict between the Bernoulli brothers, which also had repercussions for Leibniz who had carried on a correspondence with both of them. From Johann Bernoulli Leibniz received a long emotional account of the drawn-out conflict with his brother, as a PS to a letter of May 25, 1697.98 Jacob suspected that Leibniz had taken the side of 95 “Libenter dabo operam ut Tua quoque problemata in Galliam et Italia perveniat, quamquam (excepto Dn. Marchione Hospitalio[)] nihil est quod a Gallis et multo minus quod ab Italis speremus” (A III,7 N. 88, p. 359). 96 “Volui ut statim acciperes quia Dn. frater Tuus Tibi potissimum nova problemata proponit termino et praemio statuto. Quod videtur faciendum sibi putasse quia problemata quae proponit non satis elegantiae per se vel utilitatis habere videntur nisi quod forte artem inveniendi augebunt” (A III,7 N. 101, pp. 416f.). 97 Cf. A III,7 N. 106, pp. 439f. 98 Cf. A III,7 N. 98, pp. 398–400.

632

Chapter 5

Johann, and he failed to react at first when Johann looked to Leibniz as an adjudicator who should decide about the award of the prize money.99 The dispute about the isoperimetric problem may have been the reason for the disruption of Leibniz’s correspondence with Jacob Bernoulli. The latter may also have taken offence at Leibniz’s letter of early April 1697, in which he expressed reserved criticism of Jacob’s behavior towards his brother Johann.100 This letter remained unanswered until 1702. 3

Mathematics: The Priority Dispute

In a further skirmish concerning David Gregory in 1697 – which had relevance for the smoldering priority dispute with Newton  – the editorial policy of Mencke became an issue. Subsequently, in a letter of August 8, 1698, to Johann Bernoulli, Leibniz accused Mencke of giving preferential treatment to foreigners in order to ensure their goodwill in the following words: He wrote to me that in the next number of the Acta Eruditorum the article of David Gregory on the catenary from the Philosophical Transactions was to appear. It would have been more appropriate to consult us first[,] regarding whether there was anything of value worthy of being reported [in it]. But he is seeking the goodwill of foreigners, [which is] in contrast to the way strangers treat us.101 The cause for Leibniz’s complaint was Mencke’s decision to reprint Gregory’s solution for the catenary problem,102 from the Philosophical Transactions of August 1697,103 in the Acta Eruditorum in July 1698.104 Leibniz considered the publication to be inappropriate as Gregory’s solution was coming far too late, and so he wrote the following lines to Johann Bernoulli on September 1, 1698: 99 Cf. for example, A III,7 N. 106, p. 440. 100 Cf. A III,7 N. 88, pp. 359 and p. 363. 101 “Scribit mihi in proximis Actis comparere debere Davidis Gregorii Catenariam ex transactionibus. Rectius consuluisset nos prius, an aliquid afferat dignum referri. Sed ille exterorum benevolentiam captat, secus quam exteri faciunt nostris” (A III,7 N. 215, p. 860), and also A III,7, p. XXXIII. 102 Cf. A III,5, p. XXII. 103 Cf. D. Gregory, “Davidis Gregorii M. D. Astronomiae Professoris Saviliani & S. R. S. Catenaria”, Philosophical Transactions, vol. 19, no. 231, (August 1697), pp. 637–652. 104 Cf. D. Gregory, “Transcripta ex Actis Philosophicis Anglicanis mensis Augusti 1697 (pp. 633 segg)”, Acta Eruditorum, (July 1698), pp. 305–321.

July 1696–1698

633

I have not yet seen the Catenaria of Gregory, but I learn from Mencke’s letter that it will appear in the Acta Eruditorum. Once I receive it, I will forward it at once. I replied to him that I will look at it once it arrives after the holiday, and that we will not refer to the English unless they have something new and important.105 In the event, the solution turned out to defective, and Leibniz did write an anonymous reciprocation, which – in order to shroud its provenance – was forwarded by Johann Bernoulli to Mencke. The latter then reluctantly let it appear in the Acta Eruditorum in February 1699.106 When Gregory in turn reacted in the Philosophical Transactions to Leibniz’s anonymous criticism, Mencke saw himself obliged – not least because of the kindness Gregory had shown to his son Johann Burkhard Mencke while at Oxford – to reprint this reply in the Acta Eruditorum in July 1700,107 and so to avoid any accusations of censorship. He accordingly informed Leibniz, on November 11, 1699, in the following words: I do not wish to see that Mr Gregory complains about an imagined censorship against him in the Acta Eruditorum, because this man has shown enormous courtesy to my son in Oxford and in the said place he is seen as a consistently honest and well-behaved person. You see therefore, Sir, how we have to manage such censures, and we cannot avoid dealing with the matter and, if Mr Gregory were to send a reply, including it in the Acta Eruditorum.108 When Johann Bernoulli, in a subsequent letter of January 25, 1701,109 desired a resolute reaction in which fresh contradictions in Gregory’s solution would be 105 “Gregorii Catenariam nondum vidi, sed tantum ex literis Menkenianis intellexi Actis insertum iri; ubi accepero mittam statim. Respondi ipsi, videri mihi eam venturam post festum, nec Anglos nostra, nisi aliquid novi et digni habeant referre” (A III,7 N. 221, p. 883). 106 Cf. G. W. Leibniz (anon.), “Animadversio ad Davidis Gregorii schediasma de catenaria”, Acta Eruditorum, (February 1699), pp. 87–91. 107 Cf. D. Gregory, “Responsio ad Animadversionem ad Davidis Gregorii catenariam”, Philosophical Transactions, vol. 21, no. 259, (December 1699), pp. 419–426; Acta Eruditorum, (July 1700), pp. 301–306. 108 “Ich sehe ungern, daß der H. Gregorius uber die wieder ihn denen Actis einverleibte censur klage, weil dieser Mann meinem Sohn in Oxford ungemeine Höfligkeit erwiesen, undt daselbst durchgehends vor einen honnéten braven Mann passiret. Siehet also mein Hochgeehrter Patron, wie wir mit solchen censuren anlaufen können, undt werden wir wenigstens unß nicht entbrechen können, wan H. Gregorius eine andwordt schicken solte, selbige gleicher gestalt in die Acta zu bringen” (A I,17 N. 373, pp. 626f.). 109 Cf. A III,8 N. 200, pp. 514f.

634

Chapter 5

laid bare, Leibniz composed a response three days later in which he called for Gregory to obtain Newton’s approval of his proof. Thus he wrote: I did not see what Mr Gregory recently said, [and] I ask you to specify the month [in question]. There is nothing further that could be given in reply to him. It would suffice perhaps to say that he was asked to obtain the approval of Newton but he was perhaps not able to obtain that.110 However, it may also be that Leibniz did not pursue this demand in order not to tax Mencke’s patience too much. The episode with Gregory had nonetheless repercussions for the smoldering priority dispute. And so, when Leibniz complained to Wallis about Fatio de Duillier’s accusations against him, Wallis compared (on September 8, 1699) Fatio’s behavior to the critique of Gregory’s solution of the catenary problem.111 In the person of Wallis, with whom he established contact at the end of 1695 by means of a billet,112 Leibniz had once again a correspondent from Newton’s milieu interested in mathematics. Another billet, which was addressed to Newton himself, produced no reply.113 It was nonetheless a favorable moment for the exchange of views on the emerging disgruntlement between the mathematicians around both Leibniz and Newton.114 The first two volumes of Wallis’ Opera mathematica had appeared in 1693 and 1695, respectively.115 Wallis’ tract, entitled De algebra tractatus of 1693 (in Opera, vol. 2), contained a short presentation of Newton’s calculus of fluxions, that had previously not been published, and Leibniz’s calculus was only referred to as being similar to that of Newton. In 1694 Leibniz had received from Huygens the relevant extract from Wallis’ second volume, and on November 23, 1695, Mencke sent him the first two volumes of the Opera.116 In his anonymous review in the Acta Eruditorum

110 “Non vidi quae Dn. Gregorius nuper dixerit, indica quaeso mensem. Non est quod ipsi amplius respondeatur. Suffecerit forte dici, petitum fuisse ut obtineret approbationem Newtoni sed eam fortasse non potuit impetrare” (A III,8 N. 201, p. 519, annotation). 111 Cf. A III,8 N. 72, pp. 219f. 112 Cf. A III,6 N. 185, pp. 577f. 113 Cf. A III,6 N. 183, pp. 575f. 114 Cf. also A III,6, pp. LVIIff. and A III,1, pp. XXXIIIff. 115 Cf. J. Wallis, Opera mathematica, 3 vols, Oxford, 1693–1699 (vol. 1, 1695; vol. 2, 1693; vol. 3, 1699). 116 Cf. A III,6 N. 54, specifically p. 161; HO 10, pp. 664–672; A I,12 N. 121, p. 146; Leibniz’s copy with marginal entries in his hand at the Gottfried Wilhelm Leibniz Library, Hanover, Shelf mark: Leibn. Marg. 100.

July 1696–1698

635

of June 1696, Leibniz then criticized the one-sided representation by Wallis.117 In a letter to Leibniz of August 10, 1696, Johann Bernoulli commented that the differential calculus had not received appropriate praise from Wallis,118 and two weeks later, on August 25, he conjectured that Newton had developed the calculus of fluxions on the foundation of information he had received from Leibniz.119 In his reply, on September 2, Leibniz relativized Bernoulli’s suspicion, without however contradicting him. It was true that he had  – twenty years earlier – communicated the foundations of the differential calculus to Newton, and indeed before the latter had communicated anything about his methods. However, whether or not this had helped Newton, he could not say and was unwilling to pass judgement in the matter. Thus he wrote here: I had not observed a certain matter in Wallis noted by you, as I had not been free enough to read all attentively. It is true that I communicated to Newton twenty years ago the fundamentals of my differential method, before he had revealed anything whatsoever to me about his. Whether he gained anything from this[,] I can hardly know sufficiently well. In the meantime I could easily believe that he was in former times already in a position to greatly cultivate its elaboration.120 Wallis defended himself, in his first letter to Leibniz on December 11, 1696, against the criticism expressed in the review, the author of which he correctly assumed to be none other than Leibniz himself.121 Wallis was familiar with only two articles of Leibniz, one of which, namely “The true proportion of the circle to the square”, had appeared in the Philosophical Collections in 1682.122 117 Cf. G. W. Leibniz’s anonymous review of Wallis’ Opera mathematica, vol. 1 and vol. 2, Acta Eruditorum, (June 1696), pp. 249–259. 118 Cf. A III,7 N. 17, p. 75. 119 Cf. A III,7 N. 27, pp. 103f. 120 “Quaedam in Wallisio a Te notata non animadverteram, cum omnia attente satis legere non vacavit. Verum est me Dno Newtono ante 20 annos meae methodi differentialis fundamenta communicasse, antequam ille mihi quicquam de suis huc spectantibus. An nonnihil inde profecerit haud satis scio neque ideo dicere ausim. Interim praeclara illum jam tum habuisse facile crediderim procedente tempore ut fieri solet magis expolita” (A III,7 N. 29, p. 112). 121 Cf. A III,7 N. 55, pp. 206–208. 122 Cf. G. W. Leibniz, “De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus”, Acta Eruditorum, (February 1682), pp. 41–46 (Leibniz: Parmentier, 1989, chap. 1, pp. [61]–81; Leibniz: Essais Scientifiques, 2005, N. 7; Leibniz: Heß-Babin, 2011, chap. 3, pp. 9–18), and “The true proportion of the circle to the square”, Philosophical Collections, (April 1682), pp. 204–210.

636

Chapter 5

Acceptance of the fact that often a limited circulation of scholarly results, rather than malicious intentions, was the reason for their non-percipience, enabled Wallis and Leibniz to unbiasedly discuss priority issues in their correspondence. Accusations of plagiarism were not the issue here. Leibniz wrote, in a letter to Wallis of June 7, 1697, that he had first learned about the similarities between his own and Newton’s calculus through the brief reference given in Newton’s Principa mathematica,123 and of course through the presentation in Wallis’ Opera. Thus he wrote on this occasion: That the method of fluxions124 conceived by the most profound Newton is not greatly different from my differential method, I did not note sufficiently after his opus, and yours, appeared, but in fact I admitted this in the Acta Eruditorum, and I acknowledged it elsewhere also.125 Wallis, in his reply of August 9, did not take a stance regarding priority in the matter of the differential or fluxional calculus, but he merely stressed that, for him, the difference between Leibniz’s differential calculus and Newton’s calculus of fluxions was simply a question of nomenclature. He offered examples of further mathematical concepts, which had appeared under different names in the writings of different authors, before expressing his desire for an elucidation of the similarities and differences of the two forms of the calculus in the following words: I have likewise desired that you present your differential calculus, and Newton his fluxional method, in the right order, so that we might understand what is common to both, and what provides evidence of a difference, and which of the two is more distinct.126 Wallis also pointed to a relationship of the differential calculus with other forms of calculus like, for example, his own tangent method.127 At first he 123 Cf. A III,7 N. 103, p. 429, and annotation, and also I. Newton, Philosophiae naturalis principia mathematica, London, 1687, specifically lib. II, lemma II, scholium. 124 underlined in the manuscript. 125 “Methodum Fluxionum profundissimi Neutoni cognatam esse methodo meae differentiali non tantum animadverti postquam opus ejus et tuum prodiit, sed etiam professus sum in Actis eruditorum, et alios quoque monui”, p. 429 (note 123); cf. also J. Wallis, Opera mathematica, vol. 2, pp. 391–396 (note 115 above). 126 “Optaverim item ut Tibi vacet tuum Calculum Differentialem, et Neutono suam Fluxionum methodum, justo ordine exponere; ut quid sit utrique commune, et quid intersit discriminis, et utramque distinctius, intelligamus” (A III,7 N. 128, p. 519). 127 Cf. pp. 526f.

July 1696–1698

637

appeared to acknowledge the advances made by the differential calculus in comparison with other methods. Later, however, for example in his letter of August 1, 1698, he reverted to a comparison of the differential calculus with his own method of tangents, and he described the two forms as being essentially equivalent.128 Leibniz, for his part, in a letter to Wallis of June 7, 1697, objected to the equalization of his own and Newton’s calculus, except perhaps under the broader heading of infinitesimal analysis. Thus he wrote: That Newton’s most profound method of fluxions129 is related to, or similar to, my differential method, I have not noted sufficiently following the appearance of his opus and of yours, but in fact I admitted this in the Acta Eruditorum, and I acknowledged it elsewhere as well. For I deemed, in my sincerity no less than on the basis of intrinsic merit, that there was a coming together here. And so I adhere to the practice of designating it as infinitesimal analysis, which is broader than the scope of the tetragonist method [viz. of arithmetical tetragonism].130 And a year and a half later, in a letter to Wallis on January 8, 1699, Leibniz pointed out – in opposition to any suggestion of such identicalness – the fundamental differences between his and the correspondent’s method, and also those of others, like Fermat and even Archimedes, recalling the recognition accorded him for his calculus by Christiaan Huygens towards the end of his life. Here he wrote: As regards the differential calculus, I acknowledge that it has much in common with those methods which were investigated by you, Fermat and others, indeed even already by Archimedes. Perhaps however the matter has advanced much further now, and it is already possible to

128 Cf. A III,7 N. 211, pp. 837–841. 129 underlined in the manuscript. 130 “Methodum Fluxionum profundissimi Neutoni cognatam esse methodo meae differentiali non tantum animadverti postquam opus ejus et tuum prodiit, sed etiam professus sum in Actis eruditorum, et alios quoque monui; id enim candori meo convenire judicavi, non minus quam ipsius merito. Itaque communi nomine designare soleo, Analyseos Infinitesimalis, quae latius quam methodus tetragonistica patet” (A III,7 N. 103, p. 429).

638

Chapter 5

achieve that which formerly appeared impenetrable even for the greatest mathematicians, as was acknowledged by Huygens131 himself.132 The form of parlance in Leibniz’s correspondence with Wallis was accommodating, even then when achievements, as well as the honor and pride, of the respective nations were at stake.133 Nonetheless, Wallis’ unuttered motivation, and agenda, was to help the calculus of fluxions assert itself against the differential calculus. Wallis had learned of the success of the differential calculus in continental Europe, specifically in the Netherlands, shortly before his correspondence with Leibniz began, as he mentioned in his first letter to Leibniz, on December 11, 1696, in the following words: I had not yet seen  … either your incomparable mathematics or analysis of the infinite … nor had I heard the name of differential calculus … when sure enough a certain friend of mine notified me … he having been abroad when such a method was being extolled in the Netherlands, for it concurred with the method of fluxions of Newton.134 The same sentiment was expressed by Wallis in a letter to Newton, when he wrote: “your Notions (of Fluxions) pass there with great applause, by the name of Leibnitz’s Calculus Differentialis”.135 Thereafter Wallis pursued the goal of having Newton’s letters to Leibniz, of June 23 and November 3, 1676 – viz. the “epistola prior”,136 and the “epistola posterior”,137 respectively  – published. When he learned of the existence of Leibniz’s replies to those letters, he tried to obtain them. Already in his first letter to Leibniz he requested copies of the 131 Cf. Ch. Huygens, “De problemate Bernoulliano”, Acta Eruditorum, (October 1693), pp. 475f. 132 “Quod Calculum differentialem attinet fateor multa ei esse communia cum his quae et Tibi, et Fermatio aliisque, imo jam ipsi Archimedi erant explorata; fortasse tamen res multo longius nunc provecta est, ut jam effici possint, quae antea etiam summis Geometris clausa videbantur Hugenio ipso id agnoscente” (A III,8 N. 3, p. 10). 133 Cf. A III,7, p. XXXV. 134 “Tuam Geometriam Incomparabilium vel Analysin Infinitorum  … ego nondum vidi  … Neque Calculi Differentialis vel Nomen audiveram … Quippe tum me monuit amicorum quidam … qui peregre fuerat, tum talem methodum in Belgio praedicari, tum illam cum Newtoni methodo Fluxionum coincidere” (A III,7 N. 55, pp. 207f.). 135 Cf. I. Newton (Turnbull, H. W. et al., eds), The correspondence of Isaac Newton, vol. 4, pp. 101f. 136 Cf. A III,1 N. 88,5, pp. 533–554; H. W. Turnbull et al. (eds), The correspondence of Isaac Newton, vol. 2, (1960), pp. 20–47. 137 Cf. A III,2 N. 38, pp. 83–116; H. W. Turnbull et al. (eds), The correspondence of Isaac Newton, vol. 2, (1960), pp. 110–129.

July 1696–1698

639

letters.138 His enquiry to Newton  – who proved anything but cooperative in this matter – met with no success at first. Later, however, he did receive transcriptions of Leibniz’s letters, from Newton and Hans Sloane. Whereas, at first, the issue had only been to establish that Newton was already in possession of the calculus of fluxions in 1676, the possibility of plagiarism was now in the air. Wallis’ academic colleague at Oxford, David Gregory, who was actively involved in obtaining the letters, noted on September 24, 1697, that: “By Libnitz’s letter to Mr Oldenburg dated 27 August 1676 its plain that Libnitz then knew nothing of his after [later] differential Methode”.139 And, after expanding on this thesis on the basis of the other letters, Gregory continued with the words: “These letters are to be printed in the folio [volume] that Dr Wallis is now a printing, in the order of their dates, without any notes or commentaries or reflections: but let the letters themselves speake”.140 In correspondence with Leibniz, Wallis referred only to a scholarly interest as motivation for his plan to edit the letters. He even offered Leibniz the possibility of preventing the publication of his letters, or of undertaking changes.141 Leibniz, who himself was not able to locate his letters, expressed his trust in Wallis. The letters were then printed in 1699 in the third volume of Wallis’ Opera mathematica, as indicated in Gregory’s letter of September 24. However, it remains unclear whether or not Wallis followed Gregory’s argumentation. At all events, in the conflict that ensued from the accusations brought forward by Fatio de Duillier against Leibniz, and that were printed by the Royal Society,142 Wallis did defend Leibniz, indeed successfully, at the Society. 4

Mathematics: Criticism of the Differential Calculus

The success of the differential calculus led not only to envy, as Leibniz and Johann Bernoulli continued to suspect, but also to criticism of its foundations. By 1696, discussions along these lines with Bernard Nieuwentijt and Detlev Clüver had already been carried on for some time. After a range of technical aspects had been exhaustively treated, the central question in Leibniz’s circle was then, how to deal with persistent and obstinate critics. In the person of 138 Cf. A III,7 N. 55, p. 208. 139 Cf. W. G. Hiscock, David Gregory, Isaac Newton and their circle, Oxford, 1937, pp. 6f. 140 Cf. pp. 6f. 141 Cf. A III,7 N. 154, p. 629, annotation, and N. 211, p. 842. 142 Cf. N. Fatio de Duillier, Lineae brevissimi descensus investigatio geometrica duplex, London, 1699.

640

Chapter 5

Burchard de Volder, a new critic had also arrived on the scene who, however, could quickly be convinced. Nieuwentijt considered among other things the use of differentials of second and higher order to be contradictory, and he devised an alternative to the differential calculus from which these had been removed.143 Leibniz had defended his calculus in the Acta Eruditorum against Nieuwentijt’s objections, and he had exposed mistakes that his antagonist had made. Nieuwentijt’s reciprocation  – the publication of which in the Acta Eruditorum had been refused by Mencke  – was published at Amsterdam in 1696 with the title Considerationes secundae circa calculi differentialis principia et responsio ad … G. G. Leibnitium.144 In this tract Nieuwentijt renewed his criticism of the differential calculus. In addition, Mencke received a further manuscript of Nieuwentijt that replied to an article of Johann Bernoulli.145 On July 28, 1696, Mencke delegated to Leibniz the decision about the best course of action to be taken in the matter of this manuscript.146 Leibniz then forwarded the manuscript to Johann Bernoulli, who in turn added marginal notes for Mencke to add in the form of a commentary in the event of the manuscript being published, before returning it to Leibniz on August 25.147 Thereafter, Leibniz moderated somewhat the tone of Bernoulli’s interjection before finally returning the manuscript to Mencke. Simultaneously, he advised Mencke against publication, with the result that three quarters of a year later Nieuwentijt had to enquire about the fate of his work. Mencke replied that the contribution had found no resonance there, or in the words of his letter to Leibniz on March 2, 1697: “An answer has been provided, however, [to the effect] that nobody here was interested in it”.148 Nieuwentijt’s Considerationes secundae were likewise no longer taken seriously by Leibniz and Bernoulli, since they found in the work to be no more than a repetition of the author’s previous objections,149 and furthermore an adventurous treatment in dealing with the infinite.150 Their discussions, in late 1696 and early 1697, concentrated mainly on how best to react to Nieuwentijt. 143 Cf. A III,6, p. XXXf. and Chapter 4 of the present work. 144 Cf. B. Nieuwentijt, Considerationes secundae circa calculi differentialis principia; et responsio ad virum nobilissimun G. G. Leibnitium, Amsterdam, 1696. 145 Cf. A III,7 N. 17, pp. 70f. (annotation). 146 Cf. A I,12 N. 475, pp. 742f. 147 Cf. A III,7 N. 27, p. 99. 148 “Es ist aber geandwort[et] worden, es hätte hier niemand davon wissen wollen” (A I,13 N. 356, p. 594). 149 Cf. the PS to A III,7 N. 54, pp. 203f. 150 Cf. A III,7 N. 75, pp. 312f., and N. 82, pp. 333f.

July 1696–1698

641

The fact that Mencke too was disconcerted in this matter led to further complications. At first, Leibniz considered keeping his counsel to be the best course of action in the matter. However, since Nieuwentijt was not prepared to listen, and continued to defend his position stubbornly, he was to be treated like a heretic, who – according to Sacred Scripture – ought to be avoided, once admonitions had proved to be of no avail, which was the view Leibniz expressed in a letter to Johann Bernoulli, written on January 7, 1697.151 Nonetheless, Bernoulli prepared a response to Nieuwentijt’s critique of his treatment of exponential equations. Mencke did not want to alienate Nieuwentijt, and so he considered it unwise to publish Bernoulli’s harsh criticism, without at least first having presented Nieuwentijt’s Considerationes secundae in the Acta Eruditorum. Accordingly, he requested Bernoulli to provide an objective summary account of the book. This was however preempted by a review of the work, which was submitted by Martin Knorr(e) and which duly appeared in the Acta Eruditorum in March 1697.152 Immediately following this review, the rejoinder, from which the editor had removed what he referred to as “the rather hard expressions from the outline of Mr Bernoulli”,153 was printed.154 Notwithstanding Mencke’s efforts, Leibniz considered the book to have been overrated in the review,155 and he prepared a compilation of the (in his view) most absurd passages from Nieuwentijt’s tract,156 with the motto “to recite is to refute” (“recitasse est refutasse”) in mind.157 Reluctantly, Mencke conceded and approved the publication of the series of extracts in question, as he informed Leibniz on June 1, 1697.158 Finally, Jacob Bernoulli also replied to Nieuwentijt by pointing out – in his solution of the brachistochrone problem159 – the value of second order differentials.160 151 “Si Dn. Nieuwentiit non vult aut non potest capere meliora, et tamen pervicacem sese ostendit, tractandus est instar Haeretici, quem post unam alteramve admonitionem devitandum esse scriptura docet” (A III,7 N. 62, p. 243). 152 Cf. M. Knorr(e) [anon.], Review of B. Nieuwentijt, Considerationes secundae (1696), Acta Eruditorum, (March 1697), pp. 124–125. 153 “die etwas harte expressiones auß des Hn. Bernoulli Schediasmata” (A I,13 N. 381, p. 637). 154 Cf. Joh. Bernoulli, “Principia calculi exponentialium seu percurrentium”, Acta Eruditorum, (March 1697), pp. 125–133. 155 Cf. A III,7 N. 84, pp. 347f., and A I,13 N. 427, p. 693. 156 Cf. A III,7 N. 75, p. 314, N. 88, p. 359, and A I,13 N. 374, pp. 626–628. 157 Cf. A I,13, p. 628. 158 Cf. A III,7 N. 84, pp. 344 and 347f., A I,14 N. 144, p. 245; G. W. Leibniz, “Excerpta ex Dn. B. Nieuwentiit Considerationibus secundis circa calculi differentialis principia”, Acta Eruditorum, (June 1697), pp. 256–260. 159 Cf. Jac. Bernoulli, “Solutio problematum fraternorum”, Acta Eruditorum, (May 1697), pp. 211–216, and note 67 above. 160 Cf. A III,7 N. 71, pp. 278f., and p. 282.

642

Chapter 5

In 1686–87, Clüver had published a couple of enigmatic articles in the Acta Eruditorum in which he also announced a new ‘scientia infiniti’.161 This matter was, however, only first discussed in correspondence with Leibniz in the year 1694, although the two had already been in sporadic contact over a longer period. Clüver explained his principal criticism in a letter of June 14, 1694, which, however, only reached Leibniz a year later.162 According to Clüver, the differential calculus was not sufficient to achieve ultimate geometrical precision. The supposition that the relationship of unity to infinity (one over infinity) be equal to zero was impossible, and that was for Clüver the source of the imperfection. His objections were directed not just against Leibniz’s differential calculus, but also against Archimedes’ quadrature of the parabola, and they were debated not only in correspondence with Leibniz but also with Jacob Bernoulli. The responses of both Leibniz and Jacob Bernoulli make clear the degree of accuracy they ascribed to the differential calculus, as well as their different attitudes to dealing with critics.163 As regards Clüver’s correspondence with Leibniz, a point was finally reached where the dispute no longer seemed meaningful to Leibniz, and he advised the correspondent to henceforth devote himself to astronomy and other areas of mathematics. On June 3, 1697, he explained to Clüver, in diplomatic terms, his approach in dealing with critics, and he referred in particular to Nieuwentijt. And so he wrote on this occasion: “Thus I do not disesteem at all that which you will give”. To this he added the following: My temperament being not to disesteem anything lightly. That was the reason why I replied to the first considerations of Mr Nieuwentiit, although I had not found anything new other than difficulties arising from a poor understanding[,] or without foundation[,] and why I remarked that he was trying to say in other words that which I had already said. But as I saw from his response[,] or from his secondary considerations[,] that my reply had been to no avail, the best course proved to be to abandon the dispute and to refer it to the judgement of adept persons.164 161 Cf. A III, 4, N. 148, p. 285; D. Clüver, “Quadratura circuli infinitis modis demonstrata”, Acta Eruditorum, (July 1686), pp. 369–371. 162 Cf. A III,6 N. 43, pp. 116–119, specifically p. 118. 163 Cf. A III,7, p. XXXVIIIf. 164 “Ainsi je ne meprise point ce que vous donnerés. Mon humeur estant de ne rien mepriser aisement. C’est pour cela aussi que j’ay repondu aux premieres considerations de Mons. Nieuwentiit, quoyque je n’y trouvasse rien de nouveau que les difficultés mal entendues ou sans sujet et que je remarquasse qu’il cherchoit de dire en d’autres termes ce que j’avois deja dit. Mais comme j’ay vu par sa replique ou par ses considerations secondes que ma

July 1696–1698

643

Johann Bernoulli reported to Leibniz about Burchard de Volder’s difficulties with the infinitesimal calculus, having made his acquaintance in Leiden during a journey through the Netherlands.165 On July 22, 1698, Leibniz wrote the following words regarding de Volder to Bernoulli: “For the rest, you would do me a favor if you would communicate to me what you have written, or are writing, to D. de Volder, or have received from him”.166 Then, as an attachment to his letter of August 2,167 Bernoulli sent Leibniz extracts from his letter to de Volder of July 7, under the heading “Excerpta ex literis ad Volderum datis d. 27. Juni st. v. 1698”,168 following which Leibniz sent a detailed reply on August 8.169 In contrast to Nieuwentijt and Clüver, de Volder had no alternative conception. He had occupied himself with the infinitesimal calculus out of interest and, while considering the quadrature of the hyperbola, he had encountered a (supposed) contradiction. De Volder’s mathematical difficulties were no doubt dispelled following Johann Bernoulli’s explanations,170 and their main effect was to initiate a lengthy discussion between Bernoulli and Leibniz about the nature of the infinite. In general, the main allegation brought against the differential calculus was that its proofs did not have the same rigor as those of the ancients, or of classical mathematics. However, this was not the ambition of the differential calculus, which was essentially an analytical method for obtaining results. Leibniz usually answered, as he explained for example in a letter to Bodenhausen on September 30, 1697, by indicating that one could avoid the infinite and reduce “Our infinitesimal calculus to rigorous demonstrations, by considering only my incomparable lemmas, which I once published in the Acta Eruditorum171”.172 reponse n’avoit de rien servi, le meilleur sera d’abandonner la dispute et de se remettre au jugement des personnes entendues” (A III,7 N. 99, pp. 401f.). 165 Cf. A III,7 N. 176, p. 702. 166 “De caetero rem gratam facies si communicabis quae Dno Voldero scripsisti scribesve aut ab illo recipies” (A III,7 N. 208, p. 827). 167 Cf. A III,7 N. 212. 168 Cf. A III,7 N. 213, pp. 848–850. 169 Cf. A III,7 N. 215, in particular pp. 853–855 and p. 857. 170 Cf. A III,7 N. 212 and N. 213. 171 Cf. G. W. Leibniz, “Tentamen de motuum coelestium causis”, Acta Eruditorum, (February 1689), pp. 82–96, in particular p. 85f., and the translation: “An essay on the causes of celestial motions” in: D. Bertoloni Meli, 1993 and 2002, pp. 126–142 (Introduction, notes 73 and 74). Also, cf. the reference in Leibniz’s letter to Joh. Bernoulli of August 8, 1698 (A III,7 N. 215, pp. 857f.). 172 “Unsere Calculos infinitesimales ad demonstrationes rigorosas zu bringen, darff man nur meine Lemmata incomparabilium consideriren, die ich einsmahls in Actis gegeben” (A III,7 N. 141, p. 576); cf. also M. Kline, 1953 and 1964 (Introduction, note 39).

644

Chapter 5

As a member of the Académie des Sciences, Philippe de La Hire was one of the most influential supporters of the old methods. Leibniz availed of the sole letter to him, on October 18, 1697, in which terrestrial magnetism was the center of attention, to deal with La Hire’s skepticism, writing near the close of that letter: I continue to esteem the trouble one takes to demonstrate the beautiful discoveries using the methods of the ancients; although I believe myself to be able to dispense with these through my incomparable lemmas which show that which one can let disappear with impunity.173 5

Mathematics: Mathematical Textbooks and Sundry Topics

L’Hospital’s textbook Analyse des infiniment petits,174 which appeared in 1696 and which Leibniz received via Tschirnhaus in November of that year,175 represented a major contribution to the spread, and dissemination, of the differential calculus. L’Hospital’s opus contained material assimilated from private lessons, which Johann Bernoulli had given him in Paris in 1691 and 1692, as well as from Bernoulli’s letters to him. Notwithstanding L’Hospital’s acknowledgement of Bernoulli’s influence in the preface, and the annual payments made by the author to him since 1694 for the relinquishment of scholarly results, Bernoulli experienced the publication as an affront, although he did manage to keep his counsel in public.176 L’Hospital did not include the integral calculus in his textbook, in order not to preempt Leibniz’s planned – but never elaborated  – opus on ‘scientia infiniti’. Leibniz’s satisfaction following the appearance of L’Hospital’s textbook is in evidence in numerous letters he wrote.177 Above all, the fact that the author had characterized – in the foreword to the book – Leibniz’s calculus as being superior to Descartes’ geometry, was a source of pleasure for Leibniz and a backing for him against his Cartesian

173 “j’estimeray tousjours le soin qu’on a de demonstrer des belles decouvertes à la maniere des anciens; quoyque je croye m’en pouvoir dispenser par mes Lemmes des incomparables qui font voir ce qu’on peut faire evanouir impunement” (A III,7 N. 150, p. 618). 174 Cf. G. F. A. de L’Hospital, Analyse des infiniment petits pour l’intelligence des lignes courbes, Paris, 1696. 175 Cf. A III,7 N. 42, p. 163, annotation. 176 Cf. Joh. Bernoulli, Briefwechsel, vol. 1, pp. 149ff. and p. 202, and also A III,7 N. 180, p. 735. 177 Cf. A III,7 N. 64 (p. 258), N. 117 (p. 488), and A I,13 N. 59 (p. 85), N. 248 (p. 375), N. 321 (p. 524) and N. 325 (p. 533).

July 1696–1698

645

critics.178 To those correspondents, who were interested in the differential calculus, Leibniz recommended the book as an introduction, as for example to Domenico Guglielmini and to Johann Balthasar von Wernher.179 To the latter, he expressed the desire that the book be translated into Latin, and he arranged for the work to be reviewed in the Nouveau Journal des Sçavans, and in the Acta Eruditorum.180 The fact that John Wallis was acquainted with the book, when writing his letter of August 9, 1697, is evidence not just of its rapid and widespread distribution, but also of the fact that the development of the differential calculus was now also being followed with attention in England.181 A series of other topics in pure mathematics are to be found in Leibniz’s correspondence between 1696 and 1698. These included the use of the infinitesimal calculus in the investigation of families of curves, which was a subject of overriding importance in his correspondence with Johann Bernoulli,182 the “problema alterum pure geometricum” (which was first enunciated by Bernoulli in connection with the brachistochrone problem), the calculation of numerical series using differential equations, and the question as to which quadratures, and rectifications, could be expressed algebraically. Each of these topics was discussed in the first instance with Johann Bernoulli.183 In the correspondence with Wallis, quadrature methods were likewise discussed, as were a range of other topics in mathematics, and history of mathematics, including the extension of Cartesian geometry to transcendental curves.184 Leibniz’s interest in the communication, and dissemination, of mathematical knowledge found expression in his correspondence, both with Augustinus Vagetius185 – where the conception of a textbook for teaching mathematics was at the center of interest – and with Caspar Büssing, who reported about the mathematical society in Hamburg, viz. the ‘Kunst-  Rechnungs-  liebende Gesellschat’ there.186 Finally, whereas binary arithmetic, and in particular the binary number system, was not discussed in Leibniz’s correspondence in mathematics, science and technology at this juncture, it arose in a philosophical

178 Cf. A III,7 N. 63 (p. 253), A I,13 N. 270 (p. 419), and A I,13 N. 299 (p. 474). 179 Cf. A III,7 N. 142, p. 578, and N. 148, pp. 591f. 180 Cf. A I,13, pp. Lf. and the reviews in Journal des Sçavans, (September 1696), pp. 424–428, and in Acta Eruditorum, (March 1697), pp. 137–139. 181 Cf. A III,7 N. 128, p. 530. 182 Cf. A III,7, pp. XLI–XLVI. 183 Cf. A III,7, pp. XLVIIf. 184 Cf. A III,7, pp. XLVIIIff. 185 Cf. A III,7 N. 4 (p. 23), N. 53 (p. 192), and N. 61 (p. 230). 186 Cf. A III,7 N. 60, p. 229.

646

Chapter 5

vein in Leibniz’s famous ‘New Year’s Letter’, of January 12, 1697, to duke Rudolf August of Wolfenbüttel.187 6

Natural Philosophy: The Controversy with Papin about “Vis Viva” and “Actio”

The reawakening of Leibniz’s correspondence with Papin – 40 letters were exchanged in the thirty-month period between mid-1696 and December 1698 – had a long and woebegone history. Leibniz acquaintance with Papin can be traced back to their time together in Paris where he first met the then assistant of Christiaan Huygens. Papin’s natural-philosophical views had essentially been shaped by the philosophy of Descartes and, not surprisingly therefore, he experienced Leibniz’s attack on Cartesianism, in the article “Brevis demonstratio erroris memorabilis Cartesii” in the Acta Eruditorum of March 1686,188 and in the Nouvelles de la République des Lettres six months later,189 as a provocation. Three years later – and after he had taken up a mathematical professorship in Marburg – Papin composed a response with the title “De gravitatis causa et proprietatibus observationes”.190 For Papin, the cause of gravity was an ether vortex that acted on the body with infinite velocity. Since this effect occurred at every instant with an equal number of equally strong impacts, it had to be proportional to the elapsed time (and accordingly to the velocity attained by the body), and not to the traversed distance (and thus to the square of the velocity attained by the body). Leibniz replied a year later with an article entitled “De causa gravitatis, et defensio sententiae suae”.191 There he concluded that, in the sphere of operation of terrestrial gravity, forces are 187 Cf. A I,13 N. 75, pp. 116–121, and N. 76, pp. 121–125. 188 Cf. G. W. Leibniz, “Brevis demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae, secundum quam volunt a Deo eandem semper quantitatem motus conservari; qua et in re mechanica abutuntur”, Acta Eruditorum, (March 1686), pp. 161–163, and “A brief demonstration of a notable error of Descartes and others concerning a natural law”, in: Leibniz: Loemker, 1989 (2nd ed.), chap. 34, pp. 296–302 (Introduction, note 15). 189 Cf. G. W. Leibniz, “Demonstration courte d’une erreur considerable de M. Descartes & de quelques autres touchant une loi de la nature selon laquelle ils soutiennent que Dieu conserve tousjours dans la matière la même quantité de mouvement, de quoi ils abusent même dans la mechanique”, Nouvelles de la République des Lettres, (September 1686), pp. 996–999. 190 Cf. D. Papin, “De gravitatis causa et proprietatibus observationes”, Acta Eruditorum, (April 1689), pp. 183–188. 191 Cf. G. W. Leibniz, “De causa gravitatis, et defensio sententiae suae de veris naturae legibus contra Cartesianos”, Acta Eruditorum, (May 1690), pp. 228–239.

July 1696–1698

647

proportional to the product of weight and height or elevation. The condition for the validity of this conclusion is the supposition (in considering the collision of bodies) both of the substitutability of the bodies, and of the total transferability of the force. Then, at the beginning of 1691, Papin maintained in his article entitled “Mechanicorum de viribus motricibus sententia”,192 that an effect is to be measured neither by the distance traversed, nor by the time interval of movement, but rather solely by the resistance to be overcome. As a consequence of this, he denied, among other things, the possibility of the total transferability of the force. Leibniz, in his following contribution to the debate, in September of the same year, entitled “De legibus naturae et vera aestimatione virium motricium contra Cartesianos”,193 attempted to refute Papin’s argument about the non-transferability of the total force from one body to another. By means of a thought experiment, he presented the proof of a complete transfer of force from a massive body to one of lesser mass. According to Leibniz, equal forces existed there where an equal number of elastic springs (having equal tension force and being in the same stress state) are traversed or overcome. For the determination of the measure of force, only those physical effects were admissible in which the force that is absorbed can be ceded once again, as for example in the case of a tensioned spring, or that of an ascended or attained height of fall under the influence of terrestrial gravity. Finally, through the intercession of Johann Sebastian Haes, a direct correspondence between Leibniz and Papin materialized at the end of January 1692. Papin’s reply to Leibniz’s “De legibus naturae” now followed in letter form.194 Thus, the dispute between Leibniz and Papin moved from the public domain (viz. the journal Acta Eruditorum) to the domain of personal correspondence. However, in both the private and public debates, Papin persisted in stressing the importance of momentum or impulse (viz. mass times velocity and operating force times duration, respectively), and he held their conservation to be paramount. Leibniz, on the other hand, adhered to the importance of the height of fall (in terrestrial gravity) and of the path or distance which a body subject to a force covers, i.e. the work performed, or the energy expended, and he underlined their conservation. However, the essential difference between Leibniz’s and Papin’s conceptions did not reside in the physical realm, but rather in that of natural philosophy and of metaphysics. Leibniz wanted to 192 Cf. D. Papin, “Mechanicorum de viribus motricibus sententia adversus Leibnitii objectiones asserta”, Acta Eruditorum, (January 1691), pp. 6–13. 193 Cf. G. W. Leibniz, “De legibus naturae et vera aestimatione virium motricium contra Cartesianos”, Acta Eruditorum, (September 1691), pp. 439–447. 194 Cf. A III,5 N. 56 and N. 57.

648

Chapter 5

identify the overall physical and metaphysical contexts of the world. His efforts for a metaphysical foundation of the laws of dynamics also encompassed explanations in his “Specimen dynamicum pro admirandis naturae legibus” of April 1695.195 Starting from a scrutiny of the concept of movement, Leibniz also arrived at the concept of force. He distinguished here, on the one hand, between a metaphysical “vis primitiva” and a physical “vis derivata” and, on the other hand, between a virtual “vis mortua” and a real “vis viva”. On the basis of the laws of motion, Leibniz arrived, from the example of motion in the sphere of terrestrial gravity, at a quantification of forces as being proportional to the product of mass and the square of velocity. In correspondence with Papin, Leibniz attempted, again and again, to persuade the correspondent of the fallacy of his standpoints. The latter proved to be unpersuadable, however. The antagonists were unable to agree either about the terminology, and the theory upon which it was based, or about the physical phenomena and their interpretation. As Leibniz had no clear notion of the physical processes involved in the tensioning (or the release of tension) in a spring, or in the transmission of force between colliding bodies or from a falling body to other bodies, he was unable to convince Papin, either by means of his thought experiments, or by drawing a theoretical distinction between “vis mortua” and “vis viva”. For the refutation of his opponent, Leibniz availed of, among other things, the method of syllogisms, beginning in his letter of April 19, 1696.196 However, even these formalization efforts proved to be of no avail. In the further course of the correspondence with Papin, matters such as composite movement, the laws of colliding bodies, and the example of oblique collision were discussed using thought experiments. In this context the physical quantity ‘action’ (“actio”) was introduced and explained by Leibniz. As regards the formulation of the laws of colliding bodies, Leibniz could, on his fiftieth birthday (July 1, 1696), look back at developments over a period of half a century and more. Writing to Papin on that day, he mentioned in particular the contributions of Galileo Galilei, Joachim Jungius, the Jesuit Johann Marcus Marci von Kronland, Giovanni Alfonso Borelli, Christiaan Huygens, Christopher Wren, John Wallis, and Edme Mariotte, adding the following words addressed to Papin: “But there is much to be said for the perfection of this doctrine and I believe myself to be able to contribute demonstratively and

195 Cf. G. W. Leibniz, “Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis, et ad suas causas revocandis”, Acta Eruditorum, (April 1695), pp. 145–157. 196 Cf. A III,6 N. 225, pp. 744–747.

July 1696–1698

649

apriorily using my principles”.197 He then offered the prospect of further proofs for his measure of force, and indeed, independent of experiment. However, in his reply of July 12, Papin reacted with skepticism writing the following: I believe that all that one can hope for in these matters is to form hypotheses, in conformity with reason, and to find that all the consequences that one can draw are confirmed by experiment. I admit however that that which you are proposing, namely to establish a doctrine a priori198 and independently of sensible bodies, would represent something superior and more certain; but until now I have not seen anything approaching this.199 In Leibniz’s view, expressed in his letter of July 26, two bodies separate following a collision, as a result of the elasticity of their constituent parts, which was represented by an intervening spring. The bodies first mutually repel each other only after they have lost the total force, with which they had previously impacted each other, and after their relative velocities have fallen to zero. Independent of their respective forces, viz. those which the bodies have at the beginning of the impact, they are reduced to a state of rest relative to the intervening spring. In that instant the law of “vis mortua” (like that of equilibrium) becomes operative, and such that the respective values of the two bodies are inversely proportional to their masses. Following separation, the change of velocity, which results from the elastic resilience of the spring, is in every instant infinitely small. Two bodies having unequal forces, but with velocities that are inversely proportional to their respective masses, mutually cause each other to reverse their motions. However, the equilibrium of the “vis mortua” values leads to an inequality of the “vis viva” values, which for Leibniz was the true measure of force. He illustrated the difference between the two measures of force with the help of an analogy from geometry, writing that “the dead forces are like lines and the living forces like their squares”.200 197 “mais il y a encor bien à dire pour la perfection de cette doctrine et je crois d’y pouvoir contribuer demonstrativement et a priori par mes principes” (A III,7 N. 1, p. 15). 198 underlining by Papin. 199 “Je crois que tout ce que l’on peut esperer dans ces matieres c’est de former des Hypotheses conformes à la raison et de trouver que toutes les consequences qu’on en tire sont confirmées par l’experience: J’avoue pourtant que ce que Vous proposez, d’etablir une Doctrine a priori et independamment des corps sensibles, seroit quelque chose de meilleur et de plus asseuré: mais jusques à present Je n’ay rien veu qui approchast de cela” (A III,7 N. 2, p. 21). 200 “les forces mortes estant comme les lignes et les vives comme les quarrés” (A III,7 N. 8, p. 34).

650

Chapter 5

Since Papin saw no reason for making such a distinction between a “vis viva” and a “vis mortua”, and could not conceive infinitesimal velocity changes, he elaborated his position yet again in his next letter (of August 7) to Leibniz,201 who in turn responded on August 20 by explaining his understanding of infinitesimal physical changes, and resorting once again to a comparison with mathematics, by writing that: “The infinitely small [changes] are determined in a way one can recognize from the flections of curved lines, which change in infinitely small steps”.202 Nonetheless, in his letter of August 30, Papin continued to reject the introduction of a “vis viva”, and for him the law of “vis mortua” was valid everywhere. Thus he wrote: I am unable to comprehend the benefit to be obtained by the introduction of a living force [since], be it in communicating the force [or] be it in receiving it, it is always the law of the dead force which holds, and I do not see what the benefit for a body is that its force be living since, in the event that it has to act, it does not have any more effect than if the force were dead.203 For Leibniz, as he outlined in his letter of September 24, the “vis mortua” was effective only in relation to relative effects, which manifested themselves as instantaneous, infinitely small velocities. Bodies having the same quantity of motion were indeed in a position to mutually stop each other in their tracks, but they did not have to have the same “vis viva”, which operated in relation to absolute effects, and was subject to force conservation. His words on this occasion were: But when one considers all the force that there is, and the absolute effect, or all that the body is capable of producing, measured by the precise repetition of the same power of impact for example the number of identical springs [or clips] in between which can be inflected before the body’s

201 Cf. A III,7 N. 16, pp. 69f. 202 “les infiniment-petits sont determinés, comme on le peut connoistre par les flexions des lignes courbes, qui se changent par des degrés infiniment petits” (A III,7 N. 25, p. 95). 203 “Je ne puis pas comprendre à quoy bon introduire une force vive puisque, soit en communiquant la force soit en la recevant c’est tousjours la loy de la force morte qui a lieu: et Je ne vois pas de quoy sert à un corps que sa force soit vive puisque dans l’occasion où il faut agir il ne fait pas plus d’effet que si sa force estoit morte” (A III,7 N. 28, p. 106).

July 1696–1698

651

movement is consumed, then the law of the living force is operative and it is only the quantity of this force that is always conserved.204 In order to establish contradictions in Leibniz’s argumentation, Papin, in his reply of October 4, conceived a thought experiment involving the collision of a larger with a smaller body.205 Between the two bodies there is a spring. In the instant in which the velocity of the smaller body is reduced to zero, it is replaced by a much larger body, which then absorbs the recoil of the spring and the impact of the other body. Since the distribution of the quantity of motion follows the law of “vis mortua”, the surrogate body has a lower velocity (and less “vis viva”) after the collision than the smaller body had before the collision. Accordingly, there would be a loss of force in the world following the event, which was tantamount to a contradiction in Leibniz’s conservation principle. In his reply to this, on November 11, Leibniz maintained that a portion of the force of the stalled body is transferred to its inner spring, that is into the form of motion of its intestinal constituent parts. The replacement of a body by a larger body was only admissible if the “vis viva”, which is lodged in the inner spring of the body, were to be transferred to the surrogate body. And so he wrote that: It is necessary to consider that the small body, although reduced to rest as far as its whole is concerned, has for that not lost all of its force, because a part of its total force is transferred to its spring, that is to say to the movement of its constituent parts. This makes clear that a simple substitution by another larger body is not sufficient, if one does not find the means to transfer to this body the living force lodged in the spring of the small body.206

204 “Mais quand on considere toute la force qu’il a, et l’effect absolu, ou tout ce que le corps est capable de produire, mesuré par la repetition precise d’une meme puissance par exemple combien de ressorts egaux entre eux puissent estre bandés avant qu’il consume son mouvement, la loy de la force vive a lieu et ce n’est qu’elle dont la quantité se conserve tous jours” (A III,7 N. 34, p. 142). 205 Cf. A III,7 N. 37, pp. 151f. 206 “Il faut considerer que le petit corps quoyque reduit en repos quant à son entier, n’a pas perdu, pour cela toute sa force, parce qu’une partie de la force totale est transferée sur son ressort c’est à dire sur le mouvement de ses parties. Ce qui fait voir qu’une simple substitution d’un autre corps plus gros ne suffit pas, si on ne trouve moyen de transferer sur luy la force vive logée dans ce ressort du petit corps” (A III,7 N. 44, p. 170).

652

Chapter 5

Leibniz’s position now meant that Papin saw himself constrained to investigate more closely the exact mechanism of such a substitution. The 13th in a series of syllogisms, which was enunciated in Papin’s letter of November 15,207 was now at the center of the dispute. It was founded on the following thought experiment:

Figure 6

Sketch of Papin’s thought experiment regarding the substitution or replacement of a body by a surrogate body during a two-body collision Source: Denis Papin to Leibniz, November 15, 1696 (A III,7, p. LV and p. 172)

Here, two perfectly hard bodies A and B meet and, through the collision, tension is produced in the spring C between them. In the instant in which the smaller body B almost comes to a stand-still, it is struck by a considerably larger body D moving in the direction ED (slightly inclined to the direction BF). The body D moves considerably slower than the smaller body B before impact with the spring C. The velocity of D is just sufficient to effectuate that it replaces B and (as soon as the recoil of the spring C becomes operative) it receives the total force that had previously been transferred from B to C. The surrogate body D would therefore have less force than B had before the collision and the total force would thus have decreased. The interpretation of this thought experiment is intimately connected with the possible existence of a perfect hardness of physical bodies. Both of the adversaries in the dispute quickly agreed that such a state of complete hardness was unattainable in reality. Nevertheless, Leibniz believed, as he explained in his letter of November 19, that, on the assumption of an almost perfect hardness, a substitution would be possible, viz. that only a small part of the force would be transferred to the parts of the bodies A and B with by far the greatest 207 Cf. A III,7 N. 45, pp. 172f.

July 1696–1698

653

portion going to the spring C. In spite of this, there would be no loss in the quantity of force. The surrogate body D would namely experience the impact of the recoil of the spring not centrally (like B) but rather partly off-centered, and it would therefore be subject to a rotation which would lead to a diminution of its resistive potential, and in sum there would be no loss of force or “vis viva” in the world. Thus he wrote: Now however, while D will be pushed eccentrically, it will be subjected to a rotation, following which the course of action is then very different to that of central actions; and once one has taken everything exactly into account (something which is not easy) one will find that notwithstanding the fact that the dead force exists in the infinitely small changes, nonetheless the same quantity of living force will always remain; just like that the body D, [which] although it is larger than B and should resist with advantage, in terms of magnitude, yet nevertheless it should resist less by virtue of another matter, namely the eccentricity; and so one [factor] is able to compensate for the other and there is no reason to doubt that this will in effect occur.208 Papin then responded, on November 25, by formulating the major premise of his 14th syllogism, which, while taking account of the rotation effect, still entailed a loss of “vis viva”, expressing the matter in the following words: If, notwithstanding the eccentricity of the action of the spring on the body D, one could arrange that the body in question should nonetheless receive, in accordance with your hypothesis, less force than the smaller body B would have lost, it follows that your response is inadequate.209 On the basis of a numerical example, he claimed to have demonstrated the correctness of this major premise of the syllogism. Under the heading of his 208 “Or, durant que D sera poussé eccentriquement, il receuvra un tournoyement, en quel cas le procedé alors est bien different de celuy des actions centrales; et quand on aura tout mis exactement en compte (ce qui n’est pas aisé) on trouvera que non obstant que la force morte a lieu dans les changemens infiniment petits, neantmoins la même quantité de la force vive demeurera tousjours; d’autant que le corps D, quoyque il soit plus grand que B, et qu’il doit resister d’avantage, quant à la grandeur, doit pourtant moins resister par un autre chef, qui est l’eccentricité; ainsi l’un peut recompenser l’autre Et il ne faut point douter, que cela n’arrive en effect” (A III,7 N. 48, pp, 181f.). 209 “Si l’on peut faire que non obstant l’excentricité de l’action du ressort sur le corps D le dt corps reçoive pourtant, selon vostre hypothese, moins de force que le petit corps B n’en aura perdu: il s’ensuit que vostre response ne suffit pas” (A III,7 N. 52, p. 190).

654

Chapter 5

15th syllogism, he introduced the following variant of his earlier thought experiment illustration:

Figure 7

Another sketch of Papin’s thought experiment regarding the substitution or replacement of a body by a surrogate body during a two-body collision Source: Denis Papin to Leibniz, November 25, 1696 (A III,7, p. 190)

Then, in the last letter of the year 1696 to Papin, on December 24, Leibniz denied at once the validity of the premise. He argued that the total force following the collision was composed of the force of the movements of the bodies A and D as well as the elastic resilience of B. Thus he wrote: “And in order to have the total force, it is necessary to bring together, after the blow, that of the movement of A, that of the movement of D, and that of the recoil of B”.210 Papin, replying in the new year, on January 14, 1697, then saw a contradiction in Leibniz’s previously-presented explanations (viz. until the end of 1696).211 Whereas Leibniz had, in his letter of November 19 of the previous year,212 assumed an almost perfect hardness of the bodies A and B, and an almost total transfer of the force to the spring C, he had subsequently, in the letter of December 24,213 talked about an elastic body B with tensioned parts in which a part of the force was retained. However, one could, according to Papin, reduce the elastic resilience of the parts of the body to almost zero, with the result that it would be negligible in comparison with the loss of force in the total substitution process. Furthermore, it would be possible to arrange, in the substitution process, for the body D to advance fast enough (or for its broadside 210 “Et pour avoir la force totale il faut mettre ensemble apres le choc celle du mouvement d’A, celle du mouvement de D, et celle du ressort de B” (A III,7 N. 58, p. 223). 211 Cf. A III,7 N. 66, pp. 260–262. 212 Cf. note 208. 213 Cf. note 210.

July 1696–1698

655

to be accordingly altered) in order for it to absorb the recoil of the spring at its central point. Thus, in his letter of January 14, he formulated his 16th syllogism as follows: If we are permitted to suppose the spring C between the bodies A and B to be as long as we desire in order that it would require the requisite amount of additional time to reposit itself, and if it be permitted also to assume the side DE of the body D to be as short as we desire in order that its center be able to find itself in a sufficiently shorter time in a position opposite the spring, then it follows [firstly] that it is not impossible to arrange for the body D to have its center exposed to the recoil of the spring long before the spring is semi-restituted and [secondly] that therefore your pretended impossibility is annulled. And to this he added the conclusion, following the antecedent-consequent syllogistic rules, as follows: “So the antecedent is true, and therefore the consequence is likewise true”.214

Figure 8

Yet another sketch of Papin’s thought experiment regarding the substitution or replacement of a body by a surrogate body during a two-body collision Source: Denis Papin to Leibniz, January 14, 1697 (A III,7, p. 261)

214 “S’il nous est permis de supposer le ressort C entre les corps A et B autant long qu’il nous plaist afin qu’il emploie d’autant plus de temps à se restituer: et qu’il soit permis aussi de supposer le costé DE du corps D autant court qu’il nous plaist afin que son centre puisse d’autant plus tost se trouver vis à vis du ressort: il s’ensuit qu’il n’est pas impossible de faire que le corps D ayt son centre exposé à l’action du ressort longtemps avant que le ressort soit à demi restitué: et qu’ainsi l’impossibilité que Vous avez marquée est nulle. Or l’Antecedent est vray: donc le consequent l’est aussi” (note 211 above, p. 261 with Figure 8).

656

Chapter 5

At the beginning of the year 1697, Leibniz suspended the intensive exchange with Papin for two months in order to thoroughly consider the matter at issue here. When, on March 7, 1697, he resumed the correspondence he had reconsidered the course of the debate since July 1696.215 In this renewed consideration, he had arrived again at Papin’s 13th syllogism.216 As a concession to his opponent he now declared his willingness to put aside, for the time being, his objections relating to the hardness of the bodies and the practical execution of the substitution. The manner of carrying out of the substitution would not play a role as long as there was neither gain nor loss of force involved. However, he maintained that the entire force that is transferred from the body B to the spring C is returned to the surrogate body D. To make his assertion clear, he presented an example with numerical values for the masses and velocities of the bodies involved. His result was based on the assumption that the spring C experienced a greater resistance from the body D than it did from the body B. Thus he wrote: It should not appear strange at all, that the spring experienced more resistance from the side of D than it had met from that of B, and in effect it would be necessary that the bodies A and D, in order to give to the spring C this same force as that which the bodies A and B had given it with their velocities specified above, should have had the velocities which I assigned them, which you will find without doubt yourself on examining the matter, be it that one understands the spring to be a separate body, by supposing that the colliding bodies do not retain any force on their parts, or that one understands the spring to be that which the bodies enclose within themselves. For the one ought to return to the other.217 In the spring of the year 1697, Papin had other commitments and he announced, on May 13, a time-out on his part in the contest with Leibniz.218 Not until October 24 of that year did he see himself in a position to continue 215 Cf. A III,7 N. 77, pp. 318–321. 216 Cf. A III,7 N. 45, p. 172. 217 “Ce qui ne doit point paroistre estrange, le ressort trouvant plus de resistence du costé de D qu’il n’en auroit trouvé en B, et en effect il auroit fallu que les corps A et D pour donner au ressort C cette même force que les corps A et B luy ont donnée avec leur susdites vistesses eussent eu les vistesses que j’ay assignées, comme vous trouverés sans doute vous même en examinant les choses, soit qu’on entende par le ressort un corps à part, en supposant que les corps concourans ne gardent point de force en leur parties, ou qu’on comprenne sous le ressort celuy que les corps enferment en eux mêmes. Car l’un doit revenir à l’autre” (note 215, p. 321). 218 Cf. A III,7 N. 93, pp. 385f.

657

July 1696–1698

the dispute. After Leibniz had appeared to concede regarding the feasibility of carrying out a substitution, Papin was confident that he could soon bring an end to the controversy. He then conceived the following experiment:219 masse 10 vitesse 4

A

E

C

fig. 1

Figure 9

A

C

B

P

masse 10 vitesse 4

E

masse 1 vitesse 10

fig. 2 P

masse 2 vitesse 5 D

Sketch of Papin’s thought experiment to demonstrate the equivalence of separate collisions of a body with two other bodies Source: Denis Papin to Leibniz, October 24, 1697 (A III,7, p. 626)

A body A (of mass 10 and velocity 4) collides with a body B (of mass 1 and velocity 10) and later (in a separate thought experiment) with a body D (of mass 2 and velocity 5). On the basis of his calculations, Papin believed he could present a proof that, in substituting D for B, a loss of force would occur whereas inversely, in the substitution of B for D, a gain of force would result. The process could be continued in that one continually reduced the mass of B and correspondingly increased its velocity. This argumentation would then of necessity lead to a violation of the conservation of force requirement. Thus he wrote: But the forces of the masses in question would always develop by scaling themselves up as the squares of the same lines EB, in such a way that it could happen, following your way of calculating the forces, that two bodies on colliding would produce a force incomparably greater than that which they had before the collision.220

219 Cf. A III,7 N. 153, pp. 626–628, specifically p. 626. 220 “mais les forces des dittes masses iroient tousjours en s’augmentant comme les quarrez des mesmes lignes EB: de sorte qu’il pourroit arriver, suivant vostre maniere d’estimer les forces, que deux corps en se chocquant produiroient une force incomparablement plus grande que celle qu’ils auroient eue avant le choc” (p. 628).

658

Chapter 5

In his reply on November 18, Leibniz countered with the argument that it would be impossible by means of two separate collisions of A with B and D, respectively, to produce the same conditions as those which resulted from the substitution of the body B with D following impact with A.221 The bodies A and D would have to be provided with movements such that, in the course of their collision, three conditions would be met, namely the following: D would have to come to a stand-still; A would receive the same movement through the impact as in the case of the collision with B that brings the latter body to a stand-still; the tension of the spring between A and D would have to be the same as that between A and B in the instant of the stand-still.222 Leibniz’s view was that these conditions were not being fulfilled in the experiment conceived by Papin; in particular there was absolutely no consideration relating to the third condition. Leibniz maintained that he had determined the stress conditions of the spring in three ways, and he proceeded to explain the simplest of the three calculations using a numerical example. His conclusion was that the two situations were not equivalent and, accordingly, that the forces of the bodies A and D after collision would not be the same as those of the bodies A and B. Papin had based his considerations on the law of “vis mortua” whereas, for an explanation of the substitution process, the “vis viva” would have to be taken into account, or in his words: It is necessary to take into account the living forces to carry out the required substitutions. In contrast the dead forces establish simply which bodies are in a position to mutually bring each other to a standstill, and not which bodies are capable of producing the same absolute effect.223 On December 5 then, Papin replied that the two bodies D and B would (on the basis of the law of the “vis mortua”) have the same effect on the spring due to the reciprocity of their masses and velocities.224 Even the circumstance accepted by Leibniz, that the bodies B and D produced the same effect in colliding with the body A, required the same tensioning of the spring. Papin recalled that he himself had previously – in fact in his letter of August 30, 1696225 – introduced yet another objection, namely that, according to Leibniz’s interpretation of the 221 Cf. A III,7 N. 156, pp. 632–638. 222 Cf. pp. 635f. 223 “il faut avoir égard aux forces vives pour faire des substitutions dües. Au lieu que les forces mortes marquent seulement quels corps sont en estat de s’arrester mutuellement, et non pas quels corps sont capables de produire le même effect absolu” (p. 637). 224 Cf. A III,7 N. 161, in particular pp. 648f. 225 Cf. A III,7 N. 28, p. 108.

July 1696–1698

659

process, it would be possible that, following a collision, the stronger of the two bodies would be forced into reverse whereas the weaker of the two could continue on its path. Once again, Papin contested some fundamental distinctions introduced by Leibniz, in particular the existence of a “vis viva” alongside a “vis mortua”. He likewise rejected Leibniz’s adherence to an absolute effect, as well as the capability of arresting a body. Thus he wrote: I have already alluded, Sir, to other matters capable of preventing a lot of people sharing your sentiments, as, for example, that, according to you, [in the case of] two bodies having impacted each other, it can occur that the one which is much stronger will nonetheless be constrained, by the impact, to reverse entirely its direction of motion, while the weaker one will conserve once again some force in order to continue in the same direction that it had before the collision. I noticed likewise that, according to you, a body only overcomes a spring by virtue of its dead force and nevertheless in doing so it consumes all of its living force which is often incomparably larger.226 Leibniz, in his final letter of the year 1697 to Papin, on December 12,227 emphasized that it would be sufficient for his line of argumentation if the correspondent were to concede the following two points, namely that, firstly, two bodies of different magnitudes can be provided with the same quantity of force and, secondly, a substitution can be carried out in such a way that the quantity of force of the bodies is conserved. Thus he wrote: I believe that I have shown in several ways that the force of a large body can almost pass into a smaller body, but I have no need of this; it is sufficient for me that it is possible to arrange for a small body to have a force equal to that of a large body, and that you concede that, on substituting one for the other, one would not acquire more force than beforehand.228 226 “J’ay desjà, Monsieur, remarqué d’autres choses capable d’empecher bien des gens d’entrer dans vos sentiments: comme, par exemple, que, selon Vous, deux corps venants à se chocquer il pourra arriver que celuy qui sera de beaucoup le plus fort sera pourtant contraint, par le choc, de retourner tout à fait en arriere, tandis que le plus foible conservera encor de la force pour avancer de méme costé qu’il faisoit avant le choc. J’ay de méme remarqué que, selon Vous, un corps ne bande un ressort que suivant sa force morte et neantmoins il ŷ consomme toute sa force vive qui souvent est incomparablement plus grande” (note 224 above, p. 649). 227 Cf. A III,7 N. 163, pp. 656–670. 228 “Je crois d’avoir monstré en plusieurs manieres que la force d’un grand corps peut passer à peu prés dans un petit corps; mais je n’en ay point besoin, il me suffit qu’il est possible

660

Chapter 5

In the collisions of the body A with B and D, respectively, the intervening spring would experience a different tension in each case, although A behaved in exactly the same way in both cases. Here the body A might even be replaced by a wall. From this consideration, he conceived the following thought experiment to help provide a decision in the dispute: against a spring that is attached to a wall on one side, two bodies, designated L (of mass 6 and velocity 1) and M (of mass 1 and velocity 6), respectively, impact the other side in separate trials. In each case a considerable difference in the tensioning of the spring was to be expected.229 Accordingly, L and M would have unequal forces although both of them would in turn be stopped by the collision. Thus he wrote: You therefore see that two bodies are able to forestall each other, such as L and M, which nonetheless will be equal in force, calculating them according to the definition of more strong,230 which I have posited. And it is following this definition[,] that I understand the absolute and living force.231 In the context of the thought experiments pertaining to the nature of percussion and elastic spring, Leibniz pointed to a further conservation law of his, namely that of the quantity ‘progress’ (“progrès”), which was given as the product of mass and directional velocity, and which was the counterpart of “force morte”. Thus he wrote: All that one can say here is that it a curious matter, and one worthy of the comment, that the difference is to be found solely in the spring, and is not divided between A and the spring. But one clearly sees here the cause or reason by means of my grand principle of the conservation of progress. For the progress in the first case is the same as in the second before the impact  … And therefore, behold the same conclusion [has

d’assigner un petit corps égal en force à un grand corps, et que vous accordés, qu’en substituant l’un à l’autre, on ne doit pas acquerir plus de force qu’auparavant” (p. 658). 229 “on verra une grandissime difference dans la tension entiere du resort” (p. 659). 230 underlining by Leibniz. 231 “Vous voyés donc que deux corps se peuvent empecher mutuellement, sçavoir L et M, qui neantmoins seront inegaux en force; en l’estimant selon la definition du plus fort, que je viens de poser. Et c’est suivant cette definition que j’entends la force absolue et vive” (p. 660).

July 1696–1698

661

been] demonstrated in two ways, here by the quantity of progress, and in the previous case by the law of dead force.232 Regarding Papin’s objection that – according to Leibniz’s interpretation – in the collision of two bodies the stronger one might possibly be forced into reverse, while the weaker one would continue along its path, Leibniz maintained that this circumstance would depend on the definition of ‘stronger’ and ‘weaker’, and in any case would lead to linguistic paradoxes.233 For this very reason it was necessary to introduce two very different kinds of force that were compared to angles and lines in mathematics. Leibniz characterized these two forces as living, productive, absolute and spatial (the first) and as dead, disabled, relative and plane (the second), respectively. The first force is that which is conserved in nature. Also, the circumstance that Papin found so strange, namely that the tensioning of a spring arises from the law of the “vis mortua”, while contemporaneously the “vis viva” is consumed, was explained by Leibniz by resorting to a comparison with the relationship between the peripheries and areas of geometrical figures. Here he wrote: “It is like in the case … of peripheries and areas … When one consumes all of the dead forces, the living force is also consumed, although it has a different proportion”.234 The ascent of a weight against the force of gravity was in this respect similar to the tensioning of a spring. The “vis mortua” represented the distributive law of the changes, whereas the “vis viva” embodied the collective law of the conservation. Papin’s designation of an effect in which a body is brought to a standstill as “absolute”, induced Leibniz to explain his use of the terms “absolute” and “relative” in the following terms: By an absolute effect I understand the production of a certain force where there is a certain determined movement … But to simply change the determination of a body, as happens on preventing it from advancing

232 “Tout ce qu’on peut dire icy, est que c’est une chose curieuse et digne de remarque que la difference se trouve dans le seule ressort, et n’est pas partagée entre A et le ressort. Mais on en voit clairement la raison par mon grand principe de la conservation du progrés. Car le progres dans le premier cas estant le meme que dans le second avant le choc … Ainsi voilà une meme conclusion demonstrée de deux façons, icy par la quantité du progrés, et dans la precedente par la loy de la force morte” (p. 662). 233 Cf. pp. 666f. 234 “C’est comme dans le cas  … des peripheries et aires  … Quand on consume toutes les forces mortes, la force vive est consumée aussi, quoyque elle garde une autre proportion” (p. 668).

662

Chapter 5

and forcing it to reverse its direction, that is an effect which I may perhaps be permitted to call relative.235 Papin, in his first letter to Leibniz of the new year, on January 6, 1698, then rejected the allegation of a paradox resulting from his interpretation, and he maintained the paradoxes that had arisen only existed within Leibniz’s system. He explained that, notwithstanding different tensions in the spring, an equal breaking effect could be achieved, since the duration of the event had also to be taken into consideration. Thus he wrote here: If the body A is retarded to the same extent by a lesser-tensioned spring as by a greater-tensioned spring, this happens because the more tensioned spring has acted for a shorter time, and this shortening of the time was the cause that the body A was not able to receive such a large number of blows from the elastic material.236 The correspondent then proceeded to explain the difference between his and Leibniz’s approach by means of the following analogy. Two observers arrange for the collision of two bodies A (of mass 1 and velocity 2) and B (of mass 2 and velocity 1) in a space devoid of air without gravitational influence, and they establish the existence of equal quantities of motion, and of equal forces, also for other relations of mass and velocity. His exact words here were: Let us also suppose [firstly] that there be two spectators who observe that which happens when the bodies strike each other and [secondly] that, on watching the impact of body A of mass 1 and velocity 2 against B of mass 2 and velocity 1, they conclude that the force and the quantity of movement are the same thing, since both of these bodies having an equal quantity of movement also have equal forces to mutually bring each other to a halt, [and thirdly] that they observe thereafter whatever number one wishes of other strikes by sensible bodies, but with different proportions of masses and velocities[;] no one will be found who is not 235 “j’entendois par un effect absolu la production d’une certaine force où il y a un certain movement determiné … Mais changer seulement la determination d’un corps, comme il arrive en l’empechant d’avancer et en l’obligeant de tourner en arriere, c’est un effect qu’il me sera peut estre permis d’appeller relatif” (p. 669). 236 “lors que le corps A est autant retardé par le resort moins bandé comme par le resort plus bandé, cela arrive parce que le resort plus bandé a agi en moins de temps, et cette brieveté de temps a été cause que le corps A n’a pu recevoir un si grand nombre de coups de la matiere elastique” (A III,7 N. 171, p. 692).

July 1696–1698

663

confirmed in the original conviction that the force and the quantity of movement are the same thing.237 Then, the observers are transferred to another location in space where a hailstorm is raging. The non-observable particles of the hail are unimaginably small, and their velocity is extraordinarily large. The observers now observe two bodies having the same magnitude that are moving against the hail stream. They notice to their surprise that the bodies lose their movement after travelling a short distance, and subsequently move backwards, apparently without having encountered other bodies. Papin then told that the amazement of the observers increases once they establish that the traversed distances (until the loss of their respective movements) are not proportional to the quantities of motion. A body with double the quantity of motion of its counterpart has to traverse four times the distance before coming to a halt. The first observer (Papin’s alter ego) explains the occurrence by supposing the existence of the hailstorm, and seeing the laws of colliding bodies at work, whereas the second observer (Leibniz by proxy) prefers to introduce a new force to explain the event. Papin then posed the following rhetorical questions regarding the two observers: “In truth, Sir, do you not find that this first observer would be in the right to a high degree? … and would one not be right to say to this second observer that his trouble has been to no avail and even embarrassing?”238 In his reply, on January 26, 1698,239 Leibniz complained about a certain prevailing camp thinking, in which the two contenders, like hostile armies following a skirmish near the Meuse or Scheldt rivers (part of the Rhine- Meuse- Scheldt delta), claim victory for themselves among their partisans without ever having joined battle, or in his words: We are going to fall (if we do not take care) into the manner of discussing a situation where everyone is correct to the letter and to the extent 237 “supposons aussi qu’il ŷ ayt deux spectateurs qui observent ce qui arrive quand les corps se chocquent: et que voiant heurter le corps A masse 1 vitesse 2 contre B masse 2 vitesse 1, ils concluent que la force et la quantité de mouvement sont la méme chose: parce que ces deux corps qui avoient egale quantité de mouvement avoient aussi egalement de force pour s’entre arrester: qu’ils observent ensuitte tel nombre qu’on voudra d’autres chocs de corps sensibles; mais avec differentes proportions de masses et de vitesses il ne s’en trouvera aucune qui ne les confirme dans leur premiere pensée que la force et la quantité de mouvement sont la mesme chose” (pp. 692f.). 238 “En verité, Monsieur, ne trouveriez Vous pas que ce premier spectateur auroit grande raison? … n’auroit on pas raison de dire à ce dernier qu’il se donneroit une peine inutile et mesme embarassante?” (pp. 693f.). 239 Cf. A III,7 N. 177, pp. 702–728.

664

Chapter 5

he talks, just like two hostile armies who never meet. The one moves towards the Meuse, the other towards the Scheldt, and each of them celebrates with bonfires in their respective camps.240 Accordingly, he sought to reply in a formal fashion citing articles like in a legal dispute. Leibniz attempted to show that Papin’s interpretation must, in the final analysis, lead to the possibility of a perpetuum mobile. This could happen, for example, if the principle of the equality of cause and effect were to be infringed at the location in space where Papin had placed his observers. Thus, he solicited Papin in the following words: I request that you say if you believe that, in that vast space, where you place your observers, it could happen that the effect would be greater than the cause, or if one must rule that the equality of cause and effect be observed in the manner I have explained it.241 Leibniz then introduced two basic principles from which the laws of colliding bodies could be derived, namely the equality of cause and effect, and the conservation of progress, i.e. of the product of mass and the directional quantity of motion. In order to prove his standpoint solely on the basis of the law of “vis mortua” combined with the rules for the composition of movements, he conceived the following thought experiment.242 A ball (or sphere) B strikes two other balls of the same magnitude, namely A and C, diagonally (viz. at an oblique angle of incidence) along the path 1B2B and comes to a standstill at the point 2B. Since the movement of ball B with velocity 1B2B is transferred into the movements of ball A, having the velocity 1A3A (= F2B), and that of ball C with velocity 1C3C (= E2B), Leibniz concluded, from the Pythagorean theorem, that it is not the movement but rather the force that is conserved. The collision event could also take place in reverse. Thus, if the balls A and C, travelling in reverse, were to come from the corresponding directions and simultaneously strike the ball 240 “Nous allons retomber (si nous n’y prenons garde) dans ces manieres de conferer, où chacun a raison dans sa lettre et tant qu’il parle, à peu prés comme deux armées ennemies, qui ne se rencontrent point. L’une va vers la Meuse, l’autre vers l’Escaut, et chacune fait des feux de joye dans son camp” (cf. pp. 702f. and p. 722). 241 “je vous prie de dire, si vous croyés que dans ce vaste espace, où vous mettés vos deux spectateurs, il puisse arriver que l’effect soit plus grande que sa cause; ou s’il faut juger que l’egalité de la cause et de l’effect s’y observe de la maniere que je l’explique” (p. 722). 242 Cf. pp. 709f. and pp. 724f.

July 1696–1698

665

Figure 10 Sketch of Leibniz’s thought experiment regarding the collision of a body moving along the diameter of a square with two other bodies resting at a corner Source: Leibniz to Denis Papin, January 26, 1698 (A III,7, p. 709, p. 724 and p. 880)

B lying at rest at the point 2B, they would come to rest at 2B, and the ball B would move forth along the diagonal with the velocity 2B1B. In this manner, a quantity of force would have been transferred from a greater to a smaller part of matter. For Leibniz, this showed that his interpretation would apply, not only on earth, but also in free space without gravitational force. However, the hail, imagined by Papin, would have to be taken into account in considering the quantity of motion. Thus he wrote: And I find, on examining it, that the quantity of movement gained by the heavy body on descending, is equal to the quantity of movement which the hail had on colliding with this body[, and] which this same hail still has on reflecting (being reflected). And so one gains movement during the descent just as one loses [it] during the ascent.243 243 “Et je trouve en l’examinant, que la quantité de movement gagnée par le corps pesant en descendant, est egale à la quantité de movement que la grêle avoit en frappant avec celle que cette même grêle a encor en reflechissant. Ainsi on gagne du movement durant la descente comme on perd durant la montée” (p. 725).

666

Chapter 5

Leibniz also dealt with the effects, arising from his standpoint, which Papin experienced as paradoxical, as for example, the circumstance that two bodies, which mutually arrested each other, would produce the same effect.244 While two bodies A (of mass 2 and velocity 1) and B (of mass 1 and velocity 2) would put each other into reverse, B would produce double the effect of A. Furthermore, a body at rest could, without force and by virtue of its inertia alone, bring a moving body of the same magnitude to a halt. A measure of force based on the capability to stop moving bodies would of course become infinite. The true measure of force, and that which is conserved in nature, was to be measured in terms of the production of other forces. While Papin continued to find Leibniz’ interpretation paradoxical, he, for his part, found the explanation of Papin to be not just paradoxical, but also absurd. He insisted that, in his treatment of the matter, he had shown that the position taken by Papin offended against reason, and might sometimes result in a perpetuum mobile. Leibniz reported optimistically that he had found a criterion by means of which – and with the support of a physical experiment – a decision in the dispute could be reached. Inevitably for him, in the case of two bodies producing a certain degree of tension in a spring, it was always the sum of the forces, and not the sum of the quantities of motion, that remained constant. Thus, he concluded that: [For] two bodies the [effect of the] tightening [or tautening] of a spring to one degree of tension, and that of their being set in motion [again] when it releases the sum of their forces, should be the same in accordance with the manner of estimation [of force], and not the sum of the quantities of movement. And I assert that, in this, experiment will work in my favor.245 However, Papin was still not impressed by Leibniz’s arguments, as he made clear in his reply of April 20.246 Solely Leibniz’s thoughts concerning the impact of a ball against two stationary balls at an oblique angle of incidence appeared to him to be cogent. Thus he wrote on this occasion: “I find that it is effectively 244 Cf. pp. 725f. 245 “Deux corps bandant un ressort à un degré de tension, ou estant mis en mouvement lors qu’il s’est debandé la somme de leur forces selon ma maniere d’estimer doit estre la meme, et non la somme des quantités de mouvement. Et je pretends qu’en cela l’experience me favorisera” (p. 726). 246 Cf. A III,7 N. 186, pp. 751f.

July 1696–1698

667

a kind of apriori247 proof and, as for that arising from this position, I assert that I do not see what one could say in reply to it”.248 Four months later then, on August 28, Papin finally entered into the details of the matter.249 He now argued that the two bodies A and C, when they are simultaneously impacted by the body B, are not impacted for as long, and not as forcibly, as when each of them is impacted separately. Each receives a smaller velocity than 2C3C. Also when the collision process takes place in reverse, the course of events would be different to what Leibniz imagined. Papin claimed to be able to prove that, in the case of the simultaneous impact of the two moving bodies A and C against the stationary body B, the entire force would not be transferred but only a portion of it, and that the bodies A and C would continue their movements after the impact and without any change of direction. The velocity of the body B would be greater than the velocity 2BE, but less than 2B1B. Papin was now also convinced that the matter could be decided by a physical experiment, and that he himself would be in a position to carry out such an experiment. Alas, his overwrought situation at that point in time did not allow him the time and leisure to follow this course. His words here were: I am convinced that, if I had the leisure, I could carry out this experiment with enough precision for the decision to be incontestable, but, having as little support as I have, I am not able to resolve to put aside the other matters on which I am working at present.250 Leibniz for his part, in his letter of September 7, now also favored an experimental decision in the matter of the collision or oblique impact of a body against two other bodies at rest, as he too sensed an opportunity of obtaining a submission from Papin on the issue. Thus he wrote: It would however be up to me to prove the point in question by experiment, or by reason, and the way of experiment appears to be the shortest,

247 emphasis by Papin. 248 “Je trouve que c’est effectivement une espece de prevue a priori et pour ce qui est de cet endroit J’avoue que Je ne vois pas ce qu’on peut ŷ répondre” (p. 752). 249 Cf. A III,7 N. 220, pp. 879–881. 250 “Je suis persuadé que, si J’avois du loisir, Je pourrois faire cette experience avec assez d’exactitude pour que la decision en fust incontestable: mais, ayant si peu de secours que J’en ay, Je ne puis me resoudre à quitter les autres choses à quoy Je travaille presentement” (pp. 880f.).

668

Chapter 5

and it is also in that respect that you have expressed your willingness to submit.251 He contradicted Papin’s argumentation however. The force transfer would be independent of whether the moving body B encountered the body C on its own, or the bodies C and A together. The same applied, when the collision process takes place in reverse, that is regarding whether the body A impacts the stationary body B on its own, or simultaneously with the body C. He then expressed his intention of pursuing the experimental approach to complement reason in the following words: I will look for the means to carry out the experiment with the three balls under consideration in order to conclude this controversy, which is rather important. And pending a decision, I consider that the agreement of reason and experiments already undertaken gives me occasion to expect from this success in my favor, in as far as the matter will allow.252 However, in the meantime Papin was having doubts once again about whether the matter could indeed be decided in the short term by means of a physical experiment, and in his letter of October 9, he retracted his previous conviction in the following words: “As I fear that we will not be able to decide the question about compound movements in the short term by means of experiment, I will try once again to support my sentiment with reason”.253 Both the adversaries remained stubborn and, at the end of the year 1698, neither party had budged from its own view of things. Papin maintained at first, in a letter of November 17, that the body B yielded to the two bodies (C and A) faster than to only one of them, and as a consequence offered less resistance, or consumed less force. Both bodies together would lose less force compared to the situation where they individually impacted the body at rest.254 On November 28, Leibniz then countered with the argument that the resistances, just like the velocities, 251 “Il seroit donc à moy de prouver le point dont il s’agit par l’experience, ou par la raison: et la voye de l’experience paroist la plus courte, et c’est celle aussi où vous temoignés estre prest de vous sousmettre” (A III,7 N. 224, p. 892). 252 “Je chercheray les moyens de faire l’experience des trois boules de question pour vuider cette controverse, qui est assez importante. Et en attendant je m’imagine que l’accord des raisons et des experiences deja faites me donne sujet d’en attendre un succes favorable, autant que la matiere le permettra” (p. 892). 253 “Comme Je crains que nous ne puissions pas si tost decider par experience la question sur les mouvements composez, Je vais encor tacher de soutenir mon sentiment par raison” (A III,7 N. 234, p. 914). 254 Cf. A III,7 N. 241, p. 933.

July 1696–1698

669

are geometrically compounded, and could be resolved into components, or as regards the thought experiment under discussion, he wrote: “It is true that the body B with regard to the diagonal cedes faster when it is impacted simultaneously by A and C, but as it only resists each of them, in proportion to the sides, it does not resist them any less for that”.255 In the final communication of the year 1698, on December 11, Papin maintained that while the body C impacted the body B with reduced force (because of the skew angle of inclination), the reaction of B to C is similarly reduced which leads to the same result as if the collision had taken place centrally, and with the velocity represented by the diagonal. Thus he wrote: I reply to this that, if the obliquity or skewness causes B to move away less quickly from the place where C came from, it will also cause C to act less strongly against B and that, as a consequence, the reaction of B against C is also less strong because it is oblique; and accordingly this comes down to the same thing as if B had moved away directly with all the speed being represented by the diagonal.256 Besides the dispute about the correct measure of force, the discussion about the concept of ‘action’ (“actio”) was an important issue in Leibniz’s correspondence with Papin from the summer of 1696. The starting point was a proposition formulated by Leibniz at the end of his letter of August 20, 1696. There he presented the following assertion, regarding a body moving uniformly without experiencing gravity, or resistance, through a space of a league, or a mile, during time spans of one, two or three hours, in the following words: “To traverse a league in one hour is to effectuate the double (triple, etc.) in value, of that which the same mobile would effectuate in traversing a league in two (three, etc.) hours”.257 Then, at the end of his letter of November 11, 1696, he stated his proposition more precisely. The basic statement was that a body has double 255 “Il est vray que le corps B par rapport à la diagonale cede plus viste quand il est frappé par A et C à la fois, mais comme il ne leur resiste à chacun, que selon les costés, il ne leur en resiste pas moins pour cela” (A III,7 N. 245, p. 949). 256 “J’ay à répondre à cela que, si l’obliquité fait que B s’eloigne moins vîte de la plage d’où vient C, elle fait aussi que C agit moins fortemt sur B et que, par consequent, la reaction de B sur C est aussi moins forte puis que ell’est oblique: et ainsi cela revient à la même chose que si B s’eloignoit directement avec tout la vîtesse de la diagonale” (A III,7 N. 247, pp, 954f.). 257 “parcourir une lieue dans une heure est faire la double (triple, etc.) en valeur, de ce que le même mobile feroit en parcourant une lieue dans deux (trois, etc.) heures” (A III,7 N. 25, p. 96).

670

Chapter 5

the action of another body, if (or when) it covers a certain distance in half the time taken by the other. Thus he wrote: In saying that to traverse a league in one hour is double that of traversing a league in two hours, I understand that the path is without resistance. I also do not speak either of velocity, or of force, but rather of action. For I take it as agreed that the one which acts uniformly, exercises more action when it continues to act for a longer time. I also suppose that two bodies A and B are equal and moved uniformly, and [with both] traversing the same path, the one which does so in less time has exercised a greater action. That being stated, I ask you if you do not agree that it is exactly double the action if the body completes the same path in half the time? [And to this he added:] If you continue to be in agreement, I could construct a certain demonstration regarding the above.258 However, in his reply of November 15, Papin doubted the very cogency, or validity, of the concept of action. Citing the maxim “omne agens agendo repatitur”, he insisted that there is no action in nature without re-action. Since the body encounters nothing against which it could act, or through which it could be changed, the process represented nothing other than a continuing state. And so he wrote: Concerning your question regarding the action of bodies which do not encounter any resistance, it is necessary that I confess to you, Sir, that I am not able to embrace your sentiment, and that I hold the following axiom to be incontestable viz. omne agens agendo repatitur [.] Supposing therefore that a body moves without encountering anything to act against and from which it is also possible for it to experience an alteration, I say that such a body does not act at all but that it simply persists in the state in which it is.259 258 “En disant que parcourir une lieu dans une heure est le double du parcourir une lieu dans deux heures, j’entends que le chemin est sans resistance, je ne parle aussi ny de vistesse, ny de force, mais d’action. Car je prends pour accordé que celuy qui agit uniformement, exerce plus d’action lors qu’il continue plus long temps d’agir; je suppose aussi que deux corps A et B estant egaux et mûs uniformement, et parcourant le même chemin celuy qui l’a parcouru en moins de temps a exercé une plus grande action: cela posé je demande si vous n’accordés pas que c’est justement le double de l’action, lors que le corps a fait le même chemin dans la moitié du temps? Si vous en demeurés d’accord je puis bastir quelque demonstration là dessus” (A III,7 N. 44, pp. 170f.). 259 “Pour ce qui est de vostre question touchant l’action des corps qui ne rencontrent point de resistence il faut que Je Vous avoue, Monsieur, que Je ne puis entrer dans vostre sentiment,

July 1696–1698

671

There then followed, in Leibniz’s letter of November 19, a more precise specification of the concept of action from his side, namely that action exists by virtue of the movement of a body. If a body moves more quickly, it covers a greater distance in a given time and its action increases. In the case of constant velocity, the action also increases if the body continues its movement over a longer period. For him, movement in itself represented a kind of action. And so he wrote: “Accordingly, when a body moves in a medium that is extremely tenuous, which hardly resists it at all, or when it turns about its center, and generally when it moves, I call this Action, such that the movement is, according to me, a kind of action”.260 However, he was prepared to accept a different terminology, which might appeal to Papin, and so he continued: “If you do not wish that one accordingly uses the word: action,261 do take another one as you please, such as change (mutatio), since there is at least a change of place”.262 Papin then reacted with skepticism, on November 25. He was unable to comprehend Leibniz’s distinction between force and action. And besides he could not identify Leibniz’s change of location (“changement de lieu”) with the distance covered by a body. Thus he wrote on this occasion: As regards what you said, that the body which moves fast changes location even more, I do not believe that this is for sure, since it can very easily happen that the slowest body will suffer [or undergo] more change of situation, in relation to the other bodies, than the faster body will suffer [or undergo]. For this change of situation depends just as well on the movement of the other bodies as on that which we are examining. All that one can say therefore, in my sense, is that the body which appears to us to have the greater velocity also appears to us to traverse the greater

et que Je tiens cet axiome pour incontestable omne agens agendo repatitur supposant donc qu’un corps se meut sans rencontrer rien sur quoy agir et de qui il puisse aussi recevoir de l’alteration, Je dis qu’un tel corps n’agit point mais qu’il persiste seulement dans l’estat où il est” (A III,7 N. 45, p. 173). 260 “Ainsu quand un corps va dans un milieu extremement mince, qui ne luy resiste presque point, ou quand il tourne à l’entour de son centre, et generalement quand il se meut j’appelle cela Action, de sorte que le mouvement est, chez moy une espece d’action” (A III,7 N. 48, p. 182). 261 emphasis by Leibniz. 262 “Si vous ne voulés pas qu’on se serve ainsi du mot: action, prenez un autre tel qu’il vous plaira, comme changement (mutationem), puisqu’il y a au moins changement de lieu” (p. 182).

672

Chapter 5

path, but, as that is done without any effort, I believe it is not correct to say that such a body exerts its force.263 Leibniz responded, on December 24, expressing the view that a force also manifests itself where there is no resistance to be overcome. This would be the case if the force of a body acted on its own mass, as for example when it rotates around its axis. This exercise of force is conservative just like that of the universe as a whole. The action of a body meant for Leibniz the succession of the states of a body during a change of location. Papin’s assertion, that the change of location also depends on the movements of other bodies, was affirmed by Leibniz, but with the caveat that in each of these bodies a part of the total change is to be found. Here he wrote then: As regards the action in movement, I believe that one could say that the force manifests itself also even then when it does not encounter any obstacle, and in conserving itself, that is when it only acts on its own body, like when a globe rotates around its own axis, and this exercise of force is conservative, as is in effect that of the universe as a whole. But without speaking of that I have given, as it were, that which I called action here, [namely] that successive state which is in the body when it changes location or situation. You say, Sir, that this change of situation depends just as well on the movement of the other bodies as on that which we are examining. Agreed! (I say to you) but there will also always truly be some part of it in this body, as in the other bodies to which you attribute it, each one contributing for its part to the total change.264 263 “pour ce qui est de ce que Vous dittes que le corps qui se meut viste change davantage de lieu, Je ne crois pas que ce soit une chose seure: puis qu’il peut fort bien arriver que le corps le plus lent souffrira plus de changement de situation entre les autres corps que n’en souffrira le corps le plus viste: car ce changement de situation depend aussi bien du movement des autres corps que celuy que nous examinons. Tout ce qu’on peut donc dire, à mon sens, c’est que le corps qui nous paroist avoir le plus de vitesse nous paroist aussi parcourir le plus de chemin: mais, comme cela se fait sans aucune effort, Je crois que c’est parler improprement que de dire qu’un tel corps exerce sa force” (A III,7 N. 52, p. 191). 264 “Quant à l’action dans le mouvement, je crois qu’on peut dire que la force s’exerce encor lors meme qu’elle ne trouve point d’obstacle, et en se conservant, sçavoir lors qu’elle ne s’exerce que sur son propre corps, comme lors qu’un globe tourne à l’entour de son axe, et cet exercice de la force est conservativ; comme est effectivement celuy de l’univers tout entier: mais sans parler de cela j’avois donné à entendre, que j’appellois action icy cet estat successiv qui est dans le corps lors qu’il change de lieu ou de situation. Vous dites Monsieur que ce changement de situation depend aussi bien du mouvement des autres corps que de celuy que nous examinons. Soit, (vous diray je) mais il y en a tousjours

July 1696–1698

673

While Papin attributed an intrinsic movement to a body, Leibniz wanted to assign to it a true action, or change, determined both by its celerity or promptitude (“intension” viz. temporal change) and the duration or the extension of its movement (“extension” viz. spatial change). Thus, he continued: “Accordingly, if you attribute to a certain body a veritable movement, by designation truly intrinsic, I will also attribute to it a veritable action or change which I accordingly estimate both by its intension or promptitude, as by its extension or duration”.265 Papin, in his reply of January 14, 1697, then argued that, in absolute terms, all bodies with the same mass possess the same force. A body at rest would exert the same force as a moving body in the sense that it would be in a position to offer the same resistance. A moving body, which is in motion without resistance and without consuming force, operates with the same ease as a body at rest. He wrote accordingly: I tell you, Sir, that, speaking absolutely, I believe that all bodies having the same mass have equality of force, because, in as much as the movement gives them force towards a certain side, it detracts it from them towards the opposite side. Accordingly a body at rest exercises as much force as a moving body, that is to say it maintains itself in a position to offer as much resistance to bodies which are capable of striking it on all sides, just as a moving body is capable of doing.266 Papin concluded his consideration of the topic action with an offer to continue their discussion of the issues involved. Thus, he wrote: “I approve, Sir, that which you ask of me and if only that is required to establish your demonstrations you can commence with them whenever you like”.267

veritablement en luy aussi bien que dans les autres corps à qui vous en attribués, chacun contribuant du sien au changement total” (A III,7 N. 58, p. 224). 265 “Ainsi si vous attribués un veritable mouvement à quelque corps de nominatione vera intrinseca je luy attribuera aussi une veritable action ou changement que j’estimeray tant par son intension ou promtitude, que par son extension ou durée” (p. 224). 266 “Je Vous diray, Monsieur, qu’absolument parlant, Je crois que tous les corps de mesme masse ont egalement de force: parce que, autant que le mouvement leur donne de force vers un certain costé, autant il leur en oste vers le costé opposé: ainsi un corps en repos exerce autant de force qu’un corps en mouvement, c’est à dire se maintient en estat de faire autant de resistence aux corps qui peuvent le venir frapper de tous costez, comme en peut faire un corps en mouvement” (A III,7 N. 66, p. 262). 267 “Je Vous accorde, Monsieur, ce que Vous me demandez et s’il ne faut que cela pour fonder vos demonstrations Vous pouvez les commencer quand il Vous plairra” (p. 262).

674

Chapter 5

The exchange of ideas concerning action was however interrupted for an entire year, before Leibniz returned to the matter once again early in 1698. On January 26 of that year, he could announce a new insight into the proportionality between action and his measure of force. He emphasized, however, that he was willing to share his thoughts on the matter only with those with whom he had found approval for his views, writing as follows: And this consideration shows that the true quantity that one should measure in the movement, or, as I call it, the quantity of the Action,268 is not that which one commonly calls the quantity of movement, but just something proportional to the force understood in my sense. But I communicate this thought only to those with whom my other arguments have found a certain resonance.269 Only three months later, on April 24  – after a certain degree of agreement had been achieved with Papin regarding the composition of mechanical movements  – did Leibniz finally present his proposition for the uniform motion of a body, namely that action is proportional to the product of path and velocity, and thus also to that of time and the square of the velocity. And so, in a preparatory sketch for the letter sent to Papin,270 he presented the following two demonstrations formulated using syllogistic reasoning: I have two demonstrations in which I establish that the action, exerted over a given time interval but involving a doubling of the velocity, is quadrupled. The prior271 [or first] demonstration is as follows: 1) The action involved in covering two leagues in two hours is double the action involved in covering one league in one hour. 2) The action involved in covering one league in one hour is double the action involved in covering one league in two hours.

268 emphasis by Leibniz. 269 “Et cette consideration fait voir que la veritable quantité qu’on doit estimer dans le mouvement, ou, comme je l’appelle, la quantité de l’Action, n’est pas ce qu’on appelle volgairement la quantité de mouvement, mais justement quelque chose de proportionnel à la force prise en mon sens. Mais je ne communique cette meditation qu’à ceux où mes autres raisons ont trouvé ingrés” (A III,7 N. 177, p. 714). 270 Cf. A III,7 N. 187, pp. 752–754, and the attachment N. 188, pp. 754–757. 271 emphasis by Leibniz.

July 1696–1698

675

3)

Therefore the action involved in covering two leagues in two hours is quadruple the action involved in covering one league in two hours. Thus the posterior [or second] demonstration holds that 1) space stands in a proportion composed of times and velocities. 2) Action stands in a proportion composed of spaces and velocities. 3) Therefore action stands in a proportion composed of the simple time and the duplicates of the velocities.272 From his conservation law for force  – but of course not from that of Papin and the Cartesians – Leibniz then concluded that the quantity of action in the world was conserved.273 In his belated reply, on August 4, Papin rejected Leibniz’s proposition regarding the uniform motion of a body on the grounds that that, which he had always contested, was once again being postulated here. As far as he was concerned, the resistance to be overcome had to be measured, and this was not necessarily proportional to the velocity. Thus he wrote: I find, Sir, that it is most subtle but, to be honest, it does not appear to me to be of the same force as the other, for when you present as a principle that actions are in a proportion composed of traversed spaces and of the velocities with which they are traversed, it appears to me that it is begging the question. Since I have always contested that with you, in asserting that the action should be measured by the quantity of resistance which is overcome, and that it often happens that one overcomes much more

272 “Duas habeo demonstrationes, quibus conficio actionem eodem tempore dupla velocitate exercitam esse quadruplam. prior demonstratio haec est: 1) Actio absolvens duas leucas duabus horis est duplam actionis absolventis unam leucam una hora. 2) Actio absolvens unam leucam una hora est duplum actionis absolventis unam leucam duabus horis 3) Ergo Actio absolvens duas leucas duabus horis est quadruplum actionis absolventis unam leucam duabus horis posterior demonstratio ita habet 1) spatium est in ratione composita temporum et velocitatum 2) Actio est in ratione composita spatiorum et velocitatum 3) Ergo Actio est in ratione composita ex simplice temporum et duplicata velocitatum” (pp. 754f.). 273 “Itaque secundum meam quantitatis virium conservandarum aestimationem aequalis semper quantitas actionis servatur in mundo” (p. 756).

676

Chapter 5

resistance on traversing a certain space slowly rather than traversing it more quickly.274 To this Papin added that Leibniz needed to prove this second assertion, or premise, before his “posterior demonstratio” could have validity, writing as follows: “It appears to me that before your demonstration could be considered valid, it would be necessary to have proved your assertion (2) which I have cited”.275 Leibniz reacted almost immediately, on August 8, with a formal counterargument that was again divided into articles like in a legal document.276 He considered a medium without resistance, and free of gravity, in which a body is transported from one location to another. By virtue of its natural inertia it offers resistance to the movement. Then the action of the body is taken to be proportional to the traversed path and to the velocity. As a result, actions over equal time intervals (“actions contemporaines”) are proportional to the squares of the velocities.277 All other assumptions as, for example, that the actions are proportional to the velocities and to the times, or to the traversed paths and to the reciprocals of the times, would lead inevitably to absurdities. Solely through his measure of force, in combination with his principle of action, could such contradictions be ruled out. The error in the common (or Cartesian) interpretation lay, in Leibniz’s view, in the confusion of quantity of action with quantity of movement. And so he wrote on this occasion: It is also much more reasonable to say that the actions stand in a proportion composed of spaces and velocities, rather than to take any other reasonable composition. In saying, for example, that the actions stand in a proportion composed of the velocities and the times, one falls into an absurdity. For the velocities themselves having without doubt a proportion composed of the immediate spaces, and of the reciprocal of the times, it follows that the actions would be in proportion to the traversed spaces. And so it would be of no import for the magnitude of the action 274 “Je trouve, Monsieur, qu’il est fort subtil mais, à dire le vray, il ne me paroist pas de la méme force que l’autre: car quand Vous posez comme un Principe que actiones sunt in ratione composita spatiorum percursorum et velocitatum quibus percursa sunt il me semble que c’est supposer ce qui est en question: puisque je Vous ay tousjours contesté cela, en soutenant que l’action se doibt mesurer par la quantité de resistance qu’on surmonte, et qu’il arrive souvent qu’on surmonte bien plus de resistance en parcourant un certain espace lentement qu’en le parcourant plus vite” (A III,7 N. 214, p. 851). 275 “Il me semble qu’avant que vôtre demonstration puisse passer pour valable il faudroit avoir prouvé votre (2) assertion que je viens de citer” (p. 851). 276 Cf. A III,7 N. 216, pp. 862–865. 277 Cf. p. 863.

July 1696–1698

677

with what velocity the mobile undertakes its course, which is absurd. But this absurdity is obviated using my estimation [of the force], where the actions stand in a proportion composed of the simple times and the duplicate velocities. If someone were to say that the actions stand in a proportion composed of the direct [or simple] velocities and the reciprocal of the times, he would fall into another absurdity, for the action would then be greater in proportion to the brevity of its duration at the same velocity. Finally, saying that the actions stand in a proportion composed of the direct space (or traversed path) and the reciprocal of the times, something which is more simple and appears accordingly to be the most reasonable, one falls again into absurdity. For the actions would simply be as the velocities, and it would not matter at all what duration they would have, and so a short action of a uniform velocity would be just as large as if it had lasted for a longer time at the same velocity and, as a consequence, the outcome would be equal above all because the same action is redoubled by the duration. One sees from this that, regardless of how one spins it, one is obliged to return to my estimation [of the force].278 In this letter of August 8, Leibniz also verified his measure of action in detail in the following manner. It is assumed that the action involved in traversing two feet, or units of path, in two scrupels (viz. sixtieth parts of a minute, or seconds) is double that involved in traversing a single unit in one second, and that the latter is twice as great as that for the passage through one unit of path in 278 “Il est bien plus raisonnable aussi de dire que les actions sont en raison composée des espaces et des vistesses, que de prendre toute autre composition de raisons. En disant, par exemple, que les actions sont en raison composée des velocités et des temps; on tombe dans l’absurdité. Car les velocités estant sans doute elles mêmes en raison composée de la directe des espaces, et de la reciproque des temps, il s’ensuit que les actions seroient comme les espaces parcourus: Ainsi il n’importeroit point pour la grandeur de l’action avec quelle vistesse le mobile fournisse sa carriere, ce qui est absurde. Mais cette absurdité s’evite dans mon estime, où les actions sont en raison composée de la simple des temps, et de la doublée des vistesses. Si quelqu’un disoit que les actions sont en raison composée de la directe des velocites, et de la reciproque des temps, il tomberoit dans une autre absurdité; car l’action seroit d’autant plus grande, qu’elle dureroit moins avec la meme velocité. Enfin disant que les actions sont en raison composée de la directe des espaces et de la reciproque des temps ce qui est plus simple, et paroist d’abord ainsi le plus raisonnable; on tombe encor dans l’absurdité. Car les actions seroient simplement comme les vistesses, et il n’importeroit point quelle durée elles auroient, ainsi une action courte d’une velocité uniforme seroit aussi grande que si elle duroit davantage avec la même vistesse et par consequent la partie seroit égale au tout puisque la même action est redoublée par la durée. On voit par là que de quelque maniere qu’on se tourne on sera obligé de revenir à mon estime” (pp. 864f.).

678

Chapter 5

two seconds. From this, Leibniz concluded that the action involved in traversing two units of path in two seconds is four times that involved in the passage through one unit of path in two seconds. Thus he wrote that: In the uniform motion of the same body and putting aside gravitation and extrinsic resistance 1)  The action involved in covering two feet in two scrupels or seconds is double the action involved in covering one foot in one scruple or second. This proposition is apparent, for the prior action is precisely repeated once again in the posterior action. 2)  The action involved in covering one foot in one second is double the action involved in covering one foot in two seconds. This I assume as an axiom, as I already said, or [it] is to be introduced as a worthy proposition. 3)  Therefore the action involved in covering two feet in two scrupels or seconds is quadruple the action involved in covering one foot in two scrupels or seconds.279 Only with the proviso that with action no force is consumed, was Papin willing, in his letter of October 9, to concur with Leibniz’s syllogistic reasoning, and the proof given in the letter of August 8. He recalled once again that for him action arose solely through the overcoming of resistance. From this Papin concluded that he himself and Leibniz were employing different definitions of the concept of action. For his concept of action Leibniz’s arguments had no validity. Having cited both the major and the minor premises, and the conclusion given by Leibniz, he replied as follows: I respond: if Action be understood as not consuming force, I concede the whole argument. If, however, Action is understood as consuming force, 279 “in motu uniformi ejusdem corporis seposita gravitate et extrinseca resistentia 1) Actio absolvens duos pedes duobus scrupulis secundis est duplum actionis absolventis unum pedem uno scrupulo secundo Haec propositio manifesta est, nam posterior actio praecise repetitur adhuc semel in priore 2) Actio absolvens unum pedem uno secundo est duplum actionis absolventis unum pedem duobus secundis Hoc assumo ut axioma, uti jam dixi, seu ut propositionem dignam admitti 3) Ergo Actio absolvens duos pedes duobus scrupulis secundis, est quadruplum actionis absolventis unum pedem duobus scrupulis secundis” (p. 864).

July 1696–1698

679

then I deny both the major and minor premises. For indeed, the quantity of this latter action ought to be measured neither by the quantity of traversed space, nor by the time over which it continues, but rather by the sole means of the quantity of resistance which is overcome.280 In fact, in his letter of September 7 to Papin, Leibniz had also differentiated between two forms of action, namely between actions in which the acting force is conserved, and actions in which this acting force is consumed, which he designated as “actions violentes ou contingentes”. His main focus of attention was the first type, which he wished to call formal action because of its essential connection with force. This action was in fact equal to the product of force and time. Whereas he also had had thoughts about the second type of action, he had found the a priori nature of the formal action to be of fundamental importance. Both forms of action would nonetheless lead to the same measure of force. On that occasion he had written: I have already previously made use of the assessment of actions which meet with resistance, but I judge this estimation of the force by the formal actions to be more profound and more apriori, everything having the obligation to be estimated at its source. And the source of the power[,] capable of producing actions of the second type, is the faculty of being able to produce the formal actions or those of the first species. And with the two manners of estimating the actions allowing each other the same quantity of force, be it that one estimates the force by its formal or natural action, [viz.] that which accompanies it as long as it perseveres, or be it that one estimates it by the violent or contingent actions, which consume it, one arrives at the same conclusion which is that the forces of two equal bodies are in the duplicate proportion of the velocities.281 280 “Respondeo: si intelligatur Actio non consumens vires, concedo totum argumentum: si vero intelligatur Actio consumens vires, et majorem et minorem nego: hujus enim posterioris actionis quantitas neque ex quantitate spatii decursi, neque ex tempore per quod continuatur, aestimari debet; sed solum modo ex quantitate resistentiae quae vincitur” (A III,7 N. 234, p. 914). 281 “Je me suis servi deja auparavant de l’estime des actions qui trouvent de la resistence, mais je juge cette estime de la force par les actions formelles plus profonde et plus a priori, chaque chose devant estre estimée dans sa source; et la source de la puissance capable de produire des actions de la seconde espece, est la faculté de produire les actions formelles ou de l’espece premiere. Et les deux manieres d’estimer les actions s’accordent à donner une même quantité de la force soit qu’on estime la force par son action formelle ou naturelle, qui l’accompagne tant qu’elle persevere, ou qu’on l’estime par des actions

680

Chapter 5

Then, in his letter of October 9, Papin actually contested the view that the existence of a force always implied an action. He believed that all bodies with the same volume have the same force, and indeed independently of whether they are in motion or not. His words on this occasion were: I therefore remark that you are putting forward as an incontestable matter that there, where there is action of the first species, there is force, and vice versa.282 And nonetheless, Sir, I contest the second part of this assertion, for, as I have told you previously, I believe that, in absolute terms, all bodies having the same volume have an equality of force, be it that they are in motion[,] which is your first species of action, or be it that they are not.283 In the PS to his reply, in the third week of October, Leibniz rejected Papin’s claim, and once again he referred to the inertia that a body in motion must overcome, and for which force is required. This was equal to the resistance it has to overcome. The resistance, for its part, was nothing other than a repugnance, or an aversion, to the production of such a force. Leibniz distinguished between an absolute resistance, which was involved here, and a relative resistance, writing that: This resistance is only the inertia or the repugnance to the production of a force. It is true that besides the absolute resistance, of which I speak here, there is another directional one blended with it. But they are not mutually confusing or confounding, and nature renders to each that which belongs to it.284

violentes ou contingentes, qui la consument; on vient à la meme conclusion qui est, que les forces de deux corps egaux sont en raison doublées des velocités” (A III,7 N. 224, p. 891). 282 emphasis by Papin. 283 “Je remarque donc que Vous avancez comme une chose incontestable que là où il ŷ a action de la premiere espece il ŷ a de la force; et vice versa: et neantmoins, Monsieur, Je conteste la seconde partie de cette assertion: car, comme Je vous l’ay dit autresfois, Je crois que, à parler absolument, tous les corps de mesme volume ont egalement de force soit qu’ils soient en mouvement qui est vostre premiere espece d’action; soit qu’ils n’ŷ soient pas” (note 280 above, p. 914). 284 “cette resistence n’est que l’inertie ou la repugnance à la production d’une force. Il est vray qu’outre la resistence absoluë, dont je parle icy, il y a une autre de direction qui s’y mêle; mais elles ne se confondent point, et la nature rend à chacune ce qui luy appartient” (A III,7 N. 237, p. 924).

July 1696–1698

681

In fact, the distinction between absolute and relative made here corresponded to Leibniz’s differentiation elsewhere between absolute and relative forms of force, action and velocity. And so, regarding the forms of action, he added here: “And I distinguish exactly [between] these resistances, as I distinguished [between] the forces formerly,285 and [between] the actions presently”.286 Then, on November 17, Papin withdrew his endorsement of the designation of action as a resistance-free movement of a body.287 He negated that the quantity of action is determined by the time and the path traversed. Furthermore, he contested Leibniz’s claim that a body in motion continually acts on itself. And in addition, Leibniz’s distinction between force and inertia had also become incomprehensible for him. Replying on November 28, Leibniz then tried once again to find a common vantage point.288 Even if his opponent was not willing to designate the change of location of a body as action, it would be sufficient if he would accept that an alteration was involved. For, since location and time were being changed, the alteration would also have to be measured by location and time. Papin’s measure of force (the quantity of motion) was, in the last analysis, likewise rooted in space and time, and this ought also to apply for his (Leibniz’s) measure of force. Finally – in this last letter of the year 1698 to Papin – Leibniz referred to the correspondent’s remarks concerning inertia, and he elaborated his own position once again. Inertia would always exist in a body whether it was in motion or not, and its magnitude would depend on the quantity of matter involved. Force, on the other hand, existed only if the body was in motion, and it varied with the velocity. Inertia was to be counted among the passive abilities, or acquirements (“potentia”), of a body whereas, on the other hand, force belonged to its active abilities, or acquirements. At the end of 1698 then, the dispute was once again reduced to the conflicting definitions of force or in Leibniz’s words: When you estimate the force by the quantity of movement, you are only taking account of location and time, or indeed of movement in itself, without introducing the resistance of the medium for, in your view, the forces stand in a proportion composed of the masses and of the velocities of movement or of the change of location. But you do not wish at all that that which was granted to you, and to all the others, be also allowed to 285 Cf. for example, A III,6 N. 213, pp. 699f. 286 “Et j’ay distingué exactement ces resistences, comme j’ay distingué les forces autres fois; et les actions presentement” (note 284, p. 924). 287 Cf. A III,7 N. 241, pp. 932f. 288 Cf. A III,7 N. 245, pp. 947–950.

682

Chapter 5

me. If you would like to act with justice, you should at least at the same time also retract your opinion of the estimation of force by the quantity of movement, and thereafter we could see what has to be done for the rest of the matter.289 In his final letter of 1698 to Leibniz, on December 11, Papin also remained totally intransigent as regards his understanding of action, and his uncompromising adherence to the Cartesian definition of force, citing the same maxim as in his letter of November 15, 1696,290 namely “omne agens agendo repatitur”, and insisting that there is no action in nature without re-action, he expressed himself in the following words: I would indeed say, Sir, that I do not believe at all in changing the ordinary manner of speaking, because that which I say is founded on an age-old axiom, omne agens agendo repatitur, but on the contrary I believe that to call Action a movement that does not surmount any resistance is a novelty regarding which one would have trouble producing some example from any author whatsoever.291 Thus the year 1698 ended with both parties in the dispute entrenched once again in their starting positions. 7

Physics: Optics

In 1697 and 1698, the work of the Delft resident and microscopist Antoni van Leeuwenhoek continued to attract Leibniz’s interest, and microscopy became 289 “Lors que vous estimiés la force par la quantité du mouvement, vous n’aviés egard qu’au lieu et au temps, ou bien au mouvement en luy même, sans y meler la resistance du milieu car les forces chez vous estoient en raison composée des masses et des vistesses du mouvement ou du changement de place. Mais vous ne voulés point que ce qui estoit permis à vous et à tous les autres, le soit aussi à moy, si vous vouliés agir avec justice, vous deviés au moins en meme temps retracter aussi vostre opinion de l’estime de la force par la quantité du mouvement, et apres cela nous verrions ce qu’il y auroit à faire pour le reste” (pp. 948f.). 290 Cf. A III,7 N. 45, p. 173. 291 “Je diray donc, Monsieur, que Je ne crois point changer la façon de parler ordinaire: puisque ce que Je dis est fondé sur un axiome receu de toute ancienneté, omne agens agendo repatitur, mais au contraire Je crois que d’appeller Action un mouvement qui ne surmonte aucune resistence c’est une nouveauté dont on auroit peine à produire quelque exemple d’aucun auteur” (A III,7 N. 247, p. 953).

July 1696–1698

683

the main focus for him in optics. Leibniz now used his correspondence with Hendrik van Bleiswijk (or Bleiswyck) – the influential burgomaster of Delft – to revive his contact with Leeuwenhoek. In a letter to Bleiswijk on May 7, 1697, he outlined his interest in Leeuwenhoek and his work.292 He pleaded for measures to be taken for the preservation of Leeuwenhoek’s methods and instruments for posterity, by arranging timely assistance for the master by apprentices and students. In this context, Leibniz distinguished between, on the one hand, great discoverers or innovators – like Christiaan Huygens and Jan Hudde  – who excelled by virtue of their ingeniousness and intellectual prowess and, on the other hand, great observers like Leeuwenhoek, who stood out because of their special abilities and their assiduity. Leibniz saw the latter category as being subordinate, or ancillary, to the former, but he stressed in this connection that he appreciated an observer (“Observator”) like Leeuwenhoek more than a painter of the Italian Renaissance like Raphael of Urbino (i.e. Raffaello Sanzio da Urbino, 1483–1520). Half a year later, on November 7, 1697, Bleiswijk answered Leibniz’s letter.293 From this communication, it is apparent that Bleiswijk agreed with and supported Leibniz’s recommendation, and that he had even shown Leibniz’s letter to Leeuwenhoek. In Leibniz’s following letter to the burgomaster, on January 3, 1698, his admiration for Leeuwenhoek once again found expression in a comparison with Raphael of Urbino, Michelangelo and the “Oracle delphique” Hugo Grotius (1583–1645). Leibniz saw great benefits for medicine coming from an increased commitment to microscopy and microscopic observation. Thus he wrote on this occasion: As regards Mr Leeuwenhoeck I admit that there are certain grounds for keeping secret his manner of observation, which merits being appreciated. But if the public were to give him encouragements by putting him in a position to obtain assistance from students, he would be greatly mistaken if he continued to make difficulties; nothing could be more advantageous for him. Because of the fact that, by such means, he could make ten observations in place of one, one could discover treasures of knowledge which otherwise would perhaps still remain unknown after a long time, and he would have so much more glory while remaining silent in the face of a thousand opponents. Furthermore, this kind of discovery could be of service even in medicine and contribute some day to the relief of humans. Accordingly Christian charity enters here and 292 Cf. A I,14 N. 90, pp. 152f. 293 Cf. A I,14 N. 388, p. 668.

684

Chapter 5

there will be merit in pursuing it. For me, as one who esteems these works infinitely more than those of a Raphael of Urbino or of a Michelangelo, I can believe that Delft could become a place of honor in the republic of letters, and that this beautiful town, however renowned it is already by virtue of its ‘Delphic Oracle’, that is to say of the incomparable Grotius, would receive a significant addition to its glory while contributing to a considerable elucidation of the secrets of nature.294 From Bleiswijk’s reply of February 17, 1698, it is evident that Leibniz was planning a journey to Holland and the Netherlands. Bleiswijk had once again forwarded Leibniz’s letter to Leeuwenhoek in order to reinforce the effort to persuade him to work for the conservation for posterity of his secret observational methods. However, the letter also reveals that Leeuwenhoek had taken appropriate measures in this respect himself. Thus Bleiswijk wrote: I learned with much pleasure … that you plan to make a tour in Holland, and in the Netherlands … I would have the honor in the event … to take you to our Mr Leeuwenhouck to whom I forwarded your letter, with which he was very pleased and particularly satisfied with the tributes which you had the goodness to pay him. However[,] as regards your exhortation for him to take some students in order to instruct them in his secret method of observation I also added mine, but he once again could not resolve to do that, and all that I could obtain from him was the information that he will bequeath his method in written form, so that posterity will be able to avail of it.295 294 “Pour ce qui est de Monsieur Leeuwenhoeck j’avoue qu’il a quelque sujet de faire un secret de sa maniere d’observer, qui merite d’estre estimée. Mais si le public luy donne des encouragemens pour estre en estat de se faire aider par des eleves, il auroit grand tort s’il continuoit de faire le difficile; rien ne luy pouvant estre plus avantageux. Puisque par ce moyen il fera dix observations pour une[,] on decouvrira des tresors de connoissances qui peutestre sans cela demeureroient inconnus encor pour long temps et il en aura d’autant plus de gloire fermant la bouche à mille contredisans; outre que ces sortes de decouvertes pourront servir meme dans la medecine, et contribuer un jour au soulagement des hommes. Ainsi la charité chrestienne y entre et il y aura du merite à les pousser. Pour moy qui estime ces travaux infiniment au dessus de ceux d’un Raphael d’Urbin, ou d’un Michel Ange je croirois que Delpht s’en pourroit faire un point d’honneur dans la republique des lettres, et que cette belle ville quelque celebre qu’elle soit déja par son Oracle delphique, c’est à dire par l’incomparable Grotius, recevroit un accroissement notable de sa gloire en contribuant à un éclaircissement considerable des secrets de la nature” (A I,15 N. 120, p. 155). 295 “J’ay appris avec beaucoup de joye … que vous avez dessein de faire un tour en Hollande, et aux Pays Bas  … j’auray l’honneur en ce temps  … de vous mener ches nostre Mons.

July 1696–1698

685

In a letter to Bleiswijk on January 6, 1699, Leibniz continued to advocate an effort for the conservation of Leeuwenhoek’s observations, and observational methods, including the granting of a pension to him by the Dutch republic, which would serve both for the advancement of science and the honor and glory of the town of Delft. Thus, he wrote the following lines to the burgomaster: As for your Mr Leeuwenhoek, whom I consider to be a luminary of your town, I admit that there are grounds for keeping his methods of observation secret, although the Republic is not supporting him as it should. But if one were to give him a deserved pension and put young people at his disposal, suitable for disburdening him in his experiments, also because he on his own is not able to see and examine an infinity of things which he could have observed with the help of others using his method, I hold that he [would be] obliged to do so, and if he really loves the public good, as an honest person should do … [then] in this case, Sir, it would be up to your Republic to bring about order in the matter. Forgive me for speaking in this way, it is only for the advancement of the sciences, and on a subject which is pivotal for the glory of your town … His offer to bequeath his method in written form is not sufficient.296 8

Power Technology

By the beginning of the 30-month period under consideration (from July 1696 to the end of 1698), the second period of Leibniz’s involvement in mining in the Leeuwenhouck, auquel j’ay communiqué vostre lettre, dont il estoit fort aise, et particulierement satisfait des Eloges que vous avez la bonté de lui donner, mais pour ce que regarde vostre exhortation, pour prendre quelque[s] Elévez, pour leur apprendre sa secrette methode d’observer, j’ay aussi adjouté la mienne, il ne pouvoit encore se resoudre pour cela, et tout ce que j’ay pu obtenir de lui, estoit, qu’il laissera par escrit cette methode, afin que la posterité s’en pourra servir” (A I,15 N. 223, p. 332). 296 “Pour vostre M. Leeuwenhoek que je considere comme une lumiere de vostre ville; j’avoue qu’il a raison de tenir ses manieres d’observer secrets, tant que la Republique ne l’aide point comme il faut. Mais si on luy donnoit une honneste pension, et luy entretenoit des jeunes gens, propres à le soulager dans les experiences, puisqu’aussi lui seul ne peut voir et examiner une infinité de choses, qu’il pourroit faire observer aux autres par sa methode; je tiens qu’il y est obligé; et s’il aime veritablement le bien public, comme doit faire un honneste homme … En ce cas, ce seroit Mons. à vostre Republique d’y mettre ordre. Pardonnés moy que je parle ainsi, ce n’est que pour l’avancement des Sciences, et dans un Sujet, qui tourneroit à la gloire de vostre ville. … Son offer de laisser la Methode par ecrit, ne suffit pas” (A I,16 N. 260, pp. 403f.).

686

Chapter 5

Harz mountains (1693–1696) – where the development and improvement of power sources for draining the mines and for hoisting ore were central issues – had by and large come to an end. Power technology continued, nonetheless, to be an important topic in Leibniz’s correspondence after 1696, above all in the context of the exchange of ideas with Papin about his steam pump, as well as about the possibility of using steam and other vapors to power a machine or a vehicle. The starting point was Leibniz’s conjecture, expressed in his letter of November 18, 1697, that the explosive effect of gunpowder could be attributed to the compression, or compressive pressure, of the air. On that occasion, he wrote the following lines to Papin: “I believe that the effect of gun powder could be explained by the compression of the air, which hardly does less than the powder itself, if [only] we could also delve as far into the compressions as nature [itself] does”.297 As is clear from Papin’s reply on December 5, this line of thought had reawakened memories for him of his earlier work, in particular his Nouvelles experiences du vuide (1674),298 which dated from the time when he was assistant to Christiaan Huygens in Paris, but perhaps also of his more recent article of September 1688, entitled “Excerpta  … ex litteris  … de novo pulveris pyrii usu”.299 On the basis of his calculations carried out while in Paris, he had concluded that the air contained in gunpowder causes the force that is released in gunfire. In order to be able to make more advanced pronouncements here, he explained to Leibniz that he would need to carry out further research on the powder and its constituent parts. Thus he wrote: During the time when I was with Mr Hu[y]gens I had printed a little report of experiments where, among other things, I presented a calculation of the quantity of air which is in gun powder and of the degree of compression it undergoes there, and from that I concluded there is every reason to believe that the force of the powder only comes from the air which is compressed or squeezed in there. But as soon as one will have carried out several experiments, both regarding the powder itself as well

297 “Je crois que l’effect de la poudre à canon se peut expliquer par la compression de l’air, la quelle ne feroit gueres moins que la poudre, si nous pouvions aller aussi loin dans les compressions que la nature” (A III,7 N. 156, p. 632). 298 Cf. D. Papin, Nouvelles experiences du vuide, avec la description des machines qui servent à les faire, Paris, 1674. 299 Cf. D. Papin, “Excerpta ex viri clarissimi, Dionysii Papini, mathematum in Academia Marpurgensi professoris publici, litteris ad -- de novo pulveris pyrii usu”, Acta Eruditorum, (September 1688), pp. 497–501.

July 1696–1698

687

as the ingredients of which it is composed, I hope that one will be able to say something more positive and more exact.300 Then, a week later, on December 12, Leibniz greeted their mutual agreement about the nature and power of gunpowder on the basis of experiment, but not however without taking a gibe at Papin’s philosophical standpoint in the following extract: I am most relieved that my judgement is in agreement with yours regarding gun powder. When one has found the cause of an effect explicable on the basis of sensible matter, why revert to the suppositions of little certitude of the Cartesians and others? I already declared my support for this sentiment in the year 1671. But I see you have justified it on the basis of specific experiments.301 On April 20, 1698, Papin then reported that the landgrave Karl, or Charles of Hesse-Kassel, had charged him with the determination of the origin of the salt contained in salt or brine wells. In connection with this, he had carried out experiments on lifting water from a depth using the power of fire, i.e. of steam. In addition he had conceived far more important applications for the new power source than pumping water from a depth. And so, he wrote to Leibniz on this occasion: To achieve one’s goals it would be most advantageous to be able to easily raise a large quantity of water to a considerable height; and so I have carried out a number of trials to test the utile employment of the force of fire for this purpose. Certain rather joyful successes have led me to be persuaded that this force could be applied to applications much more important than raising water, so much so that I have devoted myself 300 “Dez le temps que J’etois chez Mr Hugens Je feis imprimer un petit recueil d’experiences où, entre autres, Je donnois un calcul de la quantité d’air qui est dans la poudre à canon et du degré de compression qu’il ŷ soufre: et de là Je concluois qu’il ŷ a tout lieu de croire que la force de la poudre ne vient que de l’air qui ŷ est comprimé: mais quand on aura fait plusieurs experiences tant sur la poudre que sur les ingredients qui la composent J’espere qu’on pourra dire quelque chose de plus positif et de plus exact” (A III,7 N. 161, specifically pp. 647f.). 301 “Je suis bien aise que mon jugement s’accorde avec le vostre sur la poudre à Canon; quand on a la cause d’un effect expliquable par des choses sensibles; pour quoy recourir à des suppositions peu certaines avec les Cartesiens et autres? Je me declara déja pour ce sentiment l’an 1671. Mais je voy que vous l’aves justifié par des experiences particulieres” (A III,7 N. 163, p. 658).

688

Chapter 5

entirely to this work, knowing the great difficulties which are always encountered in such enterprises and which can only be overcome by an extraordinary assiduousness.302 Thereupon, on April 24, Leibniz enquired as to whether the correspondent had made use of the principle of expansion in raising water by means of the power of fire, or steam, a matter which he himself had also contemplated, and concerning the realization of which he now wished to consult with Papin. Thus he wrote here: As regards the use of fire to raise water, may I take the liberty to ask you if it was by the principle of rarefaction, about which you have already published, or if it was by means of some other principle. I also have a [line of] thought concerning this, but I would like to carry out a little trial in order to consult you about the execution.303 On August 4, Papin then confirmed that he had in fact employed the expansion of steam but in such a way that he could exploit both suction and compressive effects. Referring to his publication “Nova methodus ad vires motrices … comparandas” of August 1690,304 in which he first published the principle of the atmospheric steam engine, he expressed the conviction that the power of fire, or steam, might indeed find other applications in addition to the raising of water. Here he wrote then:

302 “pour en venir à bout il seroit fort avantageux de pouvoir tirer facilement une grande quantité d’eau à une hauteur considerable: si bien que J’ay fait quantité d’epreuves pour tácher d’emploier utilement à cela la force du feu: quelques success assez heureux ont fait que Je me suis persuadé que cette force se pourroit appliquer à des choses bien plus importantes qu’à lever de l’eau: si bien que Je me suis donné tout entier à ce travail, sçachant les grandes difficultez qui se rencontrent tousjours dans de telles entreprises et qui ne se peuvent surmonter que par une assiduité extraordinaire” (A III,7 N. 186, pp. 751f.). 303 “Quant à l’usage du feu pour elever eau, oserois je vous demander, si c’est sur le principe de la rarefaction que vous avés deja publié, ou si c’est sur quelque autre principe. J’ay aussi une pensée là dessus, mais je veux en faire une petite epreuve pour vous consulter sur l’execution” (A III,7 N. 187, p. 753). 304 Cf. D. Papin, “Nova methodus ad vires motrices validissimas levi pretio comparandas”, Acta Eruditorum, (August 1690), pp. 410–414, and Tab. X, Fig. 1; reprinted (with an English translation) in: J. P. Muirhead, Origins and progress of the mechanical inventions of James Watt, London, 1854, III, pp. 139–154.

July 1696–1698

689

The manner in which I presently employ fire to elevate water is always based on the principle of the rarefaction of the water; I merely do it at present in a way that is much more simple to carry out compared to that which I have published, and furthermore, besides the suction which I make use of, I also employ the force of the pressure which the water exerts on other bodies by virtue of its expansion, the effects of which are not limited like those of suction. And so I am persuaded that this invention, if it be pursued as required, can produce very significant applications; however one has not yet achieved any major progress.305 Papin also related in this letter that he had constructed a model of a vehicle powered by steam that operated in a pan or pot. However, he doubted that this form of propulsion would be suitable for normal wagons or carriages on land, above all because of the imperfections of existing roadways. On the other hand, he believed he possessed the competence to build a marine vehicle powered by steam. Thus he wrote: I believe that one could employ this invention for many things other than for raising water. I have made a little model of a carriage powered by this force, and it produces, in my pan or ladle, the effect I had expected. But I believe that the irregularities and the bends of the major roadways would make this invention very difficult to perfect for vehicles on land. But for vehicles on water I flatter myself in the belief that I could achieve my goal rather quickly if I had more support than I actually have.306 Finally, near the end of the letter, he requested Leibniz’s thoughts and plans about the application of steam power in the following words: “I would have great pleasure in learning if you also have designs for exploiting the motive 305 “La maniere dont J’emploie à present le feu pour elever l’eau est tousjours sur le Principe de la rarefaction de l’eau: seulement Je le fais à present d’une maniere bien plus facile à bien executer que celle que J’ay publiée: et deplus, outre la suction dont Je me servoit, J’emploie aussi la force de la pression que l’eau exerce sur les autres corps en se dilatant, dont les effets ne sont pas bornez comme sont ceux de la suction: ainsi Je suis persuadé que cette invention si on la pousse comme il faut, pourra produire des utilitez tres considerables: mais on n’a pas encor fait de grands progrés” (A III,7 N. 214, pp. 851f.). 306 “Je crois qu’on peut emploier cette invention à bien d’autres choses qu’à lever de l’eau, J’ay fait un petit modele d’un chariot qui avance par cette force: et il fait, dans mon poele, l’effect que J’en avois attendu: mais Je crois que l’inegalité et les detours des grands chemins rendront cette invention tres difficile à perfectionner pour les voitures par terre; mais pour les voitures par eau Je me flatterois d’en venir à bout assez promptement si J’avois plus de secours que je n’en ay” (p. 852).

690

Chapter 5

force of fire and I very much hope that the little trial which you told me about has succeeded to your liking”.307 Leibniz, replying four days later on August 8, concurred with the view that the expansion of steam could produce a greater effect than the atmospheric pressure accompanying the condensation of steam. The expansion of steam had the same effect as the explosive power of gunpowder in a receptacle, whereby water had the advantage of not behaving so explosively on ignition. Like Papin, he had also contemplated the possibility of employing the expansion of other liquors or vapors in place of water vapor or steam. However, water was more practical as it was freely and plentifully available everywhere. Thus he wrote on this occasion: I understand very well that the force of expanding water vapor does more than the pressure of the air does when it (the water vapor) is recondensed and it is exactly this which I have contemplated just as with regard to gun powder, where however one has reason to fear lest the receptacle should burst if one does not have any (elastic) play due to the promptness of the explosion. But as regards the water, the force of its expansion would be less violent; it would be good to see if there are not liquors which are also superior to water. But water has the advantage that it does not cost anything and is available everywhere.308 Furthermore, Leibniz greeted the fact that experiments, which he himself had contemplated – in order to test the superiority of a steam engine over a pneumatic engine – but had been unable to carry out due to a lack of resources in Hanover, had now been carried out by Papin. Thus he continued: My plan was to carry out a trial to learn if the expansion of water vapor could raise appreciably more than the air column. However I lack workers here, but I am [also] more distracted here than I could possibly explain. 307 “J’ay eu bien de la joie d’apprendre que Vous avez aussi des desseings pour mettre à profit la force mouvante du feu et Je souhaitte fort que la petite epreuve dont Vous me parlez ayt reussi à vótre gré” (p. 852). 308 “Je comprends fort bien que la force de l’eau dilatée fera encor plus que la pression de l’air fera quand elle sera recondensée et c’est justement ce que j’avois pensé aussi bien qu’à l’egard de la poudre à canon, où pourtant on a sujet de craindre que les vases ne se rompent si on ne luy donne point de jou[e]r à cause de la promptitude de l’explosion. Mais à l’egard de l’eau l’effort de sa dilatation sera moins violent, il seroit bon de voir s’il n’y a des liqueurs qui feroient encor mieux que l’eau. Mais l’eau a cela de bon, qu’elle ne couste rien, et se trouve par tout” (A III,7 N. 216, p. 866).

July 1696–1698

691

That is what has prevented me from executing my plan. But I am very relieved now that you, Sir, have already undertaken the experiment in question and that you accordingly know approximately how the internal force of the air varies with heat and time.309 He himself – just like Papin – had previously contemplated the use of such an engine to power a vehicle and to facilitate transport, and so he added the following: “I have previously had thoughts about improving transport, about what the force should be which one should employ. And I believe that it would also serve here in many [other] instances”.310 Then, he outlined his own ideas about the use of pneumatic machines introducing the following illustration of the device he had contemplated.

Figure 11 Sketch of Leibniz’s design for sealing, or making airtight, the contact between a piston and a pump cylinder Source: Leibniz to Denis Papin, August 8, 1698 (A III,7, p. 866)

309 “Mon dessein estoit de faire une epreuve pour apprendre si l’eau dilatée peut elever utilement beaucoup plus que la colonne de l’air. Mais je manque d’ouvriers icy, mais je suis plus distrait que je ne sçaurois expliquer. C’est ce qui m’avoit empeché d’executer mon dessein. Mais je suis bien aise maintenant d’apprendre que vous avés déja fait, Monsieur, l’experience dont il s’agit et vous sçaurés ainsi à peu pres qu’elle est la force de l’air interieur selon la chaleur et le temps” (p. 866). 310 “J’ay eu d’ailleurs des pensées pour faciliter le charriage, quelle que pourroit estre la force qu’on y doit employer. Et je crois qu’elles serviroient encor icy en bien des rencontres” (p. 866).

692

Chapter 5

He had thought of using mercury for sealing, or making airtight, the contact between a piston and a pump cylinder. Furthermore, the mercury would balance, or equalize, the air pressure inside the cylinder, which was produced following the expansion of water vapor. His detailed outline was as follows: One could exempt oneself from employing, in these pneumatic machines, air pipes or cylinders that are uniformly regular and exactly sealed by the piston, by means of the use of mercury, which would prevent the air from passing between the piston and the body of the pump because the mercury would act to the benefit both of the cylinder ab inserted into the outer cylinder of this body, and of the height of the body of the cylinder, and [thus] of the stroke of the piston, capable of balancing the effort of the air by its height. The height ab would be such that when the piston is most elevated[,] or pulled out at the end of the stroke[,] it is always retained within the cylinder at the height of the barometer, in order to balance the weight of the exterior air. And the height bc or de would be such that the mercury could again provide the means to balance the pressure of the interior air produced by the dilation of the water. These cylinders of mercury could withstand certain grime or dirtiness which could arise; and by this means one could easily obtain and use every kind of pipe or cylinder appropriate for this kind of design, and overcome the friction as well. But as the mercury would always be balanced or in equilibrium, one might perhaps employ it to support the movement of the piston in order that this force not be lost entirely due to friction.311 At first, as he explained, he had contemplated such machines for improving transportation but had then become skeptical regarding their aptitude or 311 “On pourroit s’exemter dans ces machines pneumatiques des tuyaux exactement fermés par le piston et regulierement egaux; par le moyen du Mercure, qui empecheroit l’air de passer entre le piston et le corps de la pompe par ce que le mercure feroit luy meme à la faveur tant du creux ab entaillé dans l’apaisseur de ce corps, que de la hauteur du corps et du piston, de un cylindre capable par sa hauteur de contrebalancer l’effort de l’air. La hauteur ab seroit telle que lors que le piston est le plus elevé ou sorti il reste tousjours encor enfoncé dans le creux à la hauteur du barometre, pour balancer la pesanteur de l’air exterieure. Et la hauteur bc ou de seroit telle que le mercure pourroit encor balancer par son moyen la pression de l’air interieur produit par la dilatation de l’eau. Ces cylindres du Mercure suffiroient quelques minces qu’ils pourroient estre; et par ce moyen on pourroit obtenir et employer aisement toute sorte de tuyaux propres pour ces sortes de desseins, et retrancheroit encor la friction. Mais comme le Mercure seroit tousjours en balancement, on pourroit peut estre l’employer à aider le mouvement du piston à fin que cette force ne fut point perdüe entierement” (p. 867).

July 1696–1698

693

suitability for the purpose. The concluding text of this communication was then as follows: All of this could find applications in many instances, but it would not be appropriate in transportation. One could object to the use of the dilatation [or expansion] that there is no need to raise anything other than the cylinder of air, just to the point where the exterior air and the interior air have an equal consistency [or constancy]. For the cylinder of air gives to the machine the force which it has received. But the response to this is that it is necessary to promptly employ the exterior air before its cooling-down in the course of its exchange in the expansion. That would cost fire [power] which one could employ more usefully for new dilatations.312 Following further experiments, Papin reported, on August 28, that he had been able to pump water only to a height of 70 feet using steam power. His recently gained knowledge included ascertainment of the fact that a small increase in the degree of heat would lead to greater effect. Papin believed one could achieve – through the further development of such machines and the use of higher degrees of heat – that a pound of water would produce a greater effect than a pound of gunpowder. Thus he wrote here: I will try also to make observations of the degree of heat which is necessary to produce a certain effect with a certain quantity of water. But until now all that I have been able to do using the dilatation or expansion of vapors was to raise water to a height of 70 feet, and to establish that a small augmentation of the degree of heat is capable of greatly increasing the magnitude of the effect. And this has convinced me that, if one were to bring these machines to perfection in such a way that one could employ very great degrees of heat, one could achieve that a pound of water would have a greater effect than a pound of gun powder.313 312 “Tout cela pourroit avoir de l’usage en bien des rencontres; mais il ne seroit point si propre pour le chariage. On pourra objecter à l’employ de la dilatation qu’on n’a pas besoin d’elever autre chose que le cylindre de l’air, jusqu’à ce que l’air exterieur et interieur soyent d’une constance egale. Car le cylindre de l’air rend à la machine la force qu’il a receu. Mais la reponse à cela est qu’il faut employer promtement l’air exterieure avant qu’il se refroidisse sur de l’entrevenir dans la dilatation. Cela cousterois du feu, qu’on peut employer plus utilement à des dilatations nouvelles” (p. 867). 313 “Je tacheray aussi de faire des observations sur le degré de chaleur qu’il faut pour faire un certain effect avec une certaine quantité d’eau: mais jusques à present tout ce que J’ay pu

694

Chapter 5

As regards Leibniz’s ideas for the improvement of transport, or transportation, Papin underlined their importance and urged Leibniz – in the event of him being unable to implement these in practice – to at least make them available for posterity through publication. Thus he continued: Transport is one of the greatest useful applications in the world so that I have no doubt that you would render a very important service to the public if you were to communicate your thoughts in order to facilitate this work. And it appears to me that having so many other occupations, which prevent you from realizing such matters, it would be preferable to publish them on time rather than to run the risk of having things of such great consequence lost.314 Furthermore, Papin cast doubt on the functionality of Leibniz’s mercury-pump idea since it contained three interlaced tubes. The alternating movement of the tubes and the mercury would inevitably lead to considerable friction and resistance losses. On this matter he wrote: As regards the pump employing mercury, I believe that it will never work in practice, both because of the abashment of having three interlaced tubes which would have to be very long if one wanted to apply force or pressure that was in any way considerable, and also because of the fact that it will always be necessary to give a reciprocating movement to one of these tubes as well as to a large quantity of mercury, something which would, as I believe, cause much extra resistance in addition to the frictional rubbing of the ordinary pumps. And regarding that which you say, Sir, that one could employ this force to aid the movement of the piston, I very much fear that the parts required for that along with the fuss they cause would not pay dividends to any extent through the advantages that one might have from them, above all in view of the fact that it is easy to faire, par la dilatation des vapeurs, a été d’elever l’eau à 70 pieds; et de remarquer qu’une petite augmentation du degré de chaleur est capable d’augmenter beaucoup la grandeur de l’effect: Et cela me persuade que, si on perfectionne ces machines en sorte qu’on puisse emploier de tres grands degrez de chaleur, on pourra faire qu’une livre d’eau fera plus d’effect qu’une livre de poudre à canon” (A III,7 N. 220, p. 881). 314 “Le charriage est d’une si grande utilité dans le monde que Je ne doute point que Vous ne rendissiez un service tres important au Public si Vous luy communiquiez vos pensées pour faciliter ce travail: et il me semble qu’ayant tant d’occupations qui Vous empéchent de mettre ces sortes de choses à execution, il vaudroit mieux les publier de bonne heure que de courir le risque de laisser perir des choses de si grande consequence” (p. 881).

July 1696–1698

695

make pumps that are rather good in the sense that the resistance involved would be inconsiderable in comparison with the overall resistance which is overcome.315 In addition, Papin had, through experimentation, gained the insight that the effectivity of gunpowder increases with the resistance to be overcome. It appeared then that gunpowder would set off its charge more completely, and provide a greater effect or yield, when confronted with a high resistance, for example in raising a column of water. Finally, he insisted that the means to control the expansion of the exploding gunpowder conglomerate would need to be researched and found, in order to obtain the greatest benefit. Thus, on this issue, he wrote: Regarding the objection you raise against the use of dilatation or expansion, and to which you give forthwith the response, I once again add the following: it is the case that the force of the dilatation is so great that the resistance of the column of air is not proportional to it at all, and accordingly this force will be almost entirely lost if one does not apply it to overcome some resistance which is very much larger than that of the weight of the air, and this is to be observed principally with gunpowder. For indeed, I have proved that if one raises water solely through a short pipe where the resistance is small, it will produce but a small effect, but if it is a pipe where the water causes much resistance because of the height, it occurs that the same quantity of powder will not only raise the water to a greater height, but also that it will raise a much greater quantity of it. It appears that this is because the powder ignites more completely when there is more resistance. If then one does not present it with any resistance other than that of the air, there will be much of it which does

315 “Pour ce qui est de la pompe par le moien du vif argent Je ne crois pas qu’elle se mette jamais en pratique: tant à cause de l’embarras d’avoir trois tuyaux les uns dans les autres et qui devront étre fort longs si on veut faire des pressions un peu considerables: qu’à cause aussi qu’il faudra tousjours donner un mouvemt reciproque à un des ces tuyaux et à une grande quantité de vif argent: ce qui, à ce que Je crois, feroit bien autant de resistence que le frottement des pompes ordinaires: et sur ce que Vous dittes, Monsieur, qu’on pourroit emploier cette force à aider le mouvement du piston: Je crains fort que les pieces qu’il faudroit pour cela avec l’embarras, ne paiassent trop cher les avantages qu’on en tireroit, vû, surtout, qu’il est facile de faire des pompes assez bonnes pour que le frottement soit peu considerable en comparaison du reste de la resistence qu’on surmonte” (p. 881).

696

Chapter 5

not ignite at all, and accordingly there are several reasons which should oblige us to seek the means to really profit from its dilatation.316 As regards the connection between the strength of the expansion force and the height attained in lifting a body by means of steam power, Leibniz argued, in his reply on September 7, that consideration ought to be given to the circumstance that force was actually being lost through the cooling of the steam during expansion, revealing perhaps a certain premonition of what was to be later known as adiabatic expansion in thermodynamics. Thus he wrote: There is nothing which deserves more to be cultivated than the force of the dilation [viz. expansion]. If one objects that the dilated water does nothing but raise the air cylinder, and that it raises it all the more in accordance with its increased strength, and that accordingly it will suffice to employ the weight of this redescending cylinder, then I reply that with this greater elevation, demanding more time than a more rapid elevation of a greater weight, the vapor would partly cool down [viz. recondense], and that one would thus loose force or alternatively one would need to employ more fire. Your reasoning is again considerable, in knowing that the air cylinder has too small a proportion there, that is to say, as I believe, that it would be necessary to raise it to a greater height in order to achieve that the dilation applies all of its force effect against it.317 316 “Sur l’objection que Vous apportez contre l’emploi de la dilatation et à quoy Vous donnez incontinent la réponse: J’adjouteray encor celle cŷ: c’est que la force de la dilatation est si grande que la resistence de la columne d’air ne luy est point proportionnée: et ainsi cette force se perd presque toute si on ne l’emploie à vaincre quelque resistence bien plus grande que celle du poids de l’air: et cela s’observe principalement dans la poudre à canon: car J’ay eprouvé que, si on fait monter l’eau seulement par un tuyau court où la resistence est petite, il ne se fait que peu d’effect; mais si c’est un tuyau où l’eau fasse beaucoup de resistence à cause de sa hauteur; il arrive que la méme quantité de poudre non seulement eleve l’eau bien plus haut, mais encor que elle en eleve une plus grande quantité. Il ŷ a apparence que c’est parce que la poudre s’allume plus parfaittement quand il ŷ a plus de resistence: quand donc on ne luy donnera autre resistence que le poids de l’air, il ŷ en aura beaucoup qui ne s’allumera point: et ainsi il ŷ a plusieurs raisons qui nous doivent obliger à chercher les moiens de bien profiter de sa dilatation” (p. 882). 317 “Il n’y a rien qui merite mieux d’estre cultivé que la force de la dilatation; si on objecte que l’eau dilatée ne fait qu’elever le cylindre de l’air, et qu’elle l’eleve d’autant plus qu’elle est plus forte; et qu’ainsi il suffit d’employer le poids de ce cylindre retombant; je reponds que cette elevation plus haute demandant plus de temps qu’une elevation plus promte d’un plus grands poids, la vapeur se refroidit en partie, et qu’ainsi on perd de la force ou bien on a besoin d’employer plus de feu. Vostre raison est encor considerable, sçavoir que le cylindre de l’air y a trop peu de proportion, c’est à dire comme je crois qu’il faudroit

July 1696–1698

697

Leibniz decided that he wanted to organize his thoughts concerning transport, or transportation, and so he passed over this matter. As regards Papin’s objection to his mercury pump, he responded that, the greater the length of the pump cylinder (and accordingly of the stroke of the piston), the smaller the friction would be in relation to the performance of the pump, since the friction increased in relation to the cylinder diameter, while the performance grew in proportion to the square of the diameter. Thus he continued: I will organize my thoughts a little in relation to transport, and as regards the mercury, which raises the friction in the pumps, I imagine that its weight could be balanced by the piston and would help to move it, and that accordingly there would be scarcely any force lost. But I do avow that with all of that which can most often happen, and the more extensive the body of the pump is, the less considerable the friction will be in proportion to the principle effect. For the frictions increase in relation to the diameters, while the effects grow in proportion to the squares of the diameters of the body of the pump.318 As Papin was not able or willing to communicate any further details of his research on the steam pump  – as he made clear in his letter of October 9, 1698 – the considerations regarding the matter ended at this juncture. His final words here were: As I am not free to do so, I should not dispose absolutely of [viz. reveal] the inventions on which I am working, and certain considerations have prevented me to date from communicating the manner by which we employ the force of the dilation but that does not inhibit me from being very obliged for your offers.319 l’elever trop haut pour faire que la dilatation fasse tout son effect sur luy” (A III,7 N. 224, pp. 892f.). 318 “Je mettray un peu en ordre mes pensées sur le chariage, et pour ce qui est du mercure, qui leve la friction dans les pompes, je m’imagine que son poids pourroit estre balancé avec le piston et aideroit à le remuer, et qu’ainsi il n’y auroit gueres de force perdüe; mais j’avoue avec tout cela qu’on s’en peut bien passer le plus souvent, et plus le corps de la pompe est ample moins la friction sera considerable à proportion de l’effect principal. Car les frictions croissent comme diametres, et les effects croissent comme les quarrés des diametres du corps de la pompe” (p. 893). 319 “Comme Je ne suis pas à moy Je ne sçaurois disposer absolument des inventions à quoy Je travaille, et quelques raisons m’empéchent jusques à present de communiquer la maniere dont nous emploions la force de la dilatation mais cela n’empéche pas que Je ne Vous sois tres obligé de vos offres” (A III,7 N. 234, p. 915).

698

Chapter 5

Finally – as regards Papin continuing research in this area in the first decade of the new century – he sent (in the year 1707) a monograph to the Royal Society in which he described the design of an engine which he had developed on high-pressure principles and, in the following year, he returned to London to seek support for his invention. Although Leibniz had admired it, and had suggested refinements, Newton turned it down and Thomas Savery criticized it most severely, accusing Papin of stealing his ideas.320 9

Civil Engineering, Garden Design and Architecture

The beginning of the period under consideration, from mid-1696, marked the commencement of Leibniz’s involvement with the waterworks and fountains for the electoral gardens at Herrenhausen in Hanover. His involvement, and commitment, is reflected above all in his correspondence with the military engineer Andreas Du Mont who resided in the town of Hameln. From the draft of Leibniz’s letter to Du Mont of July 21, 1696, we learn about the commission he had received from the elector Ernst August to work for the provision of the waterworks and fountains at the gardens in Herrenhausen.321 In this matter, Leibniz sought the expert advice of authorities like Du Mont. In his letter to the correspondent in question, Leibniz elaborated three options for the development of the waterworks and fountains. The first option envisaged the construction of a vertical water wheel on the river Leine, directly opposite the gardens at Herrenhausen, with which water could be raised into a storage tank in a tower. From there it would pass through pipes, either directly to the fountains in the gardens or into a reservoir. Alternatively, the water wheel might be erected on a branch of the river in the vicinity of Hanover’s new town district (‘Hannover Neustadt’) and used additionally for water-supply there. This option had the disadvantage that the water for the fountains would have to be delivered through a lengthy system of wooden pipes from the town to the gardens at Herrenhausen. The third possibility, and in Leibniz’s view the best, would involve the construction of a canal from a location on the river, and its passage in a straight line to the gardens before veering back to another location further along the course of the river. The costs, Leibniz claimed, would be moderate as long as the only function was to supply water for the fountains. The exploitation of the canal for other purposes like navigation, would naturally lead to additional expense. On the other hand – in view of the considerable 320 Cf. A. Smith, 1995 and 1998 (Introduction, note 112). 321 Cf. A III,7 N. 7, pp. 26–32.

July 1696–1698

699

head of water it could provide – the canal might also be used to power water mills along its course. The engineering hydraulics works on the canal would be less exposed to dangers than any alternative engineering works on the main river, and they would entail no impairment of shipping traffic along the river. The water could be raised into a tower, and from there be directed to fountains in the immediate vicinity, or it could be conducted by means of a ditch or a hydraulic flume supported on stands  – like those used in mining in the Harz district – to other locations in the gardens. Gondolas might even be used on the canal for transportation, and they would represent an added attraction for Herrenhausen. The water supply of Hanover’s new town district would then have to be realized independently of the plans for the gardens at Herrenhausen, which were located outside the town. In his expert’s report,322 which was attached to a letter of July 30, 1696, to Leibniz,323 Du Mont argued in favor of the construction of a canal between the river and the gardens. Furthermore, he recommended using the earth obtained in the excavation works to build a dike as a protective measure against flooding, specifically on the side facing the town. A lock should be built at the location where canal and river met, in order to keep the water level of the canal constant and to regulate the quantity of water for the operation of the water wheel. Such a canal might serve as a waterway for gondolas between Hanover town and Herrenhausen. For the return flow of the water into the river, a cascade would have to be built. This would also allow for the canal to be drained on occasions in order to undertake cleaning operations. The second suggestion of Leibniz, namely that of combining the water supply of Hanover’s new town district with the water provision for the garden fountains at Herrenhausen by means of an extended system of water pipes, was rejected by Du Mont as being impractical. While the proposal for the construction of a canal as envisaged by Leibniz found the support of Du Mont in principle, he pointed out that a number of difficulties would arise, like dealing with the sandy and swampy ground near the river. To avoid erosion of the sides of the canal, the cladding of its walls would be necessary, and this measure would considerably increase the costs involved. And, of course, a lock would be required in order to regulate the water flow and to protect the canal and gardens.

322 Cf. A III,7 N. 13, pp. 44f. 323 Cf. A III,7 N. 12, p. 43.

700

Chapter 5

Du Mont failed to meet Leibniz during a visit to Hanover in mid-August 1696. As is evident from entries in Leibniz’s diary for August 13 and 14, 1696,324 consultations took place at this time at the court in Hanover about the planned water-fountain system at Herrenhausen. Here the decision was taken to build the facility in accordance with Leibniz’s first proposal, and to forgo the construction of the canal because of the costs involved. Accordingly, Leibniz reported to Du Mont, on August 20, that a Persian (or scoop) wheel of 50-foot diameter was to be built on the river opposite Herrenhausen, and that it was to be combined with a mill in order to offset the costs.325 The water was to pass through pipes to a reservoir, which would then supply the fountains. Leibniz regretted the rejection of his proposed plan to build a canal, and he cast doubt on the calculation of the costs involved. He believed that extensive and costly hydraulic construction measures on the main river would be necessary, and that such expense might have been saved by the provision of a canal. Furthermore, since the canal would have been connected with an arm of the river, it would have been protected from the current, and also from ice formation on the main river. In contrast, the planned scoop wheel and mill, at their locations on the river, would be exposed to all the forces of nature. From Du Mont’s final letter to Leibniz, from the last week of August 1696, it is clear that he shared Leibniz’s skepticism about the durability of a scoop wheel on the river.326 He likewise continued to adhere to the view that the construction of a canal with a dike would be the best option. Alas, the construction of such a canal, as projected and favored by both Leibniz and Du Mont, was never realized during their lifetimes. In the spring of 1697, Leibniz’s correspondence with the miller and master carpenter Hans Linsen blossomed once again. Linsen, who then worked at the Heyersum salt works near Hildesheim, had apparently been entrusted by Leibniz with the task of producing and testing a piston for a water pump. In addition, an unnamed gunsmith from Hildesheim was also involved.327 Furthermore, as is evident from a note of May 23, 1697, sent to Leibniz, Linsen had also been engaged by him to work on a model for a carriage. Linsen’s water pump was possibly intended for the waterworks at Herrenhausen. At all events, the correspondent offered Leibniz his services for this undertaking in the following words: 324 Cf. Leibniz: Gesammelte Werke, viz. G. H. Pertz (ed.), Leibnizens Gesammelte Werke, 4 vols, Hanover, 1843–1847, in particular vol. 4 pp. 183–186. 325 Cf. A III,7 N. 23, pp. 88–91. 326 Cf. A III,7 N. 26, pp. 97f. 327 Cf. for example, A III,7 N. 87, p. 357.

July 1696–1698

701

And I have heard that the work at Herrenhausen is to proceed for they are already working on the ditch, and I have to ask if you, Sir, the privy counsellor, might be able to help me in the matter. I would like to be involved in the work, both the water wheel and the mills, if you should desire this.328 In August 1697, the master builder Leonhard Christoph Sturm  – the son of the astronomer and mathematician at the University of Altdorf (near Nuremberg) Johann Christoph Sturm  – having been appointed professor at the military academy in Wolfenbüttel, commenced a correspondence with Leibniz. His motivation was, first and foremost, his professional advancement. His express desire was to work in the fields of mathematics, civil and military engineering, and mechanics (“Geometria, Architectura tam civili quam Militari, et Mechanica”).329 Through his writings Sturm had already made a name for himself. In particular, he had edited and published in 1696 the chief civil-engineering work of the architectural theoretician and mathematician Nicolai Goldmann (1611–1665), with the title Vollständige Anweisung zu der Civil Bau-Kunst (Complete instruction in civil engineering).330 Although Sturm had the prospect of being appointed professor of mathematics at the university of Helmstedt, as he informed Leibniz in a letter of September 12,331 he enquired in a later letter of October 19 about the possibility of his being appointed master builder in Hanover, since he was convinced that a professorial appointment in Helmstedt would mean a deterioration in his professional standing.332 Then, in a letter of January 3, 1698, he presented himself as a master builder, a mathematics professor and a prospective preceptor at the court in Hanover, or in his words: “Firstly I have the hope to be master builder in Hanover and at the same time mathematics professor, and to provide good and useful services for the young princes”.333 He admitted that 328 “Vnt ich habe gehöret das die arbeit zu herrihausen sol fohrgeen den sie wehren albereitz an den graben, als habe ich zu bitten das mihr doch der her geheimraht dar zu helffen möchte, ich wolte die arbeit wol dingen, beide die kunst unt auch die mühlen, wen sie es begehren wehren” (A III,7 N. 96, p. 389). 329 Cf. A III,7 N. 132, p. 544. 330 Cf. N. Goldmann (L. Ch. Sturm. ed.), Vollständige Anweisung zu der Civil Bau-Kunst … auß den besten Überresten des Alterthums, auß den außerlesensten Reguln Vitruvii, Vignolae, Scamozzi, Palladii, und anderer zusammen gezogen, Wolfenbüttel, 1696. 331 Cf. A III,7 N. 137, p. 565. 332 Cf. A III,7 N. 151, p. 619. 333 “Erstlich habe gehoffet in Hanover als Baumeister und zugleich als Professor Matheseos, sonderlich bei den jungen Printzen, gute und nützliche dienste thun zu können” (A III,7 N. 170, p. 690).

702

Chapter 5

he also had hopes of receiving an appointment in Berlin, and that he was even contemplating the option of a quiet university life, be it in Helmstedt or at his (and Leibniz’s) alma mater in Altdorf. Then, in a letter of February 3, 1698, written just one day after the death of Leibniz’s sovereign Ernst August, Sturm additionally offered his services as draughtsman, architect, poet and polymath for the design of a “castrum doloris”, or castle of grief, in honor of the deceased elector. Thus, he wrote here in relation to his own person: There will however be required for the right execution of a castle of grief, not only draftsmanship or the art of drawing and architecture but also poetry, and indeed many other scholarly subject areas of the learned, with all of this coming together in a single subject.334 Following journeys to the Netherlands (1697), and to France (1699), Sturm finally obtained an appointment as mathematics professor in Frankfurt an der Oder in 1702. Leonhard Christoph Sturm outlived Leibniz by two and a half years, and before his death (in June 1719) he witnessed the publication of his father Johann Christoph’s posthumous work Kurtzgefasste Mathesis Oder Erste Anleitung zu Mathematischen Wissenschafften (Mathematics summarized or first introduction to the mathematical sciences) in 1717335 – whose 12 chapters or sections included those on military engineering (“Der Kriegs=Bau=Kunst”) and on civil engineering (“Der bürgerlichen=Bau=Kunst”) – as well as his own Architectura civili-militaris (1719).336

334 “Es werden aber allerdings zu guter Execution eines Castri Doloris, nicht nur die Zeichenkunst und Architectur sondern auch die Poesie, ja noch viel andere wißenschaften der gelehrten, und dieses in einem subjecto zugleich beysammen erfordert” (A III,7 N. 179, pp. 731f.). 335 Cf. J. C. Sturm, Herrn Johann Christoph Sturms,Weyland der Mathematischen- und NaturWissenschafften Hochverdienten Professoris Publici zu Altorff, Kurtzgefasste Mathesis Oder Erste Anleitung zu Mathematischen Wissenschafften, in Tabellen verfasset. Deren folgende sind: Der allgemeinen Mathematick I / Der Rechen-Kunst IV/ Der Algebrä III / Der Meß-Kunst, d.i. der Geometrie samt der Trigonometrie V / Der optick III / Der Kriegs-Bau-Kunst VI / Der bürgerlichen Bau-Kunst VIII / Der Himmel- und Erde-Beschreibung IV / Der Chronologie III / Der Horographie I / Der Mechanick I / Der Chiromantie I, Coburg, 1717. 336 Cf. L. C. Sturm, Architectura civili-militaris. Oder Vollständige Anweisung, Stadt-Thore, Brucken, Zeug-Häuser, Kasematten und andere Souterrains der Wälle, Casernen, Baraquen, Corps des Gardes und Proviant-Häuser behörig anzugeben, Augsburg, 1719.

July 1696–1698

10

703

Other Engineering Enterprises

In the fields of engineering and technology (as in natural philosophy and physics), Leibniz’s correspondence with Papin was surely the most important in the period from mid-1696 to the end of 1698. From his letter of August 30, 1696, Papin’s inventive genius and richness of ideas, but also his frustration, are evident. He explained to Leibniz that he had conceived numerous new machines of which he could hope to realize not even half during his lifetime. Thus, he wrote on this occasion: Concerning my thoughts on theory, I tell you, Sir, that I have abandoned them at present, because the number of new machines and inventions has for some time been greatly multiplied in my mind, and I would want passionately to see all the astounding and most useful effects which they would produce if one were to be in a position to effectively execute them … I see also that notwithstanding my assiduousness in matters of this kind it will be inevitable that I die before I will have been able to realize the half of that which I already have in my head.337 In his reply, on September 24, Leibniz encouraged the correspondent to continue to dedicate himself to the progress of technology, and he promised him his support in the endeavor writing that: “It would be to do a disservice to the sciences to divert you from your wonderful practical thoughts. I recognize very well that which you are capable of doing”.338 In this context, Leibniz too complained that he was not in a position to realize his own engineering discoveries. He specifically mentioned here his calculating machine which, even after 24 years of development, still had not been completed, principally due to lack of time and assistance. And so he wrote: It has only been in the past few years that I have been able to execute [the design for] my calculating machine, which as you know I had 24 years 337 “Pour ce qui est de mes meditations pour la Theorie: Je vous diray, Monsieur, que Je les ay à present abandonnées: par ce que le nombre des Machines et inventions nouvelles s’est fort multiplié dans ma teste depuis quelque temps: et Je souhaitterois passionnement voir tous les effets surprenants et fort utiles qu’elles produiroient si on pouvoit les biens mettre à execution … Je vois aussi que nonobstant mon assiduité à ces sortes de choses il faudra que Je meure avant d’avoir pu faire seulement la moitié de ce que J’ay desjà dans la teste” (A III,7 N. 28, p. 108). 338 “ce seroit faire tort aux sciences, que de vous detourner de vos belles meditations de practique; je reconnois si bien ce que vous estes capable de faire” (A III,7 N. 34, p. 144).

704

Chapter 5

ago. For me it has been something of very great consequence, and the expense would not have put me off at all if I had had the time or the proper personnel to assist me.339 In the fall of 1696, Papin submitted a petition (or application) for his release from the service of his prince, namely the landgrave Charles of Hesse-Kassel, a copy of which he sent to Leibniz on October 4.340 In this petition, Papin emphasized the importance of his centrifugal ‘Hesse pump’ of 1689 (namely the “Rotalis Suctor et Pressor Hessiacus”) especially for shipping and navigation. He desired to return to England, since navigation had a special significance there. Leibniz expressed his skepticism, and he was relieved when Papin’s petition to the landgrave was rejected, as he learned from a letter of January 14, 1697.341 Four months later, on May 13, Papin was able to report that, while his main objective in submitting the petition had not been achieved, he had been successful in having some of his demands granted.342 Thus, he was given better conditions for his research activities that were concerned with glass-kiln development, in particular for the improvement both of a process for glass melting using his ‘Hesse pump’, and of a newly-developed oven. His efforts were directed, first of all, to testing and bringing to perfection a scaled-down version of the process. Only following the directive of the landgrave, however, was the realization on a large scale to take place. Replying on May 25, Leibniz stressed the importance of glass melting for optics, and he recalled Tschirnhaus’ research on concave mirrors and convex lenses in the following words: I would wish that one had contemplated sooner the melting of glass with the intention of improving the glass forms used in dioptrics or in catroptics. For I have no doubt but that these glasses have pretty well the form of a foundry mold. I ask you, Sir, to think about this, for I believe that one could make remarkable things, which would clearly surpass those which Mr Tschirnhaus has made, be it with his mirrors, or his burning glasses. It is true that he himself is still working to improve them even more. But

339 “ce n’est que depuis quelques années que j’ay pû executer ma machine Arithmetique, que vous sçavés que j’ay eue il y a plus de 24 ans. J’en ay de bien plus grande consequence, et la depense ne m’auroit point rebuté si j’avois eu du temps ou des personnes propres à m’assister” (pp. 144f.). 340 Cf. A III,7 N. 38, p. 155. 341 Cf. A III,7 N. 66, pp. 262f. 342 Cf. A III,7 N. 93, pp. 385f.

July 1696–1698

705

it is good that several people contemplate the same matter and combine their views and their works.343 Papin was then able to report, on June 19, that his trials on small-scale glass melting had in the meantime been successful. He was confident that the large-scale version of the process would also function. The landgrave had observed his experiment, and he had given instructions for the construction of a laboratory for the continuation of the series of experiments. And so, the correspondent wrote on this occasion: As regards my experiment on the melting of glass, I have succeeded very well on a small scale. Anyway I heated the brick furnace and melted the glass over the period of an hour, and so there is every reason to believe that the matter will succeed very well again on a large scale, for one knows that the large furnaces produce a greater effect, in proportion, compared to their smaller counterparts. H. S. H.344 paid me the honor of coming and seeing this experiment and he appeared to be very satisfied. He even ordered that I be given a workplace in a certain laboratory where I could very conveniently execute the matter on a much larger scale.345 Nonetheless, Papin had to show patience since, to begin with, a new oven had to be constructed, and so he added: “but until now I have not been able to have this place and I have been told that another furnace will have to be built first”.346 In the spring of 1698, on April 20, he could then report to Leibniz that construction was underway. The new melting furnace – a key element of 343 “Je souhaiterois qu’on pensat plus tost à la fonte de verre à dessein de pousser plus avant les verres servans à la dioptrique ou à la catoptrique. Car je ne doute point que ces verres ne prennent assez bien la forme d’un moule. Je vous prie d’y penser, Monsieur, car je crois qu’on pourroit faire des grandes choses, qui passeroient meme de beaucoup ce que Monsieur Tschirnhaus a fait tant par ses miroirs, que par ses verres ardens. Il est vray que luy même travaille tousjours à les pousser plus loin. Mais il est bon que plusieurs pensent à la meme chose et joignent leur veues et leur travaux” (A III,7 N. 97, p. 390). 344 Namely, His Serene Highness, the landgrave Charles, or Karl von Hessen-Kassel. 345 “Pour ce qui est de mon experience pour la fonte du verre elle m’a fort bien reussi en petit: car J’ay echauffé le fourneau de brique et fondu le verre en une heure de temps: et ainsi il ŷ a tout lieu de croire que la chose reussira encor mieux en grand: car on sçayt que les grands fourneaux font plus d’effet, à proportion, que les petits. S. A. S. m’a fait l’honneur de venir voir cette experience et en a paru fort satisfaitte: elle avoit mesme donné ordre pour me faire donner place dans un certain laboratoire où J’aurois pu fort commodement executer la chose beaucoup plus en grande” (A III,7 N. 108, p. 451). 346 “mais jusques icŷ Je n’ay pu avoir cette place et on me dit qu’il faut encor bastir un autre fourneau auparavant” (p. 451).

706

Chapter 5

which was Papin’s own ‘Hesse pump’ – was however not intended for the production of polished sheet or mirror glass, but solely of iron retorts or alembics. His account was as follows: I am presently having the new furnace built, which I previously told you about. I am not making it as large as I would for mirror glass, but I am making it simply in order to make certain large retorts forged from iron which will be most useful for producing the grand effects which I expect from the force of fire. I have also made for this furnace a large Hesse pump which is more perfect than those I made previously.347 Finally, on October 9, 1698, Papin communicated a detailed description and the following drawing of his new blast furnace.348

Figure 12 Papin’s drawing of his new blast furnace Source: Denis Papin to Leibniz, October 9, 1698 (A III,7, p. 916)

In this blast furnace, the air was made to pass both above and below the burning wood by the use of a centrifugal pump. The flames were blown by the ventilator pump in the direction of the melting crucible, and simultaneously 347 “J’en suis à present à faire bátir le nouveau fourneau dont Je Vous ay parlé autresfois. Je ne le fais pas si grand que Je l’aurois fait pour les glaces de miroir; mais Je le fais simplement pour faire certaines grandes cornues de fer forgé qui seront fort utiles pour produire les grands effets que J’attens de la force du feu: Je fais aussi pour ce fourneau un grand soufflet de Hesse plus parfait que ceux que Je faisois auparavant” (A III,7 N. 186, p. 752). 348 Cf. A III,7 N. 234, pp. 915–918, and also N. 241, pp. 933f.

July 1696–1698

707

they were drawn to there by the suction effect of the smokestack. Through openings, located in the upper oven wall, a heating plate could be introduced and used for the extraction of the glass melt. This could also be carried out using a machine. The blast and suction air regulation would prevent the flames from rising through the openings, and thus impairing the servicing of the melting crucible or even producing the curtailment of the fire. Papin informed Leibniz that the glass melt produced in the oven could be used for various product applications like mirrors, window glass, or hollow cylinders. Furthermore, the oven could also be used for the production of iron products by virtue of the great heat impact of the fire. However, Papin conceded that he had not been able to realize the full potential of his invention since his blast furnace was not large enough. In particular the height of the smokestack was restricted to two feet. In his reply from the third week of October, Leibniz recalled his own earlier experiments with melting furnaces,349 especially those carried out in the summer of 1679 in the course of his cooperation with the discoverer of phosphorus, Heinrich Brand – from whom he would soon receive a letter of November 7, 1698,350 requesting the settlement of outstanding payments from that time – as well as the ovens built by Johann Daniel Crafft. However, all these experiments had not been undertaken using a blast furnace. Leibniz, although impressed by Papin’s innovation, was of the opinion that, to begin with, ordinary bellows might be employed. Since the fire could now be regulated, the use of a heating plate for the removal of the molten glass seemed to him to be superfluous. The melting operations could be entirely undertaken on such a plate, provided the intensity of the fire was not so great as to be able to damage the plate. Leibniz acknowledged that he himself had often contemplated the process of glass melting, and that he continued to have the ambition to develop new ideas regarding it. Papin, writing on November 17, emphasized the superiority of his method in comparison with the normal process, especially as regards the production of plate or mirror glass. In the conventional process, the glass melt was drawn from the oven and then polished. With the new process, the molten glass was to be drawn onto oven plates. To begin with, he wanted to test this idea using smaller plates. However, the key innovation in his new oven was that the flame passed both above and below the material to be heated. Thus he explained:

349 Cf. A III,7 N. 237, pp. 923f. 350 Cf. A III,7 N. 240, pp. 931f., and also H. Breger, “Notiz zur Biographie des Phosphor-Entdeckers Henning Brand”, Studia Leibnitiana, vol. 19(1), (1987), pp. 68–73.

708

Chapter 5

I did see certain descriptions of furnaces in which the flame passes to the sides and above the material which one wants to heat. But to have the flame strike the material with force from above to below and then to pass again underneath, that is what I do not believe has hitherto been done, and yet, this [would] very much augment the rapidity of the operation.351 Leibniz, for his part, was – as he wrote in his reply of November 28 – not really convinced that Papin’s process was entirely new. According to him, such oven plates were already being used in the production of mirror glass, and so he wrote: I do not know if you are well-informed about the method currently used to make large mirrors. You say, Sir, that one simply macerates them to the degree necessary for them to spread on a large stone, and that one then removes them instantly from the furnace for fear that they might attach themselves to the stone. But I understand the molten glass is spread over a well-polished large plate of iron by means of another plate which passes above it.352 Like Papin, Leibniz considered it worthwhile, however, to render the polishing of the plate superfluous. And so he added: “But it is also my sentiment and desire that one should manage the whole and bring about that the plate would no longer need to be polished. One would do well to contemplate the whole in good faith and to commence with ordinary trials”.353 Papin’s final letter of the year 1698, written on December 11, contained a request to Leibniz for additional information regarding the normal process of producing plate or mirror glass. Papin confessed that his own knowledge 351 “J’ay bien vû quelques descriptions de fourneaux qui font passer la flame aux costez et par dessus la matiere qu’on veut chauffer: mais de faire venir la flame avec force frapper de haut en bas sur la matiere et ensuitte passer encor par dessoubs: c’est ce que Je ne crois pas qu’on eust encores fait: et pourtant cela augmente beaucoup la promptitude de l’operation” (A III,7 N. 241, p. 934). 352 “Je ne sçay si vous estes bien informé de la maniere dont on fait maintenant les grands miroirs. Vous dites, Monsieur, qu’on les rammollit seulement autant qu’il est necessaire pour les etendre sur une grande pierre, et que puis on les tire incontinent du fourneau crainte qu’elles s’attachent à la pierre. Mais j’ay appris, que le metail du verre est etendu sur une grande plaque de fer bien polie par le moyen d’une autre plaque qui coule dessus” (A III,7 N. 245, pp. 949f.). 353 “Mais c’est aussi mon sentiment et souhait, qu’on menage le tout en sorte, que la plaque n’ait plus besoin d’estre polie. On feroit bien d’y penser tout de bon, et de commencer par des epreuves mediocres” (p. 950).

July 1696–1698

709

was based on observations he had made on the island Murano, near Venice, in the year 1681. At that location, parts of a hollow glass cylinder were moved on a large stone into an oven. The molten glass was then spread out over the stone with the help of a draw-plate, or drawing die, before the whole was again removed from the oven. His exact words were: I also request that you send me more details about the method by which one presently makes large mirrors. For, as far as I am concerned, I only know that which I saw at Murano near Venice where, after having cut the hollow glass cylinder from one end to the other, one placed it on a large stone plate which one then placed in the furnace, and as soon as the glass was macerated one opened the said hollow cylinder and one spread it over the stone with large iron spatulas [or palette-knives], following which one withdrew the whole from the furnace.354 11

Process or Chemical Engineering

Further key aspects of the correspondence between Leibniz and Papin included chemical or process engineering, and techniques for the conservation of foodstuffs. On June 19, 1697, Papin indicated that he was working on a discovery that would be of practical importance, and through which chemical processes could be carried out in the open air. He promised to keep Leibniz informed, writing that: I am working at present on another invention which could be most useful because I could carry out almost all the operations of chemistry in the open air, and accordingly one could have a quantity of totally new production processes, since one knows that the supply of the air brings about great changes regarding the effects of fire. Once I have completed some experiments[,] I will be honored to inform you about them.355 354 “Je Vous supplie aussi de me mander plus particulierement de quele maniere on fait presentement les grands miroirs: car pour moy Je n’en sçays que ce que J’en ay vu à Muran proche de Venise où, apres avoir coupé d’un bout à l’autre le cylindre de verre creux, on le mettoit sur une grande pierre platte qu’on faisoit entrer dans le fourneau, et si tost que le verre se ramollissoit on ouvroit ledt cylindre creux et on l’étendoit sur la pierre avec de grandes spatules de fer, puis on retiroit le tout du fourneau” (A III,7 N. 247, p. 955). 355 “Je travaille à present à une autre invention qui pourra estre fort utile parceque Je pourray faire presque toutes les operations de chymie à l’air ouvert: et ainsi on pourra avoir quantité de productions toutes nouvelles: car on sçayt que la communication de l’air apporte

710

Chapter 5

A little later, on August 5, Papin reported that he had achieved a breakthrough. For the distillation of sulfur, he had developed distillation equipment consisting of six alembics, or retorts, in series. The outlet of the final retort led into the open air. In this final stage of the distillation apparatus, a considerably greater quantity of spirit of sulfur, or oil of sulfur, was liquefied in comparison with the first stage. By the use of additional retorts, a complete liquefaction could be achieved without having acid fumes escape into the air. Thus, the correspondent explained: I have succeeded very well in my experiment in carrying out the operations of chemistry in the open air. For in the combustion of some sulfur whose flue gases were forced to pass through six alembics in series, with the final one having its outlet into the open air, I discovered that in the sixth retort more spirit is condensed than in the first one where the sulfur was combusted (apparently for the reason that the flue gasses are condensed more easily in cold rather than in heat), something which shows very clearly that with the ordinary method one suffers heavy losses since one retains only that which is able to condense in the retort where the sulfur combusts. It remains to establish the number of retorts which will be necessary to condense all of the spirit by achieving that there is nothing in the last one, and so one will be assured that nothing more will escape to the outside. One could carry out the same experiment on all the combustible bodies themselves, and also on those which need an additional fire, but it is indeed true that their flue gases will be mixed with those of the wood or coal which act on them.356

de grands changements aux effets du feu: Quand J’en auray fait quelque experience Je me donneray l’honneur de Vous en entretenir” (A III,7 N. 108, p. 451). 356 “J’ay fort bien reussi à mon experience pour faire les operations de chymie à l’air ouvert: car en bruslant du soulfre dont les fumées estoient obligées de passer par six alembics l’un apres l’autre et dont le dernier avoit sa sortie dans l’air ouvert, J’ay trouvé que dans le sixiesme il se condensoit encor plus d’esprit que dans le premier où le soulfre brûloit (apparemment à cause que les fumées se condensent plus facilement au froid qu’au chaud) ce qui fait bien voir que par la methode ordinaire on pert extremement, puisqu’on ne recueille que ce qui se peut condenser dans la cloche où le soulfre brusle. Il reste d’eprouver quel nombre d’alembics sera necessaire pour condenser tout l’esprit en faisant qu’il ne s’en trouve point dans le dernier, et alors on sera asseuré qu’il ne sortira aussi rien dehors. On pourra faire la mesme experience sur tous les corps combustibles d’eux mesmes: et aussi sur ceux qui ont besoing d’un autre feu; mais il est vray qu’alors leur fumées seront meslées avec celles du bois ou du charbon qui agira sur eux” (A III,7 N. 125, p. 513).

July 1696–1698

711

Papin stressed here that his method might also be used with other combustible materials, and it could provide insights into other chemical processes, or as he wrote: “I believe however that this could always be useful for many things and throw much light on the matter”.357 And, in a later letter of October 24, he continued this line of thought, referring to flowers of niter purified by sublimation and the extraction, or production, of sulfuric acid, writing that: I am very much persuaded, Sir, by that which you have said[, namely] that our new instruments of chemistry could provide things which could not be found at all in other ways: where principally I have already seen flowers of niter purified by sublimation and which resolve themselves in air much more quickly than ordinary fixed niter. But until now I have hardly worked on anything other than on perfecting more and more the extraction of the acid of sulfur through the approach I told you about.358 Leibniz recognized at once the importance of the Papin’s new process for the production of the strong acids, viz. oil of vitriol (sulfuric acid), aqua fortis, spirit of niter or saltpeter acid (nitric acid), and spirit of salt (hydrochloric acid). He then wrote the following lines to the correspondent on November 18: Since your new methods of distilling provide a means of making the spirit of sulfur at a better price, I have no doubt at all that one can find there considerable wisdom[,] particularly since this spirit is rather similar to that of vitriol. Following that, the spirit of salt and above all that of niter or aqua fortis, merit your attention. For the use of aqua fortis is very considerable. If therefore you continue to advance your discoveries, the public will be greatly indebted to you.359 357 “Je crois pourtant que cela pourra tousjours estre utile à bien des choses et donner beaucoup de lumieres” (p. 513). 358 “Je suis fort persuadé, Monsieur, de ce que Vous dittes que nos nouveaux instruments de chymie pourront fournir des choses qu’on ne trouveroit point par d’autres voies: où principalement que J’ay desjà vu du nitre fixe sublimé en fleurs et qui se resolvoit à l’air bien plus promptemt que le nitre fixe ordinaire: mais jusques icŷ Je n’ay gueres travaillé qu’à perfectionner de plus en plus l’extraction de l’acide de soulfre, par les raisons que Je Vous ay dittes” (A III,7 N. 153, p. 626). 359 “Puisque vos nouvelles manieres de distiller donnent moyen de faire l’esprit de souphre à meilleur marché, je ne doute point qu’on n’en trouve des sages considerables d’autant que cet esprit est assés semblable à celuy de vitriol. Apres cela l’esprit de sel, mais sur tout celuy du nitre, ou l’eau forte meriteroient vostre soin. Car l’usage de l’eau forte est tres grand. Si vous continués de pousser ainsi vos découvertes, le public Vous aura des obligations immenses” (A III,7 N. 156, p. 632).

712

Chapter 5

Papin in turn, in his letter of December 5, 1697, emphasized the importance of spirit of sulfur, particularly for chemistry and medicine, but also for the conservation of meat. And so he wrote on this occasion: The spirit of sulfur is preferred to the spirit of vitriol by authors in medicine and in chemistry, and also it is much more expensive and more difficult to prepare using the ordinary methods. Yet I would not make a great issue of this if its uses were limited to medicine. However I find that it could be very useful in kitchens and at sea in order to always have fresh meat and water free of contamination, so that I believe that this would go much further if one were to have the large instruments to produce this spirit promptly and in quantity. This is what I am working on at present, but I am not making rapid progress for the reasons I gave you previously. I have also obtained spirit of salt and spirit of niter by the same means, but I have not worked any further either on alum or on vitriol.360 And so, as Papin explained in his first letter to Leibniz of 1698, on January 6, spirit of sulfur (“l’esprit de soulfre”) diluted with water could serve as a conservation fluid for foodstuffs. He had himself successfully conserved pears, raspberries, apples, and plums, as well as several types of meat and vegetables. In addition, he intended investigating the conservation of fish and he offered to make such conserved products available to Leibniz. Thus he wrote: In the month of September I filled a glass with pears that were already soft and which would certainly not have failed to become putrefied within two days. I even cut some of them in two in order to let the morsels into the interstices in order that they should turn foul only a little of the liquid I used for totally filling the glass and, in spite of all, these pears have not changed since that time. I have conserved in the same way other fruits such as raspberries, apples, and plums or prunes. I can also conserve several types of meat and vegetables even in vessels made of wood, 360 “L’esprit de souphre chez les auteurs de Medecine et de chymie est preferé à l’esprit de vitriol: et aussi il est bien plus cher et plus difficile à preparer par les voies ordinaires: Je n’en ferois pourtant pas grand cas si ses usages se bornoient à la medecine: mais J’ay trouvé qu’il peut étre si utile dans les cuisines et sur la mer pour avoir tousjours des viandes fraiches et de l’eau exempte de corruption, que Je crois que cela doibt aller fort loing quand on aura de grands instruments pour tirer cet esprit promptement et en quantité. C’est à quoy Je travaille presentemt; mais Je n’avance pas vite pour les raisons que J’ay dittes autresfois. J’ay aussi tiré de l’esprit de sel et de l’esprit de nitre de la mesme maniere, mais Je n’ay point encor travaillé sur l’alun ni sur le vitriol” (A III,7 N. 161, pp. 647f.).

July 1696–1698

713

and I have the intention also of soon carrying out an experiment on the conservation of fish because, if that succeeds, it will be easy for us to have fresh seafood in Kassel at any time. If you, Sir, or any of your friends, have an interest in undertaking such a trial … I will not hesitate to supply you with some.361 In addition, Leibniz and Papin discussed certain medical benefits in connection with the conservation of meats, fish and fruit like, for example, the application of spirit of sulfur as a remedy for scurvy.362 12

Projects: Cryptography

In the course of their mathematical correspondence, Leibniz attempted (alas without success) to persuade John Wallis to share his knowledge of cryptography. To begin with, on March 29, 1697, and again on April 3, 1698, he attempted to persuade the correspondent to impart his knowledge to the younger generation.363 In these letters, Leibniz characterized cryptography with esteem as a certain pediment and likewise a delicacy of human endeavor (“fastigium quoddam subtilitatis simul industriaeque humanae”), and as a specimen of the pinnacle of human penetration (“summum specimen humanae penetrabilitatis”), respectively. Later, from the end of 1698, Leibniz pleaded for the sending of a younger man to Wallis to partake in his knowledge. To this end, he turned to prince Ferdinand of Tuscany on November 3,364 as well as in the following year to the courts of Brandenburg (on February 24),365 and of Sweden (on April 17).366 Leibniz’s motive was surely not the political benefits that 361 “au mois de Septemb. J’emplis un verre avec des poires desjá molles et qui n’auroient pas manqué d’étre pourries au bout de deux jours: J’en coupay mesme quelques unes afin d’en mettre les morceaux dans les interstices afin qu’il ne fallust que peu de ma liqueur pour remplir tout à fait le verre: et neantmoins, depuis ce temps là ces poires n’ont point changé. J’ay conservé de mesme d’autres fruits comme des framboises, des pommes, des prunes. Je conserve aussi plusieurs sortes de viandes et de legumes mesmes dans des vaisseaux de bois: et J’ay dessein aussi d’en faire bien tost des experiences sur le poisson: parceque, si cela reussit il nous sera facile d’avoir en tout temps de la marée fraische à Cassell. Si Vous, Monsieur, ou quelcun des vos amis avez envie d’en faire quelque essay … Je ne manqueray pas de Vous en envoier” (A III,7 N. 171, p. 691). 362 Cf. A III,7 N. 163, p. 658, and N. 171, p. 691. 363 Cf. A III,7 N. 85, p. 353 and N. 184, p. 747, respectively. 364 Cf. A I,16 N. 152, pp. 250f. 365 Cf. A I,16 N. 349, pp. 577f. 366 Cf. A I,16 N. 444, pp. 726f.

714

Chapter 5

accompanied a knowledge of cryptography – even if these played a role in his argumentation at court – but rather the advancement of the ‘ars inveniendi’, and the fear that the cryptographic knowledge of the 80-year-old Wallis could be lost to posterity at his death, just as in the case of François Viète (1540–1603) almost a century before.367 Thus, in relation to the former concern, he wrote the following words to Wallis on October 12, 1697: “I would wish that you would also take care to have both specimens conserved as stratagems of your cryptographic art … Nor do I treasure just that in itself but more so for the advancement in this way of the ars inveniendi”.368 Regarding the latter concern, he then quoted the following text from his review of Wallis’ A treatise of algebra (1685) in a letter to the author on March 29: For the rest, regardless of the way we have learned that the celebrated author excels in solving[,] or as it is commonly expressed[,] in deciphering cryptographs, and by virtue of that science in possessing a great affinity to those who pass on to posterity, he is emphatically entreated to hand on his precepts or rules. This is especially so since those, which are presently being offered, are most imperfect. And so in this way the matter corresponds to the praises sung for Viète; he will however succeed, if he reveals a lasting specimen to posterity.369 In the review in question, Leibniz had – in addition to the appeal to Wallis to share his knowledge  – placed cryptography in the proximity of algebra and compared the author to Viète. He had already committed his desire to paper as early as 1673,370 and he continually repeated it to other English correspondents in the 1690s.371 However, Wallis’ reaction was noncommittal. As a specimen of his capability, he sent an encoded letter – together with his notes for its decoding – to Mencke who, however, because of political considerations, 367 Cf. D. Kahn, 1967 (and 1996), pp. 116–188, and P. Pesic, 1997 (Introduction, note 138). 368 “Optarem non specimina tantum, sed et artificia artis tuae Cryptolyticae conservari curares … Neque ego ista per se, sed potius ob artem inveniendi hinc promovendam [aestimanda] censeo” (A III,7 N. 146, p. 586). 369 “Caeterum, cum celeberrimus autor, quemadmodum intelleximus, excellat in solvendis, vel ut vulgo loquuntur deciphrandis Cryptographematibus, eaque scientia magnam cum illis quae hoc opere traduntur affinitatem habeat, orandus magnopere est ut praecepta ejus tradat. Praesertim cum ea quae hactenus prostant valde sint imperfecta. Ita in hoc quoque genere Vietae laudes aequabit, imo vincet, si duraturo ad posteritatem specimine ostendat” (A III,7 N. 85, p. 353); cf. the anonymous review of Wallis’ A treatise of algebra (1685) which appeated in the Acta Eruditorum, (June, 1686), pp. 283–289. 370 Cf. A VII,3, p. 253. 371 Cf. A I,8 N. 303a, (p. 502), I,11 N. 296 (p. 432) and I,13 N. 197 (p. 300).

July 1696–1698

715

refused publication and informed Leibniz accordingly on June 1, 1697.372 Hereupon, Wallis published the letter in the third volume of his Opera.373 Furthermore, he failed to react to Leibniz’s proposals. However, he did avail of Leibniz’s interest in negotiations with the English court, and he was duly granted a pension in order to enable him to instruct his grandson William Blencow in cryptography.374 While Leibniz’s attempts to persuade John Wallis to share his cryptographic knowledge proved to be futile, at least until the end of 1698,375 the matter continued to be a topic in his correspondence with Wallis thereafter, in 1699 and 1700.376 Following persistent pressure, Wallis finally admitted that political considerations had influenced his decision not to respond to Leibniz’s request for him to publish his methods, or at least to educate someone in these matters. Encryption was often necessary in negotiations, and therefore a dissemination of cryptographic methods was not at all desirable. Furthermore, as he informed Leibniz on April 9, 1700, he was unwilling to part with his knowledge in this area without the express consent of his sovereign, or, as he wrote here “For[,] in the carrying out state business of great moment, it proves to be of great use to be able to communicate matters in secret”.377 A further reason, as he had explained to Leibniz in an earlier letter of January 26, 1699, lay in the nature of the matter itself. Cryptography was difficult to transmit since it consisted not merely of a method, but rather of a clouded pursuit in the course of which the method of operation needed to be continually adapted. “Cryptolytics”, he wrote, was a matter which demanded a certain very special “acumen of ingenuity”.378 Ultimately, however, Wallis’ work on cryptography dating from the year 1653 was posthumously edited and published by John Davys in An essay on the art of decyphering (1737).379

372 Cf. A I,14 N. 144, p. 245. 373 Cf. Wallis: Opera Mathematica (note 115 above), in particular vol. 3, pp. 659–667. 374 Cf. D. E. Smith, 1917 (Introduction, note 139), and P. Beeley, 2016 (Introduction, note 137). 375 Cf. A III,7, p. XLIX. 376 Cf. A III,8, p. L. 377 “Nam in negotiis magni momenti transigendis, magno usui esse solet, posse secreto res communicare” (A III,8 N. 153, p. 399). 378 “De Cryptolyticis … poscit haec res peculiare quoddam ingenii acumen” (A III,8 N. 10, p. 46). 379 Cf. J. Davys, An essay on the art of decyphering. In which is inserted a discourse of Dr. Wallis. Now first publish’d from his original manuscript in the publick library at Oxford, London, 1737, specifically p. 9 (Dr Wallis to the Reader) – p. 58 (Finis), and also K. Ellison, 2017 (Introduction, note 140), in particular pp. 1–20 (Introduction: crises of expression in seventeenth-century criptography manuals).

716 13

Chapter 5

Projects: Brandy Distillation

The final economic project of importance, which was developed by Leibniz together with Johann Daniel Crafft, was the plan for the production of brandy from treacle by means of a process that Crafft professed to have tested and proven. In May 1694, Leibniz and Crafft concluded a contract forming a company for the production of brandy.380 The project was planned as a tactical move in an envisaged trade war against France. The strategy was that imports of brandy products from France were to be impaired by the domestic production of substitute distillates. The production process was to be prepared and perfected in Holland, and for this purpose Leibniz and Crafft travelled to Amsterdam at the beginning of November 1694. Leibniz returned in the same month, but Crafft spent the final two and a half years of his life in Amsterdam. The brandy project failed to find the hoped-for response and the its realization was subject to repeated delays. By mid-1696 the project seemed wholly and permanently debilitated, with the result that that Crafft had to seek new possibilities to secure his livelihood. The frequency of letters to Leibniz decreased, and the two long-time companions became increasingly estranged. In the last nine months of his life, Crafft wrote a total of three letters to Leibniz.381 The final stroke then, that would wipe the slate clean in a correspondence, that had been conducted since 1671, was inflicted by Leibniz on March 8, 1697, just one month before Crafft’s death.382 At the outset of the period under consideration, on September 26, 1696, Crafft could, in spite of all, report progress on the brandy project to Leibniz. He was still hoping to be able to live from this project in the future, and even to generate surpluses. In addition, he informed Leibniz about contacts to a business partner named Ludwig Wilhelm von Stauff zu Löwenstadt, who was, however, regarded as dubious and unsavory by Leibniz. Among other things, Crafft wrote in this letter that the two of them had, in addition to plans for the continuation of the brandy project, developed a remarkable finance plan for presentation to the States General of the United Provinces of the Netherlands. Crafft hoped to further develop the brandy project in Amsterdam, whereas von Stauff favored the “free city” and a self-proclaimed sovereign seignory (or seigniory) of Vianen, a location (near Utrecht) which was also a haven for dubious characters and adventurers, a fact most likely known to Leibniz. Thus Crafft wrote: 380 Cf. A III,6, pp. LXVIf., and Chapter 4 of the present work. 381 Cf. A III,7 N. 35, N. 36 and N. 73. 382 Cf. A III,7 N. 79.

July 1696–1698

717

And so I will return to my Brandy works which is a project from which I may expect to be able to adequately subsist, according to the samples hitherto obtained, and which may be put into practice nowhere better than here, although Baron von Stauff would prefer to see these works continued in Vianen  … In addition to this, we have the vision of presenting to the States General a remarkable finance plan concerning the acceptance of which we have no doubts. It could bring us an enormous return, and provide me with an annual income of at least 5000 florins.383 Notwithstanding this (no doubt overly) optimistic outlook, he now found himself in the role of solicitant before Leibniz. The planned (but never undertaken) relocation of his wife to join him in Amsterdam, and payments to an assistant there had led to a financial shortfall, so that he was now being forced to request a payment of 40 Taler from Leibniz. Then, when on February 26, 1697, he complained to Leibniz about the outstanding payment of the requested sum, he must have realized that his relationship to his former friend and associate had suffered. He presented, among other things, a follow-up project to the brandy project, that he claimed would be much better and to which he had aspired over a period of forty years. However, being gout-ridden he had been prevented from pursuing this and further projects. Crafft’s desperate situation was repeatedly articulated in between moments of excitement about his conceptions and discoveries, as when he wrote the following lines: If I do not pay soon the debts, which I acquired in the time of my indisposition, as well the outstanding semi-annual rental payments, the result will be that I can receive no further credit and will be confronted rather with seizures of belongings however small and with the prospect that I, as an old man without means, will be taken willy-nilly as an act of mercy to the charitable hospital [or infirmary] … I would rather die of hunger than to experience this insult and humiliation, for I would in this way have attained my civil deceased status, and would be lost along with all my wonderful concepts and inventions.384 383 “vnd kehr mich wieder zue meinen Br.W. welcher eine Sach ist, wordurch ich den befundenen Proben nach genugsamb subsistiren kann, vnd nirgends beßer alß alhier zu practicieren ist, wiewohl B. v. Stauff solches lieber in Viane fortgesezzet sahe. …Vber dieses haben wir ein Concept, den Staaten General eine sonderbahre Finanz vorzutragen, So dieselbe, wie wir nicht zweifeln, angenommen wird, kann es vns ein großes eintragen, vnd … mir jährlich zum wenigsten 5000 fl. abwerfen” (A III,7 N. 35, p. 147). 384 “wenn ich die Schulden, so ich die zeit meiner kranckheit gemachet, vnd den halbjährigen haußzinß nicht bald bezahle, daß man mir nichts mehr credidirt, sondern alles, so

718

Chapter 5

Crafft wanted Leibniz to seek financial support for the brandy project from the court in Celle. Furthermore, he once again insistently requested money from Leibniz and he warned him, in the following words, that: If you were to be so unmerciful towards me, Sir, and were to let me be subject to this insult and humiliation, then you could not blame me and my poor honest housewife if we were to vengefully decry you, Sir, as long as we live, because, at the same time, you tore us apart and are now not prepared to help us come together again.385 Leibniz’s reply, on March 8, reveals the fact that he had already supported Crafft financially to a considerable degree and that he had, as quid pro quo, called for a continuation of their correspondence on a regular basis. However, he had been bitterly disappointed by Crafft’s failure to meet this condition, and so he wrote in this final letter to the correspondent that: “All has however been squandered in such a fashion that I find myself in the end having to be ashamed of myself for my good faith”.386 Leibniz complained above all about the circumstance that the promised communication of information had not materialized. He felt himself exploited and treated “like a cow being milked”.387 And he insisted that he was not pursuing personal advantage, but rather the public interest or the commonweal. He expressed doubts concerning the prospects for the brandy project, in particular, and on the practicability of Crafft’s projects in general, demanding presentable results in advance of any further financial support. He reproached Crafft with the circumstance that his ambitious plans with Baron von Stauff had come to nothing, since there had been no further mention of them. In the final sentence of the letter, Leibniz then laid down the conditions for a continuation of the business partnership with Crafft: “I expect, Sir, that you finally embrace reason and fairness, put aside the

wenig es auch sein möchte, durch execution hinweg nimbt, vnd mich alß ein alten Mann quasi aus barmhertzigkeit nolentem volentem in das Hospital bringet, … wollte ich lieber hunger sterben, alß diesen Schimpf erleben, denn ich were dadurch civiliter mortuus, vnd mit allen meinen herrlichen Concepten vnd Inventionen verlohren” (A III,7 N. 73, p. 298). 385 “Wenn derselbe so vnbarmhertzig gegen mich wäre, vnd in diesen Schimpf … verfallen laßen wollte, so würde Er mich vnd meine arme ehrliche haußfraw nicht verdencken, daß wir biß in vnser grab Raach über M. h. H. schrien, daß Er vns gleichsamb von ein ander gerißen, vnd nun nicht wieder zusammen helfen will” (p. 299). 386 “Es ist aber alles dergestaldt in windt geschlagen worden, daß ich mich endtlich meiner eigenen guthwilligkeit schähmen müssen” (A III,7 N. 79, p. 325). 387 “alß eine melckende kuh” (p. 326).

July 1696–1698

719

finesse, and deal with me earnestly, in which case, and not otherwise, we can continue to do business together”.388 A month later, on April 9, 1697, Johann Daniel Crafft died in Amsterdam. In connection with the death of this correspondent stood Leibniz’s correspondence with the widow, Dorothea, as well as with Crafft’s Dutch correspondents Nicolaas Listingk and Ameldonck Block. Leibniz had met Listingk during his stay in Amsterdam in November 1694, and it was from this correspondent that he learned  – in reply to his query about Crafft’s well-being  – of the latter’s death from a letter of July 9, 1697. Listingk wrote as follows: Now I went myself, on receipt of your letter, to the place itself at the extreme end of the town where I learned he, being indisposed, had gone to live with a certain Jacobus de Rijke in a side street called the ‘Reguliers dwars straet’, in a room above a cabinetmaker-carpenter, near the Butter market, whom I looked up and from whom I learned that Dr Crafft, totally wasted away and fallen into great poverty, had died in God’s grace on the past third day of Easter and was buried in the St Anthony’s Church Cemetery (‘Sint Anthonis Kerkhof’), some days later. I was most surprised that I did not receive the least information about the matter, because otherwise I would have rendered assistance to the good man.389 In mid-July 1697 Leibniz passed on the sad tidings from Listingk’s letter to the widow, Dorothea Crafft, in the following words: When I wrote to Mr Nicolaus Listing, a famous advocate in Amsterdam, asking for news, he replied to me that which is contained in the attachment containing the following information, that the late Mr Crafft

388 “Erwarte also daß M. h. H. endlich einmahl raison undt billigkeit gelten lasse die finessen beyseits sehe undt auffrichtig mit mir umbgehe, auff welchen fall undt anders nicht wir ferner in commercio stehen können” (p. 328). 389 “Nu hebbe, op uw Eeds schrijven, selfs daer na toe geweest, op ’t uijtterste eijnde van de Stadt, daer vernam dat was gaen woonen, sieck sijnde, bij eenen Jacobus de Rijke in de Reguliers dwars straet op een Camer, boven een halemaker, bij de Booter marct, dewelcke ick ging opsoeken en van deselve verstondt dat d. he Dr Kraft gansch uijtgeteert ende tot groote armoede vervallen sijnde godtsalighlijk op den 3 paesdag laestleden gestorven ende op ’t Anthonis Kerkhof, eenige daegen daer na, begraven was. Ick was seer verwondert dat mij daer van geen de minste kennisse was gegeven: want anders noch wel assistentie aen die goede heer soude hebben gedaen” (A III,7 N. 113, pp. 470f.).

720

Chapter 5

died on the third day of Easter in the house of Jacob de Ryke in the ‘Reguliersdwars straat’ and was gracefully buried.390 He justified his dealings with Crafft in this letter to the widow, and he pointed to his financial support for the deceased that had been misappropriated again and again. Leibniz likewise spoke critically of Crafft in another letter of mid-July to Ameldonck Block, with whom Crafft also had debts.391 From this source it becomes evident how objectionable and malodorous Leibniz had found Crafft’s business relationship with Baron von Stauff, and which ultimately had led to his demise. Here he wrote that: If he had chosen to follow my advice, he would have earned all that he needed to subsist and pay his debts. But he always embarrassed himself with new projects of a frivolous nature. He was never able to free himself from the chimera of being able to make gold. And in the end he joined up with a certain German Baron … and this company brought about his downfall.392 While Leibniz praised Crafft as a chemist, and a technician, in this letter, he attested him impaired judgment and an inability in managing money, and he complained about his ungratefulness and greed for profit. Crafft had hoped through a great discovery to become rich someday. Leibniz told that he had again and again cautioned him to follow an ordinary profession and, like himself, to work for the common good. Leibniz explained further how he had supplied Crafft with money, partly from his own pocket, and that he had been willing to continue doing so provided Crafft adhered to the terms of their mutual agreement.

390 “Als ich an Herrn Nicolaus Listing einen berühmten Advocaten in Amsterdam umb nachricht geschrieben, antwortet er mir, was in der beylage enthalten darauß so viel abzunehmen, daß der seel. H. Krafft den 3 Oster tag in Jacob de Ryke hause in der Reguliersdwars straate seel. verstorben und ehrlich zur erden bestattet worden” (A III,7 N. 118, p. 489). 391 Cf. A III,7 N. 117, pp. 484–486. 392 “S’il avoit voulu suivre mon conseil, il auroit gagné tout ce qu’il fallout pour subsister et pour payer ses dettes. Mais il s’embarassoit tousjours des nouvelles choses sur des apparences frivoles. Il ne se pouvoit point défaire de la chimere de faire de l’or. Et il s’estoit enfin engage avec un certains Baron Allemand … et cette compagnie l’a achevé” (p. 484).

July 1696–1698

14

721

Alchemy and Chemistry

With a letter of May 24, 1698, Johann Andreas Stisser – who was a university professor in Helmstedt – initiated a correspondence with Leibniz.393 The prelude to this correspondence was the transmission (as an attachment to this letter) of a work on chemistry by Stisser entitled Actorum laboratorii chemici … specimen tertium (1698).394 This work dealt with, among other things, a certain “Tinctura vitrioli”, to which Leibniz referred in his reply on June 1. In doing so, he recalled the medieval alchemical text ‘Turba philosophorum’, in which mercury was treated as a basic principle of metals. Leibniz now saw vitriol in this role, expressing himself in his reply (on June 1) as follows: Although I do not share the opinion of the philosophers, who say that there is something in vitriol sought by the wise (Est in vitriolo quicquid quaerunt sapientes), and am rather of the opinion that nature shares its treasures among many bodies, I have nonetheless thoughts that a large part falls to vitriol and, for that reason, that this deserves a more thorough cognizance.395 Leibniz’s interest in alchemy had of course existed since his stay in Nuremberg, between the spring and fall of the year 1667, when he became secretary of an alchemical society there. When – almost thirty years later, on August 10, 1696 – Gottfried Thomasius reported to him about an alchemist called Friedrich Kleinert,396 Leibniz recalled – in his reply of December 17 of that year – the names of certain alchemists of earlier times, including Ramon Lull, Nicolas Flamel, Daniel Keller, Johann Conrad von Richthausen (a baron with the title ‘Freiherr von Chaos’), as well as a former monk called Johann Wenzel Seyler. Keller had been a practitioner of the art of the gold-maker in sixteenth-century Augsburg, whereas Baron Chaos had demonstrated in Mainz, in the year 1658, an alleged process for the transmutation of mercury into gold. Wenzel Seyler had possessed a powder with the help of which gold could allegedly be 393 Cf. A III,7 N. 195, pp. 778f. 394 Cf. J. A. Stisser, Actorum laboratorii chemici in Academia Julia specimen tertium medicochemica observata quaedam rariora exhibens, Helmstedt, 1698. 395 “Ob ich nun aber der Meinung der philosophorum nicht bin, die da sagten Est in vitriolo quicquid quaerunt sapientes, sondern dafür halte daß die Natur ihre schäze unter viel Cörper vertheilet; so bin doch gleichwohl in den gedancken, daß ein großes Theil den vitriol zugefallen, und solches daher eine gründtlichere erkentniß wohl verdiene” (A III,7 N. 197, pp. 782f.). 396 Cf. A III,7 N. 19, pp. 80f.

722

Chapter 5

produced, and he stood in high regard until his process was found to be fraudulent. On his way to Italy, on May 17, 1688, Leibniz himself had inspected – at the Imperial Treasury in Vienna – the counterfeit, or fake, gold from the workshops of Chaos and Seyler. He now told his correspondent Thomasius that he had personally witnessed the demise of practitioners in the field, like Johann Joachim Becher and others, and he urged circumspection in judging alchemical activity. Thus, he wrote to Thomasius: Gratifying is the intelligence you provide regarding your Alchemist. I, for my part, could weave a certain history under the false name of ancient and recent achievements. Regarding Lull and Flamel, the learned have long recognized how improbable that was which they pronounced. [The dupability of] Keller, Baron Chaos and the ex-monk Wenzel Seyler took the form of presenting as a treasure what they call coal, thus by charring [carbonization]. I was first imbued in chemical studies in Nuremberg and I do not regret having learned while growing up what would become certainty in manhood. For later I was often motivated not just by that which had been assigned to me, nor did I lack curiosity, but was accordingly guided by circumspection. I witnessed the demise of Becher and other men very well known to me who were carried away by chemical hopes or daydreams just like being blown away with the wind. And so I always cautioned inquisitive friends about this in investigating nature, advising that they should detach chemical studies from the plans or intentions of life, nor should they at any time cut off anything whatsoever of their activities from the foundations of the laboratory, no more than occupy themselves with chimeras or fantasies.397

397 “Jucunda sunt quae de Alchemista vestro narras. Possem ego Historiam quandam texere Falsi nominis Adeptorum veterum et recentiorum: de Lullo et Flamello dudum notarunt docti parum verisimilia esse quae jactantur[.] Kellerus, Baro Chaos, Baro ex monacho Wenceslaus dedere credulis pro thesauro, quod ajunt carbones. Me Noriberga primum chemicis studiis imbuit nec poenitet adolescentem didicisse quod viro cautioni esset. Nam postea crebro pulsatus sum, non tam mea quam principum gratia, apud quos mihi aditus erat, neque defui curiositati, sed ita ut circumspectione temperaretur. Vidi Becheri naufragia aliorumque mihi notissimorum hominum qui spe chemica tanquam secundo vento ferebantur. Itaque illud semper monui amicos naturae indagandae curiosos, ut chemica studia secernerent a vitae consiliis, neque unquam quicquam rerum suarum fundamentis laboratorii inaedificarent, non magis quam somniis” (A III,7 N. 57, pp. 217f.).

July 1696–1698

723

His Swedish correspondent in Florence, Magnus Gabriel Block, who commenced the correspondence with a short letter of May 12, 1698,398 had the same attitude to alchemy as Leibniz himself, and he wrote accordingly on July 1, 1698: As regards alchemy I did not want to embark upon it again, for I am terrified by those who in seeking to attain opulence have landed in the [mental] hospital, and I approve of the Spanish proverb Alequimia399 provada es tener rienta y no gastar nada.400 Thus, the wording of Block’s admonition, which was based on the Spanish proverb cited, was to the effect that it is tried alchemy to have return and spend nothing. Saving is a great revenue source! 15

Paleontology and Earth History

Investigation of large mammals was a pronounced interest of Leibniz and his correspondents in the period under consideration. The general context of Leibniz’s interest in the anatomy of large mammals was his commitment to natural history and, in particular, the history and form of the earth. His Protogaea sive de prima facie telluris, which was posthumously-published in the mid-eighteenth century,401 was composed in the early 1690s, and it was publicly announced for the first time in an advertisement in the Acta Eruditorum 398 Cf. J. Nordström, “Leibniz och Magnus Gabriel Block. En brevväxling” [Leibniz and Magnus Gabriel Block, a correspondence], Lychnos. Lärdomshistoriska Samfundets Årsbok [Annual of the Swedish History of Science Society], 1965–1966, pp. 181–260, specifically p. 194, and A III,7 N. 190, p. 763. 399 Translation: a penny saved is a penny earned / saving a penny at a time might get you a fortune. 400 “pour l’alchimie je n’ai pas voulû m’embarquer encore, quoniam me vestige terrent tot opulentium qui s’en sont allé à l’hôpital et je approuve le proverb des Espagnols Alequimia provada es tener rienta y no gastar nada” (A III,7 N. 203, pp. 798–803, specifically p. 802; Leibniz: Nordström, pp. 195–198). 401 Cf. G. W. Leibniz, Chr. L. Scheidt (ed.), Protogaea sive de prima facie telluris et antiquissimae historiae vestigiis in ipsis naturae monumentis dissertatio, Göttingen, 1749; Protogaea, oder Abhandlung von der ersten Gestalt Der Erde und den Spuren der Historie in den Denkmaalen der Natur, Leipzig, 1749, and also L. Dutens (ed.), Gothofredi Guillielmi Leibnitii  … Opera Omnia, 6 vols, Geneva 1768, in particular vol. 2, part 2, pp. 181–198 (preface) and pp. 199–240; Leibniz: Cohen-Wakefield, 2008, and Leibniz: Scheid-Engelhardt-Wellmer, 2014 (Introduction, note 190).

724

Chapter 5

in January 1693.402 This projected work also forms the context of Leibniz’s correspondence with the Hamburg pastor Caspar Büssing, and in particular their exchange of views regarding the theories of Thomas Burnet and William Whiston. In his De situ telluris … dissertatio mathematica (1695),403 Büssing had published a critique of Burnet’s views, as expounded in the work entitled Telluris theoria sacra (1681–1689),404 and on October 16, 1696, he informed Leibniz in the following words: Over and above this, however, it deserves more than my merely semiperfect dissertation against Burnet … There is but one point in Burnet which I have treated, namely that regarding the siting [position] of the earth, in which case, if my demonstration be valid, there is no praise due to me for the truth of it.405 However, he was not sure if his publication had reached England, and if Burnet would heed it and answer, and he expressed himself accordingly in this letter of October 16 to Leibniz.406 Büssing’s opus was at all events reviewed by Christoph Pfautz, in the Acta Eruditorum in November 1695, and was admired by Leibniz and subsequently referred to by him in correspondence with, among others, Wilhelm Ernst Tentzel and Thomas Burnett of Kemney.407 402 Cf. G. W. Leibniz, “Protogaea Autore G.G.L.”, Acta Eruditorum, (January 1693), pp. 40–42. 403 Cf. C. Büssing, De situ telluris Paradisiacae et Chiliasticae Burnetiano, ad eclipticam recto, quem T. Burnetius in sua theoria sacra telluris proposuit, dissertatio mathematica, Hamburg, 1695. 404 Cf. T. Burnet, Telluris theoria sacra, originem et mutationes generales orbis nostri, quas aut jam subiit, aut olim subiturus est, complectens. Accedunt archaeologiae philosophicae, sive doctrina antiqua de rerum originibus, 2 vols, London, 1681–1689, and Amsterdam, 1694; The theory of the earth, London, 1684 (3rd ed., 1697); Heilige beschouwinge des aardkloots, Amsterdam, 1696. 405 “Quod superest, non equidem meruit mea vix semiperfecta Dissertatio Anti-Burnetiana … Vix unicum punctum est quod in Burnetio tetigi, nempe illud de Situ Telluris, quo in, si quid valet mea Demonstratio, veritati, non mihi Laus sit” (A III,7 N. 40, pp. 160f.). 406 “Nescio an in Angliam pervenerit multoque minus num ipse Burnetius quid repositurus sit” (p. 161). 407 Cf. Acta Eruditorum, (November 1695), pp. 504–512. Leibniz’s admiration for Büssing’s opus was expressed in a letter from the end of January 1696 to Burnett of Kemney in the following words: “Je trouve que ceux qui ont écrit contre M. Burnet, l’ont fait avec trop d’aigreur, excepté M. Bussing[,] Ministre et professeur des mathematiques à Hambourg, qui s’est attaché aux choses, sans rien exagerer” (A I,12 N. 248, p. 369). The Burnet critique referred to here was: E. Warren, Geologia: or a discourse concerning the earth before the deluge, London, 1690. Regarding Clüver’s later work Geologia, and the references to it in Leibniz’s correspondence, cf. D. Clüver, Geologia sive philosophemata de genesi ac

July 1696–1698

725

On December 26, 1696, Büssing then reported to Leibniz,408 that he had just received Burnet’s publication Archaeologiae philosophicae (1692).409 This work had angered some English theologians, but Burnet, enjoying the protection of the king, was able to retain his standing. Büssing was also disappointed by Burnet’s publication, and he was of the opinion that it represented no more than a kind of literary history (“historiam quandam literarariam”) and failed to dispel any of the doubts that had been uttered. Leibniz could then inform Büssing in early January, 1697, about William Whiston’s A new theory of the earth (1696).410 In this work, Whiston had postulated the origin of the earth from the atmosphere of a comet, and all major changes in the earth’s history were attributed by him to the action of comets.411 It was also directed against Burnet’s Archaeologiae philosophicae, and Leibniz had been informed accordingly through a letter, which was sent from London by Burnett of Kemney to the electress Sophie of Hanover on December 16, 1696.412 Thus, Leibniz wrote to Büssing on January 3: From England I have most recently been informed that a certain Whiston has opposed Burnet’s new theory of the earth with maximal approbation. I think the latter work will soon reach you, for books from England are readily available in Hamburg, or certainly can be obtained there.413

structura globi terreni: Oder: Natürliche Wissenschafft von Erschaffung und Bereitung der Erd-Kugel, Hamburg, 1700, and A I,19 N. 302, p. 590, and A I,20 N. 248, p. 413. 408 Cf. A III,7 N. 59, p. 226. 409 Cf. Th. Burnet, Archaeologiae philosophicae: sive doctrina antiqua de rerum originibus, libri duo, London, 1692. 410 Cf. W. Whiston, A new theory of the earth, from its original to the consummation of all things wherein the creation of the world in six days, the universal deluge, and the general conflagration, as laid down in the holy scriptures, are shewn to be perfectly agreeable to reason and philosophy: with a large introductory discourse concerning the genuine nature, stile, and extent of the Mosaick history of the creation, London, 1696. 411 Cf. Introduction, note 192, specifically the following titles: M. Farrell, 1973 and 1981, chap. 2 (Speculations in earth history 1660–1700. Whiston’s contribution to this debate); P. Rossi, 1984, chap. 10 (Burnet’s heritage); J. E. Force, 1985, chap. 2 (Whiston, the Burnet controversy, and Newtonian biblical interpretation); T. Heidarzadeh, 2008, pp. 129–135 (The post-Newtonian theory of comets: William Whiston and Edmond Halley); W. Poole, 2010, chap. 5 (The world makers: Burnet, Woodward, Whiston). 412 Cf. A I,13 N. 441, pp. 715f. 413 “Ex Anglia mihi scribitur novissime Witsonium quendam novam Theoriam telluris Burnetianae opposuisse, quae plurimum approbetur. Eam mox ad Vos perventuram puto, libri enim ex Anglia facile Hamburgi habentur, aut certe haberi possunt” (A III,7 N. 60, p. 228).

726

Chapter 5

Burnet had presented the view that God had created the earth in a perfect and regular form, but that it had been transformed into its present form by the deluge. Büssing’s alternative scenario assumed a spongy solidification of the earth’s crust through which, as a result of the subsidence or settlement of the earth’s surface, subterranean waters had been pressed upwards causing the deluge. Büssing’s explanation of the deluge appealed to Leibniz, as is evident from his letter of January 3, 1697. However, he was of the opinion that a sinking of the earth’s surface would not have been possible without fissures in the existing crust of the earth. Leibniz’s questions as to where such a quantity of water might have disappeared following the deluge, and whether, for example, the water had sunk back into cavities in the earth’s interior, remained no doubt unanswered by the correspondent. Leibniz’s words here were as follows: What you claim pleases me, namely that in the great deluge waters were pressed upwards following the subsidence of the earth itself. However I do not think that this sinking of the earth’s surface would have been possible without fractures and land-slips, for I believe the crust of the earth was previously firm. And to where did such a great quantity of water go afterwards? Did it perhaps sink back into certain cavities in the earth’s interior?414 16 Biology In Leibniz’s letter to Hendrik van Bleiswijk, on January 6, 1699, the theory of animal preformation is referred to in connection with a recent discovery of Antoni van Leeuwenhoek. Thus, Leibniz wrote: I am told that Mr Leeuwenhoek has recently discovered something, I do not know what but new, concerning the origin of animals, but I am not talking about the little animalcula in semen, of which he had already given an account to the public.415

414 “Mihi perplacet quod ais, in diluvio generali aquas ex ipsa terra subsidente fuisse expressas. Hunc tamen subsidentis superficiei descensum non putem factum sine fracturis et ruinis, jam enim credo firma erat crusta. At quorsum ivit postea tanta aquae copia? an effractis repagulis in hiatus quosdam magis interiores penetravit?” (p. 228). 415 “On me dit que Mons Leewenhoek a decouvert je ne sçay quoy de nouveau depuis peu, touchant l’origine des animaux, car je ne parle point des petits vers de la semence, dont il avoit deja donné connoissance au public” (A I,16 N. 260, p. 404).

July 1696–1698

727

The discovery in question may in fact be that referred to in an article by Martin Lister, which had been published in September 1698 in the Philosophical Transactions with the title “An objection to the new hypothesis of the generation of animals from animalcula in semine masculino”.416 However, Leibniz’s line of thought here might also be connected with two communications he received from Johann Bernoulli in Gronningen during the second half of 1698. In a letter of August 2, Bernoulli – in contemplating the infinite and the infinitely small in mathematics, like in the coexistence of lines and surfaces, of surfaces and bodies, or of differentials and integrals  – drew parallels to the ongoing dispute between ovists and animalculists in the theory of preformation, and he alluded to works by William Harvey, and by Leeuwenhoek.417 Thus Bernoulli wrote on this occasion: If a finite body has an infinite number of parts, I have always believed, and still believe today, that a minimum of those parts should have an unassignable or infinitely small relation to the whole. Nor is there a need of an actual division; it suffices for such a particle to coexist in toto, in the same way that a mathematical line coexists with a surface or a surface with a body, or any differential whatsoever with its integral or, to speak more appropriately, in the same way that, according to Harvey and others but not according to Leeuwenhoek, in animals there are innumerable ovula, in each and every ovulum an animalculum or many animalcula, in each and every animalculum (female) again innumerable ovula and so on to infinity.418

416 Cf. M. Lister, “An Objection to the new hypothesis of the generation of animals from animalcula in semine masculino”, Philosophical Transactions, vol. 20, no. 244, (September 1698), specifically p. 337. 417 Cf. W. Harvey, Exercitationes de generatione animalium, London, 1651, and Amsterdam, 1651; A. van Leeuwenhoek, “Observationes de natis e semine genitali animalculis”, Philosophical Transactions, vol. 12, no. 142, (December 1677–February 1678), pp. 1040–1043; A. van Leeuwenhoek, “An abstract of a letter … concerning generation by an insect”, Philosophical Transactions, vol. 15, no. 174, (August 22/ September 1, 1685), pp. 1120–1134. 418 “si corpus finitum habet partes numero infinitas, credidi semper et etiamnum credo minimam istarum partium debere habere ad totum rationem inassignabilem seu infinite parvam. Nec opus est actuali divisione, sufficit talem particulam in toto coëxistere, quemadmodum linea Mathematica coexistit cum superficie vel superficies cum corpore, vel quodlibet differentiale cum suo integrali vel ut aptius loquar quemadmodum secundum Harvaeum et alios sed non secundum Leuwenhoeck in animali innumera sunt ovula, in quolibet ovulo animalculum vel plura, in quolibet animalculo (faemella) iterum innumera ovula et ita in infinitum” (A III,7 N. 212, pp. 847f.; cf. the annotations).

728

Chapter 5

In a further letter of November 18, where the relationship between infinity and the infinitely small was likewise at issue, the mathematician Bernoulli – alluding to discussions he had in 1697 and 1698 with Pierre Varignon on these issues – referred to the micro-cosmos and the world of the animalcula observed by Leeuwenhoek, and he suggested that those animalcula might in turn, if provided with appropriate microscopes, observe a further micro-cosmos within their own, and so forth. Thus he wrote: For this argument was used against Varignon. Or at least because the infinite and infinitely small in the nature of things displeases you, we assume not the infinite but the incomparable, for in this way we detect with microscopes animalcula incomparably smaller than ourselves and all other animals familiar to us, and without doubt if those animalcula and theirs had in turn microscopes they would for their part detect others incomparably smaller than themselves, and so forth.419 Referring then to Leeuwenhoek’s observation of animate beings, or little animals, in water interfused with pepper,420 Bernoulli envisaged yet another sub-cosmos within the greater one, expressing himself as follows: Concede or imagine at least a grain of pepper (in which there are likewise many millions of living beings, witness those observed under the microscope by Leeuwenhoek and myself) having its parts throughout the whole proportional or corresponding to the parts of our world, namely its sun, its fixed stars, its planets with satellites or moons, its earth furnished with mountains, fields, woods, cliffs, rivers, lakes, seas and various animals.421

419 “hoc enim argumento ad Varignonium utebar: Vel saltem quia infinitum et infinite parvum in rerum Natura Tibi displicet sumamus non quidem infinita sed incomparabilia; quemadmodum enim microscopiis detegimus animalcula incomparabiliter minora quam nos et caetera animalia nobis consueta, et proculdubio ista animalcula si et sua haberent microscopia iterum detegerent alia se iterum incomparabiliter minora et sic porro” (A III,7 N. 242, p. 938). 420 Cf. A. van Leeuwenhoek, “Observations, communicated to the publisher by Mr. Antony van Leewenhoeck, in a Dutch letter of the 9th Octob. 1676. here English’d: concerning little animals observed in rain- well- and snow-water, as also in water wherein pepper had lain infused”, Philosophical Transactions, vol. 12, no. 133, (25 March 1677), pp. 821–831. 421 “Concede vel finge saltem granulum piperis (in quo pariter multae myriades viventium teste Lewenhoeckiana et mea ipsa microscopio conspiciuntur) habere suas partes nostri mundi partibus per totum proportionales, scilicet suum Solem, suas stellas fixas, suas

July 1696–1698

729

The interest of Leibniz and his correspondents in botany and zoology is also reflected in other correspondences between 1696 and 1698. Although chemistry was the main focus of the correspondence with Johann Andreas Stisser in Helmstedt, botany was also an interest of this correspondent.422 Stisser had set up a botanical garden in 1692, and he was the author of a book entitled Botanica curiosa published in 1697.423 Zoology and, in particular, the anatomical investigation of large mammals was likewise an important topic in Leibniz’s correspondence at this juncture. It was stimulated by the study of the skeletons of dead or extinct animals, and it was a natural by-product of the discussion of the issues arising in natural history. Thus, on January 3, 1697, Caspar Büssing posed the following question to Leibniz: “I do not know if you have seen that which D. Tentzel has published about the elephant-like animal unearthed in Thuringia”.424 Wilhelm Ernst Tentzel had reported the excavation of bones of an elephant-like creature at Gräfentonna (or Tonna) in his journal Monatliche Unterredungen (April 1696), and in an open letter addressed to Antonio Magliabechi, entitled Epistola de sceleto elephantino Tonnae nuper effoso, published in Latin and German at Gotha and Jena in the same year.425 Tentzel, for his part, hoped to obtain a report from the addressee of his Epistola about the skeleton of an elephant in Florence. In a letter to Leibniz on April 22, 1696 – to which the official judgement of the Collegium Medicum in Gotha concerning the discovery at Gräfentonna was attached  – Tentzel referred specifically to two additional publications, namely Allen Mullen’s twin tracts entitled An anatomical account of the elephant accidentally burnt in Dublin on Fryday June 17 [viz. June 27 new style] in the year 1681 … Together with a relation of new anatomical observations in the eyes of animals (1682), which were addressed to William Petty and Robert planetas cum satellitibus, suam Tellurem ornatam montibus, campis, sylvis, rupibus, fluviis, lacubus, maribus variisque animalibus” (note 419 above, pp. 938f.). 422 Cf. A III,7 N. 195, p. 778. 423 Cf. J. A. Stisser, Botanica curiosa, oder nützliche Anmerckungen, wie einige frembde Kräuter und Blumen in seinem Anno 1692 zu Helmstedt angelegten medicinischen Garten bishero cultiviret und fortgebracht, Helmstedt, 1697. 424 “Nescio an videris quae Dn. Tentzelius edidit de Sceleto animalis Elephantiformis in Thuringia effosso” (A III,7 N. 60, p. 228). 425 Cf. W. E. Tentzel, Epistola de sceleto elephantino Tonnae nuper effosso, ad virum toto orbe celeberrimum Antonium Magliabechium serenissimi magni Hetruriae Ducis Bibliothecarium & consiliarium. In 12. Gothae, Gotha and Jena, 1696; Inhalt eines Lateinischen Schreibens an Den Welt-berühmten Herrn Antonio Magliabechi, Rath und Bibliothecarium des Groß-Hertzogs zu Florentz / von dem zu Tonna ausgegrabenen Elephanten-Cörper, Gotha and Jena, 1696.

730

Chapter 5

Boyle, respectively,426 and John Ray’s Synopsis methodica animalium quadrupedum et serpentini generis (1693).427 Thus, Tentzel wrote on this occasion: I send you the report published here about the unearthed mammoth bones, in which these are taken to be fossils. I take them nevertheless to be elephantine, and I have recently made known the reasons for my sentiments in a letter addressed to Magliabechi, asking that I be sent a copy of the account of the complete elephant skeleton which is at Florence. I will examine everything relating to the anatomy of the Irish elephant and that of Ray, and I will show that there were real bones which were changed into mineral stone in the wet sand.428 Thus, Tentzel’s letter to Leibniz of April 22 reveals that, fifteen years after the event, Mullen’s dissection of the elephant was still attracting attention. Similarly, in a report on Tentzel’s Epistola de sceleto elephantino, in the Journal des Sçavans four months later, on August 20, 1696, the reviewer commented on Mullen’s autopsy of the elephant in the following words: The anatomy of an elephant published in English at Dublin by Mr Mullen in 1681 agrees perfectly with the observations made on the bones unearthed from the mound in Thuringia, both regarding the large number of cells into which the head is divided, as well as the size of the cranium [or skull]. It is true that the size of the cranium described in Dublin exceeds by a factor of two that of the cranium found in Thuringia, which

426 Cf. A. Mullen, An anatomical account of the elephant accidentally burnt in Dublin on Friday, June 17 in the year 1681: sent in a letter to Sir William Petty, fellow of the Royal Society: together with a relation of new anatomical observations in the eyes of animals, communicated in another letter to the Honourable R. Boyle, London, 1682. Regarding Mullen and his extant manuscripts, cf. Hoppen (ed.), 2008 (Introduction, note 203), vol. 1, nos. 184–189, pp. 399–413 and vol. 2, pp. 959f. 427 Cf. J. Ray, Synopsis methodica animalium quadrupedum et serpentini generis: vulgarium notas characteristicas, rariorum descriptiones integras exhibens: cum historiis & observationibus anatomicis perquam curiosis: praemittuntur nonnulla de animalium in genere, sensu, generatione, divisione, &c., London, 1693. 428 “Mitto nuperrime apud nos editum judicium de ossibus praegrandibus effosis, quo illa pro fossili habentur. Ego tamen pro Elephantinis habeo, proximeque edam rationes sententiae meae in epistola Magliabecchio inscribenda, ut exemplar integri sceleti Elephantis, quod Florentiae est, accipiam. Omnia ad Anatomiam Elephantis Hibernicam et Rajanam examinabo, ostendamque, vera ossa fuisse, sed in arena succo minerali in lapidem conversa” (A I,12 N. 357, p. 561).

July 1696–1698

731

is evidence that the latter elephant was inferior in size to the former by a factor of a half.429 As in the case of the autopsy of the elephant, the physician Mullen had recorded his observations on the eyes of fowl and of fish, as well as on the ears of fowl, drawing inferences between the organs of animals and of humans. Whale hunting, and the import of exotic animals from distant lands, offered yet another means of studying the anatomy of the largest mammals. On September 28, 1697, Georg Franck von Franckenau – who was then personal physician to the king of Denmark – reported to Leibniz that he had received precious minerals as well as coral, or coral algae, from the mining official Heinrich von Schlanbusch in Trondheim, Norway. In addition the remarkable penis, as well as the mandible, or lower jaw – commonly known as boning or Fischbein – of a whalebone or baleen whale had been received. Thus the correspondent wrote: Recently I received from Trondheim, Norway, from Schlanbusch, the most senior mining official of the metal ore mines there, exquisitely curious | gold |430 and | silver | mineral samples as well as Nidrosian (or Norwegian) Litophyton marine soft coral. In addition to this matter, a few days ago the remarkable penis, as well as the mandible or lower jaw of a whalebone or baleen whale, commonly called boning or Fischbein used by tailors or in the tailery, were offered.431 The same correspondent also reported that he had obtained specimens of animals like the large spotted civet cat and tiger, the long-tailed monkey, and the brown squirrel from East India. 429 Cf. the review of Tentzel’s Epistola de sceleto elephantino Tonnae nuper effosso, 1696 (note 425 above), in: Journal des Sçavans, (August 20, 1696), pp. 393–395, and in particular the following text: “L’Anatomie d’un elefant publiée en Anglois à Dublin par Monsieur Moulin en 1681 s’acorde parfaitement avec les observations faites sur les os tirez de la colline de Turinge, soit pour le grand nombre de cellules qui partagent la tête, ou pour l’étenduë du crâne. Il est vrai que l’étenduë du crâne decrit à Dublin exceed du double le crâne trouvé en Turinge, ce qui persuade que ce dernier élefant estoit unefois moins grand que l’autre” (p. 393). 430 alchemical symbols for gold and silver in the manuscript. 431 “Nuper e Regiomonte Norvegiae a metallifodinarum supremo Praefecto Schlanbusch exquisite curiosas | aurum | et | argentum |ae mineras accepi, nec non Nidrosia, volgo Drontheim, litophytum marinum. Inde res quoque paucos ante dies insignis balaenae priapus et mandibulae unde vulgo dictum Fischbein in Sartorium usum offerebantur” (A III,7 N. 139, p. 569).

732

Chapter 5

After he had learned of the impending return of the Jesuit priest Joachim Bouvet to China, the president of the Academia Leopoldina Lucas Schröck commenced a correspondence with Leibniz on January 16, 1698.432 As an attachment Schröck sent a non-sealed letter addressed to Andreas Cleyer, originally from Kassel, who had become a physician, botanist, pharmacist, and respected figure in the Dutch East India Company’s (the ‘Vereenigde Oostindische Compagnie’) Batavian society, as well as a questionnaire intended for Cleyer about, among other things, the musk plant and the Levant wormseed (‘semen sanctum’). Two weeks later, on January 30, Leibniz forwarded Schröck’s letter and questionnaire for Cleyer to Joachim Bouvet, together with an accompanying letter.433 As is evident from Bouvet’s reply from La Rochelle on February 28, he intended having Schröck’s letter copied and gathering relevant information himself.434 Cleyer had previously published a Specimen medicinae Sinicae (1682),435 about heartbeat or cardioplegia, and he had edited the edition of Michael Boym’s Clavis medica ad Chinarum doctrinam de pulsibus (1686).436 In a letter to Leibniz of July 17, 1698, Schröck also made reference to Georg Eberhard (or Everhard) Rumpf from Hanau, the residential seat of power of the dukes of Hanau in Hesse.437 Like Cleyer, the latter had gone as a physician to East India and had become Consul and Senior Merchant of the Moluccan Island Ambon.438 In the service of the Dutch East India Company, he wrote a number of works about the natural history and the natural science of the Moluccan Islands, and he devoted himself to the study of botany. Schröck, in this letter to Leibniz, referred to another letter of Rumpf, from September 1696, that had duly been published in the Miscellanea Curiosa under the title “De Caryophyllis Regis Ambonicis”.439 In addition, Schröck referred to a joint publication of Cleyer and Herbert de Jager, who had investigated a species of flowering plants called ‘artemisia abrotanum’ (southernwood or

432 Cf. A III,7 N. 174, p. 697, and annotation. 433 Cf. A I,15 N. 175, pp. 247f. 434 Cf. A I,15 N. 238, pp. 353–358, specifically p. 354. 435 Cf. A. Cleyer (ed.), Specimen medicinae Sinicae, sive opuscula medica ad mentem Sinensium, continens I. De pulsibus libros quatuor e sinico translatos. II. Tractatus de pulsibus ab erudito Europaeo collectos, Frankfurt am Main, 1682. 436 Cf. M. P. Boym (A. Cleyer, ed.), Clavis medica ad Chinarum doctrinam de pulsibus, Nürnberg, 1686; also published in Miscellanea Curiosa, Decur. II, Ann. IV, Appendix, (1686), pp. [1]–144. 437 Cf. A III,7 N. 207, pp. 824f. 438 Cf. G. Yoo, 2018 (Introduction, note 204). 439 Cf. G. E. Rumpf, “De caryophyllis Regis Ambonicis”, Miscellanea Curiosa, Decur. III, Ann. V and VI (1697–1698), pp. 308f.

July 1696–1698

733

southern wormwood) in Persia.440 Moreover, Schröck provided Leibniz with intelligence  – received from Christian Mentzel and Rumpf himself  – about work on a planned six-part botanical opus of Rumpf, the first part of which had following dispatch unfortunately been lost in a shipwreck while en route to Holland in 1692. Thus, the correspondent wrote regarding Rumpf and his opus: Almost all the time he spent in India was applied to the utmost to the study of botany, and he compiled a work on the rhizomes [rootstocks] of outlandish plants comprising VI books, whose first part he had sent to Holland in the year 1692, which however was lost en route in a shipwreck. If it has not already been completed for a second time, with the six remaining books attached, it is being worked upon in Batavia [i.e Jakarta] in order that the entire work be completed, with regard to both the text and the figures, so that it can be sent to Holland.441 Rumpf died in 1702, and his posthumous multi-volume work Herbarium Amboinense was first published only in the year 1741.442 17 Medicine Leibniz’s correspondents in the field of medicine during the period under consideration, from July 1696 to December 1698, included Georg Franck von Franckenau, Lucas Schröck, Gottfried Thomasius and of course Bernardino Ramazzini. The Italian was throughout the 1690s no doubt Leibniz’s internationally most renowned correspondent in the medical field but the letters they 440 Cf. A. Cleyer, H. de Jager, “Observatio I. De sementina”, Miscellanea Curiosa, Decur. II, Ann. III, (1684), pp. 1–17. 441 “Is totum fere tempus, quod in India consumsit, in studio botanico maxime trivit, atque de stirpibus peregrinis opus collegit, in VI libris comprehensum, cujus priorem partem A. 1692 in Hollandiam miserat, quae tamen in itinere naufragio periit; ob id jam, addit, secunda vice, adjectis sex reliquis libris, Bataviae laboratur, ut totum opus perficiatur tam in scriptis quam in figuris, et in Hollandiam mitti possit” (note 437 above, p. 825). 442 Cf. G. E. Rumpf, Herbarium amboinense: plurimas conplectens arbores, frutices, herbas, plantas terrestres & aquaticas, quae in Amboina et adjacentibus reperiuntur insulis adcuratissime descriptas iuxta earum formas, cum diuersis denominationibus cultura, usu, ac virtutibus, quod & insuper exhibet varia insectorum animaliumque genera, plurima cum naturalibus eorum figuris depicta, 6 vols, Amsterdam, 1741–1750; W. Buijze, 2006 (Introduction, note 205), in particular the appendix “Bijlage 2 Personen in Rumphius’ Wereld” (pp. 214–339), and specifically regarding Andreas Cleyer (pp. 228–246), Herbert de Jager (pp. 282–296), and Christian Mentzel (p. 309).

734

Chapter 5

exchanged, in mid-August 1696,443 and in mid-January 1697,444 respectively, were primarily concerned with matters of physics, in particular with barometric investigations. As regards anatomical studies, Franck von Franckenau then emerged as Leibniz’s most important correspondent at this juncture. Physicians’ reports about postmortem examinations of corpses, as well as reports about birth deformities and monstrous births, had long been a source of information for Leibniz in the area of anatomy. Both are to be found in a report of Franck von Franckenau – given in his letter of September 28, 1697, to Leibniz – about the postmortem examination of the remains of a stillborn two-headed female child. In August of that year, the wife of a schoolmaster near Copenhagen, who was already mother of several children, gave birth to this two-headed girl. The stillborn child was brought to the Royal Palace where the remains were examined by Franck von Franckenau. The correspondent informed Leibniz accordingly as follows: Recently, on August 9, two milestones removed from Copenhagen, the wife of a schoolmaster who was already mother of several children gave birth to a two-headed girl who was otherwise quite fine. On the day after the day of birth, this was brought to us at the Royal Palace where I presented and displayed the spectacle.445 Franck von Franckenau’s eldest son, Georg Friedrich, then carried out the post-mortem examination. It was found that several organs were duplicated including the trachea, or wind-pipe, with outgrowths, the oesophagus or gullet, the stomach with the small intestine extending to the middle of the ileus and terminating in an ample or spacious sac, the spine, the lungs and the ribs. And so the report continued: We encountered many duplicate parts, [like] the trachea with outgrowths, the oesophagus, the stomach with the small intestine to the

443 Cf. A III,7 N. 22, pp. 87f. 444 Cf. A III,7 N. 67, pp. 263–265. 445 “Nuper d. 9. Aug. duobus Hafnia lapidibus ludimagistri uxor, plurium antea liberorum mater edidit puellam bicipitem, cetera satis elegantem. Eam altero a partu die ad nos delatam in aula Regia augustissimi conspectui exposui et demonstravi” (A III,7 N. 139, p. 569).

July 1696–1698

735

middle of the ileus where it terminated in an ample sac, the spine, the lungs and the ribs.446 The remaining organs were found singly, and these included the heart, the liver, the spleen, the kidneys with succenturiates (viz. substitutes for, or accessories to the organ), the adrenal glands, the urinary bladder, the uterus, the pancreas, the mesentery and the cunt. Thus the correspondent continued: “The remaining [organs] were single and rational, e.g. the heart, the liver, the spleen, the kidneys with succenturiates, the bladder, the uterus, the pancreas, the mesentery and the cunt”.447 In addition the body had two arms and two legs, all provided with nails.448 Finally, the correspondent explained that following the exenteration, and a public viewing by several thousand visitors at his residence, the remains of the dead-born girl were laid in a container filled with a fluid of florantibalsam (spiritus balsamicus), and they were taken to the Royal Museum for preservation there.449 Following the death (in May 1698) of Leibniz’s correspondent and collaborator at the Court in Florence, Rudolf Christian von Bodenhausen, an autopsy was likewise carried out on the remains. Previously, on July 28, 1696, Bodenhausen had informed Leibniz about his insistence on self-treatment during illness and his reluctance to seek medical assistance in Italy. Bodenhausen’s reservations were centered on a perceived abuse of phlebotomy there. Thus he wrote on that occasion: Furthermore, I have lived here for the past several months almost inhumanly, in that I suffered a total lassitude of mind and body in the last two months … there was not much missing in order to finish me off in that I did not turn to the tormentors and bloodletters, the most powerful here who without the use of any medicament would, through the use of indiscrete venesection leading to obtenebration, send one to an early grave.

446 “offendimus multas partes geminas, tracheam puta cum thymis, oesophagum, stomachum cum intestinis tenuibus ad ilei usque mediam, ubi in amplum desinebant saccum, spinam dorsi, pulmones, costas” (p. 569). 447 “reliquas vero simplices et rationales[,] e.g. cor, hepar, lienem, renes cum succenturiatis, vesicam, uterum, pancreas, mesenterium; cunnumque” (p. 569). 448 “brachia duo, totidemque pedes, utrinque unguibus suis instructos” (p. 569). 449 “Post exenterationem et confluxum multorum millium hominum ad aedes meas puellam liquori balsamico spirituoso immersimus in vitro capaci, museoque Regio intulimus” (p. 569).

736

Chapter 5

I therefore wanted to be my own guide and I have regained my former powers.450 Alas, Bodenhausen’s new lease of life was relatively short-lived. When his death ensued the corpse was duly dissected. The twenty eight year old Swedish physician to-be, Magnus Gabriel Block, who assisted during the postmortem examination, availed of the opportunity to commence a correspondence with Leibniz, and he informed him on May 12, 1698, about the passing of his correspondent and collaborator three days earlier, and about the cause of death. Writing in Italian, Block informed Leibniz that the autopsy had shown that Bodenhausen had died of an abscess of the liver in which, it was reported, four pounds of pus had been found. Thus he wrote: “On the 9th day of the present month Baron von Bodenhausen passed away to a better life … having died of an abscess of the liver in which we found four pounds of pus after we opened up his corpse”.451 In his reply to Block’s letter of May 12, written probably in the first half of June, Leibniz requested the return,452 firstly, of the manuscript of his Dynamica which Bodenhausen had transcribed from his notes,453 and secondly, of his own letters exchanged with Bodenhausen,454 and thirdly, of other writings of the deceased in the sciences.455 In a letter of August 12, Block then announced that he was about to leave for Vienna, on the first leg of his journey back to Sweden, and for reasons of security he thought of taking the requested manuscripts with him and of handing them over to Pandolfio Mendlein, the

450 “Sonsten habe ich etliche Monaht hero fast nicht wie ein Mensch gelebet, in dem ich bey 2 Monathen eine totalem lassitudinem mentis et corporis erlitten … hat auch nichts gefehlet den rest zu stielen, als daß ich die Schinder v. Aderlaßer nicht geruffen, welche allhier auch die stärcksten ohne einig medicament  … mit indiscreten aderlaßen usqv’ ad deliqvium ins grab schicken. Habe mich also selbst leiten wollen, v. bin … zu vorigen Kräfften kommen” (A III,7 N. 10, pp. 37f.). 451 “Alli 9 del Corrente mese passò à miglior vita il. S. Barone di Bodenhausen … morto d’un ascesso del Fegato, in cui trovammo 4 libre di Marcia, aperto ch’avemmo il suo Cadavere” (A III,7 N. 190, p. 763; Leibniz: Nordström, p. 194). 452 Cf. A III,7 N. 199, p. 785, with underlining by Leibniz. 453 “un traité Manuscrit du Mouvement, qu’il avoit copié et mis au net sur mon brouillon” (GWLB, Hanover, Manuscript LH XXXV 11,18C); cf. G. W. Leibniz, Dynamica de potential et legibus naturae corporeae, parts 1–2, in: Leibniz (C. I. Gerhardt, ed.), Mathematische Schriften, vol. 6, pp. 283–514. 454 “En second lieu, il a échangé plusieurs lettres avec moy” (cf. GWLB, Hanover, Manuscript shelfmark: L.Br. 79; published in A III, vols. 4–6). 455 “En troisieme lieu, … il aura laisse plusieurs papiers sur les sciences” (cf. GWLB, Hanover, Manuscript shelfmark: LBr. 79, annex. 1–6).

July 1696–1698

737

Hanoverian agent in Venice.456 This was also the first stage of the return journey for Leibniz’s Dynamica, along with other Bodenhausen manuscripts. Considerations by Leibniz regarding the medical profession, advances in the medical field, and medicine as an empirical or rational science, were further themes in his correspondence at this juncture. After Block had explained, in a long letter of July 1, 1698, why, following studies in history, law and theology, he had opted for the medical profession,457 Leibniz, in his reply of July 30, welcomed the decision and expressed the view that medicine had previously been primarily an empirical science, and that most of the theories and hypotheses in the field were hardly reliable or useful. For that reason, it was also the desire of the renowned physician Heinrich Meibom that the discipline be established on an empirical foundation. Nonetheless, Leibniz himself welcomed the conjectures of competent physicians. Thus, he wrote to the correspondent on this occasion: I very much approve of the choice you have made, Sir, for the medical profession. After the study of virtue it is the most necessary. Since you have previously studied history and public law, and in addition even theology, that highlights that you are far from being small or narrow-minded; in effect all knowledge is highly interrelated. Medicine to date has been strongly empirical and, excepting that which one has learned through experiments, one knows very little about it, with the majority of hypotheses that have been made, and are still being made, having little certitude and being of little use. That is likewise the sentiment of the renowned Meibom, who is one of the most capable physicians in Germany, who has told me that he desires that one should have institutions founded uniquely on experiment without a mélange or mixture of hypotheses. I avow nonetheless that the conjectures of competent people should not be disesteemed [or scorned], in order that they be intelligible.458 456 “come io sono di partenza per Vienna … voglio per maggior sicurezza portarli meco … Comunque sia fò conto di non lasciargli dal Sr Mendlin à Venezia” (A III,7 N. 217, pp. 868f.). 457 Cf. A III,7 N. 203, pp. 798–803; Leibniz: Nordström, pp. 195–198. 458 “J’approuve fort le choix que vous avez fait, Monsieur, de la profession de la médecine. Après l’etude de la vertu c’est la plus nécessaire. Comme vous avez étudié auparavant l’histoire et le droit public, et puis mème la théologie, cela marque que vous ne vous étes point borné: en effet toutes les connoissances ont bien de la liaison ensemble. La médecine jusqu’ici est fort empirique; et horsmis ce qu’on sait par des expériences on en sait peu de chose; la plûpart des hypotheses qu’on a faites, et qu’on fait encor, etant peu sûres et peu utiles. C’est aussi le sentiment du célebre Meibonius, qui est un des plus habiles médecins de l’Allemagne, qui me dit de souhaiter qu’on eût des institutions fondées uniquement sur l’experience, sans mêlange d’hypothèses. J’avoue cependant que les

738

Chapter 5

Writing on October 30, 1698, from Stralsund, on his journey home to Sweden, Block, for his part, also desired “istitutioni di Medicina” which would not be speculative, or concerned with occult speculation, but rather rooted in empiricism. He had his doubts, however, that medicine could be built up solely on the foundation of experience, or experiment, the occurrence of events and infinite coincidence or chance being extremely complicated.459 He compared the subject-matter of medicine, namely the human body, to a closed machine, like a clock, that one could not correct without opening it up, and thus risking its destruction.460 A possible way out of this dilemma, Block saw in the form of a possible panacea or universal remedy.461 Leibniz replied then, on December 2, that hypotheses and conjectures served as tentative solutions on the way to the establishment of the truth. Above all, it was important to separate certain from provisional knowledge. The mainstay of medicine was empiricism and practice. As regards the possibility of finding a panacea or universal remedy, Leibniz recalled the investigations of the then recently-deceased English physician Richard Morton. The renowned Morton had established that, in the case of fever patients, a remission often occurs that makes it possible for the physician to save the patient. In the event of an extreme weakness of the body, on the other hand, such a recovery would no longer be possible. Morton had never been able to find a means for the procurement of a remission. Leibniz himself chose nonetheless to continue to adhere to this idea. His words to Block were as follows: My opinion is simply that one ought not to give up conjectures entirely within the institutions of medicine. That would effectively mean denying oneself of a quantity of fine thoughts which could give occasion for more exact research, and serve for its provision. But that which I would like is, namely that one should indeed separate what is certain from that which is uncertain, and that one should draw all that is possible from the sure foundations of experience [or experiment] and from demonstration. The conjectures des habiles gens ne sont pas à mepriser, pourvû qu’elles soient intelligibles” (A III,7 N. 210, pp. 830–834, specifically p. 832; Leibniz: Nordström, pp. 200–202). 459 “Sarebbero à bramare mà non da sperare l’istitutioni di Medicina prive di congietture, nè meno veggo si potessero fondare unicamente sopra le Sperienze sole, sopragiugnendo casi ed accidenti infiniti, e molti complicati” (A III,7 N. 238, pp. 925–929, specifically pp. 927f.; Leibniz: Nordström, pp. 207–209). 460 “e ciò in una machina chiusa che non si puol disfare e correggere à guisa d’oriuolo senza destruzzione del composito e quello che giova ad uno fà danno ad un altro” (p. 928). 461 “l’unico Scampo che ci rimane da sperare sarebbe forse una Panacea se ritrovar si possa” (p. 928).

July 1696–1698

739

best of medicine is empirical, that is to say entirely founded on experience, and that which one pretends to justify or give a reason for is very often not at all certain and of little use. As regards a panacea, it appears that one could hope at least for something which would have the capability to augment and to reestablish, so to speak, the explosion of spirits. It appears nonetheless that this is still wanting or unavailable to us. The renowned English physician Morton said that he had witnessed that one could indeed often save people when continued fevers are accompanied by a certain remission but that, for the case when the weakness is so great that nature itself no longer appears to make an effort for recovery, he admitted not having yet found anything of use. Notwithstanding this, I do not despair at all that one will find it one day.462 Leibniz advocated a comprehensive scientific training of medical doctors. Writing to Franck von Franckenau in May 1698, he recalled a meeting in Paris with Gui-Crescent Fagon, the personal physician of the king. Fagon had arranged for a law to be enacted that would filter out in advance charlatans and quacksalvers, and requiring that henceforth medics and persons in the medical profession should have to produce evidence of their knowledge of anatomy, botany and chemistry. According to Leibniz, Fagon also wanted to get rid of the accusation – disseminated not least by Jean-Baptiste Poquelin, alias Molière, the satirist of seventeenth-century French medicine463 – that the repertoire of treatment methods of French physicians was limited to the application of clysters, enemata, purgatives or cleansing enemas, and venesection or phlebotomy. Thus he wrote:

462 “Mon opinion n’est pas qu’on doive s’absentir entierement des conjectures dans les institutions de Medecine; ce seroit se priver de quantité de belles pensées qui peuvent donner occasion à des recherches plus exactes; et servir par provision. Mais c’est que je voudrois qu’on separât bien certum ab incerto, et qu’on tirât des fondemens certains de l’experience et de la demonstration tout ce qui se peut. Le meilleur de la Medecine est empirique, c’est à dire fondé entierement sur l’experience, et la raison qu’on pretend rendre, est bien souvent peu seure, et peu utile. Pour ce qui est d’une panacée, il semble qu’on pourroit esperer au moins quelque chose qui soit capable d’augmenter et de retablir, pour ainsi dire, l’explosion des esprits. Il paroist pourtant que cela nous manque encor: Morton celebre Medicin Anglois a dit qu’il a vû qu’on peut sauver bien souvent les gens, lors que les fievres continues sont melées d’un peu de remission mais que lors que la foiblesse est si grande, que la nature ne paroist même plus faire des efforts pour se relever il avoue de n’avoir rien encor trouvé qui serve. Cependant je ne desespere point qu’on ne le trouve, un jour” (A III,7 N. 246, pp. 950–952, specifically pp. 951f.; Leibniz: Nordström, pp. 209f.). 463 Cf. for example H. Gaston Hall, 1977, and A. Calder, 1993, chap. 12 (Introduction, note 228).

740

Chapter 5

You will not be unaware of the fact that Fagon, the first medical authority of the king of France, arranged that a law be enacted to the effect that in the future medical honors will only be granted to those Parisians who will have produced commendable works in anatomy and botany, and chemistry. With this law I believe he wanted to put into effect that which he himself once personally acknowledged to me before he had advanced to his present position at court, notwithstanding the scoldings of French physicians, namely that they often so behave as if they had nothing to offer other than the three applications decried by Molière, namely the use of clysters, venesection and purgatives.464 Of such medical treatment methods it was bleeding or bloodletting, that was most often referred to in Leibniz’s correspondence as, for example, in Bodenhausen’s letter of July 28, 1696.465 In his letter of May 1698 to Franck von Franckenau, Leibniz told that he had received a work hostile to bloodletting, written by Dominico La Scala and entitled Phlebotomia damnata (1696).466 Leibniz himself, however, favored the moderate application of bloodletting, the value of which was evident from application with animals.467 In his letter to Block, on July 30, 1698, Leibniz justified his standpoint with the following argument: bloodletting might work in the same way that arsenic could act as an antipyretic. Thus, nature reacts to the artificially-produced health threat, and reverses the path previously taken. On this occasion he wrote: A learned physician from Sicily recently published a book against venesection, but I consider that one should not reject it entirely, witness its use with animals for which it is often clearly useful. It is necessary nevertheless to acknowledge that it should be handled with great circumspection, 464 “Non ignorabis Fagonium primarium Regis Galliae medicum autoritate Regia effecisse ut lex ferretur, ne inposterum honores Medici Parisiis nisi illis conferantur, qui etiam Anatomicis et Botanicis, et Chemicis operam laudabilem dederint; qua re credo eum voluisse dare operam ut tollatur quod ipse olim nondum in Aula ad hunc gradum productus erga me agnoscebat, opprobrium Medicorum Gallicorum, qui ita agunt saepe ac si praeter tria illa Molierio decantata, clysterem dare, venam aperire, purgare denique; nihil nossent” (A III,7 N. 191, p. 766). 465 Cf. A III,7 N. 10, p. 37. 466 Cf. D. La Scala, Phlebotomia damnata  …, sive, Anidii, Chrisippi-Cnidii, Aschlepiadis, Erasistrati, et Aristogenis contra sanguinis missionem doctrina e vetustatis tenebris in lucem … revocata, & luculentius enucleata … In qua singula rationum momenta, quae sanguinis eductioni adversantur, aequa veritatis lance expenduntur, Padua 1696. 467 “usum tamen ejus omnem tolli debere, nisi Tibi aliter videtur, non putem, cum et in animalibus brutis manifeste appareat” (note 464 above, p. 768).

July 1696–1698

741

and perhaps it often just acts as an antipyretic like arsenic that is to say by diverting nature, from the path which it has taken, on seeing the peril with which it appears to be confronted by the bloodletting.468 In his letters to Block and Franck von Franckenau in 1698, Leibniz again referred to the positive effects of the method in treating animals.469 Block, in his letter of October 30, agreed with Leibniz’s opinion of La Scala’s Phlebotomia damnata, and he too rejected the idea of a general ban on the use of bloodletting.470 He was also of the same opinion as Leibniz that with fever, blood heat, unconsciousness, or disturbance of consciousness, or with blood congestion in the lungs or heart, bloodletting could indeed be applied. Phlebotomy, he wrote, was however the last resort of the Galenists and, in France, Spain and Italy, there was an enormous abuse of the method in evidence.471 The fact that Leibniz was fully aware of this abuse is evident from his letter to Ramazzini of April 22, 1699, in which he once again referred to La Scala’s opus and requested the correspondent’s judgement on the issue in the following words: The book of the distinguished physician Dominico [La] Scala [entitled] Phlebotomia damnata is of great merit. There is nevertheless hardly anyone within these shores who dares, also because of abuse, to reject all use of the remedy [which is] so great and certainly far removed from causing damage. I would however like above all to learn your opinion on the matter.472

468 “Un savant médecin de Sicile a publié depuis peu un livre contre la vénésection, mais je m’imagine, qu’on ne doit point la rejetter entièrement, temoins même les animaux, à qui elle est souvent utile visiblement. Il faut avouer cependant qu’elle doit être ménagée avec bien de la circomspection, et peut être souvent elle ne sert que comme l’arsenic est un febrifuge, c’est à dire en détournant la nature du cours qu’elle a pris, par la vûe d’un péril dont la saignée la semble ménancer” (A III,7 N. 210, p. 832). 469 Cf. A III,7 N. 191 and N. 210 (cf. notes 458, 464, 468 above). 470 “V.S. Illma mi scrisse del libretto di Domenica Scala Siciliano intitolato Phlebotomia Damnata, non approvando l’essilio generale del Cavar sangue” (A III,7 N. 238, p. 927). 471 “anch’io son della medema opinione che V. S. Illma come v. g. nelle febri ardenti ed altri bollori del Sangue nella Syncope etc. quando il sangue stagnasse ne’ polmoni o nel cuore overo il pericardio ove non si potrebbe far di meno, però non si puol negare che in Francia Spagna ed Italia non vi sia un grandisissimo abuso del salasso, essendo egli l’unico Refugio de Galenisti” (p. 927). 472 “Egregii medici Dominici Scalae phlebotomiae damnata liber magni fit merito; vix tamen quisquam est qui ausit in his oris cum abusu omnem etiam usum rejicere remedii tam magni et certe ab omni saepe noxa remote. Tuum autem judicium inprimis intelligere velim” (A III,8 N. 31, p. 100).

742

Chapter 5

Finally, Leibniz’s thoughts on the idea of a rational medicine found expression in his correspondence with the “medico-mathematicus” Domenico Guglielmini in the year 1697. To the latter, he expressed, in a letter of January 7, the hope that mathematics might, with the support of the correspondent, find a place in medicine. Thus he wrote: “For it is ultimately possible above all to obtain the prize for efforts to achieve a rational medicine, that brings mathematical light into this darkness, [something] which could be done magnificently by you”.473 Guglielmini, for his part, writing on June 18, expressed his intention of attempting to deduce mathematical laws in physiology. However, thoughts about the organization of medicine as an exact science, or the training of “medico-mathematici”, Guglielmini considered to be wishful thinking and removed from reality. Medics were as a rule not versed in mathematics, and they would spurn rather than approve such ideas. Here he wrote: In my future studies I will henceforth follow your advice. I will try namely to apply mathematical theorems to medical physiology. First of all however it is necessary to explain the application of theoretical medicine to practice, and the frailty of its empirical parts, in order to shake up the relentlessly steadfast teaching methods in our regions. However I hesitate as a medical mathematician to throw off the mask in public. This I could conceal to some degree until now, or had to communicate under a false name, in order to first hear the judgement of the literary world from a hidden tableau, as up to that point I had not relinquished my good name [by entering] into uncertain waters. Since Medics are not versed in mathematics, I do not doubt that they would spurn rather than approve such ideas, as they rarely understand, and just follow the whiff of common medical practice, lest they lose theirs by commending useless speculations of this kind.474 473 “Is enim demum in rationali Medicina operae pretium prae caeteris facere potest, qui lumen mathematicum ad has tenebras affert, quod a Te praeclare fieri posse” (A III,7 N. 64, p. 257). 474 “In meis regendis studiis tuum posthac sequar consilium; mathematica enim Theoremata pro viribus in Phisiologiam medicam inferre tentabo; prius tamen probanda est medicinae Theoreticae ad Praxim necessitas, et Empyricae sectae fragilitas, ut haeresim in nostris hisce regionibus non ita pridem suscitatam pro virili convellam. At aperta facie in publicum prodire Medico-Mathematicus vereor; hinc aliquid suppresso, vel ficto nomine evulgandum mihi est, ut orbis literarii judicium post tabulam latens prius audiam, quum adeo incerto pelago nomen meum committam. Medici enim mathematicarum ignari, ne talia spernant dubito, cum raro intelligant, et qui vulgi auram praxi medica aucupati

July 1696–1698

743

Leibniz replied at the end of September with a profession of faith in the higher value of rational over speculative thoughts in medicine, whereby plausible hypotheses ought to replace less certain conjectures. As he had previously done with Block, Leibniz stressed here how important it was to keep certain and provisional knowledge separate. Conjectures should be taken into consideration only to the extent to which they were expedient or purposeful. And so, from Guglielmini he hoped for no mean contribution for the advancement of a rational medicine. Thus he wrote: For the rest, it must be admitted that medically there is much that has reason and is more powerful than its conjectural counterpart, and perhaps plausible hypotheses sometimes can engulf conjectures that are insufficiently probable. And so it is desirable to finally proceed at some point from that which separates certain from uncertain and, as for conjectures themselves, which are not always disdainful, they should provide much, as much as deputed [to them]. From you, being of outstanding erudition and ingenuity, [and] instructed in this matter, I expect the spawning of nothing mediocre here.475 sunt, ne sua perdant, hujusmodi speculationes ut inutiles praedicabunt” (A III,7 N. 107, pp. 449f.). 475 “De caetero fatendum est multos qui rationales habentur Medici potius esse conjecturales, et fortasse interdum per Hypothesibus plausibilibus nobis conjecturas obtrudere parum probabiles. Itaque optandum esset exoriri tandem aliquando qui certa ab incertis discriminaret atque ipsis conjecturalibus quae non semper sunt aspernenda tantum tribueret, quantum oportet. A Te praeclaris doctrinae et ingenii opibus ad hanc rem instructo, nihil in eo genere mediocre expecto” (A III,7 N. 142, pp. 577f.).

Chapter 6

1699–1701 Nam collegii experimentalis unam Lectionem centum metaphysicis, Logicis, Ethicis, quales vulgo audiuntur, facile praetulerim.1 Leibniz to Friedrich Hoffmann, November 1, 1701

⸪ 1

Biographical Background (1699–1701)

Leibniz’s correspondence in mathematics, science and technology in the three-year period between January 1699 and December 1701, consists of 321 communications, of which 131 were written by Leibniz himself, and it involves a total of 34 correspondents, or addressees, of which half (17) were newcomers.2 Among these newcomers, Friedrich Hoffmann, Ole Christensen Rømer, Hans Sloane, Pierre Varignon, and Francesco Bianchini – with whom correspondence was resumed after an interruption of ten years  – deserve particular mention. The frequency and volume of the correspondence with Johann Bernoulli ebbed in this period, while those with Magnus Gabriel Block, Guillaume François Antoine de L’Hospital, Johann Andreas Stisser, and John Wallis were concluded. In addition, in the spring of 1700, the extended discussion with Denis Papin concerning “vis viva”, and the correct measure of force, came to an end. The densest correspondence in the period under consideration was that with the aspirant mathematics professor in Helmstedt, Rudolf Christian Wagner, who acted as Leibniz’s assistant and organized for him a variety of practical and technical matters, such as those relating to calculating machines. Wagner’s correspondence with Leibniz reveals also the important role his mentor had in his academic advancement. To overcome the reservations expressed by the vice chancellor in Hanover, Ludolf Hugo, in a letter to Leibniz on December 4, 1699, regarding Wagner’s application for 1 A III,8 N. 306, p. 785; Translation: For I would certainly prefer a single lesson of a ‘collegium experimentale’ to a hundred corresponding lessons in metaphysics, logic or ethics, such as those normally heard. 2 Cf. Ch. Wahl, J. G. O’Hara, A III,7, Introduction, pp. [XXV]–LXXIX.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_008

1699–1701

745

the professorship – namely that Wagner’s achievements in applied mathematics (in “artibus Mathematicis”) had been at the cost of his negligence of pure mathematics (“Scientias Mathematicas”)3 – the applicant prepared, under Leibniz’s supervision, a disputation on the errors of the Renaldine circle graduation rule (viz. that of Carlo Renaldini, 1615–1698). In the end, with the support of the Helmstedt professor Johann Andreas Schmidt, and not least through Leibniz’s political influence at the court in Wolfenbüttel, Wagner was preferred to a rival candidate, and he was able to commence his duties as professor in November 1701. Two important events, namely the foundation of the Berlin Society of Sciences (“Berliner Sozietät der Wissenschaften”), and the Protestant calendar reform, were to leave major footprints in Leibniz’s correspondence in the three-year period under consideration. For the scholar and scientist Leibniz, a long-held desire was fulfilled in February 1699, when L’Hospital informed him about his appointment as a foreign member of the newly-reformed Académie des Science.4 And in addition, the circumstance that the brothers Johann and Jacob Bernoulli  – who had distinguished themselves in the further development of the differential calculus – had received the same honor was tantamount to an additional tribute being paid to Leibniz. His joy over this development is reflected in his correspondence with Johann Bernoulli who, through his correspondent Pierre Varignon, had even closer contact with the Académie than Leibniz himself. From Bernoulli’s letter of May 26, 1699, he learned the names of the remaining members,5 and from other sources, including John Wallis’ letter of April 30,6 he obtained information about the financing of the Académie,7 and he learned in particular that he could expect no remuneration from the appointment. Even more important for Leibniz, however, was the foundation in July 1700 of the Berlin Society of Sciences, and his appointment as its first president. It led to extended stays in Berlin in the middle (May to August 1700), and at the end (between October 1701 and January 1702), of the period under consideration. Of significance also were two secretive journeys to Vienna (in the last months of 1700, and in May–June 1701, respectively) in connection with his efforts for a reunification of the Christian churches, and with his admittance to the ‘Court Council of the Empire’ and the ‘Aulic Council’. These activities, and further secretive activities in the forefront 3 4 5 6 7

Cf. A I,17, N. 84, pp. 106f. Cf. A III,8 N. 12, pp. 48f. Cf. A III,8 N. 45, pp. 134f. and annotations. Cf. A III,8 N. 35, pp. 108f. Cf. A III,8 N. 50, pp. 149f. and N. 55, p. 169.

746

Chapter 6

of the War of the Spanish Succession, are also reflected in Leibniz’s correspondence in mathematics, science and technology in the years 1700 and 1701.8 2 Mathematics In comparison with previous years, mathematics was no longer center stage in Leibniz’s correspondence between 1699 and 1701. In addition to his numerous other activities, one reason for the reduced importance of mathematics, specifically in his correspondence with Johann Bernoulli, was a shift in his mathematical interests. Leibniz now devoted himself increasingly to binary calculus, which was discussed mainly in his correspondence with Philippe Naudé and Pierre Dangicourt, whereas his exchanges with Bernoulli petered out on this issue. Likewise, the discussion between Leibniz and Johann Bernoulli regarding the existence of the infinite and the infinitely small, which had begun in 1698, ended with Leibniz’s clarification of his conception of the infinite, but without agreement being reached between the two.9 Bernoulli assumed the existence of the infinite and the infinitely small. Leibniz, for his part, accepted – as he outlined in a letter of March 6, 1699 – an infinite quantity or amount, as for example that of all numbers, but with a caveat expressed as follows: “I concede an infinite multitude, but this multitude does not constitute a number, or one whole”.10 Leibniz correspondence with Jacob Bernoulli was interrupted at this juncture. The estrangement between the two led to a brief alliance between Jacob and his compatriot Nicolas Fatio de Duiller.11 Jacob’s correspondence with Fatio between July 1700 and August 1701 mirrored Leibniz’s dispute with Fatio.12 Following Fatio’s return to England from his temporary residence in his native Swiss municipality (Duillier), and Jacob’s admission to the Berlin Society of Sciences in 1702, the alliance evidently ended. However, Leibniz’s dispute with Fatio went public in the year 1699. In the summer of that year, Fatio sent a short tract of his entitled Lineae brevissimi descensus investigatio geometrica duplex,13

8 Cf. A III,8, pp. XXVIf. 9 Cf. A III,7, pp. Lff., III,8, p. XLIX and II,3 p. LXIIf. 10 “Concedo multitudinem infinitam, sed haec multitudo non facit numerum, seu unum totum” (A III,8 N. 17, p. 66). 11 Cf. A III,7, p. XXXI. 12 Cf. D. Speiser, A. Weil et al. (eds.), Der Briefwechsel von Jacob Bernoulli, Basel, 1993. 13 Cf. N. Fatio de Duillier, Lineae brevissimi descensus investigatio geometrica duplex, London, 1699.

1699–1701

747

which was attached to a work entitled Fruit-walls improved,14 to L’Hospital as well as to Varignon, who referred to it in a letter to Johann Bernoulli on July 12, 1699,15 both of whom found it to be outrageous. It contained a belated solution of the brachistochrone problem, as well as the derivation of the problem of the solid of revolution of least resistance (for rarified fluids), which Newton had included (without proof) in his Principia mathematica (1687).16 Already on the first page of his tract, Fatio took umbrage at Leibniz’s “Communicatio”, in which he had commented on the solutions of the brachistochrone problem in the Acta Eruditorum of May 1697.17 There Leibniz had insisted on the vigor and superiority of his calculus, stressing the difficulty of the task in hand, and praising the solutions that had been submitted. Fatio felt that he had been demoted, since Leibniz had not included him among those – like Newton – he attested the ability to solve the problem, and to whom he had communicated its enunciation in advance. However, Fatio’s criticism was of a more fundamental nature. He accused Leibniz of acting, as it were, from a mathematical throne, and of distributing praise at his own discretion, and furthermore, he condemned the practice of posing mathematical challenge questions. Towards the end of the tract, Fatio placed the accusation that surely was most offensive to Leibniz. To begin with, he stated that he himself had developed similar methods to those of Leibniz and Newton, and he went on to insinuate that Leibniz could even have plagiarized Newton. Thus, he wrote concerning this matter: I recognize however that Newton was the first inventor of this calculus, and many years in advance, according to the compelling evidence in the matter, from which Leibniz, its second inventor, possibly exchanged something, concerning which mischief those like me, who will have seen

14 Cf. N. Fatio de Duillier (anon.), Fruit-walls improved, by inclining them to the horizon: or, a way to build walls of fruit-trees; whereby they may receive more sun shine and heat than ordinary, London 1699. 15 Cf. P. Costabel, J. Peiffer (eds.), Der Briefwechsel von Johann I Bernoulli, vol. 2 (Der Briefwechsel mit Pierre Varignon), 1998, pp, 226–231, specifically p. 229. 16 Cf. I. Newton, Philosophiae naturalis principia mathematica, London, 1687, specifically pp. 326f. (book 2, sect. VII, prop. XXXIV, theor. XXVIII, scholium). 17 Cf. G. W. Leibniz, “Communicatio suae pariter, duarumque alienarum ad edendum sibi primum a Dn. Jo. Bernoullio, deinde a Dn. Marchione Hospitalio communicatarum solutionum problematis curvae celerrimi descensus”, Acta Eruditorum, (May 1697), pp. 201–205 (Leibniz: Parmentier, 1989, chap. 21, pp. [345]–358; Leibniz: Essais Scientifiques, 2005, N. 84; Leibniz: Heß-Babin, 2011, chap. 40, pp. 297–307).

748

Chapter 6

the letters of Newton and different codices of the same manuscript, can be the judge.18 Fatio was referring here to the contemporaneously-published third volume of Wallis’ Opera, in which the earlier correspondence between Leibniz, Oldenburg and Newton had been published.19 L’Hospital forwarded Fatio’s tract to Leibniz, on July 13, 1699, and he also pointed to Wallis’ edition whose purpose he saw through. Thus, he wrote on this occasion: I do not know if you have been informed that Wallis has had printed a third volume of his mathematical works in which he has included some of your letters to Mr Newton and others, and that I believe with the thought of attributing to the latter the invention of your differential calculus which Newton refers to as that of fluxions. It appears to me that the English are trying in every way to attribute the glory for this invention to their nation.20 Johann Bernoulli, who felt himself under attack because he had disseminated the brachistochrone problem, also informed Leibniz of Fatio’s invectives, and he passed on Pierre Varignon’s letter of July 12 in which these were quoted in detail.21 Bernoulli was especially surprised since he had (in 1691) instructed Fatio’s older brother, Jean Christophe Fatio de Duiller, in differential calculus, and he now suspected Fatio himself could have profited from this.22 Varignon likewise judged Wallis’ edition as an attack on Leibniz’s right to claim the invention.23 In point of fact, however, Leibniz – who regarded his earlier correspondence with Oldenburg and Newton as innocuous – had been consulted in advance by Wallis, and he had granted him permission to publish the letters 18 “Newtonum tamen primum, ac pluribus Annis vetustissimum, hujus Calculi Inventorem, ipsa rerum evidentia coactus, agnosco: a quo utrum quicquam mutuatus sit Leibnitius, secundus ejus Inventor, malo eorum, quam meum, sit Judicium, quibus visae fuerint Newtoni Litterae, aliique ejusdem Manuscripti Codices” (note 13 above, p. 18). 19 Cf. J. Wallis, Opera Mathematica, 3 vols, Oxford, 1693–1699 (vol. 1, 1695; vol. 2, 1693; vol. 3, 1699). 20 “Je ne scais si vous etes instruit que Wallis a fait imprimer un troisieme tome de ses oeuvres mathematiques dans lequel il a inseré quelques unes de vos lettres à Mr Neuton et autres, et cela je crois dans la pensée d’attribuer à ce dernier l’invention de vôtre calcul differential que Neuton appelle des fluctions. Il me paroist que les Anglois cherchent en toute maniere d’attribuër la gloire de cette invention à leur nation” (A III,8 N. 56, p. 173). 21 Cf. note 15 above. 22 Cf. A III,8 N. 57, pp. 175f. 23 Cf. p. 230 (note 15 above).

1699–1701

749

as he then explained to Bernoulli (on August 4, 1699), as well as to L’Hospital (on August 7).24 Leibniz was at all events surprised at the intensity of Fatio’s allegations. At first he did not see any connection with the previous history, to which Fatio was to refer a year later in a letter of August 30, 1700, for him and Otto Mencke.25 In fact, Leibniz did have indirect contact to Fatio through Christiaan Huygens, in 1691–1692, with the objective of arranging an exchange of their respective inverse tangent methods. From Huygens’ letter of March 15, 1692, Leibniz had learned that Fatio, who had a close relationship with Newton, believed: “That Mr Newton knows regarding this matter all that he, and all that you, Sir, have ever found, and [he has] once again a clear advantage”.26 Leibniz had declined in the end Fatio’s offer to reveal his method, which he thought he could deduce for himself.27 For Fatio, the fact that he had been overlooked in the announcement of the competition to solve the brachistochrone challenge problem amounted to a deliberate exclusion. However, Leibniz and Johann Bernoulli had little sympathy for Fatio’s apparent desire for recognition. In their eyes this ought to be earned, and exactly those challenge problems, which had been criticized by Fatio, offered an opportunity of doing so. The fact that the idea of a competition of methods had arisen here also led to disgruntlement elsewhere. Thus, Leibniz criticized David Gregory’s belated solution of the catenary problem,28 in an anonymous contribution in the Acta Eruditorum in February 1699,29 with the result that Wallis complained to Leibniz, on September 8 of that year, as did Gregory to Mencke, who duly informed Leibniz on November 11.30 Leibniz, for his part, orchestrated a two-track reaction to Fatio’s publication, namely in the form of a complaint to the Royal Society – whose imprimatur the work contained – and by means of official rejoinders in the Acta Eruditorum, in November 1699.31 The complaint he directed to Wallis, in a letter of August 16, whereby he kept his counsel regarding any accusation of 24 Cf. A III,8 N. 60 (p. 181), N. 62 (p. 189), and A III,7, pp. XXXVf. 25 Cf. A III,8 N. 182, pp. 463–467. 26 “que Mr Newton scait sur cette matiere et tout ce que luy, et tous ce que vous Monsieur ayez jamais trouvé, et encore bien d’avantage” (AIII,5, N. 65, specifically p. 280; HO10, pp. 268–270). 27 Cf. A III,5, N. 69, specifically p. 290; HO 10, pp. 283–286. 28 Cf. Chapter 5 of the present work. 29 Cf. G. W. Leibniz (anon.), “Animadversio ad Davidis Gregorii schediasma de catenaria”, Acta Eruditorum, (February 1699), pp. 87–91. 30 Cf. A III,8 N. 72, pp. 219–221, and A I,17, N. 373, pp. 626f., respectively. 31 Cf. the review of Fatio’s work by Leibniz in the Acta Eruditorum, (November 1699), pp. 510–513.

750

Chapter 6

plagiarism.32 Wallis forwarded Leibniz’s suit to Hans Sloane, and both of them condemned his actions at once, and without having seen Fatio’s tract. Wallis included the following extract, from Sloane’s letter (in the English language) to him of September 5, with his letter to Leibniz of September 8: Sir, I received yours. I have considered what Mons[ieu]r Leibnitz writes to you; and am very much concerned to find he is any ways abused by any Member of the Society. The Society are [sic] adjourned til October, as usually they are this time of the year. But you may satisfy him as much as if they mett, that they have a very great respect for him, and every thing [that] comes from him; and that they are no ways concerned in approving any thing that may any ways reflect on him. For the license, it may be to the book. ’Tis a matter customary to the Vice-presidents to license books of the Members of the Society, without consulting ye Society, Counsell, or perhaps the Books themselves, otherwisz [sic] than turning them over cursoryly, and it may be onely part thereof. So that I am perswaded, the Vice-President never knew Mr Leibnitz was named in it. And I am sure that the Society never knew any thing of the matter: but, on the contrary, have a great Veneration, as all learned men have, for Mr Leibnitz: And they are very much concerned, that the commerce by Letters with him hath of late been interrupted. It was lost before the Society did me the honour to concern me in their busyness: Else I had not lett slip such an opportunity of receiving now and then a line from a Person who merits so well of the World. Pray do me the favour to let him know, that if he will give me leave I will be very glad to write to him, and send him the Transactions, or do him any service here. And that I am very confident, when the Society meets, if there be any thing for his service to be desired of them on his part, he may have it. Your most obedient and most humble servant[,] Hans Sloane.33 In the event, Leibniz actually profited from the dispute with Fatio, in that he gained a new correspondent in the guise of Sloane, and was thus in official contact once again with the Royal Society of London. Sloane even offered to send Leibniz the Philosophical Transactions to which he otherwise had only irregular access. For his public response to Fatio, Leibniz obtained a placet in advance from Mencke – who, in general, was anxious to keep his journal free from such disputes  – addressing the matter in a letter of August 2, 1699, to 32 Cf. A III,8 N. 64, pp. 193–195. 33 Cf. A III,8 N. 72, pp. 219–221, and the attachment N. 73, pp. 222f.

1699–1701

751

which Mencke replied on August 8.34 On August 7, he sent a draft to Johann Bernoulli,35 who, in his reply of August 17,36 provided some additional commentarial information about Fatio, which he had learned from a passing traveler. Bernoulli added his derivation of the problem of the solid of revolution of least resistance, which he claimed to have developed without paper while lying in bed. Leibniz could publish it, Bernoulli wrote: In order that Duillier might see to what an amazing extent he has until now been off the true and natural path, and that he himself should be ashamed of his horrendous Labyrinth, which he has gotten into through his calculus.37 However, Bernoulli himself was horrified when Leibniz – overriding the resistance of Mencke who, in his letter of November 11, accused both of them of defamation of character38 – published not only the solution but also Bernoulli’s letter, in only a slightly tempered and shortened form, in the November number of the Acta Eruditorum.39 For Bernoulli the issue had arisen at an unfavorable moment. He had – in the belief that the latter had died – just publicly described Wallis as an overzealous defender of English glory, as he explained to Leibniz on December 1, 1699.40 He now feared not only Wallis’ notorious revenge, but also that Fatio’s ire would be directed against him, as he made clear in his letter to Leibniz of April 17, 1700.41 In addition, it adversely affected his position in relation to Mencke, who had become increasingly less inclined to publish the polemical exchanges of the Bernoulli brothers. In his reply of April 25, Leibniz excused his behavior with the circumstance that Bernoulli had reacted with little enthusiasm to the mathematical result attached to his response.42 Finally, in accordance with Bernoulli’s wishes, Leibniz published his response in a revised form in the May number of the Acta Eruditorum,43 which was greeted by Bernoulli, on June 19, with the words: “It was pleasant 34 35 36 37 38 39 40 41 42 43

Cf. A I,17 N. 226, p. 370 and N. 234, p. 381. Cf. A III,8 N. 61, p. 187. Cf. A III,8 N. 65, pp. 195–209. “ut videat Duillierius se mirum quantum adhuc abesse a vera et naturali via, et ut ipsummet pudeat horrendi sui Labyrinthi, in quem per calculum suum incidit” (p. 199). Cf. A I,17 N. 373, pp. 626f. Cf. Joh. Bernoulli, “Excerpta ex literis”, Acta Eruditorum, (November 1699), pp. 513–516. Cf. A III,8 N. 87, pp. 254f. “ita sane jam solus expositus sum irae Fatianae” (A III,8 N. 158, p. 411). Cf. A III,8 N. 162, p. 420. Cf. G. W. Leibniz, “Responsio ad Dn. Nic. Fatii Duillierii imputationes. Accessit nova artis analyticae promotio specimine indicata, dum designatione per numeros assumtitios

752

Chapter 6

to learn that you have sent your apologia (or defense of your position) against Fatio to the Acta”.44 Fatio de Duillier then responded both to Johann Bernoulli, and to Leibniz, sending both replies through Jacob Bernoulli to Mencke along with permission for their publication. Leibniz had the response intended for Johann Bernoulli sent to him, and he arranged for its publication in a (in part at least) considerably shortened and revised form.45 In particular, he replaced in the derivations of the isochrone and of the solid of revolution of least resistance – which were once again given there – the notation of the Newtonian method of fluxions with that of the differential calculus. He himself answered Fatio in a letter of January 4, 1701.46 In this way he conformed with Mencke’s desire to fill his journal with “realia” and not with polemical disputes. Fatio communicated his closing reaction only to Jacob Bernoulli, with whom he had found agreement regarding his complaints about Leibniz’s dominance. In fact, Jacob saw in the foundation of the Berlin Society of Sciences “a new application of the authority and of the power which this gentleman exercises over the empire [viz. the republic] of letters”. And furthermore, with respect to himself, he concluded that: “it would be woe to us, if we should happen to fall again from grace in his eyes!”.47 Fatio also gave Jacob an account of the English resentment against Leibniz resulting from Wallis’ edition. Because of the close connection between Leibniz and Henry Oldenburg, it was assumed in England that Leibniz had been informed about Newton’s calculus.48 In his letter for Mencke and Leibniz of August 30, 1700, Fatio had written: I admit however that I am no less inclined than the other mathematicians in England to tolerate the first invention of this excellent calculus being attributed to Mr Leibniz[, as] I have conceded in various places.49

44 45 46 47 48 49

loco literarum algebra ex combinatoria arte lucem capit”, Acta Eruditorum, (May 1700), pp. 198–208. “Gratum fuit intelligere, quod Apologiam Tuam contra Fatium ad Acta miseris” (A III,8 N. 171, p. 441). Cf. A III,8 N. 183, pp. 467–473, in particular p. 467 (annotation). Cf. A III,8 N. 196, pp. 503–505. “un nouvel appuy de l’authorité & du pouvoir, que ce Monsieur exerce dans l’empire des lettres” and “Malheur à nous, s’il nous arrive plus, de tomber dans sa disgrace!”, respectively (cf. D. Speiser, A. Weil et al. (eds.), note 12 above, p. 195). Cf. note 12, p. 182. “Fateor tamen me non minus impatienter, quam reliquos in Anglia Mathematicos, tulisse primam Inventionem Calculi hujus excellentissimi Domino Leibnitio passim tribui” (A III,8 N. 182, p. 465).

1699–1701

753

Fatio also admitted that Newton did not approve of his attacks against Leibniz, who therefore saw himself as someone who enjoyed the support of Wallis and Newton, and who had found support in his strategy of not taking accusations of plagiarism seriously. And so Leibniz wrote to Fatio on January 4, 1701: Whether or not English mathematicians are inclined to tolerate attributing authorship of the differential calculus to me, I do not know. Primarily among them, the excellent men Wallis and Newton have shown themselves to be very much of another mind. They have much of excellence themselves, much also related or similar to mine[, which is] especially true [for] Newton.50 In France, while the admission of Leibniz and the Bernoulli brothers to the Académie des Sciences represented an endorsement for the differential calculus, it could not hide the fact that it was still being rejected by a number of powerful members of the Académie. Already in the year 1697, Varignon had characterized himself as a “vray martyr”, who had to defend the differential calculus in place of the frequently absent L’Hospital.51 While the latter’s solution of the brachistochrone problem silenced the opponents at first, Michel Rolle’s criticism of the foundation of the calculus – about which Varignon informed Johann Bernoulli in September 1700 – marked the beginning of a long lasting dispute. Although, in the autumn of 1701, the Académie set up a commission to settle the conflict,52 an expansion of the dispute was in evidence at the end of 1701.53 This dispute, like that between the Bernoulli brothers,54 is also reflected in Leibniz mathematical correspondence at this juncture. Dyadic (or binary) mathematics began to appear more frequently in Leibniz’s correspondence around the year 1700.55 Already in 1696, Leibniz had, in discussion with duke Rudolf August of Wolfenbüttel, lauded the dyadic or binary number system with which one could represent – like in a mirror – the creation, or the origin of things, out of ‘God’ and ‘Nothing’, a message also

50 “Utrum Angliae Mathematici impatienter ferant me Calculi differentialis autorem laudari, nescio. Primarii ex illis Wallisius et Newtonus excellentes Viri, longe alio se animo esse ostenderunt. Multa ipsi praeclara habent, multa etiam cognata meis maxime vero Newtonus” (A III,8 N. 196, p. 505). 51 Cf. A III,7, N. 134, pp. 560f. 52 Cf. P. Costabel, J. Peiffer (eds.), p. 306 (note 15 above). 53 Cf. A III,8, pp. XLIIf. 54 Cf. A III,8, pp. XLIII–XLVI. 55 Cf. A III,8, pp. XLVI–XLIX.

754

Chapter 6

formulated in his letter of May 18 of that year to the duke.56 He had suggested using it in the missions, or in the words of this letter, in order “to illustrate how unjust the pagan or heathenistic philosophy [was,] to have set matter alongside God as a joint origin”.57 To this letter he attached a text entitled “Prodigious origin of all numbers out of 1 and 0 which provides a beautiful archetype of the secret of creation, since all comes into being from God and otherwise from nothing”.58 These ideas he had likewise communicated to the China missionary Claudio Filippo Grimaldi in January (or early February) 1697.59 To the latter he had also indicated that he saw the main use of binary arithmetic in the investigation of the properties of numbers, writing that: “Real therefore is the use of this calculus for discovering the mystery of numbers and for perfecting analysis and revealing sources or origins. In which matter I have much that is unforeseen and that I will bring forth some day”.60 In Leibniz’s mathematical correspondence, however, binary arithmetic had previously played hardly any role, although he had, in the early 1680s, referred to it in letters to Johann Jakob Ferguson, Detlev Clüver, and Ehrenfried Walther von Tschirnhaus.61 Some reasons for Leibniz’s long silence on binary mathematics, and the interruption of this silence around 1700, can be deduced from his correspondence. To L’Hospital he explained, on September 26, 1701, that he had wanted to advance his investigations further but – because of his numerous other occupations – he now feared that his ideas might be lost.62 Already on March 23, 1699, he had expressed sentiments to L’Hospital concerning his analysis situs, which surely also applied for binary mathematics. On that occasion he wrote: I am displeased myself because I have not been able to develop to my liking a thought which appears to me to be of some consequence. But 56 “gleichsam als in einem Spiegel die Schöpfung oder den Ursprung der dinge aus Gott und sonst Nichts” (A I,12 N. 66, p. 65). 57 “anzudeuten, wie unrecht die heidnischen Philosophi, die Materia als einen Mit-Ursprung, Gott gleichsam an die Seite gesezet” (p. 65). 58 “Wunderbarer Ursprung aller Zahlen aus 1 und 0 welcher ein schöhnes Vorbild gibet des Geheimnißes der Schöpfung; da alles von Gott und sonst aus Nichts, entstehet” (A I,12 N. 67, pp. 66–72). 59 Cf. A I,13 N. 321, pp. 518–522. 60 “Verus igitur hujus calculi usus est ad mysteria numerorum detegenda perficiendamque Analysin et fontes aperiendos. In quam rem multa habeo inexpectata quae aliquando producam” (p. 522). 61 Cf. A III,3, N. 48 (p. 138), N. 106 (p. 263) and N. 368 (pp. 655f.). 62 Cf. A III,8 N. 297, pp. 761f.

1699–1701

755

nothing is more repugnant than works without an associate and which one is not able to discuss with anyone. This viva voce communication between those enthused by the same investigation is one of the best dressings for desiccated meditations in themselves.63 In February 1701, as he informed L’Hospital on April 4, he sent an essay, entitled Essay d’une nouvelle science des nombres,64 to Bernard le Bovier de Fontenelle, in order to encourage the Académie des Sciences to undertake further investigations on binary mathematics.65 However, he refused to provide a publication, since – as he explained to Fontenelle – that which he had at his disposal would not yet be sufficient to create excitement about binary mathematics.66 Leibniz’s assessment was confirmed in the brief exchange on this topic with Johann Bernoulli, in the spring of 1701, that quickly came to an end. Binary arithmetic reminded Bernoulli, as he announced in his letter of April 11,67 of Erhard Weigel’s work of 1673, entitled Tetractys, summum tum arithmeticae tum philosophiae discursivae compendium.68 Leibniz then defended himself, on April 19, with the argument that number systems other than the decadic or decimal system were generally known before Weigel.69 Leibniz saw his own contribution not just in the discovery of the dyadic, or binary, system but rather in its number-theoretical applications. That the consideration of other number systems was in the air, he had already illustrated at this juncture with examples in the Essay d’une nouvelle science des nombres sent to Fontenelle in February 1701 and referred to above. The fact that binary mathematics was increasingly discussed in Leibniz’s correspondence around 1700 was therefore no surprise. The necessary 63 “Je suis faché moy même que je n’ay pas encor pû pousser à mon gré une pensée qui me paroit de quelque consequence. Mais rien n’est plus rebutant que des travaux sans compagnon et dont on ne peut parler avec personne. Cette communication de vive voix entre ceux qui se plaisent à la meme recherché est un des meilleurs assaissonemens des meditations seches en ells mêmes” (A III,8 N. 21, p. 77). 64 Regarding Leibniz’s Essay d’une nouvelle science des nombres, cf. pp. 250–261 in H. J. Zacher, Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein Beitrag zur Geschichte des binären Zahlensystems, Frankfurt am Main, 1973. 65 Cf. A III,8 N. 231, pp. 596f. 66 Cf. pp. 208f. in A. Foucher de Careil (ed.), Lettres et opuscules inédits de Leibniz précédés d’une introduction, Paris, 1854 (Leibniz: Lettres et opuscules inédits). 67 Cf. A III,8 N. 240, p. 614. 68 Cf. E. Weigel, Tetractys, summum tum arithmeticae tum philosophiae discursivae compendium, artis magnae sciendi genuina radix, Jena, 1673. 69 Cf. A III,8 N. 246, pp. 637–640.

756

Chapter 6

investigations, and test calculations, could then easily be delegated, and the academies offered a suitable forum for realizing this. Through these institutions Leibniz hoped to obtain personnel and assistants. Accordingly, during his visit to Berlin in the summer of 1700, he made the effort, through the intermediation of Philippe Naudé, to motivate Pierre Dangicourt to devote himself to binary mathematics.70 The introduction of Dangicourt to dyadics duly led to a cooperation under Leibniz’s direction, and this culminated in a publication of Dangicourt in the Miscellanea Berolinensia in 1710.71 However, since the exchange of ideas took place viva voce during Leibniz’s visits to Berlin, it is sparsely documented in his correspondence. With the Académie des Sciences, Leibniz was less successful. L’Hospital proposed Antoine Parent as a suitable mathematician for the task in hand, but Leibniz was not in a position to provide the requisite funding. In addition, he was discouraged by L’Hospital’s statement concerning Parent, in his letter of June 9, 1701, namely that “This young man has difficulty in setting aside his own thoughts in order to follow those of others”.72 And so, Parent did not match Leibniz’s idea – as expressed in a letter to L’Hospital of March 23, 1699 – namely of a young man able and willing to immerse himself in his views.73 It was in quite a different vein, that the China Jesuit missionary Joachim Bouvet took up binary mathematics, namely after Leibniz had communicated to him (on February 15, 1701) the theological interpretation and his latest results.74 Bouvet’s two communications from Beijing, on November 4, 1701 (“A Peking ce 4e de novembre 1701”), reveal that this correspondent saw an analogy to the Chinese figures of Fohy (or ‘FuXi hexagrams’), which are found in the binary – and indeed octal and hexadecimal  – Fohy (or FuXi) sequence, and which Leibniz subsequently elaborated in a letter sent from Berlin to Hans Sloane, for forwarding to John Flamsteed, on April 17, 1703.75 70 Cf. A III,8, pp. XLVIIIf. 71 P. Dangicourt, “De periodis columnarum in serie numerorum progressionis arithmeticae dyadice expressorum”, Miscellanea Berolinensia, (1710), pp. 330–376. 72 “Ce jeune homme a de la peine à quitter ses pensées pour suivre celles des autres” (A III,8 N. 267, p. 696; cf. also N. 297, p. 764). 73 “quelque jeune homme propre à entrer dans mes vues” (A III,8 N. 21, p. 77). 74 Cf. A I,19 N. 202, pp. 404–409. 75 Cf. A I,20 N. 318, pp. 533–555, and N. 319 (Darstellung der 64 Hexagramme aus dem Yijing in der Fuxi-Ordnung), pp. 555f.; Leibniz’s letter to Hans Sloane, Berlin of April 17, 1703 (III,9 N. 84, pp. 294–297); the following publications (Introduction, note 42): E. J. Aiton (1981), D. Guangbi (1996), E. G. (and M.) Forbes et al. (2002), R. Widmaier and M.-L. Babin (eds.), (2017).

1699–1701

3

757

Natural Philosophy

In Leibniz’s correspondence with Papin the disputes concerning the true measure of force, and the correct concept of action (“actio”), were continued in the new year of 1699 with unabated intensity and passion. In the 30-month period that ended in December 1698, a total of 40 letters had been exchanged between Leibniz and Papin. In the 36-month period that began in January 1699, 20 letters were exchanged, of which 19 had been dispatched by the spring of the year 1700, when the controversy finally came to a standstill. In the course of the debate with Papin in 1699, and in early 1700, the themes of the previous years were once again played through time and time again. In January 1699, Leibniz began to have doubts about the forthrightness, and the probity, of his correspondent, as the beginning of the never-dispatched first version of his letter to Papin of January 1699 reveals. Here he wrote: “I could have begun to believe on reading that which you wrote to me recently, that you would like to elude my reasoning by means of chicanery”.76 He expressed himself somewhat more diplomatically at the beginning of the second dispatched version of this letter, where he attributed the (for him) incomprehensible argumentation of Papin to inattention on the part of the correspondent. His desire was for a return to a formal argumentation regime with the help of a train of syllogisms, and so he wrote: Your reasoning seems to be to a very small extent in line with mine, for some time now, so that I am very surprised about it, and do not know what to say. And so in order to henceforth avoid every topic of contestation and reproach, it is necessary [for us] to return to formalization.77 Accordingly, Leibniz summed up, in the form of syllogisms, the state of the debate regarding the principal points at issue, namely his concept of action (“actio”), and his thought experiment regarding the impact of a spherical body moving along the diagonal of a square figure against two similar bodies resting at a corner.

76 “j’aurois commence à croire en lisant celles que vous m’écrivés depuis peu, que vous voulés eluder mes raisons par des chicanes” (A III,8 N. 5; cf. L1, p. 18). 77 “Vos raisonnemens semblent si peu convenir aux miens, depuis quelque temps, que j’en suis tout surprise, et ne sçay qu’en dire. Ainsi pour eviter doresnavant tout sujet de contestations et de reproches, il faut revenir à la forme” (cf. L2, p. 24).

758

Chapter 6

As regards Papin’s argument that there could be no action without the body experiencing resistance, Leibniz had initially proposed using the term “changemens” instead of “actions”. However, this had only added to the confusion, since Papin had replaced  – in the syllogism with which Leibniz had expressed the action for uniform motion as depending on the traversed distance and the velocity  – the expression traversed spaces (“espaces parcourus”) with changes of place or location (“changemens de lieu”, or “mutationes loci”). Papin did in fact differentiate between that produced and that which produces (“mutationes loci productae”, and “mutationes loci producendae”), and he was therefore not confronted with a contradiction in Leibniz’s syllogism. Nonetheless, that was not what Leibniz intended. Accordingly, he then tried, on the one hand, to explain the difference between changes of spaces and spaces changed (“changemens des espaces”, and “espaces changés”), and, on the other hand, to return to the concept of action which he needed to make plausible in another way. He discussed in detail why action also exists in the event of a resistance-free movement, a matter which Papin had rejected by referring to the axiom “omne agens agendo repatitur”, or that there is no action in nature without re-action. To postulate a resistance would  – according to Leibniz – mean “to destroy immanent actions. It would also be to withdraw the action from God who does not retort at all”.78 Finally, he presented further reasons for presupposing an action, writing that: Otherwise I could prove, for my part, that there is action here, because you have agreed in one of your earlier letters,79 that there is force. And this force is exercised effectively here for there is no simple conatus. Now however every exercise of the force passes for an action. I could also argue, that a new situation is always produced, and that every production is an action.80

78 “détruire les actions immanentes. Ce seroit aussi oster l’action à Dieu qui ne repatit point” (p. 26). 79 Cf. A III,7 N. 234 (October 9, 1698). 80 “Au reste je pourrois prouver à mon tour, qu’il y a action icy; car vous avés accordé dans une de vos precedents, qu’il y a force. Et cette force est exercée icy effectivement car il n’y a pas un simple conatus, Or tout exercice de la force passe pour une action. Je pourrois aussi argumenter, qu’il se produit tousjours une nouvelle situation, et que toute production est une Action” (note 77 above, p. 27).

1699–1701

759

Figure 13 Sketch of Leibniz’s thought experiment regarding the collision of a body moving along the diameter of a square with two other bodies resting at a corner Source: Leibniz to Denis Papin, January 1699 (A III,8, p. LVI and p. 29)

For the diagonal collision of the three bodies,81 Leibniz assumed that the resultant of the event consisted of two components, namely the mutually independent movements of A and B, and of C and B, respectively. Papin had rejected this, with the argument that, since B, in its movement along the diagonal, would – in the event of a simultaneous meeting of the three balls – experience less resistance from each individual sphere or, in the reversal of the process, be pushed off faster than in the case of separate collisions. Therefore, the total result would not be the sum of the individual collisions. Leibniz replied here that what mattered was not how rapid the repulsion of B along the diagonal would be, but rather what the velocities along the extended straight lines, parallel to CB and AB, respectively, would be. Both of these themes, namely the interpretation and the measure of the action, and the understanding of the diagonal collision, were at the center of the Leibniz-Papin correspondence until its extended interruption in the spring of the year 1700. Accordingly, the different positions were recapitulated again and again, reformulated and stated more precisely, however without a convergence of those positions being achieved. In his reply to Leibniz’s letter of January 1699, on February 23, Papin also regretted the lack of agreement in the matters at issue, but he did insist however that he was motivated solely by the search for truth, and he went into detail regarding Leibniz’s main argument.82 In his view, Leibniz’s explanations concerning the distinction between changed spaces (“espaces changés”) and changes of spaces (“changemens d’espaces”) failed at this point to clarify the issues of terminology. Papin proposed equating the concept of “action” with perseverance, or persistence, in the same manner 81 Cf. p. 29. 82 Cf. A III,8 N. 15, pp. 58–61.

760

Chapter 6

of being (“perseverance dans la même maniere d’être”), which however was independent of the movement.

Figure 14 Papin’s sketch of the thought experiment regarding the collision of three spheres at a corner of a square Source: Denis Papin to Leibniz, February 23, 1699 (A III,8, p. LVII and p. 60)

The situation, assumed by Leibniz, of the simultaneous collision of two balls against a third one at rest,83 was for Papin only valid in the first instant when the diameter oo of the sphere C coming from E strikes the diameter nn of the sphere B at rest. Since the collision taking place was not an instantaneous one, but rather a physical collision of elastic bodies, the diameter oo would instants later, in the wake of the impact of the ball A against ball B, no longer impact the diameter nn but rather the chord pp. For that very reason, in the case of the simultaneous collision of the three balls, B would receive less force from C than in the case of the impact of B and C alone. The discussion about the role of the resistance also led to considerations about inertia and mass. The conflicting positions remained, in Leibniz’s view, 83 Cf. p. 60f.

1699–1701

761

unreconciled alongside each other. And so, in his reply of March 10, he wrote: “If that which I said about the inertia of the mass, and of the forces or entelechies is not to your taste, Sir, as you say, I am piqued about it”.84 Notwithstanding this, Leibniz did find that they were in agreement about the circumstance that a body resisted a change from a state of motion to that of rest, and vice versa. However, while for Papin there was no fundamental difference between the states of rest and motion, for Leibniz, in the state of rest – which he regarded as a simple deprivation (“une simple privation”) – the mass, or the inertia, of matter resisted motion. Yet, for bodies in motion an entelechy – being an inherent or intrinsic and purposive force – provided for the maintenance of the state. Mass constantly reacted against, or resisted, this entelechy, and thus action and reaction would take place here within a body. However, Papin’s assumption of a general inclination to conserve its manner of being (“inclination generale pour conserver sa maniere d’estre”) contradicted the phenomenon, since, for a movement along a flexuous line, or curve, only the direction and not the curvature is conserved after the constraining force is removed. Which magnitudes in nature were really conserved would have to be scientifically established. Leibniz proclaimed here that he had established that the measure of force, as well as that of action, but not the quantity or measure of motion (viz. the momentum or impulse) were conserved, or as he wrote: “It is so that I found that it is the quantity of force and that of motive action that are conserved, and in no way that of movement”.85 However, Leibniz did consider Papin’s objections against his discussion of the diagonal-collision thought experiment to be well founded. Yet, in the abstract consideration of the event, one could assume perfect hardness, and an instantaneous or momentary collision of the three balls, and therefore that the force of both the balls A and C would be totally transferred to B. The total transfer (and conservation) of the quantity of motion would however result in a perpetuum mobile. And so he wrote: Nevertheless one will always find that, notwithstanding this little irregularity, very little is required for the bodies A and C, arriving with the speeds [represented by] the sides and striking the body B, not to come to a standstill, and give all of their force to B, such that it [then] moves with the velocity of the diagonal. And the event will always be abundantly 84 “Si ce que je dis de l’inertie de la masse, et des forces ou entelechies n’est pas a vostre goust, Monsieur, comme Vous dites; j’en suis faché” (A III,8 N. 18, p. 68). 85 “C’est ainsi que j’ay trouvé que c’est la quantité de la force et celle de l’action motrice qui se conservent, et nullement celle du mouvement” (p. 70).

762

Chapter 6

approached with very hard bodies thus showing that almost all of the force of a greater mass A + C will have been transferred to a much smaller one, that is to say to its half, [namely] B, and that accordingly the same quantity of movement will be conserved. There would be [in this event] perpetual mechanical motion.86 Papin, in his letter of April 2, adhered to the notion of change of place or location (“changement de lieu”), which he considered to be decidedly more distinct than that of “action”.87 His assumption of an absolute indifference for every sort of manner of being (“indifference absolue pour toutes sortes de manieres d’être”) appeared to him to be more natural, simpler, and more complete than Leibniz’s distinction between the states of rest and motion. Leibniz’s concept of the entelechy meant for him an added complication, or a multiplication of entities (“multiplier les êtres”). Papin considered the movement of bodies along a flexuous line, or curve, to be in conformity with his assumption, which he explained by the example of centrifugal force. The bodies would possess this force in order to conserve their state. As regards the diagonal collision thought experiment,88 Papin stuck to his conviction that, even with the assumption of a perfect hardness, the sum total of the quantities of motion following the collision would be less than before the event. It was similar to the case of free fall under the influence of terrestrial gravity. If an arbitrarily hard ball were to fall freely, and rebound from an anvil, it would never rise again to the height from which it fell. However, there were instances in which the quantity of motion might be increased following collision. Leibniz, replying in the second half of April, then resolved to no longer speak of action, and instead he insisted on hearing Papin’s view of the following assertion, namely that “to traverse a league in one hour is more than to traverse a league in two hours”.89 The exact proportion in the ratio of 2 to 1 (“en raison de deux à un”) could be determined later. The question concerning inertia, and the entelechy, was for Leibniz not decisive. However, a simpler, more natural 86 “Cependant on trouvera tousjours, non obstant cette petite irregularité, qu’il s’en faudra peu que les corps A et C, venus avec les vistesses des costés et rencontrant le corps B, ne se reposent; et donnent toutes leur forces à B, en sorte qu’il aille avec la vistesse de la diagonale. Et l’evenement en approchera tousjours assez dans les corps bien durs, pour monstrer que presque toute la force d’une plus grande masse, A + C aura esté transferée sur une bien moindre, sçavoir sur sa moitié B et qu’ainsi s’il se conservoit la meme quantité de mouvement; il y auroit le mouvement perpetuel mecanique” (p. 71). 87 Cf. A III,8 N. 23, pp. 82f. 88 Cf. pp. 83f. 89 “parcourir une lieue en une heure est plus que parcourir une lieue en deux heures” (A III,8 N. 29, p. 95; underlining by Leibniz).

1699–1701

763

and more understandable hypothesis, would be worthless if it did not conform with the phenomena of nature, as was to be seen in the comparison of the Keplerian ellipses with the circular planetary paths of the ancients. If matter were indifferent, as Papin maintained, then a smaller body in motion could carry off a larger body at rest without suffering loss. However, Papin would also have to presuppose an inherent or intrinsic predisposition of the body, namely that of being present. The inertia, and the entelechy, represented for Leibniz nothing other than such a preference for the existing states of rest and motion, respectively. The inertia was of an essential nature, whereas in contrast the entelechy was changeable. Thus he wrote: The difference between the inertia and the entelechy is that the former is always the same in the matter or material and is essential for this, because it still belongs to it when it is merely at rest which is just a simple privation; but the entelechies are changeable.90 Unlike Papin, Leibniz saw the transition from movement along a flexuous line, or curve, to that in a straight line as a change of state and, accordingly, a proof that there were to be found in matter, inclinations that were still contrary to a certain existing manner of being.91 As regards the diagonal-collision thought experiment, Leibniz contradicted Papin’s assertion that the alteration of the quantity of movement, be it an increase or a decrease, would be only small and as a result would, following the common or Cartesian interpretation, inevitably lead to perpetual motion, a sentiment he expressed in the following words: On examining it you will find, Sir, that it is not just by a little as you say, but by a lot, that the quantity of movement increases or diminishes and that, if the common estimation were to apply, mechanical perpetual motion would be attained according to your own view of former times. For behold, this is a means by which almost all of the force of a greater mass is transferred to a lesser one. Now however you have recognized that, if I demonstrated this, perpetual motion would follow from the common estimation [of force].92 90 “La difference entre l’inertie et Entelechie est, que la premiere est tousjours la meme dans la matiere et luy est essentielle, parce qu’elle luy appartient encor quand elle n’a que le repos qui n’est qu’une simple privation: mais les entelechies sont changeables” (pp. 96f.). 91 “qu’il y a dans la matiere des inclinations encor contraires à une certaine presente maniere d’estre” (p. 97). 92 “En l’examinant vous trouverés, Monsieur, que ce n’est pas un peu seulement comme vous dites, mais beaucoup, que la quantité de mouvement s’augmente ou se diminue et que si

764

Chapter 6

The example of free fall (and rebound from an anvil) was of a different nature. For a small change in height it would be scarcely noticeable, whereas for a small change in the direction of oblique impact there would in time be accumulation, or continued divergence, with the obliquity becoming more appreciable as the lines move further apart. Thus he wrote on this matter: The example of a hard body which falls on an anvil does not square [with this] at all, because in this case it is simply a matter of the height and not at all of the obliquity. A small difference in the height is not perceptible, but a small difference in the obliquity becomes appreciable in due course, for the more the lines are continued, the more they drift apart.93 Regarding Leibniz’s question as to whether the covering of a distance in half the time amounted to more, Papin replied, on May 7, that an increase of velocity was involved here, but not a change of place or location (“changement de lieu”).94 Since the change of place is compounded of velocity and duration, a compensation occurs; both of the activities are identical. He considered that Leibniz had the obligation to prove his hypotheses about inertia and the entelechy. And he interpreted the encounter of a small body in motion with a large body at rest differently to Leibniz. In the meeting of two bodies in incompatible states (e.g. those of rest and motion), both have to concede equally, for otherwise matter would not be indifferent but would have a penchant for motion. Furthermore, one could often not distinguish between bodies in motion and those at rest. For Papin movement along a curve constituted not a single state, but rather a concatenation of an infinite number of states. Only when the body in motion is freed from constraint, does it remain in a single state. And, finally, Papin insisted that in a collision there would always be a loss of quantity of motion, with the result that a perpetuum mobile would not be produced. In his next letter, written in the second half of May, or the first half of June, 1699, Leibniz assessed Papin’s answer to his question – namely, as to whether l’estime vulgaire avoit lieu le mouvement perpetuel mecanique seroit trouvé selon vostre propre aveu d’autres fois. Puisque voila un moyen par le quel presque toute la force d’une plus grande masse est transferée sur une moindre. Or vous avés reconnu, que si je monstrois cela le mouvement perpetuel suivroit de l’estime vulgaire” (p. 97; underlining by Leibniz). 93 “L’exemple d’un corps dur qui tombe sur l’enclume ne quadre point, car dans ce cas il s’agit seulement de la hauteur et nullement de l’obliquité: une petite difference de la hauteur n’est pas sensible, mais une petite difference de l’obliquité devient sensible par le progrés, car plus les lignes sont continuées, plus elles s’eloignent l’une de l’autre” (pp. 97f.). 94 Cf. A III,8 N. 39, pp. 116f.

1699–1701

765

the covering of a distance in half the time amounted to more namely that the velocity increases but not the change of location – as a partial agreement of their standpoints, which he now stated more precisely using the concepts of “extension” (viz. spatial change) and “intension” (viz. temporal change). He wrote accordingly: I am satisfied, for the perfection or the degree of reality in things, and particularly in movement, can be estimated on two grounds, that is to say by extension, which is here the magnitude of the amount of space or change of location, and by intension, which is here the promptitude or the speed of change or movement.95 If one could agree about the proportionality factor, the dispute could be resolved at least on that point, Leibniz thought. He then presented to that end a formal proof in the guise of the following syllogism that formed the basis of the ensuing discussion: To traverse two leagues in two hours is more than to traverse one league in one hour by a ratio (or in a proportion) of two to one, for the first contains the second precisely two times. To traverse a league in one hour is more than to traverse a league in two hours in a ratio of two to one[.] It is the proposition being discussed presently[.] Yet to traverse two leagues in two hours, is more than to traverse one league in two hours, by a ratio of four to one[.] That which was required to be proved.96

95 “J’en suis content, car la perfection ou le degré de la realité dans les choses, et particulierement dans le movement se peut estimer suivant deux raisons, sçavoir par l’extension, qui est icy la grandeur du lieu ou de l’espace change, et par l’intension, qui est icy la promptitude ou la vistesse du changement ou mouvement” (A III,8 N. 44, p. 129). 96 “Parcourir deux lieues en deux heures est plus que parcourir une lieue en une heure en raison de deux à un, car le premier contient le second precisement deux fois[.] Parcourir une lieue en une heure est plus que parcourir une lieue en deux heures en raison de deux à un[.] C’est la proposition discutée presentement[.] Donc parcourir deux lieues en deux heures, est plus que parcourir une lieue en deux heures, en raison de quatre à un[.] Ce qu’il falloit demonstrer” (p. 129).

766

Chapter 6

In the major premise here, the “extension” is doubled (viz. in doubling the path and the time, one obtains more in the proportion 2:1). In the minor premise, the “intension” is doubled (viz. the same proportion results if, for a constant path, the time is halved). Taken together a factor of 4:1 results. Leibniz’s understanding was that in this way Papin’s proposition – namely that the changes of place behaved like the product of velocity and time – had been refuted. As regards an understanding of collision, the rival positions were still far apart. Leibniz argued that the force lost in the transfer would be small with the result that the Cartesian measure of force would lead to a perpetuum mobile. As regards the difference between rest and motion, Leibniz emphasized that he was concerned with the true or real state of rest, and not an apparent state of rest. This had the same relation to motion that zero had to the positive numbers. Just the same, Leibniz saw here a certain proximity to Papin. Rest could also be regarded as inertia, and it would then be nothing other than Papin’s concept of incompatibility, or of resistance. Movement along a flexuous line, or curve, was also for Leibniz a concatenation of states. However, one could understand every movement, even uniform motion, in the following way; there would be a past state, a future state and a third state, namely the location change itself, that would be conserved. However, the change of direction too would be a state that was altered. Leibniz explained this difference on the grounds that motion could be made attributable to an intrinsic principle, namely the entelechy, which formed the basis of the distinction between real and apparent movement. Yet, the change of direction would be attributable to an external cause, just like an acceleration, a retardation or any change of speed whatsoever. As soon as the external cause ceased to be operative, the change would also come to an end. Here he stated more precisely that this involved not just a simple change, but rather the change of a change. In his reply, on June 18, Papin emphasized that, without external resistance, slow and fast motion would have the same perfection, force, and reality.97 Since the quantity of the location changes depended only on the traversed path, he considered an a priori proof of Leibniz’s standpoint to be impossible. Furthermore, he insisted that his own position could be refuted, neither by the power of judgement, nor by experiment. While Papin did concede to Leibniz that the assumption of a complete transfer of the quantity of motion would inevitably result in a perpetuum mobile, he continued to insist that the laws of motion would prevent this ever happening, since there would always be, in his words, “a depletion or ullage sufficient to prevent that perpetual motion could be produced”. And to this he added the statement: “In view of a lack of rigorous 97 Cf. A III,8 N. 52, pp. 154–157.

1699–1701

767

precision, I believe that, when one will put it to the test of experiment, one will find it to be greater than you think”.98 In addition, Papin made clear once more why the loss of velocity in the collision of a small moving body with a larger body at rest could be explained by the indifference of matter. There was no reason why only the large body should experience a change, while its smaller counterpart did not. In principle, in the collision of two balls, the quantity of change of both would tally, or be in agreement. Finally, Papin could not comprehend that (for Leibniz) not only curvilinear motion, but also uniform motion, consisted of several states. If one were to keep intrinsic and extrinsic factors apart, one would not find any such plurality. Naturally, the position of a body in relation to other bodies could change, but that would only affect the external circumstances, he insisted. Leibniz, replying on July 4, 1699, emphasized once again the importance of formalization, which he justified with the abstractness of the subject matter, and for which one could not simply resort to numbers or figures for support. The essential touchstones for him were, a priori, the form and, a posteriori, experience or experiment. Thus, he wrote on this occasion: There are two touchstones of reason or reasoning: experience [or experiment] a posteriori, and rigorous form a priori, of which I have often reminded you. Every single time that we are standing apart regarding the form, one puts on airs and graces which have resulted in contestations which are not at all pleasant. Your last letter has only given me further grounds if I wanted to hold off [or deter myself]. But each and every time that one restricted oneself to the form, one disputed placidly and without introducing anything that might be consternating. And as the profit that one could draw from our discussion on this subject would not cost any displeasure, which there would be on dispensing with these manners, the best course would be to dispute only formally [or by form], above all regarding matters which are somewhat abstract, where one is not guided either by numbers or by figures.99 98 “un dechet suffisant pour empêcher que le movement perpetual ne puisse en être produit. Quant au defaut de precision rigoureuse: Je crois que, quand on en viendra à l’experience, on le trouvera plus grand que Vous ne pensez” (p. 155). 99 “Il y a deux pierres de touche des raisonnemens: l’experience a posteriori, et la forme rigoureuse a priori, à la quelle je vous ay souvent rappellé. Toutes et quantes fois que nous nous sommes écarté de la forme, on s’est donné des airs qui ont fait naistre des contestations peu agreables. Vostre derniere lettre n’en donneroit que trop de sujet si je m’y voulois arrester. Mais toutes et quantes fois, qu’on s’est astreint à la forme on a disputé paisiblement, et sans rien mêler qui choquât. Et comme le profit qu’on pourroit tirer de

768

Chapter 6

The first matter of dispute, namely as to whether the transit of a path in half the time is more, or represents a gain, Leibniz considered to have been decided in his favor, now that Papin had (in his view) in effect concurred with him. He thus considered his standpoint to have been confirmed and the opposing standpoint to have been reduced to absurdity.100 Papin’s continuing opposition represented for him simply tactics for the purpose of saving face. Also, in regard to the second matter of dispute viz. the collision along the diagonal of a square, Leibniz saw a toing and froing on Papin’s part. The latter had accepted that a total transfer of the quantity of motion would lead to a perpetuum mobile, but had assumed a loss in practice from the transferred quantity. Leibniz was now of the opinion that this loss could be kept arbitrarily small, namely by replacing the balls, or spheres, with long thin cylinders.101 Regarding collision, Leibniz proceeded to state the differing standpoints more precisely. While Papin held the states of the bodies involved to be incompatible, for him movements were fundamentally compatible. On bringing the bodies together in a single body, this would move with the compounded movement. If one assumed an indifference of the matter, then, in the collision, each body would receive the movement of the other in addition to its own, which would lead to the previously mentioned antithesis, namely that a smaller body could carry off a larger one without velocity loss. Here he wrote then: You say that I should not deny that two bodies A and B which collide have their respective incompatible manners of being. But I have said nonetheless why I could, and should, deny it. For two movements are always compatible because on putting them together, the joint body proceeds with a composite movement. Accordingly, if matter was indifferent to movement or rest, the body A in the collision would keep its movement, and would receive also that which B tries to give it, and would be moved with a composite movement. And B would do the same. From which it follows that a small body A would carry off a large body B, which precedes it moving more slowly, without losing anything of its velocity.102 nostre conference sur ce sujet, ne vaudroit point le deplaisir qu’il y auroit d’essuyer ces manieres, le meilleur est de ne disputer qu’en forme, sur tout dans les matieres tant soit peu abstraites, où l’on n’est point guidé par les nombres ou par les figures” (A III,8 N. 54, pp. 165f.). 100 Cf. p. 164. 101 Cf. pp. 164–166. 102 “Vous dites que je ne sçaurois nier, que deux corps A et B, qui concourent[,] ont leur manieres d’estre incompatibles. Mais j’avois pourtant dit pour quoy je puis et dois le nier. Car deux mouvemens sont tousjours compatibles puisque en les joignant ensemble, le

1699–1701

769

Regarding movement along a curvilinear path, Leibniz repeated and elaborated his interpretation. Here a state was involved, which was, however, not a single state, but rather a compound one. Indeed the much simpler rectilinear motion was for Leibniz a composite entity. A conservation of state was involved in rectilinear motion, but not in curvilinear motion. Responsibility for this lay in the circumstance that the change of location had an internal cause, whereas the change of direction was attributable to an external cause. Differentiation between “intrinsic” and “extrinsic” properties of bodies was essential for Leibniz. Regarding this point, he saw a certain degree of agreement with his correspondent, however. On the basis of this distinction, he argued, Papin should finally recognize that a greater velocity would lead to greater perfection, and independent of external resistances. He wrote accordingly: I also recognize that the movement in a straight line approaches simplicity more, but it no longer allows being a composite manner of being as I have demonstrated without you providing a reply to it. It is therefore not this matter which constitutes the difference, which effects [firstly] that rectilinear movement is a manner of being that is conserved and [secondly] that curvilinear movement is one which is not conserved, but [rather] the circumstance that the change of location comes from an internal principle, and the change of direction from an external one, as I explained in my previous letter. You see that I am reduced everywhere to being a provider of repetitions, for lack of form, which has given you occasion to pass over that which I have said. You are correct nonetheless, Sir, to distinguish with me that which is intrinsic in the body from that which is extrinsic, and if you had still wanted to apply this distinction to movement, you would not have failed to recognize that it is more perfect when there is more promptitude, with all of the external and accidental resistances being put aside.103 corps va d’un mouvement composé. Ainsi si la matiere estoit indifferente au mouvement ou repos, le corps A dans le concours garderoit son mouvement, et recevroit encor celuy que B tache de luy donner, et seroit mû d’un mouvement composé. Et B feroit de même. D’où il s’ensuivroit, qu’un petit corps A, emporteroit un grand corps B, qui le precederoit plus lentement[,] sans rien perdre de sa vistesse” (p. 166). 103 “Je reconnois aussi que le mouvement en ligne droite approche plus de la simplicité, mais il ne laisse pas encor d’estre une maniere d’estre composée comme j’ay monstré sans que vous y répondiés. Ce n’est donc pas en cela que consiste la difference, qui fait que le mouvement droit est une maniere d’estre qui se conserve, et que le mouvement courbe en est une qui ne se conserve pas, mais en ce que le changement de lieu vient d’un principe interne, et que le changement de direction d’un externe comme j’ay expliqué dans ma precedente. Vous voyés que je suis reduit par tout aux repetitions, faute de forme, qui vous

770

Chapter 6

In his reply, on September 21, Papin then disputed Leibniz’s reproach that he was failing to abide by the agreed formalized forms of argumentation. As regards the question as to whether the passage through a certain distance in a shorter time was more than when a longer time interval was involved, Papin stated his position more precisely. His principal objection here related to the general expression “it is more” (“c’est plus”). Identical bodies would have the same force independent of the velocity. This was so, because for every force acting in a particular direction, there was a compensating weakness (“foiblesse”) operating in the opposite direction. As far as the velocity was intended, he was able to be in accord with this. However, if it was intended that the movement were to be something stronger, more real, or more perfect, than the state of rest, then he would continue to deny this, and so he wrote: I will always very willingly agree with you, but in as far as you say absolutely it is more104 without any restriction, as if the movement was something much stronger, more real and more perfect than the state of rest, I will always deny to your face the said proposition and I have always denied it to your face.105 As regards the diagonal-collision thought experiment, Papin doubted that losses could be avoided, as Leibniz suggested, by substituting long thin cylinders for the colliding balls, or spheres. He justified his concept of incompatibility with the circumstance that, in the collision, one or both of the bodies would of necessity have to change its state, or their states. Leibniz’s splitting of the regular motion into several states meant for Papin nothing less than an unnecessary complication, or an unnecessary multiplication of the entities involved (“multiplier les êtres sans necessité”). He rejected an intrinsic reason for the regular movement, and accordingly also Leibniz’s concept of the entelechy, and so he concluded: “I am not able to recognize any composition or intrinsic

a donné lieu de passer ce que j’avois dit. Vous avés raison cependant, Monsieur, de distinguer avec moy ce qui est intrinseque dans le corps de ce qui est extrinseque, et si vous aviés encor voulu appliquer cette distinction au mouvement, vous n’auriés point manqué de reconnoistre, qu’il est plus parfait, quand il a plus de promtitude, toutes les resistences externes et accidentelles mises à part” (pp. 166f.). 104 Underlining in manuscript by Papin. 105 “Je Vous l’accorderay toûjours fort volontiers: mais tant que Vous direz absolument que c’est plus sans aucune restriction, comme si le mouvement êtoit quelque chose de plus fort, plus reel ou plus parfait que le repos, Je Vous nieray toûjours laditte Proposition et Je Vous l’ay toûjours niée” (A III,8 N. 77, pp. 230f.).

1699–1701

771

change in movement, if it is not when some external cause changes either its velocity or its determined direction”.106 Leibniz’s reply, on October 30, was short, since further discussion with Papin now appeared to him to be superfluous. And so he wrote: If there is the same amount of force in the state of rest as in that of movement, and in slow movement the same amount of force as in rapid movement, there is always the same amount of force everywhere and in everything, and the whole question of the estimation of forces is useless, or indeed it must of necessity be that I do not understand you at all. And as I have reasoned for the ears of those who admit a difference in the forces, it is sufficient for me that my estimation be demonstrated just hypothetically (ex hypothesi) and with respect to them.107 Responding on December 3, Papin only briefly dealt with the dispute about the measure of force. However, he did controvert the accusation that he would not admit different forces. For, even if a force were to be compensated by a weakness, one could still measure it but, in doing so, would have to avail of the Cartesian, and not of Leibniz’s measure, or in his words: I am strongly persuaded that this force can be estimated, but I maintain that to make this estimate it is necessary to make use of our method and not of yours; and it seems to me that there is nothing in that which should be difficult to understand.108 Then, in his final letter of 1699 to Papin, on December 27, Leibniz briefly expressed his incomprehension concerning the circumstance that Papin wanted to incorporate a weakness in the opposite direction, since naturally 106 “Je ne puis recognoître aucune composition ni changement intrinseque dans le mouvement, si ce n’est quand quelque cause exterieure change ou sa vitesse ou sa determination” (p. 231). 107 “S’il y a autant de force dans le repos que dans le movement; et dans le movement lent autant de force que dans un movement promt; il y a tousjours autant de force par tout et en tout; et toute la question de l’estime des forces est inutile: ou bien il faut que je ne vous entende point. Et comme je n’ay raisonné qu’à l’egard de ceux qui admettent une difference dans les forces; il me suffit que mon estime soit demonstrée ex hypothesi et à leur egard” (A III,8 N. 81, pp. 243f.). 108 “Je suis fort persuadé que cette force se peut estimer; mais Je tiens que pour faire cette estime il faut se servir de nôtre methode et non pas de la vôtre: et il me semble qu’il n’ŷ a rien en cela qui soit difficile à entendre” (A III,8 N. 88, p. 256).

772

Chapter 6

the core of the matter was an action in the direction of motion. His words here were: Since that which is involved is the Force to the side to which the movement tends, one cannot see at all to which subject you have put forward its connection to the opposite side; and it is that which, it appeared to me, is difficult to understand. For it is about knowing if the action which accomplishes one league in one hour is not greater than the action which accomplishes one league in two hours, and one understands without doubt that the magnitude of the action as being to the side to which it goes.109 Finally, in the spring of the year 1700, the exchange of views with Papin about the true measure of force gathered pace once again, and it entered its final phase. In his letter of March 4, Papin recapitulated his view of the respective positions as follows.110 Leibniz had maintained that the location changes of bodies moving along a certain path depended on the velocities. He even assumed that a faster motion would lead to greater perfection and greater reality. He himself, on the other hand, held the view that all states had the same degree of reality, force, and perfection. In a certain sense, however, a rapid motion would actually have an advantage over a slower motion because the path would be completed in a shorter time. The actions which Papin equated, as he had previously done, to changes of location, manifested themselves, in his own view, as the product of the times and velocities. Once again Papin referred here to Leibniz’s statement that it is more to cover a certain distance in one hour rather than in two hours. With respect to the velocity, this would be correct. However, as far as he was concerned, it was only a matter of the distance, or stretch, covered. The circumstance that one body required double the time span, whereas another body had double the velocity, resulted in a compensation, or equalization. Whether one considered the quantity of changed locations or the quantity of changes of location (“la quantité des lieux changez ou la quantité de changements de lieu”), would, according to him, be of no consequence here. All in all then, Papin considered that he had responded adequately to the issues Leibniz had raised, or in his words: 109 “Puisqu’il s’agit de la Force du costé où tend le mouvement, on ne voit point à quel sujet vous avés mis en avant son rapport au costé opposé: et c’est ce qui m’a paru difficile à entendre. Car il s’agit de sçavoir si l’action qui acheve une lieue en une heure n’est pas plus grande que l’action qui n’acheve une lieue qu’en deux heures, et on entend sans doute la grandeur de l’action du costé où elle va” (A III,8 N. 94, p. 267). 110 Cf. A III,8 N. 133, pp. 357f.

1699–1701

773

At present, Sir, [after] that I have satisfactorily answered the questions which you have considered appropriate to pose to me, you can see if there are some good instances to be brought against this response which I have already given you in my previous letters.111 Less than a week later, on March 10, 1700, Leibniz replied. He tried to portray Papin’s views as absurd, or beside the point. The whole world would prefer a more rapid movement to a slower counterpart, and would consider it to be more perfect. If duration and velocity were to mutually compensate, or offset each other, that should also hold for liabilities and assets, like for debts and wealth assets, for that which one person lacks is in the possession of another, or in his words: “But it appears that it is like as if a person in debt were to say that he has just as much as another who is rich because he owes just as much as the other might have”.112 Furthermore, Papin’s assumption would, according to Leibniz, lead to the situation that the actions of all movements would be equal, since for bodies in motion a reciprocal relationship between velocities and times always exists. However, this would only apply if the distances covered were to be equal. In the general case, with Papin’s assumption, a proportionality would result between action and the product of distance and time. This would lead to the absurd consequence that a uniform movement, in which two units of length were covered in two hours, would have fourfold the action of a movement in which one unit of length was covered in one hour, or in his words: It would follow that the velocities being equal, the actions would be in proportion or consideration composed of the paths and the times. From which it follows that the action of a body F, which traverses two leagues in two hours, is quadruple (or at least more than double) the action of an identical body G which traverses one league in one hour (I always intend uniform movements here) which is manifestly an absurdity, the one being precisely double the other. From which it is also manifest that the compensation of the velocity by the time is not sustainable at all and that it would be necessary to omit the time here, [while] being satisfied 111 “A present, Monsieur, que J’ay satisfait aux questions que Vous avez jugé à propos de me faire, Vous pouvez voir s’il ŷ a quelque bonne instance à apporter contre cette reponse que Je Vous avois dêjà faitte dans mes precedentes” (p. 358). 112 “Mais il semble que c’est comme si un homme endebté disoit, qu’il a autant de bien qu’un autre qui est riche parce qu’il doit autant que l’autre peut avoir” (A III,8 N. 137, pp. 367–369, specifically p. 368).

774

Chapter 6

to say, as I am, that the actions are composed in proportion to the paths and the velocities.113 And so, for Leibniz the bottom line (or the “bout du compte”) was that the acceptance of his measure of force was the only means of avoiding such an embarrassment.114 Four weeks later, on April 8, Papin once again insisted that a more rapid movement had advantages, but that in relation to the states (“manieres d’être”) bodies at rest would have exactly the same amount of reality, perfection, and force, as those in motion. While a body in motion acts more strongly in the direction of motion, a body at rest acts more strongly in the reverse direction.115 He denied that velocity and time always stood in a reciprocal relation, or inverse proportion, to one another, and he then demanded from Leibniz a formal proof for the minor premise of the syllogism under consideration, writing as follows: “Accordingly, Sir, I do not see the least embarrassment in our hypothesis, and I will always continue to deny your minor [premise] until you will have proved it by some formal argument”.116 In his final letter to Papin dealing with the measure of force and action, written in the second half of April 1700, Leibniz elaborated his views about the still unanswered matters of dispute under nine headings in an attempt to structure the discussion.117 He then accused Papin of not having answered all his arguments. Papin’s assertion, that all states had the same amount of reality, would lead to the paradoxes that: “Privation contains as much as possession, rest or ignorance as much as action and science [respectively], darkness as much as light [Enlightenment]”.118 Once again Leibniz emphasized that the essence of the matter was the measure of action in the direction of motion. In addition, he attempted to provide 113 “il s’ensuivroit que les vistesses estant egales les actions seront en raison ou consideration composée des chemins et des temps. D’où il s’ensuit que l’action du corps F, qui parcourt deux lieues en deux heures, est quadruple (ou du moins plus que double) de l’action du corps egal G qui parcourt une lieue en une heure (j’entends tousjours des mouvemens uniformes) ce qui est une absurdité manifeste, l’un estant precisement le double de l’autre. D’où il est manifeste aussi que la compensation de la vistesse par le temps n’est point soutenable et qu’il falloit ici omettre les temps, en se contentant de dire comme je fais, que les actions sont en raison composée des chemins et des vistesses” (pp. 368f.). 114 “Ainsi vous verrés, Monsieur, au bout du compte qu’il n’y a pas moyen de sortir de l’embarras sans venir à mon estime” (p. 369). 115 Cf. A III,8 N. 151, pp. 394f. 116 “Ainsi, Monsieur, Je ne vois pas le moindre embarras dans nôtre Hypothese et Je persisteray toûjours à nier vôtre mineure jusques à ce que Vous l’ayez prouvée par quelque argument en forme” (p. 395). 117 Cf. A III,8 N. 161, pp. 416–419. 118 “la privation contient autant de realité que l’habitus; le repos ou l’ignorance, autant que l’action et la science, les tenebres que la lumiere” (p. 417).

1699–1701

775

a proof for the minor premise of the syllogism referred to. This he rejected, however, and he concluded with the words: “I have distinguished or specified the whole by numbers or articles to give you the opportunity, Sir, to respond distinctly if you consider it appropriate; and one will see then, if I have need of a proof again”.119 A reply from Papin to this letter has not been found. Perhaps Leibniz’s letter of April 1700 did not reach the correspondent, since he had embarked on a journey to Holland. The outcome was that the correspondence between the two was interrupted for a period of a year and a half. In Papin’s last communication to Leibniz of the year 1701, on December 5, no further reference was made to the dispute about the correct measure of force, and the concept of action, and the controversy thus came to an abrupt end.120 4 Physics Throughout the 1690s, Bernardino Ramazzini was no doubt Leibniz’s internationally most renowned correspondent in the medical field. But Ramazzini also made significant contributions in field of physics, and in particular by undertaking thermometric and barometric investigations in the subterranean wells of Modena, following a suggestion of Leibniz himself. During his stay in Modena – from December 30, 1689 to February 2, 1690 – Leibniz had proposed the undertaking of temperature measurements in the subterranean wells there.121 These measurements were then conducted, along with atmospheric pressure measurements, beginning in October 1690. At the end of September 1696, Ramazzini availed of the return from Modena of the duchess-dowager Benedicte to send copies of his medical and barometric ephemerides to Leibniz in Hanover.122 Leibniz, for his part, referred to the measurements undertaken in the subterranean wells of Modena, along with similar investigations of the Académie des Sciences from the year 1679, in a letter to Ramazzini of January 1697. On that occasion he wrote: I remember having once advocated that it be investigated, with the aid of a thermometer, if indeed, and by how much, the heat increases in winter in your Modenese subterranean wells. Of course the French Royal Academy has [already] observed that the increase of heat appeared to 119 “J’ay distingué le tout par nombres ou articles pour vous donner lieu Monsieur, de repondre distinctement si vous le trouvés à propos; Et on vera alors, si j’ay encor besoin de preuve” (p. 419). 120 Cf. A III,8 N. 314, pp. 801f. 121 Cf. A III,5 N. 20. 122 Cf. A III,7 N. 22, pp. 87f.

776

Chapter 6

be greater than in a similar case, and it was found that the thermometer was a more reliable judge in comparison with the use of human senses.123 Leibniz may even have intended undertaking barometric investigations himself when, at the end of 1697, he entrusted Rudolf Christian Wagner with the construction of a portable barometer.124 When, in a letter of April 22, 1699, to Ramazzini, Leibniz once again recalled the temperature and atmospheric pressure measurements made by the correspondent in the wells of Modena, his interest was to establish whether there existed, as had been claimed, an antiperistasis, or whether they were simply dealing with an illusion, or a false perception. Thus, he wrote the following text: Although you have successfully carried out the aerometric investigation, I would like to know if there was any convenience or ease for you brought about by the thermometer (which I desired) in your wonderful subterranean wells at that time, when they were being operated by workers but had until then not yet been bored or drilled through, in order that the degree of heat inside could be examined, from which it would be clear whether they were dealing with what they call an antiperistasis, or somehow with a deception of the senses as is sometimes encountered in such [locations].125 Replying on June 17, Ramazzini then promised to undertake further measurements as soon as new wells would be dug or excavated, and to communicate his results, writing the following: “As soon as any new well will be excavated, I will be able to diligently observe the degree of heat in the thermometer and I will communicate my observation [to you]”.126 In Leibniz’s correspondence with Ramazzini, in 1699 and 1700, there was also a detailed discussion about the correspondent’s dispute with Günther 123 “Memini aliquando optare, ut ope Thermometri exploretur an vere et quantum hyeme crescat calor in vestris puteis Mutinensibus. Sane in Academia Gallorum Regia observatum est calorem auctum magis videri quam esse in simili casu, estque in his thermometrum judex humanis sensibus fidelior” (A III,7 N. 67, specifically p. 264, and annotation). 124 Cf. A III,7 N. 160, pp. 645–647, and N. 166, pp. 683f. 125 “Quoniam rem aerometricam feliciter tractasti, nosse velim an Tibi aliquando commoditas vel otium fuerit, thermometro illato (quod optabam[)] in puteos vestros mirabiles tunc cum nondum perfossi adhuc ab operariis exercentur, curandi ut examinetur quis intus sit gradus caloris; quo appareat vera ne sit, quam ajunt Antiperistasis, an subsit aliqua sensuum deceptio, ut in talibus aliquando solet” (A III,8 N. 31, p. 100). 126 “Ubi novum aliquem Puteum effodient, quia potero diligentia observabo gradus caloris in Thermo et observationem meam communicabo” (A III,8 N. 51, p. 153).

1699–1701

777

Christoph Schelhammer concerning the rise and fall of the barometric mercury column accompanying weather changes. The fact that the level fell in rainy weather, and therefore that the air is lighter than during brighter weather, seemed to contradict intuition. Leibniz followed the debate with interest, as he too had sought an explanation of the phenomenon, which he confided to Ramazzini in his letter of April 22, 1699.127 He thought the problem might be settled by proofs and mechanical experiments, as he explained to the correspondent on January 7, 1700, in the following words: That D. Schelhammer has responded to you is something you will not be unaware of. I think I once explained to you my opinion regarding the descent of the barometer preceding rain or snow, something which it is possible to confirm with demonstrations and mechanical experiments.128 He explained his solution of the problem to Ramazzini, on March 18, by means of the following thought experiment.129

Figure 15 Sketch of Leibniz’s physical thought experiment regarding the operating principle of the barometer Source: Leibniz to Bernardino Ramazzini, March 18, 1700 (A III,8, p. 371)

127 Cf. note 125. 128 “Dn. Schelhammerum Tibi reposuisse aliquid non ignorabis. Meam circa Barometri descensum pluviae vel nivis praeeuntium sententiam Tibi olim explicuisse puto, quae demonstrationibus et experimentis Mechanicis confirmari potest” (A III,8 N. 103, p. 281). 129 Cf. A III,8 N. 139, pp. 371f.

778

Chapter 6

At one end of a beam balance there hangs a pipe filled with water and, at the other end, a weight such that the balance is in equilibrium. On the water a hollow ball is floating. If water enters the ball, then it sinks. However, the ball is waterproof to the extent that the water enters only slowly. According to Leibniz there is an infringement of the equilibrium state during the sinking process and the water pipe rises. The analogy to the behavior of the barometer he explained as follows: the sinking ball corresponds to a rain drop in the air and the balance weight at the other end of the beam to the mercury column of the barometer. The formation of rain was compared by Leibniz to butter production: just as the fat particles at first swim on the surface of the milk, the raindrops also do not sink during bright weather. And so he concluded: Therefore the solution of the anomaly appears manifest, and reason is returned to the paradox as to why serene air is lighter than pluvial air. For the descent of the mercury precedes in a very short time the onset of rain among us, since drops begin to be formed before they reach us.130 Friedrich Hoffmann likewise made a contribution to the debate in a dissertation, entitled Dissertatio … de potentia ventorum in corpus humanum, ubi simul agitur de ascensu et descensu argenti vivi in barametro (1700),131 over which he had presided, and which he sent to Leibniz with a letter of March 1700, requesting his opinion in the following words: I send to you the slender schediasm on the influence of winds on the human body. And although the renowned gentlemen Ramazzini and Schelhammer have hitherto discussed publicly in writings about the motion of mercury in the Torricellian tube, I have nevertheless likewise presented my sentiments. I look forward with pleasure, Most Learned Sir, to your perceptive judgement regarding this matter.132 130 “Ita manifesta videtur solutio nodi, et ratio redditur paradoxi, cur ita aer serenus levior sit pluvio. Nam et praevenit aliquantulo tempore hydrargyri descensus pluviae apud nos casum, quia guttae formari incipiunt antequam ad nos pertingant” (p. 372). 131 Cf. F. Hoffmann (Praes.); Ch. Ockel (Resp.), Dissertatio inauguralis physico-medica de potentia ventorum in corpus humanum, ubi simul agitur de ascensu et descensu argenti vivi in barametro, Halle, 1700. 132 “transmitto levidense schediasma de potentia ventorum in corpus humanum: Et quoniam Clarissimi Viri Ramazinus et Schelhamerus hactenus publice in scriptis de motu mercurii in tubo Torricelliano disceptaverint, et meam sententiam obiter tamen ibi exposui. Judicium Tuum acutissimum circa hanc rem Vir consummatissime lubenter expectarem” (A III,8 N. 132, p. 356).

1699–1701

779

Hoffmann’s work in turn induced Leibniz to send him a year later  – with a letter of March 19, 1701133 – a text with his explanation of the barometric phenomena. Thus, he wrote on that occasion: “I add here the explanation of the barometric phenomena which has recently harrowed [some] famous men. It is in your hands to add your outstanding work to this, should you wish”.134 Alas, for the imprint of Leibniz’s ideas in Hoffmann’s Observationes barometrico-meteorologicae, et epidemicae Hallenses anni MDCC (1701),135 this letter arrived too late. In a PS to his letter of May 30, 1699, Johann Bernoulli reported to Leibniz about his new process for measuring the heaviness, or the weight, of the air. Bernoulli maintained that, while other processes were based on an attenuation, or rarefaction, of the air, his was a condensation, or compaction, method which would lead to an error reduction and power-requirement reduction (3 or 4 instead of more than 20 cylinder strokes). Thus Bernoulli wrote: I ask you to inform me, if it be known to you, who has arranged to gauge air by condensation. I indeed have recently contrived, and deduced in practice, the method (that appears novel to me) of exploring the proportion of the weight of the air to the weight of water, which is by far more convenient, easier and more accurate than the common [method]. For that which others achieve by rarefaction, I attain by condensation and, by means of a certain small vessel or receptacle, I test at the same time a great quantity of condensed air with the balance or weighing pan, to the extent that an error of one grain, which otherwise would be sufficiently notable, introduces nothing of significance here. On the other hand the method by refraction requires more than 20 cylinder piston strokes before the greatest part of the air is extracted from the receptacle, whereas here with 3 or 4 strokes of the piston a sufficient quantity of air is introduced into my receptacle.136 133 Cf. A III,8 N. 225, pp. 576–578; a manuscript copy of the attached text is preserved at the Gottfried Wilhelm Leibniz Library in Hanover (Shelfmark: LBr. 413, Bl. 48). 134 “Addo hic explanationem phaenomeni in Barometro, quod nuper Viros Claros exercuit. Penes Te est utrum eam adjicere insigni labori Tuo velis” (p. 577). 135 Cf. F. Hoffmann, Observationes barometrico-meteorologicae, et epidemicae Hallenses Anni MDCC, Halle, 1701. 136 “Mihi indicari rogo an Tibi quis notus sit, qui aerem ponderare per condensationem instituerit: ego quidem nuper excogitavi et in praxim deduxi rationem (ut mihi videtur novam) explorandi proportionem gravitatis aeris ad gravitatem aquae, quae vulgari longe expeditior, facilior et accuratior est. Quod enim alii per rarefactionem, ego per condensationem efficio et exiguo quodam vase magnam aeris condensati quantitatem simul ad lancem examino, adeo ut error unius grani qui alias notabilis satis esset, nihil

780

Chapter 6

Bernoulli subsequently presented his ideas in a publication entitled Dissertatio philosophica de aëris gravitate et elasticitate (1701).137 Replying to Bernoulli on July 6, 1699, Leibniz pointed to the experiments of Robert Boyle – published in 1660,138 and defended by the author in a piece entitled A defence of the doctrine touching the spring and weight of the air (1662),139 following a critique in Francisco Linus’ Tractatus de corporum inseperabilitate (1661)140 – on the relation between density, temperature and expansion force (“vis dilatandi”), which had revealed a perturbation or violation of the expected proportionalities, and accordingly deserved further investigation. Leibniz referred specifically in this context to Boyle’s first formulation of a certain law – later to known as ‘Boyle’s Law’ – and he even proposed a clarifying experiment himself. Thus, he wrote to Bernoulli: I do not remember reading who [first] contemplated compressed air. I remember Boyle, in that which I believe Franciscus Linus put in writing, or added in a calculation of experiments, had grasped for himself that the elastic force of air was almost reciprocally proportional to the occupied space or volume. Similarly in considering weight it appears that Boyle also noted for himself that rarefacted air received greater force from heat in expanding than he had expected from the proportion of the rarities of the air. It would be appropriate to carry out that [experiment] and at the same time to observe whether or not in similar fashion compressed air acquired less force in expanding than in the proportion of the densities. That which I once observed, I was of the view, came from an unplanned [or improvised] experiment.141 hic aut parum importet: praeterquam quod modus per rarefactionem requirat ultra 20 emboli suctiones antequam maxima pars aeris ex recipiente sit extracta, loco quod hic 3 aut 4 pressionibus emboli sufficiens aeris copia in vas meum intrudatur” (A III,8 N. 48, pp. 144f.). 137 Cf. Joh. Bernoulli, Dissertatio philosophica de aëris gravitate et elasticitate.[Resp.] Phaebus Themmen, Groningen, 1701. 138 Cf. R. Boyle, New experiments physico-mechanicall, touching the spring of the air, and its effects, (made for the most part, in a new pneumatical engine) written by way of a letter to the Right Honorable Charles Lord Vicount of Dungarven, eldest son to the Earl of Corke, Oxford, 1660; Boyle: The works, 14 vols. London, 1999–2000, specifically vol. 1, pp. [141]–306. 139 Cf. R. Boyle, A defence of the doctrine touching the spring and weight of the air propos’d by Mr. R. Boyle in his new physico-mechanical experiments, against the objections of Franciscus Linus; wherewith the objector’s funicular hypothesis is also examin’d, by the author of those experiments, London, 1662. 140 Cf. F. Line, Tractatus de corporum inseperabilitate, London, 1661. 141 “Non memini legere qui aerem compressum ponderaverit. Memini Boilium in his credo quae Franc. Lino reponit, aut adjectis calculo experimentorum deprehendere sibi visum

1699–1701

781

This interrelationship of air density, temperature and expansion force was discussed in detail in further correspondence with Bernoulli, in 1699 and early 1700, with the help of thought experiments and physical models for the air. However, Leibniz and Bernoulli could not agree even about the fundamental properties of the air. Bernoulli’s processes were based on a proportionality between density and weight, or as he expressed himself to Leibniz on July 28: “There is no doubt that the weight of the air is proportional to its density, for the quantities of air of equal volumes, and therefore also the weights, are as the densities”.142 Leibniz, writing on August 4, then objected that there might be incompressible parts involved.143 In a letter of October 6, Bernoulli, for his part, argued that, notwithstanding this, the proportionality would be maintained; either the air as a whole would be incompressible, like water, or, although it might contain incompressible parts, it would nevertheless be compressible, like for example steam.144 There remained the question, as to whether or not a compression would be possible to the extent that the incompressible parts could touch each other, as Leibniz thought, and so Bernoulli added: And thus the total airy mass would be incompressible like water content, indeed the immediate contact of the particles would resist the compression by the applied force, unless as said it were possible to expel these very subtle particles through the pores of the air pump; you do not really suppose this[?].145

aeris vim Elasticam fere reciproce proportionalem esse spatio. Idem in pondere examinandum Boilius etiam notare sibi visus est, aerem rarefactum a calore accipere vim se dilatandi majorem quam proportione raritatis expectarat. Id dignum excuti simulque observari an non similiter aer compressus minorem dilatandi vim acquirat quam pro ratione densitatis. Quod ego aliquando observasse mihi visus sum facto tumultuarie experimento” (A III,8 N. 55, p. 171; cf. annotations). 142 “Dubium non est pondus aeris densitati ejusdem esse proprtionale, quantitates enim aeris aequalium voluminum adeoque etiam pondera sunt ut densitates” (A III,8 N. 57, p. 175). 143 Cf. A III,8 N. 60, pp. 182f. 144 “eodem nempe modo quo aqua alias incomprimibilis sed in vapores resoluta una cum aere cui admixta est comprimitur” (A III,8 N. 78, p. 234–236, specifically p. 235). 145 “Et sic tota massa aerea foret incomprimibilis instar aquae, immediatus quippe contactus particularum vi compressionem tentanti resisteret, nisi quis dixerit has particulas tam subtiles esse ut per poros antliae pneumaticae expelli possint; hoc vero Tu non supponis” (p. 235).

782

Chapter 6

Leibniz and Bernoulli were only in agreement about the circumstance that nothing in nature was totally incompressible, as Leibniz’s letter of October 30, and Bernoulli’s reply of December 1, reveal.146 In the end, on January 22, 1700, Leibniz concluded that further experiments were necessary to decide the matter of expansion by heat and contraction by cold, and so he wrote in this letter: “Regarding the condensation, rarefaction, calefaction of air, or contraction by cold, the carrying out experiments is an absolute necessity”.147 Finally, geophysics, and in particular terrestrial magnetism, and astronomy were also touched on in Leibniz’s correspondence in the year 1701. On July 9, Hans Sloane, thanked Leibniz for an astronomical table of the Berlin astronomer Gottfried Kirch, which had been sent for presentation to Edmond Halley, and he informed Leibniz about the journeys of the buccaneer-scientist, and global circumnavigator, William Dampier as well as those of Halley himself. He also forwarded to Leibniz a map prepared by Halley of the seas he had traversed (between 1698 and 1700), and in which also the variation of the magnetic declination had been recorded. Thus, Sloane wrote on this occasion: I have herewith sent you the transactions for some time past … I have added to them a map graven by Mr Halley upon his return from his late voyage wherein you will see some matters very curious in relating to the variation of the needle as well as the true situation of sevll places observed by him. He gave me one for my selfe which I make you a present of. Wee do not yet hear of Mr Dampier since he was at St Helena in his voyage home  … I shewed the Astronomicall table you sent me to Mr Halley who tells me it agrees very exactly with the tables he uses here and lett me see the tables he used for computations at St Helena many years ago wherein there was not the difference of a second in many of the numbers.148 5

Astronomy and Calendar Reform

On September 23 (old style or Julian)/ October 3 (new style or Gregorian) 1699, the ‘Protestant Imperial Estates’ at the Perpetual Diet (“Immerwährender Reichstag”) meeting at Regensburg introduced the so-called improved 146 Cf. A III,8 N. 80, pp. 241f., and N. 87, pp. 253f., respectively. 147 “De aere condensato, rarefacto, calefacto, aut frigore contracto, experimenta tantum facienda supersunt” (A III,8 N. 114, p. 300). 148 Cf. A III,8 N. 276, pp. 717f.

1699–1701

783

calendar.149 Following a leap from February 18 to March 1, 1700, the Protestant Julian calendar was merged with the Catholic Gregorian calendar. For the architects of the change there was one major unsolved issue remaining, namely the determination of the calendar date of Easter. It was defined as falling on the Sunday following the full moon that follows the northern spring equinox. Instead of the solar and lunar cycles used to determine Gregorian Easter, the German Protestant states now decided to use, from 1700, an astronomical Easter based on a determination of the spring equinox and full moon following the Rudolphine Tables of Johannes Kepler (and Tycho Brahe) – the Tabulae Rudolphinae of 1627.150 Leibniz, for his part, supported the intention of the reform, namely of achieving the greatest possible agreement regarding both the civil and ecclesiastical calendars in the confessionally-mixed German empire, and he informed his correspondents accordingly, as for example, in a letter to Sloane on February 9, 1700.151 He likewise helped carry the discussion about the calendar reform beyond the German Protestant territories, as for example in his letter to Ole Christensen Rømer on March 5, 1700, advocating a discussion at equal eye level between Catholics and Protestants in the adoption of the Gregorian calendar.152 At the beginning of 1700, he also called on the Académie des Sciences – through his correspondents Jean-Paul Bignon and Christophe Brosseau – to show that the Gregorian Easter calculation was in agreement with astronomical truth.153 The outcome was that – following a directive of Louis XIV – the Italian-born French astronomer Gian Domenico Cassini established contact with the Vatican with the intention of making clear that the Gregorian Easter calculation was indeed capable of improvement.154 The reaction from Rome was positive and, on March 5, 1700, Leibniz reactivated his correspondence with the Roman astronomer Francesco Bianchini.155 From him Leibniz hoped for, among other things, contact to the Curia, and in particular to Cardinal Marco Delfini, who as Nuncio in Paris had negotiated with Cassini but who had in the meantime returned to Rome,156 and to Cardinal Gian Francesco Albani who was destined to become pope Clemens XI. Shortly 149 Cf. A III,8, pp. XXVII–XXXIII. 150 Cf. J. Kepler, Tabulae Rudolphinae, quibus astronomicae scientiae, temporum longinquitate collapsae restauratio continentur, Ulm, 1627. 151 Cf. A III,8 N. 124, pp. 321–323. 152 Cf. A III,8 N. 135, pp. 362–364. 153 Cf. A I,18 N. 155, p. 406, and N. 186, pp. 478f. 154 Cf. A III,8 N. 162, pp. 420–422, and A I,18 N. 240, p. 430. 155 Cf. A III,8 N. 134, pp. 359–361. 156 Cf. A I,19 N. 89, pp. 156f.

784

Chapter 6

after the latter began his pontificate, and in a memorandum intended for him and attached to a letter of late February, 1701, Leibniz picked up on Cassini’s assessment and suggested  – as he had previously done with Bianchini  – a course of action that Protestants could also follow.157 These initiatives met with no reaction at first, with the result that Leibniz had to resort to contacting Bianchini once again, on December 27, 1701,158 following the establishment of a calendar congregation at the Vatican in the autumn of 1701. The reply would follow one year later. From his own coreligionists, Leibniz kept his involvement – that was also motivated by his efforts for church reunion – secret, in order not to endanger the process through outside criticism, or as he wrote at the end of his letter to Johann Bernoulli on April 25, 1700: “For I do not wish that ulterior associations disseminate the plan (which could initially displease the many highly fractious elements in our midst) before it is ripe”.159 In accordance with the goal of advancing the formation of opinion in the matter, Leibniz promoted  – in his correspondence  – communication between astronomers, and he commented on, evaluated, and disseminated their proposals without, however, presenting a precise standpoint of his own. Rømer sent a memorandum, entitled “Dubia circa novam correctionem calendarii Evangelicorum”,160 which was attached to his first letter to Leibniz of December 29, 1699,161 and which had been prepared in accordance with a directive of the Danish king for communication to the Imperial Diet. In this memorandum, he pointed out that in Regensburg not just the question as to the best set of astronomical tables had been left open. Likewise unclear was, for example, the question of whether the determination of the equinoxes, and of the full moons, was to be based on actual or average astronomical movements. For the year 1704 alone this distinction would lead to different dates for Easter. The astronomer of the Berlin Society of Sciences, Gottfried Kirch, had complained about this und further points of uncertainty. In Regensburg, Kirch’s opinion had been regarded as being amiss, a matter which he confided to Leibniz in early April 1701.162 The decisions of the Council too were questioned. Rømer, for example, in a memorandum for Leibniz entitled “De Paschate

157 Cf. A I,19, p. LXXIII, N. 41, pp. 67f., and N. 42, pp. 68–71. 158 Cf. A III,8 N. 319, pp. 811–814. 159 “nolim enim consilium ulterioris conciliationis (quod multis morosioribus apud nos initio displicere posset) re nondum matura vulgari” (A III,8 N. 162, p. 422). 160 Cf. A III,8 N. 97, pp. 269–272. 161 Cf. A III,8 N. 96, pp. 268f. 162 Cf. A III,8 N. 230, pp. 587–596.

1699–1701

785

correcti calendarii”,163 which was attached to his letter to Leibniz of February 3, 1700,164 established that the new calculation of Easter was considerably more tedious than its Gregorian counterpart, although in end effect both were usually in agreement. His alternative suggestion was radical: Easter ought to be always celebrated on the Sunday between April 5 and April 11 which, although a simplification for civil life, would have meant a radical departure from the Catholic calculation. In his reply of March 5, Leibniz considered this suggestion to be hardly realistic, as the purpose of the reform had been to establish the greatest possible unification of the calendars.165 Nonetheless, Rømer forwarded his proposals to Ulrich Junius in Leipzig, and to Gottfried Kirch in Berlin, for their judgements in the matter. Junius’ reply from the second week of April, 1700,166 and that of Kirch from early April, 1701,167 were sent to Leibniz. Argumentation diametrically opposed to Rømer’s came from Samuel Reyher and Joachim Tiede in Kiel, who advocated using solar and lunar cycles developed by the latter, and that were supposed to be more exact than the Gregorian lunisolar calendar. Leibniz  – as he informed Hans Sloane on December 27, 1701  – considered the rearrangement of the leap years arising from Tiede’s cycles to be politically unenforceable. Here he wrote: “Reyher and Tiede are also proposing an understandably much more accurate inter-calendrical modus, but I fear for its possible reception by political men”.168 Nevertheless, the cycles seemed to be well suited for negotiations with the Vatican, by virtue of the small deviation from their Gregorian counterparts. Thus, Leibniz wrote the following lines to Tiede on November 16, 1701: “You will not be unaware that an improvement or a review of the Gregorian calendar has already been considered in Rome”. And to this he added the words: “And so the time has come for you to see to it that, for you there, your thoughts are also brought forward”.169 Leibniz had sent a corresponding report to Bianchini, on March 5, 1700,170 and he now persuaded Reyher and Tiede to write a letter to Cardinal Enrico 163 Cf. A III,8 N. 122, pp. 315–317. 164 Cf. A III,8 N. 121, pp. 312–315. 165 Cf. A III,8 N. 135, pp. 361–364. 166 Cf. A III,8 N. 155, pp. 405–408. 167 Cf. note 162 above. 168 “Proponunt etiam Reiherus et Tidius, intercalandi modum sane recepto multo accuratiorem, sed vereor ut homines politici ad eum recipiendum adduci possint” (A III,8 N. 320, p. 817). 169 “Non ignoras Romae jam ipsius Gregoriani Calendarii sive emendationem sive explicationem aliquam agitari. Itaque tempus est, ut Vos ibi quoque vestra cogitata produci curetis” (A III,8 N. 311, p. 797). 170 Cf. A III,8 N. 134, pp. 359–361.

786

Chapter 6

Noris, who was a member of the papal Calendar Congregation, and whom he had met in 1689 during his Italian journey. Accordingly, in his letter to Tiede of November 16, 1701, he added: Not only is Lord Abbot Bianchini, recently appointed Secretary of the Congregation for this matter (viz. Calendar reform), a friend of mine, but also Cardinal Noris recently recalled this for my benefit through a friend, and so if you were able to highlight that which does not overly shy away from the Gregorian undertaking, and advocate the desired matter, then I would willingly communicate it. I ask you to convey my commendations to the most personable Reyher.171 Reyher’s letter to Norris, dated December 12, 1701, was attached to a letter, dated December 10, 1701, sent to Leibniz and he duly forwarded it to the addressee with a letter of March 8, 1702.172 Furthermore, Leibniz sought external opinions about Tiede’s cycles, from Gottfried Kirch,173 and, in particular, from the Royal Society174 – which had excellent astronomers like John Flamsteed, Edmond Halley and Isaac Newton at its disposal – and from Cassini through an intermediary, namely the perpetual secretary of the Académie des Sciences Fontenelle.175 In addition, Leibniz enquired about attitudes abroad to the calendar reform. Thus, in a letter with new style date (“Hanoverae 25 April 1700”), he asked Johann Bernoulli in Groningen about the situation in the Netherlands, and about the views of Burchard de Volder in particular, writing the following: I suspect that you will have been consulted by your Groningen acquaintances as will our de Volder have been by his Dutch acquaintances. I will

171 “Dominus Abbas B[i]anchinus, Congregationis novae in eam rem institutae secretarius, mihi est amicus, sed et Cardinalis Norisius nuper mei benevole meminit erga amicum, itaque si qua suggere[re] possetis, quae non nimis ab instituto Gregoriano abhorrerent, gratam rem praestaretis, quam ego communicarem libens. Amplissimo Reyhero me commendari peto” (cf. note 169 above, p. 797). 172 Cf. A III,8 N. 315, p. 802 and annotation. 173 Cf. A III,8 N. 230, pp. 587–596. 174 Cf. A III,8 N. 320, p. 817. 175 Cf. A. Foucher de Careil (ed.), Lettres et opuscules inédits de Leibniz, Paris 1854 [Leibniz: Lettres et opuscules inédits], specifically p. 212, and p. 229.

1699–1701

787

be grateful nonetheless to learn the answers given, how you see [things] and in due course to learn your sentiments [on the matter].176 Then, exactly nine months later, at the beginning of a letter, also with new style date (“Groningae d. 25. Jan. 1701”), Bernoulli enthusiastically reported about the adoption of the new style calendar by the provinces Groningen and Friesland at the turn of the year 1700–1701, i.e. with a leap from December 31, 1700, to January 12, 1701. Thus the correspondent wrote here: The letter which you wrote to me on the eve of the new century and the Gregorian year, I also received on the eve of the same, but still Julian, year, which was a noteworthy day, admittedly one which contained a long night of eleven days and on the passing of which, behold for us!, it was already the dawn of the twelfth of January. The same [step] was also undertaken by the West Frisians.177 Already in February 1700, Leibniz informed both the Royal Society and the Académie des Sciences about the improved calendar, and he requested their views. Thus, in his first letter to the secretary of the Royal Society, Hans Sloane, on February 9, he gave details of the Protestant calendar reform that had not been adopted in England.178 His closing words and petition addressed to Sloane were: From You therefore, Admirable Sir, I request that you please propose this in the assembly of the Royal Society with my express appreciation for its established rites and customs, and that you impart its view to me. This matter will be of value to the republic (or commonweal), and welcome to all who cultivate this study.179 176 “Suspicor Te a Tuis Groningensibus et Volderum nostrum ab Hollandis suis consultum iri. Quid respondendum, vos videritis, gratum tamen erit mihi, mature intelligere sententiam vestram” (A III,8 N. 162, pp. 420–422, specifically p. 421). 177 “Quas mihi scripsisti litteras pridie novi seculi et anni Gregoriani, ego quoque pridie ejusdem anni, sed Juliani accepi, qui dies notabilis fuit, quippe quem excepit longa nox undecim dierum, ea enim finita, nobis ecce! jam duodecimus Januarii illuxit; idem quoque apud Frisios occidentales factum est” (A III,8 N. 200, pp. 512–516, specifically p. 512). 178 Cf. A III,8 N. 124, pp. 321–323. 179 “A TE igitur, Vir Egregie peto, ut haec in conventu Societatis Regiae cum multa Cultus a me significatione, proponere, et sententiam ejus mecum communicare velis. Erit ea res utilis Reipublicae, et grata omnibus qui haec studia colunt” (p. 323).

788

Chapter 6

John Wallis was one of the few individuals who fundamentally criticized the Gregorian reform notwithstanding its precision, it – in his words – “haveing caused a confusion of stile throughout Christendome”. With a letter of July 15 (dated “London July 4 s.v. 1700”),180 Sloane sent Leibniz an extract copied from a letter received from Wallis of May 22 (dated “Oxford May 11th 1700”),181 that contained this remark in the opening paragraph. Wallis saw no necessity for an astronomically-exact fixing of the civil year. The Julian calendar was simpler and the ecclesiastical year could be uncoupled from the civil year, he thought. He therefore predicted that in the future many countries would not adopt the new calendar. Besides the Rudolphine Tables, Wallis referred to the Tables and rules for the moveable, and immoveable feasts in the Book of common prayer (the 1662 version),182 and of further tables in Thomas Streete’s Astronomia Carolina, seu nova theoria motuum coelestium (1661),183 and The description and use of the planetary systeme (1674),184 respectively, as well as John Flamsteed’s The doctrine of the sphere (1680).185 The core text of Wallis’ letter of May 22, 1700, is as follows: Sir, I thank you for your letter of May 7 with the papers inclosed. As to the Gregorian correction (as they call it) of the Kalendar; I think it was very unhappily introduced at first. Not only, as not perfectly true; but, principally, as haveing caused a confusion of stile throughout Christendome. Which, from that time, hath continued hitherto; nor do I see, when it is like to end. The Julian Civil Year, is a much better form: as being (though not perfectly exact) of a more simple composition; and much better accommodated for computation of times, far distant; and of greater antiquity. And the Gregorians themselves, in their computations, are fain to make use (oftentimes) of the Julian Year, and thence reduce it to the Gregorian. And, the anticipation of the Aequinoxes, (by three days, in about four 180 Cf. A III,8 N. 174, pp. 447f. 181 Cf. A III,8 N. 175, pp. 448–450. 182 Cf. The book of common prayer, London, 1662. 183 Cf. T. Streete, Astronomia Carolina, seu nova theoria motuum coelestium, London, 1661; Astronomia Carolina. A new theorie of the coelestial motions. Composed according to the best observations and most rational grounds of art. Yet farre more easie, expedite and perspicuous then any before extant. With exact and most easie tables thereunto, and precepts for the calculation of eclipses &c., London, 1661. 184 Cf. T. Streete, The description and use of the planetary systeme, together with easie tables, London, 1674. 185 Cf. J. Flamsteed, The doctrine of the sphere, grounded on the motion of the earth, and the antient Pythagorean or Copernican system of the world: in two parts, London, 1680.

1699–1701

789

hundred years,) is a thing very inconsiderable as to the civil year: and, as to the astronomical year, it is as easily rectified as other inequalities of motion. As to the Eclesiastical year, and the seat of Easter; It might have been easily rectified (if need were) without affecting the civil year at all; Leaving it to the astronomers (as did the Nicene Council) to calculate the Aequinoxes and full-moons (as they do the rest of the Almanack) from time to time. I find by Mr Leibnitz’s Letter, (a copy of which you have been pleased to send me,) that the Protestants in Germany (for the redressing of inconveniences in Trade with their neighbours, amongst whom they wer intermixed) are content to comply with the Gregorians, as to their civil year: Leaving the Eclesiastick (as to the seat of Easter and the moveable Feasts) to the care of astronomers, (without regard had to the Gregorian Epacts or the pope’s authority) wherein (supposing them to find it necessary to make a Change) I think they do, [is] not amiss. But, in other Protestant countries, I think it continues as before so that the Difference of Old and New Stile, must still be kept up. But, when Mr Leibnitz (speaking of the Day of the Full-moon next after the Vernal Aequinox) says quam sequens proxime dominica dies debet esse Paschalis; he should rather have said in quam Incidens, vel proxime sequens, etc. for, if that full-moon be Sunday; Easter is to be that Sunday; not, the Sunday next after. There is (I confess) such a mistake in the rule for Easter in our common-Prayer Book; but, in the Tables, it is rectified. In the Latine Church, before the Nicene Council, it was indeed wont to be kept, not on the full-moon, though it chanced to be Sunday; but on the Sunday after. But this was altered by the Nicene Council; and, thence forth, the Latine Church (as well as the Eastern) keep Easter on the day of the (Reputed) full-moon, if Sunday; not, on the Sunday after. And it hath been so ever since the Nicene Council. Of which I think, it may be well to give Notice to Mr Leibnitz. For though, I beleeve, he may mean the same; it is fit to express it more distinctly. The day of the full-moon, must be after186 (not on) the day of the Aequinox: But Easter-day may be on the day of the full-moon, if that be Sunday; not the Sunday after it. I find also (by his Letter) that they are inclined to follow the Rudolphin Tables; but with some Rectification. Concerning which, he desires advice from our Royal Society. 186 underlining by Sloane in manuscript.

790

Chapter 6

Now, the Rudolphin Tables may perhaps be the truest of any yet Printed in Latine: But, I understand (from those who have better considered it than I have) that the Tables of Mr Street are more correct than the Rudolphin: And those of Mr Flamsted (for the Sun and Moon) better than those of Mr Street: Both published in English, many years ago. But from later observations, Mr Newton and Mr Flamsted have agreed on numbers (for the motions of the Sun and Moon) more exact that either of those Printed Tables.187 Besides the Royal Society, and learned individuals in England, Leibniz also lobbied for the acceptance of the calendar reform in political circles there. In a letter of February 9, 1700, to the diplomat James Cressett, he referred to his letter to Sloane of the same day,188 and he elaborated his vision for the calendar reform as follows: Our ministers have found it appropriate that I write in order to get the opinion of the Royal Society, and those of excellent astronomers who are there, regarding the calendar reform that one has, at Regensburg, purported to have organized for the future according to astronomical truth, and not according to the Gregorian cycles which are sometimes deceptive. But to realize this it is necessary that those holding public office pay attention to astronomy, as one did in a certain way on your part by establishing the Royal Society. The ministers of the Protestant states at Regensburg have written to the king in the name of their masters, asking that his majesty arrange that England conforms with us. I did not go into this at all and I consulted the Society only to learn their sentiments regarding that which we have to do on our part. Nevertheless if England were to make the same resolution to regulate its time in the future in accordance with astronomical truth, it would be doing that which is the most reasonable or rational, and that would serve by having astronomy flourish with public authority, as in China. The matter could even bring about in the king’s council, or in the parliament, something of advantage for the Royal Society which, as I believe, has to the present only enjoyed the honor and the name. I convey to you, Sir, all of my thoughts in order

187 Cf. A III,8 N. 175, pp. 449f. 188 Cf. A III,8 N. 124, pp. 321–323.

1699–1701

791

to, unless otherwise stipulated by your other ministers, reflect on these to the extent you find them convenient.189 As regards France, Leibniz also sought – in addition to his secretive personal initiatives – the judgement of the Académie des Sciences in an official letter, on February 8, 1700. In this – as in the letter of a day later to the English diplomat James Cressett, cited above – he pleaded for a course of action in line with astronomical truth. Thus, the mathematicians of the Académie might, for example, adopt a comparable role as the astronomers of Alexandria, or the members of the calendar office in China, once did. Accordingly, the calendar reform might serve a similar purpose as in China, making mathematics flourish under public authority.190 In particular, Leibniz saw in the decision of the ‘Corpus Evangelicorum’ – the league of Protestant imperial states within the Holy Roman Empire  – an opportunity to advance astronomy, which in his opinion, as expressed in his letter to Joachim Tiede on December 27, 1701,191 was still in its infancy.192 He considered earlier observations to be uncertain and erroneous,193 and one did not even know for sure, nor had one found the best hypothesis, regarding the solar year and its constancy.194 His interest in the quality of astronomical tables was rooted above all in the desire for an increase of knowledge, rather than in a correct determination of 189 “Nos Ministres ont trouvé apropos que j’ecrivisse pour avoir les avis de la Societé Royale, et ceux des excellens Astronomes qui y sont sur la Reforme du Calendrier, qu’on pretend à Ratisbonne regler doresnavant suivant la verité Astronomique, et non pas suivant des cycles Gregoriens qui trompent quelques fois. Mais pour cet effect, il faudra que le public prenne soin de l’Astronomie, comme on a fait en quelque façon chez vous par l’etablissement de la Societé Royale. Les Ministres des Estats protestans à Ratisbonne ont ecrit au Roy au nom de leur Maistres, priant sa Majesté de faire en sorte que l’Angleterre veuille se conformer avec nous. Je n’entre pas là dedans, et je ne consulte la societé que pour avoir ses sentimens touchant ce que nous avons à faire chez nous. Cependant si l’Angleterre prenoit la meme resolution de regler doresnavant son temps suivant la verité Astronomique, elle feroit ce qui seroit le plus raisonnable, et cela serviroit à faire fleurir l’Astronomie par autorité publique, comme dans la Chine. La chose pourroit meme tourner dans le Conseil du Roy, ou dans le Parlement à quelque chose d’avantageux à la societé Royale, qui comme je crois jusqu’icy n’en a eu que l’honneur et le nom. Je Vous dis, Monsieur, toutes mes pensées, sauf à vous autres Messieurs d’y faire reflexion autant que vous le trouverés convenable” (A I,18 N. 205, pp. 349f.). 190 “comme dans la Chine, à faire fleurir les Mathematiques par autorité publique” (A I,18 N. 204, pp. 344–349, specifically p. 348). 191 Cf. A III,8 N. 321, p. 818. 192 “Quis enim in hac Astronomiae accuratioris ut sic dicam infantia” (p. 818). 193 “et veterum observationum vel incertitudine vel defectu” (p. 818). 194 “vel de optima hypothesi nunc aliquid certius spondeat cum ne illud quidem constet, eandem semper anni quantitatem mansuram” (p. 818).

792

Chapter 6

the date of Easter. But, even in respect to the latter problem, Leibniz called for a transnational and an inter-confessional exchange. The fact that the Tabulae Rudolphinae were founded on erroneous observations had been known even to Kepler himself. Thus, Leibniz wrote to Rømer, on March 18, 1700, that the calculation of the vernal equinox, on the basis of Kepler’s data, deviated systematically by three hours from more exact calculations. Here he wrote then: The said [Tabulae] Rudolphinae do not suffice for the determinations of the true vernal equinox. Indeed it has been demonstrated that, on assigning this equinox according to those tables, a result was obtained that was three hours premature, and in contrast the autumnal equinox was delayed by the same amount.195 Ulrich Junius had, in a short tract entitled Epistola de dispositione ephemeridum ad seculum XVIII conficiendarum,196 presented his project for more exact tables based on ephemerides, and he called for representations from others in the matter. Leibniz forwarded this tract to the Académie des Sciences, with a letter of February 8, 1700,197 and to Rømer, whose commentary (of February 3)198 he in turn sent to Junius, and to Kirch.199 Furthermore, through Wagner’s letter of July 21, 1700, Leibniz learned of Cassini’s recommendations for Junius.200 Already from this limited number of responses, fundamental differences became apparent. Rømer and Kirch recommended taking the tables of a single author as a basis, while Junius wished to follow an eclectic or comprehensive approach. Thus, Leibniz wrote the following to Rømer on March 18, 1700: “And so if now these ephemerides, and then those tables, be followed, according to their suitability, a kind of eclectic work form may be advanced to perfection and to admiration in the future”.201

195 “Determinationi verae Aequinoctii verni ait non sufficere Rudolphinas, imo certissime demonstratum esse, hoc aequinoctium secundum Tabulas istas justo maturius trihorio assignari, et contra autumnale tantundem retardari” (A III,8 N. 140, pp. 373–377, specifically pp. 375f.). 196 Cf. U. Junius, Epistola de dispositione ephemeridum ad seculum XVIII conficiendarum, Leipzig, 1699. 197 Cf. A I,18 N. 204, p. 348. 198 Cf. A III,8 N. 121, pp. 314f. 199 Cf. A III,8 N. 155, p. 405, and N. 230, p. 589 (annotation). 200 Cf. A III,8 N. 176, pp. 453f. 201 “Itaque si Ephemerides nunc has, nunc illas Tabulas sequantur, prout quaeque optimae sunt, Eclectico quodam laboris genere, ad eam perfectionem posse promoveri quae admirationi sit futura” (note 195 above, p. 374).

1699–1701

793

Here Rømer considered Kepler’s tables to be adequate once a small number of corrections had been undertaken. Other points that were in part controversial related to true or average movement, the use of right ascension and declination versus longitude and latitude, as well as of heliocentric versus geocentric positions. Rømer wanted to exclude aspects that were important for astrology, and he found himself on this point in agreement with the ‘Corpus Evangelicorum’, which sought to preempt the abuse of astrology through the calendar. Kirch, for his part, was however more pragmatic, and he would not rule out all meanings, or actions, of real celestial bodies.202 Similarly, as regards the quality of available data there was no consensus. In the meantime, a multitude of newer astronomical tables had become available. Whereas Junius wanted to take those of Johannes Hevelius, John Flamsteed, and Philippe de La Hire, as a basis for solar and lunar considerations, Wallis considered the English-language ones to be the most exact – as his letter of May 22, 1700, to Sloane reveals203 – although they had already become out of date once more, as Leibniz pointed out in his letter to Rømer on March 18.204 The most recent results of Flamsteed and Newton on solar and lunar motions had not yet been published. Leibniz received nonetheless, through Sloane, a short summary written by Newton and inspected by Flamsteed. This he lent out to Kirch for his judgement, and he even passed it on also to Fontenelle, whose reply contained an advisory comment from the Académie des Sciences.205 Although Kirch, Newton, and La Hire, were in agreement that the maximum of the midpoint equation of the sun as calculated by Kepler and Hevelius was much too large – being above 2° instead of about 1° 57′ – they were not of one mind about its precise value. Nonetheless, Kirch wrote the following lines to Leibniz, at the beginning of April 1701: When I also considered after this several observations of outstanding astronomers (in addition to my own), and having contemplated the matter now and again, I found that the maximum of the equation of the sun could indeed be hardly above 1 degree, 57 minutes, 8 seconds. For that reason, I made for myself the current equation table. Now having learned that the famous English mathematician Mr Newton (who without doubt

202 Cf. A III,8 N. 230, pp. 593f. 203 Cf. A III,8 N. 175, p. 450, and J. Flamsteed, The doctrine of the sphere, 1680 (note 185 above). 204 Cf. A III,8 N. 140, pp. 374f. 205 Cf. A III,8 N. 230, p. 587 (annotation) and A II,3 N. 244, pp. 662–665.

794

Chapter 6

will have much more accurate observations himself) agrees so closely with me, it gives me great pleasure.206 Leibniz then sent (on May 15, 1701) Kirch’s own value for the midpoint equation to Sloane,207 and he in turn presented it to Halley, as he informed Leibniz (on July 9) in the following words: I shewed the Astronomicall table you sent me to Mr Halley who tells me it agrees very exactly with the tables he uses here and lett me see the tables he used for computations at St Helena many years ago wherein there was not the difference of a second in many of the numbers.208 As regards the values for lunar motion calculated by Newton, both Kirch and the Académie des Sciences could only recommend verification by observation. This was because a satisfactory mathematical description of the motion of the moon, which was required for forecasts, did not yet exist. Newton’s own theory, about which Leibniz enquired among correspondents and visitors, only appeared in 1702.209 Thus, for example, Leibniz wrote the following to Johann Bernoulli in early September 1701: “A learned Englishman who came here provided me with a more reliable report that Newton’s book on the motion of the moon will soon be published. He will have achieved a remarkable thing if he solves this enigma”.210 Even Kepler’s theory of planetary motion proved not to be infallible. After Fontenelle had confirmed that Cassini still preferred ovals to the Keplerian ellipses, and that La Hire appeared not to opt for a particular curve, Leibniz reported to Sloane in his letter of May 15, 1701, that: 206 “Als ich auch hernach, (nebenst meinen wenigen) etliche Observationes vornehmer Astronomorum betrachtete, und die Sache hin und wieder überlegete, befand ich, daß Aeqvatio Solis maxima wol schwerlich über 1 Grad 57 Min. 8 Sec. seyen könte. Machte mir derohalben gegenwärtige Aeqvations-Tabell. Nach dem ich nun erfahre, daß der berühmte Engeländische Mathematicus Herr Newton (welcher ohne Zweifel viel genaue Observationes selbst wird gehalten haben) mir so nahe beystimmet, erfreuet es mich sehr” (note 202, p. 594). 207 Cf. A III,8 N. 258, pp. 678f. 208 Cf. A III,8 N. 276, pp. 717f. 209 Cf. “Lunae theoria Newtoniana”, pp. 332–336, in: D. Gregory, Astronomiae physicae et geometricae elementa, Oxford, 1702; I. Newton, A new and most accurate theory of the moon’s motion, London, 1702. 210 “Anglus doctus qui huc advenit, me certiorem reddit Newtoni librum de motu Lunae mox editum iri. Rem insignem praestabit, si hoc aenigma solvet” (A III,8 N. 294, p. 756; cf. annotation).

1699–1701

795

From France I learned that the renowned Domenico Cassini continues to persevere in the view that ovals, regardless of how they be drawn about two corners of a plane triangle, satisfy the condition of sweeping out equal areas [in equal times] to a greater extent than the ellipses of Kepler and Newton. La Hire does not opt for a specific curve.211 And, in this letter to Sloane, he requested Newton’s opinion. Thus he continued as follows: I [myself], in considering the mechanical causes of ellipses, suspect that it is possible to reproduce these wonderfully and more easily than those of ovals which, by departing from the ellipses and ascribing them to other competing causes, no one is able to properly explain other than Newton himself, and from whom we avidly expect the new theory of the moon, notice of which he has given more than once.212 However, both this statement and a parallel enquiry to Newton through Christoph Bernhard Crusen, came to nothing. In a letter to Crusen, on July 14, 1701, Leibniz enquired about Newton and Halley, and developments in other fields including physics and mathematics. Thus he asked on this occasion: What does Newton feel about the ovals of Cassini[?] Does Halley have anything which uncovers the causes and rules and given the variation stipulates the determination of the position[?] If in due course short books appear in England on physics, mathematics, history, economics, I ask you to put them aside for me.213 Alas, Newton, because of his monetary and academic commitments in London and Cambridge, respectively, was scarcely to be encountered, as Crusen 211 “Ex Gallia intelligo insignem virum Dominicum Cassinum adhuc in ea perstare sententia Ovales a quarum puncto quovis ductarum ad ambos umbilicos rectarum rectangula aequantur areae constanti magis satisfacere quam Ellipses Kepleri aut Newtoni: La Hirius nihil de Linea certa definit” (note 207 above, p. 678). 212 “Ego considerans Ellipsium causas Mechanicas pulchre reddi posse et facilius quam illarum Ovalium suspicor discessum ab Ellipsibus ascribendum aliis concurrentibus causis quod nemo rectius explicare poterit quam ipse Newtonus, a quo et novam Lunae Theoriam cujus indicium aliquod fecit, avide expectamus” (p. 678). 213 “Quid Newtonius sentiat de [C]as[s]ini ovalibus. An Halleius aliquid attulerit quo melius aperiantur causae aut regulae constituantur et data variatione reperiendi locum. Si prodeant subinde in Anglia libri breviusculi de physicis, mathematicis, historicis, politicis, oeconomicis, mihi seponi eos peto” (A I,20 N. 177, p. 267).

796

Chapter 6

informed Leibniz in a letter from London on October 11. He was nonetheless disposed to fulfill Leibniz’s demands as soon as an opportunity might present itself.214 Flamsteed appeared to have taken an important step towards further confirmation of the heliocentric world picture with his observation of the parallax of the fixed stars, which was reported in a letter of December 30, 1698, to Wallis. The latter was included it in the third volume of his Opera,215 and he accordingly informed Leibniz about the English achievement, on April 30, 1699, writing as follows: You will see that it is true, as soon as you receive my third volume which I sent to you recently, that from the letter of Flamsteed to me, it is not at all our disport [or disposition] that he should report who, after having assiduously observed the many positions of the fixed stars, elegantly explained the phenomenon of the annual parallaxes of the earth’s orbit, [an effort] that was first undertaken by him and consolidated by continuous observations over eight years. The phenomenon, that had been sought in vain over several past centuries, and almost in desperation, has now been discovered in England for the first time.216 The very fact, that astronomers had quickly cast doubts on this, was not referred to in Leibniz’s correspondence at this juncture.217 In point of fact though, Leibniz too was skeptical, since a similar earlier observation of Robert Hooke – published in An attempt to prove the motions of the earth from observations (1674)218 – had not proved convincing, as he confided to Tschirnhaus on April 17, 1701, in the following words:

214 “Newtonum convenire nondum licuit, quem videre satis difficile, cum et rei monetariae curam agat … Tuumque Ipsi postulatum exposuerim, quod tamen prima, quae sese offeret, occasione non intermittam” (A I,20 N. 300, p. 511). 215 Cf. J. Wallis, Opera Mathematica, in particular vol. 3, pp. 701–708 (note 19 above). 216 “Verum etiam, ubi obtinueris quod ego tibi nuper misi Volumen meum Tertium; videbis, in Flamstedii ad me Epistola, non plane otiosos nostrates esse; ut qui, tum Fixarum loca plurima a se sedulo observata narrat, tum nobile exhibet Phenomenon, Parallaxeos Orbis Annui Telluris, ab ipso deprehensum, et continuis Annorum Octo Observationibus stabilitum. Phaenomenon per aliquot retro secula frustra quaesitum, et fere desperatum; nunc in Anglia primo detectum” (A III,8 N. 35, p. 109; cf. annotation). 217 Cf. for example, J. Cassini, “Reflexions sur une lettre de M. Flamsteed à M. Wallis, touchant la parallaxe annuelle de l’etoile polaire”, Memoires de Mathematique et de Physique, Année 1699, (1702), pp. 177–183. 218 Cf. R. Hooke, An attempt to prove the motion of the earth from observations, London, 1674.

1699–1701

797

As far as astronomy in particular is concerned, it appears to me that more must be done than hitherto. Mr Flamstead’s observation, that the fixed stars show a noticeable change after a change in diameter of the great circle [viz. following the orbital motion of the Earth], is certainly important, provided one can be sufficiently sure of the latter [observation]. For, if all depends on small parts in observations, the matter is difficult, just like already with Mr Hooke whose observations on this [matter] were also without success. Therefore I am of the opinion that all such [observations], although most likely correct, ought to be made more sensitively.219 However, he did not consider a proof of the Copernican world view based on parallax to be at all necessary, as he had explained to the physician Georg Wolfgang Wedel, in a letter of September 9, 1699, writing as follows: Thus it is as you write that today the principles of the science of astronomy support the view that our earth is one of the [solar] planets and Wallis wrote to me recently that the Englishman Flamsteed, through aversive work over several years, finally obtained much [insight] regarding the annual parallax of the earth’s orbit. But although that would be non-observable because of the distance [involved], so much of the Copernican system is in agreement with the nature of things and of the [parallax] phenomenon. [And so] to understand the matter, following countless confirmations, where our contrary vantage point led to a discerning of the opposite, let it be up to God to counter absurd and undignified imprecations for the most beautiful work.220

219 “Was aber insonderheit die Astronomi anbelanget, so düncket mich daß etwas mehreres als bißher zu thun. Herrn Flamstead observation, daß die fixsterne eine merckliche veranderung nach der Veranderung im diametro orbis magni zeigen, ist freylich wichtig, wenn man sich nur derselben gnugsam versichern kan. Denn wenn es auf so kleine theile in observationibus ankomt, ist die sach mißlich, gleich wie schohn bey Hn Hookij auch dahin gerichteter observation der Verfolg ermanglet. Daher ich vermeyne, daß solches alles wenn es richtig wohl sensibler zu machen” (A III,8 N. 243, p. 632; cf. annotation). 220 “Ita est ut scribis Astronomicae scientiae principes hodie consentiunt tellurem nostram ex planetarum numero esse et scribit mihi Wallisius nuper Flamstedium Anglum improbo aliquot annorum labore, tandem aliquam consecutu[m] orbis annui parallaxin. Sed etsi illa ob distantiam inobservabilis foret; tanta tamen est Copernicani systematis cum natura rerum phaenomenisque consensio; ut re intellect, post innumerabiles confirmationes, quas nostrum dedit speculum contrarium sentire, sit Deo pro pulcherrimo opera molitiones obtrudere absurdas et indignas” (A III,8 N. 74, p. 224).

798

Chapter 6

Wedel had opened the correspondence with Leibniz, on August 24, 1699, by expressing his objections against the movement of the planet earth. According to him, this would contradict the story of genesis, or of the creation, from the Book of Moses, according to which the earth had been created first, and later the sun and other celestial bodies. Here he wrote: When one speaks today about the planetary motion of the earth, and no less about other errant [or itinerant] resemblances, and [whilst] among most mathematicians the matter appears to be valid and decided, I, for my part, cannot but express my doubts. Without doubt, [and based on] borne indisputable witness, heaven and earth, just like all else remaining, were created by God. In the [first of the] B[ooks of] M[oses] we read that on the first day, at all events inarticulately, but on the third day truly and distinctly [there was the creation of] dry or arid land and marine environments. In truth, the sun, the moon, and the remaining stars were finally created on the fourth day, and thus far the earth was already left constant and unspoiled. From which, it having been created at a distinct time and as a basis for that remaining, I have [only] with difficulty [been able to] suppose a connection with the stars, be they errant or fixed, but certainly of a heterogeneous nature, being either constituted of their kind or conceived [as such].221 Leibniz, however, pleaded for a metaphorical, and not a literal interpretation of the bible. In the case of dubiety or ambiguity, of obscurantism and controversy, that interpretation should be followed which is confirmed by the very nature of the matter itself, and thus he wrote the following text in his letter of September 9 to Wedel: Neither is it credible however to fight sacred scripture at times with the book of nature. Accordingly it will be useful, with interpretations that are convenient [in certain instances], to cultivate their use in other places 221 “Cumque hodie de terrae motu planetario, ut ita loquar, non minus ac conditione cum reliquis erraticis simili, apud plerosque mathematicos res velut rata ac decisa videatur, non possum, quin levidense meum dubium exponam. Enim vero testibus indubiis Coelum et terram tanquam basin omnium reliquorum creatam a Deo O. M. legimus primo die, saltim confusam, distinctam vero in aridam et maria die tertio. Sol vero, luna, et stellae reliquae creatae fuere die quarto demum, adeoque terra sibi jam constante et relicta. Unde distincto tempore creatam et pro basi reliquorum vix putavero associandam stellis, seu erraticis, seu fixis illis, sed heterogeneum plane quid seu sui generis constituendam seu concipiendam” (A III,8 N. 66, p. 209).

1699–1701

799

and with other difficulties  … Various other [differing] opinions can be derived from the sense of the words of Moses; and so in matters obscure and controversial, that should be followed which is confirmed by the very nature of the matter itself.222 Flamsteed’s observation of the parallax of the fixed stars, and the doubts that had arisen about it, underlined the importance of precise astronomical values. For this reason, Leibniz canvassed at the Berlin Society of Sciences advocating the acquisition of good astronomical instruments. Thus, an excerpt he made from a letter received from John Wallis of November 16, 1700, contains the following text: You will be able to remember perhaps the observation which our Flamstead revealed in his published letter [addressed] to me with the aid of a certain instrument whose radius was about six feet. If the Brandenburg Society were to commit to making such an instrument, but with telescope probes of 12 or 20 feet, [and if] correctly set up it would be possible to bring together with this an amazing quantity [of observations] for the true determination of the system of the world.223 Moreover, through his correspondents, Leibniz gathered proposals for the building and equipment of the planned Berlin Observatory that was to be located on the roof of the new pavilion there. Rømer argued, in a letter of December 15, 1700, that the building should be designed to accommodate the instruments, if it were intended to serve the purpose of utility rather than pomp, and he recommended the construction of a meridian circle which he himself had designed.224 In a letter to Wagner on April 9, 1700, Leibniz commissioned him, and Johann Andreas Schmidt who had contacts in southern Germany, to make enquiries regarding the observatories of Erhard Weigel, and 222 “Neque vero unquam scripturam sacram cum libro naturae pugnare credendum est. Itaque interpretationibus utendum erit commodis quales in aliis locis difficultatibusque usurpari solent … Variae sententiae aliae feruntur de verborum Mosis sensu; itaque in re obscura et controversa, is sequendus est, quem ipsa rei natura confirmat” (note 220 above, p. 224). 223 “Meminisse forte poteris quid Flamsteadius noster observatum ostendit in sua ad me Epistola typis edita ope cujusdam instrumenti, cujus radius pedum sex circiter. Si Societas Brandeburgica instrumentum tale curaret fieri, sed 12 aut 20 pedum specillis Telescopiis rite instructum mirum quantum illud conducere posset vero mundi systemati constituendo” (A III,8 N. 191, p. 493). 224 Cf. A III,8 N. 193, pp. 495–499.

800

Chapter 6

of Georg Christoph Eimmart, in Jena and Nuremberg, respectively.225 Wagner also had contact with the master builder Johann Heinrich Gengenbach in Zeitz, whom Leibniz decided to consult. Public representation was certainly a priority for Leibniz and so  – citing the example of the recently-deceased Erhard Weigel – in his letter to Gegenbach, in the last week of March 1700, he envisioned the possibility of being able to direct simultaneously the eyes of many observers to a certain star.226 6

Power Technology

In Leibniz’s correspondence between 1699 and 1701, the most recent developments in engineering and technology were discussed, in particular with Papin, Magnus Gabriel Block and Tschirnhaus. Block informed Leibniz from Stockholm, on January 10, 1699, about, among other things, the machines of the Swedish engineer Christopher Polhammar (later called Polhem) being used for quarrying out stone.227 Polhammer had developed a conveyor system with conveying machinery for the ‘King Charles XI’ mineshaft at Falun, where he had been head of the mining machinery since 1698, and where, at the beginning of 1700, he was elected to the position of “Kunstmeister”, or senior mining engineer. As Block wrote to Leibniz on June 24, 1699, Polhammer’s machine was particularly suitable for inclined, or slanting, pits like those he thought Leibniz might be familiar with. His words were: Mr Polhammar has made diverse other beautiful machines and inventions for our mine. I imagine that which you, Illustrious Sir, have seen in an engraving might also serve for inclined or slanting pits; I have allowed myself to be informed accordingly.228 Replying on September 8, Leibniz was able to point out from personal experience that the mine pits in the Harz mountains were not only slanting, but that in addition their slope varied along the veins. Thus he wrote:

225 Cf. A III,8 N. 152, p. 396. 226 “vieler spectatorum augen zugleich … auff einen stern zu dirigiren” (A III,8 N. 146, p. 389). 227 Cf. A III,8 N. 4, pp. 13–17, specifically p. 14; Leibniz: Nordström, pp. 211–213. 228 “Sr Polhammer hà fatto diverse altre belle machine ed inventioni in prò delle nostre mine. M’imagino che quella che V. S. Ill. hà visto in rame possa anche servir ne’ pozzi obliqui, conforme mi son lasciato informare” (A III,8 N. 53, pp. 158–161, specifically p. 159; Leibniz: Nordström, pp. 214–216).

1699–1701

801

Accordingly Mr Polhammar could very well succeed in his design. The pits in the greater part of our mines are not only slanting, but they often even change the slant or the inclination, since one has followed the vein in the course of sinking or excavating of the shaft, whereas in some other regions one has excavated the pits straight ahead without bothering about the [course of the] vein.229 On June 18, 1699, Papin reported about the steam pump constructed by Thomas Savery, and about the patent granted to him by the English parliament for the invention. Alas, the pump failed to live up to the expectations raised by the inventor, Leibniz was told. However, the correspondent was not in a position to provide him with a design description. Papin’s account was as follows: Dr [Frederick] Slare informed me recently from England that, in the presence of a committee of parliament, a machine for lifting water by the power of fire has been put to the test but that the matter had been far removed from having the success which the entrepreneur had hoped for. But I was not informed at all about the manner of construction of the machine.230 Savery’s tract The miners friend: Or, an engine to raise water by fire appeared in 1702,231 and two years later, in 1704, he was  – no doubt with Leibniz’s knowledge – invited to provide a description of his steam pump, and to demonstrate his invention at the court in Hanover. However, the visit to Hanover never did materialize, and Savery’s letter of October 7, 1704,232 marks the end of Leibniz’s indirect correspondence with him. As regards Papin, he for his 229 “Ainsi M. Polhammer pourra bien reussir dans son dessein. Les puits dans la plus part de nos mines ne sont pas seulement obliques, mais même ils changent souvent d’obliquité et d’inclination, parce qu’on a suivi la veine en les abbaissant ou creusant; au lieu qu’en quelques autres endroits, on a creusé les puits tout droit sans se soucier de la veine” (A III,8 N. 71, pp. 216–218, specifically p. 217; Leibniz: Nordström, pp. 217f.). 230 “Mr le Dr Slare m’a mandé depuis peu d’Angleterre que, en presence d’un Committé du Parlement, on a eprouvé une machine pour lever l’eau par la force du feu, mais que la chose a été bien eloignée d’avoir le success que l’entrepreneur en avoit fait esperer: mais on ne me mande point de quelle maniere la machine êtoit construitte” (A III,8 N. 52, p. 157). 231 Cf. T. Savery, The miner’s friend: Or, an engine to raise water by fire, described. And of the manner of fixing it in mines, with an account of the several other uses it is applicable unto ; and an answer to the objections made against it, London, 1702. 232 Gottfried Wilhelm Leibniz Bibliothek (Gottfried Wilhelm Leibniz Library), Hanover, Manuscipt shelfmark: LBr. 801, Bl. 1–2.

802

Chapter 6

part sent (in 1707) a monograph to the Royal Society in which he described a design of an engine, which he had developed on high-pressure principles, and in the following year, he returned to London to seek support for his invention. Whereas Leibniz had admired it and suggested refinements, Newton rejected it, and Savery criticized it most severely, and he even accused Papin of stealing his ideas.233 Leibniz – as he informed Papin on March 10, 1700 – was acquainted with a new process for transporting earth, and that was used by the renowned French military engineer Sébastien Le Prestre de Vauban, between 1699 and 1703, on the construction site of the fortification works at Neuf-Brisach (Neu-Breisack). Here new machines, which were driven using manpower and horsepower, were in operation. In Leibniz’s view the discovery was not at all remarkable (“pas fort considerable”), but nevertheless he sent Papin a sketch or drawing as a sign of respect for the landgrave. Here Leibniz also referred to a news report in the Gazette d’Amsterdam of February 25, 1700, with the following information: “From The Hague on the 23rd of February … one demonstrated yesterday a newly-developed machine for easily moving a large quantity of sand from one location to another”.234 And so, Leibniz wrote the following, in the letter of March 10, to Papin: Alas, I would have initially sent you the machine of Neuf-Brisach if I had known you were in the country. It appears to me not to be very remarkable, and I would have liked to express my officious respect to the Landgrave with something better. But the great princes are like heaven above which is content with our good intentions. I learned nothing of the one in Holland except for that reported in the gazette.235 Papin’s own discoveries were also discussed in correspondence with Leibniz. Thus, in the PS to his letter of September 21, 1699, he reported how in a coal mine he had successfully employed his centrifugal pump, or the so-called 233 Cf. their remarks accompanying a translation from the French of Papin’s monograph, and the transcripts of his proposals in: A. Smith, 1998, and also A. Smith, 1995 (Introduction, note 112). 234 “De la Haye le 23 Février. … On fit hier l’épreuve d’une machine de nouvelle invention, pour jetter facilement une grande quantité de sable d’une place à l’autre” (A III,8 N. 133, p. 358). 235 “Je vous aurois envoyé d’abord la Machine de Brisac, que voicy, si j’avois sçû que vous estes dans le pays. Elle ne me paroist pas fort considerable, et je voudrois marquer mon zele à S. A. S. par quelque chose de meilleur; mais les grands princes sont comme le Ciel qui se contente de nostre bonne volonté. Je n’ay rien appris de celle de Hollande que ce que la gazette en a dit” (A III,8 N. 137, p. 367).

1699–1701

803

“Hesse pump”, together with a long air conduction pipe made from wood and serving as a mine aeration, or ventilation, system. And so he wrote here: I have however recently been very active at a coal mine where one had not been able to work because of the impurity of the air. But I pumped in fresh air using the Hesse pump for which I adapted a large wooden pipe which extends to the bottom of the mine. And that succeeds just as well as for the lamps, which had previously been extinguished before one had reached halfway and which now burn perfectly right to the bottom, without the man who operates the pump having to exert himself more than a little. I am presently working for another mine which is even deeper.236 In his reply of October 30, Leibniz referred to the connection between breathing difficulties and the extinguishing of lamp flames in the pits, both of which he attributed to inadequate air circulation. Here he wrote: One observes in the mines that the difficulty of breathing and of the burning of the lamps is the same and that it comes principally from the circumstance that the air does not change at all and does not have its path pretty free. Accordingly, I have no doubt that your pump was most useful. Just as well as that other enterprise of which you speak.237 Already in the year 1692, the Hesse pump had been employed for the air exchange in Papin’s submergible vehicle, which was tested on the river Fulda.238 Now, at the end of the decade, it was also to be the key element of a machine for seawater desalination with which fuel use might be economized. Papin reported to Leibniz, on December 3, 1699, about the first successful experiments with the device, writing as follows: 236 “J’ay pourtant êté depuis peu fort occupé pour une mine de charbon où on ne pouvoit travailler à cause de l’impureté de l’air: mais J’ŷ ay poussé de l’air frais par le moien du soufflet de Hesse auquel J’ajuste un gros tuyau de bois qui va jusques au fonds de la mine: et cela reussit si bien que les lampes, qui s’êteignoient avant qu’on fust à mi chemin, brûlent parfaitement bien jusques au fonds: sans que l’homme qui fait jouer le soufflet se fatigue que fort peu: Je travaille à present pour une autre mine encor plus profonde” (A III,8 N. 77, p. 232). 237 “On observe aux mines que la difficulté de respirer et de faire bruler les lampes est la meme et qu’elle vient principalement de ce que l’air ne change point et n’a point son Cours assez libre. Ainsi je ne doute point que vostre soufflet n’ait esté fort utile. Aussi bien que cette autre entreprise dont vous parlés” (A III,8 N. 81, p. 244). 238 Cf. A III,5, pp. LXVf. and Chapter 3 of the present publication.

804

Chapter 6

Our machine to evaporate salt water at a low cost succeeds very well, and in a wooden vessel which contains 30 buckets of water besides the pipes through which the fire passes, we have found that 39 pounds of wood would suffice to put 30 buckets of water on the boil, whereas to boil 4 buckets of water in an ordinary cauldron 22 pounds of wood are required, although we would have taken the greatest precautions that were available to us to burn the wood most advantageously in order to effectively heat the water. We are working at present to gain experience in a wooden vessel 7 or 8 times larger than the first. And regarding the Hesse pump, he added: And the Hesse pump works wonders for this, for it is the flame just like the other bodies in relation to which the force depends on the speed as well as on the quantity of the material, [and that] in such a way that the same quantity of fire produces more or less effect according to whether our pump gives it more or less speed. For the machine I am making at present the pump has its opening of 16 square root inches.239 7

Engineering: Manufactories

On June 24, 1699, Block described a smelting process of Francesco Maria Levanto, who was one of a number of foreign smelters, and chemists, who attempted to improve copper smelting at the Falun mine in Sweden. Leibniz had already enquired, asking correspondents on a number of occasions, about this process as, for example, on January 16, 1694, in a letter to Gustav Daniel Schmidt,240 and on July 23, 1697, in letters to Lorenz Hertel,241 and to 239 “Nôtre machine pour evaporer l’eau salée à peu de frais, reussit fort bien: et dans un vaisseau de bois, qui contient 30 seaux d’eau outre les tuyaux par où passe le feu, nous avons trouvé que 30 livres de bois suffisoient pour mettre les 30 seaux d’eau en train de bouillir; au lieu que pour faire bouillir 4 seaux d’eau dans un chauderon ordinaire il a fallu 22 livres de bois: quoyque nous eussions pris nos precautions le mieux qu’il nous êtoit possible pour faire brûler le bois le plus advantageusement pour bien êchauffer l’eau. Nous travaillons à present pour faire l’experience dans un vaisseau de bois 7 ou 8 fois plus grand que le premier … et le soufflet de Hesse fait merveilles pour cela; car il est de la flame comme des autres corps dont la force depend de la vitesse aussi bien que de la quantité de la matiere: de sorte que la même quantité de feu fait plus ou moins d’effect selon que nôtre soufflet luy donne plus ou moins de vitesse. Pour la machine que Je fais à present le soufflet a son ouverture quarrée de 16 pouces de racine” (A III,8 N. 88, pp. 257f.). 240 Cf. A I,10 N. 123, p. 212. 241 Cf. A I,14 N. 16, pp. 27f.

1699–1701

805

Johann Gabriel Sparwenfeld.242 At the heart of the process was a reverberatory furnace – viz. one that isolates the material being processed from contact with the fuel, but not from contact with combustion gases – for roasting or calcination, that could be fueled with twigs or branches. The roasted blende, or the ore produced by calcination, was then to be melted in an air furnace, but it was, alas, ruined by the air flow from the pump. Block’s detailed description, in his letter of June 24, was enhanced by the following sketch of the furnace, to which he directed Leibniz’s attention.243

Figure 16 Drawing of Francesco Maria Levanto’s reverberation furnace Source: Magnus Gabriel Block to Leibniz, June 24, 1699 (A III,8, p. 160)

As the desired success failed to materialize, Levanto had to leave without recompense. Block’s account of this was as follows: Using the means with which Mr Levanto was unable to keep his promise to save firewood and to economize the aforementioned roasting in the oven of his invention and melting in the air furnace, it was necessary for him to depart without recompense, whereas if he had succeeded he would have received 100 000 Scudi.244 242 Cf. A I,14 N. 208, p. 341. 243 “la fornace di riverbero la cui figura qui inclusa si vede” (A III,8 N. 53, p. 160). 244 “Di maniera che il Sr Levante non potendo mantener la parola di sparagnar le legna e di contentarsi solo del sopradetto rösten in dem offen seiner invention und gießen im windoffen fù necessitato à partirsi senza ricompensa, però se gli fusse riuscito havrà avuto 100 000 Scudi” (p. 161).

806

Chapter 6

This fate Levanto shared with Johann Kunckel von Löwenstern, who subsequently unsuccessfully tried out a very similar process before – according to Block’s report  – having to depart “with dishonor und in disgust”.245 Leibniz proposed operating the roasting furnace and the air furnace in a different way. One ought, he wrote to Block on September 8, 1699, to leave the material longer in the roasting oven in order that it becomes thicker, and to power up the air furnace slowly in dependence on the consistency of the material. Thus, he wrote to his Swedish correspondent on that occasion: I thank you very much for the descriptions of the trials and designs of Francesco Levanto. That what you say is the most reasonable [or rational] matter in the world. I believe that the air furnace would have needed a particular location for its design, such that at the outset the air pump would have operated but a little, and then with advantage once the material had been thickened or concentrated. I believe also that in the roasting oven or calcination furnace, even if after the extraction of the odor of sulfur one would have left the roasted blende without stirring it, it would have regained more consistence through not having been placed in the air produced by the force of the pump.246 Reverberatory furnaces were also employed in the eighteenth century for tempering and annealing bar or rod iron, as well as for china or porcelain ovens and for glass ovens in manufactories, and presumably also in Tschirnhaus’ new glass-making plant about which he informed Leibniz in letters, written on May 18 and October 16, 1700, respectively.247 He had even set up a grindery, or grinding shop, for precious stones and jewels. In the first of these communications he wrote: I have already set up two beautiful laboratories from which remarkable things may come. The first is concerned with the polishing of transparent 245 “Kunckel volea introdurre un modo poco differente di quello mà non riuscendogli partì anch’esso con disonore e disgusto” (p. 161). 246 “Je vous remercie fort de la description des épreuves et desseins de Francesco Levante. Ce que vous en dites est la chose la plus raisonnable du monde. Je crois que le Fourneau à vent auroit eu besoin d’une adresse particuliere pour son dessein; en sorte qu’au commencement le souflet n’auroit agi que peu, et puis d’avantage, quand la matiere se seroit epaissié. Je crois aussi que dans le Röstofen ou fourneau de calcination même, si apres l’odeur du soufre ostée on y avoit laissé la paste sans la plus remuer, elle auroit repris plus de consistence, pour n’estre pas envoyée dans l’air par la force du souflet” (A III,8 N. 71, pp. 216f.). 247 Cf. A III,8 N. 166, p. 434, and N. 189, pp. 489f., respectively.

1699–1701

807

jasper, the other is a glassworks; now I am indeed familiar with what they make in Venice, now also in Berlin, [and] particularly in France from where the most beautiful samples are a wonderful spectacle; but all that is just child play [compared to] what we have in mind and of which samples have already been made. Time will verify the truth of my words. I have had in this winter a perspective glass [or burning glass] ground with a diameter of 5/4 of an ell, which can be used within a radius of 36 feet.248 The second communication then provided the following details about his new glass foundry, or glass-making plant, and his plans for the production of convex lenses for telescopes and burning glasses: I will have something executed in Dresden, because in my laboratories there is much to do, particularly with the newly-established glassworks there, which has the approval of the most informed who had not seen the likes of it, with which [and] with so little firewood such beautiful glass can be fabricated, even from a particular person who was director of the Berlin glassworks [and] who wanted to buy glass there for 24 Taler. Yet this scarcely flatters me; the greatest [reward] is that I henceforth have a constant fire at no cost, and can try out many things there, and [that I] have already come to understand many special matters, and that I will be able to have wonderful glass in order to bring optics to such perfection, the idea for which I have. I have already made last winter a perspective [or burning] glass of 5 quarters of an ell, with which at a distance of 3 German miles from Dresden one can see everything clearly all the way to [the fortress] Königstein, and with which at a distance of 36 feet a strong fire in wood can be produced.249 248 “habe zwey Schöne laboratoria alda auffgerichtet, auß welchen sonderbahre sachen kommen möchten. Daß eine ist in polirung des durchsichtigen Jaspis occupat, das ander [eine] glaßhütte, nun weiß Ich gar wohl waß man in Venedig fabriciret, auch nuhmero in Berlin, besonders in Franckreich, wovon die Schönsten proben selbst mit augen gesehen, aber gewieß es ist alles Kinderwerck was wir vorhaben, und wovon bereit von allen proben gemacht sein. Die zeit wird meine worte verificiren. Ich habe diesen winter ein perspectiv glaß schleifen laßen So in Diametro 5/4 der Ellen, welches auß einen radio von 36 fuß … gebraucht kann werden” (N. 166, p. 434). 249 “Ich werde etwas in Dreß[d]en permoriren, weilen in Meinen laboratoriis alda viel zu thun; besonders Bey der Newen alda auffgerichteten glaßhütte; welche von den verständichsten die Approbation hatt, daß Sie dergleichen nicht gesehen, da man mitt so wenigen holtzfewer ein so Schönes glaß fabriciret, auch Selbst von einen, der Director der Berlinischen glaßhütten geweßen, welcher Vor 24 thl. glaß alda kauffen wolte. Doch

808

Chapter 6

While Tschirnhaus lauded his lenses in particular in his letters to Leibniz, the latter obtained technical details about Tschirnhaus’ laboratories from Wagner. While on an exploratory science and engineering tour through Saxony – having been spurred on to undertake it by Leibniz – Wagner visited Tschirnhaus in Dresden. His host showed him the glassworks, or glass kiln, regarding which Wagner sent a drawing and a detailed description to Leibniz. As regards the ingredients used to manufacture glass, Wagner learned little or nothing, other than that arsenic and borax were not used, since they would give glass a dark color. The visit to Tschirnhaus’ laboratory for precious stones proved to be even more secretive. The king of Saxony – viz. elector Friedrich August I, and king August II of Poland  – had forbidden visits by strangers, as well as the issue of materials from there. In spite of this, Wagner was able to take a quick look inside and to take a sample away with him. However, he had to abandon any hope of visiting Tschirnhaus’ private laboratory on his estate in Kieslingswalde, since his host had become quite secretive in this regard. Wagner, in letters on June 26 and July 21, 1700, revealed to Leibniz the tricks with which he tried to elicit as much information as possible from his conversation partners.250 He also visited the architect Johann Heinrich Gengenbach, during which visit he was able make numerous drawings of a fortification model and of other discoveries and curiosities as, for example, of a pull-out or fold-out table, of an Italian andiron, as well as of carriages and lanterns, as he reported to Leibniz on August 1.251 On the occasion of the failed trials of Levanto, Leibniz – in a letter to Block on September 8, 1699 – pointed to the general difficulties in the realization, and implementation, of such engineering innovations. Large-scale trials often proved expensive. But these were necessary not only for testing discoveries, but also in order to establish trust in them, and to counter the widespread skepticism towards innovations, or in his words to Block on that occasion: But it is difficult to make progress at all in these matters without an exact experiment and large-scale experiments cost a great deal. And furthermore, it is difficult to get people to change their customary methods, also fichtet Mich dieses wenig an; daß vornehmste ist; daß nuhmero ein stettes fewer umbsonst habe, da vieles probiren kan, wie bereit hinter viele besondere sachen kommen, und daß herrliche gläßer werde haben können, umb die Opticam ad talem perfectionem zu bringen, wie in Idea habe. Ich habe bereit vergangenen winter ein perspectiv glaß von 5 viertel der Ellen gemacht, mitt welchen in distanz 3 teutscher meilen von Dreß[d]en auß distincte zu Königs Stein alles erkennen können, und welches in distanz 36 fuß einen starcken brand in holtz causiret” (note 247, N. 189, pp. 489f.). 250 Cf. A III,8 N. 172, pp. 443–446, and N. 176, pp. 451f. 251 Cf. A III,8 N. 177, pp. 456f.

1699–1701

809

they are only able to thrust innovations after a long series of proofs the costs of which an individual [entrepreneur] is not able to meet.252 Following a request by Leibniz, in this letter of September 8,253 Block also passed on, with a letter of November 28, a recipe for making iron malleable (and hard again), that surely did awake memories for Leibniz of the Douceur process of twenty years before. Before communicating the process of Amund (Anund) Tyresson, also called Falkenstjerna or Falkenhjelm, Block told Leibniz that: All of his secret consists of a material which is rather fusible viz. meltable or molten, for which reason it is melted down into plaster cast and the cast taken is not pressed easily. Perhaps one could make cannons from the same iron. For the rest I imagine that this could succeed easily like for someone having the secret of softening steel to be like lead. Just as they do in Naples and in Milan.254 Late in 1699, the head bailiff, or administrator, of the location Aerzen in the Weser Uplands (‘Weserbergland’), namely Jobst Heinrich Voigt, presented a threshing-machine of his design to Leibniz, in the form of a drawing attached to a letter of November 28, sent by another official Cord Plato von Gehlen, and in which it was claimed that the machine could be operated by a single person, do the work of fifteen others, and accordingly reduce costs considerably. Here von Gehlen wrote: I have the honor of sending you a mechanical invention of the senior administrator of Aerzen for threshing grain at low cost. He calls it a threshing-mill, [and] he claims that a single individual who operates this machine could do as much as 15 others and avoid much expense in this way. The senior administrator in question would very much like to learn your opinion about the [machine] above, and as to whether one could 252 “Mais il est difficile de rien avancer de bon sur ces choses sans une exacte experience, et les experiences en grand coustent beaucoup. Et de plus il est difficile de faire changer aux gens leur methodes accoustumées, aussi ne peuvent-ils pas se fier aux nouvelles qu’apres une longe suite d’epreuves dont un particulier ne sçauroit soûtenir les frais” (A III,8 N. 71, p. 217). 253 Cf. p. 218. 254 “tutto il suo secreto consistea nella materia ch’era assai fusile geschmeidig od. flüßig perche egli le fondea in gesso e ne presero facilmente l’impronto. Si fanno qui canoni del medesimo ferro. Del resto m’imagino che ciò riuscirebbe agevolmente a chi avesse il secreto di rammollire l’acciaio come piombo. Come fanno à Napoli ed à Milano” (A III,8 N. 84, pp. 247f.; Leibniz: Nordström, pp. 218–220).

810

Chapter 6

add or remove anything. He has informed me that he can effectively operate the machine and that he feels comfortable with it. I do not know, Sir, if all is well explained in the paper which will give you every elucidation that you desire.255

Figure 17 Drawing of Jobst Heinrich Voigt’s threshing-machine Source: Cord Gabriel Plato von Gehlen to Leibniz, November 28, 1699 (A III,8, p. 251)

Leibniz, in his reply in mid-December 1699, expressed his appreciation of the new machine in the following words: “As regards the machine intended to thresh grain, I believe that the matter is very straightforward and could very easily succeed. The principal is also very well explained in the figure, both the battering mechanism as well as the manner of advancing”.256 However, he did make a proposal for the optimization of the threshing-machine transmission system, namely by replacing a three cogged wheel-lantern pinion element – a 255 “Je me donne l’honneur de vous envoyer une invention mechanique de l’Ober Ambtm[ann] d’Ertzen, pour battre le bled avec peu de frais, il l’appelle drösche mühle, il pretend qu’un seul homme qui gouverne cette machine peut faire autant qu’en feroient 15 autres et menager par là beaucoup de frais; Le dit Oberambtm. seroient bien aise de sçavoir votre sentiment là dessus, et si l’on y peut ajouter ou diminuer quelques chose, il me mande qu’il fait aller effectivement la machine et qu’il s’en trouve bien; je ne sçai, Monsieur, si tout est si bien expliqué au papier qu’il vous donne tout l’éclaircissement que vous souhaitez” (A III,8 N. 85, p. 250, and N. 86, pp. 250f.; cf. the figure on p. 251). 256 “Quant à la Machine destinée à battre le bled je crois que la chose est fort aisée, et peut fort bien reussir. Le principal aussi s’entend fort bien par la figure, tant la batterie, que la maniere d’avancer” (A III,8 N. 90, p. 261; cf. annotation).

1699–1701

811

central cogged wheel in a vertical plane engaging the horizontal staves of a lantern pinion on each side – with a two-wheel pulley system and, accordingly, reducing resistance. In this regard he wrote: I believe that one could facilitate the movement, for the double configuration with the three cogged wheels causes too much resistance. One could avail of two wheels without cogs, with instead a cord or chain which would pass from one to the other. The execution of the machine construction work and the practical operation will also provide additional facilitation, and so forth.257 Leibniz reacted not only by proposing technical improvements but he also expressed his view regarding the widely-held opinion that such machines actually rob the poor of potential earnings. In this context, he recalled the proscription, by the emperor (Leopold I) of the ribbon-loom in the year 1685, following a recommendation of the Imperial Diet at Regensburg in 1681. Leibniz rejected such concerns regarding the loss of employment though mechanization. Even if there were to be such lay-offs at first, there were besides enough other useful occupations for those affected. At most there would be some readjustment difficulties at the beginning. He also pointed out, for example, that in other countries animals were being used for trampling grain in place of human labor. Thus, machines might be employed in the same way, and so he wrote in the same letter: Many tend to complain about machines of this type which economize on human labor claiming that one was stealing the bread from the poor. That was the reason why one proscribed some years ago at Regensburg the ribbon-loom machinery. But, apart from the fact that this prohibition measure had hardly any effect, I find that one can always occupy people with some other useful activity, and if any tribulations do arise, these will only be at the beginning when the people are not accustomed to doing other things. In the orient, and even in the [French region] Provence and in Spain, one makes use of animals who trample the crop in order

257 “Je croy qu’on pourra faciliter le mouvement, car les trois roues engrainées die doppelte ablegung cause trop de resistence, on pourroit se servir de deux roues sans dens, avec une corde ou chaine plustost qui passeroit de l’une sur l’autre. L’execution et la practique donneront encor d’autres facilités etc.” (p. 262).

812

Chapter 6

to release the grain. One could therefore do it just as well using machines without denying to men the work which belongs to them.258 Leibniz returned to Voigt’s threshing machine in a letter to the correspondent from the second half of January 1700, which is extant in the form of an extract (“Extrait de ma response”). Leibniz’s basic opinion on this matter was that one ought not to refuse the assistance of machines, or the art of engineering, on the grounds of the pretext that the poor were being deprived of their livelihoods. There was besides an infinity of alternative occupations for the hands set free by mechanization. Thus, in the concluding paragraph he wrote: I hear people say that by using this machine one is doing a disservice to the poor, but it is of greater value that the poor apply themselves to more useful works and I am of the opinion that one should never refuse any support for the art [of engineering] using this pretext. For there will always be an infinity of things to do which demand more industry and for which there is a need for human hands.259 And besides he recalled a similar threshing-machine being developed at the location Linden (near Hanover) by count Franz Ernst von Platen, and of which he subsequently made a drawing.260 This drawing of Voigt’s threshing machine reveals a human operator turning a camshaft to operate the thresher-cylinders. The carriage to which the threshers were attached was moved or pedaled along the threshing-floor by means of a rack and pinion gear mechanism. To deal with the faineance of workers, Leibniz proposed remuneration of the operatives on 258 “Plusieurs trouvent à redire contre ces sortes de machines qui épargnent le travail des hommes, pretendant qu’on oste le pain aux pauvres. C’est pourquoy on defendit il y a quelques années à Ratisbonne les machines à rubans et à bas, die strumpf und bandmuhlen. Mais outre que cette défense n’a gueres eu d’effect; je trouve qu’on peut tousjours occuper les hommes à quelque autre chose d’utile, et s’il y a quelque inconvenient, ce n’est qu’au commencement, lors que les gens ne sont pas encor accoustumés à faire autre chose. En Orient, et meme en Provence et en Espagne on se sert des animaux qui foulent le bled pour en faire sortir le grain. On pourra donc fort bien le faire aussi par machine, sans derobber aux hommes un travail qui leur appartienne” (pp. 261f.). 259 “J’entends des gens dire qu’on fait du tort aux pauvres par cette machine, mais il vaut mieux que les pauvres s’appliquent à des travaux plus utiles et je suis d’opinion qu’on ne doit jamais refuser sous ce pretexte aucun secours de l’art. Car il y aura tousjours une infinité de choses à faire qui demandent plus d’industrie et pour les quelles on a besoin de main d’homme” (A III,8 N. 119, p. 308). 260 “On m’a dit que M. le Comte de Plate veut faire faire [sic] aussi une telle Machine à Linden, c’est de quoy je m’informeray” (p. 308, annotation).

1699–1701

813

the basis of performance in terms of tours, or machine runs, recorded by a hidden device. In this regard he wrote near the beginning of the “Extrait”: I thought that in order to circumvent the faineance of men employed to turn [the camshaft] one could employ something similar to that which is called a contepas,261 that is to say [a device] which would count the machine runs which they would have completed while being hidden or at a location, which they could not reach. And in this way one would pay them in proportion not to the [working] hours but to the [completed] runs which would require their diligence.262 Leibniz had also contemplated water and wind as alternatives to manpower as a prime mover for the threshing-machine. The former option, he found, would require the availability of a water raceway, and he had commenced his “Extrait” with the words: “If you have a mill race (or millrun) nearby and at your disposal, I do not have the least doubt that you would easily find the means to apply the force [or power of water] to operate the machine designed to thresh the grain”.263 On the other hand, to avail of wind power a windmill and a water reservoir system would be required to ensure operation of the machinery throughout the autumn, and for part of the winter, an idea reminiscent of his pumped-storage scheme in the Harz mining district, as of his contemplated reservoir for water supply to the fountains in the gardens at Herrenhausen. Thus he continued: Also, in the event of lacking a current of water [to turn a water wheel], one could make use of a small windmill, which would raise water at rest into a kind of small reservoir in such a way that at a time like in the autumn, and for a good part of the winter, one would have enough force [or power] to thresh all the grain which one might have.264 261 Underlining in manuscript by Leibniz. 262 “j’ay pensé que pour obvier à la faineantise des hommes employés à tourner on pourroit appliquer quelque chose de semblable à ce qu’on appelle un contepas, c’est à dire qui compteroit les tours qu’ils auroient fait estant caché ou dans un endroit, où ils ne pourroient arriver. Et par ce moyen on les payeroit à proportion, non pas des heures, mais des tours ce qui les obligeroit à estre diligens” (p. 308). 263 “Si vous avés le Canal du moulin assez proche et à vostre disposition, je ne doute point que vous ne trouviés aisement moyen d’en appliquer la force à tourner la Machine destinee à battre le bled” (p. 308). 264 “Faute d’aussi d’eau courante, on pourroit se servir d’un petit moulin à vent, qui eleveroit de l’eau dormante dans une maniere de petit reservoir de sorte que dans un temps qu’est

814 8

Chapter 6

Projects: Calculating Machines

On February 25, 1700, the death took place of Hans Adam Scherp, who had worked on Leibniz’s so-called ‘younger calculating machine’. The clockmaker Johann Levin Warnecke from Helmstedt became his successor having been recommended by Wagner, who himself assumed the role of a supervisor of the ongoing work on the machine. This course of events proved to be a stroke of good fortune, not least for posterity. Thus, on the basis of his reports concerning progress and problems in the construction of the machine, its coming into being can be retraced step-by-step. Already in the month following Scherp’s death, both the ‘younger’ machine (then under-construction) and the completed ‘older’ machine, which served as a model, were transferred to Helmstedt together with a letter of March 15 addressed to Wagner.265 The latter succeeded in striking a balance between the respective interests of Leibniz and Warnecke, and he made delays that inevitably arose plausible to the impatient Leibniz. Thus, in order to reduce expenditure, Leibniz at first wanted to have to pay only for the overhaul and reworking of individual parts, as he indicated in a letter of March 18.266 Wagner, replying on March 23, guaranteed Leibniz a daily control of the work in progress, to prevent waste and deceit, but he did point out that the unobstructed interaction of the parts of the machine in itself demanded trials lasting days at times, and that the remuneration would have to be orientated towards the effort involved rather than just the final product.267 The circumstance that progress was slow, Wagner attributed – in letters to Leibniz of early February, 1701 – to other work commitments of Warnecke, to his diligence and painstakingness, to the difficulty of working long hours by candle light in winter, and above all, to the desolate state in which he claimed Scherp had left the new machine.268 Thus progress and setbacks went hand in hand. At the beginning of February 1701 Wagner could report the completion of the drawing spindle for moving and positioning the carriage. This letter began: Last Saturday evening the screw on the machine was completed in my presence so that now [it can] continue [to turn] from below to above on the lower part of the machine below the upper [part], and soon after celuy de l’automne, et d’une bonne partie de l’hyver on auroit assez de force pour battre tout le bled qu’on peut avoir” (p. 308). 265 Cf. A III,8 N. 138, pp. 369f. 266 Cf. A III,8 N. 141, pp. 379f. 267 Cf. A III,8 N. 143, pp. 382f. 268 Cf. A III,8 N. 204, p. 524, and N. 206, pp. 528–530.

1699–1701

815

this can soon be brought down [from above to below] by the contrary rotation.269 However, Wagner and Warnecke had ascertained here that holes could not be drilled uniformly, and had to be provisionally repaired, and also that rods could not be mounted at right angles with the result that, at that juncture, the machine could only be operated by applying force. Warnecke’s predecessor Scherp had used neither compass nor protractor. Thus Wagner added: I have no other wish than that Your Excellency should once be present and see that this, [namely the fact] that the previous clockmaker made use of neither compass nor protractor here (for the visual inspection in daylight reveals this consistently on the constituent parts), is now causing so many obstacles and impediments here, there and everywhere. The large and long screw was, as sure as I am alive, all around the top about a ‘knife back’270 stronger than below.271 The rotary disk was completed but, in putting the parts together, fresh imprecisions, construction defects, as well as evidence of tinkering and botching became apparent, matters which found expression in Wagner’s letters to Leibniz in February and March, 1701.272 On April 7 then, the correspondent expressed his frustration regarding Warnecke’s deceased predecessor Adam Scherp. The latter had, Wagner asserted, been like a child. He had exploited Leibniz and only wanted to secure his income in order to indulge his passion for liquor, Leibniz learned from this communication. Here the correspondent wrote: Next to this clockmaker [Warnecke], the deceased Adam [Scherp] was an outright child … I conclude through all of this that Adam did not intend 269 “Verwichenen Sonnabend Abends ist nun in meinem beyseyn die Schraube an der machine fertig worden, so daß nun von unten biß oben an der untere Theil der machine unter dem obern fortgeführet werden, und bald herauf bald nieder durch contra drehen gebracht werden kan” (N. 206, p. 528). 270 That is, by the thickness of a knife blade viewed from the back. 271 “Ich wolte nichts mehreres wüntschen, als daß Ihr. Excell. solten einmahl gegenwärtig seyn, und sehen, was dieses, daß er der vorige Uhrmacher weder zirckel noch Winkelmaaß darzu gebraucht (denn der Augenschein ist am Tage und an denen Stücken durchgängig zu sehen) nun vor so viele hindernüß und Aufhaltungen bald hier bald da verursacht. Die große und lange Schraube ist so wahr ich lebe oben rings herüm üm meßer rücken stärcker als unten gewesen” (note 268 above, N. 206, p. 529). 272 Cf. A III,8 N. 211 (pp. 548f.), N. 216 (pp. 562f.) and N. 220 (p. 570).

816

Chapter 6

anything greater than that this machine should forever provide monetary tribute and coins for him and so deceive your Excellence, and by his ingenuity he would have been able both to indulge his passion for liquor and to appear in a hallowed light.273 Leibniz surely felt piqued when he wrote his reply four days later, on April 11, in which he also recalled, in contrast to Scherp, his worthy predecessor, namely the clockmaker Georg Heinrich Kölbing. His words here were: “There is nothing in all that you presented to me which I recognized better than what a great [difference] there was between Adam and his predecessor”.274 Pragmatically, however, he had come to terms with the shortage of such qualified tradesmen or craftsmen. Wagner in contrast, in his letter of August 12, considered Scherp’s work to have been useless. Warnecke, he claimed, could have constructed a new machine in the time he spent doing repair work on the older model. Thus, having given precise details of three specific corrections that had been carried out on the machine, he added that: “From the three diverging corrected points it is to be hoped that the state of the new machine will be much more perfect. They correspond to the prevailing standards and all were made exactly according to norms and rules”.275 In all of this, however, both Leibniz and Wagner were in agreement about the quality of the older machine, and about the fact that the structure of the new machine was superior to that of the older one. On April 26, 1701, Wagner reported the completion of the upper part of the new machine with the words: “The upper part of the calculating machine, which is made up of so many small wheels and cylinders, will already be celebrating its perfection in the near future”.276 Then, from July, Warnecke devoted himself to the improvement of the older machine. On this Wagner also carried out the first calculation examples, which he duly reported to Leibniz on July 29.277 Instead of multiplying a four digit number (4286) by 4, as intended, Wagner – after the operating rules 273 “Erga quem opificem demortuus Adamus certe totus puer fuit … Quare ex omnibus hic colligo Adamum nihil magis intendisse, quam ut haec machina ipsi perenne solveret tributum, nummisque emungeret Per-Ill. Exc. Vestram, quo genio suo indulgere gulamque Bachi proventu inungere potuisset” (A III,8 N. 234, pp. 604f.). 274 “Non est quod mihi exaggeres quae bene novi, quantum inter Adamum et ejus praedecessorem interfuerit” (A III,8 N. 239, p. 611). 275 “Ex tribus hisce punctis correctis multo perfectior novae machinae status sperandus erit, modo reliqua responderent, et exacte ad normam et regulam omnia facta essent” (A III,8 N. 289, p. 745). 276 “Machinae arithmeticae superior pars, quae ex tot rotulis cylindrisque composita est mox jam perfectione sua gaudebit” (A III,8 N. 254, p. 662). 277 Cf. A III,8 N. 285, pp. 735–737.

1699–1701

817

had slipped his mind – actually carried out the addition of this four digit number and a two digit number (16). The result he obtained contained an error in the third place (namely 4202 instead of 4302), which revealed that the decimal carrying operation was incomplete. However, a further addition (of 16) led to the correct final result (4318). In his non-extant reply, Leibniz surely pointed to the role of the series of pentagonal disks incorporated in the carrying mechanism, which served for the manual through-connection of all those positions that were, although activated, not brought to completion. Although Wagner heeded these disks in his following calculations, as reported on August 5,278 these multiplication examples were also flawed. Wagner and Warnecke then developed a correction procedure, which combined the requisite corrective horizontal positioning of the pentagonal disks with a renewed manual rotation of the crank that operated the value transfer mechanism between the setting mechanism (or input) and the result mechanism (or output) of the machine. They were also able to eliminate some further errors by making precision-engineering alterations, whereas other errors Wagner considered to have already been eliminated in the new machine, as he reported to Leibniz on August 12.279 Then, for a short time late in the year 1701, everything was once again in the balance when Warnecke became gravely ill. To Wagner, who observed night watches at the bedside of the patient, the further development of the calculating machine appeared for a time to be cataclysmal, with the impending death of the clockmaker coming after that of his predecessor in the previous year. However, in his final letter of the year 1701, on December 16, Wagner was able to announce to Leibniz the resumption of work on the calculating machine, recounting the episode as follows: In fact the illness of the craftsman has delayed until now by an excessive amount the continuing perfection of the calculating machine, for indeed a creeping pleurisy threw him for an extended period into an extreme danger of life. With difficulty, by means of strong medicine, with the grace of God and with my support, he was snatched from the jaws of death … Let God be my witness, also for the cause of our machine, for I have spent several sleepless nights as a vigilant warden, lest once again we should have to seek a new craftsman … But God has averted such most serious hindrances; otherwise, it appears to me that it would have been an ordeal

278 Cf. A III,8 N. 287, pp. 739–741. 279 Cf. A III,8 N. 289, pp. 744f.

818

Chapter 6

for the machine in the wake of the ill-fated life of the craftsman, had he met his last day dying the same kind of death as his predecessor.280 Work on the perfection of the calculating machines continued for the rest of Leibniz’s life, and beyond.281 9

Projects: the Berlin Society of Sciences and the Organization of Science

In connection with the establishment of the Berlin Society of Sciences, membership was offered – not least through Leibniz’s influence – to mathematicians, scientists and physicians, like Johann Bernoulli, Friedrich Hoffmann, Philippe Naudé, Pierre Dangicourt, and Georg Wolfgang Wedel. In taking this step, Leibniz was guided as well by his own interests, like, for example, in the construction of an astronomical observatory. While he hoped for support from Hoffmann in the realization of his long-entertained project for gathering medical and meteorological ephemerides, he tried to influence Naudé and Dangicourt to do research on dyadic or binary mathematics. Leibniz would have liked to be able to entice Bernoulli into his proximity – possibly by providing him with a mathematical professorship at Frankfurt an der Oder – but the Berlin Society did not have at that point the requisite emolumental resources, as he remarked in his letter of June 24, 1701, to Bernoulli.282 The foundation of the Society did indeed meet with goodwill, but the dilatory start of the undertaking also led to some skepticism. At first, Bernoulli hoped that the new society would develop, in comparison with its foreign counterparts, like a cypress among its fellow botanical species viburnum (or arrowwood), a sentiment which he expressed to Leibniz on October 16, 1700, in the following words: “I hope in particular that this recently established society will rise among its Italian, French, English, etc. neighbors like a cypress among 280 “Machinae vero Arithmeticae ulteriorem perfectionem nimium quantum morbus artificis usque huc remoratus est, quippe qui pleuritide correptus in extremo vitae periculo diu graviter jacuit, vix per validissima medicamina et div. gratia adjuvante a me ex mortis faucibus eripiendus … Deum testor, quod etiam machinae nostrae causa noctes aliquot penes eundem vigiles atque insomnes duxerim, ne novum denuo quaerendum haberemus artificem … Sed haec impedimenta gravissima avertat Deus, alias actum erit de vita ejus Fatale mihi videtur hoc machinae, cum alter artifex eodem mortis genere diem obierit supremum” (A III,8 N. 317, pp. 807f.). 281 Cf. F.-S. Morar, 2015 (Introduction, note 135). 282 “Optaremus Te nobis viciniorem, sed nulla nobis hactenus occurrit ratio ea emolumenta quae habes” (A III,8 N. 271, p. 707).

1699–1701

819

the viburna”.283 However, having first rejoiced, nine months later, namely on July 9, 1701, Bernoulli had the impression – after he had neither seen nor heard anything of the Society – that it had become moribund again in a relatively short period of time.284 Hoffmann, for his part, reported on August 30, 1701, that many were beginning to seriously have doubts about the prospects for success of the Society, writing as follows: “For many, something I am not able to hide, have indeed begun either to despair about or, not insignificantly, to doubt the progress of the whole matter”.285 In this correspondent’s view, expressed in a letter of October 4, only Leibniz’s influence, and involvement, could guarantee the success of the undertaking, or in his words on that occasion: “I am not able to conceal [the fact] that without the support of your advice, your authority and your assistance in overcoming the difficulty, there would hardly be hope of a happy successful outcome”.286 Then, in a letter of November 8, Hoffmann articulated an additional fear, namely that too many members had been accepted, and that this was to the detriment of the reputation of the Society abroad, or in his words of caution: It should not however be that the number of members familiar to our court be extended all that much, but that this honor be reserved only for the dignified and famous; for otherwise the dignity of this society abroad will soon be breathing its last breath.287 Writing to Tschirnhaus, on April 17, 1701, Leibniz referred in the following words to the fact that the financing of the project was a major problem: “Now, although the purpose has been understood, in the realization there can not be a rapid

283 “quando praesertim recens haec fundata Societas, inter vicinas ut spero Italicam, Gallicam, Anglicam etc. sese extollet quantum Cupressus inter Viburna” (A III,8 N. 188, p. 483). 284 “quam florere incipere gaudeo, credebam enim, quod nihil de ea vel viderem vel audirem, jam ante instantem calamitatem temporis iterum esse extinctam” (A III,8 N. 275, pp. 715f.). 285 “Plures enim, quod dissimulare non possum, totius rei progressum, aut plane desperare aut non leviter de eo dubitare coeperunt” (A III,8 N. 292, p. 751). 286 “Non dissimulo, nisi Tuo consilio, Tua autoritate et auxilio difficultati progressus succurratur, vix de felici successu esse sperandum” (A III,8 N. 298, p. 765). 287 “ne scilicet numerus membrorum, quod nempe Aulae nostrae familiare est, nimis extendatur, sed pro dignis saltem et celebribus hic honor reservetur, alias apud exteros dignitas hujus Collegii mox exspirabit” (A III,8 N. 308, pp. 787f.).

820

Chapter 6

start due to considerable known obstacles and other pending expenses”.288 It is therefore understandable, that Leibniz did not respond to Bernoulli’s repeatedly expressed desire for financial support for his experiments.289 For Bernoulli – whose articles were on occasions rejected by Otto Mencke, the editor of the Acta Eruditorum, because of the provocations they contained  – a particular interest was the prospect of having access to a journal of his own, a matter that was alluded to by Leibniz in letters of September 6, 1700, and September 13, 1701, respectively.290 The first volume of the envisaged journal, namely the Miscellanea Berolinensia, appeared however only in the year 1710. Also unresolved at the end of the year 1701 was the financing of Hoffmann’s lectures in experimental physics in Halle which, while not directly connected with the Berlin Society, was rooted in the broader context of the promotion of science by the court at Berlin. Leibniz backed this endeavor in the wake of his meeting with Hoffmann in Halle in September 1700, since he was convinced of the great benefit to be gained from experimental science. In his letter of November 1, 1701, Leibniz informed the correspondent that the authorities – namely the Berlin court and the provincial estates – had finally agreed to provide about a hundred Taler per year for the lectures at his academy in Halle.291 In this context, Leibniz expressed the sentiment that a single lesson (or lecture hour) of a “collegium experimentale” – concerned with physical-mathematical inventions and experiments – had a greater value for him than a hundred corresponding lessons in metaphysics, logic, or ethics.292 However, Hoffmann’s problem was not just of a financial nature, as he informed Leibniz on November 8, 1701. His advocacy of an empirical science – on the foundation of a mechanical world view inspired by Descartes – was being thwarted at the University of Halle by Christian Thomasius, who was offering his own experimental lectures in order to promote his spiritualistic approach.293 Leibniz attempted to communicate enthusiasm for science to the Prussian king Friedrich I – who was also elector Friedrich III of Brandenburg-Prussia – by means of spectacular experiments. Thus, writing on February 16, 1701, 288 “Nun ist der zweck zwar wohl begriffen, aber mit der vollstreckung kan es wegen großer bekandter hinderniße, und ander angelegener ausgaben, nicht so geschwind von statten gehen” (A III,8 N. 243, p. 631). 289 Cf. for example, A III,8 N. 188, p. 483, and N. 300, p. 772. 290 Cf. A III,8 N. 186, p. 478, and N. 295, p. 758. 291 “Circa annum centum thalerorum ajunt Regem adhuc in controversia esse cum vestris statibus provincialibus, Academiae vestrae causa” (A III,8 N. 306, p. 785). 292 “Nam collegii experimentalis unam Lectionem centum metaphysicis, Logicis, Ethicis, quales vulgo audiuntur, facile praetulerim” (p. 785). 293 Cf. A III,8 N. 308, p. 788.

1699–1701

821

he requested that Hoffmann, for his part, confide to him a recipe for a fiery spirit,294 by which two oils catch fire on being mixed together, for presentation to the king (and elector). The spectacle he thought would benefit both the Society and the correspondent himself.295 The circumstance that Johann Bernoulli applied, on October 16, 1700, for membership in the Berlin Society, by presenting mercury vessels of a kind that could be made to glow following shaking, also proved to be highly welcome.296 Leibniz suggested to Hoffmann (on March 19, 1701) and to Wagner (in a letter to Johann Andreas Schmidt on February 12,1701) that they produce, with the aid of Bernoulli’s process, curiosa such as luminescent insignia, scepters and crowns, as well as a luminous showcase, or “museolum”, which he might present to the king in the name of the Society.297 The attempts to replicate Bernoulli’s experiments had a prominent place in Leibniz’s correspondence with Wagner in February and March 1701. In the vessels a vacuum had to be created, and Wagner had first to construct the requisite instruments. In his letter of March 29, he revealed to Leibniz that he had succeeded in producing a luminescence which, however, was not comparable with that of Bernoulli.298 In the event, a luminous vial sent by Bernoulli was presented by Leibniz himself at the court, in the wake of which he reported to this correspondent, on December 27, 1701, as follows: Your truly perpetual (as predicted) phosphorus [vial] I have shown myself to the king and queen and it was met with the applause of the court audience. I think I can achieve that the king will express his appreciation of the invention with some reward for him [, namely the inventor].299 The interpretation of Bernoulli’s experiments thereafter played only a backstage role, even though the latter had provided starting points for an explanation.300 In addition to impressing the king, Leibniz hoped – as is clear from his earlier letter to Bernoulli of December 31, 1700 – through a comparison 294 “ut mihi vicissim Tui spiritus ignei confectionem communices” (A III,8 N. 212, pp. 551f.). 295 “Haec inventa puto magni apud Regiam Majestatem ponderis fore, tum in honorem societatis, tum etiam in usum tuum” (p. 552). 296 Cf. A III,8 N. 188, pp. 483–487. 297 Cf. A III,8 N. 225, pp. 577f. and A I,19 N. 198, pp. 396f. 298 Cf. A III,8 N. 229, pp. 585f. 299 “Tuum phosphorum vere (ut auguror) perpetuum Regi et Reginae ipse ostendi habuitque plausum spectantis aulae. Puto me effecturum, ut Rex gratum sibi inventum aliquo honorario testetur” (A III,8 N. 318, p. 809). 300 Cf. A III,8 N. 188, pp. 486f.

822

Chapter 6

of different luminescence phenomena, like mechanoluminescence or luminescence resulting from mechanical action on a solid (such as the sparkle produced when hard sugar is broken or scraped in the dark), to gain an insight into the cause of refulgence, or of luminescence in general. Thus he wrote on that occasion: And we know besides that there is much in Mercury that is not abhorrent to the effects of salt where it is impregnated by the sea. And not unlike light brought forth by a blow to sugar cane. This is to be considered in the first place in relation to whether an understanding of light can help here.301 Notwithstanding all difficulties, the Society’s project of establishing a system of medical ephemerides appeared to have achieved success by the end of the year 1701. Leibniz presented Hoffmann’s “spiritus igneus” to the royal family in the autumn of 1701, following which the king ordered the establishment of the ephemerides program, as Leibniz informed Hoffmann on November 1, 1701, in the following words: The affairs of the Society are progressing not badly, the king himself being sympathetic just like his first ministers. I am already pressing for the purpose of establishing missions in remote regions, so that the youth may, in addition to gaining a knowledge of languages, receive instruction in mathematics and in medical-surgical doctrines. The structure of the observatory will be decided by next spring.302 This success marked the conclusion of a long standing commitment. Shortly after Hoffmann had established contact with him at the end of 1699, Leibniz took up again the project that he had initiated back in 1691.303 On January 19, 1700, he then asked Hoffmann to endeavor to establish a system of annual observations, under the aegis of the Academia Naturae Curiosorum, the

301 “Et scimus alias multa esse in Mercurio non abhorrentia ab effectibus salis quo mare impraegnatur. Nec absimilis lux editur saccari ictu. Illud inprimis considerandum an hinc adjuvari possit cognitio lucis” (A III,8 N. 194, p. 501). 302 “Res societatis non male procedunt, Rex ipse favet, favent etiam Ministri primarii. Jam urgeo negotium missionum in remotas regiones instituendarum, ut habeantur juvenes praeter in linguarum [cognitione] in Mathematicis et Medico[-]chirurgicis doctrin[is instructi.] Structura observatorii proximo vere constituetur” (A III,8 N. 306, p. 785). 303 Cf. A III,5 N. 30, pp. 137–139.

1699–1701

823

Academia Leopoldina, following the example of Bernardino Ramazzini. Thus, he wrote in this letter: Now I had the thought of asking your view as to whether or not you think it possible to achieve that a renowned institution could publish medical ephemerides for a particular year, [be it] by maintaining and continuing the form, or separately structuring, or even joining that of the ephemerides of the Leopoldina Society, almost in the fashion of the specimen which the renowned Bernhardino Ramazzini has given.304 Just like the past and present efforts of the theologians and mathematicians in their support for the calendar reform, physicians could, he thought, serve the public interest by collecting observations regularly at specific times throughout the secular year.305 And to this sentiment he added that: The utility of the plan is not why I comment on it to you, who will best understand me regarding the value there will be in setting up and continuing useful observations. I would wish that your celebrated society would take this concern upon itself, distributing tasks to those for whom it will give the most pleasure and who [for their part] will please [in return] the most; I ask that you recommend this, for the sake of the public good, to those friends, to whom you [previously] commended the Society itself.306 Leibniz had indeed found the right addressee, since Hoffmann himself had for years been recording barometric, thermometric, and hygroscopic data, as well as producing occasional ephemerides. His goal had been to understand the connection between weather and maladies, as well as the mode of operation 304 “Nunc venit in mentem sententiam tuam exquirere, an non effici posse putes, ut praeclarum institutum Ephemerides cujuscunque anni Medicas sub ejus exitum [dandi] conservetur continueturque, ut sive separatim excudi, sive Ephemeridibus Leopoldinae societatis adjungi possint, ad eum fere modum cujus specimen dedit V. Cl. Bernhardus Ramazzinus” (A III,8 N. 110, p. 291). 305 “Ita dum Theologi nunc et Mathematici circa Calendarii constitutionem sunt occupati, vester ordo majore, si quid judico, in publicum fructu et anni secularis admonitu, ut temporum distinctione utetur ” (p. 291). 306 “Utilitatem consilii non est cur apud Te commendem, qui melius me intelligis, quanti momenti ad observationes utiles instituendas et conservandas sit futurum. Optarem inclytam Societatem vestram, hanc in se suscipere curam, distributis in eos officiis, quibus placebit maxime, et qui maxime placebunt. Hoc quaeso ut boni publici causa, cum illis amicis, tum ipsi societati commendes” (p. 291).

824

Chapter 6

of the barometer. And so, he wrote the following to Leibniz at the end of January 1700: For five years already I have been noting every day the position of the mercury in a barometer, just as the changes of heat and cold in a thermometer, similarly of humidity in hygroscopes, and I also recorded (albeit in passing) diseases raging over individual months, with the thought in mind, that I might observe not only the motions of mercury in the barometer, but above all the origin of raging diseases, which is without doubt attributable to changes of air and storms.307 Hoffmann most likely did not make the requisite effort to bring about an involvement of the Academia Leopoldina that had previously not gone beyond a reprinting of Ramazzini’s ephemerides from the early 1690s. However, he did keep his promise to publish, for the following year, observational data that he had been systematically collecting in consultation with practitioners. Hoffmann’s publication, which was dedicated to Leibniz, was entitled Observationes barometrico meteorologicae, et epidemicae Hallenses anni MDCC (1701).308 It was sent to Leibniz as an attachment to a letter of April 10, 1701,309 together with a letter of dedication.310 The appearance of this work prompted Leibniz’s proposal to work towards achieving that the Prussian king decree the public funding of physicians in the provinces, in order to record weather and ephemeral data following Hoffmann’s example. Leibniz was flattered by the dedication of the work to him, and he expressed his gratitude accordingly at the beginning of his letter of April 18, 1701, to Hoffmann, adding the sentiment that: “I judge therefore that it is scarcely possible to do anything more progressive. I have already expressed the desire that the repetition of this achievement of yours be obtained by public authority in the Royal domains”.311 307 “Jam dum a quinque annis curiosius annotavi singulis diebus Mercurii posituram in barometro, nec non caloris et frigoris mutationem in thermometro, item humiditatis in hygroscopiis, et singulis quoque mensibus adjeci (obiter tamen) morbos grassantes, eo animo, ut non tantum causas Mercurii motus in barometro, sed maxime morborum grassantium ortum, qui sine dubio mutationi aeris et tempestatum debetur, perspicerem” (A III,8 N. 120, p. 310). 308 Cf. note 135 above. 309 Cf. A III,8 N. 236, pp. 608f. 310 Cf. A III,8 N. 237, pp. 609f. 311 “Ita enim censeo, vix fieri quicquam posse proficuum magis; jamque optandum, ut in Regiis ditionibus publica autoritate imitatio hujus curae Tuae obtineatur” (A III,8 N. 244, p. 634).

1699–1701

825

Subsequently, Leibniz and Hoffmann strove to achieve this goal during visits to Berlin, and in correspondence with the court. The measure, that would be easy to implement and cost nothing, could  – as Leibniz wrote to the Brandenburg-Prussian minister Paul von Fuchs, on April 17, 1701 – provide an incomparable treasure of knowledge important for life.312 However, the theologian Daniel Ernst Jablonski considered it advisable to await the constitution of the Berlin Society, as Hoffman informed Leibniz on June 15, 1701.313 Nonetheless, Leibniz and Hoffmann continued to plan the concrete organization and implementation of such a royal mandate. Hoffmann translated a part of his Observationes into German, composed (in German) an “Outline for the establishment of [a system of] medical-meteorological observations”,314 which was revised as a “Short announcement of the wonderful use of the observations regarding thunderstorms and illnesses, and of the method of conducting these conveniently at different locations”.315 He also compiled, as an example, the data for a month, prepared drafts for a mandate, and proposed the names of certain suitable physicians.316 He considered it necessary that, at every location, the data be recorded by two physicians for the sake of mutual control. Thus he wrote: “So the best medics must be chosen for this according to eligibility. They must not only have much practical experience but also be knowledgeable in physics … it will be better if one sends two of them to every location”.317 Besides weather and illnesses, they should also observe the welfare of animals and field crops, and furthermore, in order to explain the connection with illnesses, he suggested that it would be most useful if each and every “Medic who made these observations were also to communicate, at the outset once and for all, the position of the location, of natural waters, of its inhabitants, their circumstances of life, drinks and beverages, etc.”.318 Hoffmann did not insist on the 312 “un tresor incomparable de connoissances importantes pour la vie” (A I,19 N. 316; cf. the PS, pp. 608f.). 313 Cf. A III,8 N. 268, pp. 698f. 314 “Entwurf zur Einrichtung von medizinisch-meteorologischen Beobachtungen”. 315 “Kurtze Anzeige. Deß vortrefflichen Nutzens derer observationum aus dem Gewitter v. Krankheiten, v. auff was Arth dieselben an unterschiedenen Orten füglich anzustellen”. 316 Cf. notes 135 and 308 above, and also: A III,8 N. 299 (pp. 766–771), N. 303 (pp. 780f.), and N. 309 (pp. 788–795). 317 “So müßen dazu eligiret werden die besten Medici, welche nicht alleine viel praxin, sondern sich auch auff die Physicam verstehen … beßer seyn wird daß man an jeglichen Orte 2 dazu bestelle” (N. 299, p. 770). 318 “Medicus der diese observation machet den situm loci, naturam aquarum, derer Einwohner, Lebensart, Geträncke etc. in anfang einmahl vor allemahl mit communicire” (N. 299, p. 771).

826

Chapter 6

employment of barometers and thermometers, but rather, only recommended them, since Leibniz had expressed doubts, in his letter of September 23, 1701, that all participants would have access to such instruments. Leibniz’s words were: “I think that not everyone will be able to provide either exact meteorological observations, nor indeed will they all have barometers and other similar aerometric instruments to hand”.319 The correspondent, for his part, lauded the undertaking not only with the expectation that insights into the occurrence and prevention of epidemics were to be expected, but he also hoped to throw light on the connection between weather, the human condition, and planetary aspects. Although astrology was rejected by most philosophers and astronomers, nonetheless experience seemed to suggest a certain influence of celestial bodies. Hoffmann recalled here that even Kepler had been affine to a meteorological astrology (an “astrologiam meteorologicam”).320 Leibniz formulated the edict for king Friedrich I, along with detailed instructions based at least in part on Hoffmann’s drafts.321 Thus, borrowing from Hoffmann, he referred to lunar and solar phases but not, however, to the planetary aspects. An annotation “non communic[atum]”, found on a copy of the edict, is an indication of the fact that this part of the project came to grief in its final stages. However, at the end of 1701, Leibniz was still optimistic, as he reported to Sloane on December 27, about the mandate that had been approved by the king. On this occasion he wrote: It is delightful [to report] among other things that recently, throughout all the provinces of the king, instructions were due to be sent that learned medics should bring together annual observations[, thus] edifying yearly physical-medical histories [viz. almanacs or ephemerides]. Similarly, if elsewhere it were [also] to happen we would soon be in possession of a valuable treasure for mankind.322

319 “Puto non omnium fore tam exactas dare observationes Meteorologicas, neque enim omnes barometra et alia instrumenta similia aerometrica ad manus habent” (A III,8 N. 296, p. 760). 320 Cf. A III,8 N. 299, p. 769, and N. 309, p. 793. 321 Cf. A III,8, p. XXXVI. 322 “Placuit inter alia nuper per provincias omnes Regis mandata mitti debere ut Medici eruditi observationes annuas conferant condendae Historiae anni physico-medicae. Idem si alibi fieret brevi thesaurum essemus habituri utilium humano generi notitiarum” (A III,8 N. 320, p. 815).

1699–1701

827

Further projects of the Berlin Society played only a subordinate role in Leibniz’s correspondence at this juncture. In 1701 he enquired of Wagner and Johann Bernoulli, on March 15 and December 27, respectively, about fire engines which the Society was willing to finance.323 The topics he mentioned to Tschirnhaus, in his letter of April 17, 1701, included a calendar monopoly, the drainage of swamps and marshlands, and the idea of a German technical or specialized dictionary. Regarding the latter project he wrote: “I have proposed in particular that the collection of technical terminology in German should be simultaneously made available for adoption in the sciences and in the language”.324 On the occasion of the appearance of Leibniz’s Novissima Sinica (1697),325 Wallis had reported about journeys to China by English merchants, and which were concerned both with Christian missionary ambitions and with the advancement of science. Then, on April 9, 1700, the English correspondent could inform Leibniz that mathematical instruments were to be acquired in China.326 Leibniz announced to Wallis, in his reply of September 3, that the Berlin Society wished to support the mission along the overland route to the orient, and could accordingly contribute to the advancement of the Anglican missionary efforts.327 That the propagation of the faith by means of science was an objective of the Berlin Society, Leibniz confided to Sloane, on December 27, 1701, after he had learned of the newly founded ‘Society for the Propagation of the Gospel’ in England.328 All in all then, and particularly in relation to these missionary ambitions,329 it may be concluded that, regardless of whether Leibniz was interested in submarine navigation, and the requisite technical resources for this, such as pumps, barometers, et cetera, or in subterranean mining work in the Harz mountains, and the requisite technical improvements for greater profitability there, or in a range of other innovations in science technology and medicine, he did not act simply out of curiosity, but always also in order to unite theory 323 Cf. A III,8 N. 221, p. 571, and N. 318, p. 810. 324 “Ich habe insonderheit vorgeslagen, daß die zusammentragung der Kunstworthe in teutsch denen scienzen und der Sprache zugleich zum aufnehmen gereichen würde” (A III,8 N. 243, p. 632). 325 Cf. G. W. Leibniz, Novissima Sinica, [Hanover,] 1697; 2nd ed. 1699 [with the addition] Accessione partis posterioris aucta, [vol. 2 with title:] Icon regia monarchae Sinarum nunc regnantis. Ex Gallico versa. 326 Cf. A III,8 N. 153, pp. 397f. 327 Cf. A III,8 N. 185, p. 476. Regarding Leibniz’s missionary zeal, cf. for example, F. J. Swetz, 2003 (Introduction, note 173). 328 Cf. note 322 above, p. 815. 329 Cf. for example, F. J. Swetz, 2003 (Introduction, note 173, and note 327 above).

828

Chapter 6

and practice, and not just for the betterment of the arts and sciences, but also for the improvement of the country and the people – specifically of agriculture, manufacturing and commerce, and of foodstuffs – and, furthermore, so that such innovations and discoveries might add to the glory of God, and the betterment of the understanding of his marvels.330 All this incorporated a certain missionary zeal for the spread of the Christian religion, and the advancement of a German-style cameralism manifest for example in the form of a good police regime or orderliness, which was to be a key element in this process.331 And so, in a ‘pro memoria’ written on the occasion of the foundation of the Berlin Society of Sciences (probably in the first half of June 1700), and later published under the (translated) heading The thoughts of Herr von Leibnitz regarding the establishment of a Society of the Sciences and Arts, its scale and utility, the persons that are drawn to it; likewise regarding its finances or financial intake,332 these sentiments found expression in the following words: Accordingly, the goal would be to unite theory and practice, and to improve not only the arts and sciences but also land and people, tillage and cultivation of land, manufactories and commercial enterprises and, in one word, foodstuffs. Over and above this [the goal would also be] to make discoveries of such a kind, that the effusive honor of God might be spread more, and his wonders be better recognized than hitherto, and thus as a consequence that the Christian religion, together with good police order and customs, might be planted or spread further among peoples, [including] among those partly heathenish and partly still barbarous, even those barbarian peoples.333 Besides the Berlin Society, Leibniz continued to have his sights on other national academies. In 1699, Denis Papin was offered the post of curator of 330 Cf. A III,5, p. LXVIII. 331 Cf. A. Wakefield, 2009 (Introduction, note 147). 332 Des Herrn von Leibnitz Gedancken von Aufrichtung einer Societatis Scientiarum et artium, deren Umfang und Nutzen, der Personen, so darzu gezogen werden; ingleichen die Einkünffte davon betreffend. 333 “Wäre demnach der Zweck Theoriam cum praxi zu vereinigen, und nicht allein die Künste und die Wissenschafften, sondern auch Land und Leute, Feld-Bau, Manufacturen und Commercien, und mit einem Wort die Nahrungs-Mittel zu verbessern, über dieß auch solche Entdeckungen zu thun, dadurch die überschwengliche Ehre Gottes mehr ausgebreitet, und dessen Wunder besser als bißher, erkannt, mithin die Christliche Religion auch gute Policey-Ordnung und Sitten theils bey Heydnischen theils noch rohen, auch wohl gar Barbarischen Völckern, gepflanzet oder mehr ausgebreitet würden” (A IV,8 N. 78, pp. 425–429; cf. p. 426).

1699–1701

829

experiments by the Royal Society of London. He considered returning to England since, as he wrote to Leibniz on June 18, 1699: “Being enlightened by the lights of such a learned company, I could do much more than in the service of a prince who has so many other important affairs [to manage] that he is only rarely able to contemplate new machines and experiments”.334 However, Leibniz advised the correspondent against pursuing this offer.335 The commitment of the Royal Society was not as great as in former times, and the landgrave, of whose “curiosité grande et universelle” he had a high opinion, could achieve more for Papin. Leibniz had already expressed to Wallis, on April 9, 1699, his desire that the Royal Society be reinvigorated, just like the restructured Académie des Sciences, writing the following: “Indeed, just as the French Academy of Sciences has most recently been rehabilitated by its king, your Royal Society might likewise be reinfused with a new warmth”.336 In his reply on April 30, Wallis then informed him about new rules that would support scientific investigations, but he also pointed out the contrasting institutional contexts, and financial endowments, of the two academies in the following words: “But between that French Academy and our Royal Society there exists this difference. They [their members] benefit from the royal expenditure, and they enjoy their individual emoluments; ours [have to] cover all their own expenditure”.337 10 Alchemy Leibniz had been interested in alchemy since 1667 when, as a twenty-year-old, he became secretary of an alchemical society in Nuremberg. More than thirty years later, in his correspondence between 1699 and 1701, his continuing interest 334 “êtant éclairé des lumieres d’une si sçavante Compagnie Je pourrois faire beaucoup plus qu’au service d’un Prince qui a tant d’affaires importantes qu’il ne sçauroit penser que rarement aux nouvelles machines et experiences” (A III,8 N. 52, p. 157). 335 Cf. A III,8 N. 54, p. 163 and p. 167. 336 “Utinam, ut Gallica Scientiarum Academia nuperrime a Rege suo restituta est, etiam vestrae Regiae Societati novus quidam calor infunderetur” (A III,8 N. 28, p. 93). 337 “Sed inter Gallorum illam Academiam, nostramque Societatem Regiam hoc interest discriminis: Fruuntur illi sumptibus Regiis, suisque gaudent singulatim salariis; nostri suis sumptibus agunt omnia” (A III,8 N. 35, pp. 108f.). Regarding the Institutional context of the French Academy, cf. J. B. Shank, Before Voltaire: The French origins of “Newtonian” mechanics, 1680–1715, Chicago, 2018, and in particular Part 1. (The institutional sources of analytical mechanics: mathematics at the Académie Royale des Sciences in the late seventeenth century) and Part 3 (Making analytical mechanics in the new Académie Royale des Sciences, 1692–1715).

830

Chapter 6

in the field is reflected in letters exchanged with Magnus Gabriel Block, Peter Moller, Johann Andreas Stisser, and Georg Wolfgang Wedel. Block enquired about Leibniz’s views on astrology, palmistry (palm reading or chiromancy), necromancy (necromantia), and the branch of alchemy concerned with transmutation. Leibniz’s skeptical reaction in a non-extant letter of April 17, 1699, can be sensed from the tenor of Block’s reply two months later, on June 24. Thus the correspondent wrote: I do not know what to say regarding judicial astrology nor regarding chiromancy but simply that which I have seen and heard from philosophers [who are] highly-respected by others of somewhat strange persuasion, likewise from fortuitous events, from [all of] which I do not know which party I should follow. As regards alchemy, I have received with the greatest veneration your beneficent advice not to get involved and I will adhere to this throughout for [that which is] morally false; however, metaphysically [considered], and in relation to the disciples of that art, I consider it to be a non-phantasm and non-entity of reason; at the very least I will be not a skeptic but [rather] a Cartesian, doubting but not negating.338 Leibniz warned, again and again, against investing time and money in the search for possible transmutations. The probability of success would be less than 1:100,000. But, one ought not to discredit alchemy entirely, or as he wrote in his reply to Block on September 8: “As regards alchemy the best expedient is not at all to lose inquisitiveness; but also to be on one’s guard. For the chance of succeeding is much less than one to a 100 thousand”.339 Nevertheless, he argued that one ought not to abandon alchemy entirely, expressing himself with the words: “I do not desire that it be discredited entirely because to this imagination we owe an infinity of beautiful realities”.340 338 “Non sò cosa debba dire dell’ astrologia judiciaria nè della Chiromanzia mà pure ci hò veduto e sentito da’ uomini Filosofi degni per altro di fede cose stravaganti, anche ne’ casi forttuiti, onde non sò à che partitio io mi debba appigliare. Intorno l’Alchimia ricevo il Suo caritativo consiglio con somma venerazione à non imbarcarmici e la terrò per moraliter falsa, mà Metaphysice et inter filios artis la tengo per non-chimera et non-ens rationis almeno sarò non Scepticus sed Cartesianus dubitando senza negazione” (A III,8 N. 53, pp. 158–161, specifically p. 159; Leibniz: Nordström, pp. 214–216, with Latin words in italics). 339 “A l’egard de l’Alchymie le meilleur expedient est de n’en perdre point la curiosité; mais aussi de s’en donner de garde. Car l’apparence de reussir est bien moins qu’un à 100 mille” (A III,8 N. 71, pp. 216–218, specifically p. 217; Leibniz: Nordström, pp. 217–218). 340 “Je ne voudrois pas qu’on la decreditât entierement, parceque nous devons à cette imagination une infinité de belles realités” (N. 71, specifically pp. 217f.).

1699–1701

831

He did not fundamentally cast doubt on the notion of a transmutation which he certainly considered to be possible. However, many claims of such transformations failed to pass the test of proof. And so he wrote in his last letter of 1699 or first letter of 1700 (between mid-December and the end of January) to Block – indeed probably the final communication in this correspondence – the following text: The cause of my doubts regarding transmutation is not that I find it to be impossible, but it is rather that every time that I delved into the tales that are in circulation, I found them to be most uncertain. It is rather like the great number of miracles and fantasizing sorceries which very often also cast doubts on authentic [counterparts].341 Unlike contemporaries (and correspondents) like Gottfried Kirch and Friedrich Hoffmann, Leibniz condemned outright “astrologia judiciaria”, or judicial astrology, and he saw himself here in the company of renowned astronomers like Cassini, Huygens and Hevelius. Thus, in his letter of September 8, 1699, to Block he wrote: “The astrological soothsayings are absolutely contrary to reason; the most excellent astronomers of the century, like the gentlemen Cassini, Huygens and Hevelius, and the likes of them, have derided these resoundingly”.342 Leibniz proposed exposing or unmasking the astrologists by means of a statistical experiment that would show that the fulfillment, or coming true, of their predictions was entirely accidental. For him, the fact that transmutation was difficult to achieve, and at best only revealed to adepts in well-informed circles, was a work of providence that in turn contributed to the maintenance of the world order and – also for this reason – the quest for it seemed to him to make no sense. That one might find a small particular or singular process that worked, he considered to be more likely. Writing to the Hamburg resident Peter Moller on January 2, 1699, he complained that in spite of his contacts to renowned chemists, his intensive study of alchemistic writings, and his

341 “La cause de mes doutes sur la Transmutation n’est pas que je la trouve impossible: mais c’est que toutes les fois que j’ay approfondi les Historiettes qui en courent, je les ay trouvées peu seures. C’est à peu près comme ce grand nombre de miracles et de sorciers imaginaires, qui bien souvent font douter encor des veritables” (A III,8 N. 93, pp. 265f., specifically p. 266; Leibniz: Nordström, pp. 220–221). 342 “Les divinations Astrologiques sont absolument contraires à la raison; les plus excellens Astronomes du siecle comme M. Cassini, M. Hugens, M. Hevelius et leur pareils s’en moquoient hautement” (note 339 above, N. 71, p. 218).

832

Chapter 6

visitations to laboratories, he had witnessed no credible transmutation but, on the contrary, had encountered a number of impostors. Thus, he wrote here: I must admit that, although I have known many of the most famous chemists in Europe some of whom were considered to be adepts and enjoyed the assistance of great potentates who relished these studies, I had the opportunity to achieve this, [but] notwithstanding this [I] saw no delectable truth of the great work. Therefore I am still very attached to this although, in the philosophies which treated it, I have, more than but a few others, looked around [for new horizons] even to the extent that already in the 22nd year of my life I achieved a great harmony of the same and offered it to a great elector,343 who found a special pleasure in this and I would like to wish, for the sake of curiosity, that I were now to have [to hand] the writings again.344 Moller, replying on January 7, found it hardly surprising that Leibniz had little success in his dealings with chemists of fame, since, in contrast to these, the true adepts in the field operated incognito, and worked secretly, with the result that he thought it no wonder: That you found nothing [when dealing] with the most famous chemists, since the true adepts take the greatest care to hide away and to live incognito, whereas those artists who become famous in chemistry, while they do indeed understand many tasks and operations, do however lack that which is right (required).345

343 No doubt a reference to the elector of Mainz, Johann Philipp von Schönborn (1605–1673). 344 “Ich muß bekennen, daß ob ich schohn viele der beruhmtesten Chemicorum in Europa deren theils pro Adeptis gehalten worden gekennet und vermittelst großer Potentaten die diese studia geliebet, dazu gelegenheit gehabt, ich dennoch keine vergnügende Wahrheit des großen werks gesehen; daher ich noch allezeit sehr angestanden, ob ich gleich in den philosophis die davon gehandelt, so viel als wenige andere mich umbgesehen so gar daß ich bereits im 22ten Jahr meines Alters eine harmoniam derselbigen gemacht und einem grossen Churfursten offerirt, welcher daran ein besonderes vergnügen gefunden und möchte ich umb der Curiosität willen wundschen, daß ich die Schriften jetzo wieder hätte” (A III,8 N. 1, p. [3]). 345 “daß Sie bey den beruhmsten Chemicos nichts gefunden, Sintemahl, die veri Adepti sich mit allen fleiß verstecken v. incognito leben da hingegen die jenige Kunstlers in der Chymia berühmt sindt so zwar vielerley labores v. operationes verstehen, denen aber das rechte fehlet” (A III,8 N. 2, p. 4).

1699–1701

833

Moller told Leibniz that he had contact with several alchemists working more or less in secret. He had, for example, just learned from an old acquaintance of his that he was involved in alchemy. Alas, the individual in question could only survive as a “capitalist”, and not as a chemist. Regarding him the correspondent wrote: “He has gained almost nothing in Hamburg and is now a capitalist, notwithstanding the fact that, although he enjoys the bourgeois right to carry on business and trade, he cannot avail of the advance of chemistry”.346 Yet another adept Moller knew had resigned from his “good and new (I believe) service”, or employment, in Brandenburg, because he had been discovered, and had then moved to Hamburg, Leibniz was told.347 The correspondent was impressed by Leibniz’s early involvement with alchemy more than thirty years before and, although he himself had seen a lot, he admitted that he had not carried out any laboratory work due to lack of instruction in the field. Thus he added: That you Sir, highly-respected Counsellor, already completed a [work of] harmony [in chemistry] in your 22nd year is something about which I am more than a little surprised. I would be interested in seeing this. As far as the operations are concerned, I am very inept (unqualified) in the matter … Through continuous reading I have, as I think, attained certain insights in that I know the material but [the manner] how it is to be treated has escaped me.348 The discoverer of phosphorus, Heinrich Brand, was also still living in Hamburg, and he had touted to Leibniz an ostensibly very lucrative process for metal ennoblement.349 Leibniz had then sought the judgement of Moller in the matter. However, the latter considered Brand to be a braggart who, although he had come far, had in fact not discovered phosphorous himself at all. Thus Moller added:

346 “Er haet in Hamburg nichts fast eingebracht v. ist nun ein Capitalist wiewohl daß Er gute bürgerliche Nahrung treibet, kann also eben nicht dem Vorschub der Chymiae zuschreiben” (p. 5). 347 “Noch weiß ich daß alhie ein Adeptus auß dem Brandenb. sich hie retirirt habe, der seinen guten v. neuen (puto) dinst abandonnirete. Weil Er ist entdekket worden” (p. 5). 348 “Daß Mein Hochgeehrter H. Rath schon fort ins 22te Jahr eine Harmoniam gemacht daruber wundere mich nicht wenig: hätt woll lust selbige zu sehen: was die operationes anlanget, darinnen bin ich gantz rüde … Durch die continurliche lectur habe zwar, wie ich vermeine einig licht erlanget daß ich die materiam weiß, aber wie Sie zu tractiren diß fehlet mir” (p. 5). 349 Cf. A III,7 N. 240, p. 931.

834

Chapter 6

As far as Mr Brand is concerned, the person in question does not have a good reputation here, and while he presents himself here as an inventor of phosphorus, he is not that really, although he has come pretty far with this, and was able to improve and extend this craft (or skill).350 Besides, Moller claimed that Brand was unable to finance laboratory work, explaining that “because he is in such poverty, he lacks the means of trying out something in the laboratory”.351 For the claimed effect, a universal or pansophist knowledge would be required which Brand simply did not have. Moller had not yet met such a person, but he was convinced that an acquaintance of his did possess a very lucrative particular (or singular) process, and he promised to inform Leibniz as soon as he received intelligence in the matter. And so he wrote the following in his second letter of July–August 1699: I will also not renege on my former promise, namely as soon as it has been acquired to notify you Sir, highly-respected Counsellor, for I have already been sufficiently assured that a certain friend possesses this [secret] skill and earns yearly around 2, 3 to 4000 Taler with it.352 Johann Joachim Becher had, in the 1670s hoped, and tried in vain, to become rich by means of a process that purported to turn sand into gold.353 Stisser had been a witness to one such demonstration – carried out in both Amsterdam and Hamburg – but one where the announced effect had failed to materialize. The Helmstedt professor now reported this to Leibniz, who had enquired about the transmutation of salts, with or without useful applications. Stisser confirmed, in this letter of February 5, 1699, that he himself was aware of some transmutations of salts, albeit without particular use and only in small quantities. He thus informed Leibniz: 350 “Was anlanget den Mr Brandt so ist derselbige Mensch alhie eben nicht in großen credit, v. ob Er zwar woll sich für einen inventorem phosphori ausgibt so ist er es doch nicht: Wie woll er zimlich weit damit gekomen, v. diese Kunst beßer excolirt hat” (note 345 above, p. 5). 351 “weilen Er in solcher paupertate ist daß ihn die Mitteln etwas laborando zu versuchen mangeln” (p. 6). 352 “Ich werde auch von meinem vorigen Versprechen nicht abgehen scil[icet] so baldt Sie erlangen es an M. H. Rath zu notificiren dann einmahl bin deßen Satsamb versichert daß ein gewißer freundt diese Kunst besitzet vndt Jahrlich bey 2, 3, à 4000 rth. damit lucriret” (A III,8 N. 59, p. 178). 353 Regarding the “gold from sand project”, cf. H. A. M. Snelders, 1993, pp. 103–114 (Introduction, note 186).

1699–1701

835

Furthermore, I obediently give your Excellency information that different transmutations of salt are indeed known to me, but without particular use and only in small quantity. D. Becher promised a number of years ago in Amsterdam and also thereafter in Hamburg (at both of which locations I saw him) to do great things in this area and he pretended that he would become pretty rich in this way. It came down however to loud promises and the effect, as I learned from good friends, failed to materialize.354 For Leibniz, as he wrote in his letter of April 3 to Stisser, the gain of enlightening experimental knowledge (like that concerning the transmutation of salts) meant more than that of lucrative, or lucre-bringing, experimental knowledge. Although efforts were indeed being made everywhere to bring chemistry into the form of an art, hitherto little light had been shed on the foundations of the subject, he thought. Many had postulated principles that were more melodious than veritable. And so he hoped that Stisser might advance chemistry through a combination of method and experiment. Thus he wrote: I was pleased to learn that veritable examples of the transmutation of salts are known to you, even if they lack monetary or lucrative value. For we are not concerned with this here, and we require luciferous [or enlightening] experiments more than lucriferous [or profit-bringing] experiments.355 In his belated reply of June 2, which he attributed to his having to care for his botanical garden,356 Stisser promised to actively work for the consolidation of chemistry provided the means were made available to him for the meticulous experimental examination of the entire subject.357 He then communicated to Leibniz some examples of salt transmutations from all three kingdoms of 354 “Im übrigen gebe Ew. Excell. Zur gehorsahmen nachricht, daß mir zwarten unterschiedene transmutationes salium bekand, aber ohne sonderbahren nutzen und nur in kleiner quantität. D. Becher versprach für einigen jahren in Amsterdam auch nachgehendß in Hamburg (an welchen beyden orten ich ihn gesehen) grosse dinge in dergleichen zu thun, und vermeinete einige reich dadurch zuwerden, es lieff aber auff großsprachen auß und wollte der effect, alß ich von guten freunden hörete, nicht erfolgen” (A III,8 N. 11, p. 48). 355 “Gratum est intelligere, quod Tibi notae transmutationes salium verae, etsi utilitate pecuniaria vel lucro destitutae. Neque enim id hoc loco curamus, et experimenta lucifera magis quam lucrifera quaerimus” (A III,8 N. 25, p. 85). 356 “Serius quam par est, ob horti mei curam, honoratissimis Tuis literis respondere cogor” (A III,8 N. 49, p. 145). 357 Cf. p. 145.

836

Chapter 6

nature, namely the mineral, vegetable and animal realms.358 However, for Leibniz, in his reply on December 22, it remained unclear whether in fact in each of these examples a “transmutatio” was involved, and not simply a “transplantatio”, in which chemical substances were merely exchanged in the reaction or process. Taking the example of Glauber’s salt treated in the third part of Johann Rudolph Glauber’s Prosperitatis Germaniae or Theütschlandes Wohlfahrt of 1659,359 and considering also Robert Boyle’s discussion of Glauber’s works in “Some specimens of an attempt to make chymical experiments usefull to illustrate the notions of the corpuscular philosophy” of 1661 (and 1669),360 Leibniz considered different alternative explanations of the transmutation of chemical substances – including the revivification or transanimation of Glauber’s salt – for which he also proposed further investigations. Chemical substances could be veiled or unveiled in reactions, and the products of such a process might be already contained as subtle particles in the starting substances, or elements could possibly alter their form depending on the environment. Thus he wrote: The question is of great moment, [namely] as to whether really a transmutation of salts exists there where no necromancy is suspected. For I remember it was called into doubt by certain other things, and it is certain how easily these bodies cover and again uncover themselves, which the resuscitation of Glauber’s salt revealed, that was subsequently elaborated by Boyle. Following this there were those who suspected that, in the spirit of niter, natron [i.e. soda or sodium carbonate] itself is being simply dispersed in extremely agitated parts and also, they judged, in the spirit of salt, and through its elements or the unaltered figures of its miniature parts. But their hypothesis is overturned, if it be admitted that a similar 358 Cf. pp. 145f. 359 Cf. J. R. Glauber, Prosperitatis Germaniae pars tertia … in qua salpetrae … extrahendi modus traditur, Amsterdam, 1659, and Theütschlandes Wohlfahrt, dritter Theil. Darinnen gelehret wird, wie vnd auff was weise aus vnterschiedlichen subjectis … vnd auch in Copia ein güter Salpeter zu bereiten, Amsterdam, 1659. 360 Cf. “The preface giving an account of the two following treatises, and proposing the desirableness of a good intelligence betwixt the corpuscularian philosophers and the chy|mists” (pp. 119–128) and “Sect. XL” (p. 158) of the work “Some specimens of an attempt to make chymical experiments useful to illustrate the notions of the corpuscular philosophy” (pp. 119–158) of the 1669 edition of R. Boyle, Certain physiological essays, and other tracts written at distant times, and on several occasions, London, 1661 and 1669 (2nd ed.). Furthermore, cf. R. Boyle: The works, vol. 2 (publications of 1661), and M. Hunter, The Boyle papers: Understanding the manuscripts of Robert Boyle, Aldershot (England) and Burlington (VT), 2007, in particular p. 236, note 60.

1699–1701

837

salt is jointly obtained from natron, or vice versa. For, as a consequence, it follows that a single element is transformed into another element, or is common to both elements.361 Stisser’s open letter of February or March, 1700, addressed to Leibniz and entitled De variis erroribus, chemiae ignorantia in medicina commissis dissertatio epistolaris ad illustrem atque excellentissimum virum Dominum Godefr. Guilielmum Leibnitium,362 maked the end of the correspondence. The author and correspondent died on April 21 of that year. Leibniz’s reply, written before he learned of Stisser’s demise, is erroneously dated May 25 instead of the probable date, April 25.363 In his Dissertatio epistolaris Stisser had, to begin with, characterized chemistry as the oldest of the arts. This prompted Leibniz in his reply to consider the importance and reliability of tradition from the ancients in relation to chemistry. He did believe that chemical knowledge had existed in antiquity and that distillation had been known then. Alchemical interpretations, for example the legend of “The Golden Bough” from Virgil’s epic the Aeneid, he considered to be more elegant than credible. And the portrayal of the Egyptian art of gold making found in the Byzantine encyclopedia of the ancient Mediterranean world, the Suda, he considered to be hardly reliable either, since other authors chose not to mention it. Of course, the fact that he himself had once pursued the idea of editing the alchemical writings of the ancients, he had previously revealed to Block.364 Leibniz had likewise attempted to motivate the Dutch classicist Jacobus Tollius (1633–1696) to obtain alchemical information from mythology, not least with the intention of dissuading him from pursuing any further what he saw as a senseless undertaking.365 After Georg Wolfgang Wedel had sent him two writings regarding “The Golden Bough”, Leibniz, referring to Plato and Aristotle, made clear to this correspondent, in a letter written between February and 361 “Quaestio est magni momenti an vera salium detur transmutatio quae larvae suspecta non sit; id enim memini a quibusdam in dubium vocari, et constat quam facile ista corpora et tegant se et redetegant, quod resuscitatio Nitri Glauberiana ostendit, quam deinde Boylius excoluit. Unde sunt qui suspicantur in spiritu Nitri ipsum Nitrum tenuissimas tantum in partes fortissime agitatas dispersum latere, idemque de spiritu salis judicant, elementis cujusque seu minutarum partium figuris semper salvis. Sed horum everteretur Hypothesis, si liceret ex nitro salem parare communi similem, vel contra. Ita enim sequeretur vel elementa unius mutari in elementa alterius, vel communia esse utriusque elementa” (A III,8 N. 92, p. 264). 362 Cf. A III,8 N. 131, pp. 337–355. 363 Cf. A III,8 N. 163, pp. 422–426, specifically p. 422 (annotation). 364 Cf. A III,8 N. 71, pp. 216–218, specifically p. 218; Leibniz: Nordström, pp. 217–218. 365 p. 424 (note 363 above); cf. also A I,14 N. 94 (p. 160), N. 194 (p. 320) and A III,5 N. 64 (p. 273).

838

Chapter 6

April, 1700, how difficult it was to identify substances described in the writings of antiquity because of the strange terminology employed.366 Wedel’s solution of an alchemical number puzzle of George Starkey (published under the pseudonym Eirenaeus Philalethes)367 also appeared to Leibniz as uncertain, and he pointed out to Wedel that there was an infinite number of solutions. To begin with, one ought to convince oneself of the scientific pedigree of the author. The vague notation of Philalethes gave the impression that one was dealing with a sophist rather than an adept. Wedel had searched in vain in Erfurth for a manuscript on the quintessence of Basilius Valentinus (1394–1450),368 and he asked Leibniz, on August 24, 1699, to search for it in the library at Wolfenbüttel. Thus he wrote: I require from the works of Basilius Valentinus a manuscript opus entitled de Quinta Essentia, one [book of] which emerged in Erfurth at a renowned monastery, the rest, having been taken to Sweden or elsewhere, was lost nevertheless … It came to mind that it might exist at the Ducal Library (the Bibliotheca Augusta Guelfica) in Wolfenbüttel, and where I remember having seen a certain manuscript of Paracelsus [i.e. Theophrastus Bombastus von Hohenheim, 1493–1541] in 1672.369 However, in his reply on September 9, Leibniz, who was the director of the Ducal Library, had to disappoint the correspondent writing as follows: “I fear that the book of Basilius, de quinta essentia is far removed from those we have from him”.370 Nonetheless, Leibniz’s opinion, expressed in this letter, was that, in contrast to those of Philalethes and others, the writings of Basilius Valentinus371 – although he considered them to be feigned – stood out among and above many others because of their concrete character.372 366 Cf. A III,8 N. 149, pp. 392f. 367 Cf. G. Starkey [pseudonym: Eirenaeus Philalethes], Enarratio methodica trium Gebri medicinarum: In quibus continetur lapidis philosophici vera confectio, London, 1678. 368 Cf. B. Valentine [Basilius Valentinus], Tractatus chymicus de quinta essentia … ans Licht gestellet worden von Sincero Aletophilo, Erfurt, 1738. 369 “Desideratur in operibus Basilii Valentini liber mss. de Quinta Essentia, qui Erffurti in incluto coenobio extitit unus, reliquis in Sueciam vel aliorsum delatis, sed periit tamen … In mentem venit, annon in bibliotheca Augusta Guelfica forte extet, ubi memini et mss. quaedam Paracelsi 1672. vidisse” (A III,8 N. 66, p. 210). 370 “Vereor ut liber Basilii, de quinta essentia multum distet iis quae ab ipso habemus” (A III,8 N. 74, p. 225). 371 Cf. B. Valentine [Basilius Valentinus], Chymische Schriften, Hamburg, 1677. 372 “In Basilio Valentino plus experientiae agnoscimus quam in plerisque aliis qui feruntur” (note 370, p. 225).

1699–1701

839

The identity of alchemical authors, and the contents of alchemical records, were often the subjects of speculation in Leibniz’s correspondence. On November 28, 1699, Block reported to Leibniz from Stockholm that his deceased correspondent and collaborator in Florence, Rudolf Christian von Bodenhausen, had left behind numerous records and notes on chemical processes, and concerning transmutation. One particular note provided the intelligence – obtained from a conversation in Italy with the meanwhile deceased Christof Pratisius  – that Leibniz possessed the manuscript of the work Lucerna salis philosophorum, that had been published in 1658 under the pseudonym “Sendivogius filius”,373 and that Johann Joachim Becher was its real author,374 although the matter remained in doubt.375 Thus Block wrote: I find among the manuscripts of Baron [von] Bodenhausen the following text. This says, he speaks of a doctor called Pratisius, that Becher is the author of Lucerna | salis376 | and Mr Leibniz/ Ducal Counsellor and Librarian in Hanover/ is in possession of this manuscript, something I do have my doubts about.377 This was disputed by Leibniz in his reply of December 1699, or January 1700. He himself had indeed known the author in Nuremberg, whose identity was Johann Harprecht and who was synonymous with Johann Hiskia Cardilucius. Becher, on the other hand, had preferred the pseudonym Solinus Salzthal Regiomontanus.378 Thus Leibniz wrote: 373 Cf. Sendivogius Filius (pseudonym, ed.), Lucerna salis philosophorum. Hoc est delineatio nuda desiderati illius principi tertii mineralium Sendivogiani, sive salis pontici, quod est subiectum omnis mirabilitatis  … communicata à filio Sendivogii, anagrammaticè vocato, Amsterdam, 1658. 374 Cf. J. J. Becher [pseudonym: Solinus Salzthal Regiomontanus] Solini Salzthals Regiomontani Discurs von der Großmächtigen Philosophischen Universal-Artzney / von den Philosophis genannt Lapis Philosophorum Trismegistus, MS (of 1654) published as: Discursus Solini Saltztal Regiomontani De potentissima philosophorum Johann Joachim Heilmann, Theatrum Chemicum, Strasbourg, 1661, pp. 675–694. 375 Cf. P. H. Smith, The business of alchemy: Science and culture in the Holy Roman Empire, Princeton, 2016, in particular pp. 40f. 376 | alchemical symbol for salt |. 377 “Io trovo frà i MSS del Sr Bodenhausen queste parole. Idem saget, parla d’un dottore che si chiamava Pratisio, daß Beccherus der Autor Lucernae |salis| sey u. habe deßen eigen MS / der H. Leibnits / Fürstl. Hoffrath u. Bibliothec. zu Hannover / in Händen; daran ich doch zweiffele” (A III,8 N. 84, p. 249; Leibniz: Nordström, pp. 218–220). 378 Regarding the identities of pseudonymized alchemical authors referred to in Leibniz’s correspondence, cf. the previously cited works (Introduction, note 188) of W. R. Newman (2006), P. H. Smith (2016), W. S. Shelley (2017), and C. Wahl (2017).

840

Chapter 6

The late Mr Pratisius will have made a mistake. I knew myself the pretended son of Sendivogius, author of the book de sale philosophorum. His real name was Johannes Fortitudo Harprecht, but in the meantime he has become better known under the name Johann Hiskia Cardilucius whom I believe is still living in Nuremberg, where he continues to produce books but far removed from the great promises of former times. It is a very different book that I would attribute to Becher although it is about the same matter. It is a book entitled Solinus Salzthal Regiomontanus which is to be found in the Theatrum Chymicum, and of which the friends of Becher have assured me that he is the author. You can see from this, Sir, how errors slip into accounts of things, when they are passed on from hand to hand.379 In an earlier letter of June 24, 1699, Block also promised Leibniz transcriptions of Bodenhausen’s alchemical records, some of which had never been intended for dissemination. In order that the amanuensis would not be able to understand these, Block planned to encrypt them, and he sent Leibniz the “cifra ò l’alfabetto”, viz. his secret-key encryption.380 11

Geology, Mineralogy, Paleontology, Ethnography and Etymology

On August 16, 1699, Leibniz reported to John Wallis about Gustav Daniel Schmidt’s geographical explorations of the coasts of the North Sea and of the Baltic Sea.381 Leibniz was also interested in the geological formation history of the English Channel, and accordingly in being able to establish temporal changes of the earth’s surface. Following inducement by Leibniz, Schmidt had prepared a questionnaire on the configuration of the coasts near Calais 379 “Feu M. Pratisius aura pris un sbaglio. J’ay connu moy même le pretendu fils de Sendivogius auteur du livre de sale philosophorum. Son veritable nom estoit Johannes Fortitudo Harprecht, mais depuis il a esté plus connu sous le nom de Joh. Hiskias Cardilucius que je crois vivre encor à Nurenberg, où il fait tousjours des livres mais bien eloignés des grandes promesses d’autres fois. C’est un tout autre livre que j’aurois attribué à Becherus quoyqu’il soit sur la même matiere. C’est le livre intitulé Solinus Salzthal Regiomontanus qui se trouve dans le Theatrum Chymicum, et dont les amis de Becher m’ont asseuré qu’il estoit l’auteur. Vous voyés par là Monsieur, comment les erreurs se glissent dans les recits, quand ils passent de main en main” (A III,8 N. 93, pp. 265f.; Leibniz: Nordström, pp. 220–221). 380 “La cifra ò l’alfabetto di cui sopra parlay è questa” (A III,8 N. 53, pp. 161f.; Leibniz: Nordström, pp. 214–216). 381 Cf. A III,8 N. 64, p. 193.

1699–1701

841

and Dover, which Leibniz then sent to Hans Sloane, on May 15, 1701,382 and to the Abbé Jean-Paul Bignon one day earlier, on May 14.383 Furthermore, in correspondence with Wallis, Leibniz discussed Olof Rudbeck’s geographical interpretation of mythology which, although rooted in literary legend, might, it was thought, just contain some truth, or as Wallis wrote on April 30, 1699: “And all this from the mythology of the poets is embellished with singled-out, not exactly uncouth characters, such that they, even if not genuine, have at least a great resemblance to the authentic”.384 Rudbeck had located Atlantis and Odysseus’ journey in northern Europe and Block, for his part, considered Rudbeck’s hypotheses to be ridiculous, or as he wrote to Leibniz on January 10, 1699, about his compatriot: “One sees clearly that his hypotheses are for the most part ludicrous and exorbitant, as is likewise the application of various hollow quotations of ancient and foreign authors”.385 Block also reported in this letter about rejoinders to Rudbeck’s theory. On the other hand, in Leibniz’s correspondence with Wallis, it was the origins of the peoples and languages of Great Britain and Ireland that were primarily considered. Thus, Leibniz’s words written on December 4, 1699, refer to the Anglo-Saxon settlement, and they reveal an inkling of the later division of the Celtic peoples and languages into two groups, namely the Brythonic (“Cymraeos  … vel Cambros”) and Gaelic (“Scotos antiquos seu Hibernos”). Leibniz’s thoughts expressed in this letter reveal a premonition of the division of the Celtic peoples and languages into two groups, namely the Brythonic or P-Celtic, and the Goidelic or Q-Celtic, the split first formulated and published by Edward Lhuyd in his Glossography of 1707.386 Leibniz alluded in his letter to Wallis of December 4, 1699, to recent works of Lhuyd,387 and specifically about observations concerning the Irish language, in the following words: 382 Cf. A III,8 N. 258, p. 677 (annotation). 383 Cf. A I,19 N. 369, pp. 685f. 384 “Omniaque haec ex Poetarum Mythologia desumptis characteribus adornat haud invenuste; ut, si vera non sint, magnam saltem habeant veri similitudinem” (A III,8 N. 35, p. 109). 385 “vede bene che i suoi hypotesi per la maggior parte sono ridicoli e spropositati, come altresì l’applicazione delle diverse citazioni cavate da autori antichi e stranieri” (A III,8 N. 4, pp. 13–17, specifically p. 15; Leibniz: Nordström, pp. 211–213). 386 Cf. E. Lhuyd, Archaeologia Britannica: Giving some account additional to what has been hitherto publish’d, of the languages, histories, and customs of the original inhabitants of Great Britain, vol. I. (Glossography), Oxford, 1707, and also J. Lennon, 2004 and 2008 (Introduction, note 197), in particular chap. 2 (Ogygia, pp. [58]–114) and, regarding the P-Q split of the Celtic languages, p. 90. 387 Cf. E. Lhuyd, Lithophylacii Britannici ichnographia, sive, lapidum aliorumque fossilium Britannicorum singulari figura insignium quotquot hactenus vel ipse invenit vel ab amicis

842

Chapter 6

I do not know where I have learned that your D. Lhuyd (if I remember correctly), a distinguished man who has done much work in investigating the layers of the earth and other things of this kind, investigated the antiquity of peoples, [and] observed things out of the ordinary concerning the Irish language, and if I am not mistaken deduced a relationship to old Latin. This deserves to be examined. Indeed I believed that you English have come from the recent inhabitants of our shores, the Saxons, and thus your Cymri or Cambrians [native Welshmen] came from our ancient inhabitants, the [Germanic tribe] Cimbri, and your ancient Scoti or Hiberni [Scots or Irish] up to now appear to have come from more ancient inhabitants of our shores.388 Leibniz’s discussion of the Irish language in his correspondence probably began in 1694.389 In a letter to Edward Bernard, on January 6 of that year, he wrote: It has been established that the Scots are the same as the Irish. But where did the Irish come from? And what was their language, for, if I am not mistaken, it is very different from Welsh, and possibly there is a kinship, as it appears to Wallis, to whose judgement I certainly attribute much.390 Leibniz was referring here to John Wallis’ Grammatica linguae Anglicanae (1653),391 in which the author had criticized in particular Joseph Justus accepit, distributio classica, London, 1699; “Part of a letter … concerning several regularly figured stones”, Philosophical Transactions, vol. 20, no. 243, (August 1698), pp. 279f. and Fig. 1. 388 “Nescio ubi notavi Dn. Lluydium vestrum (si bene memini) Virum egregium qui multam operam in telluris stratis aliisque id genus examinandis ponit, antiquitatesque gentium investigat, de lingua Hibernica quaedam non vulgaria observasse, et ni fallor latinae antiquae affinem judicare. Haec merentur discuti. Sane crediderim ut vestri Angli a recentioribus nostri litoris incolis, Saxonibus, venere ita Cymraeos vestros vel Cambros esse ab antiquioribus habitatoribus nostris Cimbris, et vestros Scotos antiquos seu Hibernos, adhuc antiquiores orae nostrae incolas indicare” (A III,8 N. 89, p. 260). 389 Cf. E. Poppe, 1986, pp. 65–84 (Introduction, note 195). 390 “Scotos fuisse eosdem cum Hibernis constat. Sed unde Hiberni? Et quae lingua eorum; nam, ni fallor multum a Wallica abit, et si Wallisio vicina videatur, cujus judico equidem multum tribuo” (A I,10 N. 104, pp. 183f.). 391 Cf. J. Wallis Grammatica linguae Anglicanae. Cui praefigitur, de loquela sive sonorum formatione, tractatus grammatico-physicus, Oxford, 1653; Editio quarta prioribus auctior, Oxford, 1674.

1699–1701

843

Scaliger  – with his Diatriba de Europaeorum linguis (1610) in mind392 – for separating Irish from Welsh, and placing it among the “matrices”, viz. the independent or unrelated languages of Europe, like Basque, Hungarian, Finnish and Lappish. Near the end of his letter to Bernard, Leibniz ruled out a connection between the Irish and Basque languages, posing the following question: “But what do you think about the Basque language? I do not know if it differs much at all from our European [languages and] came perhaps in ancient times from Africa. I do not think there is a kinship with Irish”.393 And in a letter to Daniel Larroque a month later, on February 5, 1694, Leibniz suggested once again that Irish seemed to be one of the languages of Europe which appeared isolated and difficult to relate to others, although there were people (like Wallis) who did see a connection with Welsh and Breton. Thus he wrote on this occasion: We have languages in Europe which are rather singular  … Irish again appears rather different to that of the others, although they say that it has some connection with Breton and with the language of Wales, which is apparently ancient Gaulish, and which has [had] much [influence] from Germany.394 A connection between Irish and Welsh, based on a comparison between contemporary texts of the ‘Lord’s Prayer’ in these languages, was a focus of Leibniz’s correspondence with Thomas Smith in late 1694 and early 1695,395 but it was not until the years after 1703 that Leibniz (alongside Johann Georg Eckhart) developed a more complex theory in which the Irish language was integrated into his concept of the history, and the relationships, of the European languages.396 The culmination, and conclusion, of this collabora-

392 Cf. J. J. Scaliger, Opuscula varia, antehac non edita, Paris, 1610; Frankfurt, 1612, in particular pp. 119–122 (Diatriba de Europaeorum linguis). 393 “Sed quid de Biscaina judicas? qua nescio an ulla magis abeat a nostris Europaeis forte antequissimis temporibus ex Africa venit. Hibernicam cognatione attingere non puto” (cf. note 390 above, p. 184). 394 “Nous avons des langues en Europe qui sont assez singulieres  … L’Hybernoise encor paroist assez differente de celle des autres, quoyqu’on dise qu’elle a quelque connexion avec le Bas Breton, et avec la langue du pays de Galles, qui est apparemment l’ancienne Gauloise, et qui a beaucoup de l’Allemand” (A I,10 N. 145, p. 250). 395 Cf. A I,10 N. 411 (p. 602), N. 450 (p. 654) and A I,11 N. 188 (p. 273f). 396 Cf. E. Poppe, 1986, pp. 69–72 (note 389 above, and Introduction, note 195).

844

Chapter 6

tion with Eckhart was no doubt the posthumous publication of Leibniz’s Collectanea etymologica in 1717.397 12 Biology In the spring of 1701 Leibniz’s correspondence with Alexander Christian Gakenholz gained a special significance, particularly in the fields of biology and medicine. Following a discussion with Leibniz (probably in March 1701) Gakenholz composed an open letter addressed to him, dated April 14, 1701, with the title Ad illustrem atque excellentissimum virum Dominum Godefr. Guilielmum Leibnitium … epistola … de emendanda ac rite instituenda medicina.398 The first printed version of this epistola was sent as an enclosure to Gakenholz’s letter to Leibniz dated April 21, 1701. The correspondent attributed the inspiration for his composition to the discussion he had with Leibniz a few weeks earlier, and so he wrote the following text: I have had, after I had the honor a few weeks ago of showing you my reverence, through your learned discourse with me concerning res medica and particularly botany, some thoughts which I recently developed further in the short dissertation attached here, in order to be able to present them to your Excellency’s astute judgement.399 At their meeting, Leibniz had proposed considering roots as the basis for a system of plant classification. Following up on this proposal Gakenholz had, in his epistola, discussed various established classification systems based on fruit, seeds and, more recently, flowers. As in his remarks concerning medicine, Gakenholz complained here also about the predominant orientation towards antiquity, where writings were interpreted, annotated and even provided with plant illustrations without a comparison with the real world having been undertaken. That had only begun to change in recent decades. However, 397 Cf. G. W. Leibniz, J. G. Eckhart (Intro), Collectanea etymologica, illustrationi linguarum, veteris Celticae, Germanicae, Gallicae, aliarumque inserventia, Hanover, 1717, and Hildesheim, 1970. 398 Cf. A III,8 N. 241 (E1), pp. 614–626. 399 “Ich bin, wie ich vor einigen Wochen die Ehre gehabt deroselben meine reverence zu machen, durch dero de re medica et imprimis herbaria [ars] gegen mir geführte gelehrte discourse auf einige Gedanken gekommen, welche in beygehender kleinen dissertation kürtzlich entworfen, um solche Ew. Excellence scharfsinnigen Urtheil zu unterwerfen” (A III,8 N. 252, p. 652).

1699–1701

845

the new methods that strove for mathematical exactness were hardly suitable for general use, since the classification on the basis of flowers and fruit made long-term observation necessary. The advantage of roots, as a basis for a classification system was that they were constantly available. On the other hand, the fact that roots did not present any great number of variations made them unsuitable as a sole classification characteristic, although otherwise relatively easy to deal with. The central message of Gakenholz’s epistola was thus that, besides anatomy and chemistry, botany had a particular significance. And a special desideratum in the subject area of botany was the development of a taxonomy, or classification system, on the basis of parts of plants such as flowers, fruit, seeds, or roots. From Leibniz’s reply of April 23, 1701, it is clear that Gakenholz had picked out and developed suggestions introduced by Leibniz himself at their meeting some weeks earlier, including thoughts about the taxonomy of plants.400 Thus, from this letter, it is evident that a classification of plants according to a single criterion, such as the form of flowers, fruit, seeds, or roots, was for Leibniz insufficient. Combinatorics, and in particular his own dissertation on the combinatorial art viz. the Dissertatio de arte combinatoria of 1666, appeared to offer a way forward.401 In addition to mathematics, philosophical, and even juridical, categories also seemed to have a certain relevance for the development of botanical systematics and classification. That the criteria depended on the focus of the particular discipline, he illustrated by making reference to geometry, and in particular Ramist geometry, which was based on the teachings of Petrus Ramus (1515–1572). Despite its crudity, this form of geometry had enjoyed popularity in the late sixteenth-century and early seventeenth-century, providing a method of systematizing all branches of knowledge. It did not heed proofs like those of Euclidean geometry, and it judged figures on the basis of their form with practical geometry putting the focus on benefit or usefulness. While the knowledge derived from Ramist geometry was inferior to that obtained from Euclidean geometry, it was of benefit to those not capable of understanding higher mathematics. According to Leibniz, botany found itself on an analogous level, since the internal structures of the machines of nature, viz. of plants, were not really known. For Leibniz, therefore, further progress seemed to depend above all on improved knowledge of the inner workings of these machine-like entities. 400 Cf. A III,8 N. 253, pp. 653–662, and also “On botanical method (1701)” in: J. E. H. Smith, 2011, appendix 5, pp. [301]–310 (Introduction, note 191). 401 Cf. G. W. Leibniz, Dissertatio de arte combinatoria, Leipzig, 1666; reprint Frankfurt am Main, 1690, and also A VI,1 pp. 163–228.

846

Chapter 6

Organic bodies produced by nature, like plants and animals, represented machines for the fulfillment of certain duties and functions, such as nutrition, reproduction and – in the case of human beings – the preservation and perpetuation of knowledge. Here he wrote: Plants and animals and, in short, organic bodies which nature produces, are machines for the perpetuation of certain customized functions which relate to the propagation of the species or the provision of nourishment for the individual … And indeed it is manifest that the human body is a machine adapted to the perpetuation of contemplation.402 Just as one differentiated between theoretical and practical mathematics, one ought to distinguish between theoretical biology, on the one hand, and practical biology and medical practice, on the other hand. To theoretical biology belonged the classification of plants according to one or several criteria. Plants, animals and humans were, for him, machines that were adapted for certain tasks: humans for contemplation, and plants and animals, among other things, for helping humans in the fulfilling such tasks. The challenge was then to explain these tasks as well as the mechanisms involved in their realization. Leibniz had long been interested in the animate beings of earlier epochs, and in the science of these creatures. In 1696 and 1697, for example, he obtained intelligence about a trove of bones in Gräfentonna (Tonna in the territory of Thuringia).403 In his letter to Gakenholz on April 23, 1701, Leibniz then employed concepts from the field of comparative anatomy such as the comparison or collation of animals (“collatio animalium”), and from reproductive, developmental, and evolutionary biology, like the connection between plants and animals (“plantarum cum animalibus connexio”), or the transition from plants to large animals through intermediaries (“transitus a plantis ad animalia majora per intermedia”). He spoke of a link between plants and animals on the common basis of respiration, or respiratory organs, and of insects as an intermediate form between plants and animals, particularly with Jan Swammerdam’s Historia insectorum generalis (1669) in mind.404 His exact words here were: 402 “Plantae et animalia et, ut verbo dicam, Organica corpora, quae natura producit, sunt Machinae ad perpetuanda quaedam munia aptatae, quod faciunt tum propagatione speciei tum nutrimento individui  … Et humanum quidem corpus manifestum est machinam esse aptatam ad contemplationem perpetuandam” (note 400, p. 656); cf. also R. Andrault, 2011 (Introduction, note 209). 403 Cf. A I,12 N. 357 (p. 561), A III,7 N. 60 (p. 228) and Chapter 5 of the present work. 404 Cf. J. Swammerdam, Historia insectorum generalis, ofte algemeene verhandeling van de bloedeloose dierkens, Utrecht, 1669, and 1693 (second edition); H. C. von Hennin (transl.),

1699–1701

847

But just as the collation of animals is also usefully applied in other areas, as comparative anatomy shows, I continually commit myself so that there may be found, in particular in the lungs or respiratory organs, a certain connection and also continuity of the plants themselves with animals, not unlike a transition from plants to large animals through intermediaries, namely the insects exhorted by Swammerdam.405 A further influence on Leibniz thought in relation to the classification and, in particular, the reproduction of plants was no doubt the letter sent to him by Johann Heinrich Burckhard, on February 21, 1701, following a meeting between the two in Wolfenbüttel a few days earlier.406 In Leibniz’s letter to Gakenholz of April 23, Burckhard’s reference407 to the work of the Tübingen professor Rudolph Jacob Camerarius, entitled De sexu plantarum epistola (1694),408 was duly acknowledged with the words: New, and above all of great moment, will be the comparison of the plants [which] the new observations (if they be further confirmed) of the two sexes in plants will deliver, regarding which the gentleman Rudolph Jacob Camerarius, [who is] outstanding and exceedingly eager for knowledge of nature, is beginning to perform excellently and whom recently D. Burcardus, a young man excellently acquainted with these studies, began to follow, [and] who [for his part] wrote an erudite letter to me about this matter.409 In the letter of February 21, Burckhard had provided a detailed representation of the sexual organs of plants, and in particular of the phenomena of monoecy Historia insectorum generalis, in qua quaecunque ad insecta eorumque mutationes spectant, dilucide ex sanioris philosophiae et experientiae principiis explicantur, Leiden, 1685. 405 “Sed quemadmodum collatio animalium etiam in aliis partibus utiliter adhibetur uti Anatomia comparativa ostendit, usque adeo ut in pulmonibus potissimum vel respirationis organis reperta sit plantarum ipsarum cum animalibus connexio ac series quaedam, et velut transitus a plantis ad animalia majora per intermedia, ut sic dicam, insecta Swammerdamii monitu” (note 400 above, pp. 657f.). 406 Cf. A III,8 N. 213, pp. 552–555. 407 Cf. p. 554. 408 Cf. R. J. Camerarius, Ad mich. Bern. Valentini de sexu plantarum epistola, Tübingen, 1694. 409 “Novam etiam et magni inprimis momenti futuram comparationem Plantarum suppeditabunt novae (si porro stabiliantur) Observationes de duplicis sexus imitamento in plantis, de quibus agere maxime coepit egregius ex Naturae Curiosis Vir Rudolphus Jacobus Camerarius et prosequi instituit nuper Dn. D. Burcardus juvenis in his studiis cum laude versatus, qui eruditam super ea re ad me Epistolam scripsit” (note 400 above, p. 659).

848

Chapter 6

and dioecy, viz. of monoecious and dioecious plants. Leibniz, in his letter to Gakenholz of April 23, saw in the reproduction process in plants – described by Burckhard and set in connection with the reproduction of animals – a connecting element between the vegetable and animal kingdoms. Accordingly, the very fine pollen of seed-producing, or flowering, plants corresponded to mammalian sperm.410 Similarly, the style of a flower corresponded to the vagina in placental mammals, and the ovary at the bottom of the style corresponded to a mammalian ovary.411 The style went to the top of the flower and was opened by the heat of the sun, and by means of the buffeting of the wind, the pollen was transferred and applied. Fertilization occurred then when a kind of spirit coming from the pollen penetrated the ovary where either the eggs or the seeds were duly fecundated.412 In this context Leibniz recalled the rival theories of preformation of the Dutch microscopist Antoni van Leeuwenhoek, and of his compatriot the anatomist Theodor Kerckring. In the context of the ovist-animalculist controversy, Leibniz saw here a possible reconciliation, but his own position was close to that of the animalculist Leeuwenhoek and removed from that of the ovist Kerckring. The preformist theory assumed that the entire organism was preformed either in the sperm (the animalculist position), or in the egg (the ovist position), of the mammal and had only to unfold, or deconvolve itself, in the process of fertilization. Here again Leibniz saw a connection between the vegetable and animal kingdoms, and so he wrote: This, if it be further proved by observation, will greatly support the reconciliation of the doctrine of Kerckring with that of Leeuwenhoek, which has always appeared to me to be more probable. For it has long since become possible for something subtle and organic, which can already be designated by the name of plant or animal, to direct the male seed to the female egg, where it is transformed as if on its own earth and undergoes through nourishment a major development under the name of generation to produce a foetus.413 410 “Nam in polline subtilissimo florum quaerunt masculi seminis analogiam” (p. 659). 411 “Adesse … capsulas ovario foemineo comparandas: A capsula exire stylum vel analogum aliquid tanquam uteri vaginam” (pp. 659f.). 412 “Cujus ad summitatem ex flore per solis calorem aperto, concutientis venti ministerio, se transferat applicetque pollen: Ex pollinis autem granulis spirituosum aliquid perductum ad ovarium, ut sic dicam, vel siliquam penetrare, atque ova vel semina illic foecundare” (p. 660); cf. also J. G. O’Hara, 2016b (Introduction, note 211). 413 “Quae si observatione porro comprobabuntur, magis firmabunt conciliationem Kercringianae atque Leewenhoekianae doctrinae; quae mihi semper verisimillima visa

1699–1701

849

Following his correspondence with Gakenholz in 1701, Leibniz continued to refer to the theory of preformation in his learned correspondence. Thus, for example, in a letter to queen Sophie Charlotte and John Tolland in early December 1702, Leibniz explained his views on preformation,414 referring to Swammerdam’s Historia insectorum generalis (1669),415 and Leeuwenhoek’s article “Observationes de natis e semine genitali animalculis”(1677/78).416 Leibniz also referred to Leeuwenhoek, and admitted his penchant for the latter’s interpretation of theory of preformation, in his major philosophical writings composed between 1704 and 1714, notably in the Theodicy (1710),417 the Monadology (1714),418 and in the Nouveaux essais (1704). In the latter work he expressed the view that Leeuwenhoek had enhanced the status of the male sex, and accordingly degraded the female sex which merely provided a nutrient medium for the seed, writing that: “Mr Leeuwenhoek has upgraded the masculine sex and downgraded in turn the other sex, as if it only had the function of a nutrient earth for the seeds, providing them with a place of rest and nourishment”.419 Finally, on August 5, 1715 – almost forty years after their meeting in Delft in November 1676  – Leibniz commenced a direct correspondence with Leeuwenhoek, and a total of eight letters were exchanged between the two before Leibniz’s death on November 14, 1716. A final letter of Leeuwenhoek, dated November 17, was written before he learned of Leibniz’s passing.420

est. Nempe subtile aliquid dudum organicum, quod jam plantae vel animalis nomine censeri possit, ex masculo semine in foeminea ova pervenire, atque illic tanquam in propria terra transformatum et nutrimento in majus elaboratum generationis nomine in foetum prodire” (p. 660). 414 Cf. A I,21 N. 410, pp. 722f. 415 Cf. J. Swammerdam, Historia insectorum generalis, ofte algemeene verhandeling van de bloedeloose dierkens Utrecht, 1669 and 1693. 416 Cf. A. van Leeuwenhoek, “Observationes de natis e semine genitali animalculis”, Philosophical Transactions, vol. 12, no. 142, (December 1677–February 1678), pp. 1040–1043. 417 Cf. G. W. Leibniz, Essais de theodicée sur la bonté de Dieu, la liberté de l’homme et l’origine du mal, Amsterdam, 1710, in particular Preface and § 90f. 418 Cf. G. W. Leibniz, Lehr-Sätze über die Monadologie, Jena, 1720, in particular § 73–76. 419 “Mr Leewenhöeck a rehabilité le genre masculin et l’autre sexe est degradé à son tour, comme s‘il ne faisoit que la fonction de la terre à l’egard des semences, en leur fournissant le lieu et la nourriture” (A VI,6, pp. 316f.). 420 Cf. Leeuwenhoek: Palm, vol. XVII, London, 2018, in particular Letters 316–320, 322, 323, 326; J. G. O’Hara, 2016a, and A. Becchi, 2016 (Introduction, note 212).

850

Chapter 6

13 Medicine Medicine continued to play an important role in Leibniz’s correspondence between 1699 and 1701, particularly in the letters exchanged with Magnus Gabriel Block, Jacques Bouquet, Alexander Christian Gakenholz, Freiedrich Hoffmann, Bernardino Ramazzini, Johann Andreas Stisser and Rudolf Christian Wagner. Medicine received a critical appraisal in the aforementioned open letters addressed to Leibniz by Gakenholz and Stisser. In Gakenholz’s letter on the emendation and the proper organization of medicine, entitled Ad illustrem atque excellentissimum virum Dominum Godefr. Guilielmum Leibnitium … epistola … de emendanda ac rite instituenda medicina,421 the author and correspondent complained that the subject was still in its infancy while other sciences, and mathematics in particular, had made great strides. He put the blame on a superstitious veneration for the ancients, as well as wrong priorities in medical studies and training. Gakenholz propagated an anatomy of fluids, and he pleaded for the reform of the system of anatomical or postmortem examination, that ought to be guided by the understanding that the body should be viewed simply in the context of the vessels and organs. One should begin with the circulation of the blood, with particular interest being paid to the arteries, veins, and the heart chamber, and avoid incisions and pay attention to connectivity and interrelation. He himself had tested injections, and re-injuries, of vessels in corpses. Experimental infusions and blood transfusions could be undertaken with animals. Gakenholz emphasized the role of chemistry in medicine. Physicians should study this subject in order to understand the processes in nature. At the same time, he criticized the excrescence of chemical pharmacy, which had produced a multitude of salts where, he reckoned, a single specimen might be sufficient. He recommended the study of plants with regard to their powers of healing, but he considered the established methods not to be very meaningful. Besides color, odor, taste, and combustion or incineration properties, the reaction of plant sap with blood had been investigated in order to establish the effect on the human body. Gakenholz, for his part, suggested that there were differences in the reactions with arterial, and with venous blood. Furthermore, the effectiveness of such a medicament – following intake and digestion – was for him not at all clear. On April 23, 1701, Leibniz excused himself for entering solely into Gakenholz’s further remarks on botany, claiming to be unable to contribute any further to the discussion of medicine. However, he pointed out his special interest in 421 Cf. A III,8 N. 241 (E1), pp. 615–626 (and note 398 above).

1699–1701

851

public health, and he acclaimed his proposed project with Hoffmann for the collection (and annual publication) of meteorological-medical observational data.422 In the same month, April 1701, there appeared a summary and review in German of Gakenholz’s work in Leibniz’s house journal Monat[h]licher Auszug.423 In this review, the writer – perhaps Johann Georg Eckhart – outlined Gakenholz’s criticism of the existing system of medical studies. There the reader learned that, according to Gakenholz, the core of medical studies should be anatomy, or the science dealing with the structure of plants, animals and the human body, which was to be considered as a machine or automaton. The heart was the prime mover of the machine, and anatomy served the purpose of the meticulous study of the vessels emanating from the heart in their natural state. Thus, the circulation of the blood would be revealed and, for example, the passage of blood from the heart through the largest artery, namely the aorta, and then through the body to the kidneys would be illustrated. Thus, the reviewer wrote: Should however the human body be a machine or automaton, then it would be necessary first of all that one occupied oneself with this and how it was put together, which is done through [the study of] anatomy. This must be undertaken according to the natural method, [by] starting with the heart as prime mover, from which all vessels emanate, and then [by] following and carefully examining these vessels, cutting as little as possible into pieces and leaving everything if possible in its natural state. In this way one would recognize how the parts fit together and see e[xempli] g[ratia] how the blood comes from the stalks or shafts of the large artery [the aorta] through the emulgent vessels [two large arteries and veins] into the kidneys.424

422 Cf. A III,8 N. 253, pp. 660–662. 423 Cf. A III,8 N. 241 (E2), pp. 626–629. 424 “Wenn  … der Menschliche Leib aber eine Machine oder Automaton sey, so müsse man erstlich nothwendig dieselbe und wie sie zusammengesetzt sey, wohl inne haben; welches durch die Anatomie geschehe. Diese müsse … nach der natürlichsten methode gehen, vom Hertzen als primo mobili, daraus alle Gefässe fliessen, anfangen: die daraus rinnende Gefässe verfolgen und sorgfaltig examiniren: Wenig in stücken schneiden und alles nach möglichkeit in seinen natürlichen stande lassen. Auf diese weise würde man erkennen wie die theile zusammen hangen und z. e. sehen, wie das Blut aus den struncke der grossen Arterie durch die emulgentes in die Nieren komme” (p. 626).

852

Chapter 6

The blood, and other body fluids, were the focus of the anatomy of fluids and here experimental science, and particularly chemistry, had a special role to play. Aspirants in the field of chemistry ought to be mainly concerned with the subject as revealed in the works of nature, with, for example, the chemical reactions of life, and the seat of most illnesses, being found in body fluids. Thus the reviewer continued: The other part of the human body is made up principally of the fluid parts [namely] the blood and serum as well as the vital (or animal) spirits, since the most diseases arise from their constitution. For this reason the anatomy of fluids is very necessary, but also very difficult because they are not to be recognized with the eyes but rather through all kinds of experiments and chemistry. For [indeed] anyone wanting to study chemistry would have to mainly learn through these [the progression of] nature in its works, [like] things of natural creations, destructions and changes.425 Stisser’s open letter of February–March 1700 addressed to Leibniz was a passionate plea for a pronounced inclusion of chemistry in medicine, and in the study of medicine.426 To those hostile to chemistry – whom he characterized as “misochemists” (“Misochymici”)427 – he pointed out the omnipresence of the subject. Foodstuffs, like bread, beer, or wine, were prepared with the help of chemical processes, just as with the pretended non-chemical medicaments. His argumentation was founded, on the one hand, on Hippocrates and numerous other deceased and living authorities and, on the other hand, on case studies in which wrongly prepared medication had brought about undesired reactions. Like Gakenholz and other medical authors, Leibniz – in his letter to Stisser (probably) on April 25, 1700428 – complained about the enormous multiplicity of pharmaceutical products, but he was otherwise in agreement with Stisser. To abstain from using chemical medicaments would of course 425 “Das andre theil des Menschlichen Leibes machen die partes fluidae das Blut und serum wie auch die spiritus animales vornemlich aus, als aus deren constitution die meisten kranckheiten fliessen. Daher die Anatomia fluidorum sehr nöthig, aber auch sehr schwer sey, weil sie nicht mit den Augen, sondern durch allerhand experimenta und die Chymie müste erkandt werden. Denn wer die Chymie studieren wolle, müsse hauptsächlich durch sie die Natur in ihren wercken, der Natürlichen dinge erzeugungen, vernichtungen und veränderungen und deren uhrsachen erlernen” (p. 627). 426 Cf. A III,8 N. 131, pp. 337–355 (and note 362 above). 427 Cf. p. 338. 428 Cf. A III,8 N. 163, pp. 422–426.

1699–1701

853

mean forgoing great advantages of the natural world. More effective medication against illnesses that affected the body fluids could, in Leibniz’s opinion, be found either solely by accident, or as a result of advances in chemistry. By 1699, accounts of autopsies had long been a source of information for Leibniz in the field of anatomy. The post-mortem examination of corpses was important not only for obtaining new anatomical knowledge, but it also served for the development of examination and treatment methods for physicians, and even for obtaining medicaments and medicinal, or pharmaceutical, products. In this context then, Leibniz came into contact with medical cannibalism that was then in widespread use.429 Thus, on October 30, 1699, he requested information from Papin about the so-called “king’s drops”, which he had learned about from a traveler, an unnamed English musician who had been to Muscovy, and who had shortly before come from Kassel. He related that the electress Sophie, at the court in Hanover, had also heard wonderful or miracle stories about this medicament. Thus, he wrote to Papin from Hanover: There passed through here an Englishman coming from Cassel, a musician among other things who has been to Muscovy, who spoke emphatically of the king’s drops or the drops of the king of England, about which he told us wonders. Madame the electress confirmed his reports, partly after having heard panegyrics [about the substance]. Should you have more detailed information, Sir, I would ask you to share it with me.430 The basis of these drops was a recipe for the liquefaction of material taken from inside human skulls, often from executed prisoners. The distillate has found a place in the history of medicine under the name ‘Goddard’s drops’ – after the discoverer Jonathan Goddard – or otherwise, as in Leibniz’s correspondence, as “king’s drops” after the Stuart king Charles II, who carried out the distillation in his private laboratory. Whether or not Leibniz knew what kind of medicament was involved is not clear. At all events Papin’s response, on December 3, 1699, was short and decidedly skeptical about what he called “ces sortes de remedes”; thus he wrote:

429 Cf. R. Sugg, 2011 (Introduction, note 222), in particular chap. 2, chap. 8, and the Conclusion. 430 “Il passa icy un Anglois venant de Cassel Musicien d’ailleurs et qui avoit esté jusqu’en Moscovie, qui parloit fort des Kings drops ou gouttes du Roy d’Angleterre, dont il nous disoit des merveilles. Madame l’Electrice confirmoit ce qu’il disoit, en partie en ayant oui faire des grands eloges. Si vous en sçavés des particularités, Monsieur, je vous supplie de m’en faire part” (A III,8 N. 81, pp. 244f.).

854

Chapter 6

During the time I spent in England I certainly heard talk of the king’s drops, but I never used them myself, and I am certainly inclined to defy or affront [the use of] these kinds of remedies, [and] this above all when they are attributed to the glory of persons of such standing likely to attract flattery.431 Also the remedy “mumia”  – a substance obtained from pulverized Egyptian mummies  – is referred to in Leibniz’s correspondence. Wagner related, on March 15, 1701,432 that he had, as a result of clumsiness, suffered a breast injury, and had then obtained, as a remedy from the apothecary, the following substances: crab’s eyes, dragon’s blood, prepared mumia, prepared native cinnabar and diaphoretic antimony.433 A note which the surgeon Jacques Bouquet handed to Leibniz on August 5, 1701, provides an example of the use of parts of corpses for therapeutic purposes. A woman from the French émigré community in the town of Hameln had formerly had a wart, or a swelling, on her hand. After a variety of plasters had proved worthless, it was recommended that she rub the swelling with the finger of a corpse, where the person had died following a lengthy illness. Some years earlier, while in Hamburg, a neighbor of a general, whom she had served there as a governess, died. Alas, this first opportunity to test the proposed treatment method proved unsuccessful. Later, however, the general himself died, and she tried the procedure again of rubbing the swelling with the finger of the corpse, and – according to the note Leibniz received – was permanently cured in a short time. The text of the note was as follows: One advised her to apply to her hand the corpse of a person who had died after a long illness, and having experienced that a neighbor of a general of Hamburg, whom she served in the capacity of a governess of children, had died, she went there and applied the hand of the deceased to her growth or swelling, rubbing it with this hand for quite a while, but there ensued a period of time in which there was no sign that the growth would disappear. But when the General himself with whom she was staying died, she carried out the same procedure with the hand of the deceased 431 “Dans le temps que J’êtois en Angleterre J’ay bien oui parler des King’s drops; mais Je ne m’en suis jamais servi: et J’ay beaucoup de penchant à me deffier de ces sortes de remedes: surtout quand on en attibue la gloire à des personnes d’un rang proper à attirer des flatteries” (A III,8 N. 88, p. 257). 432 Cf. A III,8 N. 222, p. 572. 433 Namely “Krebssteine”, “Drachenblut”, “präparierte Mumia”, “präparierten Bergzinnober”, “Schwitzspießglas”.

1699–1701

855

for a second time, and on the following day in the morning her growth had disappeared, and has never reappeared since, that is over a period of 8 or 10 years.434 Both in the use of medicaments derived from human remains (such as the “king’s drops”), and in the application of corresponding therapies (like in Bouquet’s communication), the death struggle and the mortal agony of the deceased was an essential aspect of the presumed medicinal benefit. The agonal state of tortured and executed prisoners, of soldiers in their death throes on the battlefield, or of long-suffering patients, could – according to the line of rational thought behind the method – lead to the production of substances having curative or immunization effects, and which might serve as ingredients for medication. The prevailing positive attitudes towards phlebotomy, or bloodletting, were perhaps akin to those relating to medical cannibalism. The bloodletting might thus contribute to improved defense mechanisms of the body under attack. Leibniz received regular reports from Wagner  – who also worked as a physician – concerning both his own ailments, as well as the illnesses he was confronted with, and the therapies applied. In the spring and summer of 1701, Wagner reported about a female patient of his from the town of Halberstadt, who had a swelling or tumor on her cheek, and which he illustrated in a drawing.435 He was able to provide relief at first and the swelling declined. However, after visiting the market in Helmstedt with friends, and joining a night-long celebration, she fell head over heels down a stairway thus undermining the recovery process, according to Wagner. In 1699 and 1700, several university professors at Helmstedt died in quick succession, whereas others suffered from chronic illnesses. Thus, Wagner reported to Leibniz on April 21, 1699, about the recurring hemorrhages experienced by the hemophiliac Johann Andreas Schmidt, who had to observe a strict diet.436 A little later, Wagner assisted the medical professors Heinrich 434 “On luy consseilla d’y appliquer la main d’un cadavre mort d’une longue maladie, et s’etant Rencontré qu’un voisin du Jeneral de Hambourg, chés quy elle demeuroit, en qualité de gouvernante des enfans, mourut, elle y alla et se mit la main du mort sur sa Tumeur, et la frota avec cette main assés long-Tems, mais elle fut quelques Tems sans s’appercevoir que sa Tumeur diminuasse, mais le Jeneral mesme chés quy elle demeuroit estant mort, elle fit une seconde fois la méme opperation avec la main du mort, et le lendemain au matin sa Tumeur estoit disparüe, et n’en a Rien appercüe du depuis, ce sont Il y a 8 ou 10 ans” (A III,8 N. 286, p. 738). 435 Cf. A III,8 N. 234 (p. 605), N. 273 (p. 711) and N. 281 (p. 729). 436 Cf. A III,8 N. 30, p. 99.

856

Chapter 6

Meibom and Friedrich Schrader in the treatment of a fourteen year old who complained about hoarseness, coughing, intense headache, as well as the accompanying fear of asphyxia. On May 5, 1699, Wagner elaborated for Leibniz his explanation of the course of the illness, and he told that an opening of the temporal artery had brought little relief.437 Then, on May 16, Leibniz recalled, in this context, a new treatment method for headache involving the opening of the temporal artery about which he had been informed previously by a “virum insignem”, namely the “eminent gentleman” Johann Gebhard Rabener. On this occasion he wrote to Wagner: It should be urgently asked if the youth among you, who was first afflicted with hoarseness and coughing and soon thereafter was in danger of suffocating, and finally was troubled by intense head-ache, would not feel alleviation by the application of medicinal leeches [or bloodsuckers]. For I remember that a prestigious gentleman experienced relief from a most persistent migraine by this method, and raised hope accordingly that the opening of the temporal artery had been of use to some extent.438 On March 23, 1700, Wagner reported that the renowned Meibom had been suffering for a number of days with a not-insignificant illness and, being threatened with suffocation, he had already indulgently abided his time. However, the affliction developed into a pleurisy, the treatment of which demanded the immediate application of venesection.439 He had first contracted his illnesses, Leibniz was told, through contact, during a night visit, with the vice rector of the university, Christoph Tobias Wideburg, whom he was treating for a slumbering fever.440 Bloodletting proved to be of no avail in the case of Meibom, and three days later (on March 26) Wagner reported his passing on that day, and he explained in detail the course of the illness that had led to the professor’s demise.441 Just two weeks later (on April 8), Ilse Stisser (née Petersen), 437 Cf. A III,8 N. 38, p. 114. 438 “Rogitandum an juvenis apud vos primum raucedine et tussi mox periculo suffocationis, demum intensissima cephalalgia vexatus non sit sensurus levamen ab applicatione sanguisugarum. Nam memini virum insignem a pertinacissima Hemicrania hoc uno levamentum sensisse, et spem juvat, quod sectio arteriae temporalis profuit nonnihil” (A III,8 N. 42, pp. 123f.). 439 “Exc. Meibomius noster morbo haud levissimo jam per aliquot dies detinetur, periculo suffocationis minitato, Mitior tamen jam degit. In pleuritidem abiit malum, cui medendae statim in principio sibi venam secari jussit” (A III,8 N. 143, p. 383). 440 “Primordia morbi sensit ex eo cum Dnum D. Wideburgium, vicerectorem febri continua correptum media nocte visitasset” (p. 383). 441 Cf. A III,8 N. 145, p. 386.

1699–1701

857

the wife of Johann Andreas Stisser, died in childbirth leaving her distressed husband with six children. Stisser himself then suffered a collapse resulting from grief and exhaustion, as Wagner reported to Leibniz on April 10.442 Furthermore, Wagner reported on this occasion that another colleague, the professor of eloquence Caspar Cörber, had fever and that his sallow complexion was frightening. Cörber survived just a week with this condition. That the news of the death of Stisser himself (on April 21) had devastated the correspondent is hardly surprising. Wagner himself had already been suffering from headache and lassitude, a condition which was then aggravated by hot flushes and states of anxiety. The narrative of his short but intense illness, accompanied also by a fear of dying, was related by Wagner to Leibniz in great detail, as soon as he began to feel better again a few days later (on April 27). His recovery, he reported, had come following consumption of large quantities of medicinal beer made from Scorzonera (or “Schwarzwurzeln”).443 The study of diseases was a particular interest of Leibniz’s internationally most renowned correspondent in the field of medicine, namely Bernardino Ramazzini. In replying to Leibniz’s letter of April 22, 1699,444 Ramazzini announced, on February 24, 1700, his forthcoming tract about the diseases of workers,445 in which he was, as he explained, aiming among other things at disposing of flippancies or frivolities.446 Leibniz, in his letter of March 18 to Ramazzini, then referred to works on the ailments of miners and pitmen, both by Georg Agricola who had been most knowledgeable not only in res medicae but also in metallurgy or “res metallariae”,,447 and above all by the physician Samuel Stockhausen from Goslar in the Harz mining district, who had published a work entitled Libellus de lithargyrii fumo noxio morbifico (1656).448 The latter had described the lung diseases that occurred among miners, namely the pulmonary disease “Bergsucht”, or occupational lung cancer – later to be called “Schneeberg disease”, following the vicissitudes of miners in the Schneeberg district of Saxony in the nineteenth century  – and the pulmonary phthisis, 442 Cf. A III,8 N. 154, p. 404. 443 Cf. A III,8 N. 164, pp. 427f. 444 Cf. A III,8 N. 31, pp. 100f. 445 Cf. B. Ramazzini, De morbis artificum diatriba, Modena, 1700. 446 “Tractatum meum de morbis Artificum inter caeteras meas nugas abjeceram” (A III,8 N. 130, p. 336). 447 “qui ipse erat Medicus reique metallariae scientissimus” (A III,8 N. 139, p. 373). 448 Cf. S. Stockhausen, Libellus de lithargyrii fumo noxio morbifico, ejusque metallico frequentiori morbo vulgo dicto die HüttenKatze oder HüttenRauch: cum appendice de montano affectu asthmatico metallicidis familiari, quem Germanica lingua appellamus die Bergsucht oder BergKranckheit, Goslar, 1656.

858

Chapter 6

or consumption, known as “Hüttenkatze”. Leibniz’s words to Ramazzini on March 18, 1700, were as follows: Just as you treat the diseases of workers, regarding which you are writing a fine tract, it would be no bad thing to add the maladies of metal workers, who operate in the mines and metal foundries. We have observed that the diggers in ours [viz. the mines and foundries], who are particularly occupied at dry locations in shattering stones or rocks, laboring as other stonecutters do, contract asthma, which our medics call mountainous or mining asthma, in German berg-sucht; they are in point of fact occupied in mines or foundries where lead is being disaggregated or poured out, [and] from the lead fumes obstructions (disabilities) or excruciations are produced which are commonly called Hütten-Kazze, regarding which kind of disease Stockhausen, a medic from Goslar, has published a dedicated little book. Something of this kind is also to be found, I believe, among [the works of] Georg Agricola, who was a medic himself, and also most knowledgeable in metallurgy.449 The project for the annual publication of medical-meteorological observations pursued by Leibniz and Hoffmann, under the aegis of the Berlin Society of Sciences, was of course inspired above all by the ephemerides which Ramazzini had published (in 1690, 1692 and 1695) – not least with the encouragement of Leibniz – for the years from 1690 to 1694, and in which he described the epidemic outbreaks that had occurred around Modena in those years. The publications for the years 1695 and 1696 failed to appear which motivated Leibniz to enquire about the continuation of the series in his letter of April 22, 1699.450 Replying, on February 24, 1700, Ramazzini justified the interruption on the grounds that the data collection had proved cumbersome for physicians, not least due to the lack of remuneration, but also because there had been no 449 “Ubi de morbis artificum ages, de quo argumento libellum Te molitum scribis, non male addes mala metallariorum, qui in fodinis et fusoriis officinis agunt. Notamus in nostris fossores, qui praesertim locis siceis in saxis frangendis sunt occupati, laborare ut alii lapicidae, asthmatis genere, quod Medici nostri vocant Asthma montanum, germanis berg-sucht, qui vero in officinis occupantur, ubi plumbum funditur, ex fumo plumbi laborant obstructionibus et torminibus quod vulgo vocant Hütten-Kazze, de quo morbi genere Stockhusius, Medicus Goslariensis peculiarem libellum edidit. Quaedam hujus modi apud Georgium Agricolam, qui ipse erat Medicus reique metallariae scientissimus, credo reperientur” (note 447 above, p. 373). 450 “An pergas in Historia Annua Medica, intelligere aliquando gratum erit” (A III,8 N. 31, p. 100).

1699–1701

859

new notable epidemic occurrences in the meantime.451 In a previous letter, on June 17, 1699,452 Ramazzini had announced the republication of his collected ephemerides in a single volume, which, alas, only appeared in 1714.453 Leibniz also advocated data collection even in times (which were rare) when there were no special occurrences; at least one would then have the assurance that no change had taken place, as he wrote in his letter of March 18, 1700.454 Leibniz’s thoughts on the idea of a rational medicine had previously found expression particularly in his correspondence the “medico-mathematicus” Domenico Guglielmini.455 Between 1699 and 1701, it was above all to Friedrich Hoffmann that Leibniz turned for progress in this area. Hoffmann, in a work of 1699, had picked up on the public part of the metaphysical controversy between Leibniz and Johann Christoph Sturm.456 Hoffmann’s dispatch of his work – in particular the dissertation over which he had presided entitled Dissertatio inauguralis physico-medica de natura morborum … mechanica457 – to Leibniz, in September 1699, was to be the overture to their correspondence.458 In his reply, on October 7, Leibniz treated Hoffmann’s work in detail, and he commented on the mechanical world picture, on substance, and on the soul.459 However, he quickly changed over to his ideas on the representation of nature. Since one could not immediately establish the mechanism of nature from the Cartesian principles of magnitude, figure and motion, one ought to reduce composite principles to simpler ones, in the same way that chemists reduce many things to secondary principles. However, he criticized their oftentimes vague terminology. For principles firm concepts should be chosen, and so he wrote:

451 “Ephemerides meas Medicas fateor ad aliquot annos mihi intermissas fuisse  … Intermissionis causa fuit quod in quinque Annorum Constitutionibus, quae Medicis ob lucri defectum nefastae fuerunt, nihil singulare contigerit, in hoc quoque aliqua observatione dignae sunt” (A III,8 N. 130, p. 336, and note 446 above). 452 Cf. A III,8 N. 51, p. 153. 453 Cf. B. Ramazzini, Constitutionum epidemicarum Mutinensium annorum quinque, Padua, 1714. 454 “arbitrorque etiam cum nihil singulare occurrit (quod tamen raro fiet), tamen continuationem mereri … et cum nulla sunt bella aut memorabilia, vel ut hoc ipsum sciamus, nihil mutationis contigisse” (cf. notes 447 and 449 above, p. 372). 455 Cf. the conclusion of Chapter 5 of the present work. 456 Cf. II,3, pp. XLIX–LII, and III,8, p. LIIf. 457 Cf. F. Hoffmann (Praes.); S. Cellarius (Resp.), Dissertatio inauguralis physico-medica de natura morborum medicatrice mechanica, Halle, 1699. 458 Cf. A III,8 N. 76, pp. 229f. 459 Cf. A III,8 N. 79, pp. 237–240.

860

Chapter 6

Hence I expect from you at some point elements of a rational medicine, [namely such] that are not overly insistent for intellectuals regarding the use of the remote arts, as is found among Cartesian medics, nor overly entrenched in the escapades of the imagination, as is cherished among chemists, but which report intelligible causes of sensible things where, be they admissible or non-admissible, one can at least derive useful effects from them, which [have] a certain sense although not yet reduced to causes.460 In this sense then, Leibniz desired a contribution from Hoffmann towards the development of a rational medicine. Alas, he did not live to see the publication of Hoffmann’s multi-volume work entitled Medicina rationalis systematica (1718–1734).461 460 “Itaque aliquando a Te expecto quaedam rationalis Medicinae elementa non nimis insistentia intellectualibus ab usu artis remotis, ut fit apud Medicos Cartesianos, nec nimis imaginationis ludibriis affixa, ut fieri solet apud Chemicos; sed quae causas intelligibiles afferant rerum sensibilium ubi licet, aut ubi non licet consequentias saltem utiles effectuum ducant ex iis, quae sensu certa sunt, etsi nondum ad causas reducta” (p. 239). 461 Cf. F. Hoffmann, Medicina rationalis systematica, 6 vols., Halle, 1718–1734, and the English translation: A. Duncan (ed.) and W. Lewis (trans.), A System of the practice of medicine, London, 1783 (Introduction, note 234).

Epilogue: Core Theses and Conclusion itaque in re obscura et controversa, is sequendus est, quem ipsa rei natura confirmat.1 Leibniz to Georg Wolfgang Wedel, September 9, 1699

⸪ 1

The Ten Theses

Leibniz’s correspondence in science, technology and medicine, in the last quarter of the seventeenth century and at the turn of the eighteenth century, provides a panorama of the world of science a third of a millennium ago. It resembles a maze, a labyrinth or puzzle, with more than two thousand pieces, that reflects the ideas and thoughts of Leibniz himself, of his correspondents, more than 200 in number, and of the three hundred and more individuals, referred to in their communications. Leibniz’s words to Jacob Bernoulli in early April 1698 “Scripsi innumera, et de innumeris, sed edidi pauca et de paucis” – the leading quotation of the Introduction of the present work – epitomize the significance and multifariousness of his correspondence.2 We find here a series of ideas, concepts, theories and methods arising, whose realization, completion or confirmation would take another century and more. These included the differential and integral calculus in mathematics, the “vis viva” concept, or that of the force represented mathematically by the product of mass and square of the velocity, the concept of “progress” (or momentum) represented mathematically by the product of mass and velocity, the concept of velocity (in this context) as an entity having both magnitude and direction, the laws of conservation of both “vis viva” and of “progress”, the concept of “actio”, or action, theories of gravitation and planetary motions, particle and wave theories of light and optics, the mathematization of mechanics, engineering and technology, the emergence of the genre of ‘civil engineer’, innovatory ideas in energy conversion and in the uses of water and wind power, of battery power 1 Cf. A III,8 N. 74, p. 224. Translation: and so, in matters obscure and controversial, that should be followed which is confirmed by the very nature of the matter itself. 2 Cf. A III,7 N. 88, p. 364. Translation: I have written countless texts on countless topics, but I have published but sparsely on a sparsity of such topics.

© Koninklijke Brill BV, Leiden, 2024 | doi:10.1163/9789004687363_009

862

Epilogue: Core Theses and Conclusion

and of pumped storage in power supply, the power of fire and steam and the corresponding enginery, early notions of a submarine vessel, as well as of a steam-driven marine vessel, pneumatic engines, “explosion” or combustion engines, adiabatic expansion in thermodynamics, ideas of social change following engineering and technological progress, development of calculating machines and cryptography, the earth’s geological formation and development, the origins and relationships of peoples and languages, rational approaches to alchemy and analytical chemistry, the evolution of biological species, the development of a rational medicine, social and occupational health issues, states of health in populations, air pollution and toxicity, infectious diseases, social and even veterinary epidemiologies, the organization of education and science, pedagogical, school and academy reform projects, the education of women – as projected by Daniel Defoe in 1697 – and the emergence of female mathematicians and mathematical practitioners (like Charlotte de L’Hospital), and much more besides. Leibniz’s correspondence reveals that – in the context of his biographical development – his recurrent interests in a range of areas in science, technology and medicine, advanced by leaps and bounds throughout the twenty-five year period under consideration. The following words – which Leibniz wrote to Rudolf Christian von Bodenhausen, on December 30, 1693 – epitomize his behavior in many respects: “Mir gehet es wie dem tiegerthier, von dem man sagt, was es nicht im ersten andern oder dritten sprung erreiche, das laße es lauffen”.3 Here Leibniz compared the observed behavior of the tiger animal – involving limited strikes and the economization of reserves in pursuing its prey – to his own. He was referring to what would later be called “Competitive Exclusion and Functional Redundancy in Tigers”, and to his own self-confessed excursiveness and identification with the animal in question, namely the ‘panthera tigris’.4 In this vein then, Leibniz’s saltatory prowess, or habit of hopping, as it were, from problem to problem, extended to the ten subject areas in science, technology and medicine, in which the basic tenets of his scientific world 3 Cf. A III,5 N. 201, p. 672. Translation: I am like the tiger, the animal of which it is said that the hunt prey, which it fails to grab in its first, second or third leap, it allows to escape. 4 As ambush predators, tigers hunt by stalking followed by very short rushes (chases rarely extend beyond 150 m) with high success rates. In effect, these high success rates, short chase distances, and long intervals between kills result in low energy expenditures; cf. for example, J. Ray, K. H. Redford, R. Steneck, J. Berger (eds.), Large carnivores and the conservation of biodiversity, Washington, Covelo, London, 2005, and in particular pp. 200–203 (“Competitive exclusion and functional redundancy in tigers and wolves”); R. Tilson, P. J. Nyhus (eds.), Tigers of the world: The science, politics and conservation of panthera tigris, Amsterdam, Boston, Heidelberg, London, 1987 (and 2010).

Epilogue: Core Theses and Conclusion

863

view found expression. For each of these subject areas, a thesis is presented here, and is based on an expression, formulation or utterance of Leibniz, as found in his correspondence, and which epitomizes a central line of thought of his in relation to that subject area. The ten subject-related theses are followed by a concluding thesis, which underlines Leibniz’s commitment to the development of rational scientific thought in the last quarter of the seventeenth century, and to his adherence to the principle of the detachment of science from religion. This – combined with an autobiographical self-characterization of his tiger-like vivacity and sprightly manners – yields the unofficial title of this book, which is expressed in the final sentence of this epilogue, providing, as it were, a final punctuation mark, like a period or full stop, a perfect cadence or complete harmonic and melodic closure of the work. 1.1 The Field of Mathematics In a letter from the end of June, or the first half of July, 1696, Leibniz wrote the following words to Detlev Clüver: “Tout ce que nous trouvons par nos methods est justifié encor par les experiences autant que le reste de la Geometrie”.5 Thus, Leibniz underlined here his conviction that his calculus, and indeed all of mathematics, was rooted in experience (or experiment) in the physical world. This then represents the first thesis, following an idea, or line of thought, that was expressed as a clear statement by Leibniz in his correspondence. In his first seven years in Hanover, the newly created infinitesimal calculus developed into a widely diversified discipline with multifarious – in particular physical  – applications. In the course of this development came the fundamental publications on the differential and integral calculus (in October 1684 and July 1686, respectively). There then followed, in rapid succession, a series of journal articles in which physical themes were treated mathematically, and quantitatively, and the public controversy about the true measure of force brought Leibniz to prominence in learned circles. Also in connection with this dispute stood the first mathematical competition, initiated by Leibniz, namely the challenge to solve the isochrone problem, which called for the determination of the curve along which a body, descending in the sphere of terrestrial gravity, reaches a datum, or base line, in the same period of time regardless of the point on the curve from which the descent began. The publication of Leibniz’s solution of the problem  – the isochrone curve or semi-cubic parabola  – in April 1689, represented, accordingly, a landmark in the protracted dispute with 5 Cf. A III,6 N. 247, p. 810; Translation: All that which we find by our methods [in calculus] is justified also by practical experience or experiment, just like in the rest of mathematics.

864

Epilogue: Core Theses and Conclusion

the Cartesians (in particular with François Abbé de Catelan). After Leibniz had enunciated the isochrone problem, in the Nouvelles de la République des Lettres in September 1687, his correspondence with Christiaan Huygens was revived, in January 1688, with a letter he wrote on seeing Huygens’ solution of the problem in the October number of the same journal. Having established agreement between Huygens’ and his own solution, Leibniz sketched his method for the determination of this curve. The curve in question was the desired solution to the first of a series of mathematical contests, or challenge questions, conceived to demonstrate the superiority of his infinitesimal calculus. Jacob Bernoulli, who – in addition to Leibniz and Huygens – had solved the isochrone problem, combined his solution in May 1690 with a retaliation challenge question, namely to mathematically determine the form of the catenary, or hanging chain curve. In July 1690, Leibniz, who immediately solved the problem for himself, set the turn of the year 1690–91 as a deadline for other mathematicians to submit their solutions. In early December 1690, Jacob Bernoulli’s younger brother Johann sent, as first, his solution to the editors of the Acta Eruditorum, as Leibniz learned from a letter sent by Christoph Pfautz, on February 14, 1691. Huygens too, after some hesitation, forwarded his solution through Leibniz to the journal editors in Leipzig. Leibniz was thus able to present two solutions (in addition to his own) of the catenary problem in the June 1691 number of the Acta Eruditorum. The initiator of the competition, Jacob Bernoulli, published his solution in an article that immediately followed Leibniz’s solution. In a letter of July 25, 1690, Leibniz had presented Huygens with the main features of his infinitesimal calculus and had referred to the relevant articles in the Acta Eruditorum. Replying on August 24, Huygens alluded to a certain obscurity he sensed in Leibniz’s calculus, and he claimed to be in possession of an equivalent method himself. He accordingly presented another challenge for Leibniz’s calculus in the form of two problems involving the inverse tangent method, essentially the task of determining two curves having been given their respective sub-tangents. Leibniz’s efforts to solve the inverse tangent problems, presented by Huygens, as well as the latter’s reaction, are revealed in their continuing correspondence in the last quarter of 1690. Huygens could not, however, be convinced at this point of the superiority of the Leibnizian calculus, and misunderstanding and confusion about the respective solution curves employed, as well as Huygens’ aversion to the exponential equations used by Leibniz, only reinforced the correspondent’s skepticism. For mathematical tasks derived from the physical world in particular, the value of the inverse tangent method is evident as, for example, in the determination of curves like the catenary. From the multitude of special curves,

Epilogue: Core Theses and Conclusion

865

which were treated in Leibniz correspondence in the early 1690s, those having real-world applications deserve particular mention here like, for example, the Archimedean spiral, the catenary and auxiliary or related curves. In the discussion of the catenary problem, Leibniz pointed out, for example, the connection with the loxodrome or rhumb-line curve – or the line cutting all meridians at the same angle and that which was followed by a ship sailing in a fixed direction  – specifically in his correspondence with Huygens, on July 24 and September 21, 1691. Of the mathematical problems treated in Leibniz’s correspondence in mathematics, science and technology between 1691 and 1693, one still remained to be solved in 1694, namely that concerning the “isochrona paracentrica”. This problem of finding the paracentric isochrone was in fact an extension of the first challenge question posed by Leibniz in 1687, namely to determine that curve along which a body approaches the earth’s surface at a constant velocity and, when he published his solution of the problem in April 1689, he presented the additional challenge question, namely to find the curve under the modified condition that the body, still under the influence of terrestrial gravity, veer away from a given point at a constant velocity. The problem was to remain unsolved until 1694, and Jacob Bernoulli was the first to publish a solution, in June and September of that year. In the month of August, Leibniz presented his own solution and two months after that, in October, there followed Johann Bernoulli’s solution. Huygens – to whom Leibniz had forwarded the solution of Jacob Bernoulli (on July 27) – identified, in his reply (of August 24), some shortcomings but was happy merely to give passing mention of these in his article in September of that year. Two problems in pure mathematics were also at the center of contests to demonstrate the superiority of the differential calculus over alternative geometrical methods. Galileo’s disciple Vincenzo Viviani had secretly prepared the ‘Florentine problem’ (as it was later to be designated) and it was circulated in a pamphlet of April 4, 1692. This Aenigma geometricum called for the cutting out of four windows from a hemisphere such that the remaining surface area be squarable. Leibniz received the pamphlet through the Florentine envoy in Vienna on May 27, 1692. He solved the problem on the same day, and sent his solution with a letter to the Florentine prince Ferdinand, on May 29, before publishing a single-page problem enunciation with his solution in June. Jacob Bernoulli’s solution then appeared two months later. On July 12, 1692, Bodenhausen forwarded to Leibniz the solution of L’Hospital that had been achieved in cooperation with Johann Bernoulli but it remained unpublished at the time. After Huygens had seen Viviani’s solution  – in the latter’s tract Formazione e misura di tutti i cieli (1692)  – he too solved the problem, but

866

Epilogue: Core Theses and Conclusion

he hesitated, and then reneged on his intention of forwarding it to Leibniz. Thereafter, Jacob Bernoulli pointed out a mistake in Leibniz’s published solution, following which he published an Additio in January 1693. The other problem from pure mathematics, which was frequently mentioned in Leibniz’s correspondence at this juncture, was the so-called ‘Bernoulli problem’, formulated by the younger Bernoulli brother, Johann, in May 1693. The call here was for the determination of the curve, whose axis intercept from the origin to the intersection with the tangent has a constant proportion, or ratio, to the length of the tangent. In the course of the year 1693, Bernoulli’s older brother Jacob, Leibniz, L’Hospital and Huygens all published, or communicated, their solutions of this problem. Huygens communicated his solution – at which he had arrived in consultation with L’Hospital – to Leibniz, on September 17, 1693. This problem, the solution of which had posed problems for Huygens, led to an admission on his part, namely that his previous skepticism about the power of Leibniz’s calculus was possibly unfounded. It appeared to him that it might be possibly superior to his own much appreciated geometrical methods. And he acknowledged his change of mind not only in private correspondence but also in his publication “De problemate Bernoulliano”, in the Acta Eruditorum in October 1693. This long-awaited moment of recognition of the value of his new calculus from his mentor of the Parisian years was a source of joy for Leibniz, and he reciprocated, in his reply on October 11, 1693, with praise both for a new curve of Huygens  – which had previously been communicated only in encrypted, or enciphered, form – namely a limiting curve of a tautochrone, or isocrone double pendulum (analogous to the cycloid as limiting curve of a simple tautochrone or isochrone pendulum), and for his treatment of the involute of the catenary viz. the tractoria or tractrix. First and foremost, however, Leibniz relished the recognition of his differential calculus, and the fact that Huygens had taken the trouble to grapple with it. Whereas the series of mathematical task assignments, or challenge questions, did not fade away entirely after 1693  – as is evidenced for instance by Jacob Bernoulli’s inverse tangent problem in the Acta Eruditorum of October 1694  – they no longer had the intensity or consistency of previous years. In April 1695, for example, Leibniz commented on the drawbridge problem of Joseph Sauveur – namely that to find the curve along which a counterweight continually keeps a drawbridge in balance – which had already been solved by L’Hospital, in the late summer of 1692, but whose special solution (the “limaçon” or snail of Pascal) first appeared in print only in February 1695. In that month, the solution of Jacob Bernoulli also appeared, as did his brother Johann’s generalized conceptual formulation. Subsequently, Leibniz turned

Epilogue: Core Theses and Conclusion

867

his attention to other mathematical questions, and it was only in mid-1696 that he was enthused by the task setting of Johann Bernoulli, in June 1696, namely the brachistochrone problem, or the task of determining the curve of fastest descent of a body, under the influence of terrestrial gravity, between a certain point and a lower point which was not directly below the first. Having been informed by Johann, on the 19th of June (the month in which it was made public) about the task formulation, Leibniz communicated his solution (a segment of a cycloid) to Bernoulli, on June 26. Johann reciprocated by sending Leibniz, on July 31, two solution procedures, one which utilized the law of refraction of light, and another method that was, however, to remain unpublished. Johann had to resort to a printed flysheet to remind mathematicians of his challenge question after the original deadline set (the end of the year 1696) had passed. When, on June 19, 1696, Bernoulli communicated the brachistochrone problem to Leibniz, he also informed him that he had forwarded the problem to France and to England, namely to Pierre Varignon and to John Wallis, respectively. Leibniz shared Bernoulli’s excitement about the problem and joined the effort to make it known through correspondence and in journal articles. Bernoulli himself had a flysheet about the problem printed in Groningen with the title Acutissimis qui toto orbe florent mathematicis (1697). A six-month deadline was announced at first, but it was subsequently extended until Easter 1697 to accommodate participants from Italy and France. Already on June 27 and 28, 1696, Leibniz had communicated the problem to two of his Italian correspondents, namely Magliabecchi and Bodenhausen, in order to have it announced in the Giornale de’ Letterati. Bodenhausen’s draft for an announcement was superseded, however, by a communication sent by Leibniz himself, in September 1696, to yet another Italian correspondent, namely to Ramazzini, and it duly appeared in the same month in the Giornale. Bodenhausen – who at first relished the prospect of piquing or deriding the honor of Galileo’s descendants and followers in Italy – provided Leibniz with detailed information about the disappointing reaction in Italy to this challenge problem. In the Netherlands, the brachistochrone problem was disseminated through Johann Bernoulli’s flysheet. In addition, Bernoulli prompted the publication of a note on the problem in the Rotterdam journal Histoire des Ouvrages des Savans, in February 1697. His efforts met with a mixed response, and he failed to arouse any great interest. In fact, following the passing of Christiaan Huygens, the sole contribution with a solution to the problem from the Netherlands came (anonymously) from Nicolaas Dierquens, which, although based on the differential calculus, was nonetheless flawed.

868

Epilogue: Core Theses and Conclusion

In France, Leibniz publicized the problem in the Journal des Sçavans, in November 1696. Already in May of that year, it had been forwarded by Pierre Varignon to L’Hospital, who duly presented it to the Académie des Sciences. Also through L’Hospital, Bernoulli received a solution attempt by the Parisian mathematician Joseph Sauveur, which he then forwarded to Leibniz as an attachment to a letter of January 29, 1697. The mistakes in this attempt, which followed from a false application of the differential calculus, were contentiously analyzed in the on-going correspondence between Leibniz, L’Hospital  – the author of the first textbook on the differential calculus, namely the Analyse des infiniment petits (1696) – and Johann Bernoulli in 1697. Bernoulli explained to Leibniz, on August 24, that Varignon had complained about certain ‘old-school’ mathematicians, who would do anything and everything to depreciate the differential calculus, whereby Bernoulli suspected that, in particular, the Abbé de Catelan, Michel Rolle, Philippe de La Hire, and some other more obscure persons, were the ones intended. From Basnage de Beauval, Bernoulli learned that La Hire had arrived, by three different routes, each time at the same incorrect solution, namely a semicubical parabola, as he informed Leibniz in a letter of June 17. L’Hospital’s solution of the brachistochrone problem, which he presented to the Académie des Sciences, on April 20, 1697, then proved to be an important victory over the opponents of the infinitesimal calculus. In his letter of August 24 to Leibniz, Johann Bernoulli could then include an extract from a letter of August 6, received from Varignon, regarding L’Hospital’s success and the blow dealt to his opponents. The brachistochrone problem first reached England, in the summer of 1696, in the form of a communication from Johann Bernoulli to John Wallis. In addition, Bernoulli sent two copies of his flysheet to Wallis and Newton, respectively, in January 1697. The brachistochrone problem was to be the only mathematical contest, in Leibniz’s ambit, in which Newton participated. It provoked an allegation of plagiarism by Fatio de Duillier and, accordingly, a new phase in the priority dispute was initiated. In the light of this, English reactions to the brachistochrone problem, as well as those in Leibniz’s circle to Newton’s solution, have a special significance. Already in March 1697, Bernoulli received from Basnage de Beauval an anonymous solution to the problem from England  – without details being given of the exact approach taken  – which had appeared two months earlier in the Philosophical Transactions. Bernoulli sent a copy to Leibniz, on March 30, and he correctly concluded that Newton was the author of the solution in question. For Leibniz, the fact that Newton had needed but a single day to solve the problem – as he had indicated in presenting his solution – was

Epilogue: Core Theses and Conclusion

869

a welcome proof of the effectiveness of the infinitesimal calculus. The view that Leibniz presented to Bernoulli here was that Newton had partly studied the differential calculus, and partly an analogous method. Words of a similar tenor – namely that only those had been able to solve the problem who had used the differential calculus – are to be found in a letter, of May 7, he sent to Etienne Chauvin, which was then partly reproduced in the Nouveau Journal des Sçavans, in May–June 1697, and in Leibniz’s own contribution regarding the brachistochrone problem, in the Acta Eruditorum in May 1697. The only correct solutions then of the brachistochrone problem, which reached Otto Mencke, the editor of the Leipzig journal, before the deadline had elapsed, came from Jacob and Johann Bernoulli, L’Hospital and Newton. Johann Bernoulli had already sent his solution to Leibniz, on July 31, 1696, with the request that he forward it on time to Mencke. Leibniz complied with this request but he also persuaded Johann to keep one of his two solution approaches secret. The first approach, which was published, established an analogy to the problem of finding the path of a ray of light in homogeneous media. This allowed him to embrace a general hypothetical connection between path and velocity, in place of Galileo’s law of falling bodies. From the law of refraction, as it applied to the infinitely small, Bernoulli derived his differential equation. Jacob Bernoulli sent his solution directly to Mencke, as he informed Leibniz on February 6, 1697. L’Hospital first sent a solution attempt to Johann Bernoulli, on February 25, and he forwarded it to Leibniz on March 5. He then returned it to L’Hospital, on March 8, and he sent his ultimate solution to Leibniz, on March 17, for forwarding to Leipzig. Leibniz declined to publish his own solution and, in his contribution or introduction to the four solutions being published, he could only comment on the competition, describing that which he considered novel in this kind of extremum problem. From Tschirnhaus, who rejected the differential calculus, no solution of the brachistochrone problem was to be expected from the outset, especially in view of his earlier failure to provide a solution to the catenary problem, and notwithstanding the fact he had been publicly invited to do so after he had announced a new method of his own. This and further announcements in Tschirnhaus’ article “Nova et singularis geometriae promotio”, of November 1695, led to skepticism and criticism being expressed by the Bernoulli brothers, in letters they sent to Leibniz in 1696 and 1697. Tschirnhaus’ article “De methodo universalia theoremata eruendi”, of May 1697 – which Mencke had placed among the solutions of the brachistochrone problem – provoked further criticism in Leibniz’s correspondence with Johann Bernoulli and L’Hospital. In his article, Tschirnhaus only briefly mentioned the problem. He presented the cycloid as the solution, but he left open the question as to whether he had solved the

870

Epilogue: Core Theses and Conclusion

problem himself. Both Bernoulli and Leibniz suspected that he had most likely learned the solution from Mencke, during the Leipzig Spring Fair of 1697. Fifteen years earlier – in letters Leibniz and Tschirnhaus exchanged between May and August 1682 – considerable attention had been given to a detailed discussion of Tschirnhaus’ problem of the catacaustic curve, as well as related problems like that of the diacaustic curve, these being curves which arise in connection with the reflection and refraction of light. The brachistochrone problem was likewise a mathematical problem rooted in the physical world, and the considerations concerning it were subject to physical influences. Thus, for example, in connection with the solution of this problem, Leibniz and Johann Bernoulli discussed orthogonal trajectories, or specifically a family of curves in a plane that intersect another family of curves at right angles. Methods for the determination of orthogonal trajectories had already been developed by Leibniz and Bernoulli in 1694. An important influence here came from physics, and in particular from ‘Huygens Construction’ – published in the Traité de la lumiere (1690) – in the theory of light propagation, in which the light waves were shown to be orthogonal to the rays. All in all then, Leibniz’s views on the practical orientation of mathematics appears to be epitomized in the sentiment expressed in his letter to Christoph Pfautz on April 28, 1682 – the leading quotation in Chapter 1 of the present work – namely to the effect that he was only willing to tackle mathematical problems if they were particularly elegant, particularly relevant for the world of physics and mechanics, or revealed new methods for the solution of an infinity of other problems.6 This conviction was expressed once again some fourteen years later in the statement found in his letter to Detlev Clüver (in June or July 1696) – the basis of the first thesis presented here – namely to the effect that his calculus, as indeed all of mathematics, was rooted in practical experience (or experiment) in the physical world. 1.2 The Field of Natural Philosophy In a letter of November 17, 1695, Leibniz wrote, in relation to his views on natural philosophy, the following words to Denis Papin: “Mon sentiment est fondé en raisons et en experiences”.7 Thus, Leibniz underlined here his conviction that his natural philosophy was rooted both in reason and in experiment, or at 6 “Ego nullum problema Geometricum curo, nisi sit vel valde elegans; vel valde utile ad rem mechanicam aut physicam; vel denique novam methodum nobis ostendat ad infinita alia problemata solvenda” (A III,3 N. 345, p. 597). 7 Cf. A III,6 N. 172, p. 533. Translation: My sentiment is rooted [both] in reason and in practical experience or experiment.

Epilogue: Core Theses and Conclusion

871

least thought experiment. It represents the second thesis presented here that is clearly based on a formulation by Leibniz in his correspondence. Leibniz’s conviction that his natural philosophy was rooted both in reason and experiment found expression above all in his debate with Papin about the correct measure of force, which was carried on in the public domain (from 1686 to 1691), and in their private correspondence (from 1692 to 1699). In his published articles, Leibniz tried to demonstrate, by means of a thought experiment, the possibility of perpetual motion, or a “motus perpetuus mechanicus”, which would arise if Papin’s, or the Cartesian, definition of force were to apply. With such thought experiments in mind, Leibniz also introduced notions like the complete substitutability of the bodies, incorporated in the definition of force, and the complete transferability, or transmission, of the force between bodies. Papin tried to refute Leibniz’s thought experiment, and he denied above all the possibility of a complete transferability of the force from one body to another. Leibniz in turn attempted to refute Papin’s argument by declaring the pure-thought assumption of such a transfer to be sufficient. The proof of the complete transfer of force from a body of greater mass to one of lesser mass, he provided once again by means of a thought experiment. With the relocation of the dispute (in January 1692) to their private correspondence, Leibniz continued his efforts to convince Papin – on the explanatory grounds of both reason and experiment, or thought experiment – of the correctness, and superiority, of his definition of force (based on a “vis viva”), and of the erroneousness of the Cartesian definition of force (based on a “vis mortua”). In relation to physical experiment, or engineering practice, Leibniz thought he could reduce the controversy to a simple consideration in his letter of November 17, 1695. Thus, he thought the controversy could be reduced to a consideration of two identical bodies having the same simple velocity, and whose joint force would be double that of either of the bodies on its own. In the same way, four such identical bodies would have quadruple the force of any one of them on its own. Now, however, an individual body having double the simple velocity in question could impart this simple velocity not just to two but to four other identical bodies. Therefore, one of the bodies on its own, having a twofold velocity value, would have quadruple the force of another one of the identical bodies, having but the simple velocity, which for Leibniz was that which was to be demonstrated. And, furthermore, for him, an estimation of the force in terms of the product of mass and velocity, i.e. the quantity of movement, had to be incorrect, and he insisted that the error involved would be very considerable in practice. In a letter of December 9, 1695, Papin, for his part, also resorted to a thought experiment by imagining an arrangement in which weights were placed at the

872

Epilogue: Core Theses and Conclusion

circumference of a horizontal wheel that was powered, and caused to rotate, by means of a falling weight below it. Writing on January 1, 1696, Leibniz then reformulated Papin’s problem by contemplating an engineering design with an undershot vertical water wheel in a stream which powered the horizontal wheel, carrying the weights above, by means of an intervening cog-wheel and lantern-pinion gear mechanism. A weight on the circumference of the horizontal wheel above was made to rotate at a certain velocity and, in order to double this velocity, the radius of the horizontal wheel, on whose circumference the weight rested, had to be doubled. To achieve this end, it would be necessary to quadruple the cross section of the stream  – while keeping the depth of the current and the slope constant – and to enlarge the surface area of the radial vanes of the vertical water wheel by a factor of four. The same effect could also be achieved by quadrupling the specific gravity of the fluid, while keeping the current and the area of the vanes constant. Accordingly, Leibniz insisted that Papin’s thought experiment would ultimately lead to a four-fold force increase, and so be in accordance with his definition of force. Again in a letter of October 4, 1696, Papin, in an effort to establish contradictions in Leibniz’s argumentation, conceived another thought experiment, involving the collision of a larger with a smaller body, and between which there was a spring. At the instant in which the velocity of the smaller body was reduced to zero, it was replaced by a much larger body, which then absorbed the recoil of the spring and the impact of the other body. Since the distribution of the quantity of motion follows the law of “vis mortua”, the surrogate body would have a lower velocity (and less “vis viva”) after the collision than the smaller body had before the collision. Accordingly, there would be a loss of force following the event, which implied a contradiction in Leibniz’s conservation principle. In his reply, on November 11, Leibniz maintained, however, that in this experiment a portion of the force of the stalled body was transferred to its spring in the form of motion of its constituent parts. The replacement of a body by a larger body was, he insisted, only admissible if the “vis viva” lodged in the spring of the body were to be completely transferred to the surrogate body. In a letter of December 12, 1697, in the context of a further thought experiment pertaining to the nature of percussion and elastic spring, Leibniz once again pointed to an additional conservation law of his, namely that of the quantity “progress”, which was given as the product of mass and directional velocity and was the counterpart of the “force morte” in Papin’s interpretation. In a letter of January 26, 1698, in an effort to prove his standpoint, solely on the basis of the law of “vis mortua” combined with the rules for the composition of movements, Leibniz conceived yet another thought experiment. A ball, or sphere, passing along the diagonal of a square, strikes simultaneously two

Epilogue: Core Theses and Conclusion

873

other balls of the same magnitude resting at the upper right-hand corner of the square. The first ball then comes to rest, and its movement is transferred to the other two balls, which move off along the extension of the upper horizontal side and that of the right-hand vertical side of the square, respectively. This thought experiment, depicted both in this way and in reverse, was then discussed in great detail in subsequent letters. In due course, the adversaries also contemplated physical experiments, by means of which the dispute might be settled. On August 28, 1698, Papin seemed convinced that the matter could indeed be finally decided by means of such a physical experiment, and he suggested that, given the necessary leisure, he himself would be in a position to carry out such an experiment. Leibniz, for his part, in his letter of September 7, then also favored an experimental decision in the matter of the collision, or oblique impact, of a body against two other bodies resting at a corner of a square. In the meantime, however, Papin had doubts once again about whether the matter could really be decided in the short term by means of such a physical experiment, and he retracted his previous conviction, in his letter of October 9. In the final phase of the “vis viva” controversy, from January 1699, the adversaries remained in their entrenched positions. In the context of Leibniz’s thought experiment, regarding the impact of a ball or sphere passing along the diagonal of a square against two other balls of the same magnitude resting at the upper right-hand corner, Papin had argued that the first sphere, in its movement along the diagonal, would – in the event of a simultaneous meeting of all three balls – experience less resistance from each individual sphere at rest or, in the reversal of the process, be pushed off faster by simultaneous collision than in the case of separate collisions. The total result therefore would not be the sum of the individual collisions. The discussion about the role of the resistance here also led to considerations about inertia, mass, and states of rest and motion. While, for Papin, there was no fundamental difference between the states of rest and motion, for Leibniz, in the state of rest, the mass or the inertia of matter resisted motion. For bodies in motion, however, an entelechy – that is an inherent, or intrinsic, and purposive force which realized, or made actual, what was otherwise merely potential – provided for the maintenance of the state. Mass constantly reacted against, or resisted, this entelechy. Thus, action and reaction would take place here within a body. Leibniz proclaimed here that he had established that the measure of force, as well as the measure of action, but not the quantity or measure of motion, were those which were conserved. As regards the diagonal-collision thought experiment, Leibniz insisted that, following the common or Cartesian interpretation, perpetual motion would result. However, Papin stuck to his conviction that, even with the assumption

874

Epilogue: Core Theses and Conclusion

of a perfect hardness, the sum total of the quantities of motion following the collision would be less than before the event. It was similar to the case of free fall in terrestrial gravity. If an arbitrarily hard ball were to fall freely and rebound from an anvil, it would never rise again to the height from which it fell. As regards an understanding of the collision process, the rival positions were still far apart. In a letter, written in the second half of May or the first half of June, 1699, Leibniz argued that the force lost in the transfer would be small with the result that the Cartesian measure of force would inevitably lead to a perpetuum mobile. In his reply, on June 18, Papin did concede to Leibniz that the assumption of a complete transfer of the quantity of motion would indeed lead to a perpetuum mobile, but nevertheless he continued to insist that the laws of motion would prevent this ever happening in practice, since there would always be a loss, however small it might be. Leibniz, writing on July 4, then expressed the view that this loss could be kept arbitrarily small, for example by replacing the balls, or spheres, with long thin cylinders. Papin, writing on September 21, doubted however that losses could be avoided in this way, by introducing such long thin cylinders in place of the colliding balls, and so, when the debate ended, in December 1699, both parties had once again retreated to their entrenched positions. All in all then, Leibniz was unable to convince Papin, either by means of such thought experiments, or by drawing a theoretical distinction between a “vis mortua” and a “vis viva”. Thus, with his argument “Mon sentiment est fondé en raisons et en experiences” – expressed in his letter of November 17, 1695 – Leibniz was to fail outright in his efforts to convince Papin on both of these explanatory grounds, namely of reason and of experiment. 1.3 The Field of Physics At the beginning of 1694, on January 6, Leibniz wrote the following words to Augustinus Vaget (Vagetius): “Argumentum Neutoni contra vortices mihi stringere non videtur”.8 Thus, Leibniz stated here his conviction that Newton’s argument against vortices, in the theory of planetary motion, did not appear to extirpate, or dispose of, his own sufficiently consolidated position. This then represents the third thesis, again based on a clear statement by Leibniz in his correspondence. The paragraph containing Leibniz’s assertion began with the words “Motus planetarum, quos ego Circulatione Harmonica efficio cum gravitate, Neutonus pro maximo acumine suo ostendit ex sola Trajectione et

8 Cf. A III,6 N. 2, p. 13. Translation: Newton’s argument against vortices [in the theory of planetary motion] does not appear to efface my position.

Epilogue: Core Theses and Conclusion

875

Gravitate posse explicari”,9 a reference no doubt to the ideas presented in their respective works “Tentamen de motuum coelestium causis” (Acta Eruditorum, February 1689), and the Principia mathematica (1687). Leibniz hypothesized a rotating ether vortex around the sun as the cause of planetary motion. The ‘fluidum deferens’, of which this vortex was constituted, carried the planets. The motion of planets, resulting from this vortical rotation, he resolved into a circular motion, having a rotational velocity which was inversely proportional to the radius, and into a radial motion which corresponded to the force of gravity, or centrifugal force. The combination of both components of the motion yielded the elliptical planetary motion, as well as Kepler’s first two laws. Thus, Leibniz considered that he had succeeded in presenting, for the first time, a physical explanation of Kepler’s laws of planetary motion. While he emphasized the simplicity of his celestial mechanics, and the agreement with Kepler’s laws, he saw the need to extend his own theory to cover matters like the inverse-square law of gravitational attraction, as he wrote, for example, to Bodenhausen on March 18, 1690. Celestial mechanics was also a focus in Leibniz’s revived correspondence with Christiaan Huygens, following the appearance of the latter’s Discours de la cause de la pesanteur in 1690. His drafted (but never dispatched) letter addressed to Huygens, from the first half of October, contained commentaries on the theories of Newton and of Huygens, together with annotating remarks regarding his own celestial mechanics. Leibniz found himself unable to endorse the opinions of Newton about gravity and planetary motion, resulting exclusively from gravitation. His overt adherence to Cartesian vortices, in correspondence with Huygens, is indicative of an indispensable centerpiece of his planetary theory. Leibniz actually assumed the existence of two vortices rotating about the sun. The first caused gravitation and terrestrial magnetism, while the second coarser vortical rotation of the ‘fluidum deferens’ moved the planets. In Leibniz’s comments about Newton’s Principia mathematica, admiration and rejection went hand in hand. Thus, he found an explanation of gravity, and indeed of the law of gravity, to be wanting in Newton’s work. For the law of gravity, and the photometric inverse-square law, he suspected analogous explanations. On the other hand, as regards Huygens’ understanding of gravity, he found similarities with his own conceptions of a centrifugal force produced by the rotating ether.

9 Translation: The motion of the planets, which I attribute to harmonic circulation and gravity, Newton, by virtue of his great acumen, shows can be explained solely on the basis of trajectory and gravity.

876

Epilogue: Core Theses and Conclusion

The most important discussions about gravity, or gravitation, in the mid-1690s, are to be found in Leibniz’s correspondence with Huygens, and with the Newton confidant, Fatio de Duilliers, for example in letters of April 9 (Fatio) and May 18, 1694 (Leibniz). For Newton and Fatio, the universe consisted for the most part of empty space, for otherwise the celestial bodies would be exposed to a large resistance from the particles of an ether, and would, accordingly, be decelerated. Leibniz, on the other hand, stressed the necessity of a mechanical explanation of gravity, or gravitation, as an inherent property of matter. The competing theories to explain gravitation assumed physical processes based on the effects of circular motion (Huygens) and rectilinear motion (Newton), respectively. In the case of circular motion, centrifugal force was able to provide a sufficient explanation of gravitation, but an inverse-square law (analogous to the photometric inverse-square law) could not be derived from it, Leibniz insisted. This was followed by a report about his own efforts to find an explanation for gravity, and indeed both on the basis of a circular-motion hypothesis, as of a rectilinear-motion hypothesis. He described in greater detail his second approach (based on rectilinear motion), elaborating his “explosion” theory of gravitation, and comparing it to an incendiary process in which coarse matter enriched with fine matter was attracted to rarefied matter at the center of attraction, as in a flame. As a consequence of the ensuing explosion, or ignition, and the accompanying rarefaction, the fine matter was expelled to the periphery, where it served for alimentation of the coarse material there and, accordingly, for the continuation of the cycle or process. Such an explosion would be comparable to the movement of light, and, as a consequence, the inverse-square law, analogous to the photometric inverse-square law, would also be valid. Finally, he thought nature might opt for a combination of circular and rectilinear motion, its style being to seek the optimal minimum-redundancy solution. Leibniz informed Huygens about his correspondence with Fatio, and he also elaborated for him his “explosion” theory of gravitation, on May 6, 1694. Huygens, however, was convinced of the correctness, and completeness, of his own theory. In the final year of Huygens’ life, Leibniz’s attitude towards him was however conciliatory. He henceforth characterized the different theories about gravity, or gravitation, as being essentially equivalent. Likewise, as regards explanations of planetary motions and the tails of comets, Leibniz tried to harmonize (at least partially) the theories of Newton with his own. The observed phenomenon, that all planets of the solar system, and all satellites or moons of a planet, rotate in almost the same plane, and in the same direction of rotation, could, for Leibniz, only be explained using an ether-vortex model. And, in addition, there was a further reason for

Epilogue: Core Theses and Conclusion

877

his ether-vortex, namely the analogy to the explanation of the phenomenon of terrestrial magnetism. Even for the paths of comets, it seemed to Leibniz that the ether did not present obstacles, since the rare ether-vortex scarcely impeded the trajectory of a comet. However, as regards the tails of comets, the views of Leibniz and Newton were irreconcilable. For Newton the tails had a material character, whereas Leibniz was convinced that they were simply optical phenomena. Once again, Leibniz introduced here the corresponding motion of the planets of the solar system, and the analogy between the supposed ether-vortex and magnetism, as arguments against the Newtonian gravitational theory of planetary motion. Following Huygens’ death, Leibniz continued to express his views about the cause of gravity, which he consistently attributed to a physical fluid (or an ether) in motion, as for example, in a letter of November 17, 1695, to Papin, where he compared his explanation to his understanding of that given by the correspondent. Papin’s explanation was based on the effect of a resisting, insensible fluid. Leibniz, for his part, rejected such an insensible fluid and a possible explanation of gravity on the basis of philosophical suppositions, or hypotheses, rather than of mathematics. In this vein then, the quotations from Leibniz’s letters to Papin, of November 17, 1695, and of December 12, 1697, the leading quotations in Chapter 4 (“Nostre science est mathematique, et n’a pas besoin icy de ces suppositions ou hypotheses philosophiques, bienque bonnes d’ailleurs”),10 and in Chapter 5 (“quand on a la cause d’un effect expliquable par des choses sensibles; pour quoy recourir à des suppositions peu certaines avec les Cartesiens et autres?”),11 respectively, of the present work, epitomize his stand in opposition to the correspondent regarding gravity. All in all then, Leibniz’s repeatedly-stated conviction – found throughout his correspondence with Huygens, Fatio, Papin and others – namely that Newton’s argument against vortices, in the theory of planetary motion, failed to dispose of his own sufficiently consolidated position – the essence of the third thesis presented here – proved to be unwavering. 1.4 Energy, Power Technology, Mining, Transportation In a letter of May 23, 1681, Leibniz wrote the following words to Tschirnhaus: “Ego hac aestate occupabor in absolvendis tandem meis molendinis ventaneis, 10 Cf. A III,6 N. 172, p. 537. Translation: Our science is mathematics and does not require these philosophical suppositions or hypotheses. 11 Cf. A III,7 N. 163, p. 658. Translation: When one has found the cause of an effect explicable on the basis of sensible matter, why revert to the suppositions of little certitude of the Cartesians and others.

878

Epilogue: Core Theses and Conclusion

quae fodinis applico”.12 Here Leibniz was referring to his plan to use windmills in the pits of the Harz mining district, which was the first part of a wider effort, in the field of energy conversion, to promote the use of wind power, water power and steam power in mining, in manufactories and in transportation, and which is the essence of the fourth thesis, or foundational idea, here of both a paradigm continuity, and a paradigm change, in energy conversion, transmission, storage, and in power technology. The concept of a power technology had of course, in Leibniz’s time, a long tradition going back 400 years, and more, to the medieval exploration of mechanical power when, in particular, a chase after a certain will-o’-the-wisp idea (a gleam in the eye, as it were) of achieving perpetual motion began to inspire the fantasies, and imaginations, of power-conscious technicians and engineers of the later Middle Ages, and who in turn would lay the foundation for the early-modern development of power technology in the Western World.13 In the case of Leibniz, his interest in the use of water power surely represented a paradigm continuity, whereas his efforts for the exploitation of wind power, or a combination of water power and wind power – both in mining and in other areas – must surely be seen as part of a paradigm change. In this connection also the possible use of controlled-explosion, or combustion, power – perhaps akin to his “explosion” theory of gravity, or gravitation – as well as the use of vapors, like the spirit of wine, to power a two-stroke piston engine can also be seen as part of such a paradigm change. It was in the fall, or autumn, of 1679 that Leibniz received approval for a one-year trial of the use of windmills for draining a colliery. The plan was to raise the pit water from the mine by means of a pump assembly, which was attached directly to a windmill, namely his so-called “immediate”, or direct, solution. In August 1680, Leibniz then presented a new arrangement, in the form of a plan first devised by the mining official, Peter Hartsinck (or Hartzingk), who died in that year. This alternative plan envisioned that the windmills would not be used to power the pumping machinery directly, but would rather form part of a pumped-storage system, namely his so-called “mediate”, or indirect, solution. Already in a letter from the end of November, or early December, 1679, Leibniz had informed Huygens about his windmill project for draining the mines and, in a letter of February 5, 1680, he elaborated on his mining project. A special difficulty was the corrosiveness of the water in the pits, which would 12 Cf. A III,3 N. 233, p. 428. Translation: I will be occupied this summer in completing at last my windmills which I am applying in the mines. 13 Regarding the “concept of a power technology”, cf. L. White Jr., 1962; B. S. Hall, D. C. West (eds.), 1976; S. A. Walton, 2019 (Introduction, note 99).

Epilogue: Core Theses and Conclusion

879

damage the metal components of a bucket and chain pumping system. Instead it was necessary to employ a score of pumps (having wooden cylinders), and arranged in tiers one above the other, which were powered by water wheels. His idea, Leibniz explained, was to avail of wind power to service, and replenish, the reservoirs – which otherwise might run dry in times of drought – while retaining the existing system of pumps and tiers of pumps. A second test series using the direct, or “immediate”, method was carried out in 1684 and, from the beginning of that year, Leibniz pursued simultaneously his indirect, or “mediate”, project using horizontal windmill technology. A third and final test series was carried out at the beginning of 1685 with a directly-attached windmill, but it failed to prove an unreserved success. Then, in September 1685, he presented a new proposal for improvement of the winding machinery, in the ore mines, using a closed-loop, or endless cable, to be powered by water wheels. Leibniz left the Harz mines in 1687, but his knowledge and experience is reflected in his correspondence with Friedrich Heyn in that year. On February 6, Heyn reported about a new powerful water wheel-powered pumping machine with rod engine-like sectional components, that had been designed by Johann Joachim Becher, and successfully deployed and operated in the mining district of Cornwall. The Cornish machine incorporated neither a standard “suck and press” pumping-system, nor a scoop water wheel system, but consisted rather of a “Taschenkunst”, or rag and chain pump system. A special focus was the incorporated power transmission system, which connected regular or circular motions, at both ends, by means of an irregular or retrograde linear (or alternating) motion in between. It connected a prime mover – supplying wind power, water power or horse power – with a distant load. Heyn also informed Leibniz about another water mill system, located near Ehrenfriedersdorf, in the Freiberg mining district of Saxony, and which was likewise compared to the “Stangenkunst”, or rod engine technology. The machine, referred to by the correspondent, was most likely nothing other than a variant of the well-known “Ehrenfriedersdorfer Radpumpe”. This was essentially a piston-pump system, which consisted of several pump stages arranged one above the other, and powered by a single prime mover. In his reply of mid-July 1687, Leibniz insisted that it would be necessary to compensate for the considerable frictional losses in such a transmission mechanism. While Leibniz’s most important innovation in mining was without doubt the exploitation of wind power, he was also very much occupied with water-powered and water-raising machines, an interest which became evident especially in his second period of activity in the Harz mining district between 1693 and 1696. The improvement of the mine-dewatering pumps, and an

880

Epilogue: Core Theses and Conclusion

increase in the efficiency of the winding machinery for hoisting ore, were at the center of his interest at this point. He contemplated the possibility of replacing power sources – like horse mills and the overshot reversible water wheel – by using a rod-engine power transmission system from a remote water wheel on a river to the pithead, and not just for operating the pumping machinery alone, as had previously been done, but also for simultaneously powering the winding, or hoisting, machinery. In order for such a combined system to function properly, the overall power requirement needed to be significantly reduced, and Leibniz hoped to achieve this, in the first place, by employing an endless or closed-circle winding cable or chain. In addition, he conceived a tugging or towage mechanism, with a switchable pinion gear mechanism for connecting to the main transmission line. However, he encountered considerable difficulties, including the resistance of the mining officials and, after the situation for his efforts to improve the ore-hoisting methods had considerably deteriorated, he reverted to the task of improving the pumping machinery, in the knowledge that his vision of a combined power system could only be successful, in the long term, if he were to succeed in constructing energy-saving pumps. Leibniz’s vision of a mail (or post) coach that could travel between Hanover and Amsterdam in six hours was reported, perhaps inadvertently, by Crafft to Becher, and it was ridiculed by him in his satirical work Närrische Weißheit und weise Narrheit (foolish wisdom or wise foolery) of 1682. Also, in Leibniz’s exchange of ideas with Papin about the latter’s steam pump, the possibility of using steam and other vapors to power a machine, or a vehicle, was considered. And, in this connection, the possible use of controlled-explosion or combustion power, as well as the use of vapors like the spirit of wine to power a two-stroke piston engine, were also contemplated. Thus, in his letter to Papin of November 18, 1697, Leibniz conjectured that the explosive effect of gunpowder could be attributed to the compression pressure of the air. From Papin’s reply, of December 5, it is clear that, on the basis of his earlier calculations – carried out while he was assistant to Huygens in Paris – he had concluded that the air contained in gunpowder causes the force that is released in gunfire. On December 12, 1697, Leibniz could then greet their mutual agreement about the nature and power of gunpowder on the basis of experiment. A question Leibniz had posed more than two years before, in a letter to Papin from the first half of August 1695, concerned the possible use of spirit of wine as a fuel to power a two-stroke piston engine. On September 1, Papin then conceded that Leibniz’s conjectures about the power of spirit of wine as a fuel were in agreement with the results of experiments of his, but he insisted that the costs involved in the use of this fuel would be prohibitive. In a further letter, of early

Epilogue: Core Theses and Conclusion

881

October, 1695, Papin returned again to the possible use of a cycle of rarefaction and condensation using the spirit of wine, rather than water vapor, in a piston engine. Two and a half years later, on April 20, 1698, Papin could report that he had carried out experiments on lifting water from a depth using the power of fire, or steam, following which, on April 24, Leibniz enquired as to whether the correspondent had made use of a principle of expansion in raising water by this means. On August 4, Papin confirmed that he had indeed employed the expansion of steam, but in such a way that he could exploit both the suction and compressive effects. He expressed the conviction that the power of fire, or steam, might indeed find other applications besides the lifting of water. And he related that he had constructed a model of a steam-powered vehicle that operated on water. However, he doubted that this form of propulsion would be suitable for normal wagons or carriages on land, above all because of the imperfections of existing roadways. On the other hand, he believed he possessed the competence to build a marine vehicle powered by steam. On August 8, Leibniz concurred with the view that the expansion of steam could produce a greater effect than the atmospheric pressure accompanying the condensation of steam. He told that he had also contemplated the possibility of employing the expansion of other vapors, in place of water vapor or steam, and he greeted the fact that experiments which he himself had contemplated – in order to test the superiority of a steam engine over a pneumatic engine – had in the meantime been carried out by Papin. He himself, just like Papin, had previously contemplated the use of such an engine to power a vehicle, and to facilitate transport. Papin reported, on August 28, that he too had, through experimentation, gained the insight that the effect of gunpowder power increases with the resistance to be overcome, but he insisted that the means to control the expansion of the exploding gunpowder conglomerate would need to be researched further. As regards the connection between the strength of the expansion force and height attained in lifting a body, using steam power, Papin explained that had been able to pump water only to a height of 70 feet by means of steam power. Leibniz, in his reply on September 7, argued that consideration ought to be given to the circumstance that force was actually being lost through the cooling of the steam during expansion, which reveals perhaps a premonition of future ideas on adiabatic expansion processes in thermodynamics. All in all then, this was surely the culmination of Leibniz’s innovatory efforts – in the 1680s and 1690 – to promote the use of wind power, water power and of steam or vapor power, above all in mining and in transportation, and which is the essence of the fourth thesis presented here.

882

Epilogue: Core Theses and Conclusion

1.5 Engineering and Engineering Science Having first elaborated certain thoughts on mathematics, Leibniz wrote the following words to François de la Chaise, in a letter from the second half of April, or the first half of May, 1680 : “Mais je estimeray peu tout cecy, si je ne voyois moyen de reduire les problemes de Mechanique aux termes de la pure geometrie, et de mettre les machines en calcul tout comme les figures”.14 The matter at hand here was Leibniz’s formulation of a desideratum of being able to reduce mechanics to the terms of pure mathematics, and to reduce machines to machine-equivalent figures for calculation, and this is the essence of the fifth thesis presented here. An instance of the second part of Leibniz’s desideratum, namely the representation of machines or engines in drawings for calculation purposes, can be found in his discussion of Johannes Teyler’s explanation of the principles of fortification – found in Architectura militaris (1679) – and, in particular, of the optimal provision of fire power in fusillades using a drawing which Leibniz sent to Huygens with his letter of May 6, 1694. Regarding the first part of the desideratum, it was primarily in the area of engineering and engineering science, specifically regarding the mechanics of fluids and fluvial mechanics, that Leibniz’s thoughts regarding the reduction of mechanics to the terms of pure mathematics found their greatest expression in his correspondence. Leibniz’s meetings in Italy in 1689–1690, with major figures of the second generation of Galileo’s disciples, included encounters with Bernardino Ramazzini, and with whom problems of hydraulics and hydromechanics were subsequently discussed in correspondence. The starting point of these discussions was the intelligence Leibniz received from Ramazzini, namely that Domenico Guglielmini intended to treat fundamental questions of fluid mechanics in a tract entitled Aquarum fluentium mensura nova methodo inquisita (1690–1691). From his own discussions with Guglielmini in Bologna, Leibniz also knew of the Italian’s plans to write a tract about the laws of fluid motion, and thereby to place the laws of open-channel flow on a new foundation. In the third edition of Benedetto Castelli’s book Della misura dell’acque correnti (1660), a linear velocity distribution increasing from the river bed to the water surface had been postulated. In a letter he sent to Ramazzini, on July 16, 1690, Leibniz alluded to Castelli’s theorem about the vertical velocity distribution, and – with Guglielmini’s forthcoming tract in mind – he expressed his doubts that the author might be able give a rule to supersede that of Castelli, or that an 14 Cf. A III,3 N. 61, p. 192. Technical translation: But I would esteem all of this very little, if I did not see the means of reducing the problems of mechanics to the terms of pure mathematics and of rendering machines as machine-equivalent figures for calculation.

Epilogue: Core Theses and Conclusion

883

exact rule for this velocity distribution in natural waters might be formulated at all. It was to Bodenhausen that Leibniz sent, on November 17 of that year, a first opinion about Guglielmini’s opus. At the center of Leibniz’s interest was Guglielmini’s postulated parabolic velocity increase from the water surface to the river (or canal) bed. This ‘scala fallacy’, as it was later called, was based on a false assumption of the applicability, or validity, of Torricelli’s efflux law in an open stream. Leibniz was of course convinced from the outset that the velocity distribution postulated by Guglielmini could have no validity in real rivers and canals. Guglielmini treatment of fundamental questions of fluid flow in open channels – in his Aquarum fluentium mensura – likewise instigated Papin to publish a critique, which in turn provoked a réplique from Guglielmini. This took the form of two open letters, one addressed to Antonio Magliabechi, and the other (dated December 24, 1691) to Leibniz, which were then published with the title Epistolae duae hydrostaticae in 1692. The dispute was essentially concerned with the issues of whether Galileo’s laws of falling bodies were valid in fluid flow, whether the velocity in the upper layers of a stream were influenced by the movement of the lower layers, and how the efflux velocity out of an orifice, near the bottom of a cylindrical container, compared with that from an orifice of the same diameter, in the bottom itself, under the same pressure head. Papin’s response to Guglielmini’s Epistolae duae appeared in 1695 in the form of an open letter addressed to Huygens. To answer Papin’s criticisms, in 1697, Guglielmini once again chose the form of two open letters addressed to Leibniz and Magliabechi, respectively. The publication of Guglielmini’s letter of June 5, 1697 to Leibniz was however refused by the editors of the Acta Eruditorum and it only appeared in print thirteen years later in the Miscellanea Berolinensia (1710). This letter of June 5, 1697, was concerned, among other things, with Guglielmini’s postulated parabolic velocity distribution, and increase from the water surface to the canal bed, following Torricelli’s efflux law, with the applicability of Torricelli’s theorem in general to open-channel water flow (over both horizontal and inclined canal beds), as well as with the general validity of Galileo’s laws of falling bodies in fluvial mechanics. According to Guglielmini’s Aquarum fluentium mensura the laws of fluid flow were to be explained exclusively by the fall (or head) of the channel, the slope (or inclination) of the water surface and the pressure of the water. Neither gravitation, nor resistance forces were taken into consideration here. This abstract mathematical approach could not automatically be applied to conditions prevailing in real rivers and canals. However, in a letter of June 22, 1696, Guglielmini was able to inform Leibniz that he was preparing a new tract, and one which would not be subject

884

Epilogue: Core Theses and Conclusion

to such restrictions. Leibniz greeted the new knowledge emerging in the context of Guglielmini’s fluvial mechanics, as his letter of January 7, 1697, to author reveals. And so with the appearance in 1697 of Guglielmini’s main work – that was based on engineering practice and applied mathematics – entitled Della natura de’ fiumi trattato fisico-mathematico, the academic dispute with Papin about the fundamentals of fluid mechanics was finally laid to rest. This episode in the history of fluid, and fluvial, mechanics surely accorded then with Leibniz’s vision of reducing mechanics to the terms of pure mathematics and, in engineering and engineering science, of reducing hydraulic machines, and systems, to machine-equivalent figures for calculation. 1.6 The World of Projects and Projectors A letter Leibniz wrote to Sebastian Scheffer, in mid-April 1682, contained the passage: “Solcher sterilitat nun zu hülffe zu kommen habe ich den vorschlag gethan gehabt, wie man unzahlbare neue und nüzliche anmerckungen die schohn unter den leuten sind, nur daß sie den gelehrten nicht bekand, herfür geben könne”.15 Here Leibniz recalled the proposal he had made to encourage the Academia Naturae Curiosorum (the Academia Leopoldina) to pursue utile activities. He had prompted Johann Georg Volckamer, through Scheffer, to encourage the physicians of Nuremberg, for the sake of science, to establish contact with the master tradesmen, or craftsmen, of that city and to publish the results of such discussions. Volckamer’s reply, quoted in Scheffer’s letter to Leibniz of April 3, 1682, was to the effect that, while the suggestion was by no means bad, no academician would be willing to communicate his knowledge to tradesmen, especially without appropriate compensation or remuneration. And so Leibniz confided to Scheffer, in his reply in mid-April, that he considered the reaction from Nuremberg to be ludicrous. His vision was that the bookish erudition of the scholars should be annotated with the multiplicity of useful explanatory notes of the practitioners, craftsmen, or tradesmen. In this respect, Leibniz appears to follow in the footsteps of the engineer and scientist Galileo Galilei who shared many aspects of practical knowledge including the methods and experience of foremen and engineers. Not only did Galileo share practical knowledge, but he also acted as an engineer, especially within the framework of the art of war. His scientific achievements too were largely based on, and influenced by, aspects of practical knowledge coming

15 Cf. A III,3 N. 342, pp. 588f. Translation: To counter such sterility, I had made the proposal regarding how the countless new and useful annotative expressions prevalent in the population, although unknown among the learned, might be used to this end.

Epilogue: Core Theses and Conclusion

885

from particular disciplines.16 In essence then, the sixth thesis presented here highlights Leibniz’s role as a successor of Galileo, focusing specifically on his advocacy of the inclusion of craftsmen, practitioners, and professionals from outside the academy, alongside academic scholars. This surely stands in the context of a certain ‘Artisanal Enlightenment’, which is reflected, for example, in Jacob Leupold’s introduction in Germany (in 1724) of the designations “Theoreticus”, “Practicus” and “Empiricus”, and also in the use of the corresponding terms “Savants”, “Artistes” and “Artisans” in the French enlightenment tradition.17 Among the projects in which Leibniz was involved, or followed with interest, three exemplary cases stand out as regards the important roles played by practitioners and craftsmen, namely the efforts of Leibniz and contemporaries for the development of calculating machines, the experiments carried out by Papin with a submersible vessel on the river Fulda in 1691 and 1692, and the school and pedagogical reform projects of Leibniz’s former mathematics professor Erhard Weigel. Following his departure from Paris in 1676, Leibniz attempted to entice the Parisian clockmaker Ollivier, who had been entrusted with the construction of his calculating machine, to come to Hanover, and the clockmaker possibly did come at the end of 1679, or in early 1680. When Ollivier’s model was finally completed, in the mid-1680s, Leibniz commissioned a larger machine with eight entry and twelve results positions. The work on this so-called ‘older’ machine was finally brought to a conclusion by the Hanover clockmaker Georg Heinrich Kölbing, in 1694, following a construction period of almost ten years. A first reference to the completion of the machine by Kölbing may be found in a letter sent to L’Hospital, on August 16, 1694, and in the correspondent’s reply of November 30. Yet another indication of the completion of the machine, from the year 1694, is found in Leibniz’s letter to Nicolas Toinard of October 14 (or 24). Furthermore, Crafft was able to give Huygens an account of Leibniz’s calculating machine, from his perspective, as is evident from Huygens’ letter to Leibniz of December 27, 1694. The machine was likewise presented to visitors in Hanover as, for example, on the occasion of a passing visit by Tschirnhaus, in

16 Cf. M. Valleriani, Galileo Engineer, 2010, and J. G. O’Hara, Science not metaphysical, 2013 (Preface, note 18 and note 22, respectively). 17 Cf. for example, J. Leupold, Theatrum Machinarum Generale. Schau-Platz des Grundes Mechanischer Wissenschaften, Leipzig, 1724, and in particular chap. 1, Sect. 17, p. 8; P. Bertucci, Artisanal enlightenment: Science and the mechanical arts in old regime France, New Haven, CT, London, 2017, and, in particular, pp. 1–28 (Introduction: savants, artisans, artistes).

886

Epilogue: Core Theses and Conclusion

September or October 1694, and during a visit of Thomas Burnett of Kemney, which took place in April 1695. At about the same time as the completion of the first exemplar of the so-called ‘older’ machine, work began on the counterpart or ‘younger’ machine. However, in the four years that followed, the calculating machines played no great role in Leibniz’s correspondence. Then, following the death of the clockmaker Hans Adam Scherp, in February 1700, his successor Johann Levin Warnecke, from Helmstedt, was appointed, on the recommendation of Leibniz’s assistant Rudolf Christian Wagner, who then also assumed the role of a supervisor of the ongoing work on the machine. In the month following Scherp’s death, both the ‘younger’ machine (then under-construction) and the completed ‘older’ machine, which served as a model, were transferred from Hanover to Helmstedt. The continuing work on the machine found expression in Wagner’s letters to Leibniz in February and March, 1701. Then, on April 7, Wagner expressed his frustration regarding the slovenly work of Warnecke’s deceased predecessor Scherp. In his reply, on April 11, Leibniz recalled the worthy services of Kölbing, Scherp’s predecessor. All in all, however, he had in the meantime come to terms with the basic problem, namely the shortage of such qualified craftsmen in Hanover. Then, for a short time, late in the year 1701, everything was once again in the balance when Warnecke became gravely ill and the further development of the calculating machine appeared to be once again in doubt. However, in his final letter of the year 1701, on December 16, Wagner was able to announce to Leibniz the recovery of the patient and the resumption of work on the machine. In the reports Leibniz received about the development of a submersible vessel in Kassel, the work of tradesmen or craftsmen, and of engineering practitioners also had a special significance. In the years 1691 and 1692, he received intelligence concerning Papin’s Hessian pump and, in particular, regarding its employment in the development of the new submersible vessel. This centrifugal pump had first been developed by a craftsman in Stuttgart, and had been made public in a work of Salomon Reisel in 1684 entitled Sipho Würtembergicus. Papin had studied this innovation intensively while in London, and then later (from 1688) in Marburg. Half a year after Papin first gave an account of this work, in the context of his article “Rotatilis suctor et pressor Hassiacus”, in June 1689, Reisel’s book Sipho Wurtembergicus per majora experimenta firmatus (1690) was published, and then reviewed in the Acta Eruditorum in March 1690. To this Papin then responded with an account of his investigation “Examen siphonis Wurtemburgici”, in May 1690. Finally, after an interval of five years, Papin published his concluding study of the centrifugal pump in the editions of his bilingual book, entitled Recueil de diverses pieces touchant quelques

Epilogue: Core Theses and Conclusion

887

nouvelles machines, and Fasciculus dissertationum de novis quibusdam machinis (1695), respectively. Papin employed, in the construction of his underwater vessel, first a ventilator pump, and then the centrifugal pump in combination with a hose, or tubing, reaching to the water surface for the supply of fresh air to the underwater vessel. The removal of the foul, or exhaust, air was achieved by means of a separate hose. This air exchange, through such tubing between the submerged vessel and the water surface, was crucial for the boat’s occupants in providing a supply of fresh air, both to the human respiratory system and to a lamp flame for illumination inside the vessel. Haes informed Leibniz about the progress of Papin’s efforts, in letters of May 1, May 22, and October 23, 1692. The correspondent accentuated the principal innovations of Papin, and he highlighted the centrifugal pump combined with tubing for air exchange, as well as the water containers, or ballast tanks, fitted with faucets and water pumps, to be used for submergence and reemergence, respectively, as important innovations. As regards the role of practitioners, and in particular makers of teaching aids, instruments and tools, the projects of Erhard Weigel – like his school and pedagogical reform efforts – also have a special significance. In the year 1683, Weigel started a private school project in his own house. Based on this experience, there followed a public school project in 1690. An outstanding aspect of Weigel’s School of Virtue (“Kunst- und Tugendschule”) was the range of teaching materials he developed himself, like his so-called “Schreibregel”, or writing rule, that availed of a mechanical instrument of his own design. In addition to this writing rule, there was a so-called “Leseregel”, or reading rule, for school starters and, for teaching arithmetic, a corresponding learning aid was made available. A particular attraction of Weigel’s private school was the concept of a “Schwebeclaß”, or floating class, which was intended to enable the scholars to accompany their memory exercises with swaying movements. The syllabus of instruction combined calculation and rhythmics, reading and swinging, on the “Schwebeclaß” platform. Weigel’s commitment to pedagogy and learning was reflected in his correspondence with Leibniz, for example, in a letter of April 26, 1694, in which he elaborated his school reform plans. Replying on May 20, 1694, Leibniz strongly praised Weigel’s efforts and he announced his continuing support for these in political circles. 1.7 The Fields of Alchemy and Chemistry In a letter of April 3, 1699, Leibniz wrote the following words to Johann Andreas Stisser: “et experimenta lucifera magis quam lucrifera quaerimus”,18 with which 18 Cf. A III,8 N. 25, p. 85. Translation: and we require ‘luciferous’ or enlightening experiments more than ‘lucriferous’ (viz. enriching or profit-bringing) experiments.

888

Epilogue: Core Theses and Conclusion

he expressed the view that enlightening, or enlightenment-bringing, experiments were to be preferred to lucrative, or profit-yielding, experiments. This idea, or theory, formulated by Leibniz is the underlying idea of the seventh thesis presented here. It was an essential conviction of his, in relation to the study of alchemy and chemistry. To the group of “experimenta lucifera” belong, besides knowledge-bringing and enlightenment-bringing, or enlightening, experiments, surely also the experimental investigations in the late 1670s of Leibniz, Robert Boyle and others, regarding newly-discovered substances like phosphorus, which had the properties of afterglow or phosphorescence, and offered the possibility of fire encapsulation or ignitability. To the group of “experimenta lucrifera”, on the other hand, belong a multitude of considerations, in Leibniz’s correspondence, which may be categorized under the heading of the economic utilization of chemical processes. The endeavors of Crafft and Elers, for example, encompassed a range of very different chemical processes for obtaining precious metals – and in particular gold and silver – that again and again played a role in Leibniz’s correspondences with these two projectors. And there can be no doubt about a certain interest of Leibniz himself in analytical chemistry, and specifically in the preparation, or separation, of gold and silver from suitable raw materials or chemical precursors. As in the case of a range of techno-economic projects, the filthy lucre, or shameful gain, orientation of projectors and entrepreneurs was frowned upon by Leibniz, and he continually insisted that his endeavors were, in the last analysis, being undertaken for the common good, or in the public interest. In August 1690, Leibniz wrote to Bodenhausen approving the study of a process, which was part of an investigation in Italy of a certain cinnabar process, and which involved a remarkable chemical reaction, or “transplantatio”, as it was termed. On the other hand, in a letter of June 26, 1689, he obtained intelligence from Crafft about the efforts of Johann Elias Rothmaler, in Vienna, to demonstrate a transmutation of metals. Leibniz expressed his skepticism in a comment written between the lines of Crafft’s text. On another occasion, in August 1689 and April 1690, Crafft likewise reported about a process – named after a certain count Lobkowitz  – for the transmutation of silver into gold and silver, using mercury and other substances. Yet another example was the separation process of Christian Holeysen. In the spring of 1690, Leibniz was able to carry on conversations with Holeysen, in Vienna, and to make detailed excerpts from his submissions to the emperor. Besides the possible production, or extraction, of gold and silver – by means of the chemical transmutation of metals – Leibniz was especially interested in an improvement in the processing of ores, referred to as the “maturation” of metals, and not just for obtaining new knowledge, but also for greater economic benefit, as he explained to the mining official Johann Christian Orschall, in a letter in August 1687.

Epilogue: Core Theses and Conclusion

889

Leibniz’s interest in alchemy dated back to his stay in Nuremberg – between the spring and fall of 1667 – when he became secretary of an alchemical society there. Almost thirty years later, after Gottfried Thomasius had reported to him, on August 10, 1696, about the alchemist Friedrich Kleinert, Leibniz recalled, in his reply of December 17, that he had first been imbued in chemical studies in Nuremberg, and that he had never regretted having learned growing up that which was to become certain in his manhood years. For, later on, he had often been motivated not just by that which had been assigned to him – and indeed he had not lacked curiosity, he insisted – but he had always been guided by circumspection, whereas, in contrast, others had been carried away by chemical hopes or pipe dreams. And so, he told the correspondent that he had always cautioned interested, or curious, friends about this in investigating nature, advising them not to detach chemical studies from the plans, or intentions, of life nor, at any time, to barricade anything whatsoever of their activities from the foundations of the laboratory, no more than to occupy themselves with chimeras or fantasies. He likewise recalled the names of certain alchemists of earlier times including Johann Conrad von Richthausen  – a baron called “Freiherr von Chaos” – and a former monk called Johann Wenzel Seyler. Baron von Chaos had demonstrated, in 1658 in Mainz, an alleged process for the transmutation of mercury into gold. Wenzel Seyler possessed a powder with the help of which gold could allegedly be produced, and he stood in high regard until his process was found to be fraudulent. On his way to Italy, on May 17, 1688, Leibniz had even inspected, at the Imperial Treasury in Vienna, the counterfeit, or fake, gold from the workshops of Chaos and Seyler. More than thirty years after his involvement with the alchemical society in Nuremberg, Leibniz’s continuing interest in the field is reflected in his correspondence at the turn of the century. After Magnus Gabriel Block enquired about his views on the branch of alchemy concerned with transmutation (chrysopoeia), Leibniz’s skeptical reaction  – in a no longer extant letter of April 17, 1699 – can be sensed from the tenor of Block’s reply two months later, on June 24. Leibniz warned, again and again, against investing time and money in the search for possible transmutations. The probability of success might be one to one hundred thousand. But, one ought not to discredit or abandon alchemy entirely, which was the tenor of his letter to Block of September 8. He did not fundamentally cast doubt on the notion of a transmutation, which he considered not to be impossible. However, many claims of such transformations failed to pass the test of proof, as he maintained in a letter to Block written between mid-December 1699 and the end of January 1700. For Leibniz, the fact that a transmutation was difficult to achieve, and at best only revealed to adepts in well-informed circles, was a work of providence that in turn

890

Epilogue: Core Theses and Conclusion

contributed to the maintenance of the world order, and also for this reason, the quest for it seemed to him to make no sense. That one might find a particular, or singular, process that worked, he considered to be more likely. Writing to Peter Moller of Hamburg, on January 2, 1699, he pointed out that, in spite of his contacts to renowned chemists, his intensive study of alchemistic writings, and his visitations to laboratories, he had witnessed no credible transmutation but, on the contrary, had encountered a number of impostors. In a letter of February 5, 1699, Stisser replied to a query of Leibniz about the transmutation of salts, with or without useful applications. Leibniz’s reply then, in his letter of April 3, 1699, was to the effect that the gain of enlightening experimental knowledge (like concerning the transmutation of salts) meant more than that of lucrative, or lucre-bringing, experimental knowledge, thus the statement on which the seventh thesis presented here is based. Nonetheless, on June 2, Stisser communicated some examples of supposed salt transmutations from all three kingdoms of nature, namely the mineral, vegetable and animal realms. However, for Leibniz, in his reply on December 22, 1699, it remained unclear whether in fact, in each of these examples, a “transmutatio” was really involved, and not just a “transplantatio”, in which chemical substances were merely exchanged in a reaction or process. Taking the example of (Johann Rudolph) Glauber’s salt, Leibniz considered different alternative explanations of the transmutation, or transformation, of chemical substances  – including revivification or transanimation  – for which he also proposed further investigations. Chemical substances could be veiled or unveiled in reactions, and the products of such a process might be already contained as subtle particles in the starting substances, or elements could possibly alter their form depending on the environment. 1.8 Geology, Mineralogy, and Paleontology In mid-October 1682, Leibniz informed Jean Gallois about physical observations he had made – in particular concerning the origin of minerals – in the extensive mines in the Harz mountains, or, in his words, there “où j’ay trouvé des choses si éloignées de l’opinion commune touchant l’origine des mineraux, et cependant si aisées à demonstrer par des raisons entierement mechaniques”.19 Thus, he announced that he had made discoveries about the origin of minerals, that were far removed from received opinions but, nonetheless easy to establish and purely on the basis of mechanical reasoning. Leibniz’s statement 19 Cf. A III,3 N. 407, p. 725. Translation: where I have found things far removed from the common opinion regarding the origin of minerals, and nonetheless so simple to demonstrate solely on the basis of mechanical reasoning.

Epilogue: Core Theses and Conclusion

891

here about his theory of the origin of minerals, based on mechanical reasoning, is the essence then of the eighth thesis presented here. Leibniz’s first years in the Harz mountains saw the beginning of the investigations, that would culminate ultimately in his posthumously-published work Protogaea sive de prima facie telluris (1749). This work was composed in the early 1690s, and it was publicly announced for the first time, in January 1693, in an advertisement in the Acta Eruditorum. Already in his letter of mid-October 1682 to Gallois, cited above, Leibniz explained to the correspondent that he had made important discoveries regarding the formation of rocks, and of the ore deposits found in lead and copper mines. In addition, he told that he had made unique discoveries regarding copper mines and had found an explanation for a certain wonder of nature, which was probably a reference to the fish fossils he had come across. In practical terms, Leibniz’s frequent journeys to the Harz mountains provided him with a welcome opportunity for geological and mineralogical studies, for indeed he considered a scientific treatment of all matters relating to mining to be a desideratum. In a letter to Nehemiah Grew, on March 19, 1680, he posed the question as to whether amber found in the ground near the location Wunstorf (not far from Hanover) could have originated there. And, in January and March 1682, Ferguson replied to queries received from Leibniz about a goldmine on Sumatra. Already, on November 24, 1681, Leibniz had requested information from the rich treasure trove of experience of the director of that mine, namely Benjamin Olitsch, a former Saxon mining official who had joined the Dutch East India Company. In this letter to Olitsch, Leibniz referred to fossilization specimens found in Mansfeld slate, which had revealed the likes of natural fish, and which he found to be of particular interest. In addition to this, there are some scattered reports in Leibniz’s correspondence, between 1683 and 1690, about other interesting prehistorical finds. Thus, for example, at the end of a letter to Georg Mohr, in the second half of July 1683, he told the correspondent that he had discovered fish fossils in shale, and that he suspected that the fish had lived in water before being petrified. Then, seven years later, on June 6, 1690, Friedrich Heyn sent him samples of mineral ores from the Ilmenau mines, specifically shale and limestone, in which fossilized plants were to be seen. About the time Leibniz composed his letter to Olitsch, in October– November 1681, an inspector of the mint in Zellerfeld named Becker enquired in conversation with him, specifically about the processing procedures for various ores, and on this occasion reference was also made to ores from other regions of geological or mining interest, like Muscau (near Görlitz in Saxony), or in Poland and even in East India. Then, in the mid-1680s, Leibniz began

892

Epilogue: Core Theses and Conclusion

to extend his project to write a history of the House of Welf, and to include prehistory there. His long-standing interest in the natural history of regions like the Harz district had, accordingly, led him to the idea of including earth history, and specifically the geological history of the Welf territories, as the prelude to the main dynastic history. In relation to the genesis of this work, stands also a report in the form of an extract from a letter, of January 1687, sent to the clergyman Barthold Meier about the “Baumannshöhle”, a cave near the small town of Rübeland, which Leibniz had visited in the fall of 1685. In a letter to Jean-Baptiste Du Hamel, on July 21, 1684, Leibniz reported about his recent studies, and views, concerning earth history and in particular about the formation of rocks and minerals, which were at variance with those of Agricola, Descartes and Nicolaus Steno (Niels Stensen), and which he would later summarize in the Protogaea. The same line of thought is found in a letter he wrote to Detlev Clüver, at the end of July 1686. Concerning the formation of metals, Georg Agricola had supposed  – in De ortu et causis subterraneorum (1546) – that mineral veins were formed when groundwater permeated the rocks, was then boiled by subterranean heat to attain a certain denseness, and so formed metal ore deposits. Leibniz attributed the process of the subterranean formation of minerals, by fire, to spirits trapped in the mines and he insisted he could reproduce the process in experiments. Descartes had – in his Principia philosophiae (1644) – disputed Agricola’s hypothesis, namely that groundwater was the source of the subterranean fluids from which minerals form, and he suggested instead that they form from molten rock. Leibniz considered Descartes’ account to be particularly meager, and off the mark, the author having had no experience in the mines and having been beguiled by written sources. At all events, the views expressed in Leibniz’s letters to Du Hamel, on July 21, 1684, and to Clüver at the end of July 1686, further underline the statement – found in his letter of mid-October 1682 to Jean Gallois – namely to the effect that his discoveries about the origin of minerals were indeed removed from received opinions, but were nonetheless easy to establish purely on the basis of mechanical reasoning, this of course being the essence of the eighth thesis being presented here. 1.9 The Fields of Biology and Life Sciences Already in his natural philosophy, and specifically in relation to bodies in motion and the distinction drawn between real and apparent movement, Leibniz introduced the notion of an entelechy, or an inherent or intrinsic and purposive force, to provide for the realization and maintenance of the state. In the fields of geology and mineralogy he attributed, in an analogous manner, the process of the subterranean formation of minerals by fire to spirits trapped

Epilogue: Core Theses and Conclusion

893

in the mines, and now, in biology, he also resorted to the notion of a kind of spirit trapped in the pollen to explain plant fertilization. Thus, Leibniz’s notion of an entelechy reappeared analogously, or correspondingly, as an inherent force which controlled and directed the activities and development of a living organism. In medicine, he likewise believed – as he wrote to Crafft at the end of September 1680 – that a malady actually resided in the body’s humors, and above all in the blood, since the “spiritus” or “animus” involved was nothing other than the most subtle of humors. Then, more than twenty years later, in the spring of 1701, the anatomy of fluids gained a special significance in Leibniz’s correspondence with Alexander Christian Gakenholz. Following a discussion between the two in Hanover, Gakenholz sent him, on April 21 of that year, an open letter entitled Epistola … de emendanda ac rite instituenda medicina. The central message of Gakenholz’s work, on the emendation and proper practice of medicine, was that, besides anatomy and chemistry, botany in particular had a special significance. As regards anatomy, the correspondent highlighted that of fluids, where the focus was the part of the human body made up principally of fluid parts, namely the blood and the serum, as well as the vital or animal spirits, since, it was postulated, most diseases arise from the constitution of these. The thoughts of Gakenholz found Leibniz’s approval since, in the context of biological thought and of vitalism in particular,20 there was for him an inherent force at play, which controlled and directed the activities and development of living beings. In his reply to Gakenholz, on April 23, Leibniz explained plant fertilization as being the result of a kind of spirit coming from the pollen, and which, on being led to the ovary, penetrated the silique or capsule, following which either the eggs or the seeds were duly fecundated there, or in his words: “Ex pollinis autem granulis spirituosum aliquid perductum ad ovarium, ut sic dicam, vel siliquam penetrare, atque ova vel semina illic foecundare”.21 This statement of Leibniz is at the core of the ninth thesis presented here. A further influence on Leibniz’s thought, in relation to the reproduction of plants in particular, was no doubt the letter sent to him by Johann Heinrich Burckhard, on February 21, 1701, following a meeting between the two a few days earlier. Burchard had provided a detailed representation of the sexual organs of plants and, in Leibniz’s letter to Gakenholz two months later, Burckhard’s reference to the work of Rudolph Jacob Camerarius – entitled De 20 Cf. E. Mayr, 1982 and 1997; F. J. Martínez, 2016 (Introduction, notes 201 and 211, respectively). 21 Cf. A III,8 N. 253, p. 660. Translation: Moreover, from the pollen grains a kind of spirit is led to the ovary, so to speak, or penetrates the pod and fecundates there either the eggs or the seeds.

894

Epilogue: Core Theses and Conclusion

sexu plantarum epistola (1694) – was duly acknowledged. In his letter of April 23 to Gakenholz, Leibniz saw, in the reproduction process in plants, a connecting element between the vegetable and animal kingdoms. Accordingly, the pollen of seed-producing, or flowering, plants corresponded to mammalian sperm. Similarly, the style of a flower corresponded to the vagina in placental mammals, and the ovary at the bottom of the style corresponded to a mammalian ovary. Sexual reproduction (like respiration) was for Leibniz then a key element connecting the vegetable and animal kingdoms, and is thus the idea at the center of the ninth thesis presented here. In this context, Leibniz also alluded to the rival theories of preformation of Antoni van Leeuwenhoek and of Theodor Kerckring. In the ovist-animalculist controversy, Leibniz saw a possible reconciliation of the standpoints, but his own position was close to that of the animalculist Leeuwenhoek, and accordingly, somewhat removed from that of the ovist Kerckring. The preformist theory assumed that the entire organism was preformed, either in the sperm (the animalculist position) or in the egg (the ovist position) of the mammal, and had but to unfold or deconvolve itself in the process of fertilization. In sum then, Leibniz saw in sexual reproduction a connecting element (alongside respiration) between the vegetable and animal kingdoms. In his letter to Gakenholz, of April 23, 1701, he furthermore employed concepts from the field of comparative anatomy – such as “collatio animalium” – and from reproductive, developmental and evolutionary biology – like “plantarum cum animalibus connexio” or “transitus a plantis ad animalia majora per intermedia”. And he spoke of insects as an intermediate form between plants and animals, particularly with Jan Swammerdam’s Historia insectorum generalis (1669) in mind. While sexual virility was surely not the central issue here, concepts analogous to power, prowess, vigor or potency arise in Leibniz’s texts across a broad spectrum of subject areas. As regards planetary motions, for example, a planet or a moon was transported by means of a ‘fluidum deferens’ rotating as part of a Cartesian vortex. In power technology, a pipe or a conduit was employed for the replenishment of a reservoir, as part of pumped-storage systems for use, for example, in mining, in urban water supply, in the operation of garden fountains, or in fortification works, like those at Breda, which were referred to by Johann Jakob Ferguson in his letter of July 31, 1683. Likewise in ballistics, the firepower and the line of fire of adjacent batteries was a matter of interest, and was referred to in Leibniz’s letter to Huygens of May 6, 1694, specifically with reference to Johannes Teyler’s Architectura militaris (1679). Correspondingly then, in consideration of the male reproductive organs of mammals and humans, a conduit or ‘vas deferens’ supplied the seminal vesicles, and provided for

Epilogue: Core Theses and Conclusion

895

male prowess, within in the context, of course, of the preformist-animalculist understanding of sexual reproduction. In this particular (and in the broader) context, the ninth thesis, presented here, is to be understood. 1.10 The Field of Medicine On February 20, 1690, Leibniz, in a letter to Rudolf Christian von Bodenhausen, expressed the desire that practical medicine, in as far as it is subject to reason, might become amenable to calculation, since calculus itself was nothing other than a most appropriate and compendious expression of reasoning, or of rational thought. His exact words were: “Wolte Gott daß Medicinalia und dergleichen concreta so wohl in potestate wären. Gleichwohl ist gewiß, daß auch diese dinge, in so weit sie rationi unterworfen, auch in calculum zu bringen. Denn calculus nichts anders als aptissima et compendiosissima ratiocinationum expressio”.22 These and similar ideas – regarding the desideratum of the application of mathematics, or of exact reasoning, in medicine – found expression in Leibniz’s correspondence, and are the essence of the tenth thesis presented here. In the course of, and in the wake of, his Italian journey, Leibniz was particularly impressed by certain “medici”, who distinguished themselves by their mathematical abilities, such as Guglielmini and Spoleti, the meetings with whom he recollected in his letter to Huygens, of July 25, 1690. In this context, Leibniz advocated treating medicine as an exact science and he pleaded for the mathematization of the subject. Leibniz’s deliberations regarding the medical profession, advances in the medical field, medicine as an empirical or rational science, and on the application of mathematics in medicine, were topics that continued to be discussed in his correspondence throughout the 1690s. Thus, he wrote to Huygens, on June 22, 1694, that medicine had hitherto been a purely empirical science. Empiricism in itself was no bad thing, he thought, but, since medicine had become a profession, its practitioners were often more concerned with saving and maintaining appearances. Leibniz even envisaged medicine as a charitable endeavor, under the aegis of a religious order of friars like the Capuchins. In his letter of July 30, 1698, to Block, he expressed the view that medicine had previously been primarily an empirical science, and that most of the theories 22 Cf. A III,4 N. 236, p. 462. Translation: [May it be that] God wanted that medícinalia and the like should exist both concretely and potentially. Nonetheless, it is certain that these things, in as far as they are subject to reason, can also be reduced to calculation. For, indeed, calculus is nothing other than a most appropriate and compendious expression of reasoning or of rational thought.

896

Epilogue: Core Theses and Conclusion

and hypotheses in the field were hardly reliable or useful. For that reason, he recalled the desire of Heinrich Meibom, namely that the discipline be established on an empirical foundation. Writing on October 30, 1698, the correspondent Block, for his part, also desired medical institutions that would not be concerned with occult speculation, but rather rooted in empiricism. However, he had his doubts that medicine could be built up solely on the foundation of experience and practice. For Leibniz, as he wrote to Block, on December 2, hypotheses and conjectures served as tentative solutions on the way to the establishment of the truth. Above all, it was important to separate certain from provisional knowledge. The mainstay of medicine was of course empiricism and practice. In practical terms, Leibniz advocated a comprehensive scientific training of medical doctors. Writing to Franck von Franckenau, in May 1698, he recalled a meeting in Paris with the personal physician of the king, Gui-Crescent Fagon, who had arranged for a law to be enacted that would require medics, and persons in the medical profession, to produce evidence of their professional training, requiring in particular a knowledge of anatomy, botany and chemistry. Leibniz’s thoughts on the idea of a rational medicine, based on mathematics, found expression particularly in his correspondence with the “medico-mathematicus” Domenico Guglielmini, in the year 1697. To the latter, he expressed (on January 7) the hope that mathematics might find a place in medicine. Although not uninclined to adopt a mathematical approach himself, Guglielmini was skeptical about Leibniz’s vision. Leibniz replied, at the end of September, emphasizing the higher value of rational over speculative thoughts in medicine, whereby plausible hypotheses ought to replace less certain conjectures. Thereafter, between 1699 and 1701, it was above all to his correspondent Friedrich Hoffmann, that Leibniz looked to for progress in the development of a rational medicine. In this sense then, Leibniz desired a contribution from Hoffmann towards the development of a rational medicine; alas, Leibniz never lived to see the publication of Hoffmann’s multi-volume work entitled Medicina rationalis systematica (1718–1734), later translated into English as A system of the practice of medicine (1783). Medicine received a critical appraisal in the two open letters addressed to Leibniz, in 1700 and 1701. Stisser’s open letter, of February–March 1700, contained a passionate plea for a pronounced inclusion of chemistry in medicine, and in the study of medicine. In Gakenholz’s open letter, of April 14, 1701, the author propagated an anatomy of fluids, and he pleaded for the reform of the system of anatomical, or postmortem, examination that should be guided by the understanding that the body is to be viewed simply in the context of the vessels and organs. Like Stisser, Gakenholz also emphasized the role of chemistry

Epilogue: Core Theses and Conclusion

897

in medicine; physicians should study this subject in order to understand the processes of nature. While Leibniz, in his reply to Stisser (probably on April 25, 1700), was very much in agreement with the views of the correspondent, in his reply to Gakenholz, on April 23, 1701, he emphasized above all his special interest in public health, and he acclaimed his proposed project with Hoffmann for the collection and annual publication of meteorological-medical observational data. 2

Conclusion and Concluding Thesis

In Leibniz’s correspondence in science, technology and medicine, issues which revealed a contradiction between matters of mythology and science, or matters of religion and science, occasionally came to the fore. Leibniz’s projected work Protogaea sive de prima facie telluris formed the context of his correspondence, in late 1696 and early 1697, with the Hamburg pastor Caspar Büssing and, in particular, the exchange of views regarding the theories of Thomas Burnet and William Whiston. In his work De situ telluris paradisiacae et chiliasticae Burnetiano … dissertatio mathematica (1695), Büssing published a critique of Burnet’s views as expounded in the author’s two-volume work, entitled Telluris theoria sacra (1681–1689). In a letter of October 16, 1696, Büssing then informed Leibniz about his “Dissertatio Anti-Burnetiana”. He was not sure, however, if his publication had reached England, and if Burnet would heed it and answer. Büssing’s opus was reviewed by Christoph Pfautz in the Acta Eruditorum, in November 1695, and subsequently referred to by Leibniz in his correspondence with, among others, Thomas Burnett of Kemney and Wilhelm Ernst Tentzel. On December 26, 1696, Büssing reported to Leibniz that he had just received Burnet’s publication, entitled Archaeologiae philosophicae; sive doctrina antiqua de rerum originibus, Libri duo (1692). Büssing was disappointed by Burnet’s publication, and he was of the opinion that it represented no more than a kind of literary history, and that it failed to dispel any of the doubts that had been raised. Leibniz could then inform Büssing, on January 3, 1697, about William Whiston’s A new theory of the earth, from its original to the consummation of all things wherein the creation of the world in six days, the universal deluge, and the general conflagration, as laid down in the Holy Scriptures, are shewn to be perfectly agreeable to reason and philosophy (1696), a work that was directed against Burnet’s Archaeologiae philosophicae and concerning which he had been informed through a letter sent from London by Burnett of Kemney, and addressed to the electress Sophie of Hanover, on December 16, 1696.

898

Epilogue: Core Theses and Conclusion

Burnet had presented the view that God had created the earth in a perfect and regular form, but that it had been transformed into its present form by the deluge. Büssing’s alternative scenario assumed a spongy solidification of the earth’s crust through which – as a result of the subsidence or settlement of the earth’s surface – subterranean waters had been pressed upwards causing the biblical deluge. Büssing’s model, or explanation, of the deluge appealed to Leibniz, as is evident from his letter of January 3, 1697. He was, however, of the opinion that a sinking of the earth’s surface would not have been possible without fissures in the existing crust of the earth. Leibniz’s skeptical questions, in this letter, as to where such a quantity of water might have disappeared following the deluge, and for example, whether the water had sunk back into cavities in the earth’s interior, remained no doubt unanswered by the correspondent. In correspondence with John Wallis in 1699, Leibniz discussed Olof Rudbeck’s geographical interpretation of mythology which, although rooted in literary legend, might just contain some truth, as he wrote in a letter to Wallis, on April 30. Rudbeck had located Atlantis, and Odysseus’ journey, in northern Europe. Magnus Gabriel Block considered Rudbeck’s hypotheses to be ridiculous, and these sentiments about his compatriot he expressed to Leibniz, in his letter of January 10, 1699. Block also reported, in this letter, about rejoinders to Rudbeck’s theory. Block, for his part, enquired about Leibniz’s views on astrology, palmistry (palm reading, or chiromancy), necromancy (necromantia), and the branch of alchemy concerned with transmutation (namely chrysopoeia). Leibniz’s skeptical reaction, in a non-extant letter of April 17, 1699, can be sensed from the tenor of Block’s reply two months later, on June 24. Unlike contemporaries (and correspondents), like Gottfried Kirch and Friedrich Hoffmann, Leibniz condemned outright “astrologia judiciaria”, and he saw himself here in the company of renowned astronomers, like Giovanni Domenico Cassini (1625–1712), Johannes Hevelius (or Hewelcke, 1611–1687) and Christiaan Huygens, as he wrote, in his letter of September 8, 1699, to Block. He proposed exposing, or unmasking, the astrologists by means of a statistical experiment, or study, that would show that the fulfillment, or coming true, of their predictions was entirely accidental. The physician Georg Wolfgang Wedel opened his correspondence with Leibniz, on August 24, 1699, by expressing his objections against the movement of the planet earth around the sun. In his view, this would contradict the story of genesis, or of creation, from the Book of Moses, according to which the earth had been created first, and later the sun and the other celestial bodies. Leibniz, in his reply, pleaded however for a metaphorical and not a literal interpretation of the bible, insisting that other differing interpretations could be derived

Epilogue: Core Theses and Conclusion

899

from the sense of the words of Moses. While it was not appropriate to confront sacred scripture at times with the book of nature, a useful approach would be to pursue the further use of those interpretations, which had proved their worth in certain instances. However, in the case of dubiety or ambiguity, of confrontation with obscurantism and controversy, that interpretation should be followed which is verified by the very nature of the matter itself. Thus, in his letter to Wedel of the ninth of the ninth, sixteen ninety nine, Leibniz wrote the words: “itaque in re obscura et controversa, is sequendus est, quem ipsa rei natura confirmat”.23 This statement – on which the concluding thesis of the present work is based – might be paraphrased accordingly as follows: when dealing with the physical world, and in the event of a conflict between science and controversial, or religious, obscurantism, the way of observation, of experience and systematic experimental investigation, of reason and of rational thought, should have precedence over that of mysticism, religion and theology. Thus, the way to go is that of science, and of scientific rationalism. Science should in the last analysis be separated from religion.24 Finally then, it may also be asserted here in conclusion that Leibniz’s correspondence in science, technology and medicine between 1676 and 1701 – not least also in the light of his autobiographical self-characterization based on a comparison of his behavior with that of an anthropomorphized “tiger animal” – reveals him in his very special role of ‘The Tiger who came to Science’.25 23 Cf. note 1, above. 24 Cf. O. Pedersen, 1990 (Preface, note 25). 25 Cf. J. Kerr, The tiger who came to tea, London, 1968, and notes 2, 3, and 4, above.

Bibliography

Editions and Translations (Leibniz and His Correspondents, in Alphabetical and Chronological Order)

Andrew W. Mellon Foundation / University of Oxford / Bodleian Libraries: Early Modern Letters Online (EMLO) (http://emlo.bodleian.ox.ac.uk/). Bernoulli (Jac. and Joh.): Streitschriften  =  Goldstine, H. H., Speiser, D. (eds.), Die Streitschriften von Jacob und Johann Bernoulli, Basel, 1991. Bernoulli (Jac.): Briefwechsel = Weil, A., Truesdell, C., Nagel, F. (eds.), Der Briefwechsel von Jacob Bernoulli, Basel and Boston, 1993 = vol. 4, part 2, of: Die Werke von Jakob Bernoulli (The Collected Scientific Papers of the Mathematicians & Physicists of the Bernoulli Family), 5 vols, Basel, 1969–1999. Bernoulli (Joh.): Briefwechsel (vol. 1)  =  Naturforschende Gesellschaft in Basel, Der Briefwechsel von Johann Bernoulli, Band 1: Spiess, O. (ed.), Der Briefwechsel mit Jacob Bernoulli, dem Marquis de l’Hôpital u.a., Basel, 1955. Bernoulli (Joh.): Briefwechsel (vol. 2) = Speiser, D. (ed.), Der Briefwechsel von Johann I Bernoulli. Im Auftrag der Naturforschenden Gesellschaft Basel und der Otto-SpiessStiftung; Band 2: Costabel, P., Peiffer, J. (eds.), Der Briefwechsel mit Pierre Varignon, Erster Teil: 1692–1702, Basel, 1988. Boyle: The Works = Hunter, M., Davis, E. B. (eds.), The works of Robert Boyle, 14 vols, London, 1999–2000. Fermat: Oeuvres = Tannery, P. de, et al. (eds.), Oeuvres de Fermat, 4 vols + Suppl., Paris, 1891–1912. Huygens: Oeuvres Complètes (HO) = Oeuvres complètes de Christiaan Huygens, publiées par la Société Hollandaise des Sciences, Tome 1 (I)–Tome 22 (XXII), La Haye / Den Haag (The Hague), 1888–1950. Online at: Digitale Bibliotheek voor de Nederlandse Letteren (http://www.dbnl.org/tekst/huyg003oeuv00_01/). Huygens: Yoder = Yoder, J. G. (ed.), Catalogue of the manuscripts of Christiaan Huygens including a concordance with his Oeuvres Complètes, Leiden, Boston, 2013. Leeuwenhoek: Palm = Palm, L. C., Zuidervaart, H. J., Anderson, D., Entjes, E. W. (eds.), Alle de brieven van Antoni van Leeuwenhoek. Uitgegeven, geillustreerd en van antekeningen voorzien door een commissie van Nederlandse geleerden, Deel XVII / The collected letters of Antoni van Leeuwenhoek. Edited, illustrated and annotated by a committee of Dutch scientists, Volume XVII [the 17th of a series of 19 being published since 1939], London, 2018. Leibniz: Opera Omnia = Dutens, L. (ed.), Gothofredi Guillielmi Leibnitii … Opera omnia, 6 vols, Geneva 1768.

902

Bibliography

Leibniz: Gesammelte Werke = Pertz, G. H. (ed.), Leibnizens Gesammelte Werke, 1st series, 4 vols, Hanover, 1843–1847. Leibniz: Lettres et opuscules inédits = Foucher de Careil, A. (ed.), Lettres et opuscules inédits de Leibniz précédés d’une introduction, Paris, 1854. Leibniz: Œuvres de Leibniz = Foucher de Careil, A., Œuvres de Leibniz, publiées pour la première fois d’après les manuscrits originaux, avec notes et introductions, 7 vols, Paris, 1859–75. Leibniz: Mathematische Schriften  =  Gerhardt, C. I. (ed.), Leibnizens mathematische Schriften, 7 vols, Berlin, Halle, 1849–1863; Hildesheim, Zürich, New York, 1962 (and later reprints). Leibniz: Philosophische Schriften = Gerhardt, C. I. (ed.), Die philosophischen Schriften von Gottfried Wilhelm Leibniz, Berlin, 7 vols, 1875–1890; Hildesheim, Zürich, New York, 1961–62 (and later reprints). Leibniz: Gerland = Gerland, E., Leibnizens und Huygens’ Briefwechsel mit Papin nebst der Biographie Papin’s, Berlin, 1881 and Wiesbaden, 1966. Leibniz: Academy Edition (A)  =  G. W. Leibniz: Sämtliche Schriften und Briefe, published by the Preußische (later: deutsche, most recently: Berlin-Brandenburgische) Akademie der Wissenschaften and the Akademie der Wissenschaften zu Göttingen, Darmstadt (later Leipzig, most recently Berlin), 1923–. Online at: Leibniz-Edition / Die Akademie-Ausgabe (http://www.leibnizedition.de/). Leibniz: Loemker = Loemker, L. E. (ed., trans.), Gottfried Wilhelm Leibniz: Philosophical papers and letters. A selection translated and edited with an introduction, Chicago, London, 1956; Dordrecht, Boston, London, 1969 and 1989 (The New Synthese Historical Library book series, vol. 2). Leibniz: Nordström  =  Nordström, J., “Leibniz och Magnus Gabriel Block. En brevväxling” [Leibniz and Magnus Gabriel Block, a correspondence], in: Lychnos. Lärdomshistoriska Samfundets Årsbok [Annual of the Swedish History of Science Society], 1965–1966, pp. 181–260. Leibniz: Costabel  =  Costabel, P., Leibniz et la dynamique, Paris, 1960; Costabel, P. (Maddison, R. E. W. trans.), Leibniz and dynamics: The texts of 1692, London, 1973. Leibniz: Knobloch (Combinatorics) = Knobloch, E., “Die mathematischen Studien von G. W. Leibniz zur Kombinatorik”, Studia Leibnitiana, Supplementa, vol. 11 and vol. 16, Wiesbaden, 1973 and 1976, respectively. Leibniz: Zacher  =  Zacher, H. J., Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein Beitrag zur Geschichte des binären Zahlensystems, Frankfurt am Main, 1973. Leibniz: Knobloch (Determinants) = Knobloch, E., Der Beginn der Determinantentheorie: Leibnizens nachgelassene Studien zum Determinantenkalkül, Hildesheim, 1980. Leibniz: Specimen dynamicum = 1) Dosch, H. G., Most, G. W., Rudolph, E. (eds., trans.), Gottfried Wilhelm Leibniz – Specimen dynamicum (Latin-German), Hamburg, 1982; 2) Ariew, R., Garber, D. (eds., trans.), G. W. Leibniz: Philosophical Essays, in particular

Bibliography

903

Part 1 (Basic Works), chap. 16 (A specimen of dynamics toward uncovering and reducing to their causes astonishing laws of nature concerning the forces of bodies and their actions on one another), Indianapolis and Cambridge, 1989. Leibniz: Parmentier = Parmentier, M. (ed., trans.), G. W. Leibniz: La naissance du calcul différentiel: 26 articles des Acta Eruditorum, Paris, 1989. Leibniz: Robinet = Robinet, A. (ed.), “G. W. Leibniz: Phoranomus seu de potentia et legibus naturae, Rome, Juillet 1689”, in: Physis, vol. 28, new series, no. 2 and no. 3, (1991). Leibniz: Knobloch (Arithmetic Quadrature)  =  Knobloch, E. (ed.), “De quadratura arithmetica circuli ellipseos et hyperbolae cujus corollarium est trigonometria sine tabulis”, Abhandlungen der Akademie der Wissenschaften in Göttingen, Mathematisch-Physikalische Klasse, Dritte Folge (Third series), no. 43, (1993). Leibniz: Fichant  =  Fichant, M. (ed., trans.), Leibniz: La réforme de la dynamique, De corporum concursu (1678) et autres textes inédits, Paris, 1994. Leibniz: Essais Scientifiques = Lamarra, A., Palaia, R., and Schepers, H. (eds. trans., and preface), Gottfried Wilhelm Leibniz: Essais scientifiques et philosophiques: Les articles publiés dans les journaux savants, 3 vols, Hildesheim, Zürich, New York, 2005. Leibniz: Cohen-Wakefield = Cohen, C., Wakefield, A. (eds., trans.), Protogaea. Gottfried Wilhelm Leibniz, Chicago, 2008. Leibniz: Heß-Babin = Heß, H.- J., Babin, M.-L. (eds., trans.), Gottfried Wilhelm Leibniz: Die mathematischen Zeitschriftenartikel, Hildesheim, Zürich, New York, 2011. Leibniz: Scheid-Engelhardt-Wellmer = Scheid, Ch. L., and Engelhardt, W. von., Wellmer, F.-W. (eds., trans.), Gottfried Wilhelm Leibniz: Protogaea sive de prima facie telluris et antiquissimae historiae vestigiis in ipsis naturae monumentis dissertatio, Göttingen, 1749; Stuttgart, 1949; Hildesheim, Zürich, New York, 2014. Leibniz: Widmaier-Babin = Widmaier, R., Babin, M.-L. (eds.), Philosophische Bibliothek: Gottfried Wilhelm Leibniz: Briefe (1694–1716) über China. Die Korrespondenz mit Barthélemy des Bosses S.J. und anderen Mitgliedern des Ordens, Hamburg, 2017. Leibniz: Natural philosophy = Arthur, R. T. W. (ed., trans.), and McDonough, J. Schroeder, L., Levey, S., Francks, R., Woolhouse, R., Tzuchien, T. (trans.), G. W. Leibniz: Journal articles on natural philosophy. [Forthcoming] Mariotte: Oeuvres = Oeuvres de Mr Mariotte, de l’Académie Royale des Sciences, 2 vols, Leiden, 1717. Newton: Correspondence = Turnbull, H. W., Scott, J. F., Hall, A. R., Tilling, L. (eds.), The correspondence of Isaac Newton, 7 vols, Cambridge, 1959–1977. Newton: Mathematical Papers  =  Whiteside, T. D. (ed.), The mathematical papers of Isaac Newton, 8 vols, Cambridge, 1967–1981. Papin: De la Saussaye = De la Saussaye, L., Pean, A. (eds.), La vie et les oeuvrages de Denis Papin, Paris and Blois, vol. 1, 1869, and De la Saussaye, L., Pean, A., de Belenet, L. (eds.), La vie et les ouvrages de Denis Papin, [édité] par L. de la Saussaye [1801–1878] et A. Péan; terminé par L. de Belenet, vols. 7–8 (Correspondence), Blois, 1893–1894.

904

Bibliography

Papin: Gerland = Gerland, E., Leibnizens und Huygens’ Briefwechsel mit Papin nebst der Biographie Papin’s und einigen zugehörigen Briefen und Actenstücken, Berlin, 1881 and Wiesbaden, 1966. Ramazzini: Di Pietro (Carteggio) = Di Pietro, P., “Carteggio fra Ramazzini e Leibniz”, Atti e Memorie della deputazione di storia patria per le antiche provincie Modenesi, ser. IX, vol. IV–V, (1964–1965), pp. 141–174. Ramazzini: Di Pietro (Epistolario) = Di Pietro, P. (ed.), Bernardino Ramazzini: Epistolario pubblicato in occasione del CCL anniversario della morte, Modena, 1964. Tschirnhaus: Knobloch = Knobloch, E., and Krautz, C., Ullmann, M. (eds.), Ehrenfried Walther von Tschirnhaus Gesamtausgabe: Reihe II (Amtliche Schriften), Abteilung 4 ( Johann Friedrich Böttgers Tätigkeit am Dresdner Hof ), Stuttgart, 2000. Wallis: Opera Mathematica  =  Wallis, J., Opera mathematica, 3 vols, Oxford, 1693– 1699 = Opera mathematica, volumen primum, 1695; Operum mathematicorum, volumen alterum, 1693; Operum mathematicorum, volumen tertium, 1699.



Primary Sources (in Alphabetical and Chronological Order)

Acta Eruditorum, Leipzig 1682–1782. Reprint:  10 vols (1682–1691), Hildesheim, New York, 1971–1972. Anon., “Extrait d’une letter écrite a l’Auteur du Journal touchant les bascules, pour faire travailler les personnes invalides, & touchant une nouvelle manière de piston”, Journal des Sçavans, (June 26, 1679), pp. 208–211. Anon., The book of common prayer and administration of the sacraments, and other rites & ceremonies of the church, according to the use of the Church of England; Together with the psalter or psalmes of David, pointed as they are to be sung or said in churches; And the form & manner of making, ordeining, & consecrating of bishops, priests, and deacons, London, 1662. Agricola, G., De ortu et causis subterraneorum libri V, Basel, 1546 and 1558. Agricola, G., De re metallica libri XII, Basel, 1556. Ango, P., L’Optique divisée en trois livres, Paris, 1682. Balduin, C. A., Phosphorus hermeticus, sive magnes luminaris, Frankfurt and Leipzig, 1675. Bartholin, R., Experimenta crystalli islandici disdiaclastici, quibus mira et insolita refractio detegitur, Copenhagen, 1669. Bartholin, E., Archibald, T. (trans.), Buchwald, J. Z. and Moller Pedersen, K. (Intro), Experiments on birefringent Icelandic crystal, …, with a facsimile of the original publication, Copenhagen: Danish National Library of Science and Medicine, 1991. Barba, A. A., Arte de los metales, Madrid, 1640.

Bibliography

905

Barba, A. A., Montagu, E. (trans.), The first book of the art of metals, in which is declared the manner of their generation; and the concomitants of them. Written in Spanish … in the year 1640, translated into English in the year 1669, London, 1670; The second book of the art of mettals: wherein is taught the common way of refining silver by quicksilver: with some new rules added for the better performance of the same. Written in Spanish  … and English’d by the Right Honourable Edward [Montagu, first] Earl of Sandwich, London, 1674; The Art of Metals, in which is declared the manner of their generation, and the concomitants of them. In two books … Translated in the year, 1669. By the R. H. Edward [Montagu, first] Earl of Sandwich, London, 1674. Barba, A. A., Lange, J. (trans.), Berg-Büchlein, darinnen von der Metallen und Mineralien Generalia und Ursprung, wie auch von derselben Natur und Eigenschafft … gehandelt wird, Hamburg, 1676. Bauval, B. de, “Extraits de diverses Lettres”, Histoire des Ouvrages des Savans, (February 1697), pp. 283–285. Becher J. J. [pseudonym: Solinus Salzthal Regiomontanus], Solini Salzthals Regiomontani Discurs von der Großmächtigen Philosophischen Universal-Artzney / von den Philosophis genannt Lapis Philosophorum Trismegistus, MS (of 1654) published as Discursus Solini Saltztal Regiomontani De Potentissima Philosophorum Johann Joachim Heilmann, pp. 675–694 in: Theatrum Chemicum, Strasbourg, 1661. Becher, J. J., Närrische Weißheit und Weise Narrheit oder Ein Hundert so Politische alß Physicalische Mechanische und Mercantilische Conceptem und Propositionen. Appendix: Folget zum Anhang Dr. Bechers kurtzer doch gründlicher Bericht von Wasser-wercken und Wasser-Künſten, Frankfurt, 1682. Becher, J. J., Tripus hermeticus fatidicus, pandens oracula chymica, Frankfurt, 1689. Beckmann, J., Anleitung zur Technologie oder zur Kenntnis der Handwerke, Fabriken und Manufacturen, vornehmlich derer, die mit der Landwirtschaft, Polizey und Cameral­ wissenschaft in nächster Verbindung stehn, Göttingen, 1777. Bernard, E., Orbis eruditi literatura à charactere Samaritico deducta, & ab ipso edit AD 1689, Oxford, 1689. Bernoulli, Jac., “Analysis problematis antehac propositi, de inventione lineae descensus a corpore gravi percurrendae uniformiter, sic ut temporibus aequalibus aequales altitudines emetiatur; et alterius cujusdam problematis propositio”, Acta Eruditorum, (May 1690), pp. 217–219. Bernoulli, Jac., “Specimen alterum calculi differentialis … una cum additamento quodam ad problema funicularium, aliisque”, Acta Eruditorum, (June 1691), pp. 282–290. Bernoulli, Jac., “Aenigmatis Florentini solutiones varie infinitae”, Acta Eruditorum, (August 1692), pp. 370f. Bernoulli, Jac., “Solutio problematis fraterni”, Acta Eruditorum, (June 1693), pp. 255f.

906

Bibliography

Bernoulli, Jac., “Solutio problematis Leibnitiani de curva accessus et recessus aequabilis a puncto dato mediante rectificatione curvae elasticae”, Acta Eruditorum, (June 1694), pp. 276–280. Bernoulli, Jac., “Constructio curvae accessus et recessus aequabilis”, Acta Eruditorum, (September 1694), pp. 336–338 [416–418]. Bernoulli, Jac., “De methodo tangentium inversa”, Acta Eruditorum, (October 1694), pp. 391–394 [471–474]. Bernoulli, Jac., “Solutiones superioris problematis”, Acta Eruditorum, (February 1695), pp. 65f. Bernoulli, Jac., “Observatiuncula ad ea, quae nupero mense novembri de dimensionibus curvarum publicata leguntur authore D.T.”, Acta Eruditorum, (June 1696), pp. 260f. Bernoulli, Jac., “Solutio problematum fraternorum, peculiari programmate Cal. Jan. 1697 Groningae, nec non Actorum Lips. mense Jun. & Dec. 1696, & Feb. 1697 propositorum: una cum propositione reciproca aliorum”, Acta Eruditorum, (May 1697), pp. 211–216. Bernoulli, Joh., Dissertatio chymico-physica de effervescentia et fermentatione nova hypothesi fundata, Basel, 1690. Bernoulli, Joh., “Solutio problematis funicularii”, Acta Eruditorum, (June 1691), pp. 274–276. Bernoulli, Joh., “Solutio problematis Cartesio propositi a Dn. de Beaune”, Acta Eruditorum, (May 1693), pp. 234f. Also in: Bernoulli: Streitschriften, pp. 158f. Bernoulli, Joh., Dissertatio inauguralis physico-anatomica de motu musculorum, Basel, 1694. Bernoulli, Joh., “Constructio facilis curvae accessus aequabilis a puncto dato per rectificationum curvae algebraicae”, Acta Eruditorum, (October 1694), pp. 394–399 [474–479]. Also in: Bernoulli: Streitschriften, pp. 199–204. Bernoulli, Joh., “Additamentum effectionis omnium quadraturarum et rectificationum curvarum per seriem quandam generalissimam”, Acta Eruditorum, November 1694, pp. 437–441 [517–521]. Bernoulli, Joh., “Animadversio in praecendentem solutionem Illustris. D. Marchionis Hospitalii”, Acta Eruditorum, (February 1695), pp. 59–65. Bernoulli, Joh., “Demonstratio analytica et synthetica suae constructionis curvae Beaunianae”, Acta Eruditorum, (February 1696), pp. [82]–85. Bernoulli, Joh., “Supplementum defectus geometriae Cartesianae circa inventionem locorum”, Acta Eruditorum, (June 1696), pp. 264–269. Bernoulli, Joh., Acutissimis qui toto orbe florent mathematicis, Groningen, 1697. Bernoulli, Joh., “Principia calculi exponentialium seu percurrentium”, Acta Eruditorum, (March 1697), pp. 125–133.

Bibliography

907

Bernoulli, Joh., “Curvatura radii in diaphanis non uniformibus, solutioque problematis a se in Actis 1696, p. 269, propositi, de invenienda linea Brachystochrona, id est, in qua grave a dato puncto ad datum punctum brevissimo tempore decurrit & de curva synchrona seu radiorum unda construenda”, Acta Eruditorum, (May 1697), pp. 206–211. Also in: Bernoulli: Streitschriften, pp. 263–270. Bernoulli, Joh., “Lettre de Mr. Bernoulli à l’auteur”, Histoire des Ouvrages des Savans, (June 1697), pp. 452–467. Bernoulli, Joh., “Excerpta ex literis Dn. Joh. Bernoullii Groningae 7 Augusti 1699 datis”, Acta Eruditorum, (November 1699), pp. 513–516. Bernoulli, Joh., Dissertatio philosophica de aëris gravitate et elasticitate. [Resp.] Phaebus Themmen, Groningen 1701. Blondel, F., L’art de jetter les bombes, Paris, 1683; Den Haag (The Hague), 1685. Bohun, R., A discourse concerning the origine and properties of wind: with an historicall account of hurricanes, and other tempestuous winds, Oxford, 1671. Bonfa, J., “Extrait d’une lettre … du R. P. Bonfa, …, touchant une nouvelle invention de faire des pendules de carton”, Journal des Sçavans, (January 23, 1679), pp. 23f. Boyle R., New experiments physico-mechanicall, touching the spring of the air, and its effects, (made for the most part, in a new pneumatical engine) written by way of a letter to the Right Honorable Charles Lord Vicount of Dungarven, Eldest Son to the Earl of Corke. By the Honorable Robert Boyle Esq., Oxford, 1660; Boyle: The works, vol. 1, pp. [141]–306. Boyle, R., Nova experimenta physico-mechanica de vi aeris elastica, et ejusdem effectibus, facta maximam partem in nova machina pneumatica, Oxford, 1661. Boyle, R., Nova experimenta physico-mechanica de vi aeris elastica, Rotterdam, 1669. Boyle, R., Certain physiological essays, and other tracts written at distant times, and on several occasions, London, 1661 and 1669 (2nd ed.); Boyle: The works, vol. 2 (publications of 1661). Boyle, R., A defence of the doctrine touching the spring and weight of the air propos’d by Mr. R. Boyle in his new physico-mechanical experiments, against the objections of Franciscus Linus; wherewith the objector’s funicular hypothesis is also examin’d, by the author of those experiments, London, 1662. Boyle, R., Nova experimenta physico-mechanica de vi aeris elastica, et ejusdem effectibus, facta maximam partem in nova machina pneumatica, Oxford, 1661 and Rotterdam, 1669. Boyle, R., Experimentorum novorum physico-mechanicorum continuatio secunda. In qua experimenta varia tum in aere compresso, tum in factitio, instituta, circa ignem, animalia &c. Unà cum descriptione machinarum continentur, London, 1680. Boyle, R., The aerial noctiluca, or, some new phenomena, and a process of a factitious self-shining substance, London, 1680; Boyle: The works, vol. 9, pp. 265–304.

908

Bibliography

Boyle, R., New experiments, and observations, made upon the icy noctiluca imparted in a letter to a friend living in the country: to which is annexed A chymical paradox, London, 1681/2 [1682]. Boym, M. P. (Cleyer, A. ed.), Clavis medica ad Chinarum doctrinam de pulsibus, Nürnberg, 1686; also in: Miscellanea Curiosa, Decur. II, Ann. IV, Append., (1686), pp. [1]–144. Brunswick-Lüneburg: Duke / Herzog August II. von Braunschweig-Lüneburg (Pseudonym: Gustavus Selenus), Cryptomenytices et cryptographiae libri novem. In quibus et planissima Steganographiae a Johanne Trithemio … magice et aenigmatice olim conscriptae, enodatio traditur, Lüneburg, 1624. Burnet, T., Telluris theoria sacra, originem et mutationes generales orbis nostri, quas aut jam subiit, aut olim subiturus est, complectens. Accedunt archaeologiae philosophicae, sive doctrina antiqua de rerum originibus, 2 vols, London, 1681–1689; Amsterdam, 1694; Sacred Theory of the Earth, London, 1684 (3rd ed., 1697); Heilige beschouwinge des aardkloots, Amsterdam, 1696. Burnet, T., Archaeologiae philosophicae: sive doctrina antiqua de rerum originibus, libri duo, London, 1692. Büssing, C., De situ telluris paradisiacae et chiliasticae Burnetiano, ad eclipticam recto, quem T. Burnetius in sua theoria sacra telluris proposuit, dissertatio mathematica, Hamburg, 1695. Camerarius, R. J., Ephemerides meteorologicae Tubingenses, ab anno seculi nonagesimo primo ad quartum Rudolphi Jacobi Camerarii  … Cum ill. D. Bernardini Ramazzini ephemeridibus barometricis Mutinensibus, anni M. DC. XCIV, Augsburg, 1696. Camerarius, R. J., Ad Thessalum, D. Mich. Bernardum Valentini, Professorem Giessensem excellentissimum, de sexu plantarum epistola, Tübingen, 1694. Cassini J., “Reflexions sur une lettre de M. Flamsteed à M. Wallis, touchant la parallaxe annuelle de l’etoile polaire”, Memoires de Mathematique et de Physique, Année 1699, (1702), pp. 177–183. Castelli, B., Della misura dell’ acque correnti, Rome, 1628 (1st ed.); Bologna, 1660 (3rd ed.). Catelan, F. Abbé de, “Courte remarque de M. l’Abbé D.C. où l’on montre à Mr. G. G. Leibnits la paralogisme contenu dans l’objection precedente”, Nouvelles de la République des Lettres, (September 1686), pp. 999–1003. Cleyer, A. (ed.), Specimen medicinae Sinicae, sive opuscula medica ad mentem Sinensium, continens I. De pulsibus libros quatuor e Sinico translatos. II. Tractatus de pulsibus ab erudito Europaeo collectos, Frankfurt am Main, 1682. Cleyer, A., Jager, H. de, “Observatio I. De sementina”, Miscellanea Curiosa, Decur. II, Ann. III, (1684), pp. 1–17. Cleyer, A., Clavis medica ad Chinarum doctrinam de pulsibus, Frankfurt a. M., 1680; also published in Miscellanea Curiosa, Decur. II, Ann. IV, Append., (1686), pp. [1]–144.

Bibliography

909

Clüver, D., “Quadratura circuli infinitis modis demonstrata”, Acta Eruditorum, (July 1686), pp. 369–371. Clüver, D., Geologia sive philosophemata de genesi ac structura globi terreni: Oder: Natürliche Wissenschafft von Erschaffung und Bereitung der Erd-Kugel, Hamburg, 1700. Corradi, B., Raccolta di tutto quello che fin ora estato scritto nella virtuosa gara iatro-chimica tra il dott. G. P. Stabe de Cassini e Bern. Corradi, Modena, 1690. Co(s)tentin de Tourville, A. H. de, Exercice en général de toutes les manoeuvres qui se font à la mer, Le Hâvre de Grâce, 1693. Dangicourt, P., “De periodis columnarum in serie numerorum progressionis arithmeticae dyadice expressorum”, Miscellanea Berolinensia, (1710), pp. 330–376. Davys, J., An essay on the art of decyphering. In which is inserted a discourse of Dr. Wallis. Now first publish’d from his original manuscript in the publick library at Oxford, London, 1737. Defoe, D., An essay upon projects, London, 1697. Descartes, R., Principia philosophiae, Amsterdam, 1644. Drebbel, C. J., Ein kurzer Tractat von der Natur der Elementen und wie sie den Windt, Regen, Blitz und Donner verursachen und wozu sie nutzen, durch Cornelium Drebbel in Niederlandisch geschreiben; unnd allen der Naturliebhaberen zu Nutz ins Hochteutsch getreulich vbergesetzt, Leiden, 1608 and Hamburg, 1619; Een kort tractaet van de natuere der elementen, ende hoe sy veroorsaecken, den wint, reghen, blixem, donder ende waeromme dienstlich zijn, Haarlem, 1621. Du Hamel, J.-B., Regiae scientiarum academiae historia, Paris, 1701. Eisenschmidt, J. C., Diatribe de figura telluris elliptico-sphaeroide, Straßburg, 1691. Fahrner, Ch., Widerlegung oder vielmehr Warnung vor der groß prallenden Explicatio Miraculi mundi, und der betriegerischen genandten Wolfahrt Teutschlands Johann Rudolph Glaubers, Stuttgart, 1656. Fatio de Duillier, N. (anon.), Fruit-walls improved, by inclining them to the horizon: or, a way to build walls of fruit-trees; whereby they may receive more sun shine and heat than ordinary. By a member of the Royal Society, London, 1699. Fatio de Duillier, N., Lineae brevissimi descensus investigatio geometrica duplex, London, 1699. Fermat, P. de, Analysis ad refractiones [and] Synthesis ad refractiones (1662) in: Tannery, P. de, et al. (eds.), Oeuvres de Fermat, vol. 1, pp. 170–172 and pp. 173–179, respectively. Ferguson, J. J., Labyrinthus algebrae, verdeelt in vijf deelen, The Hague (Den Haag; In ’s Gravenhage), 1667. Flamsteed, J., The doctrine of the sphere, grounded on the motion of the earth, and the antient Pythagorean or Copernican system of the world: In two parts, London, 1680. Gakenholz, A. C., Ad illustrem atque excellentissimum virum Dominum Godefr. Guilielmum Leibnitium  … epistola  … de emendanda ac rite instituenda medicina, Celle, (April 14) 1701; A III,8, N. 241, pp. 615–626.

910

Bibliography

Galileo Galilei, Sidereus nuncius magna, longeque admirabilia spectacula pandens, Venice, 1610; Van Helden, A. (trans., ed.), Galileo Galilei: Sidereus nuncius or the sidereal messenger: Second edition, Chicago and London, 1989 and 2015. Galileo Galilei, Dscorsi e dimostrazioni matematiche, intorno a due nuove scienze attenenti alla mecanica & i movimenti locali, Leiden, 1638; Stillman Drake (trans.), Discourses and mathematical demonstrations concerning two new sciences pertaining to mechanics and local motions, Madison (Wis.), 1974. Geber (Jabir ibn Hayyan), Horn, C. (ed.), Chymia sive traditio summae perfectionis et investigatio magisterii, Leiden, 1668. Glauber, J. R., Prosperitatis Germaniae; pars tertia: in qua salpetrae ex variis ubique obviis subjectis facillimè atque copiosè extrahendi modus traditur, Amsterdam, 1659; Theütschlandes Wohlfahrt, dritter Theil. Darinnen gelehret wird, wie vnd auff was weise aus vnterschiedlichen subjectis … vnd auch in Copia ein güter Salpeter zu bereiten, Amsterdam, 1659. Goldmann, N. (Sturm, L. Ch., ed.), Vollständige Anweisung zu der Civil Bau-Kunst  … auß den besten Überresten des Alterthums, auß den außerlesensten Reguln Vitruvii, Vignolae, Scamozzi, Palladii, und anderer zusammen gezogen, Wolfenbüttel, 1696. Graaf, R. de, De virorum organis generationi inservientibus, de clysteribus et de usu siphonis in anatomia, Leiden und Rotterdam, 1668. Graaf, R. de, Partium genitalium defensio, Leiden, 1673. Gregory, J., Exercitationes geometricae, London, 1668. Gregory, D., “De ratione temporis quo grave labitur per rectam data duo puncta conjungentem”, Philosophical Transactions, vol. 19, no. 225, (February 1697), pp. 424f. Gregory, D., “Davidis Gregorii M. D. Astronomiae professoris Saviliani & S. R. S. catenaria”, Philosophical Transactions, vol. 19, no. 231, (August 1697), pp. 637–652. Gregory, D., “Transcripta ex actis philosophicis Anglicanis mensis Augusti 1697 (pp. 633 segg)”, Acta Eruditorum, (July 1698), pp. 305–321. Gregory, D., “Responsio ad animadversionem ad Davidis Gregorii catenariam”, Philosophical Transactions, vol. 21, no. 259, (December 1699), pp. 419–426; Acta Eruditorum, (July 1700), pp. 301–306. Gregory, D., Astronomiae physicae et geometricae elementa, Oxford, 1702. Guericke, O. von, Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio, Amsterdam, 1672; reprint Aalen, 1962. Guericke, O. von, Glover Foley Ames, M. (ed., trans.), The new (so-called) Magdeburg experiments of Otto von Guericke, (International Archives for the History of Ideas, no. 137), Dordrecht, 1994. Guglielmini, D., Aquarum fluentium mensura nova methodo inquisita, 2 parts, Bologna, 1690–1691: part 1 (Books 1–3, 1690) and part 2 (Books 4–6 with Appendix, 1691). Guglielmini, D., Epistolae duae hydrostaticae altera apologetica aduersus obseruationes contra mens. aquarum fluentium a clarissimo viro Dionisio Papino factas … altera de velocitate, et motu fluidorum in siphonibus recuruis suctoriis, Bologna, 1692.

Bibliography

911

Guglielmini, D., Della natura de’ fiumi trattato fisico-matematico … In cui si manifestano le principali proprietà de’ fiumi, se n’indicano molte sin’hora non conosciute, e si dimostrano d’vna maniera facile le cause delle medesime, Bologna, 1697. Guglielmini, D., “Epistola Dominici Guilielmini ad Praesidem, de aquarum fluentium mensura, qua respondet epistolae D. Papini ad Hugenium”, Miscellanea Berolinensia, (1710), pp. 188–196. Haes, J. S., Steganographie nouvelle, où cet art fort imparfait jusques icy, a eté mis dans une plus grande perfection; de sorte que presentement il comprend à la fois, tous les avantages, qu’on a toujours souhaité d’y voir ensemble. Composé à fin de servir d’essay et de projet pour un ouvrage plus ample et plus achevé, si celuy a le bonheur de trouver de l’approbation; et dedié … à S. A. S. Msgr. le Landgrave de Hesse, Kassel, 1693. Hartsoeker, N., Essay de dioptrique, Paris, 1694. Harvey, W., Exercitationes de generatione animalium. Quibus accedunt quaedam de partu: de membranis ac humoribus uteri: et de conceptione, London, 1651; Amsterdam, 1651. Hoffmann, F. (Praes.), Cellarius, S. (Resp.), Dissertatio inauguralis physico-medica de natura morborum medicatrice mechanica, Halle, 1699. Hoffmann, F. (Praes.), Ockel, Ch. (Resp.), Dissertatio inauguralis physico-medica de potentia ventorum in corpus humanum, ubi simul agitur de ascensu et descensu argenti vivi in barametro, Halle, 1700. Hoffmann, F., Observationes barometrico-meteorologicae, et epidemicae Hallenses Anni MDCC, Halle, 1701. Hoffmann, F., Medicina rationalis systematica, 6 vols., Halle, 1718–1734. Hoffmann, F. (Duncan, A. and Lewis, W., eds. and trans.), A system of the practice of medicine, London, 1783. Hooke, R., Micrographia: Or some physiological descriptions of minute bodies made by magnifying glasses. With observations and inquiries thereupon, London, 1665. Hooke, R., An attempt to prove the motion of the earth from observations, London, 1674. Horne, J. van, Suarum circa partes generationis in utroque sexu observationum prodromus ad celeberr. virum Guernerum Rolfinckium, Leiden 1668. L’Hospital, G. F. A. de, “Solution du problème que Monsr de Beaune proposa autrefois à Mr. Descartes”, Journal des Sçavans, (September 1, 1692), pp. 598f. L’Hospital, G. F. A. de, “Solutio problematis physico mathematici ab erudito quodam geometra propositi”, Acta Eruditorum, (February 1695), pp. 56–59. L’Hospital, G. F. A. de, Analyse des infiniment petits pour l’intelligence des lignes courbes, Paris, 1696. L’Hospital, G. F. de, “Solutio problematis de linea celerrimi descensus”, and “Solutio problematis publice propositi a Dn. Joh. Bernoullio”, Acta Eruditorum, (May 1697), pp. 217f. and pp. 218–220, respectively. Huygens, Ch., “An account of the observations, made by the Philosophical Academy at Paris, May 12 1667 about 9. of the clock in the morning, of an halo or circle about

912

Bibliography

the sun; together with a discourse of M. Hugens de Zulechem, concerning the cause of these meteors, as also that of parelia’s or mock-suns”, Philosophical Transactions, vol. 5, no. 60, (June 20, 1670), pp. 1065–1074; Huygens: Oeuvres complètes (HO), vol. 6, p. 162 and vol. 7, pp. 11 and 41. Huygens, Ch., Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae, Paris, 1673; L’horloge à pendule 1656–1666, Huygens: Oeuvres complètes (HO), vol. 17, pp. 1–153, and Horloges marines (et sympathie des horloges), pp. 155–236; L’horloge à pendule 1666–1695, Huygens: Oeuvres complètes (HO), vol. 18, pp. 1–702. Huygens, Ch., Traité de l’aimant (1679), Huygens: Oeuvres complètes (HO), vol. 19, pp. 574–604. Huygens, Ch., “Solution du problème proposé par M. L[eibniz] dans les Nouvelles de la Republique des Lettres, du mois de Septembre 1687”, Nouvelles de la Republique des Lettres, (October, 1687), pp. 1110f. Huygens, Ch., Traité de la lumière où sont expliquées les causes de ce qui luy arrive dans la reflexion, et dans la refraction. Et particulierement dans l’etrange refraction du cristal d’Islande … Avec un discours de la cause de la pesanteur, Leiden, 1690; Huygens: Oeuvres complètes (HO), vol. 19, pp. 451–547 and vol. 21, pp. 427–499, respectively; Huygens, Ch., Treatise on Light: In which are explained the causes of that which occurs in reflexion & in refraction, and particularly in the strange refraction of Iceland crystal, London, 1912; Huygens, Ch., Treatise on light, Frankfurt am Main, 2020. Huygens, Ch., “Solutio ejusdem [i.e. funicularii] problematis”, Acta Eruditorum, (June 1691), pp. 281–282. Huygens, Ch., “Remarque de M. Huguens sur le livre de la manoeuvre des vaisseaux”, Bibliothèque Universelle et Historique, (September 1693), pp. 195–203; extract in Journal des Sçavans, (May 9, 1695), pp. 311–318. Huygens, Ch., “De problemate Bernoulliano”, Acta Eruditorum, (October 1693), pp. 475f. Huygens, Ch., “Constructio universalis problematis a clarissimo viro, Joh. Bernoullio, superiori anno mense Majo propositi”, Acta Eruditorum, (September 1694), pp. 338–339 [418–419]. Huygens, Ch. (de Volder, B., Fullenius, B., eds.), Opuscula postuma, quae continent dioptricam. Commentarios de vitris figurandis. Dissertationem de corona et parheliis. Tractatum de motu, de vi centrifuga. Descriptionem automati planetarii, Leiden, 1703; also Dioptrique (Dioptrica 1653; 1666; 1685–1692), Huygens: Oeuvres complètes (HO), vol. 13. Huygens, Ch., De coronis et parheliis, Huygens: Oeuvres complètes (HO), vol. 17, pp. 351–362; also Traité des couronnes et des parhélies, pp. 364–445; Appendices I–XV, pp. 446–516. Junius, U., Epistola de dispositione ephemeridum ad seculum XVIII conficiendarum, Leipzig, 1699.

Bibliography

913

Kepler, J., Tabulae Rudolphinae, quibus astronomicae scientiae, temporum longinquitate collapsae restauratio continentur, Ulm, 1627. Kirchmaier, G. K., Noctiluca constans et per vices fulgurans, Wittenberg, 1676, enlarged as: “Noctiluca constans et per vices fulgurans, diutissime quaesita, nunc reperta; Dissertatione brevi praevia de luce, igne, ac perennibus lucernis. Wittenberg 1676”, in: Miscellanea Curiosa, Decur. I, Ann. VIII, (1677), pp. 219–246. Knorr(e), M. (Praes.), J. J. Hartmann (Resp.), Dissertatio dioptrica de refractione luminis, Wittenberg 1693. Knorr(e), M. (anon.), Review of B. Nieuwentijt, Considerationes secundae (1696), in Acta Eruditorum, (March 1697), pp. 124f. Kunckel, J., Oeffentliche Zuschrifft von dem Phosphoro mirabili und dessen leuchtenden Wunder-Pilulen, Wittenberg, 1678. La Scala, D., Phlebotomia damnata  …, sive, anidii, chrisippi-cnidii, aschlepiadis, erasistrati, et aristogenis contra sanguinis missionem doctrina e vetustatis tenebris in lucem … revocata, & luculentius enucleata … In qua singula rationum momenta, quae sanguinis eductioni adversantur, aequa veritatis lance expenduntur, Padua, 1696. Ledel, S., “De curiosis vere curiosis”, Miscellanea Curiosa, Decur. II, Ann. VII, (1688), pp. 84–86. Leeuwenhoek, A. van, “Observations, communicated to the publisher by Mr. Antony van Leewenhoeck, in a Dutch letter of the 9th Octob. 1676. here English’d: concerning little animals observed in rain- well- and snow-water, as also in water wherein pepper had lain infused”, Philosophical Transactions, vol. 12, no. 133, (March 25, 1677), pp. 821–831. Leeuwenhoek, A. van, “Observationes de natis e semine genitali animalculis”, Philosophical Transactions, vol. 12, no. 142, (December 1677–February 1678), pp. 1040–1043. Leeuwenhoek, A. van, “An abstract of a letter of Mr. Leeuwenhoeck Fellow of the R. Society, Dated March 30th. 1685. to the R. S. concerning generation by an insect”, Philosophical Transactions, vol. 15, no. 174, (August 22 / September 1, 1685), pp. 1120–1134. Leeuwenhoek, A. van, Arcana naturae detecta, Delft, 1695; also: Arcana naturae, ope & beneficio exquisitissimorum microscopiorum. Detecta, variisque experimenta demonstrata, una cum discursu & ulteriori dilucidatione, Leiden 1696. Leibniz, G. W., Dissertatio de arte combinatoria, Leipzig, 1666; reprint Frankfurt, 1690; A VI,1 pp. 163–228. Leibniz, G. W., Hypothesis physica nova, sive theoria motus concreti, una cum theoria motus abstracti, Mainz 1671; London 1671; Philosophischen Schriften, IV, pp. 177–219. Leibniz, G. W., “Extrait de deux lettres écrites à l’auteur du journal, l’une d’Hanovre par M. de Leibnitz, Conseiller de S.A.M. le Duc d’Hanover, touchant une expérience considerable d’une eau fumante, et l’autre d’Oxford, par M. Hansen”, Journal des Sçavans, (February 17, 1681), p. 46.

914

Bibliography

Leibniz, G. W., “De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus expressa”, Acta Eruditorum, (February 1682), pp. 41–46 (Parmentier, 1989, chap. I, pp. [61]–81; Essais Scientifiques, 2005, N. 7; Heß-Babin, 2011, chap. 3, pp. 9–18). Leibniz, G. W., “The true proportion of the circle to the square”, Philosophical Collections, (April 1682), pp. 204–210. Leibniz, G. W., “Unicum opticae, catoptricae et dioptricae principium”, Acta Eruditorum, (June 1682), pp. 185–190 (Essais Scientifiques, 2005, N. 9; Heß-Babin, 2011, chap. 4, pp. 19–28). Leibniz, G. W., “L’Operation pour faire le phosphore”, Procès Verbaux des Séances de l’Académie des Sciences, Tome IX, (4.7.1682), pp. 165–166; A III,3 N. 368, p. 651 and pp. 662f. Leibniz, G. W., “Meditatio de separatione salis et aquae dulcis, novoque separationum chymicharum genere”, Acta Eruditorum, (December 1682), pp. 386–388. Leibniz, G. W., “Meditatio juridico-mathematica de interusurio simplice”, Acta Eruditorum, (October 1683), pp. 425–432 (Essais Scientifiques, 2005, N. 11; Heß-Babin, 2011, chap. 5, pp. 29–38). Leibniz, G. W., “Demonstrationes novae de resistentia solidorum”, Acta Eruditorum, (July 1684), pp. 318–325. Leibniz, G. W., “De dimensionibus figurarum inveniendis”, Acta Eruditorum, (May 1684), pp. 233–236 (Parmentier, 1989, chap. II, pp. [82]–92; Essais Scientifiques, 2005, N. 12; Heß-Babin, 2011, chap. 6, pp. 39–45). Leibniz, G. W., “Demonstrationes novae de resistentia solidorum”, Acta Eruditorum, (July 1684), pp. 319–325. Leibniz, G. W., “Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratur, et singulare pro illis calculi genus”, Acta Eruditorum, (October 1684), pp. 467–473 (Parmentier, 1989, chap. III, pp. [96]–117; Essais Scientifiques, 2005, N. 14; Heß-Babin, 2011, chap. 8, pp. 51–62). Leibniz, G. W., “Demonstratio geometrica regulae apud staticos receptae de momentis gravium in planis inclinatis, nuper in dubium vocatae: et solutio casus elegantis, in Actis Novembri 1684 pag. 512. propositi, de globo duobus planis angulum rectum facientibus simul incumbente: quantum unumquodque planorum prematur, determinans”, Acta Eruditorum, (November 1685), pp. 501–505. Leibniz, G. W., Discours de métaphysique, 1686; A VI,4 N. 306, pp. 1529–1588. Leibniz, G. W., “Brevis Demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae, secundum quam volunt a Deo eandem semper quantitatem motus conservari; qua et in re mechanica abutuntur”, Acta Eruditorum, (March 1686), pp. 161–163; translation: “A brief demonstration of a notable error of Descartes and others concerning a natural law”, Leibniz: Loemker, 1989, chap. 34, pp. 296–302.

Bibliography

915

Leibniz, G. W., “De geometria recondita et analysi indivisibilium atque infinitorum”, Acta Eruditorum, (June 1686), pp. 292–300 (Parmentier, 1989, chap. V, pp. [126]–143; Essais Scientifiques, 2005, N. 20; Heß-Babin, 2011, chap. 10, pp. 69–81). Leibniz, G. W., “Demonstration courte d’une erreur considerable de M. Descartes & de quelques autres touchant une loi de la nature selon laquelle ils soutiennent que Dieu conserve tousjours dans la matière la même quantité de mouvement, de quoi ils abusent même dans la mechanique”, Nouvelles de la République des Lettres, (September 1686), pp. 996–999. Leibniz, G. W., “Réponse à la remarque de M. l’Abbé D. C[atelan] contenuë dans l’article I de ces Nouvelles, mois de Juin 1687 où il prétend soûtenir une loi de la nature avancée par M. Descartes”, Nouvelles de la Republique des Lettres, (September 1687), pp. 952–956. Leibniz, G. W., “De lineis opticis, et alia; excerpta ex literis ad – [sic]”, Acta Eruditorum, (January 1689), pp. 36–38. Leibniz, G. W., “Schediasma de resistentia medii, et motu projectorum gravium in medio resistente”, Acta Eruditorum, (January 1689), pp. 38–47. Leibniz, G. W., “Tentamen de motuum coelestium causis”, Acta Eruditorum, (February 1689), pp. 82–96; translation: “An essay on the causes of celestial motions”, part 2, chapter 6, pp. 126–142 in: Bertoloni Meli, D., Equivalence and priority: Newton versus Leibniz including Leibniz’s unpublished manuscripts on the Principia, Oxford, 1993 and 2002. Leibniz, G. W., “De linea isochrona, in qua grave sine acceleratione descendit, et de controversia cum Dn. abbate D. C[atelan]”, Acta Eruditorum, (April 1689), pp. 195–198 (Parmentier, 1989, chap. VII, pp. [154]–165; Essais Scientifiques, 2005, N. 28; Heß-Babin, 2011, chap. 12, pp. 89–95). Leibniz, G. W., “De causa gravitatis et defensio sententiae suae de veris naturae legibus contra Cartesianos”, Acta Eruditorum, (May 1690), pp. 228–239; Mathematische Schriften, vol. 6, pp. 193–203. Leibniz, G. W., “Ad ea, quae vir clarissimus J. B., mense Majo nupero in his Actis publicavit, responsio”, Acta Eruditorum, (July 1690), pp. 358–360 (Parmentier, 1989, chap. VIII, pp. [166]–172; Essais Scientifiques, 2005, N. 30; Heß-Babin, 2011, chap. 13, pp. 97–101). Leibniz, G. W. (anon.), “Aquarum fluentium mensura nova methodo inquisita autore Domenico Gulielmino M.D.”, Acta Eruditorum, (February 1691), pp. 72–75. Leibniz, G. W., “Additio ad schediasma de medii resistentia publicatum in Actis mensis Febr. 1689”, Acta Eruditorum, (April 1691), pp. 177f. Leibniz, G. W., “Quadratura arithmetica communis sectionum conicarum quae centrum habent, indeque ducta trigonometria canonica ad quantamcumque in numeris exactitudinem a tabularum necessitate liberata: cum usu speciali ad

916

Bibliography

lineam rhomborum nauticam, aptatumque illi planisphaerium”, Acta Eruditorum, (April 1691), pp. 178–182 (Parmentier, 1989, chap. IX, pp. [173]–185; Essais Scientifiques, 2005, N. 32; Heß-Babin, 2011, chap. 14, pp. 103–113). Leibniz, G. W., “De linea in quam flexibile se pondere proprio curvat, ejusque usu insigni ad inveniendas quotcumque medias proportionales et logarithmos”, Acta Eruditorum, (June 1691), pp. 277–281 (Parmentier, 1989, chap. X, pp. [186]–199; Essais Scientifiques, 2005, N. 34; Heß-Babin, 2011, chap. 15, pp. 115–124). Leibniz, G. W., “Extrait d’une lettre de M. de Leibniz sur la question, si l’essence du corps consiste dans l’etendue”, Journal des Sçavans, (June 18, 1691), pp. 259–262. Leibniz, G. W., “De solutionibus problematis catenarii vel funicularis in Actis Junii A. 1691 aliisque a Dn. I. B. propositis”, Acta Eruditorum, (September 1691), pp. 435–439 (Parmentier, 1989, chap. XI, pp. [200]–209; Essais Scientifiques, 2005, N. 35; Heß-Babin, 2011, chap. 16, pp. 125–133). Leibniz, G. W., “De legibus naturae et vera aestimatione virium motricium contra Cartesianos. Responsio ad rationes a Dn. P. mense Januarii proximo in Actis hisce p. 6 propositas”, Acta Eruditorum, (September 1691), pp. 439–447. Leibniz, G. W., “Constructio testitudinis quadrabilis hemisphericae”, Acta Eruditorum, (June 1692), pp. 274–279 (Essais Scientifiques, 2005, N. 42b; Heß-Babin, 2011, chap. 21, pp. 161–168). Leibniz, G. W., “Extrait d‘une lettre de M. de Leibniz à M. Foucher, Chanoine de Dijon, sur quelques axiomes de philosophie”, Journal des Sçavans, (June 2, 1692), pp. 247–249. Leibniz, G. W. (ed.), Codex juris gentium diplomaticus, in quo tabulae authenticae actorum publicorum, tractatuum, aliarumque rerum majoris momenti per Europam gestarum … continentur, Hanover, 1693. Leibniz, G. W., “Protogaea. Autore G. G. L.”, Acta Eruditorum, (January 1693), pp. 40–42. Leibniz, G. W., “Additio … ad solutionem problematis”, Acta Eruditorum, (January 1693), p. 42. Leibniz, G. W., “Ad problema Majo nupero in his Actis p. 235 propositum”, Acta Eruditorum, (July 1693), p. 313 (Essais Scientifiques, 2005, N. 56; Heß-Babin, 2011, chap. 26, pp. 191f.). Leibniz, G. W., “Supplementum geometriae dimensoriae, seu generalissima omnium tetragonismorum effectio per motum: similiterque multiplex constructio lineae ex data tangentium conditione”, Acta Eruditorum, (September 1693), pp. 385–392 (Parmentier, 1989, chap. XV, pp. [247]–267; Essais Scientifiques, 2005, N. 60; Heß-Babin, 2011, chap. 30, pp. 207–220). Leibniz, G. W., “Règle générale de la composition des mouvemens”, Journal des Sçavans, (September 7, 1693), pp. 417–419. Leibniz, G. W., “Constructio propria problematis de curva isochrona paracentrica. Ubi et generaliora quaedam de natura, et calculo differentiali osculorum, et de

Bibliography

917

constructione linearum transcendentium, una maxime geometrica, altera mechanica quidem, sed generalissima. Accessit modus reddendi inventiones transcendentium linearum universales, ut quemvis casum comprehendant, et transeant per punctum datum”, Acta Eruditorum, (August 1694), pp. 364–375 (Parmentier, 1989, chap. XVII, pp. [282]–305; Essais Scientifiques, 2005, N. 67; Heß-Babin, 2011, chap. 33, pp. 239–257). Leibniz, G. W., “Considerations sur la difference qu’il y a entre l’analyse ordinaire et le nouveau calcul des transcendentes”, Journal des Sçavans, (August 23, 1694), pp. 666–671 (Essais Scientifiques, 2005, N. 66; Heß-Babin, 2011, chap. 32, pp. 233–237). Leibniz, G. W. (anon.), Lettre sur la connexion des maisons de Brunsvic et d’Este, Hanover, 1695; Lettera su la connessione delle Serme case di Brunsvic e d’Este, Hanover, 1695. Leibniz, G. W., “Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis, et ad suas causas revocandis”, Acta Eruditorum, (April 1695), pp. 145–157; Dosch, H. G. et al. (eds.), Specimen dynamicum (Lateinisch-Deutsch / Latin-German), Hamburg, 1982. Leibniz, G. W. (anon.), Review of: Nieuwentijt, B., Considerationes circa analyseos ad quantitates infinite parvas applicatae principia (1694), Acta Eruditorum, (June 1695), pp. 272f. Leibniz, G. W., “Système nouveau de la nature et de la communication des substances, aussi bien que de l’union qu’il y a entre l’âme et le corps”, Journal des Sçavans, (June 27 and July 4, 1695), pp. 294–306. Leibniz, G. W., “Responsio ad nonnullas difficultates a Dn. Bernardo Nieuwentijt circa methodum differentialem seu infinitesimalem motas”, Acta Eruditorum, (July 1695), pp. 310–316 (Parmentier, 1989, chap. XIX, pp. [316]–334; Essais Scientifiques, 2005, N. 73; Heß-Babin, 2011, chap. 36, pp. 271–282). Leibniz, G. W., “Addenda ad Dn. G.G.L. Schediasma proximo mensi Julio p. 310 et sqq. insertum”, Acta Eruditorum, (August 1695), pp. 369–372 (Parmentier, 1989, chap. XIX, pp. [335]–337; Essais Scientifiques, 2005, N. 74; Heß-Babin, 2011, chap. 37, pp. 283–286). Leibniz, G. W. (anon.), Review of: Papin, D., Fasciculus dissertationum de novis quibusdam machinis, Acta Eruditorum, (August 1695), pp. 376–382. Leibniz, G. W., Relatio ad inclytam Societatem Leopoldinam Naturae Curiosorum, De novo antidysenterico Americano, Hanover and Wolfenbüttel, 1696; also in: Lister, M. Sex exercitationes medicinales de quibusdam morbis chronicis … Accessit G. G. L. Relatio … de novo antidysenterico, Frankfurt and Leipzig, 1696, and in: Miscellanea Curiosa, Decur. III, Ann. III, Append. Leibniz, G. W. (anon.), Review of Wallis, J., Opera Mathematica, vol. 1 and vol. 2, Acta Eruditorum, (June 1696), pp. 249–259. Leibniz, G. W., “Nuovo teorema intorno al movimento de’ gravi, con un problema nuovo da risolversi”, Giornale de’ letterati, (September 1696), pp. 225–226.

918

Bibliography

Leibniz, G. W., “Extrait d’une letre de M. de Leibniz sur son hypothese de philosofie, et sur le problême curieux qu’un de ses amis propose aux matematiciens”, Journal des Sçavans, (November 19, 1696), pp. 707–713. Leibniz, G. W., Novissima Sinica. Historiam nostri temporis illustratura, In quibus de Christianismo publica nunc primum autoritate propagato missa in Europam relatio exhibetur, deque favore scientiarum Europaearum ac moribus gentis & ipsius praesertim monarchae, tum & de bello Sinensium cum moscis ac pace constituta, multa hactenus ignora explicantur [Hanover], 1697; 2. ed., 1699 [with supplement:] Accessione partis posterioris aucta. [vol. 2 entitled] Icon regia monarchae Sinarum nunc regnantis. Ex Gallico versa. Leibniz, G. W., “Communicatio suae pariter, duarumque alienarum ad edendum sibi primum a Dn. Jo. Bernoullio, deinde a Dn. Marchione Hospitalio communicatarum solutionum problematis curvae celerrimi descensus a Dn. Jo Bernoullio geometris publice propositi, una cum solutione sua problematis alterius ab eodem postea propositi”, Acta Eruditorum, (May 1697), pp. 201–205 (Parmentier, 1989, chap. XXI, pp. [345]–358; Essais Scientifiques, 2005, N. 84; Heß-Babin, 2011, chap. 40, pp. 297–307). Leibniz, G. W. (anon.)., “Nouvelles litteraires”, Nouveau Journal des Sçavans, (May–June, 1697), pp. 292f. Leibniz, G. W., “Excerpta ex Dn. B. Nieuwentiit considerationibus secundis circa calculi differentialis principia”, Acta Eruditorum, (June 1697), pp. 256–260. Leibniz, G. W. (ed.)., Accessiones historicae quibus potissimum continentur scriptores rerum Germanicarum, 2 parts, Leipzig and Hanover, 1698; Hanover, 1700 (reprint). Leibniz, G. W. (anon.), “Animadversio ad Davidis Gregorii schediasma de catenaria”, Acta Eruditorum, (February 1699), pp. 87–91. Leibniz, G. W. (anon.), Review of N. Fatio de Duillier’s Lineae brevissimi descensus investigatio geometrica duplex (London, 1699), Acta Eruditorum, (November 1699), pp. 510–513. Leibniz, G. W. (ed.), Mantissa codicis juris gentium diplomatici, 2 parts, Hanover, 1700. Leibniz, G. W., “Responsio ad Dn. Nic. Fatii Duillierii imputationes. Accessit nova artis analyticae promotio specimine indicata, dum designatione per numeros assumtitios loco literarum algebra ex combinatoria arte lucem capit”, Acta Eruditorum, (May 1700), pp. 198–208. Leibniz, G. W., Essay d’une nouvelle science des nombres (February 1701), in: Zacher: Hauptschriften zur Dyadik (1973), pp. 250–261. Leibniz, G. W., Des Herrn von Leibnitz Gedancken von Aufrichtung einer Societatis Scientiarum et artium, deren Umfang und Nutzen, der Personen, so darzu gezogen werden; ingleichen die Einkünffte davon betreffend, 1710; A IV,8 N. 78, pp. 425–429. Leibniz, G. W., Essais de theodicée sur la bonté de Dieu, la liberté de l’homme et l’origine du mal, Amsterdam, 1710.

Bibliography

919

Leibniz, G. W., “Historia inventionis phosphori”, Miscellanea Berolinensia, vol. 1, (1710), pp. 91–96; Opera Omnia, II,2, pp. 102–108. Leibniz, G. W., Eckhart, J. G. (Intro.), Collectanea etymologica, illustrationi linguarum, veteris Celticae, Germanicae, Gallicae, aliarumque inserventia, Hanover, 1717; Hildesheim, 1970. Leibniz, G. W., Lehr-Sätze über die Monadologie, Jena, 1720. Leibniz, G. W., Scheidt, Ch. L. (ed.), Protogaea sive de prima facie telluris et antiquissimae historiae vestigiis in ipsis naturae monumentis dissertatio ex schedis manuscriptis viri illustris in lucem, Göttingen, 1749; Protogaea, oder Abhandlung von der ersten Gestalt Der Erde und den Spuren der Historie in den Denkmaalen der Natur, Leipzig, 1749; Opera Omnia, II,2, pp. 181–198 (preface) and 199–240; Cohen-Wakefield (2008), 216 pages and 15 halftones; Scheid-Engelhardt-Wellmer (2014), 204 pp. and plates I–XII. Leibniz, G. W., “Dynamica de potentia et legibus naturae corporeae”, parts I–II, in: Mathematische Schriften, vol. 6, pp. 283–514. Leupold, J., Theatrum machinarum generale: Schau-Platz des Grundes Mechanischer Wissenschaften, Leipzig, 1724. Lhuyd, E., “Part of a letter … concerning several regularly figured stones”, Philosophical Transactions, vol. 20, no. 243, (August 1698), pp. 279f. and Fig. 1. Lhuyd, E., Lithophylacii Britannici ichnographia, sive, lapidum aliorumque fossilium Britannicorum singulari figura insignium quotquot hactenus vel ipse invenit vel ab amicis accepit, distributio classica, London, 1699. Lhuyd, E., Archaeologia Britannica: Giving some account additional to what has been hitherto publish’d, of the languages, histories, and customs of the original inhabitants of Great Britain, vol. I. [the only volume to appear] (Glossography), Oxford, 1707. Line, F., Tractatus de corporum inseparabilitate; in quo experimenta de vacuo, tam Torricelliana, quam Magdeburgica, & Boyliana, examinantur, verâque eorum causâ detectâ, ostenditur, vacuum naturaliter dari non posse, unde & Aristotelica de rarefactions sententia, tam contra assertores vacuitatum, quam corpusculorum demonstratur. Accessit solutio difficillimi illius problematis Aristotelici de duabus rotis, quae, licet, valde in quales, quales tamen orbitas describunt autore Francisco Lino, London, 1661. Lister, M., Sex exercitationes medicinales de quibusdam morbis chronicis, quarum prima est, de hydrope; secunda, de diabete, tertia, de hydrophobia; quarta, de lue venera; quinta, de scorbuto, sexta, de arthritide; … Accessit G. G. L. Relatio ad inclytam Societatem Leopoldinam Naturae Curiosorum de novo antidysenterico ex America allato, Frankfurt and Leipzig, 1696. Lister, M., “An objection to the new hypothesis of the generation of animals from animalcula in semine masculine”, Philosophical Transactions, vol. 20, no. 244, (September 1698), p. 337.

920

Bibliography

Malebranche, N. (anon.), Des loix de la communication des mouvemens. Par l’auteur de la recherche de la verité, Paris, 1682. Mariotte, E., Essays de physique, ou memoires pour servir à la science des choses naturelles. I. De la vegetation des plantes. II. De la nature de l’air. III. Du chaud et du froid. IV. De la nature des couleurs, Paris, 1679–1681. Mariotte, E., Traité du mouvement des eaux et des autres corps fluids, divisé en V. parties, Paris, 1686 and 1700; Mariotte: Oeuvres, Tom. II, Leiden 1717, pp. [321]–482. Meyer, A., Dissertatio mathematica de observationibus aerometricis hactenus institutis et imposterum instituendis, Kiel, 1681. Meyer, C., L’arte di restituire a Roma la tralasciata navigazione del suo Tevere, Rome, 1683. Molyneux, W., Dioptrica nova: A treatise of dioptricks, in two parts. Wherein the various effects and appearances of spherick glasses, both convex and concave, single and combined, in telescopes and microscopes, together with their usefulness in many concerns of human life, are explained, London, 1692. Monconys, B. de, Journal des voyages, 3 vols, Lyon, 1665–1666 and Paris, 1677. Morland, S., The description and use of two arithmetick instruments. Together with a short treatise, explaining and demonstrating the ordinary operations of arithmetick. As likewise a perpetual almanack and several useful tables: presented to His most excellent Majesty Charles II, King of Great Britain, France, and Ireland, London, 1673. Mullen, A., An anatomical account of the elephant accidentally burnt in Dublin on Friday, June 17 in the year 1681: sent in a letter to Sir William Petty, fellow of the Royal Society: together with a relation of new anatomical observations in the eyes of animals, communicated in another letter to the Honourable R. Boyle, London, 1682. Newton, I., “A letter of Mr. Isaac Newton, containing his new theory about light and colors”, Philosophical Transactions, vol. 6, no. 80, (19 Februar 1671 / 29 Februar 1672), pp. 3075–3087. Newton, I., Philosophiae naturalis principia mathematica, London, 1687; 2nd ed. Cambridge, 1713; Editio ultima auctior et emendatior, Amsterdam, 1714; 3rd ed. London, 1726. Newton, I., and Cohen, I. B., Whitman, A., Budenz, J. (eds., trans.), Isaac Newton: The principia. Mathematical principles of natural philosophy. A new translation  … Preceded by a guide to Newton’s Principia, Berkeley, Los Angeles, London, 1999. Newton, I., “Epistola missa ad praenobilem virum D. Carolum Mountague armigerum, scaccarii regii apud Anglos cancellarium, & Societatis Regiae prasidem, in qua solvuntur duo problemata mathematica a Johanne Barnoullo [sic] mathematico celeberrimo proposita. Jan. 30. 1696/7”, Philosophical Transactions, vol. 19, no. 224, (January 1697), pp. 384–389; extract in the Acta Eruditorum, (May 1697), pp. 223f.; Newton: Mathematical Papers, vol. 8, pp. 5f. Newton, I., A new and most accurate theory of the moon’s motion, London, 1702.

Bibliography

921

Newton, I., Opticks: Or a treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures (viz. Enumeratio linearum tertii ordinis, and Tractatus de quadratura curvarum), London, 1704; Opticks: Or a treatise of the reflexions, refractions, inflexions and colours of light. The fourth edition, corrected, London, 1730; Cohen, I. B., Whittaker, E., Roller, D. H. D. (eds.) and Einstein, A. (Foreword), Sir Isaac Newton: Opticks or a treatise of the reflexions, refractions, inflexions & colours of light: Based on the fourth edition London, 1730, New York, 1952. Newton, I., Clarke, S. (ed.), Optice: Sive de reflexionibus, refractionibus, inflexionibus et coloribus lucis libri tres, London, 1706. Nieuwentijt, B., Considerationes circa analyseos ad quantitates infinite parvas applicatae principia, et calculi differentialis usum in resolvendis problematibus geometricis, Amsterdam, 1694. Nieuwentijt, B., Analysis infinitorum, seu curvilineorum proprietates ex polygonorum natura deductae, Amsterdam, 1695. Nieuwentijt, B., Considerationes secundae circa calculi differentialis principia; et responsio ad virum nobilissimun G. G. Leibnitium, Amsterdam, 1696. Oldenburg, H., “Advertisement” of Leibniz’s Hypothesis physica nova (London, 1671) in Philosophical Transactions, vol. 6, no. 73, (July 17, 1671), pp. 2213f. Oldenburg, H. (anon.), Review of O. von Guericke’s Experimenta nova (1672), Philosophical Transactions, vol. 7, no. 88, (November 18/28, 1672), pp. 5103–5105. Papin, D., Nouvelles experiences du vuide, avec la description des machines qui servent à les faire, Paris, 1674. Papin, D., A new digester, or engine for softning bones, containing the description of its make and use in these particulars: viz. cookery, voyages at sea, confectionary, making of drinks, chymistry, and dying, London, 1681; “Novus digestor aut machina pro emolliendis ossibus  … per Dionysium Papinum”, Acta Eruditorum, (April 1682), pp. 105–109. Papin, D., La manière d’amolir les os et de faire cuire toutes sortes de viands, Paris, 1682; “La maniere d’amolir les os  … par Mr. Papin”, Acta Eruditorum, (October 1682), pp. 305–308. Papin, D., “The description of a siphon performing the same things as the sipho Wurtembergicus”, Philosophical Transactions, vol. XV, no. 167, (November 1684), pp. 847–848. Papin, D., “Description d’un siphon qui produit les mêmes effets que celui de Wurtemberg, inventé par le docteur Papin de la Société Royale”, Nouvelles de la Republique des Lettres, vol. 3, (1685), Article X, pp. 537–540. Papin, D., “Augmenta quaedam et experimenta nova circa antliam pneumaticam, facta partim in Anglia, partim in Italia”, Acta Eruditorum, (June 1687), pp. 324–335.

922

Bibliography

Papin, D., “Excerpta ex viri clarissimi, Dionysii Papini, mathematum in Academia Marpurgensi professoris publici, litteris ad  –  de novo pulveris pyrii usu”, Acta Eruditorum, (September 1688), pp. 497–501. Papin, D., “De gravitatis causa et proprietatibus observations”, Acta Eruditorum, (April 1689), pp. 183–188. Papin, D., “Rotatilis suctor et pressor Hassiacus, in Serenissima Aula Cassellana demonstratus et detectus”, Acta Erdutitorum, (June 1689), pp. 317–322; reprinted as “Antlia Hassiaca locupletata” and “Description de la pompe de Hesse”, pp. 1–17 in: D. Papin, Fasciculus dissertationum (1695) and Recueil de diverses pieces (1695), respectively. Papin, D., “Examen siphonis Wurtemburgici in vertice effluentis”, Acta Eruditorum, (May 1690), pp. 223–228. Papin, D., “Nova methodus ad vires motrices validissimas levi pretio comparandas”, Acta Eruditorum, (August 1690), pp. 410–414 and Tab. X, Fig. 1; reprinted (with an English translation) in: Muirhead, J. P., Origins and progress of the mechanical inventions of James Watt, London, 1854, part III, pp. 139–154. Papin, D., “Mechanicorum de viribus motricibus sententia, asserta a D. Papino adversus Cl. G. G. L[eibniz] objectiones”, Acta Eruditorum, (January 1691), pp. 6–13. Papin, D., “Observationes quaedam circa materias ad hydraulicam spectantes, mensi Februario hujus anni insertas”, Acta Eruditorum, (May 1691), pp. 208–213. Papin, D., Fasciculus dissertationum de novis quibusdam machinis atque aliis argumentis philosophicis, Marburg, 1695; Recueil de diverses pieces touchant quelques nouvelles machines. Et autres subjets philosophiques, Kassel, 1695. Papin, D., “Epistola de fluentium aquarum mensura ad perillustrem virum D. D. Christianum Hugenium”, pp. 68–93 in: Fasciculus dissertationum (1695); “Lettre, touchant la mesure des eaux courantes contra Mons. Dominique Guilielmini médecin et mathématicien à Boulogne, à Monsieur Christien Hugens Seigneur de Zulichem”, pp. 66–94 in: Recueil de diverses pieces (1695). Papin, D., “Navis urinatoriae Serenissimi Principis jussu constructae descriptio”, pp. 126–137 in: Fasciculus dissertationum (1695); “Description du batteau plongeant”, pp. 127–143 in: Recueil de diverses pieces (1695). Perrault, Cl., Essais de physique ou récueil de plusieurs traitez touchant des choses naturelles, 3 vols, Paris, 1680. Petty, W., Deux essays d’arithmetique politique, touchant les villes de Londres et Paris, London, 1686. Petty, W., Two essays in political arithmetick, conserning the people, housing, hospitals &c. of London and Paris, London, 1687. Piso, W. (de Laet, J. ed.), De medicina Brasiliensi libri quatuor, in: Historia naturalis Brasiliae, Auspicio et beneficio Illustriss. I. Mauritii Com. Nassau illius provinciae et maris summi Praefecti adornata. In qua non tantum plantae et animalia, sed et

Bibliography

923

indigenarum morbi, ingenia et mores describuntur et iconibus supra quingentas illustrantur, Leiden and Amsterdam, 1648. Plinius Caecilius Secundus, C. / G., (de Laet, J. ed.), Historiae naturalis libri XXXVII, Leiden, 1635. Plinius Caecilius Secundus, C. / G., (Hardouin, J. ed.), Historiae naturalis libri XXXVII in usum Delphini, 5 vols, Paris, 1685. Ramazzini, B., De constitutione anni 1690 ac de rurali epidemia, quae Mutinensi agri et vicinarum regionum colonos graviter afflixit, dissertatio, Modena, 1690; reprint in: Miscellanea Curiosa, Decur. II, Ann. IX, (1691), Append., pp. [15]–56. Ramazzini, B., De fontium Mutinensium admiranda scaturigine tractatus physicohydrostaticus, Modena, 1691. Ramazzini, B., De constitutione anni 1691, Modena, 1692; reprint in: Miscellanea Curiosa, Decur. II, Ann. X, (1692), pp. 79–114. Ramazzini, B., De constitutionibus annorum M.DC.XCII., XCIII., et XCIV., in Mutinensi civitate, et illiusditione, dissertatio, Modena, 1695. Ramazzini, B., Ephemerides barometricae Mutinenses anni M. DC. XCIV. Una cum disquisitione causae ascensus, ac descensus mercurii in Torricelliana fistula juxta diversarum aeris statum. His accessere epistolae Jo. Bapt. Boccabadati et Frc. Torti, Modena, 1695. Ramazzini, B., De morbis artificum diatriba Bernardini Ramazzini in Patavino ArchiLyceo Practicae Medicinae Ordinariae Publici Professoris, Modena, 1700. Ramazzini, B., Wright, [E.] W. C. (trans., ed.), De morbis artificum diatriba: Diseases of Workers  … The Latin text of 1713, revised with translation and notes, (History of Medicine series), Chicago, 1940. Ramazzini, B., Wright, [E.] W. C. (trans., eds.), Rosen, G. (Intro.), Diseases of workers. Translated from the Latin text De morbis artificium of 1713, (New York Academy of Medicine, History of Medicine series, no. 23). New York, London [c.1964]. Ramazzini, B., Constitutionum epidemicarum Mutinensium annorum quinque, Padua, 1714. Ray, J., Synopsis methodica animalium quadrupedum et serpentini generis: vulgarium notas characteristicas, rariorum descriptiones integras exhibens: cum historiis & observationibus anatomicis perquam curiosis: praemittuntur nonnulla de animalium in genere, sensu, generatione, divisione, &c., London, 1693. Reisel, S., Sipho Würtembergicus sive sipho inversus cruribus aequialtis fluens et refluens hactenus inauditus, Stuttgart, 1684 (2nd ed., 1690); also in: Miscellanea Curiosa, Decur. II, Ann. III, (1684), Append., pp. 461–472. Reisel, S., Sipho Wurtembergicus per majora experimenta firmatus, in vertice effluens, correctus et detectus, Stuttgart, 1689; (anon.): “Salomonis Reiselii  … Sipho Wurtembergicus per majora experimenta firmatus, in vertice effluens, correctus et detectus”, Acta Erdutitorum, (March 1690), pp. 142–147.

924

Bibliography

Renau d’Eliçagaray, B., De la theorie de la manoeuvre des vaisseaux, Paris, 1689. Renau d’Eliçagaray, B., Reponse de M. Rena capitaine de vaisseau … à la remarque de M. Huguens, sur le livre de la manoeuvre des vaisseaux, Paris, 1694; partial reprint in: Journal des Sçavans, (May 16 and 23, 1695), pp. 329–337 and pp. 355–363, respectively. Renau d’Eliçagaray, B., Replique de M. Huguens à la reponse de M. Renau, … et la reponse de M. Renau à la replique de M. Huguens, Paris, 1694. Rømer, O., “Demonstration touchant le mouvement de la lumiere”, Journal des Sçavans, (December 7, 1676), pp. 276–279. Rumpf, G. E., “De caryophyllis regis Ambonicis”, Miscellanea Curiosa, Decur. III, Ann. V and VI (1697–1698), pp. 308f. Rumpf, G. E., Herbarium Amboinense: plurimas conplectens arbores, frutices, herbas, plantas terrestres & aquaticas, quae in Amboina et adjacentibus reperiuntur insulis adcuratissime descriptas iuxta earum formas, cum diuersis denominationibus cultura, usu, ac virtutibus, quod & insuper exhibet varia insectorum animaliumque genera, plurima cum naturalibus eorum figuris depicta, Amsterdam, 1741–1750. Savery, T., The miners friend: or, an engine to raise water by fire, described. And of the manner of fixing it in mines. With an account of the several other uses it is applicable unto; and an answer to the objections made against it, London, 1702. Scaliger, J. J., Diatriba de Europaeorum linguis, pp. 119–122 in: Opuscula varia, antehac non edita, Paris, 1610 and Frankfurt am Main, 1612. Scheffer, S. [attributed to], “De rene monstroso”, Miscellanea Curiosa, Decur. 1, Ann. IX, X, 1678/1679, pp. 258–261; also in: Journal des Sçavans, (January 24, 1678), pp. 31–36. Scheffer, S., “Extracts from a letter from Andreas Cleyer of December 20, 1683”, Miscellanea Curiosa, Decur. 2, Ann. 4, (1685), pp. 1–8. Scheiner, Ch., Oculus, hoc est fundamentum opticum, Innsbruck, 1619. Schelhammer, G. Chr., De auditu liber unus. Quo plerorumque omnium doctorum sententiae examinantur, et auditus ratio nova methodo, ex ipsus naturae legibus, explicatur, Leiden, 1684. Schott, C. (or K.), Mechanica hydraulico-pneumatica: Qua praeterquam quod aquei elementi natura, proprietas demonstratur; omnis quoque generis experimenta hydraulico-pneumatica recluduntur; et absoluta machinarum aqua et aere animandarum ratio ac methodus praescribitur: Opus bipartitum … ; Accessit experimentum novum Magdeburgicum, quo vacuum alii stabilire, alii evertere conantur, Frankfurt am Main, 1657. Schott, C. (or K.), Technica curiosa sive mirabilia artis libris XII comprehensa, Würzburg, 1664 and Nürnberg, 1664. Schrader, F. [praeses.], De frigoris natura. Respondens Justus Bernhardus Slepper, Helmstedt, 1684. Sendivogius Filius (pseudonym, ed.), Lucerna salis philosophorum. Hoc est delineatio nuda desiderati illius principi tertii mineralium Sendivogiani, sive salis pontici, quod

Bibliography

925

est subiectum omnis mirabilitatis … communicata à filio Sendivogii, anagrammaticè vocato, Amsterdam, 1658. Snellius, W., Tiphys Batavus, sive histiodromice, de navium cursibus et re navali, Leiden, 1624. Starkey, G. (Eirenaeus pseud. Philalethes), Enarratio methodica trium Gebri medicinarum: In quibus continetur lapidis philosophici vera confectio, London, 1678. Stensen, N., De solido intra solidum naturaliter contento dissertationis prodromus, Florence, 1669; Leiden, 1679. Stisser, J. A., Botanica curiosa, oder nützliche Anmerckungen, wie einige frembde Kräuter und Blumen in seinem Anno 1692 zu Helmstedt angelegten medicinischen Garten bishero cultiviret und fortgebracht, Helmstedt, 1697. Stisser, J. A., Actorum laboratorii chemici in Academia Julia specimen tertium medicochemica observata quaedam rariora exhibens, Helmstedt, 1698. Stisser, J. A., De variis erroribus, chemiae ignorantia in medicina commissis dissertatio epistolaris ad illustrem atque excellentissimum virum Dominum Godefr. Guilielmum Leibnitium, [Helmstedt,] 1700; A III,8 N. 131, pp. 337–355. Stockhausen, S., Libellus de lithargyrii fumo noxio morbifico, ejusque metallico frequentiori morbo vulgo dicto die HüttenKatze oder HüttenRauch: cum appendice de montano affectu asthmatico metallicidis familiari, quem Germanica lingua appellamus die Bergsucht oder BergKranckheit, Goslar, 1656. Streete, T., Astronomia Carolina, seu nova theoria motuum coelestium, London, 1661. Streete, T., Astronomia Carolina: A new theorie of the coelestial motions, composed according to the best observations and most rational grounds of art, yet farre more easie, expedite and perspicuous then any before extant. With exact and most easie tables thereunto, and precepts for the calculation of eclipses &c., London, 1661. Streete, T., The description and use of the planetary systeme, together with easie tables, London, 1674. Sturm, J. C., Epistola invitatoria ad observationes magneticae variationis communi studio junctisque laboribus instituendas, Altdorf, 1682. Sturm, J. C., Herrn Johann Christoph Sturms, Weyland der mathematischen- und Natur-Wissenschafften Hochverdienten Professoris Publici zu Altorff, Kurtzgefasste Mathesis Oder Erste Anleitung zu Mathematischen Wissenschafften, in Tabellen verfasset. Deren folgende sind: Der allgemeinen Mathematick I / Der Rechen-Kunst IV / Der Algebrä III / Der Meß-Kunst, d.i. der Geometrie samt der Trigonometrie V / Der optick III / Der Kriegs-Bau-Kunst VI / Der bürgerlichen Bau-Kunst VIII / Der Himmelund Erde-Beschreibung IV / Der Chronologie III / Der Horographie I / Der Mechanick I / Der Chiromantie I, Coburg, 1717. Sturm, L. C., Architectura civili-militaris. Oder Vollständige Anweisung, Stadt-Thore, Brucken, Zeug-Häuser, Kasematten und andere Souterrains der Wälle, Casernen, Baraquen, Corps des Gardes und Proviant-Häuser behörig anzugeben, Augsburg, 1719.

926

Bibliography

Swammerdam, J., Miraculum naturae sive uteri muliebris fabrica, notis in D. J. van Horne prodromum illustrata, et tabulis, a clariss. expertissimisque viris cum ipso archetype collatis, adumbrate. Adjecta est nova methodus, cavitates corporis ita praeparandi, ut suam semper genuinam faciem servent, Leiden, 1672. Swammerdam, J., Historia insectorum generalis, ofte algemeene verhandeling van de bloedeloose dierkens, Utrecht, 1669 and 1693 (second edition); Hennin, H. C. von (transl.) Historia insectorum generalis, in qua quaecunque ad insecta eorumque mutationes spectant, dilucide ex sanioris philosophiae et experientiae principiis explicantur, Leiden, 1685. Tentzel, W. E., Epistola de sceleto elephantino Tonnae nuper effosso, ad virum toto orbe celeberrimum Antonium Magliabechium, Gotha and Jena, 1696; Inhalt eines Lateinischen Schreibens an Den Welt-berühmten Herrn Antonio Magliabechi, Rath und Bibliothecarium des Groß-Hertzogs zu Florentz / von dem zu Tonna ausgegrabenen Elephanten-Cörper, Gotha and Jena, 1696; and also “Wilhelmi Ernesti Tentzelii Historiographi Ducalis Saxonici Epistola de sceleto elephantino Tonnae nuper effosso, ad virum toto orbe celeberrimum Antonium Magliabechium serenissimi magni Hetruriae ducis bibliothecarium & consiliarium … Gothae. 1696”, Journal des Sçavans, (August 20, 1696), pp. 393–395. Teyler, J., Architectura Militaris, Amsterdam, [1679]; 2 ed. Rotterdam, 1697. Toland, J., Christianity not mysterious, or a treatise shewing, that there is nothing in the Gospel contrary to reason, nor above it, and that no Christian doctrine can properly be call’d a mystery, London, 1696. Tschirnhaus, E. W. von, “Nova methodus tangentes curvarum expedite determinandi”, Acta Eruditorum, (December 1682), pp. 391–393. Tschirnhaus, E. W. von, “Methodus datae figurae, rectis lineis et curva geometrica terminatae, aut quadraturam, aut impossibilitatem ejusdem quadraturae determinandi”, Acta Eruditorum, (October, 1683), pp. 433–437. Tschirnhaus, E. W. von, “Novae quaedam experientiae opticae” (article submitted to the Acta Eruditorum in 1685), GWLB, Hanover (Manuscript shelfmark: LH XXXV 15,3 Bl. 1). Tschirnhaus, E. W. von, “Nova et singularis geometriae promotio”, Acta Eruditorum, (November 1695), pp. 489–493. Tschirnhaus, E. W. von, “De methodo universalia theoremata eruendi, quae curvarum naturas simplicissime exprimunt; de problemate item Bernoulliano”, Acta Eruditorum, (May 1697), pp. 220–223. Vagetius, A., Ettmüller, M. E., De maculis in sole visis disseret praeses M. Augustinus Vagetius, [et] respondens Michael Ernestus Ettmüllerus, Wittenberg, 1693. Valentine, B. [Basilius Valentinus], Chymische Schriften, Hamburg, 1677. Valentine, B. [Basilius Valentinus], Tractatus chymicus de quinta essentia … ans Licht gestellet worden von Sincero Aletophilo, Erfurt, 1738.

Bibliography

927

Valentini M. B., “Memoria Schefferiana” [cf. Scheffer, S., above], Miscellanea Curiosa, Decur. 2, Ann. V, Append., (1686), p. 196. Valentini M. B., Oost-Indianische Sendschreiben von allerhand raren Gewächsen, Bäumen, Jubelen, auch andern zu der Natur-Kündigung und Artzney-kunst gehörigen Raritäten … aus … in Holländischer Sprach geschriebenen Originalien in die Teutsche Mutter-Sprache übersetzet, Frankfurt am Main, 1704. Varignon, P., Nouvelles conjectures sur la pesanteur, Paris, 1690. Viviani, V. (anon.), Aenigma geometricum de miro opificio testudinis quadrabilis hemisphaericae a D. Pio Lisci Pusillo [i.e. Viviani] Geometra propositum, [Firenze (Florence), 1692]. Viviani, V., Formazione, e misura di tutti i cieli: con la struttura, e quadratura efatta dell’intero, e delle parti di un nuovo cielo admirabile, e di uno degli antichi delle volte regolari degli architetti, curiosa esercitazione matematica di V. V., ultimo scolare del Galileo, Firenze (Florence), 1692. Wallis, J., “Dr. Wallis’s opinion concerning the hypothesis physica nova of Dr. Leibnitius … here inserted in the same tongue, wherein it was written to the publisher”, Philosophical Transactions, vol. 6, no. 74, (August 14, 1671), pp. 2227–2231. Wallis, J., Grammatica linguae anglicanae. Cui praefigitur, de loquela sive sonorum formatione, tractatus grammatico-physicus, Oxford, 1653; Editio quarta prioribus auctior, Oxford, 1674. Wallis, J., A treatise of algebra, London, 1685. Wallis, J., De algebra tractatus, in Wallis: Opera mathematica, vol. 2, 1693, pp. 1–482. Warren, E., Geologia: Or a discourse concerning the earth before the deluge, London, 1690. Weigel, E., Tetractys, summum tum arithmeticae tum philosophiae discursivae compendium, artis magnae sciendi genuina radix, Jena, 1673. Weigel, E., Kurtze Relation von dem nunmehr zur Prob gebrachten mathematischen Vorschlag, betreffend die Kunst-und Tugend-Information, Jena, 1684. Weigel, E., Wegweiser zu der Unterweisungs-Kunst nicht nur des Verstandes; sondern auch des Willens, Jena, 1688. Weigel, E., Von der Nothwendigkeit der Angewehnung dessen, was man in gerechter Maß und Weiß zu thun hat über das, daß man die Wissenschafft davon gelernet hat. Samt einer Kurtzen Relation, wie weit es mit der angestellten Kunst und Tugend-Schul bißher gekommen sey. Dabey die ins gemein so operos und schwer getriebene Sprachen mit pur lauter erbarer Lust, dazu die Kinder von Natur geneigt, in steten reden, lesen, schreiben, singen, rechnen, messen, mahlen, reiten, höfflich gehen und sich wenden, auff und aus Papier Figuren machen, und dergleichen, auff das leichteste geübet werden, Jena, 1691. Weigel, E., Paedagogiae mathematicae ad praxim pietatis, fundamenta et principia, 2 parts, Coburg, 1694.

928

Bibliography

Whiston, W., A new theory of the earth, from its original to the consummation of all things wherein the creation of the world in six days, the universal deluge, and the general conflagration, as laid down in the Holy Scriptures, are shewn to be perfectly agreeable to reason and philosophy: with a large introductory discourse concerning the genuine nature, stile, and extent of the Mosaick history of the creation, London, 1696. Witsen, N., Aeloude en hedendaegsche scheeps-bouw en bestier: Waer in wijtloopigh wert verhandelt de wijze van scheeps-timmeren, by Grieken en Romeynen: scheepsoeffeningen, strijden, tucht, straffe, wetten, en gewoonten, Amsterdam, 1671; 2nd ed.: Architectura navalis et regimen nauticum. Ofte aeloude en hedendaegsche scheepsbouw en bestier, Amsterdam, 1690. Witt, J. de, Schooten, F. van (ed.), Elementia curvarum linearum, vol. 2, pp. [153]–340 in: Descartes, R., Geometria, 2 vols, Amsterdam, 1659–1661. Zipffell, J., Podagrischer Triumph, das ist kurtzer doch gründlicher Bericht vom Griess / Sand / Stein / und Podagra, Altenburg, 1659.



Secondary Sources (in Alphabetical and Chronological Order)

Aiton, E. J., “The celestial mechanics of Leibniz”, Annals of Science, vol. 16(2), (1960) [published 1962], pp. 65–82. Aiton, E. J., “The celestial mechanics of Leibniz in the light of Newtonian criticism”, Annals of Science, vol. 18(1), (1962) [published 1964], pp. 31–41. Aiton, E. J., “The celestial mechanics of Leibniz: a new interpretation”, Annals of Science, vol. 20(2), (1964) [published 1965], pp. 111–123. Aiton, E. J., “An imaginary error in the celestial mechanics of Leibniz”, Annals of Science, vol. 21(3), (1965) [published 1966], pp. 169–173. Aiton, E. J., The vortex theory of planetary motions, London, New York, 1972. Aiton, E. J., “Leibniz on motion in a resisting medium”, Archive for the History of the Exact Sciences, vol. 9, (1972), pp. 257–274. Aiton, E. J., “An unpublished letter of Leibniz to Sloane”, Annals of Science, vol. 38(1), (1981), pp. 103–107. Aiton, E. J., “The mathematical basis of Leibniz’s theory of planetary motion”, pp. 209–225 in: Heinekamp, A. (ed.), Leibniz’ Dynamica: Symposion der GottfriedWilhelm-Leibniz-Gesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, (Studia Leibnitiana, Special issue, no. 13), Stuttgart, 1984. Aiton, E. J., “Polygons and parabolas: some problems concerning the dynamics of planetary orbits”, Centaurus, vol. 31, (1989), pp. 207–221. Aiton, E. J., Leibniz: A biography, Bristol and Boston, 1985, and Goldmann, C., Krüger, C. (trans.), Gottfried Wilhelm Leibniz: Eine Biographie, Frankfurt am Main, 1991.

Bibliography

929

Aldersey-Williams, H., Dutch Light: Christiaan Huygens and the making of science in Europe, London, 2020; Het leven van Christiaan Huygens, Amsterdam, 2020. Andrault, R., “The machine analogy in medicine: A comparative approach to Leibniz and his contemporaries”, chap. 7 (pp. 95–114) in: Smith, J. E. H., Nachtomy, O. (eds.), Machines of nature and corporeal substances in Leibniz, Dordrecht, Heidelberg, London, New York, 2011. Añón, R. B., “Medical biographies and their historical significance: The figure and the work of Bernardino Ramazzini (1633–1714)”, Medicina y Seguridad del Trabajo, (Special issue / Suplemento extraordinario, no. 2), (2014), pp. 34–41. Antognazza, M. R., Leibniz: An intellectual biography, New York, Cambridge, 2008. Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018; in particular Part III (chapters 11–14) “Mathematics”, pp. 211–274, and Part V (chapters 23–30) “Scientific and Technical Work”, pp. 425–542. Armytage, W. H. G., A social history of engineering, London, 1961, and 1970 (third edition). Arthur, R. T. W., Classic thinkers: Leibniz, Cambridge, UK, and Malden, MA, 2014. Arthur, R. T. W., “Thought experiments in Newton and Leibniz”, chap. 6 (pp. 111–127) in: Stuart, M. T., Fehige, Y., Brown, J. R. (eds.), The Routledge companion to thought experiments, Abingdon (Oxon., UK), New York, 2018. Baigrie, B. S., “The justification of Kepler’s ellipse”, Studies in History and Philosophy of Science, vol. 21(4), (1990), pp. 633–664. Baldassarri, F., “The mechanical life of plants: Descartes on botany”, British Journal for the History of Science, vol. 52(1), (March 2019), pp. [41]–63. Banchetti-Robino, M. P., The chemical philosophy of Robert Boyle: Mechanicism, chymical atoms, and emergence, Oxford, 2020. Barnes, L. L., Needles, herbs, gods, and ghosts: China, healing, and the West to 1848, Cambridge (MA), London, 2005. Barry, Q., From Solebay to the Texel: The third Anglo-Dutch war, 1672–1674, Warwick, 2018. Becchi, A., “Between learned science and technical knowledge: Leibniz, Leeuwenhoek and the school for microscopists”, pp. 47–79 in: Strickland, L., Vynckier, E., Weckend, J. (eds.), Tercentenary essays on the philosophy and science of Leibniz, Basingstoke, 2016. Beeley, P., Probst, S., “John Wallis (1616–1703): Mathematician and divine”, chap. 23, pp. 441–457, in. Koetsier, T., Bergmans, L. (eds.), Mathematics and the divine: A historical study, Amsterdam, Boston, Heidelberg, 2005. Beeley, P., “‘Un de mes amis’: On Leibniz’s relation to the English mathematician and theologian John Wallis”, chap. 5, pp. 63–82, in: Phemister, P., Brown, S. (eds.), Leibniz and the English-speaking world, Dordrecht, 2007.

930

Bibliography

Beeley, P., “De abstracto et concreto: Rationalism and empirical sciences in Leibniz”, chap. 4, pp. 85–98, in: Dascal, M. (ed.), Leibniz: What kind of rationalist? (Logic, epistemology, and the unity of science, vol. 13), Dordrecht, 2009. Beeley, P., “Breaking the code: John Wallis and the politics of concealment”, pp. 49–81 in: Li, W. and Noreik, S. (eds.), G. W. Leibniz und der Gelehrtenhabitus: Anonymität, Pseudonymität, Camouflage, Cologne, Weimar, Vienna, 2016. Beeley, P., “Early physics”, chap. 16, pp. 290–303, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Beeley, P., “Physical arguments and moral inducements: John Wallis on questions of antiquarianism and natural philosophy”, Notes and Records of the Royal Society, vol. 72(4), (December 2018), pp. 413–430. Beeley, P., “Practical mathematics and mathematical practice in later seventeenthcentury London”, British Journal for the History of Science, (Special issue: London 1600–1800: Communities of natural knowledge and artificial practice), vol. 52(2), (June 2019), pp. [225]–248. Berkel, K. van, “‘Cornelius Meijer inventor et fecit’: On the representation of science in late seventeenth-century Rome”, Part 2 (Networks of knowledge: Commerce and the representation of nature), chap. 11, pp. 277–294, in: Smith, P. and Findlen, P. (eds.), Merchants and marvels: Commerce, science, and art in early modern Europe, New York and London, 2002. Bernardi, G., The unforgotten sisters: Female astronomers and scientists before Caroline Herschel, Cham (Switzerland), Heidelberg, New York, Dordrecht, London, 2016. Bertoloni Meli, D., Equivalence and priority: Newton versus Leibniz including Leibniz’s unpublished manuscripts on the Principia, Oxford, 1993 and 2002. Bertoloni Meli, D., “Cosmology”, chap. 24, pp. 438–452 in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Bertoloni Meli, D., Mechanism: A visual, lexical, and conceptual history, Pittsburgh, 2019. Bertucci, P., Artisanal enlightenment: Science and the mechanical arts in old regime France, New Haven, CT, London, 2017. Bialas, V., “Der Streit um die Osterfestberechnung im frühen Mittelalter. Eine Fallstudie zum Verhältnis der römischen und der alt-irischen Kirche”, chap. 6, pp. 127–142, in: Wolfschmidt, G. (ed.), Astronomie und Astrologie im Kontext von Religionen  – Astronomy and Astrology in Context of Religions, Hamburg: tredition science (Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften; vol. 32), 2018. Blanc, P. D., “Historical perspective of occupational and environmental lung disease”, chap. 1, pp. 1–26, in: Huang, Y.-C. T., Ghio, A. J., Maier, L. A. (eds.), A clinical guide to occupational and environmental lung diseases, New York, Heidelberg, Dordrecht, London, 2012. Boas, M., Robert Boyle and seventeenth-century chemistry, Cambridge, 1958 and 2015.

Bibliography

931

Bolt, R. (trans.), Dromgoole, N. (intro.), Molière: The school for wives, a new translation, London, 1998 and 2012 (electronic). Bos, H. J. M., “Differentials, higher-order differentials and the derivative in the Leibnizian calculus”, Archive for History of Exact Sciences, vol. 14(1), (1974), pp. 1–90. Bos, H. J. M., “Huygens and mathematics”, pp. 126–146 in: Bos, H. J. M., Rudwick, M. J. S., Snelders, H. A. M., Visser, R. P. W. (eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979, Lisse, 1980. Bos, H. J. M., “L’Élaboration du calcul infinitesimal: Huygens entre Pascal et Leibniz”, pp. 115–122 in: Taton, R. (intro.), Huygens et la France: Table ronde du C.N.R.S. Paris, 27–29 mars 1979, Paris, 1982. Boschiero, L., “Machines, motion, mechanics: Philosophers engineering the fountains of Versailles”, Technology and Culture, vol. 61(4), October (2020), pp. 1108–1128. Bottomley, S., The British patent system during the industrial revolution 1700–1852: From privilege to property, Cambridge, 2014. Boudri, J. C., and McGlinn, S. (trans.), What was mechanical about mechanics: The concept of force between metaphysics and mechanics from Newton to Lagrange, Dordrecht, 2002. Brather, H.-S. (ed.), Leibniz und seine Akademie: Ausgewählte Quellen zur Geschichte der Berliner Sozietät der Wissenschaften 1697–1716, Berlin, 1993. Breger, H., “Elastizität als Strukturprinzip der Materie bei Leibniz”, pp. 112–121 in: Heinekamp, A. (ed.), Leibniz’ Dynamica. Symposion der Gottfried-Wilhelm-LeibnizGesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, (Studia Leibnitiana, Special issue no. 13), Stuttgart, 1984. Breger, H., “Notiz zur Biographie des Phosphor-Entdeckers Henning Brand”, Studia Leibnitiana, vol. 19(1), (1987), pp. 68–73. Breger, H., “Becher, Leibniz und die Rationalität”, pp. 69–84 in: Frühsorge, G. and Strasser, G. F. (eds.), Johann Joachim Becher (1635–1682), Wiesbaden, 1993. Breger, H., “Physics: Leibniz’s principles of research into natural phenomena”, pp. 65–79 in: Popp, K., Stein, E. (eds.), Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000. Brown, M., A political biography of John Toland, London, New York, 2012 (and 2016). Brown, R. C., The tangled origins of the Leibnizian calculus: A case study of a mathematical revolution, Singapore, New Jersey, London, 2012. Brown, S., “Leibniz and Robert Boyle: Reason and faith: rationalism and voluntarism”, chap. 6, pp. 83–94, in: Phemister, P., Brown, S. (eds.), Leibniz and the English-speaking world, Dordrecht, 2007. Buchanan, B. J. (ed.), Gunpowder, explosives and the state: A technological history, Oxford, New York, 2006 (and 2016).

932

Bibliography

Bukowski, J., “Christiaan Huygens and the problem of the hanging chain”, The College Mathematics Journal, vol. 39(1), (January 2008), pp. 1–11. Buijze, W., Leven en werk van Georg Everhard Rumphius (1627–1702): Een natuurhistoricus in dienst van de VOC (The Life and work of Georg Everhard Rumphius (1627–1702): A natural historian in the service of the Dutch East India Company), Den Haag (The Hague), 2006. Bussotti, P., The complex itinerary of Leibniz’s planetary theory: Physical convictions, metaphysical principles and Keplerian inspiration, (Science Networks  – Historical Studies, vol. 52), Cham (Switzerland), 2015. Calder, A., Molière: The theory and practice of comedy, London, 1993. Canguilhem, G., La connaissance de la vie, Paris, 1952, and 1965, 1992, 2003. English translations: Cohen, M., Cherry, R. (trans.), pp. 44–69 (“Machine and organism”), in: Crary, J., Kwinter, S. (eds.), Incorporations, New York, 1992, and Marrati, P., Meyers, T. (eds.); Geroulanos, S., Ginsburg, D. (trans.), Knowledge of life, New York, 2008. Cardwell, D. S. L., Steam power in the eighteenth century: A case study in the application of science, London, 1963. Cardwell, D. S. L., “Power technologies and the advance of science, 1700–1825”, Technology and Culture, vol. 6(2), (Spring 1965), pp. 188–207. Cardwell, D. S. L., “Some factors in the early development of the concepts of power, work and energy”, British Journal for the History of Science, vol. 3(3), (June 1967), pp. 209–224 (also published online by Cambridge University Press: 05 January 2009). Cardwell, D. S. L., From Watt to Clausius: The rise of thermodynamics in the early industrial age, Ithaca (NY), 1971 and Ames (Iowa), 1989. Cavarra, B., “Filosofia e scienze nell’opera di Bernardino Ramazzini: Medicina nei secoli arte e scienza”, Giornale di Storia della Medicina, Nuova Serie, ( Journal of the History of Medicine, New Series), vol. 23(2), (2011), pp. 411–423. Chareix, F., “Geometrization or mathematization: Christiaan Huygens’s critiques of infinitesimal analysis in his correspondence with Leibniz”, chap. 2, pp. 33–50, in: Dascal, M. (ed.), The practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010. Cobb, M., The egg & sperm race: The seventeenth-century scientists who unlocked the secrets of sex, life, and growth, London, 2006. Cohen, H. F., The scientific revolution. A historiographical inquiry, Chicago, 1994. Cohen, I. B., The Newtonian revolution with illustrations of the transformation of scientific ideas, Cambridge and New York, 1980 and 1983. Cohen, I. B., Smith, G. E. (eds.), The Cambridge Companion to Newton, Cambridge, 2002. Connors, J., “The one-room apartment of Cornelis Meijer”, Chap. 3, pp. [45]–64, in: Avcioğlu, N. and Sherman, A. (eds.), Artistic practices and cultural transfer in early modern Italy: Essays in honour of Deborah Howard, Farnham (UK), 2015. Cook, A., Edmond Halley: Charting the heavens and the seas, Oxford, 1998.

Bibliography

933

Cook, A., “Edmond Halley and the magnetic field of the earth”, Notes and Records of the Royal Society of London, vol. 55(3), (September, 2001), pp. 473–490 (https://doi.org/10.1098/rsnr.2001.0158). Copeman, W. S. C., A short history of the gout and the rheumatic diseases, Berkeley, Los Angeles, 1964. Cormack, L. B., Walton, S. A., Schuster, J. A. (eds.), Mathematical practitioners and the transformation of natural knowledge in early modern Europe, (Studies in History and Philosophy of Science, vol. 45), Cham (Switzerland), 2017. Coudert, A. P., Popkin, R. H., Weiner, G. M. (eds.), Leibniz, mysticism and religion (International Archives of the History of Ideas, no. 158), Dordrecht, 1998. Crippa, D., The impossibility of squaring the circle in the 17th Century: A debate among Gregory, Huygens and Leibniz (Frontiers in the history of science), Cham (Switzerland), 2019. Crouy-Chanel, E. de, Le canon au Moyen Âge et à la Renaissance: 1338–1559, Tours, 2020. Cunliffe, B., Koch, J. T. (eds.), Celtic from the west: Alternative perspectives from archaeology, genetics, language and literature, (Celtic Studies Publications, Book 15), Oxford, Philadelphia, 2012. Cunliffe, B., Koch, J. T. (eds.), Exploring Celtic origins: New ways forward in archaeology, linguistics, and genetics (Celtic Studies Publications, Book 22), Oxford, Philadelphia, 2019. Darrigol, O., A history of optics from Greek antiquity to the nineteenth century, Oxford, 2012. Dascal, M. (ed.), Leibniz: What kind of rationalist? (Logic, epistemology, and the unity of science, vol. 13), Dordrecht, 2009. Dascal, M. (ed.), The practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010, and in particular: Dascal, M., Firt, E., “Leibniz’s conciliatory approaches in scientific controversies”, chap. 6, pp. 137–168. De Risi, V., “Analysis situs, the foundations of mathematics and a geometry of space”, chap. 13, pp. 247–258 in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Dewhurst, K., Dr. Thomas Sydenham (1624–1689): His life and original writings, London, 1966, and Oakland, CA, 2021. Dickinson, H. W., A short history of the steam engine, Cambridge, 1939; reprinted 2010 in the Cambridge Library Collection: Books of enduring scholarly value. Dickinson, H. W., Sir Samuel Morland: Diplomat and inventor, 1625–1695, Cambridge, 1970. Dijksterhuis, E. J., De mechanisering van het wereldbeeld, Amsterdam, 1950, 1983, 1998 and 2006. Dijksterhuis, E. J., Dikshoorn, C. (trans.), The mechanization of the world picture, Oxford, London, New York, 1961, 1969 and Princeton, 1986.

934

Bibliography

Dijksterhuis, F. J., “Huygens’s dioptrica”, in: Palm, L. (guest ed.), Christiaan Huygens: De Zeventiende Eeuw, vol. 12(1), (1996), pp. 117–126. Dijksterhuis, F. J., Lenses and waves: Christiaan Huygens and the mathematical science of optics in the seventeenth century, Dordrecht, New York, Boston, London, 2004 (Originally published as a doctoral dissertation at Twente University, Enschede, 1999). Dijksterhuis, F. J., “Foci of interests: Optical pursuits amongst Huygens, Leibniz and Tschirnhaus 1680–1710”, pp. [261]–283 in: Kempe, M. (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung vol. 1, 2013. DiMeo, M., Lady Ranelagh: The incomparable life of Robert Boyle’s sister, Chicago, 2021. Di Pietro, P., “Le fonti bibliografiche nella « de morbis artificum diatriba » di Bernardino Ramazzini”, History and Philosophy of the Life Sciences, vol. 3(1), (1981), pp. 95–114. Dobell, C., Antony van Leeuwenhoek and his “little animals”; being some account of the father of protozoology and bacteriology and his multifarious discoveries in these disciplines, New York, 1932, and New York, 1958 (another first edition). Dooge, J. C. I., “Historical development of concepts in open channel flow”, pp. 205–229 in: Garbrecht, G. (ed.), Hydraulics and hydraulic research, Rotterdam, Boston, 1987. Droste, S., Offensive engines: Die prekäre Expertise militärischer Projectemacher (1650–1800), Stuttgart, 2022. Duchesneau, F., “Physiology and organic bodies”, chap. 26, pp. 466–484, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Dunn, R., Higgitt, R., Finding longitude: How ships, clocks and stars helped solve the longitude problem, Glasgow, 2014. Echelard-Dumas, M., “Der Begriff des Organismus bei Leibniz: „biologische Tatsache“ und Fundierung”, Studia Leibnitiana, vol. 8(2), (1976), pp. 160–186. Ellison, K., A cultural history of early modern English cryptography manuals, London, New York, 2017. Elmer, P., “Promoting medical change in Restoration Ireland: The chemical revolution and the patronage of James Butler, duke of Ormond (1610–88)”, chap. 4, in: Cunningham, J. (ed.), Early Modern Ireland and the world of medicine: Practitioners, collectors and contexts. Manchester (UK), 2019. (Online at: https://www .ncbi.nlm.nih.gov/books/NBK541883/). Erlmann, V., Reason and resonance: A history of modern aurality, New York, 2010. Evans, C., Withey, A., “An enlightenment in steel? Innovation in the steel trades of eighteenth-century Britain”, Technology and Culture, vol. 53(3), (July 2012), pp. 533–560. Evans, E., “The Irish dialect of Urris, Inishowen, Co. Donegal”, Lochlann: A Review of Celtic Studies (Norsk tidsskrift for sprogvidenskap, Universitetsforlaget, Oslo), vol. 4, (1969), pp. 1–130.

Bibliography

935

Fara, P., “Newton shows the light: A commentary on Newton (1672) ‘A letter … containing his new theory about light and colours …’”, Philosophical Transactions, A, Math Phys Eng Sci., (2015 April 13; 373(2039): 20140213 (https://doi.org/10.1098/rsta.2014.0213). Farrell, M. (F. C. J.), The life and work of William Whiston, New York, 1981; originally a Ph.D. thesis submitted to the Faculty of Technology of the University of Manchester, 1973. Favino, F., “Beyond the ‘moderns’? The Accademia Fisico-matematica of Rome (1677–1698) and the vacuum”, pp. 120–158, in: Dupré, S., and Kusukawa, S. (eds.), History of Universities, vol. XXIII/2, (Special issue: The circulation of news and knowledge in intersecting networks), Oxford, 2008. Feldman, T. S., “Barometer”, pp. 26f. in: Heilbron, J. L. (ed.), The Oxford Guide to the history of physics and astronomy, Oxford, 2005. Felton, J. S., “The heritage of Bernardino Ramazzini”, Occupational Medicine, vol. 47(3), (1997), pp. 167–79. Ferraro, G., The rise and development of the theory of series up to the early 1820s, (Series: Sources and studies in the history of mathematics and physical sciences), New York, 2008. Fiant, O., “Canguilhem and the machine metaphor in life sciences: History of science and philosophy of biology at the service of sciences”, Transversal: International Journal for the Historiography of Science, (Graduate Program in History of Federal University of Minas Gerais/ Universidade Federal de Minas Gerais, Brazil), vol. 4(4), (2018), pp. 149–162. Finocchiaro, M. A., Defending Copernicus and Galileo: Critical reasoning in the two affairs, (Boston Studies in the Philosophy of Science, vol. 280), Dordrecht, Heidelberg, London, New York, 2010. Fishbein, M., “The barber surgeons and the liberation of surgery”, Journal of the International College of Surgeons, vol. 27, (1957), pp. 766–779. Forbes, E. G. (and M.), Murdin, L., Willmoth, F. (eds.), The Correspondence of John Flamsteed: First Astronomer Royal, vol. 3 (1703–1719), Bristol and Philadelphia, 2002. Force, J. E., William Whiston: Honest Newtonian, Cambridge, London, New York, 1985. Force, J. E., Popkin, R. H. (eds.), Newton and religion: Context, nature and influence, (International Archives of the History of Ideas, no. 161), Dordrecht, Boston, London, 1999. Fors, H., The limits of matter: Chemistry, mining and enlightenment, Chicago and London, 2015. Franco, G., Meglio prevenire che curare – Il pensiero di Bernardino Ramazzini, medico sociale e scienziato visionario, 2015 (eBook). Freudenthal, G., Perpetuum mobile – The Leibniz-Papin controversy, Berlin: Max-PlanckInstitut für Wissenschaftsgeschichte (Preprint 127), 1999, pp. 1–58, Appendix with translation (pp. [i]–xv), and facsimile of Papin’s Synoppsis Controversiae; Publication

936

Bibliography

in: Studies in History and Philosophy of Science Part A, vol. 33(3), (September 2002), pp. 573–637. Friedrich, L., “Pädagogische Perspektiven zwischen Barock und Aufklärung: Die Pädagogik Erhard Weigels”, pp. 39–68, in: Schielicke, R. E., Herbst, K-D., Kratochwil, S. (eds.), Erhard Weigel – 1625 bis 1699: Barocker Erzvater der deutschen Frühaufklärung, (Acta Historica Astronomiae, vol. 7), Frankfurt am Main, 1999. Frisinger, H. H., “Mathematicians in the history of meteorology: The pressure-height problem from Pascal to Laplace”, Historia Mathematica, vol. 1(3), (1974), pp. 263–286. Gaab, H., “Die Eimmart-Sternwarte in Nürnberg”, chap. 6, pp. 213–234, in: Wolfschmidt, G. (ed.), Astronomie in Nürnberg. Anläßlich des 500. Todestages von Bernhard Walther (1430–1504) und des 300. Todestages von Georg Christoph Eimmart (1638–1705), Hamburg: tredition science (Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften; vol. 3), 2010. Gädeke, N., “ »Matières d’esprit et de curiosité« oder: Warum wurde John Toland in Hannover zur persona non grata?” pp. 145–166 in: Li, W., Noreik, S. (eds.), G. W. Leibniz und der Gelehrtenhabitus: Anonymität, Pseudonymität, Camouflage, Cologne, Weimar, Vienna, 2016. Gale, G., “Leibniz’s force: Where physics and metaphysics collide”, pp. 62–70 in: Heinekamp, A. (ed.), Leibniz’ Dynamica. Symposion der Gottfried-Wilhelm-LeibnizGesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, Stuttgart, 1984 (Studia Leibnitiana, Special issue, no. 13). Garber, D., “Leibniz: physics and philosophy”, chap. 9, pp. 270–352, in: Jolley, N. (ed.), The Cambridge Companion to Leibniz, Cambridge, 1995, 1996, 1998. Garber, D., “Steno, Leibniz, and the history of the world”, chap. 8, pp. 201–230, in: Andrault, R., Lærke, M. (eds.), Steno and the philosophers (Studies in Intellectual History, vol. 276), Leiden, 2018. Garber, D., Tho, T., “Force and dynamics”, chap. 17, pp. 304–330, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Garçon, A.-F., “The three states of technology: An historical approach to a thought regime, 16th–20th Centuries”, pp. 11–26 in: Faucheux, M. and Fores, J. (eds.), New Elements of Technology, (Collection Sciences Humaines et Technologie, UTBM: l’université de technologie de Belfort-Montbéliard), Sevenans, 2012. Garçon, A.-F., “Technologie: histoire d’un régime de pensée, XVIe–XIXe siècle”, pp. 73–102, in: Carvais, R., Garçon, A.-F., Grelon, A. (eds.), Penser la technique autrement: En hommage à l’oeuvre d’Hélène Vérin, Paris, 2017. Gaston Hall, H., “Molière: Satirist of seventeenth-century French medicine: fact and fantasy”, Proceedings of the Royal Society of Medicine, (Section of the History of Medicine), vol. 70, (June 1977), pp. 425–431. Gebelein, H., Werthmann, R., and Nomayo, S. (ed.), Johann Rudolph Glauber: Alchemistische Denkweise, neue Forschungsergebnisse und Spuren in Kitzingen, (Series: Schriftenreihe des Städtischen Museums Kitzingen, vol. 4), Kitzingen, 2009.

Bibliography

937

Gerland, E., Geschichte der Physik von den ältesten Zeiten bis zum Ausgange des achtzehnten Jahrhunderts, Munich, Berlin, Oldenburg, 1913. Gils, A., Bernardino Ramazzini (1633–1714): Leben und Werk; unter besonderer Berücksichtigung der Schrift “Über die Krankheiten der Künstler und Handwerker” (De morbis artificum diatriba), Doctoral dissertation, University of Göttingen, 1994. Gindikin, S. G., Shuchat, A. (trans.), Tales of physicists and mathematicians, Boston, Basel, 1988. Golinski, J., “A noble spectacle: Phosphorus and the public cultures of science in the early Royal Society”, ISIS: Journal of the History of Science Society, vol. 80(1), (1989), pp. 11–39. Görlich, E., Leibniz als Mensch und Kranker, Doctoral dissertation, Hanover: Medical School (Medizinische Hochschule), 1987. Gottschalk, J., “Theorie und Praxis bei Leibniz im Bereich der Technik, dargestellt am Beispiel der Wasserwirtschaft des Oberharzer Bergbaues”, Studia Leibnitiana, Supplementary vol. 22, (1982), pp. 46–57. Gottschalk, J., “Windmills and water-mills”, pp. 108–128 in: Popp, K., Stein, E. (eds.): Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000. Gowers, E., Horace satires book I, Cambridge, 2012. Grafton, A. T., “Textbooks and the disciplines”, pp. [11]–36, in: Campi, E., De Angelis, S., Goeing, A.-S., Grafton, A. T. (eds.), Scholarly knowledge: Textbooks in early modern Europe, Geneva, 2008. Grootendorst, A. W., Jan de Witt’s Elementa curvarum linearum: Liber primus, (Sources and Studies in the History of Mathematics and Physical Sciences), London, Dordrecht, Heidelberg, New York, 2000. Grootendorst, A. W., Jan de Witt’s Elementa curvarum linearum: Liber secundus, (Sources and Studies in the History of Mathematics and Physical Sciences), London, Dordrecht, Heidelberg, New York, 2010. Grote, H.-H., Johann Balthasar Lauterbach (1663–1694): Professor für Mathematik, Landbaumeister und Ingenieur am Wolfenbütteler Fürstenhof, Brundswick, 1995. Guangbi, D., “The book of changes and mathematics”, pp. 125–135 in: Dainian, F., Cohen, R. S. (eds.), Chinese studies in the history and philosophy of science and technology, (Boston Studies in the Philosophy of Science, vol. 179), Dordrecht, Boston, London, 1996. Guicciardini, N., “Isaac Newton, Philosophiae naturalis principia mathematica, first edition (1687)”, chap. 5, pp. 59–87, in: Grattan-Guinness, I. (ed.), Landmark writings in western mathematics 1640–1940, Amsterdam, Boston, 2005. Guicciardini, N., “John Wallis as editor of Newton’s mathematical work”, Notes and Records of the Royal Society, vol. 66(1), (2012), pp. 3–17. Guicciardini, N., Isaac Newton and natural philosophy, London and Chicago, 2018.

938

Bibliography

Habermann, K. (ed.), Die Kalenderbriefe des Georg Albrecht Hamberger im Kontext der Kalenderreform von 1700, Göttingen, 2012. Habermann, K., Herbst, K.-D., Erhard Weigel (1625–1699) und seine Schüler: Beiträge des 7. Erhard-Weigel-Kolloquiums 2014, Göttingen, 2016. Hall, B. S., West, D. C. (eds.), On pre-modern technology and science: A volume of studies in honor of Lynn White Jr., (Humana Civilitas: Sources and Studies relating to the Middle Ages and the Renaissance), Malibu, 1976. Hall, B. S., Weapons and warfare in Renaissance Europe: Gunpowder, technology and tactics, (Johns Hopkins Studies in the History of Technology), Baltimore (Maryland), 1997. Hall, A. R., “The scholar and the craftsman in the scientific revolution”, in: Clagett, M. (ed.), Critical problems in the history of science, Madison (Wisconsin), 1969, pp. 3–23, followed by commentaries by Merton, R. K. (pp. 24–29) and Johnson, F. R. (pp. 30–32). Hamel, J., “Erhard Weigel und die Kalenderreform des Jahres 1700”, pp. 135–156, in: Schielicke, R. E., Herbst, K-D., Kratochwil, S. (eds.), Erhard Weigel – 1625 bis 1699: Barocker Erzvater der deutschen Frühaufklärung, (Acta Historica Astronomiae, vol. 7), Frankfurt am Main, 1999. Haq, S. Nomanul, “Jabir ibn Hayyan”, pp. 459f. in: Selin, H. (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, Dordrecht, Boston, London, 1997. Harris, L. E., The two Netherlanders: Humphrey Bradley and Cornelis Drebbel, Leiden, 1961. Harrison, A., Béal eiriciúil as Inis Eoghain: John Toland (1670–1722) [Heretical Voice from Inishowen: John Toland (1670–1722)], Dublin, Belfast, 1994. Harrison, A., “Sur les origins Celtes de John Toland”, Revue de Synthèse, vol. 116(2/3), (April 1995), pp. 345–355. (https://doi.org/10.1007/BF03182049). Hasenöhrl, U., Meyer, J.-H., “The energy challenge in historical perspective”, Technology and Culture, vol. 61(1), January 2020, pp. 295–306. Hatch, R. A., “Between erudition and science: The archive and correspondence network of Ismaël Boulliau”, chap. 4, pp. 49–71, in: Hunter, M. (ed.), Archives of the scientific revolution: The formation and exchange of ideas in seventeenth-century Europe, Woodbridge, UK & Rochester, NY, 1998. Hausse, H., “The locksmith, the surgeon, and the mechanical hand: Communicating technical knowledge in early modern Europe”, Technology and Culture, vol. 60(1), (January 2019), pp. 34–64. Hecht, H., Gottfried Wilhelm Leibniz: Mathematik und Naturwissenschaften im Paradigma der Metaphysik, Stuttgart, Leipzig, 1992. Hecht, H. and Gottschalk, J., “The technology of mining and other technical innovations”, chap. 30, pp. 526–542, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

Bibliography

939

Heidarzadeh, T., A history of physical theories of comets, from Aristotle to Whipple, (Archimedes: New Studies in the History of Science and Technology, vol. 19), Cham (Switzerland), 2008. Heilbron, J. L., Electricity in the 17th and 18th centuries: A study of early modern physics, Berkley, Los Angeles, London, 1979. Heilbron, J. L., Galileo, Oxford, 2010. Heinecke, B., Knapp, W., Rubini, P., Streitenberger, P. (eds.), Leibniz und Guericke im Diskurs: Die Exzerpte aus den Experimenta Nova und der Briefwechsel, Berlin, Boston, 2019. Heinekamp A., “Kochanski als Leibniz-Korrespondent”, Organon Warszawa, vol. 14, (1978), pp. 73–106. Henderson, G. J., “Turn, Turn, Turn: The construction of the architectural spiral fluted column in the ancient Mediterranean world”, Technology and Culture, vol. 59(2), (April 2018), pp. 363–409. Henry, J., The scientific revolution and the origins of modern science, Basingstoke, New York, 1997. Hentschel, K., “Das Brechungsgesetz in der Fassung von Snellius: Rekonstruktion seines Entdeckungspfades und eine Übersetzung seines lateinischen Manuskriptes sowie erganzender Dokumente”, Archive for the History of the Exact Sciences, vol. 55, (2001), pp. 297–344. Heß, H.-J., Nagel, F. (eds.), Der Ausbau des Calculus durch Leibniz und die Brüder Bernoulli: Symposion der Gottfried-Wilhelm-Leibniz-Gesellschaft und der Bernoulli-Edition der Naturforschenden Gesellschaft in Basel, 15. bis 17. Juni 1987, (Studia Leibnitiana, Special issue, no. 17), Stuttgart 1989. Heß, H.-J., “Maturing in retirement: The unknown period of the Leibnizian calculus between Paris and publication (1676–1684)”, pp. 247–288 in: Galuzzi, M. (ed.), Giornate di Storia della Matematica, Cetraro (Cosenza) Settembre 1988, Commenda di Rende: EditEL, 1991, and 2nd extended version, November, 1993. Heß, H.-J., “Mathematics: Invention of infinitesimal calculus”, pp. 44–55 in: Popp, K., Stein, E. (eds.), Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000. Hestermeyer, W., Paedagogia Mathematica: Idee einer universellen Mathematik als Grundlage der Menschenbildung in der Didaktik Erhard Weigels, zugleich ein Beitrag zur Geschichte des pädagogischen Realismus im 17. Jahrhundert, Paderborn, 1969. Hills, R. L., Power from steam: A history of the stationary steam engine, Cambridge, 1989, 1993 (reprinted 1995, 1997). Hills, R. L., Power from wind: A history of windmill technology, Cambridge, 1994. Hiscock, W. G., David Gregory, Isaac Newton and their circle, Oxford, 1937. Hodoba-Eric, C., “Artificial apertures: The archaeology of Ramazzini’s De fontium in 17th-century earth historiography”, Centaurus, vol. 62(3), (August 2020), pp. 522–541.

940

Bibliography

Hofmann, J. E., Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672–1676), München, 1949. Hofmann, J. E., Leibniz in Paris 1672–1676  – his growth to mathematical maturity, Cambridge, London and New York, 1974 and 2008 (reprint). Hollewand, K. E., The banishment of Beverland: Sex, sin, and scholarship in the seventeenth-century Dutch republic, Leiden, Boston, 2019. Hollister-Short, G., “Leads and lags in late seventeenth century English technology”, History of Technology, vol. 1, (1976), pp. 159–183. Hollister-Short, G., “The vocabulary of technology”, History of Technology, vol. 2, (1977), pp. 125–155. Hollister-Short, G., “On the origins of the suction lift pump”, History of Technology, vol. 15, (1993), pp. 57–75. Hoppen, K. T., The common scientist in the seventeenth century: A study of the Dublin Philosophical Society 1683–1709, London, 1970. Hoppen, K. T. (ed.), Papers of the Dublin Philosophical Society 1683–1709, Dublin: Irish Manuscripts Commission, 2008, 2 vols. Hoskin, M., Stellar astronomy: Historical studies, Chalfont St Giles, 1982, and Cambridge (Science History Publication), 1986. Hunter, M., The Boyle papers: Understanding the manuscripts of Robert Boyle, Aldershot (England) and Burlington (VT), 2007. Hunter, M., Boyle: Between God and science, New Haven, CT, 2009. Iliffe, R., Priest of nature: The religious worlds of Isaac Newton, Oxford, 2017. Iltis, C., “Leibniz and the vis viva controversy”, ISIS: Journal of the History of Science Society, vol. 62(1), (1971), pp. 21–35. Inwood, S., The man who knew too much: The strange and inventive life of Robert Hook, 1635–1703, London, 2002 (and 2011). Inwood, S., The forgotten genius: The biography of Robert Hooke, 1635–1703, San Francisco, 2003 (and 2005). Israel, J. I., The Dutch republic: Its rise, greatness, and fall, 1477–1806, (The Oxford History of Early Modern Europe), New York, 1995. Jakapi, R. “Early modern natural philosophy allied with revealed religion: Boyle and Whiston”, part IV, chap. 19, pp. 233–244, in: Fuller, M., Evers, D., Runehov, A., Sæther, K.-W., Michollet, B. (eds.), Issues in science and theology: Nature  – and beyond: Transcendence and immanence in science and theology, Cham (Switzerland), 2020. Johnson, N. F., Duric, Z., Jajodia, S., Information hiding: Steganography and water­ marking-attacks and countermeasures, Dordrecht, 2001 (and New York, 2003). Johnson, W. A. (trans.), Christopher Polhem: The father of Swedish technology, Hartford, Conn., 1963. Johnston, S., “The identity of the mathematical practitioner in 16th-century England”, pp. 93–120, in: Hantsche, I. (ed.), Der “mathematicus”: Zur Entwicklung und

Bibliography

941

Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, (Duisburger Mercator-Studien, vol. 4), Bochum, 1996. Jones, A., Every pilgrim’s guide to Celtic Britain and Ireland, Norwich, 2002. Jones, M. L., Reckoning with matter: Calculating machines, innovation, and thinking about thinking from Pascal to Babbage, Chicago, London, 2016. Jones, M. L., “Calculating machine”, chap. 29, pp. 509–525, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Jonkers, A. R. T., “Finding longitude at sea: Early attempts in Dutch navigation”, pp. 186–197 in: Palm, L. (guest ed.), Christiaan Huygens: De Zeventiende Eeuw, vol. 12(1), (1996). Kahn, D., Codebreakers: The story of secret writing, New York, 1967 (and 1996). Kardel, T., Maquet, P. (eds., trans.), Nicolaus Steno: Biography and original papers of a 17th century scientist, Berlin, Heidelberg, 2013 and 2018. Kermit, H., Drake, M. (trans.), Niels Stensen[,] 1638–1686: The scientist who was beatified, Leominster, Herefordshire, UK, 2003. Kerr, J., The tiger who came to tea, London, 1968, and later. Kipper, G., Investigator’s guide to steganography, Boca Raton (FL), London, New York, Washington (DC), 2004. Klein, J., Takahata, N., Where do we come from?: The molecular evidence for human descent, Berlin, Heidelberg, New York, 2002. Klerk, S., “Natural history in the physician’s study: Jan Swammerdam (1637–1680), Steven Blankaart (1650–1705) and the ‘paperwork’ of observing insects”, British Journal for the History of Science, vol. 53(4), (December 2020), pp. 497–525. Kline, M., Mathematics in western culture, Oxford, London, New York, 1953 and 1964. Kline, M., Mathematical thought from ancient to modern times: Volume 3, New York, Oxford, 1972. Knobloch, E., “Theoria cum praxi: Leibniz und die Folgen für Wissenschaft und Technik”, Studia Leibnitiana, vol. 19(2), (1987), pp. 129–147. Knobloch, E., “Mathematics at the Prussian Academy of Sciences”, pp. 1–8, in: Begehr, H. G. W., Koch, H., Kramer, J., Schappacker, N., Thiele, E.-J. (eds.), Mathematics in Berlin, Basel, Boston, Berlin, 1998. Knobloch, E., “First European theory of determinants”, pp. 56–64 in: Popp, K. and Stein, E. (eds.), Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000. Knobloch, E., “Renaissance combinatorics” and “The origins of modern combinatorics”, pp. 123–146 and pp. 147–166, respectively, in: Wilson, R., Watkins, J. J. (eds.), Combinatorics: Ancient & modern, Oxford, 2013. Knobloch, E., “Determinant theory, symmetric functions and dyadic”, chap. 12, pp. 225–246, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

942

Bibliography

Knowles Middleton, W. E., The history of the barometer, Baltimore (Maryland), 1964 and 2002; Taunton (UK), 1994. Knowles Middleton, W. E., A history of the theories of rain and other forms of precipitation, London, 1966. Kokott, W., “Umwege zur Kalendereinheit: Der »Verbesserte Kalender« (1700 bis 1775) und die Gründung der Berliner Sternwarte”, pp. 43–48 in: Dick, W. R., Fritze, K. (eds.), 300 Jahre Astronomie in Berlin und Potsdam, Frankfurt am Main, 2000. Koller, E., Strittige Zeiten: Kalenderreformen im Alten Reich 1582–1700, Berlin, Boston, 2014. Kragh, H., Phosphors and phosphorus in early Danish natural philosophy, Historiskfilosofiske Meddelelser 88 (2002); Det Kongelige Danske Videnskabernes Selskab; The Royal Danish Academy of Sciences and Letters Commission, Copenhagen, 2003. Krafft, F., “Die aus der Literatur bekannte Korrespondenz des Otto von Guericke (d. Ä.)”, Technikgeschichte, vol. 45, (1978), pp. 37–54. Krafft, F., “Die ‚Copernicanische Revolution‘”, Antike und Abendland, vol. 40, (1994), pp. 1–30; reprinted in: Kuester, H. (ed.), Das sechzehnte Jahrhundert: Europäische Renaissance, Regensburg, 1995, pp. 181–214. Krafft, F. (ed.), Otto von Guerickes Neue (sogenannte) Magdeburger Versuche über den Leeren Raum: Mit einer einleitenden Abhandlung, Düsseldorf, 1996, pp. X–LXXXVIII. Krafft, F., “Die Schwere der Luft in der Diskussion des 17. Jahrhunderts: Otto von Guericke”, pp. 135–170 in: Klewer, W. (ed.), Die Schwere der Luft in der Diskussion des 17. Jahrhunderts, (Wolfenbütteler Arbeiten zur Barockforschung, vol. 29), Wiesbaden, 1997. Krafft, F., “Alt und Jung: Die Kontakte zwischen Otto von Guericke und Gottfried Wilhelm Leibniz: virtutes mundanae und ‘Einhorn’”, pp. 263–282 in: Heinecke, B., Kästner, I. (eds.), G. W. Leibniz und die gelehrte Welt Europas um 1700, Aachen, 2013. Krafft, F., “Gottfried Wilhelm Leibniz oder Otto von Guericke  – Protogaea oder Experimenta nova Magdeburgica? Die Rekonstruktion des vermeintlichen Einhorns von Quedlinburg”, Sudhoffs Archiv, vol. 99, (2015), pp. 166–208. Kratochwil, S., “Johann Christoph Sturm und Gottfried Wilhelm Leibniz”, pp. 104–118 in: Gaab, H., Leich, P., Löffladt, G. (eds.), Johann Christoph Sturm (1635–1703), (Acta Historica Astronimiae, vol. 22), Frankfurt am Main, 2004. Kruse, H.-J., “Johann Kunckel – der bedeutendste Plöner?”, Jahrbuch für Heimatkunde im Kreis Plön, vol. 42, (2012), pp. 89–150. Kühn, S., “Gelehrte Streitkultur und Wissenskollektive: Das Beispiel des Denis Papin”, pp. 273–280 in: Schneider, U. J. (ed.), Kulturen des Wissens im 18. Jahrhundert, Berlin, 2008. Kuhn, T. S., The Copernican revolution: Planetary astronomy in the development of western thought, Cambridge (MA), 1957 and 1992.

Bibliography

943

Kuhn, T. S., The structure of scientific revolutions, Chicago 1962, 1970, 1996 and 2012. Kutschmann, W., Die Newtonsche Kraft: Metamorphose eines wissenschaftlichen Begriffs, Studia Leibnitiana, (Special issue, no. 12), Wiesbaden, 1983. Lærke, M., “Leibniz and Steno, 1675–1680”, chap. 3, pp. 63–84, in: Andrault, R., Lærke, M. (eds.), Steno and the philosophers, (Studies in Intellectual History, vol. 276), Leiden, 2018. Laeven, A. H., Richards, L. (trans.), The »Acta Eruditorum« under the editorship of Otto Mencke (1644–1707): The history of an international learned journal between 1682 and 1707, translated from the Dutch, Amsterdam, 1990. Laeven, A. H., Laeven-Aretz, L. J. M., The authors and reviewers of the Acta Eruditorum 1682–1735, Electronic Publication Molenhoek (NL), 2014. Lane, N., “The unseen world: reflections on Leeuwenhoek (1677) ‘Concerning little animals’”, Philosophical Transactions of the Royal Society, (2015), B370: 20140344 (http://dx.doi.org/10.1098/rstb.2014.0344). Leask, I., “Constant process: The science of Toland’s Pantheisticon”, Eighteenth-Century Ireland/ Iris an dá chultúr [Ireland of the two cultures], vol. 34, (2019), pp. 11–27. Leliavsky Bey, S., “Historic development of the theory of the flow of water in canals and rivers”, The Engineer, vol. 191, (1951), pp. 466–567 (specifically p. 466, p. 498, p. 533, p. 565) and pp. 601–603. Lennon, J., Irish orientalism: A literary and intellectual history, Syracuse (NY), 2004 and 2008. Lepage, J.-D. G. G., Vauban and the French military under Louis XIV: An illustrated history of fortifications and strategies, Jefferson (NC), 2010. Lisiak, B., “Leibniz’s scientific collaboration with Adam Kochański, S.J.”, Roczniki Filozoficzne / Annales de Philosophie / Annals of Philosophy, vol. 65(2), (2017), pp. 205–222. Loeffel, H., Blaise Pascal 1623–1662, (Vita Mathematica, vol. 2), Basel, Boston, 1987. Loibl, W., “Johann Daniel Crafft (*Wertheim 1624-+Amsterdam 1697): Ein Chemiker, Kameralist und Unternehmer des 17. Jahrhunderts”, Wertheimer Jahrbuch 1997, pp. 55–251, Wertheim, 1998. Long, P. O., Artisan / Practitioners and the rise of the new sciences, 1400–1600, Corvallis (Oregon), 2011. Lüthy, C., “Atomism, Lynceus, and the fate of seventeenth-century microscopy”, Early Science and Medicine, vol. 1(1), (1996), pp, 1–27. Lüthy, C., Murdoch, J. E., Newman, W. R. (eds.), “Introduction: Corpuscles, atoms, particles and minima”, pp. 1–38 in: Late medieval and early modern corpuscular matter theories, (Series: Medieval and Early Modern Philosophy and Science, vol. 1), Leiden, Boston, 2001. Lunteren, F. van, Framing hypotheses: Conceptions of gravity in the 18th and 19th centuries, (Proefschrift/ Doctoral dissertation, Rijksuniversiteit te Utrecht), Utrecht, 1991.

944

Bibliography

Lunteren, F. van, “Nicolas Fatio de Duillier on the mechanical cause of universal gravitation”, pp. 41–59 in: Edwards, M. R. (ed.), Pushing gravity: New perspectives on Le Sage’s theory of gravitation, Montreal, 2002. Maanen, J. A. van, “Die Mathematik in den Niederlanden im 17. Jahrhundert und ihre Rolle in der Entwicklungsgeschichte der Infinitesimalrechnung”, pp. 1–13 in: Heinekamp, A. (ed.), 300 Jahre „Nova methodus“ von G. W. Leibniz (1684–1984): Symposion der Gottfried-Wilhelm-Leibniz-Gesellschaft im Congresscentrum „Leewenhorst“ in Noordwijkerhout (Niederlande), 28. bis 30. August 1984, (Studia Leibnitiana, Special issue, no. 14), Stuttgart, 1986. Maanen, J. A. van, “Johan Jacob Ferguson, geb. um 1630 im Haag (?), gest. vor dem 24. November 1706, vermutlich am 6. Oktober 1691, in Amsterdam”, Studia Leibnitiana, vol. 22, (1990), pp. 203–216. Maanen, J. A. van, “Johann Bernoulli, man of contrasts”, Nieuw Archief voor Wiskunde, ser. 4, part 11, no. 3, (Nov. 1993), pp. 241–246. Maanen, J. A. van, Een complexe grootheid: Leven en werk van Johann Bernoulli 1667–1748, Utrecht, 1995 and Amsterdam, 2016. Maanen, J. A. van, “Leibniz (1646–1716) and the curve of quickest descent”, Conference: Curves in Honour of Leibniz’s Tercentenary, Gresham College with the British Society for the History of Mathematics, Bernard’s Inn Hall, London (27 October 2016); Online presentation (2022) at: https://www.gresham.ac.uk/lectures-and-events/leibniz -and-the-curve-of-quickest-descent. MacDonald Ross, G., “Leibniz and the Nuremberg alchemical society”, Studia Leibnitiana, vol. 6(2), (1974), pp. 222–248. MacDonald Ross, G., Past masters: Leibniz, Oxford, New York, 1984. MacDonald Ross, G., “Leibniz and the origin of things”, Part III (Theology and Mysticism), chap. 17, pp. [241]–257 in: Dascal, M. and Yakira, E. (eds.), Leibniz and Adam, Tel Aviv, 1993. Mackensen, L. von, Die Vorgeschichte und die Entstehung der 4-Spezies-Rechenmaschine von Gottfried Wilhelm Leibniz, nach bisher unerschlossenen Manuskripten und Zeichnungen mit einem Quellenanhang der Hauptdokumente, Doctoral dissertation (TU München), Munich, 1968. Mackensen, L. von, “Calculating machines”, pp. 84–107 in: Popp, K. and Stein, E. (eds.): Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000. MacKillop, J., Myths and legends of the Celts, London, 2005. MacLeod, C., “The European origins of British technological predominance”, pp. 111–126 in: De la Escosura, L. P. (ed.), Exceptionalism and industrialisation: Britain and its European rivals, 1688–1815, Cambridge, 2004. Maffioli, C. S., Out of Galileo: The science of waters 1628–1718, (Nieuwe Nederlandse Bijdragen tot de Geschiedenis der Geneeskunde en der Natuurwetenschappen, no. 49), Rotterdam, 1994.

Bibliography

945

Mahoney, M. S., “Christiaan Huygens: The measurement of time and longitude at sea”, pp. 234–270 in: Bos, H. J. M. et al. (eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979, Lisse, 1980. Mancosu, P., Philosophy of mathematics and mathematical practice in the seventeenth century, Oxford, New York, 1996. Martínez, F. J., “Vitalism in Leibniz: A Deleuzian approach”, chap. 10, pp. 159–170, in: Nicolás, J. A., Gómez Delgado, J. M., Escribano Cabeza, M. (eds.), Leibniz and hermeneutics, (Cambridge Scholars Publishing), Newcastle upon Tyne, 2016. Martini, C. and Wolfschmidt, G. (ed.), Zwei Frauenleben für die Wissenschaft im 18. Jahrhundert: Eine vergleichende Fallstudie zu Émilie du Châtelet und Maria Gaetana Agnesi, (Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften, vol. 43), Hamburg, 2017. Matschoss, C., Geschichte der Dampfmaschine: Ihre kulturelle Bedeutung, technische Entwicklung und ihre großen Männer, Berlin, 1901, and Hildesheim, 1983. Mattes, J., “Mapping the invisible: Knowledge, credibility and visions of earth in early modern cave maps”, British Journal for the History of Science, vol. 55(1), (March 2022), pp. 53–80. Mayer, U., Zwischen Brennpunkt und Peripherie  – Der sächsische Mathematiker, Techniker und Philosoph Ehrenfried Walther von Tschirnhaus (1651–1708), Doctoral dissertation, Martin-Luther-Universität Halle-Wittenberg, 2001. Mayer, U., “„Kein tummelplatz, darauff gelehrte leute Kugeln wechseln“ – Principles and practice of Mencke’s editorship of the Acta Eruditorum in the light of mathematical controversies”, pp. 49–59 in: Pfeiffer, J., Conforti, M., Delpiano, P. (eds.), Les journaux savants dans l’Europe modern: Communications et construction des savoirs, (Archives Internationales d’ Histoire des Sciences, vol. 63, no. 170–171), 2013. Mayr, E., The growth of biological thought: Diversity, evolution, and inheritance, Cambridge (MA), London, 1982. Mayr, E., This is biology: The science of the living world, Cambridge (MA) and London, 1997 and 2001. Mazer, A., The ellipse: A historical and mathematical journey, Hoboken (New Jersey), 2010. McCallum, J. E., Military medicine: From ancient times to the 21st century, Santa Barbara, Denver, Oxford, 2008. McCormick, T., William Petty and the ambitions of political arithmetic, Oxford, 2009. McDonough, J. K., “Leibniz’s philosophy of physics”, in: Zalta, E. N. (ed.), The Stanford Encyclopedia of Philosophy (Fall 2019 Edition),  . McDonough, J. K., “Optics”, chap. 23, pp. 425–437, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018.

946

Bibliography

McGuinness, P., Harrison, A., Kearney, R. (eds.), John Toland’s Christianity not mysterious: Text, associated works and critical essays, Dublin, 1997. Meinel, C., “Empirical support for the corpuscular theory in the seventeenth century”, pp. 77–92 in: Batens, D., van Bendegem, J. P. (eds.), Theory and experiment: Recent insights and new perspectives on their relation, (Synthese library series, vol. 195), Dordrecht and Boston, 1988. Meinel, C., “Early seventeenth-century atomism: Theory, epistemology, and the insufficiency of experiment”, ISIS: Journal of the History of Science Society, vol. 79(1), (1988), pp. 68–103. Meinel, C., “‘Das letzte Blatt im Buch der Natur’: Die Wirklichkeit der Atome und die Antinomie der Anschauung in den Korpuskulartheorien der frühen Neuzeit”, in: Studia Leibnitiana, vol. 20, (1988), pp. 1–18. Meinel, C. (ed.), Grenzgänger zwischen Himmel und Erde: Kometen in der Frühen Neuzeit, (Kataloge und Schriften der Staatlichen Bibliothek Regensburg, vol. 1), Regensburg, 2009, and 2022 (digital edition). Melero, J. P., “The scientific revolution and enlightenment in Spanish American mining and metallurgy”, pp. 51–61 in: Rosenberg, G. D. (ed.), The revolution in geology from the Renaissance to the Enlightenment, (The Geological Society of America, Memoir 203), Boulder, Colorado, 2009. Mercer, C., Leibniz’s metaphysics: Its origins and development, Cambridge, New York, Melbourne, 2004. Mertz, D. P., Geschichte der Gicht: Kultur- und medizinhistorische Betrachtungen, Stuttgart, New York, 1990. Meyer, E., “Das Rätsel um Johannes Keplers Wohnort in der Linzer Hofgasse – Zum Jubiläum (2018): „400 Jahre Drittes Keplersches Gesetz“”, chap. 2 (pp. 19–48) in: Wolfschmidt, G. (ed.), Internationalität in der astronomischen Forschung (18. bis 21. Jahrhundert) / Internationality in the astronomical research (18th to 21th Century), Proceedings der Tagung des Arbeitskreises Astronomiegeschichtein der Astronomischen Gesellschaft in Wien 2018, (Nuncius Hamburgensis  – Beiträge zur Geschichte der Naturwissenschaften, vol. 49), Hamburg, 2019. Miller, D. P., “A new perspective on the natural philosophy of steams and its relation to the steam engine”, Technology and Culture, vol. 61(4), (October 2020), pp. 1129–1148. Mitcham, C., “Engineering as a productive activity: Philosophical remarks”, pp. 80–117 in: Durbin, P. T. (ed.), Critical perspectives on nonacademic science and engineering, (Research in technology studies, vol. 4), Bethlehem (PA), London and Toronto, 1991. Mitcham, C., Schatzberg, E., “Defining technology and the engineering sciences”, pp. 27–63 in: Meijers, A. (ed.), Philosophy of technology and engineering sciences (Technology, engineering and the sciences, vol. 9, part 1), Amsterdam, 2009. Morar, F.-S., “Reinventing machines: The transmission history of the Leibniz calculator”, British Journal for the History of Science, vol. 48(1), (March 2015), pp. 123–146.

Bibliography

947

Müller, K., Krönert, G. (eds.), Leben und Werk von G. W. Leibniz: Eine Chronik, Frankfurt am Main, 1969. Mungello, D. E., Curious land: Jesuit accommodation and the origins of Sinology, Honolulu, 1985 (and 1989); first published in: Studia Leibnitiana, Supplementa, vol. 25, (1985). Nagel, F., “Nieuwentijt, Leibniz, and Jacob Hermann on infinitesimals”, pp. 199–214, in: Goldenbaum, U., Jesseph, D. (eds.), Infinitesimal differences: Controversies between Leibniz and his contemporaries, Berlin, New York, 2008. Naragon, S., “Friedrich Hoffmann (1660–1742)”, pp. 346–348 in: Klemme, H. F., Kuehn, M. (eds.), The Bloomsbury Dictionary of Eighteenth-Century German Philosophers, London, New York, 2010 and 2016. Newman, W. R., Principe, L. M., Alchemy tried in the fire: Starkey, Boyle, and the fate of Helmontian chymistry, Chicago, London, 2002. Newman, W. R., Gehennical fire: The lives of George Starkey, an American alchemist in the scientific revolution, with a new foreword, Chicago and London, 2003. Newman, W. R., “From alchemy to ‘chymistry’”, chap. 21, pp. 497–517, in: Park, K., Datson, L. (eds.), The Cambridge History of Science, Volume 3: Early modern science, Cambridge, 2006. Newman, W. R., “The significance of ‘chymical atomism’”, Early Science and Medicine, vol. 14 (1/3), (2009), pp. 248–264. Newman, W. R., Newton the alchemist: Science, enigma, and the quest for nature’s “secret fire”, Princeton, 2019. O’Hara, J. G., “Quellen zur Geschichte der Nutzung regenerierbarer Energiedargebote – Mühlen-  und Maschinenbücher”, pp. 95–111 in: Bayerl, G. (ed.), Wind- und Wasserkraft: Die Nutzung Regenerierbarer Energiequellen in der Geschichte, (Series: Technikgeschichte in Einzeldarstellungen), Düsseldorf, 1989. O’Hara, J. G., “Leibniz and the Jacobite war: Reports and reflections on the battle of the Boyne and events in Ireland, 1689–91”, Proceedings of the Royal Irish Academy, vol. 91C, (1991), pp. 1–20. O’Hara, J. G., “Huygens, Leibniz and the ‘petit demon’: Agreement and dissension in their mathematical correspondence”, pp. 151–160 in: Palm, L. (guest ed.), Christiaan Huygens: De Zeventiende Eeuw, vol. 12(1), (1996). O’Hara, J. G., “‘A chaos of jottings that I do not have the leisure to arrange and mark with headings’: Leibniz’s manuscript papers and their repository”, chap. 10, pp. 159–170, in: Hunter, M. (ed.), Archives of the scientific revolution: The formation and exchange of ideas in seventeenth-century Europe, Woodbridge, UK & Rochester, NY, 1998. O’Hara, J. G., “‘Leibnutz’s universal principle in optics’. William Molyneux’s translation and interpretation of Leibniz’s unicum opticae”, pp. 915–919 in: Poser, H. et al. (eds.), Nihil Sine Ratione: Mensch, Natur und Technik im Wirken von G. W. Leibniz, VII.

948

Bibliography

Internationaler Leibniz-Kongreß, Berlin, 10–14 September 2001, Vorträge 2. Teil, Berlin, 2001. O’Hara, J. G., “The mathematician as engineer in the seventeenth century: Leibniz and engineering hydraulics”, pp. [77]–89 in: Duffy, M. C. (ed.), Engineering and engineers. Proceedings of the XXth International Congress of History of Science (Liège, 20–26 July 1997), vol. XVII, Turnhout, Belgium, 2002. O’Hara, J. G., “Molyneux, William (1656–1698), experimental philosopher and constitutional writer”, Oxford Dictionary of National Biography (Published in print/online: September 23, 2004). O’Hara, J. G., “Science not metaphysical: Leibniz als Naturwissenschaftler in der Nachfolge von Galilei”, pp. [33]–56 in: Kempe, M. (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung 1 (vol. 1), 2013. O’Hara, J. G., “‘J’aime mieux un Leewenhoek qui me dit ce qu’il voit, qu’un Cartesien qui me dit ce qu’il pense’: Leibniz, Leeuwenhoek und die Entwicklung der experimentellen Naturwissenschaft”, pp. 145–175 in: Kempe, M. (ed.), 1716 – Leibniz’ Letztes Lebensjahr: Unbekanntes zu einem bekannten Universalgelehrten, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung 2 (vol. 2), 2016. O’Hara, J. G., “‘ova vel semina … foecundare’: Sexual reproduction in Leibniz’s scientific correspondence”, vol. II, pp. 431–448 in: Li, W., Beckmann, U., et al. (eds.), “Für unser Glück oder das Glück anderer”: Vorträge des X. Internationalen Leibniz-Kongresses, Hannover, 18.–23. Juli 2016, 5 vols, Hildesheim, Zürich, New York, 2016. O’Hara, J. G., “‘Agnoscimus omnes quantus vir fuerit Robertus Boilius’  – kritische Anmerkungen über Boyle in Leibniz’ Korrespondenz”, pp. 319–332, in: Heinecke, B., Kästner, I. (eds.), Wettstreit der Künste: Der Aufstieg des praktischen Wissens zwischen Reformation und Aufklärung, (Europäische Wissenschaftsbeziehungen, vol. 17), Aachen, 2018. Ohly, S., Johann Bernoullis mechanische Arbeiten 1690 bis 1713, Augsburg, 2004. Op de Beeck, J., De Zonnekoning: Glorie & Schaduw van Lodewijk XIV, Antwerp, 2018. Palm, L. (guest ed.), Christiaan Huygens, De Zeventiende Eeuw: Cultuur in de Nederlanden in interdisciplinair perspectief, vol. 12(1), (1996). A collection of 23 articles (pp. 3–273), Online access at: Digitale Bibliotheek voor de Nederlandse Letteren (dbnl): https://dbnl.nl/tekst/_zev001199601_01/. Palumbo, M., “„Praeceptor, fautorque meus colendus  …“  – Weigels Werke in der Privatbibliothek von Leibniz”, pp. 249–268, in: Habermann, K., Herbst, K.-D. (eds.), Erhard Weigel (1625–1699) und seine Schüler: Beiträge des 7. Erhard-WeigelKolloquiums 2014, Göttingen, 2016. Papineau, D., “The vis viva controversy: Do meanings matter?”, in: Studies in History and Philosophy of Science, vol. 8 (2), (1977), pp. 111–141, and chap. 47, pp. 198–216,

Bibliography

949

in: Woolhouse, R. S. (ed.), Gottfried Wilhelm Leibniz: Critical assessments, vol. III, London, 1994. Partington, J. R., “The early history of phosphorus”, Science Progress, vol. 30, no. 119, (Januar 1936), pp. 402–412. Partington, J. R., A history of chemistry, 4 vols, London, 1961–1970 [= vol. 2 (1961), vol. 3 (1962), vol. 4 (1964), and vol. 1 (1970)]. Partington, J. R., A history of Greek fire and gunpowder, Cambridge, 1960. Partington, J. R., Hall, B. S. (intro.), A history of Greek fire and gunpowder, Baltimore (Maryland), 1999. Pedersen, O., Early physics and astronomy: A historical introduction, Cambridge, 1974 and 1993. Pedersen, O., “The divorce of science and religion: Historical interaction between science and religion”, pp. 139–160, in: Fennema, J., Paul, I. (eds.), Science and religion: One world – changing perspectives on reality, Dordrecht, Boston, London, 1990. Pesic, P., “François Viète, father of modern cryptanalysis  – two new manuscripts”, Cryptologia, vol. 21(1), (1997), pp. 1–29. Peters, H., “Kunckels Verdienste um die Chemie”, Archiv für die Geschichte der Naturwissenschaften und der Technik, vol. 4, (1912), pp. [178]–214. Peters, H., “Leibniz als Chemiker”, Archiv für die Geschichte der Naturwissenschaften und der Technik, vol. 7, (1916), pp. [85]–108, [220]–235, [275]–287. Pinto-Correia, C., The ovary of Eve: Egg and sperm and preformation, Chicago and London, 1997. Poole, W., The world makers: Scientists of the restoration and the search for the origins of the earth, Oxford, 2010. Popp, K., Stein, E. (eds.), Gottfried Wilhelm Leibniz: The work of the great universal scholar as philosopher, mathematician, physicist, engineer, Hanover, 2000. Poppe, E., “Leibniz and Eckhart on the Irish language”, Eighteenth-Century Ireland / Iris an dá chultúr [Ireland of the two cultures], vol. 1, (1986), pp. 65–84. Porter, R., Rousseau, G. S., Gout: The patrician malady, New Haven, London, 1998. Postma, J., The Dutch in the Atlantic slave trade, 1600–1815, Cambridge, New York, Melbourne, 1990. Postma, J., “The dispersal of African slaves in the west by Dutch slave traders, 1630–1803”, chap. 10, pp. [283]–300 in: Inikori, J. E., Engerman, S. L. (eds.), The Atlantic slave trade: Effects on economies, societies and peoples in Africa, the Americas, and Europe, Durham, NC, 1992 (and 1998). Powell, M. N., Performing authorship in eighteenth-century English periodicals, Plymouth (UK) and Lanham (Maryland), 2012. Principe, L. M., “Wilhelm Homberg: Chymical corpuscularianism and chrysopoeia in the early eighteenth century”, pp. 535–556 in: Lüthy, C., Murdoch, J. E., Newman,

950

Bibliography

W. R. (eds.), Late medieval and early modern corpuscular matter theories, (Series: Medieval and Early Modern Philosophy and Science, vol. 1), Leiden, Boston, 2001. Principe, L. M., De Witt, L., Transmutations: Alchemy in art: Selected works from the Eddleman and Fisher Collections at the Chemical Heritage Foundation, Philadelphia, 2002. Principe, L. M., The transmutations of chymistry: Wilhelm Homberg and the Académie Royale des Sciences, Chicago and London, 2020. Probst, S., “Infinity and creation: The origin of the controversy between Thomas Hobbes and the Savilian professors Seth Ward and John Wallis”, British Journal for the History of Science, vol. 26(3), (1993), pp. 271–279. Probst, S., “Leibniz und Wallis: Eine Übersicht über neuere Quelleneditionen und Forschungen”, pp. 89–101 in: Wolfschmidt, G. (ed.), Festschrift – Proceedings of the Scriba Memorial Meeting – History of Mathematics, Hamburg, 2017. Probst, S., “The relation between Leibniz and Wallis: An overview from new sources and studies”, Quaderns d’Història de l’Enginyeria, vol. 16, (2018), pp. 189–208. Probst, S., “The calculus”, chap. 11, pp. 211–224, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Purrington, R. D., The first professional scientist: Robert Hooke and the Royal Society of London, Basel, Boston, Berlin, 2009. Ranea, A. G., “The a priori method and the actio concept revised: Dynamics and metaphysics in an unpublished controversy between Leibniz and Denis Papin”, Studia Leibnitiana, vol. 21(1), (1989), pp. 42–68. Ranea, A. G., “Poiein and prattein: The concept of actio and the measurement of motive force”, pp. 226–232 in: Breger, H., Herbst, J., Erdner, S. (eds.), Natur und Subjekt: IX. Internationaler Leibniz-Kongress, (Supplementary volume), Hanover, 2012. Ranea, A. G., “Theories, rules and calculations: Denis Papin, before and after the controversy with G. W. Leibniz”, pp. [59]–83 in: Kempe, M. (ed.), Der Philosoph im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung 1 (vol. 1), 2013. Raphael, R., Reading Galileo: Scribal technologies and the two new sciences, Baltimore (Maryland), 2017. Raven, D., Krohn, W., Cohen, R. S. (eds.), Edgar Zilsel [(1891–1944).] The social origins of modern science, (Boston Studies in the Philosophy of Science, vol. 200), Dordrecht, 2003. Ray, J., Redford, K. H., Steneck, R., Berger, J. (eds.), Large carnivores and the conservation of biodiversity, Washington, Covelo, London, 2005. Redgrove, H. S., Alchemy: Ancient and modern, London, 1911 and later; most recent editions: Sweden (Ulwencreutz Media), 2008, Washington, DC, 2016, New York, 2018. Reith, R., “Technische Innovationen im Handwerk der frühen Neuzeit? Traditionen, Probleme und Perspektiven der Forschung”, pp. 21–60 in: Kaufhold,

Bibliography

951

K. H., Reininghaus, W. (eds.), Stadt und Handwerk in Mittelalter und früher Neuzeit, Cologne, Weimar, Vienna, 2000. Remmert, V., “Die Ellipse als Epochensignatur? Von Kepler am Weißen Haus vorbei zu Warburg”, pp. 274–282, in: Chihaia, M. G., Eckert, G. (eds.), Kolosale Miniaturen: Festschrift für Gerrit Walther, Münster, 2019. Renn, J., Damerov, P., Rieger, S., Giulini, D., “Hunting the white elephant: When and how did Galileo discover the law of fall?”, pp. 29–149, in: Renn, J. (ed.), Galileo in context, Cambridge, 2001. Rescher, N., Leibniz and cryptography: An account on the occasion of the initial exhibition of the reconstruction of Leibniz’s cipher machine, Pittsburgh, 2012. Rey, A.-L., “The controversy between Leibniz and Papin: From the public debate to the correspondence”, chap. 4, pp. 75–100, in: Dascal, M. (ed.), The Practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010. Rey, A.-L., “Alchemy and chemistry”, chap. 28, pp. 500–508, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Reynolds, T. S., Stronger than a hundred men: A history of the vertical water wheel, Baltimore (Maryland), 1983. Richter, A. D., Snobelen, S. D., “Guest editorial: ‘Too much for mee to speake of’. The many facets of John Wallis’s life and legacy”, Notes and Records of the Royal Society, vol. 72(4), (December 2018), pp. 407–412. Richter, A. D., “John Wallis and the Catholics: Confessional and theological antagonism in Wallis’s mathematics and philosophy”, Notes and Records of the Royal Society, vol. 72(4), (December 2018), pp. 487–503. Robertson, A., Meikle, H. W. (ed.), The life of Sir Robert Moray: Soldier, statesman and man of Science (1608–1673), London, 1922; also as: Forgotten Books’ Classic Reprint Series, London, 2018. Robertson, N. G., “The doctrine of creation and the enlightenment”, pp. 425–439, in: Crouse, R. D., Otten, W., Hannam, W., Treschow, M. (eds.), Divine creation in ancient, medieval, and early modern thought, Leiden, Boston, 2007. Robinet, A., G. W. Leibniz: Iter Italicum (Mars 1689–Mars 1690), Florence, 1988. Roero, C. S., “Gottfried Wilhelm Leibniz, first three papers on the calculus (1684, 1686, 1693)”, chap. 4, pp. 46–58, in: Grattan-Guinness, I. (ed.), Landmark writings in Western mathematics 1640–1940, Amsterdam, Boston, 2005. Rössler, R., “Hypothese, Abweichung und Traum: Keplers Ellipsen”, pp. 65–76, in: Rössler, R., Sparenberg, T., Weber, P. (eds.), Kosmos & Kontingenz: Eine Gegengeschichte, Paderborn, 2016. Roos, A. M., Web of nature: Martin Lister (1639–1712), the first arachnologist, (Series: Medieval and Early Modern Philosophy and Science, vol. 16), Leiden, 2011. Rossetter, T., The theorist: Thomas Burnet and his sacred history of the earth, Thesis submitted for degree of doctor of philosophy, Durham University, 2019. (Durham E-Theses Online: http://etheses.dur.ac.uk/13080).

952

Bibliography

Rossi, P., Cochrane, L. G. (trans.), The dark abyss of time: The history of the earth and the history of nations, Chicago and London, 1984. Roux, S., “Introduction: The emergence of the notion of thought experiments”, pp. 1–142 in: Ierodiakonou, K., Roux, S. (eds.), Thought experiments in methodological and historical contexts, (Series: Medieval and Early Modern Philosophy and Science, vol. 15), Leiden, 2011. Rowen, H. H., John de Witt: Grand pensionary of Holland, 1625–1672, Princeton, 1978. Rudolph, E., “Die Bedeutung des aristolelischen Entelechiebegriffs für die Kraftlehre von Leibniz”, pp. 49–54 in: Heinekamp, A. (ed.), Leibniz’ Dynamica: Symposion der Gottfried-Wilhelm-Leibniz-Gesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, (Studia Leibnitiana, Special issue, no. 13), Stuttgart, 1984. Rudolph, H., “Scientific organizations and learned societies”, chap. 31, pp. 543–562, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Rupert Hall, A., Philosophers at war: The quarrel between Newton and Leibniz, Cambridge, 1980 and 2009. Rupert Hall, A., Isaac Newton: Eighteenth-century perspectives, Oxford, New York, Tokyo, 1999. Sabra, A. I., Theories of light from Descartes to Newton, Cambridge, 1981. Schatzberg, E., Technology: Critical history of a concept, Chicago, 2018. Schliesser, E., Smith, G. E., “Huygens’s 1688 report to the directors of the Dutch East India Company on the measurement of longitude at sea and its implications for the non-uniformity of gravity”, in: Palm, L. (guest ed.), Christiaan Huygens: De Zeventiende Eeuw, vol. 12(1), (1996), pp. 198–214. Schulze, B.-W., Erlebnisse an Grenzen – Grenzerlebnisse mit der Mathematik, Basel 2013. Seppel, M., Tribe, K., Cameralism in practice: State administration and economy in early modern Europe, Woodbridge (Suffolk, UK) and Rochester (NY) 2017. Shank, J. B., Before Voltaire: The French origins of “Newtonian” mechanics, 1680–1715, Chicago, 2018. Shapin, S., Schaffer, S., Leviathan and the air-pump: Hobbes, Boyle and the experimental life, Princeton, Oxford, 1985 and 2011. Shapiro, A. E., “Artists’ colors and Newton’s colors”, Isis: Journal of the History of Science Society, vol. 85(4), (December) 1994, pp. 600–630. Shaw, J., Water power in Scotland 1550–1870, Edinburgh, 1984. Shelley, W. S., Science, alchemy and the great plague of London, New York, 2017. Shimony, I., “Leibniz and the vis viva controversy”, chap. 3, pp. 51–74, in: Dascal, M. (ed.), The practice of reason: Leibniz and his controversies, Amsterdam, Philadelphia, 2010. Shulman, C., “The groundbreaking water supply systems of central and eastern European cities, 1300–1580”, Technology and Culture, vol. 60(3), (July 2019), pp. 726–769.

Bibliography

953

Siebert, H., “The early search for stellar parallax: Galileo, Castelli, and Ramponi”, Journal for the History of Astronomy, vol. 36(3), (2005), pp. 251–271. Simms, J. G., “John Toland (1670–1722), Donegal heretic”, Irish Historical Studies, vol. 16, no. 63, (March 1969), pp. 304–320. Simms, J. G. (Kelly, P. H., ed.), William Molyneux of Dublin 1656–1698, Dublin, 1982. Skempton, A. W., Chrimes, M. M., Cox, R. C., Cross-Rudkin, P. S. M., Rennison, R. W., Ruddock, E. C. (eds.), “The practice of civil engineering 1500–1830”, pp. xvii–xxxiv, in: Biographical dictionary of civil engineers in Great Britain and Ireland. Volume 1: 1500 to 1830, (The Institution of Civil Engineers), London, 2002. Smith, A., “‘Engines moved by fire and water’: The contributions of fellows of the Royal Society to the development of steam power, 1675–1733”, Transactions of the Newcomen Society, vol. 66, (1995), pp. 1–25. Smith, A., “A new way of raising water by fire: Denis Papin’s treatise of 1707 and its reception by contemporaries”, History of Technology, vol. 20, (1998), pp. [139]–181. Smith, D. E., “John Wallis as a cryptographer”, Bulletin of the American Mathematical Society, vol. 24, (1917), pp. 82–96. Smith, J. E. H., Nachtomy, O. (eds.), Machines of nature and corporeal substances in Leibniz, Dordrecht, Heidelberg, London, New York, 2011. Smith, J. E. H., Divine machines: Leibniz and the sciences of life, Princeton and Oxford, 2011. Smith, J. E. H., “Thinking from traces: Nicolas Steno’s palaeontology and the method of science”, chap. 7, pp. 177–200, in: Andrault, R., Lærke, M. (eds.), Steno and the philosophers, (Series: Studies in Intellectual History, vol. 276), Leiden, 2018. Smith, J. E. H., “Medicine”, chap. 27, pp. 485–499, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Smith, P. H., The body of the artisan: Art and experience in the scientific revolution, Chicago, 2004 (and 2012). Smith, P. H., The Business of alchemy: Science and culture in the Holy Roman Empire, Princeton, 2016. Snelders, H. A. M., “Johann Joachim Becher und sein Gold-aus-Sand-Projekt”, pp. 103–114 in: Frühsorge, G., Strasser, G. F. (eds.), Johann Joachim Becher (1635–1682), Wiesbaden, 1993. Sonar, T., and Knobloch, E. (Epilogue), Die Geschichte des Prioritätsstreits zwischen Leibniz and Newton: Geschichte – Kulturen – Menschen, Berlin-Heidelberg, 2016. Sonar, T., and Knobloch, E. (Epilogue), The history of the priority di∫pute between Newton and Leibniz: Mathematics in history and culture, Basel, 2018. Speiser, D., “Le « Horologium Oscillatorium » de Huygens et les « Principia »”, Revue Philosophique de Louvain, vol. 72, (1988), pp. 485–504. Speiser, D., “Johann Bernoulli’s work on the theory of gravitation and on the weight of the atmosphere”, pp. 187–208 in: Klewer, W. (ed.), Die Schwere der Luft in der

954

Bibliography

Diskussion des 17. Jahrhunderts, (Wolfenbütteler Arbeiten zur Barockforschung, vol. 29), Wiesbaden, 1997; also pp. 105–121 in: Williams, K., Caparrini, S. (eds.), Discovering the principles of mechanics 1600–1800: Essays by David Speiser, Basel, Boston, 2008. Stedall, J. A., (ed., trans.), Sources and studies in the history of mathematics and physical sciences: The arithmetic of infinitesimals[:] John Wallis 1656, New York, 2004. Stein, E., Kopp, F.-O., “Konstruktion und Theorie der leibnizschen Rechenmaschinen im Kontext der Vorläufer, Weiterentwicklungen und Nachbauten: Mit einem Überblick zur Geschichte der Zahlensysteme und Rechenhilfsmittel”, Studia Leibnitiana, vol. 42(1), (2010), pp. 1–128. Stewart, M. J., “People, places & things: Zetes”, Greek Mythology: From the Iliad to the fall of the last tyrant, (Original content copyright 1996–2005 Michael Stewart): (http://messagenetcommresearch.com/myths/ppt/Zetes_1.html). Storni, M., “Denis Papin’s digester and its eighteenth-century European circulation”, British Journal for the History of Science, vol. 54(4), (December 2021), pp. 443–463. Strickland, L. (ed.), Leibniz on God and religion: A reader, London, 2016. Sugg, R., Mummies, to cannibals and vampires: The history of corpse medicine from the Renaissance the Victorians, London, New York, 2011. Swetz, F. J., “Leibniz, the Yijing, and the religious conversion of the Chinese”, Mathematics Magazine, vol. 76(4), (October 2003), pp. 276–291. Taiz, Li. and Taiz, Le., Flora unveiled: The discovery and denial of sex in plants, Oxford, 2017. Taylor, E. G. R., The mathematical practitioners of Tudor and Stuart England, Cambridge, 1954 and 1967. Taylor, E. G. R., The mathematical practitioners of Hanoverian England, Cambridge, 1966. Thiele, R., “Das Zerwürfnis Johann Bernoullis mit seinem Bruder Jakob”, Acta Historica Leopoldina, no. 27, (1997), pp. 257–276. Tho, T., “Vis vim vi: Declinations of force in Leibniz’s dynamics”, Studies in History and Philosophy of Science, vol. 46, Cham (Switzerland), 2017. Thorburn Burns, D., “Robert Boyle 1627–1691”, pp. 8–16 in: McCartney, M., Whitaker, A. (eds.), Physicists of Ireland: Passion and precision, Bristol and Philadelphia, 2003. Thorburn Burns, D., Müller, R. K., Salzer, R., Werner, G., Important figures of analytical chemistry from Germany in brief biographies: From the middle ages to the twentieth century, Berlin, 2014. Tilson, R., Nyhus, P. J. (eds.), Tigers of the world: The science, politics and conservation of panthera tigris, Amsterdam, Boston, Heidelberg, London, 1987 (and 2010). Timoshenko, S. P., History of strength of materials: With a brief account of the history of theory of elasticity and theory of structures, New York, Toronto, London, 1953 (reprint 1983).

Bibliography

955

Todhunter, I. (Pearson, K. ed.), A history of the theory of elasticity and of the strength of materials. Volume 1: From Galilei to Saint Venant, Cambridge, 1886 (and 2014). Toepfer, G., Historisches Wörterbuch der Biologie: Geschichte und Theorie der biologischen Grundbegriffe, 3 vols, Stuttgart, Weimar, 2011. Tönsmann, F., “Wasserbauten und Schifffahrt in Hessen um 1700 und die Forschungen von Papin”, pp. 89–104 in: Tönsmann, F., Schneider, H. (eds.), Denis Papin: Erfinder und Naturforscher in Hessen-Kassel, Kassel, 2009. Tomory, L., “London’s water supply before 1800 and the roots of the networked city”, Technology and Culture, vol. 56 (3), (July 2015), pp. 704–737. Troitzsch, U., Ansätze technologischen Denkens bei den Kameralisten des 17. und 18. Jahrhunderts, (Schriften zur Wirtschafts- und Socialgeschichte, vol. 5), Berlin, 1966. Troitzsch, U., “Technischer Wandel in Staat und Gesellschaft zwischen 1600 und 1750”, pp. 9–267 in: Paulinyi, A., Troitzsch, U., Mechanisierung und Maschinisierung 1600– 1840, (Propyläen-Technikgeschichte, vol. 3), Berlin, 1991. Troitzsch, U., “Johann Joachim Becher als Techniker und Erfinder”, pp. 85–102 in: Frühsorge, G., Strasser, G. F. (eds.), Johann Joachim Becher (1635–1682), Wiesbaden, 1993. Truesdell, C., The rational mechanics of flexible or elastic bodies 1638–1788: Introduction to Leonhardi Euleri Opera Omnia Vol. X et XI Seriei Secundae, Turici, MCMLX [Zürich, 1960]. Valleriani, M., Galileo engineer, (Boston Studies in the Philosophy of Science, vol. 269), Dordrecht, Heidelberg, London, New York, 2010. Vermij, R. H., “Bernard Nieuwentijt and the Leibnizian calculus”, Studia Leibnitiana, vol. 21, (1989), pp. 69–86. Vermij, R. H., Secularisering en natuurwetenschap in de zeventiende en achttiende eeuw: Bernard Nieuwentijt (Secularization and science in the seventeenth and eighteenth centuries: Bernard Nieuwentijt), Nieuwe Nederlandse Bijdragen tot de Geschiedenis der Geneeskunde en der Natuurwetenschappen (New Dutch contributions to the history of medicine and of the sciences), no. 38, Amsterdam-Atlanta (GA), 1991. Vibeke Vad, A., “Polidore and Théophile: The rationalist and the faithful observer”, pp. 39–47, in: Ascani, K., Kermit, H., Skytte, G., (eds.), Niccolo Stenone (1638–1686) anatomista, geologo, vescovo: Atti del seminario organizzato da Universitetsbiblioteket i Tromsø e l’Accademia di Danimarca lunedi 23 ottobre 2000 [Proceedings of a Conference on October 23, 2000], (Analecta Romana Instituti Danici, Suppl. XXXI), Rome, 2002. Wahl, C., “Diplomat in der Gelehrtenrepublik  – Leibniz’ politische Fähigkeiten im Dienste der Mathematik”, pp. [273]–291 in: Li, W. (ed.), Komma und Kathedrale: Tradition, Bedeutung und Herausforderung der Leibniz-Edition, Berlin, 2012. Wahl, C., “« Im tunckeln ist ein blinder so guth als ein sehender ». Zu Leibniz’ Beschäftigung mit Leuchtstoffen”, pp. [225]–259 in: Kempe, M. (ed.), Der Philosoph

956

Bibliography

im U-Boot: Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung 1 (vol. 1), 2013. Wahl, C., “« ich schätze Freunde mehr als mathematische Entdeckungen »  – Zum Prioritätsstreit zwischen Leibniz und Newton”, pp. [111]–143 in: Kempe, M. (ed.), 1716 – Leibniz’ Letztes Lebensjahr: Unbekanntes zu einem bekannten Universalgelehrten, Hanover: Gottfried Wilhelm Leibniz Bibliothek, Forschung 2 (vol. 2), 2016. Wahl, C., “Zum Leibniz-Korrespondenten Johann Hiskias Cardilucius – alias Johann Fortitudo Hartprecht”, Studia Leibnitiana, vol. 49(1), (June 2017), pp. 111–116. Wakefield, A., The disordered police state: German cameralism as science and practice, Chicago, 2009. Wakefield, A., “Leibniz in the mines”, Osiris: Annual Journal of the History of Science Society, vol. 25, (2010), pp. 171–88. Wakefield, A., “The origin and history of the earth”, chap. 25, pp. 453–465, in: Antognazza, M. R. (ed.), The Oxford Handbook of Leibniz, Oxford, 2018. Walsh, A.-M., The daughters of the first earl of Cork: Writing family, faith, politics and place, Dublin, 2020. Walton, S. A., Fifty years of medieval technology and social change, New York, London, 2019. Waschkies, H.-J., “Leibniz’ geologische Forschungen im Harz”, pp. 187–210, in: Breger, H., Niewöhner, F. (eds.), Leibniz und Niedersachsen: Tagung anläßlich des 350. Geburtstages von G. W. Leibniz, (Studia Leibnitiana, Special issue, no. 28), Stuttgart, 1999. Weiss, H. (ed.), Ports of globalisation, places of creolisation: Nordic possessions in the Atlantic world during the era of the slave trade, Leiden, 2016. Westfall, R. S., Force in Newton’s physics: The science of dynamics in the seventeenth century, London, New York, 1971. Westfall, R. S., Never at rest: A biography of Isaac Newton, Cambridge, 1983. Westfall, R. S., “The problem of force: Huygens, Newton, Leibniz”, pp. 71–84 in: Heinekamp, A. (ed.), Leibniz’ Dynamica. Symposion der Gottfried-Wilhelm-LeibnizGesellschaft in der Evangelischen Akademie Loccum, 2. bis 4. Juli 1982, (Studia Leibnitiana, Special issue, no. 13), Stuttgart, 1984. White Jr., L., Medieval technology and social change, London, Oxford, 1962. Wickel, G., “Landvermessung als praktische Geometrie in England um 1600”, pp. 263–280 in: Heinecke, B., Kästner, I. (eds.), Wettstreit der Künste: Der Aufstieg des praktischen Wissens zwischen Reformation und Aufklärung, (Europäische Wissenschaftsbeziehungen, vol. 17), Aachen, 2018. Wicklein, G., “Die explicatio. Ein mittelalterliches Denken von Evolution”, pp. 13–24 in: Asmuth, C. und Poser, H. (eds.), Evolution: Modell  – Methode  – Paradigma, Würzburg, 2007.

Bibliography

957

Wildgen, W., Dynamische Sprach- und Weltauffassungen (in ihrer Entwicklung von der Antike bis zur Gegenwart), (Series: Book series of the Center for the Philosophical Foundations of the Sciences; Schriftenreihe des Zentrums Philosophische Grundlagen der Wissenschaften, vol. 3), Bremen, 1985 and 2005 (in electronic / digital form). Wildgen, W., The evolution of human language: Scenarios, principles, and cultural dynamics, (Series: Advances in Consciousness Research), Amsterdam, 2004. Williams, A., The knight and the blast furnace: A history of the metallurgy of armour in the middle ages & in the early modern period, Leiden, Boston, 2003. Williams, A., The sword and the crucible: A history of the metallurgy of European swords up to the 16th century, Leiden, Boston, 2012. Williams, M. R., A history of computing technology, Englewood Cliffs, N.J., 1985 (and Los Alamitos, CA, 1997). Wilson, C. A., “From Kepler’s laws, so-called, to universal gravitation: Empirical factors”, Archive for History of Exact Sciences, vol. 6, (1969–1970), pp. 89–170. Wilson, C., “Newton and celestial mechanics”, chap. 6, pp. 202–226, in: Cohen, I. B[ernard], Smith, G. E. (eds.), The Cambridge Companion to Newton, Cambridge, 2002. Wolfschmidt, G., “Astronomie in Nürnberg  – Zentrum des Instrumentenbaus”, chap. 1, pp. 19–144, in: Wolfschmidt, G. (ed.), Astronomie in Nürnberg: Anläßlich des 500. Todestages von Bernhard Walther (1430–1504) und des 300. Todestages von Georg Christoph Eimmart (1638–1705), Hamburg: tredition science, (Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften, vol. 3), 2010. Wragge-Morley, A., Aesthetic science: Representing nature in the Royal Society of London, 1650–1720, Chicago, 2020. Wright, M. T., “On the lift pump”, History of Technology, vol. 18, (1996), pp. 13–37. Yoder, J. G., Unrolling time: Christiaan Huygens and the mathematization of nature, Cambridge, 1988, 1990 and 2004. Yoder, J. G., “Christiaan Huygens’ book on the pendulum clock (1673)”, chap. 3, pp. 33–45, in: Grattan-Guinness, I. (ed.), Landmark writings in western mathematics 1640–1940, Amsterdam, Boston, 2005. Yoo, G., “Wars and wonders: The inter-island information networks of Georg Everhard Rumphius”, British Journal for the History of Science, (Special issue: Science and Islands in Indo-Pacific Worlds), vol. 51(4), (December 2018), pp. 559–584. Zandvliet, K., De 500 rijksten van de republiek: Rijkdom, geloof, macht en cultuur [The 500 wealthiest persons in the republic: Wealth, belief, power and culture], Zutphen, 2018.

Index of Names Adolphi, Christoff 214f., 339f. Agnesi, Maria Gaetana 17, 284 Agricola, Georg 139, 227f., 256, 388f., 420f., 857f. Albani, Gian Francesco 115, 783 Alberti, Antonio (alias Tourreil, Amable de) 52, 54, 452f., 456 Alexander VIII, Pope 105, 368 Alhazen (Ḥasan Ibn al-Haytham) 284 Angeli, Stefano degli 131, 473 Ango, Pierre 120–125, 300, 376, 469, 556–558 Apollonius of Perga 449 Archimedes of Syracuse 40, 42, 180, 229, 449, 491, 637, 642 Aristotle xii, 224, 229, 837 Arnauld, Antoine 53, 130f., 362, 379f., 453, 483 Ashe, St George 281 Augustus the Younger (August II), Duke of Brunswick-Lüneburg-Wolfenbüttel (alias: Gustavus Selenus) 174, 484 Auzout, Adrien 8, 102, 104, 131, 300, 357f., 366f., 473 Babbage, Charles 169 Bacon, Francis (Verulamius) 88, 288, 554 Bagnasco, Marchese di (alias Carretto, Carlo Girolamo del) 175, 486 Balduin, Christian Adolph 209f., 329f., 332f. Barba, Álvaro Alonzo 142, 394 Bartholin, Erasmus 97, 298, 377 Bartholin, Thomas 305 Basnage de Beauval, Henri 34, 441, 624f., 868 Beaune, Florimond de 434f. Becher, Johann Joachim (pseudonym: ‘Solinus Salzthal Regiomontanus’) 7, 139–141, 146, 188, 213, 220, 222, 224f., 278, 387–392, 398f., 411, 722, 834f., 839f., 879f. Bentley, Richard 618 Bernard, Edward 230, 430, 500, 842f. Bernoulli, Hieronymus 250, 607–609

Bernoulli, Jacob 1, 11, 14, 22f., 26, 33, 37, 42, 44, 47, 58, 60, 96, 171, 264, 363, 374f., 432–435, 439, 442, 444, 458, 511–513, 526, 582, 615, 622, 629f., 632, 641f., 745f., 752, 861, 864–867, 869 Bernoulli, Johann (I) 1, 9, 11f., 14, 22f., 26–28, 31–38, 41–49, 54, 63–65, 95, 101, 108, 115f., 204f., 207, 234, 250, 264, 427, 433f., 440, 442f., 456, 507, 509, 511–513, 516, 523–526, 535, 537f., 540, 564, 606, 615, 617, 619, 621–624, 626–633, 635, 639–641, 643–645, 727f., 744–749, 751–753, 755, 779, 784, 786, 794, 818, 821, 845, 865–870 Beyrie, Wilhelm de 108f., 540–542, 553 Bianchini, Francesco 13, 104f., 115f., 263, 356, 366, 368, 425, 744, 783–786 Bidloo, Govart 559f. Bignon, Jean-Paul 114, 230, 783, 841 Bilger, Johann Friedrich 411 Billettes, Gilles Filleau des 455 Blankaart, Steven 239 Bleiswijk (or Bleiswyck), Hendrik van 132, 683–685, 726 Blencow, William 176, 715 Block (or Bloeck), Ameldonck 128, 196f., 563 Block, Magnus Gabriel 2, 14, 151, 159–161, 220f., 224f., 230, 246, 252, 264, 266, 723, 736–738, 740f., 743f., 800, 804, 806, 808f., 830f., 837, 839–841, 850, 889, 895f., 898, 902 Blondel, François 112, 370f. Boccabadati, Giovanni Baptista 164f., 403–405, 474 Bodenhausen, Rudolf Christian von xvi, 4, 10–12, 22f., 33, 51–55, 96, 105, 125, 165, 169, 171, 213f.,217f., 224f., 241, 246, 248–252, 263, 356, 363–365, 367f., 374f., 405, 412f., 415–417, 423, 425, 427, 430, 433f., 443, 451–453, 455f., 470, 483, 507, 509, 511, 525, 581–583, 606, 610–613, 617, 619–621, 643, 735–737, 740, 839f., 862, 865, 867, 875, 883, 888, 895

Index of Names Bohun, Ralf 290 Bonfa, Jean 178, 324 Borelli, Giovanni Alfonso 66, 648 Bornemann, Rudolf 143, 565 Böttger, Johann Friedrich 160 Bouilleau (Boulliau), Ismael 103f. Bouquet, Jacques M. B. 244f., 253f., 601–604, 850, 854f. Bouvet, Joachim 50, 236, 732, 756 Boyle, Charles (Third Vicount of Dungarven) 291, 780 Boyle, Richard (First Earl of Cork) 288, 291 Boyle, Robert xvf., 3, 88–92, 101, 139, 178– 180, 201, 209–211, 213, 217, 219f., 222f., 235, 243, 251, 288–294, 328f., 331–336, 348, 383, 387–411, 488–490, 499, 585, 610f., 730, 780, 836f., 888 Boym, Michael 236, 732 Bradley, Humphrey 179 Bradley, James 119 Brahe, Tycho (Brahe, Tyge Ottesen) 114, 783 Brand, Heinrich (or Henning) 159, 197, 208–211, 213, 221f., 271, 328, 330–333, 410f., 707f., 833f. Brandshagen, Jobst Dietrich 138, 143, 152, 177, 189, 211–213, 312, 323f., 336, 377, 386, 400f., 410, 412 Breatridge, Roger 209, 329 Brosseau, Christophe 54, 114, 249, 274, 456, 605, 783 Burckhard, Johann Heinrich 239f., 847f., 893 Burnet, Gilbert 583 Burnet, Thomas 228f., 583, 724–726, 897f. Burnett of Kemney, Thomas 30f., 35, 124, 171, 191, 228f., 498, 522, 555, 583, 626, 724f., 886, 897 Bussche, Albrecht Philipp von dem 145, 570 Büssing, Caspar 228f., 235, 645, 724–726, 729, 897f. Butler, James (12th earl and 1st duke of Ormonde) 331f. Camerarius, Rudolph Jacob 240, 474, 847, 893 Cardano, Gerolamo 279 Cassina, Giovanni Paolo Stabe de 190, 410

959 Cassini, Giovanni Domenico (Gian Domenico, or Jean-Dominique) 102, 114–116, 118f., 221, 265, 300, 410, 783f., 786, 792, 794–796, 831, 898 Castelli, Benedetto 119, 164f., 403–405, 477, 479, 882 Catelan, François Abbé de 19, 21, 34, 53, 56, 358f., 363, 431f., 453, 511, 623, 864, 868 Cellarius, Salomon 860 Charles I of England (Stuart monarch) 193 Charles II of England (Stuart monarch) 143, 210, 253, 330, 397, 853 Charles XI, King of Sweden 151, 172, 322, 800 Châtelet, Émilie du 17 Chauvin, Etienne 34f., 624f., 869 Chevreuse, Charles-Honoré, Duc de 328 Christian V, King (until 1699) of Denmark, Norway 152, 162, 183 Clausius, Rudolf Julius Emanuel 149 Clemens XI, Pope 115 Cleyer (Clayer), Andreas 236f., 248, 351f., 732f. Clüver, Detlev (Detlef) 7, 15, 18, 31, 41–43, 48, 89, 111f., 169, 228, 278, 284f., 289, 313f., 371, 420f., 523, 548, 550, 552, 559, 639, 642f., 724, 754, 863, 870, 892 Colbert, Jean Baptiste 6, 197, 277, 324 Collins, John 201, 500 Comiers, Claude 143, 398f. Conerding, Dietrich 247, 350 Copernicus, Nicolaus (Kopernik, Mikołaj) xiv, 105, 368 Cörber, Caspar 255, 857 Corradi, Bernardino 190, 410 Cosimo III de’ Medici, Grand Duke of Tuscany 10, 171, 582 Cotterell, Charles 170, 579 Crafft, Dorothea 196, 614, 719 Crafft, Johann Daniel 1, 4, 6–9, 11f., 128, 130, 134–136, 145f., 153, 159, 171, 183–192, 194–197, 208–211, 213–219, 252, 257, 263, 271f., 275f., 278, 304, 308f., 312, 315–318, 320–323, 328–332, 338f., 341f., 352–354, 356f., 398, 406–409, 411, 413f., 418, 427f., 497, 508, 563, 567–573, 576, 582, 591–596, 613f., 617, 707, 716–720, 880, 885, 888, 893

960 Craanen, Theodor 473 Cressett, James 117, 790f. Crusen, Christoph Bernhard 119, 795 Dampier, William 98, 782 Dangicourt, Pierre 44, 49, 204, 746, 756, 818 Danneberg (merchant in Hamburg) 192, 591 Darwin, Charles Robert 233 Davys, John 176, 715 Defoe, Daniel 12, 862 Delfini, Marco 115, 783 Della Rena, Cosimo 12, 509 Des Bosses, Barthélemy 50 Descartes, René xiii, 44, 54, 56–58, 64, 87f., 91, 98, 112, 121, 193, 205, 227f., 238, 283, 286–288, 298, 361–363, 370f., 383f., 420f., 435, 449, 455, 458, 510, 534, 537, 556, 644, 646, 820, 892 Dierquens, Nicolaas 34, 622, 867 Dierquens, Salomon 34, 622 Digby, Sir Kenelm 489 Diophantus of Alexandria 27, 279, 514 Ditfurdt, Otto Arthur von 145, 570 Dolaeus, Johann 10 Douceur, Noel 5,142, 151f., 217, 225, 273f., 312, 397, 399–401, 415, 809 Drebbel, Cornelis 178f., 181f., 190, 410, 488–491, 493, 584–586 Du Hamel, Jean-Baptiste 98, 143, 217, 227, 381f., 397, 414, 420, 892 Du Mont, Andreas 153–156, 698–700 Ebell, Heinrich Christoph 247, 350 Eckhard (Eckard), Arnold 271, 279 Eckhart, Johann Georg 230, 232, 247, 843f., 851 Eimmart, Georg Christoph 97, 120, 297f., 800 Eisenschmidt, Johann Caspar 107f., 466 Elers, Martin 6, 152, 177, 183, 185–187, 189, 214, 216, 257, 263, 275, 315, 318–323, 338f., 354f., 394, 401, 413, 888 Elsholz, Johann Sigismund 130, 304f. Essen, Theodorus van 250,607, 609 Ettmüller, Michael Ernst 465 Euclid of Alexandria 238, 449, 845 Euler, Leonhard 96

Index of Names Eyben, Huldreich von 202, 597f. Fabri, Honoré 87, 287 Fagon, Gui-Crescent 265, 739f., 896 Fahrner, Christoph 215, 252, 340f., 614 Fatio de Duillier, Jean Christophe 45, 748 Fatio de Duillier, Nicolas 24f., 28, 34f., 38, 41, 47, 103, 108, 123, 437, 445f., 518, 540f.,552, 624, 626, 634, 639, 746f., 752, 868, 876 Ferdinand (Ferdinando de’ Medici), Grand Prince of Tuscany 23, 169, 176, 213, 218, 412, 417, 433, 483, 713, 865 Ferdinando Carlo, or Carlo IV, Duke of Mantua 503 Ferguson, Johann Jakob 6, 16–18, 48, 142f., 169, 187, 200, 226, 247, 272, 275, 282–285, 312f., 327, 344, 350, 395f., 407, 754, 891, 894 Fermat, Pierre de xiii, 17, 31, 40, 121, 125, 284, 300f., 470, 523, 637f. Flach, Daniel 144, 566 Flamel, Nicolas 220, 721f. Flamsteed, John 50, 102, 116–120, 300, 756, 786, 788, 793, 796f., 799 Fohy (Fuxi), Chinese emperor 50, 756 Fontenelle, Bernard le Bovier de 49, 116, 118f., 123, 755, 786, 793f. Foucher, Simon 54f., 57, 214, 412, 451, 456f. Franck von Franckenau, Georg 91, 235, 245, 252, 262, 265f., 293, 604f., 731, 733f., 739–741, 896 Franck von Franckenau, Georg Friedrich 245, 734 Frederick William I, Elector of Brandenburg and Duke of Prussia (until 1688) 177, 183f., 263, 315, 317, 322, 365 Friedrich III, Elector of Brandenburg and Duke of Prussia (from 1688), and Friedrich I, King of Prussia (from 1701) 205f., 820, 824 Friedrich August I, Elector of Saxony (from 1694), and August II, King of Poland and Grand Duke of Lithuania (from 1697) 161, 808 Friedrich IV, King (from 1699) of Denmark, Norway 115, 784 Fuchs, Paul von 206, 825

Index of Names Gakenholz, Alexander Christian 202, 232, 237, 239–241, 246f., 598, 844–852, 893f., 896f. Galen (Galenus), Claudius 252, 348, 741 Galilei, Galileo xi, xiiif., 3, 22f., 33, 36, 66, 88, 95f., 105, 112, 119, 127, 163–167, 288, 296f., 306, 368, 370f., 375, 402f., 433f., 472, 477f., 481, 620, 627, 648, 865, 867, 869, 882–885 Gallet, Jean Charles 102, 300 Gallois, Jean 6f., 55, 197, 225f., 276–278, 324, 342f., 457, 890–892 Gehlen, Cord Plato von (Cord Plato von Chalon or Schloen, called von Gehlen) 161, 809f. Gengenbach, Johann Heinrich 120, 161, 800, 808 Georg Wilhelm of Celle, Duke of BrunswickLüneburg 152, 185, 318, 401 Gian Gastone de’ Medici, Tuscan prince 213, 412 Giordani (Giordano da Bitonto), Vitale 8, 104, 357f., 366 Giovanni Gastone, Tuscan prince 33, 621 Glauber, Johann Rudolf 215, 222f., 340f., 836f., 890 Goddard, Jonathan 253, 853 Goldmann, Nicolai 156, 701 Graaf, Reinier de 243, 347 Graevius, Johann Georg 130, 305f. Grandi, Guido 17, 284 Gregory XIII, Pope 2f., 7, 114–116, 762, 783–791 Gregory, David 7, 29, 36, 38, 40, 46, 279, 520, 629f., 632–634, 639, 749, 794 Gregory, James 17, 284, 444f. Grew, Nehemiah 90, 129, 198, 209f., 214, 226, 292, 303, 325, 329, 331, 338, 344, 891 Grillet, René 170, 578 Grimaldi, Claudio Filippo 8, 48, 248, 357, 423, 754 Grote, Otto 250f., 610 Grotius, Hugo 132, 683f. Gudenus, Johann Christoph 276, 354 Guericke, Otto von 1, 89–91, 98, 210, 290–294, 331, 382f. Guglielmini, Domenico 9, 44, 163–167, 263, 266, 402f., 405f., 425, 427, 476–482, 645, 742, 859, 882–884, 895f.

961 Haak, Theodor 169, 198, 211, 214, 314, 325, 333, 338 Haberstroh, Johann August 131, 559 Haes, Johann Sebastian 10, 57, 59f., 108, 170, 173–175, 178–181, 201f., 252, 427, 430, 451, 460–462, 483–487, 490–494, 496, 540, 578f., 584, 597, 613, 647, 887 Hagen, Johann 135, 309 Halley, Edmond 98, 102, 107, 116, 118, 122, 200f., 229, 430, 465, 468, 499, 725, 782, 786, 794f. Hanck(e)witz, Ambrose Godfrey 213, 332, 412 Hanoverian Dynasty members (House of Brunswick-Lüneburg): Duke Johann Friedrich 4f., 89, 129, 136, 151f., 210, 227, 271–273, 290, 302, 331, 384, 399f., 411, 565 Duchess Bénédicte Henriette Philippine 775 Duke and Elector Ernst August 4–6, 8, 11, 13, 134f., 137, 143, 151–153, 156, 173, 175, 187, 200, 216, 257, 261, 271, 273f., 307, 309, 321, 327, 342, 353, 357, 385, 394, 399f., 484, 486, 505, 508, 565, 617, 698, 702 Duchess and Electress Sophie 12, 229, 253, 273, 725, 853, 897 Elector Georg Ludwig (king George I) 13, 617 Hansen [von Ehrenkron], Friedrich Adolph 197, 210, 312, 330 Hamberger, Georg Albrecht 114 Harprecht, Johann (pseudonyms: ‘Sendivogius filius’ and ‘Johann Hiskia Cardilucius’) 224, 839f. Hartmann, Georg 199 Hartmann, Johann Jacob 556 Hartsinck (or Hartzingk), Peter 137, 384, 878 Hartsoeker, Nicolaas 126, 558 Harvey, William 234, 727 Heilmann, Johann Joachim 839 Helmont, Jan Baptist van 217 Heppe, Johann Philipp 181, 496 Hermann, Jacob 31 Hertel, Lorenz 160, 575, 804 Heße, Hans Caspar 387

962 Hevelius, Johannes 102, 118, 221, 300, 793, 831, 898 Heyn, Friedrich 9, 139–142, 146, 188, 190, 213, 228, 248, 358, 387–394, 409, 411, 421f., 879, 891 Hippocrates of Kos 256, 852 Hobbes, Thomas 92, 103 Hoffmann, Friedrich xiii, 13, 100f., 204–207, 221, 246, 262, 266f., 744, 778f., 818–826, 831, 850f., 858–860, 896–898 Holeysen, Christian 9, 187f., 218, 358, 406f., 418, 888 Homberg, Wilhelm 208, 214, 412 Hooke, Robert 89, 95, 119, 124, 169, 201, 211, 214, 290, 314, 333, 338, 500, 556–558, 796f. Horace (Quintus Horatius Flaccus) 523 Horne (Hoorn), Johannes van 243, 347, 380 Hörnigk, Johann Moritz von 184, 315f. Hörnigk. Philipp Wilhelm von 184, 315 L’Hospital, Guillaume François, Marquis de 9, 11, 14, 23–28, 31, 33f., 36f., 43–45, 48f., 53f., 60, 65, 126, 170f., 183, 193, 427, 434f., 437, 455f., 498, 507, 509, 512f., 416f., 523, 526, 538f., 558, 564, 581f., 589, 618f., 622–625, 627–629, 631, 644, 744f., 747–749, 753–756, 862, 865f., 868f., 885 L’Hospital, Marie-Charlotte, Marquise de (née Marie-Charlotte de Romilley de la Chesnelaye) 53, 455 Hove, Michael (or Michiel) ten 185, 318 Hudde, Johannes (Jan) 2, 33, 129f., 132, 185, 302, 304f., 318, 622, 683 Hugo, Ludolf 744 Huygens, Constantijn (Junior) 10, 302, 428 Huygens, Christiaan xi, xiii, 1, 4, 6f., 9–12, 15, 17, 19–29, 31, 33, 37, 39f., 46, 50, 52, 57, 66, 90–92, 98, 102, 105–113, 120–126, 128f., 131f., 135f., 147, 166, 169–171, 178–180, 182f., 201, 221, 263–265, 272, 276f., 279, 284, 292, 299f., 302, 309f., 356, 359–363, 369–372, 375–378, 381–383, 421, 425, 427–429, 432–452, 457f., 460–469, 471, 473, 476, 480, 483, 490–492, 500, 507, 510–512, 516–518, 520, 522f., 540–543, 545–549, 552–559, 563–565, 574f., 582f., 587–589, 614f., 617,

Index of Names 622, 630, 634, 637f., 646, 648, 683, 686, 749, 831, 864–867, 870, 875–878, 880, 882f., 885, 894f., 898 Jābir ibn Ḥayyān (also Geber) 217, 416 Jablonski, Daniel Ernst 206, 825 Jablonski, Johann Theodor 191, 498 Jager, Herbert de 236f., 732f. Jansen, Herman 342 Jenisch, Johann Jacob 143, 565 Johann Adolf, Duke of Holstein-SonderburgPlön 193, 592 Johann Georg II, Elector of Saxony (until September 1680) 186, 321 Jungius, Joachim 66, 648 Junius, Ulrich 115f., 117f., 785, 792 Justel, Henri 10, 89, 191, 197, 200f., 210, 243, 261, 289, 330, 346, 430, 497, 499, 505f. Karl (Landgraf von Hessen-Kassel), or Charles (Landgrave of Hesse-Cassel) 58, 147, 151, 157f., 170, 174, 178, 181, 202, 207, 484, 487, 492, 578f., 597, 687, 704f., 802, 829 Keller, Daniel 220, 721f. Kepler, Johannes xi, xiii, 81, 91, 103–106, 114, 117–119, 207, 366, 368, 370, 383f., 463f., 763, 783, 792–796, 875 Kerckring, Theodor 240, 848, 894 Kiefler (or Küffler, Kuffeler née Drebbel), Catharina 179, 490, 585 Kiefler (or Küffler, Kuffeler), Johannes Sibertus 179, 490, 585 Kirch, Gottfried 115f., 118, 221, 782, 784–786, 792–794, 831, 898 Kircher, Athanasius 174, 484 Kirchmaier (Kirchmayer), Georg Caspar (Kaspar) 329 Kirckby (or Kirkby), English mining engineer 201, 499 Kleinert, Friedrich 220, 721, 889 Knorr(e), Martin 32, 42, 124, 524, 556–558, 641 Kochański, Adam Adamandy 16f., 27, 87, 276, 282f., 287, 516 Kölbing, Georg Heinrich 168, 170, 172, 581, 816, 885f.

Index of Names Kornmann von Hornsbach, Johann Hartmann 328 Kunckel (von Löwenstern, from 1693), Johann 160, 209, 215, 328f., 331f., 806 Lacy, Nathan 190, 201, 410, 499 Lagrange, Joseph-Louis xiii La Chaise, François d’Aix de 16f., 87, 151, 276, 282–283, 287, 882 La Hire, Philippe de 34, 43, 53, 118f., 454, 623f., 644, 793–795, 868 Lange, Johann 394 Laplace, Pierre-Simon 100 La Roque, Jean-Paul de 4, 19, 129, 182f., 197, 210, 212, 231, 272, 302, 330, 337, 347, 359, 587 Larroque, Daniel 53, 455, 843 La Scala, Dominico 252, 740f. Lauterbach, Johann Balthasar 156, 574 Ledel, Samuel 249, 423 Leeuwenhoek, Antoni van 2, 128–132, 234, 240f., 301–306, 379f., 473f., 559f., 682–685, 726–728, 848f., 894 Leopold I, Holy Roman Emperor 162, 811 Leupold, Jacob 885 Levanto, Francesco Maria 159–161, 804–806, 808 Lhuyd, Edward 231f., 841f. Line or Linus, Francis or Francisco (Linus of Liège) 780 Linnaeus, Carl (Linné, Carl von) 232 Linsen, Hans 134f., 138f., 143, 156, 308f., 356, 386f., 566, 700 Lister, Martin 234, 249, 606, 727 Listingk, Nicolaas 196, 719 Lobkowitz (Count, alchemist) 218, 418, 888 Löffler, Friedrich Simon 474 Lohmeier, Philipp 87, 99, 287, 299, 325 Loubère, Simon de la 275 Louis XIV, King of France 16, 114, 143, 150, 265, 276, 397, 783 Lucae, Friedrich 59, 180, 460, 491 Lull, Ramon 220, 721f. Magliabechi, Antonio 10, 12, 97, 131, 166, 235, 286, 375, 430, 478f., 481, 509, 560, 729f., 883 Makreel, Johannes 33,621f.

963 Malebranche, Nicolas 53, 453–455 Malpighi, Marcello 131, 473f., 477 Marchetti, Alessandro 33, 620 Marchetti, Domenico 243, 346 Marci von Kronland, Johann Marcus 66, 648 Mariotte, Edme 3–5, 66, 88, 92f., 95f., 99, 112, 120, 123, 143, 197f., 211f., 243, 271–275, 295–297, 299f., 306, 312, 324f., 336f., 348, 370, 372, 374, 397, 399, 552f., 648 Maximilian Wilhelm, Duke of BrunswickLüneburg 244, 601 Maximilian II Emanuel, Elector of Bavaria 576 Meibom, Heinrich 216, 242, 254, 264, 342, 345f., 737, 856, 896 Meier, Barthold 227, 419, 892 Meier, Gerhard 447f. Mencke, Johann Burkhard 633 Mencke, Otto 16, 23, 27, 30, 32, 34–39, 41f., 46f., 55, 58–60, 97, 105, 165, 176, 204, 226, 257, 342, 353, 367, 375, 405, 434, 439, 458, 460–462, 477, 479, 515f., 521f., 524f., 624f., 627, 629, 632–634, 640f., 714, 749, 752, 820, 869f. Mendlein, Pandolfio 736 Mentzel, Christian 236f., 733 Mercator, Gerhard 199 Meurs von Blauenstein, Friedrich 146, 152, 398, 401 Meyer, Albert 7, 278 Meyer (Meijer), Cornelis 164, 404 Michelangelo (Buonarroti, Michelangelo) 132, 683f. Moebius, Gottfried 252, 613 Mohr, Jørgen or Georg 2, 122, 146, 188, 200, 227, 327, 377, 398, 419, 891 Moller, Peter 220–222, 830–834, 890 Moltfelt, Hans Andreas 387 Molyneux, William 125, 470f. Monconys, Balthasar 178, 488, 493 Montanari, Geminiano 477 Moray, Robert 580 Morland, Sir Samuel 143, 170, 397, 578f. Morton, Richard 265, 738f. Mullen, Allen 235, 729–731 Musschenbroek, Samuel van 304, 507

964 Napier, John 170, 578 Naudé, Philippe 44, 49, 204, 746, 756, 818 Neumann, Caspar 498 Newton, Isaac xii–xv, 2f., 9, 11, 21, 24, 28–30, 33–36, 38–41, 43, 45, 47, 50, 57f., 87, 102–109, 111–113, 116, 118f., 121–124, 150, 201, 219f., 229, 231, 240, 272, 279, 295f., 300, 365f., 369–371, 375f., 427, 431, 437, 445, 451, 462–469, 500, 507f., 513, 517–522, 540–543, 548–556, 622, 624–627, 629f., 632, 634–639, 698, 725, 747–749, 752f., 786, 790, 793–796, 802, 829, 868, 874–877 Nieuwentijt, Bernard 31–33, 41–43, 523f., 621, 639–643 Noris, Enrico 116, 786 Ode(h)lius, Eric 142, 394 Oldenburg, Heinrich (or Henry) 2–4, 15, 19, 29, 45, 47, 88f., 91, 129, 168f., 210, 257, 272, 279, 288–290, 292f., 301, 303, 314, 329f., 353, 359, 365, 519, 522, 580, 639, 748, 752 Olitsch, Benjamin 6, 226, 275, 344, 891 Olivier (or Ollivier), French clockmaker 168, 312, 581, 885 Oppel, Johann David von 257, 353 Orschall, Johann Christian 219, 418, 888 Ozanam, Jacques 619 Papin, Denis 1, 5, 9, 11, 14, 50, 57–87, 108f., 146–151, 157, 159, 162f., 166f., 178–182, 200f., 207f., 243f., 253, 275, 328, 348f., 363, 427, 451, 457–462, 477–483, 487, 493, 495f., 507, 526–536, 538f., 542, 584, 586f., 597, 617, 646–659, 661–676, 678– 682, 686–691, 693–695, 697f., 703–713, 744, 757–764, 766–775, 800–803, 828f., 853, 870–874, 877, 880f., 883–887 Paracelsus (Theophrastus Bombastus von Hohenheim) 838 Pardies, Ignace Gaston 121, 123f., 330, 376, 469, 556–558 Parent, Antoine 49, 756 Pascal, Blaise 15, 26, 100, 165, 169f., 512, 578, 582, 866 Peikenkamp, Hermann 179, 181, 488f., 496

Index of Names Pellisson-Fontanier, Paul 52, 57, 260, 451, 453, 502 Perrault, Claude 93, 295 Peter I, Tsar of Russia 13, 618 Petit, Pierre 170, 579 Petty, William 191, 235, 497f., 729f. Pfautz, Christoph 7, 9, 16, 22, 91f., 102, 120f., 126, 187, 228, 257, 271, 278, 280f., 286, 292, 295, 299–301, 305, 353, 365, 375, 379, 407, 427, 432, 724, 864, 870, 897 Pfeffer, Reinhart 135, 309, 387 Philipp, Christian 130, 304 Piso, Willem 249, 605–607 Plappert, Jürich 387 Platen, Franz Ernst von 162, 173–175, 484–486, 812 Plato 224, 837 Pliny The Younger (Gaius Plinius Caecilius Secundus) 425 Pöhler, Zacharias 145, 387, 567, 569–571 Polhammar (Polhem), Christopher 151, 800f. Poquelin, Jean-Baptiste (alias Molière) 265, 739 Pratisius, Christof 6, 142, 212, 214, 217f., 224, 249, 257, 261, 263, 275, 339, 352, 394, 413, 415f., 424f., 505, 839f. Pufendorf, Samuel von 11, 507 Pythagoras of Samos 72, 664, 788 Quarteroni, Domenico 8, 104, 357f., 366 Rabener, Johann Gebhard 254, 856 Raffaello Sanzio da Urbino (Raphael of Urbino) 132, 683f. Raison, Michel 274 Ramazzini, Bernardino 9, 12, 33, 91, 99f., 163–165, 190, 206, 249, 252, 255f., 258–263, 294, 402–405, 410, 425, 427, 474–476, 500–506, 509, 604f., 621, 733, 741, 775–778, 823f., 850, 857–859, 867, 882 Ramponi, Lodovico 119 Ramus, Petrus 199, 238, 845 Ranelagh (Lady / Viscountess = Jones, née Boyle, Katherine) 288f. Ray, John 235, 730 Reimers, Curd 213, 412

Index of Names Reimers, Balthasar Ernst 144–146, 566–571 Reisel, Salomon 178, 487f., 886 Remond, Nicolas 450 Renaldini, Carlo 745 Renau d’Eliçagaray, Bernard 182f., 588–590 Reyher, Samuel 91, 99, 102, 116, 293, 299, 325, 785f. Richer, Jean 197, 324 Richthausen, Johann Conrad von (alias: Freiherr von Chaos) 220, 721f., 889 Rijke, Jacob(us) de 719 Roberti, Gaudenzio 478 Rojas y Spinola, Christoph de 214, 339 Rolfinck, Werner (Rolfincius, Guernerus) 347 Rolle, Michel 34, 48, 623, 753, 868 Rømer, Ole Christensen 13, 102, 114–118, 120, 123, 299, 554, 744, 783–785, 792f., 799 Rothmaler, Johann Elias 218, 418, 888 Rudbeck, Olof 230, 841, 898 Rudolf August, Duke of Wolfenbüttel 27, 48, 514, 646, 753 Rumpf, Georg Eberhard (Rumphius, Georg Everhard) 236f., 732f. Ruprecht von der Pfalz (Prince Rupert of the Rhine) 5, 139, 273, 387 Saint-Venant, Adhémar Jean Claude Barré de 96 Sarotti, Ambrose 200, 327f. Sarpi, Fra Paolo (Petrus Suavis Polanus, Fra Paolo Servita) 429 Sauveur, Joseph 26, 34, 512, 623, 866, 868 Savery, Thomas 149f., 698, 801f. Scaliger, Joseph Justus 231, 842f. Scheffer, Sebastian 7, 97, 102, 167f., 198, 200, 215, 243, 247f., 263, 278, 298f., 325f., 328, 340f. 346, 350f., 355, 381, 884 Scheidt, Christian Ludwig 342, 419, 723 Scheiner, Christoph 126, 379 Schelhammer, Günther Christoph 5, 92f., 100, 212, 242–244, 247, 275, 294–296, 337, 346f., 349f., 372, 777f. Scherp, Hans Adam 171f., 814–816, 886 Schlanbusch, Heinrich von 236, 731 Schönborn, Johann Philip von (Elector of Mainz) 832 Schmid, G[-] S[-] 146, 398

965 Schmidt, Gustav Daniel 160, 229f., 804, 840 Schmidt, Johann Andreas 14, 27, 120, 205, 254, 516, 745, 799, 821, 855 Schott, Caspar 90, 170, 174, 290f., 293, 484, 579 Schrader, Friedrich 6f., 87–89, 93f., 200, 243f., 247, 254, 263, 275, 278, 287f., 290, 327f., 346, 349f., 355, 372f., 856 Schrader, Justus 131, 560 Schröck, Lucas 236, 732f. Schröder, Johann 614 Schuller, Georg Hermann 208, 271, 328 Schütz, Heinrich 135, 309 Scradetzky, Baron (medical charlatan) 262, 354 Selenus, Gustavus 174, 484 Seyler, Johann Wenzel 220, 721f., 889 Sinold (alias von Schütz), Ludwig Justus 191, 497 Siver, Heinrich 377 Slare, Friedrich 2, 5, 89, 211, 244, 275, 289, 332f., 348f., 801 Slepper, Justus Bernhard 373 Sloane, Hans 3, 13, 40, 46, 50, 98, 114, 116–119, 207f., 230, 629, 639, 744, 750, 756, 782f., 785, 787f., 789f., 793–795, 826f., 841 Smeaton, John 156 Smith, Thomas 10, 231, 430, 843 Snel van Royen (Snellius), Willebrord 91, 301, 383f., 444 Sophie Charlotte of Brunswick-Lüneburg, Electress of Brandenburg, Queen of Prussia (from 1701) 241, 849 Soudry, Abbé (17th century) 312 Soudry, brother of the Abbé (+ before October 24, 1678) 312 Southwell, Robert 200, 499 Sparwenfeld, Johann Gabriel 160, 805 Spener, Johann Jakob 21, 122, 361, 377f. Spinoza, Baruch de 2, 129, 271, 302 Spoleti, Francesco 263, 356, 425, 476, 895 Stahl, Georg Ernst 240 Starkey, George (pseudonym: ‘Eirenaeus Philalethes’) 217, 224f., 838 Stauff zu Löwenstadt, Ludwig Wilhelm von 195–197, 716–718, 720

966 Steno, Nicola(u)s (Stensen, Niels; Stenone, Niccolo) xv, 227, 420, 484, 892 Stepney, George 193f., 592 Stisser (née Petersen), Ilse 255, 856f. Stisser, Johann Andreas 14, 208, 219f., 222–224, 235, 255f., 721, 729, 744, 830, 834f., 837, 850, 852, 857, 887, 890, 896f. Stockhausen, Samuel 256, 857f., Stolberg, Dr. (or Johann Reinhard) 342 Streete, Thomas 117, 788 Stuart, Maria Henriëtte (Princess Mary of England) 193 Sturm, Johann Christoph 7, 58, 156f., 198, 257, 266, 278, 326, 458, 701f., 859 Sturm, Leonhard Christoph 156f., 701f. S[ch]wammerdam, Jan 2, 131f., 239, 241, 243, 247, 380f., 560, 846f., 849, 894 Sydenham, Thomas 258, 501 Talbot, Charles (Duke of Shrewsbury) 194, 592 Talbot, Robert 247, 350 Tentzel, Wilhelm Ernst 202, 228, 235, 598, 724, 729–731, 897 Teyler, Johannes 251, 290, 574–576, 610, 882, 894 Thévenot, Melchisédech 10, 55, 131, 430, 456f., 473, 483 Thomasius, Christian 205, 820 Thomasius, Gottfried 220, 721f., 733, 889 Tiede, Joachim 116, 785f., 791 Titel, Basilius 121, 300 Titius, Christian 191, 498 Toinard, Nicolas 8, 104, 171, 357f., 366, 582, 885 Toland, John xiiif., 229, 232 Tollius, Jacobus 224, 837 Tolomei, Giovanni Battista 50 Torricelli, Evangelista 100, 112, 165, 167, 371, 405f., 474, 477, 481, 778, 883 Tourville, Anne Hilarion de Costentin (or Cotentin), Comte de 183, 588f. Trithemius, Johannes (or Trittenheim, Johann) 174, 484 Tschirnhaus, Ehrenfried Walter von 1, 4, 6f., 9, 15f., 18–20, 22, 24, 29, 35–37, 43, 48, 102, 119, 123, 125–128, 133, 135, 158, 160f., 164, 170f., 187, 200, 202, 204, 207, 211f., 217, 249, 272, 275, 277, 279, 281f., 285,

Index of Names 299, 306, 308, 323, 327, 333, 335–337, 356, 359f., 378f., 404, 414f., 424, 427,432, 437, 440, 469, 471f., 513, 519, 557, 561–564, 579, 582f., 598, 626, 628f., 644, 704f., 754, 796, 800, 806, 808, 819, 827, 869f., 877, 885 Tyresson, Amund (Anund), also called Falkenstjerna or Falkenhjelm 225, 809 Vagetius (Vaget), Augustinus 27, 44, 87, 107, 111, 261f., 465, 507, 515, 548f., 604, 645, 874 Valentinus (Valentine), Basilius 224, 838, 847 Valentinus, Michael Bernhard 351 Vanni, Giovanni Francesco 96, 375 Varignon, Pierre 13f., 32, 34, 45, 48, 55, 110, 234, 457, 545, 620, 622–624, 728, 744f., 747f., 753, 867f. Vauban, Sébastien Le Prestre de 150, 802 Victor Amadeus II, Duke of Savoy 175, 486 Vierort, Jakob 216, 342 Viète, François 176, 283, 286, 449, 714 Virgil or Vergil (Publius Vergilius Maro) 223, 837 Viviani, Vincenzo 23, 33, 131, 433f., 473, 620, 865 Voigt, Jobst Heinrich 161f., 809f., 812 Volckamer, Johann Georg 9, 97, 198, 260f., 267, 298, 326, 427, 502, 504–506, 884 Volder, Burchard de 43, 349, 465, 559, 640, 643, 786f. Wachsmuth, Johann Christian 9, 139, 142, 248, 358, 387, 394f., 422 Wagner, Rudolf Christian 13f., 99, 118, 120, 160f., 171–173, 205, 207, 253–255, 619, 744f., 776, 792, 799f., 808, 814–817, 821, 827, 850, 854–857, 886 Wahner, Casper 387 Waldschmidt, Johann Jakob 233, 422 Wallis, John 3, 11, 13f., 29–32, 34–36, 38–41, 44–47, 66, 90, 100, 103f., 116–120, 175f., 193, 201, 208, 229–231, 292, 364, 500, 507, 517, 519–523, 618, 620, 624–626, 629f., 634–639, 645, 648, 713–715, 744f., 748–753, 788, 793, 796f., 799, 827, 829, 840–843, 867f., 898 Walther, Bernhard 97

967

Index of Names Ward, Seth 103, 366 Warnecke, Johann Levin 171–173, 814–817, 886 Watt, James 109, 688 Wedel, Georg Wolfgang 119, 204, 212, 220, 224f., 337, 797f., 818, 830, 837f., 861, 898f. Weigel, Erhard 27, 49, 105, 107, 114, 120, 202f., 367, 465, 516f., 597–600, 755, 799f., 885, 887 Wernher, Johann Balthasar von 44, 645 Whipple, Fred Lawrence 229 Whiston, William xv, 228f., 724f., 897

Wideburg, Christoph Tobias 254, 856 Wijnen, Gerard 33, 622 William (III) of Orange, StadholderKing 10, 89, 192–194, 289, 302, 428, 592 Witsen, Nicolaas 146, 398 Witt, Cornelis de 193 Witt, Johan (Jan) de 193 Woodward, John 229, 725 Wren, Christopher 66, 201, 500, 648 Zehn, Peter 387 Zipffell, Jonas 252, 614

Index of Subjects Absolute and relative Leibniz’s understanding of ‘absolute’ and ‘relative’ (or ‘respective’) – a certain determined condition providing an absolute effect – a change of determination producing a relative effect 66f., 71, 75, 77, 80, 95, 113, 296, 396, 371, 454, 461, 536f., 649f., 658–662, 673, 680f., 762, 770 Academies. See Projects, Scientific, Educational Projects Acoustics and sound. See Physics Action (‘actio’). See Disputes and Controversies, Natural Philosophy Administration (government and administration) 142, 188f., 394, 406, 408 Aerzen, Location in the Weser Uplands (‘Weserbergland’) 161, 809f. Agriculture (Tillage and cultivation of land) 828 Alchemy, Alchemists, Alchemical writings. See also Chemistry Alchemical chrysopoeia (transmutation of base metals) 208f., 220, 889, 898 Artificial production of gold 215, 341 Alchemical records 224f., 839f. Alchemical symbols 339, 341, 417, 489, 612, 731 Alchemical information from mythology – legend of ‘The Golden Bough’ (Virgil) – Byzantine/ Egyptian writings – terminology of the ancients 223f, 837f. Arab/ Arabic writers 217 Early-modern alchemy, alchemists, alchemical writings The denigration of alchemy xi The philosopher’s stone – a mythical alchemical substance 185, 220, 318, 342 Basilius Valentinus’ quintessence – his works considered feigned but outstanding (Leibniz) – noteworthy for their concrete character 224, 838

Boyle’s interest in alchemy – his fascination with alchemy and magic – in conflict with his rational thinking 219f. Bodenhausen’s notes on processes / transmutations – his alchemical records – Block’s encryption (1699) – secret-key encryption 224f., 839f. Crafft’s belief (1681–82) in the existence of very remarkable things in nature – his example of a mysterious fluid (a non-wetting water) 215f., 341f. His skeptical attitude to the presentation of an alleged transmutation at the Court in Hanover (1681) – Leibniz’s enquiries and skepticism 216, 342 Glauber’s alchemistic thought 215, 222f., 340f., 836f., 890 Leibniz and alchemy – his early interest in alchemy – his stay in Nuremberg (1667) and his role as secretary of an alchemical society there xii, 220, 721, 829, 889 His discussions with Crafft, Scheffer (1681–83) regarding chemical processes for obtaining – gold and silver from tin – silver from lead 215, 341 His intensive study of alchemistic writings 221, 831, 890 His contacts with renowned individuals thereafter – like the Elector of Mainz (von Schönborn) 221, 831f., 890 His knowledge of European alchemists – such as von Chaos, Flamel, Keller, Lull, Seyler 220, 721f., 889 His recollection (1696) of the demise of the practitioner J. J. Becher (1682) 220, 722

Index of Subjects Alchemy, Alchemists, (cont.) His remarks regarding Kleinert (1696) 721, 889 His call for circumspection regarding alchemy – Block’s corresponding skepticism and admonition regarding alchemy (1698) 220, 722f., 808, 889 His visitations to laboratories 221, 832, 890 His fundamental belief in the concept of a transmutation (1699) 221, 830f., 889 His skepticism about a successful experimental outcome – his comparison with miracles or the work of fantasizing sorcerers – his failure to witness a credible transmutation – his encounters with a series of impostors – his views regarding the nearimpossibility of a transmutation, and a corresponding intimate connection with the maintenance of a world order 220f., 830–832, 889f. His belief in the possibility of a particular or singular transmutation process 221, 831f. His correspondents and alchemy Moller of Hamburg – his view (1699) regarding adepts and their secret mode of operation 221, 832 Moller’s acquaintance in Hamburg and his survival as a ‘capitalist’ but not as chemist – his example of an adept, who had moved to Hamburg from Brandenburg 221, 833 Leibniz’s approach to Moller regarding Brand’s process for metal ennoblement 221f., 833f. Moller’s opinion regarding Brand as a braggart who had come far, but was not really the discoverer of phosphorus – his living in poverty and inability to finance laboratory work – his lacking of universal knowledge 222, 833f.

969 Moller’s reference to an acquaintance with a very lucrative particular / singular process 221f., 834 Newton’s interest in alchemy – his laboratory experiments and study of alchemical texts and the language of alchemy – his understanding of alchemy as a code to be deciphered – a basis for laboratory applications, like the decomposition (transmutation) of metals and the making of gold 219 Pseudonyms and the pseudonymous identities of alchemical authors like Philalethes / Starkey – his alchemical number puzzle 224f., 838 Sendivogius filius’/ Johann Harprecht’s ‘Lucerna salis philosophorum’ (1658) 224, 839 Synonymity with Johann Hiskia Cardilucius – as revealed (to Block) by Leibniz (1699/1700) 224, 839f. The pseudonym of Becher ‘Solinus Salzthal Regiomontanus’ 224f., 839f. The scientific pedigree of such authors 224, 838 Alexandria – Astronomers of Alexandria 117, 791 Algebra. See Mathematics Altdorf – University of Altdorf 701f. America 3, 195, 248–250, 423, 596 American alchemists 224f. American colonies 190, 408f. American physicians 224f. Latin America 319 North America 186, 321 South America 194, 594, 605–607 Brazil – Piso’s natural history (1648) 605f. Paraguay 250, 607–610 Peru 248, 250, 422, 605–609 Analysis, analytical. See Mathematics Chemistry Anatomy. See Medicine Anglo-Saxon. See England

970 Apothecary (or Pharmacy). See Medicine Arachnology. See Biology Archaeology – that of Ramazzini’s ‘De fontium’ (1691) and its influence on Leibniz 164 Architecture. See Civil Engineering Arithmetic. See Mathematics Arms and armor xi Arnstein 11, 508 Astrology 118, 207, 220, 793, 826, 830f., 898 Astrology in calendar reform. See Calendar Judicial astrology (‘astrologia judiciaria’) – a form of astrological soothsaying – absolutely contrary to reason – derided by renowned astronomers like Cassini, Huygens, Hevelius – its outright rejection (1699) by Leibniz – his proposal to counteract claims of astrologists by statistical experiment 221, 830f., 898 Meteorological astrology (‘astrologia meteorologica’) 207, 826 Astronomy Astronomical truth 114, 117, 783, 790f. See also Calendar Reform Geocentric (Terracentric) world picture 118, 793 Heliocentric astronomy – CopernicanGalilean heliocentrism xiv Heliocentric world picture – confirmation 118f. 793, 796 Astronomical observatories 120, 204, 265, 381, 799, 818, 822 Celestial appearances 112, 551 Celestial mechanics 102, 104f., 111, 299, 365f., 369, 539, 550, 875. See also Physics, Mechanics Celestial motions – causes of celestial motions 21, 103, 366, 431, 462, 643 Leibniz’s theory of the causes of celestial motions, in his ‘Tentamen’ (1689) 103–106, 121, 366–368, 376, 431, 462, 464, 466, 643, 875 Comets 102, 106f., 111f., 229, 299f., 365, 370, 381, 464f., 548f., 551f., 725, 876f. The nature and motion of comets – the tails of comets, being observed

Index of Subjects to be confined to the plane of motion around the sun, were either of a real or material nature (Newton, Fatio), or an optical phenomenon, and of an affected or emphatic nature (Leibniz) 106f., 111, 370, 465, 548f., 551, 876f. The comet of 1664 102, 300 The comet of 1680 102, 299 The comet of 1682 (Halley’s comet) 102, 299 The comet of 1683 102, 365 Newton’s theory of cometary tails 106, 370 The role of comets in earth history (1696). See Geology Moon – the moon and lunar astronomy Lunar motion – lack of a satisfactory mathematical description (1701) – call for verification by observation – theory of Newton (1702) 118, 541, 790, 794f. Lunar phases 207, 826 Planets – the sun and planets of the solar system 107, 109, 111, 463, 465, 542, 548, 550, 876 Solar eclipses – that of 1684 102, 365, 788 Sun spots 107, 465, 547 Planetary motion – mathematical and dynamical theory based on: Circular planetary paths of the ancients 81, 763 Ellipses (Keplerian ellipses) 81, 119, 464, 763, 794f. Ovals (Cassini’s theory) 119, 794f. Mechanical causes of the ellipses / ovals 795 Planetaria, planetary machines 102, 299 Planets Jupiter (and moons) – its postulated elliptical figure (Leibniz, Newton) 105, 339, 369, 466 Saturn (and moons) 105, 339, 369 Planetary astronomy – dynamics of planetary orbits Planetary motions – cause of planetary motions 102, 111, 462f., 548, 861, 876f., 894

Index of Subjects Astronomy (cont.) Cartesian vortices 369, 463, 894 Supposition of a course ether vortex – a rotating ether vortex around the sun 58, 87, 102f., 105–107, 111f., 366, 369, 458, 462–464, 545–550, 552, 646, 874–877 Curl / vorticity 167, 482 A transporting fluid (‘fluidum deferens’) 106, 548–550, 875, 894 Circular motion (‘circulatio harmonica’) 103, 109, 144, 366, 391, 463, 542f., 548f., 567, 875f., 879 Rotational velocity 103, 366, 875 Radial motion (‘motus paracentricus’) 103, 366, 463, 875 Centrifugal force (gravity) 81, 91, 103, 106, 109f., 111, 366, 369, 383, 463, 542f., 545, 549f., 762, 875f. Moons of Jupiter and Saturn – similar explanation of their motions 105, 369, 876 Newton’s theory of planetary motions – based exclusively on gravitation 109, 540 Newton’s argument against vortices 87, 111, 549, 874, 877 Huygens’ explanation of gravity 106f., 109–111, 113, 369, 371f., 463, 545f., 875 Huygens’ Discours de la cause de la pesanteur (1690) 57, 109, 111, 113, 371, 451, 462, 541 Planetary paths Circular paths of the ancients 81, 763 Keplerian ellipses 81, 119, 464, 763, 794f. Kepler’s three laws of planetary motions His first, and second law (law of equal areas) 103f., 366, 463, 875 His third law (of 1618) 104, 106, 370 Kepler’s adumbration of the cause of gravity 103, 366 Leibniz’s physical explanation of Kepler’s laws 103f., 366, 463, 875

971 Other mathematical planetary path constructions – circles, epicycloids, parabolas, polygons 103, 366 Stellar astronomy Aberration of light – observations (Hooke, Bradley) 119 Parallax of the fixed stars – early search for stellar parallax – Hooke’s observations (1674) – Flamsteed’s observations (1698) – Wallis’ announcement to Leibniz (1699) – Leibniz’s view (1699) of the non-crucial nature of a verification (based on parallax) of the heliocentric world view – Leibniz’s desire for verification (1701) through more accurate observations 119, 796f., 799 Other suns – parhelia or mock suns – Huygens’ work on parhelia 107, 465 Terra (the Earth) Tides – nature of ebb and flow – Huygens’ and Newton’s explanations 106, 370 Terrestrial and extraterrestrial or outer space – empty space without gravity or resistance 71, 74, 109, 114, 372, 541, 544, 550, 554, 662–665, 876 Attitudes – partisan mentality (camp thinking) 72, 663f. Augsburg. See Bavaria Austria Linz, Linzer Hofgasse (Alleyway) 104 Vienna 6, 8f., 14, 23, 58, 103, 141, 184–187, 189, 200, 218, 220, 257, 275, 316, 320, 352, 354, 357f., 366, 394, 408, 418, 433, 458, 462, 499, 562, 722, 736f., 745, 865, 888f. See also The Holy Roman Empire Battle / Siege of Vienna (1683) – Defeat of the Turks 189, 408 Council of the Empire 14, 745 Imperial Aulic Council 14, 745 (Privy) counsellors at the Imperial Court 6, 276 Imperial Librarian 6, 275f. Imperial Treasury 220, 722, 889

972 Ballistae, ballistics, the Science of ballistics. See Physics Barbarian invasions / migrations 10, 430, 828. See also Peoples and Languages Barometer. See Instruments Bavaria Augsburg 9, 357, 368 Munich 8, 357 Berlin, Berlin-Brandenburg, Brandenburg-Prussia Berlin 11, 14, 49f., 116, 120, 130, 183, 187, 206–208, 214, 257, 262f., 304, 315, 322, 339, 353f., 507, 605, 702, 745, 756, 782, 785, 799, 807, 818, 825 Brandenburg Court – promotion of science by the Court 11, 183, 204, 315, 354, 507, 820f. Berlin Society of Sciences (“Berliner Sozietät der Wissenschaften”) 14, 44, 47, 115, 120, 203–208, 262, 745f., 752, 784, 799, 807, 818–821, 825, 827f., 858 Astronomical observatory in Berlin (1700) 114, 120 Acquisition of quality astronomical instruments – advocated by Leibniz – a 12/20 foot telescope 120, 799 Proposals for the building and equipment of the observatory – with location the roof of a new pavilion to accommodate instruments – intended for the purpose of utility rather than pomp 120, 799 Rømer’s recommendation for the construction of a meridian circle of his design 120, 799 Leibniz’s (and Wagner’s) consultations and enquiries – regarding other observatories and buildings, in Jena, Nuremberg, Zeitz 120, 800 Bible – biblical and scriptural references. See Religion Binary mathematics. See Mathematics, Numbers Biography (Leibniz) Autobiographical selfcharacterization xvi, 863, 899

Index of Subjects Character traits (Leibniz, Huygens) 24, 449f. Personal relationships (Leibniz, Boyle, et al.) 288–291 Leibniz’s biographical milestones Sojourn in Paris (March 1672 to October 1676) ix, 15, 19, 21, 57, 168, 265, 272, 279, 359, 431, 460, 579f., 646, 739, 896 First London visit (JanuaryFebruary 1673) 168, 179, 209, 329, 490, 579f., 585 Second London visit (October 18–29, 1676) 28f., 517, 519 Visit to Amsterdam and Dutch tour (November 1676) – meeting with Leeuwenhoek in Delft 128f, 131, 241, 301f., 474, 849 First years in Hanover (from late December 1676) ix, 2, 15, 18, 87, 129, 208, 279, 287, 302, 328, 358, 863 His activities in the Harz mining district (1680s, 1690s) 1, 4f., 11, 133–136, 138f., 142–144, 146, 148, 151, 154, 162, 169, 187, 191, 225–227, 256, 273, 275, 277, 299, 307–313, 321, 342, 344, 356f., 384, 386f., 394, 396, 399, 419f., 428, 508, 565f., 591, 686, 699, 800, 813, 827, 857, 878f., 890–892 His appointment as Court Counselor and Librarian 4, 273 Grand tour of Germany, Austria and Italy (1687–1690) – meetings with mathematicians, scientists in Italy (1689/90) – stay in Rome (April to November 1689) 2, 7f., 21, 54, 58, 102–104, 131, 141f., 163, 200, 220, 263, 356f., 366, 370, 394, 424, 431, 456, 458, 462, 466, 473, 476, 499, 722, 882, 889 Director of the Ducal Library in Wolfenbüttel (1690) 7, 11, 297, 356, 508 Work on sources for international law – publication of the ‘Codex juris gentium diplomaticus’ (1693) 9, 427

Index of Subjects Journey to Holland (November 1694) 11, 194, 196, 508, 592, 716, 719 Effort to move to the Berlin Court (mid 1690s) 11, 507 Privy Counselor of Justice in Hanover (1696) 11, 13 Foreign member of the Académie des Science (1699) 7, 14, 277f., 745 First President of the Berlin Society of Sciences (1700) – extended stays in Berlin (May–August 1700, October 1701–January 1702) 14, 745 Secretive journeys to Vienna (Last months of 1700 and MayJune 1701) 14, 745 His admittance to the Court Council of the Empire (‘Reichskammergericht’) and the Aulic Council (‘Reichshofrat’) 14, 745 His mathematical maturity ix, xii His research assistants or associates 9, 13f., 49, 51, 139, 312, 358, 363, 387, 619, 744, 756, 880, 886 His life and death ix, 28, 241, 251f., 517, 849 His health. See Medicine His literary estate (‘Nachlaß’) and its repository xvii, 1 Biology, Life Sciences Theoretical biology – classification of plants – criteria 239, 846 Practical biology and medical practice 239, 846 Living, animate beings 139f., 232, 234, 239, 302, 304, 379f., 728, 846 Inanimate systems 232 Meaning and diversity of life – organicists, physicalists, vitalists 232f. Vitalism, vitalism beyond mechanism, vital force, vital spirit 233, 240, 422, 893 The characteristics of living organisms – binding and releasing of energy – growth and differentiation – perception and sense organs – self-replication,

973 reproduction – self-regulation and response to stimuli 232f. Biological thought and concepts Anatomy 235, 237, 239, 242–247, 253, 265, 345–347, 559, 601, 723, 730f., 734, 739f., 845–847, 850–853, 893f., 896 Anatomy – the science dealing with the structure of plants, animals, the human body (Gakenholz, 1701) 247, 851 Classification – science of classification of species – preLinnaean classification 232, 237–239, 844–847 Diseases – animal and plant diseases 259, 502 Evolution (evolutionary biology) – diversity and inheritance – origins without evolution – medieval thought on evolution – preDarwinian evolution 232f., 239, 846, 862, 894 Fossils, fossilized creatures, fish, plants 141f., 226–228, 231, 343f., 384, 419, 421, 730, 891 Mineral ore containing fossilized plants – received from Heyn in Leipzig (June 1690) 141f., 394, 421, 891 Precious minerals (gold, silver) and coral – received from Trondheim, Norway (1697) 236, 731 Organisms 130, 232f., 380 Animals. See Zoology Genetics 230 Plants. See Botany Physiology 4, 239, 242, 246, 266, 742 Reproduction – sexual reproduction 232f., 239f., 243, 347, 846–848, 893–895 Harvey’s ‘Exercitationes’ (1651) 234, 727 Theory of preformation (preformationism) 130, 234, 240f., 379, 727, 849 Swammerdam’s theory (1672) 131, 347, 380f.

974 Biology, Life Sciences (cont.) Leeuwenhoek’s theory (1677/78) – the animalculist (spermist) theory – human / mammalian sperm, its nature and production – the entire organism is pre-formed in animalcula, or little animals – the process of fertilization or nurturing of the animalcula  129f., 234, 240f., 302–305, 379, 726–728, 848f., 894f. Leeuwenhoek’s discovery (1677) of animalcula, in mammalian sperm 129f., 234, 379 Leeuwenhoek’s ‘Observationes’ (1677–78) – philosophical interpretation – the LeibnizArnauld correspondence (1686/87). See Philosophy Lister’s objection (1697) in the ‘Philosophical Transactions’ (1698) 234, 727 Parallels drawn by Joh. Bernoulli (1698) to the infinite and infinitely small in mathematics – the coexistence of lines and surfaces, surfaces and bodies – differentials and integrals 234, 727 Bernoulli’s conception of a world (micro-cosmos) of little animals – Leeuwenhoek’s world of animalcula with a further micro-cosmos within it – a micro-cosmos with a sun and fixed stars, having planets with satellites or moons – an earth with mountains, cliffs, fields, woods, rivers, lakes, seas, living animals 234, 728 The ovist (ovulist) theory of preformation – the entire organism pre-formed in eggs 234, 240, 727, 848, 894 The process of fertilization – the fecundation of the eggs by the seeds – unfolding or de-convolving

Index of Subjects of the offspring – role of a spirit or vital force in the fertilization process 130, 240, 379, 848, 893f. Evidence of a connection between the vegetable and animal realms – direction of the male seed to the female egg in both plants and animals – transformation and development of the seed or egg through nourishment on fertile ground – generation and production of a plant or foetus – upgrading of the male sex and downgrading of the female sex 232f., 240f., 848f., 893f. Dispute between animalculists and ovists / ovulists 234, 240, 727, 848, 894 Leibniz’s vision (1701) of a possible reconciliation of the positions – his own position being close to that of the animalculist Leeuwenhoek and removed from that of the ovist Kerckring – his views on preformation (after 1701) as expressed in his philosophical works – his penchant for Leeuwenhoek’s theory, with the enhancement of the male sex, and the corresponding degradation of the female sex 240f., 848f. Leibniz’s correspondence with Leeuwenhoek (1715–16) 241, 848 Respiration 239, 489, 585, 846f., 894 Skeletons 235, 729 Taxonomy. See Classification Biological (Botanical, zoological) experiments. See also Experiments Waldschmidt’s experiments (1687) with a vacuum flask-vacuum pump apparatus – with plant leaves placed inside the apparatus, and with the roots remaining in open air – water and sap were drawn from the roots, through the meatus to the leaves – reverse experiment (roots inside the apparatus) with a null result 233, 422

Index of Subjects Biology, Life Sciences (cont.) Waldschmidt’s explanation – based on the operation of valves in the vessels of the plants 422 Leibniz alternative explanation – based on the operation of inflected fibers in the vessels 422 Waldschmidt’s canine experiment – on the blood circulation of a dog – pumping air through a small fine tube into a vein of the animal, resulting in its sudden death 233, 422 Waldschmidt’s bell mouth tube – a ‘speaking trumpet’ or acoustic horn – voice transmission over a quarter to half a mile 233, 422 Biological instruments. See also Instruments Semen observed under the microscope – animalcula in water permeated with pepper (Leeuwenhoek) 129f., 234, 302–305, 379f., 728 Botany, Botanists Descartes (Cartesian botany) 238 Stisser’s botanical interests His botanical-medical garden in Helmstedt (1692) 235, 729 His opus ‘Botanica Curiosa’ (1697) 235, 729 Rumpf, Moluccan botanist – Consul / merchant of the island Ambon His ‘De Caryophyllis Regis Ambonicis’ (1697–1698) 236, 732f. His planned multi-volume botanical opus – the first part lost in a shipwreck (1692) 236f., 733 His opus ‘Herbarium Amboinense’ (1741–50) 237, 733 Botanical reproduction – sexual reproduction of plants – Camerarius’ ‘Epistola’ (1694) 240, 847, 893f. Burckhard’s meeting with Leibniz (February 1701) – his reference to Camerarius’ ‘Epistola’ 893f.

975 Burckhard’s outline of the sexual organs of plants – the phenomena of monoecy and dioecy – monoecious and dioecious plants 240, 847f. Leibniz’s letter to Gakenholz (April, 1701) – consideration of reproduction processes in animals and plants – a connecting element between the animal and vegetable kingdoms 240, 848 Correspondence of mammalian sperm to the pollen of seed-producing / flowering plants 848, 894 Correspondence of the style of a flower to the vagina in a placental mammal 240, 848, 893f. Correspondence of the ovary at the bottom of a style to a mammalian ovary 240, 848, 893f. Process of fertilization involving plant ovaries or eggs, pollen grains or seeds 848, 893f. A vital force in the living organism coming from the pollen, penetrating the ovary, and resulting in the fecundation of either the eggs or the seeds 240, 848, 893f. Flowers, fruit, fruit-trees, fruitwalls 45, 163, 195, 237f, 251, 596, 712f., 747, 844f. Botanical (plant) species Algae, coral, coral algae 236, 731 Arrowwood (viburnum) 204, 818 Litophyton marine soft coral, received from Trondheim, Norway (1697) 731 Cypress 204, 818 Musk plant 236, 732 Rootstocks (rhizomes) 733 Wormseed – Levant wormseed (‘semen sanctum’) 236, 732

976 Biology, Life Sciences (cont.) Wormwood (Southernwood or southern wormwood) – Persian flowering plants ‘artemisia abrotanum’– Cleyer’s and De Jager’s investigation (1684) 236, 732f. Botanical (plant) taxonomy – development of a taxonomy, or classification system – classification of plants according to certain criteria – Gakenholz’s discussion with Leibniz (March 1701) 237, 844 Leibniz proposal for a consideration of roots as the basis for plant classification 237, 844 Gakenholz’s open letter to Leibniz (April 1701) – proposal for development of a classification system based on parts of plants such as flowers, fruit, seeds or roots 237, 844 Gakenholz’s complaints about a prevailing orientation towards antiquity – a lack of comparison with the real world – a lack of suitability here for a general use of methods striving for mathematical exactness 237, 844f. Gakenholz’s thoughts on a variety of established classification systems – based on fruit, seeds, flowers – requiring long-term observation 237, 844f. Leibniz’s adherence to a classification based on roots – advantage of constant availability / accessibility – disadvantage of lacking sufficient variations, and unsuitability as a sole classification characteristic 237, 844f. Leibniz’s thoughts on plant classification (April

Index of Subjects 1701) – insufficiency of classification by a single criterion – appropriateness of combinatorics. See Combinatorics Relevance for development of botanical systematics – analogy with 16th /17th century Ramist geometry. See Mathematics, Geometry Organic bodies as machines (machine-like entities). See Machines Descartes views on the mechanical life of plants 238 Block’s comparison (1698) of the human body to a closed machine – like a clock, which one could not correct without opening it up, and risking its destruction 264, 738 Plants, animals, humans viewed as machines adapted for certain tasks 239, 846 Plants as machines of nature – their internal structures (inner workings) 238f., 845 Humans were adapted for contemplation, plants and animals adapted for helping humans in fulfilling such tasks – the challenge to explain such tasks, and the mechanisms involved in their realization 239, 846 Leibniz’s understanding of organic bodies as machines for the fulfillment of certain tasks, duties and functions – like nutrition and reproduction, and preservation and perpetuation of knowledge 238f., 846 Leibniz’s long-standing interest in prehistoric creatures, or the animate beings of earlier epochs. See Geology The science of these prehistoric creatures – Leibniz’s letter to

Index of Subjects Biology, Life Sciences (cont.) Gakenholz (April 1701), with concepts of comparative anatomy – comparison of animals (‘collatio animalium’) – concepts of reproductive biology – developmental and evolutionary biology – a connection of plants and animals based on respiration – respiratory organs (lungs) – a continuity of plant and animal realms with transition from plants to animals through intermediaries like insects – Swammerdam’s ‘Insecta’ (1669) 239, 846f., 894f. Zoology Animal behavior (Ethology) – example of tigers, the ‘tiger animal’ (‘panthera tigris’) – its aggressiveassault behavior – energy efficiency practices xvi, 4, 236, 731, 862f., 899 Animal reproduction 240, 243, 347, 846, 848, 894f. Animalcula, Larva or ghost (necromancy) 303, 420 Arachnology, arachnologist, arachnids 249 Mole (talpa) – anatomy of the mole – sexual organs of the mole 243, 346f. Mussels (bivalve shellfish) – mussels from Jakarta 248, 351f. Protozoology – Leeuwenhoek seen as father of protozoology and bacteriology 234 Rare fish species – dissection (Mariotte, 1680) 198, 324 Zoology and Leibniz – his interest in the anatomy of large mammals 235, 723 Study of the skeletons of dead or extinct animals 235, 729 Elephant-like creature found in Thuringia (1696) – its cranium

977 or skull – excavation of bones at Gräfentonna (Tonna) – report of the ‘Collegium Medicum’ in Gotha 235, 729f., 846 Skeleton of an elephant in Florence 235, 729f. Mullen’s dissection of an elephant (Dublin, 1681) – his ‘Anatomical account’ (1681) – the cranium or skull of the elephant 235, 729–731 Mullen’s anatomical observations concerning the eyes and ears of animals (1682), the eyes of fowl and fish, the ears of fowl 235, 729–731 Mullen’s comparison of the organs of animals and humans 235, 731 Ray’s ‘Synopsis methodica’ (1693), regarding quadrupeds and serpents 235, 730 Hunting of whales – a whalebone or baleen whale – parts received from Trondheim (1697) – its mandible or lower jaw (Fischbein) – its remarkable penis 236, 731 Import of exotic animals, of which specimens included Civets – a large spotted civet cat 236, 731 Monkeys – a long-tailed monkey 236, 731 Squirrels – a brown squirrel (from East India) 236, 731

Bohemia Graupen (Krupka) 8, 188f., 216f., 357, 413f. Prague 257, 352 Brandenburg. See Berlin, BerlinBrandenburg, Brandenburg-Prussia Brandy distillation Project. See Economics Bremen 447 Breslau 498 Bruchsal 414

978 Brunswick-Wolfenbüttel (principality) – courts in Wolfenbüttel and Celle 8, 11, 14, 196, 212, 247, 315, 318, 337, 350, 354, 356, 508, 718, 745 Brunswick (town and duchy) 6, 10–12, 186, 275, 321, 356, 428, 508 Calculating machines. See Machines Calculus, infinitesimal calculus. See Mathematics Calendar – Calendar reform. See also Churches, Synods Old and new styles 2, 114, 116, 331, 515, 591, 729, 782, 786f. Unification of calendars 115, 785 Leibniz’s vision for the Protestant calendar reform – as political lobbyist for acceptance of the reform – his efforts abroad for the Protestant calendar reform – his letter to Rømer (1700) 14, 114–118, 202, 206, 745, 782f., 786f., 790f., 823 Civil calendar – astronomically-exact fixing of the civil year – possible uncoupling from the ecclesiastical year 114–117, 783–789 Ecclesiastical calendar – moveable and immoveable feasts 114–117, 783, 788f. Anglican rules and tables, in the ‘Book of Common Prayer’ (1662) – mistake in the rule for Easter (Wallis) – corrected in astronomical tables 114f., 117f., 782–784, 788–793 Leibniz’s advocacy of achieving agreement between civil and ecclesiastical calendars 114, 783 Gregorian (new-style) calendar – Gregorian reform – Gregorian Easter calculation – Gregorian lunisolar calendar – Papal Calendar Congregation 2f., 114–118, 782–790 Leibniz’s aim to achieve agreement of the Gregorian Easter calculation with astronomical truth 114, 117, 783, 790f. His appeal to the Académie des Sciences (1700) 117f., 783, 787, 791, 793f.

Index of Subjects His contact with the Vatican (through Cassini) – the Papal Calendar Congregation 114–116, 783–786 The Protestant adoption / rejection of the Gregorian calendar Dutch provinces Friesland, Groningen (1700–1701) 116, 787 German Protestant states (September 23 / October 3, 1699) 114, 782f. English rejection of Protestant calendar reform Confessional and theological antagonism – anti-Catholic sentiment (John Wallis) 116 The Julian (old-style) calendar – the Julian Easter calculation 2, 114, 117, 782f., 787–789 Wallis’ purported rectification with ease of – the equinox calculations – other inequalities of motion 788f. Technicalities of the Easter calculation Moveable and immoveable feasts – date of moveable feast of Easter – Easter calculation 114, 117, 783, 788f. Date-determinations of equinoxes – autumnal and vernal (or Spring) equinox 114f., 117, 783f., 788f., 791f. Anticipation of the equinoxes – use of date and of date-after the equinox – discrepancy of c. three days in four hundred years 788f. Full moon – date-determinations of full moons – use of date (Sunday), and of date after (Sunday after full moon) 114f., 783f. Solar and lunar cycles – solar year – midpoint equation of the sun – unpublished results (Flamsteed, Newton) 114–118, 783, 785f., 793f. Years, and leap years – rearrangement of leap years – inter-calendrical modus (Reyher /Tiede, 1701) 116, 785

Index of Subjects Calendar – Calendar reform (cont.) Issues of controversy The use of – true or average movement– right ascension and declination – longitude and latitude 118, 793 Heliocentric or geocentric positions 118f., 793, 796 Astronomical tables for calendar calculation Kepler’s tables – ‘Rudolphine tables’ (1627) – founded on erroneous observations – deviations of equinox calculations from later more exact calculations – vernal equinox three hours premature – autumnal equinox delayed by three hours 114, 117f., 783, 788, 792f. Streete’s tables (1661 and 1674) 117, 788 Flamsteed’s tables (1680) 117, 788 Junius’ tables (1699) – his project for more exact tables based on ephemerides – his exchanges with Cassini and Rømer – differences regarding the inadequacy of Kepler’s tables 115f., 117f., 785, 792f. Astrology in the calendar reform – possible inclusion / exclusion of aspects appropriate for astrology – abuse of / by astrology 118, 207, 793, 826 Wallis’ preference for the use of English-language tables 118, 793 Later (then unpublished) observations The observations of Newton and Flamsteed on solar and lunar motions – considered (by Wallis) to be more accurate than previously printed tables in English 118, 793 Summary by Newton / Flamsteed – sent to Leibniz and forwarded

979 by him to others in Germany and France 793 Lobbying by Leibniz (1700) in political circles for acceptance of the calendar reform – based on astronomical truth and on reason and rationality 117, 790 Benefits of public (Royal) authority support – in England, like in China 117, 790f. Leibniz’s call for a transnational and inter-confessional exchange 117, 792 Canada – demographics and possible relocation of peoples – possible settlement of black Africans in Canada 186, 321 See also: Slavery, Slave Trade Cartesianism. See Controversies and Disputes, Natural Philosophy Celle (principality of BrunswickWolfenbüttel) – the court 6, 10f., 152, 183, 185, 196, 212, 247, 275, 315, 318, 337, 350, 354, 401, 428, 508, 718 Celtic, Celticization (Celticisation). See Peoples and Languages Chemistry. See also Alchemy Acids – strong acids Aqua fortis, spirit of niter, saltpeter acid (nitric acid) 122, 163, 217, 378, 413, 711 Oil of vitriol (sulfuric acid) 163, 613, 711 Spirit of salt (hydrochloric acid) 163, 711f., 836 Acids – weak acids Lemon juice 251, 611 Sprit of ammonia 612 Vitriol driblets (drops of vitriol) 251, 612f. Urine / Uric acid 611 Advancement of chemistry – through a combination of method and experiment – Leibniz’s suggestion to Stisser (1699) – longing (Stisser) for a consolidation of chemistry through meticulous experimental examination 222, 835 Analytical chemistry 216, 862, 888

980 Antimony. See also Mercury, Cinnabar of antimony ‘Regulus of antimony’– metallic antimony reduced from its ore 218, 417 Art of chemistry (Chemistry as an art) – characterization as the oldest of the arts (Stisser, 1700) 223, 837 Leibniz’s understanding of the tradition of alchemy / chemistry from ancient times. See: Alchemy / Alchemists in history Chemical knowledge in antiquity 223, 837 Advancement / Consolidation of chemistry 222, 835 Experimental chemistry (chemical experiments) 6, 213, 217f., 275, 412, 415, 417 Foundations of chemistry 222, 722, 738, 835, 889 Postulated chemical principles – often more melodious than veritable 222, 835 Arsenic 160, 252, 740f., 808 Regarding use as an antipyretic. See Medicine, Bloodletting Atoms, chemical atoms 223 Atomism. See also Corpuscles, Corpuscular philosophy Borax 160, 808 Chemical interactions Starting substances, or elements – their imbuement with subtle particles – veiling / unveiling of chemical substances 223, 836, 890 Chemical maturation (‘maturatio’) 219, 418, 888 Chemical revivification, resuscitation – animation, transanimation 223, 836, 890 Chemical transmutation (‘transmutatio’) – an element transformed into another element 209, 216, 218–224, 328, 342, 412, 418, 721, 830–839, 888–890, 898 Quest for such transformations. See also Metals

Index of Subjects Chemical transplantation (‘transplantatio’) – substances exchanged in a chemical interaction, reaction or process – a single ‘element’ might be common to two other starting substances – veiling / unveiling of substances in reactions – products of interactions, reactions or processes might be contained as subtle particles in the starting substances 217, 222f., 241, 415, 836, 888, 890 Process environments – elements might possibly alter their form depending on the environments 223, 836, 890 Chemical laboratories Boyle’s chemical laboratory (Pall Mall, London / City of Westminster) 213, 411 Establishment of a chemical laboratory in Hanover – under the directorship of Pratisius (1690) 218, 416 Stisser’s chemical laboratory in Helmstedt – his ‘Actorum laboratorii chemici’ (1698) 219, 721 Other laboratories. See Laboratories Chemical / alchemical literature 215, 219, 340 Chemical processes Trial of a process in Copenhagen (Elers, 1684) – involving the reduction of gold powder in aqua fortis (nitric acid) – initial success and ultimate failure 216f., 413f. Chemical visions – including chimeras, daydreams, fantasies, illusions 99, 110, 133, 545, 720, 722, 776, 830f., 878, 889 Chemical / process engineering – processes carried out in open air – of particular practical importance with the supply of air providing improvement in the effectivity of fire 162, 706, 709f.

Index of Subjects Distillation Distillation in antiquity 223, 837 Distillation of sulfur – Papin’s new process (1697) – with six (or more) alembics or retorts in series and the final outlet into the open air – production of liquefied gases – liquefied spirit of sulfur, or oil of sulfur – greatest quantity in final retort – complete liquefaction without fumes escaping into the air 162f., 710f. Combustible materials – insights into chemical processes 163, 711 Condensation of flue gases – greater in cold rather than heat 710 Phase Transition (Sublimation) – flowers of niter purified by sublimation – sublimation of mercury 163, 218, 416, 711 Production of strong acids – extraction or production of sulfuric acid 163, 711 Medicinal Chemistry Effervescence and fermentation 100, 615f. Importance of spirits of sulfur for chemistry and medicine – as a remedy for scurvy 162f. Conservation of foodstuffs Conservation in kitchens and at sea – providing fresh meat and water free of contamination 162, 709, 712 Techniques for the conservation of foodstuffs (1697/98) – conservation fluids using spirit of sulfur diluted with water 162f., 613, 709, 712 Papin’s conservation of fruit and vegetables – apples, pears, plums, raspberries – his conservation of meat and fish – associated medical benefits 163, 712f. Chemical research 215, 341

981 Chemical substances and economic utilization. See Projects Chemists. See also Alchemy, Alchemists Chemists 149, 214, 221, 267, 337, 339, 400, 804, 831f., 859f., 889f. Iatrochemists (chemical physicians)  259, 500 Misochemists (‘misochemici’) – those hostile to chemistry 256, 852 Cinnabar. See Mercury Corpuscles, corpuscular philosophy, corpuscular light rays. See Physics Corpuscular matter theories – Boyle’s theory – Newton’s theory 123, 208f., 223, 554 Gold. See also Metals Ennoblement of base metals – transmutation of base metals into gold (Chrysopoeia). See also Alchemy, Alchemical chrysopoeia 191, 208, 221, 328, 497, 883 Gold extraction (or reduction) processes. See also Economics Gold panning – technique of panning in rivers (Leibniz, Crafft, 1688) 217, 414 Gunpowder Production of gunpowder and saltpeter – its chemical properties – a process for its manufacture with leaching and concentrating in ditches or trenches 216, 413 Hypothetical process to establish a perpetual saltpeter works (Elers, 1684) 216, 413 Suggestion for improvement of saltpeter production – using a vault or dome (Leibniz, Crafft, 1688) – with the product appearing on rocks following blasting 216, 413 Iatrochemistry (chemical medicine). See also Medicine, Chemical medicine, Iatrochemists (chemical physicians), and Medicine (Chemical Medicine / Chemistry in Medicine), the

982 Chemiatric school in Medicine, its diagnostic and therapeutic teachings. Lead Douceur’s secret process for giving lead the color of molten bronze (1683) 217, 415 Lead oxide (red lead) 217, 415 Leibniz’s chemical studies His perception of Boyle and his accumulation of experimental data – his experimental industriousness and judgement – his failure to formulate theories – his reticence in drawing conclusions 88, 288 His information about J. J. Becher (+1682) – his chemical writings 140, 390, 722 His interest in chemical experiments (Dresden, early 1680s) 6, 275 His interest in a fuming liquid process (Celle, early 1680s) 5, 212, 274, 281, 337 Mercury Alleged transmutation of mercury into gold by von Chaos (1658) 220, 721, 889 Cinnabar (mercury sulfide mineral) 214, 217, 253, 339, 415, 854, 888. See also Chemical Projects A cinnabar process – investigated by Italian alchemists (1685) – Bodenhausen’s interest in the process (1690) – Leibniz’s designation as a chemical ‘transplantatio’– an adulteration of the process (1690) – falsification of the cinnabar – use of cinnabar of antimony 217, 415, 888 Medieval understanding of mercury – as a basic principle of metals – in the alchemical text ‘Turba philosophorum’ 219, 721 Quicksilver (liquid metal mercury) 416 Study of mercury (Bodenhausen, 1690) 415f.

Index of Subjects Sublimation of mercury (Geber or Gebir, ed. 1668) – Bodenhausen’s study and Leibniz’s skepticism (1690) 218, 416f. Production of mercury from the ‘Regulus of antimony’ (Florence, 1690) 218, 417 Metals. See also Metallurgy, Metallurgical Processes Alloys, alloying of metals 139, 387, 485 Chemical ‘maturation’ of metals (Leibniz, 1687) – for improving the processing of ores – for increasing knowledge – for greater economic benefit 218f., 418, 888 Chemical transmutation of metals – for the possible production and extraction of gold and silver 190, 209, 214–216, 218f., 338f, 341, 410, 418, 888 Counterfeit or fake gold – from the workshops of von Chaos and Wenzel Seyler – made by the charring (carbonization) of coal – inspected by Leibniz at the Imperial Treasury in Vienna (1688) 220, 721f., 889 The efforts of Rothmaler in Vienna (1689) 218, 418, 888 The ‘Lobkowitz’ process – for the transmutation of silver into gold and silver (Crafft, 1689–90) 218, 418, 888 The Holeysen separation process (Vienna, 1690) – gold yielded from auriferous silver – submissions to the emperor – Holeysen’s discussions with Leibniz 218, 418, 888 Brand’s (purported) process for metal ennoblement (1698) 221, 833 Moller’s (reported) very lucrative process (1699) 222, 834 Minerals, crystals, rocks. See Geology; Iceland spar. See Physics, Light and Optics Phosphorus (white phosphorus)

Index of Subjects Discovery of phosphorus – history of the discovery 208–211, 328–331, 412f. Homberg’s history (1692) 208, 213f., 412 Leibniz’s ‘Historia inventionis phosphori’ (1710) 209, 214, 328, 413 Brand’s discovery (in Hamburg, c. 1669) 159, 197, 208–211, 213, 221f., 271, 328, 330–333, 410f., 707, 833f. Crafft’s Intelligence regarding the discovery (1676) – its presentation at the Court in Hanover (May 1677) 210, 330 Crafft’s disclosure to Boyle (London, Sept/Oct 1677) 210f. 331f. Boyle’s other German informant – his laboratory assistant (Hanckwitz) 213, 411 Leibniz’s contract with Brand (July 1678) – Brand in Hanover (1678–79) – production of phosphorus 210, 331 Kunckel’s ‘Phosphorus mirabilis’ (1678) 209, 328f. Boyle’s ‘The aerial noctiluca’ (1680) – his method / process 209f., 213, 329, 331–334, 411 Leibniz’s process for the production of phosphorus – his report to Tschirnhaus (June 1682) The Leibniz / Brand’s process – repeated and protracted distillation procedures – starting or raw material (human urine) 211, 333–335 The process and intermediate stages – oil of urine – a ‘caput mortuum oleosum’ – a core firecontaining substance / a black loose or soft material – a hard salt byproduct / an amber-like hard stone 211, 334f. Special properties of the final product – brightness and luminescence 211, 334f.

983 Leibniz’s claim to superiority of his process – attributed to an additional step for the refinement of the ‘caput mortuum oleosum’ 211, 335 Other processes / presentations of phosphorus (1682) Secret formula on offer in Paris 211, 336 Experiments by members of the Académie 211, 336 Leibniz’s revelation of his production process to the Académie via Tschirnhaus (June 1682) 211, 277, 333, 335f. Leibniz’s receipt of two scientific secrets in exchange for his – a process in which ostensibly herbal salt grew like a plant in water – a process in which gold was made volatile without fulmination 212, 337, 414 Boyle’s publication of his ‘Icy noctiluca’ (1682) 336 Brandshagen’s presentation of phosphorus for the king of Denmark (1682) – his cosmetic or blemished complexion after a facial phosphorus application with adverse after-effects 211f., 336 Public performances with phosphorus – enhancement of phosphorescence in the dark 212 Theoretical importance of phosphorus Tschirnhaus on phosphorus and alchemy (1682) – the accordance of phosphorus with the second of the three universal principles of alchemy, namely salt (a solid state or fixed salt), sulfur (an oily or sulfuric liquid), and mercury (a volatile or mercurial spirit) 212, 336f. Brandshagen’s chemical experiments (Hanover, 1687) – his phosphorus production following Reimers’ urine collection (April–May 1687) 213, 412

984 Leibniz’s communication to Bodenhausen (1690) – with details of the production process and verses about phosphorus – presentation at the Florentine court – interest of princes Ferdinando and Gian Gastone 213, 412 Other phosphorus-like (luminescent) substances Boyle-Leibniz discussion (1673) 209, 329 Balduin’s ‘phosphorus hermeticus’ (1675) – a phosphorescent form of calcium nitrate 209, 329 Breatridge’s spontaneously-igniting powder (1680) 209, 329 Demonstration of a smoking / fuming liquid (1680–81) – Schelhammer’s attribution to an inner fire – Leibniz’s rejection of any similarity with phosphorus 5, 212, 274f., 281, 337 Properties / uses of phosphorus / phosphorus-like substances – afterglow (or phosphorescence) – a means of distillation without fire – combustion and ignitability – encapsulation of fire – conservation of fire / heat (on a journey) – carbonization (of wood) 212, 413, 722, 888 Salts Glauber’s salt 222f., 836, 890 Salt revivification, transanimation, resuscitation 223, 836, 890 Transmutations of salt(s) – Stisser’s understanding of transmutation (1699) – his examples from the mineral, vegetable and animal realms 222f., 834–836, 890 Salt works (Brine works) Desalination, desalinization – process for the desalination of sea water 139, 150, 190, 201, 219, 387, 410, 499, 573, 803. See also Projects

Index of Subjects Salt production processes. See also Economics Salt (or brine) wells – origin of the salt in wells 147, 687 Lacy’s desalination plant near Modena (1690) 190, 201, 410, 499 Desalination / salt extraction from seawater in Holland 219, 573 Crafft’s project based on a precipitation process – Leibniz’s interest and skepticism (1695– 1696) 219, 573f. Papin’s machine for seawater desalination (1699) 150, 803 Salt works at Halle (early 17th Century) – Leibniz’s recollection (1696) 574 Salt works at Heyersum (near Hildesheim, 1697) 156, 700 Silver mines. See Mining Soda or sodium carbonate (natron) 836f. Sulfur – the phenomenon of electric sparking. See also Physics, Magnetism and Electricity Vitriol Alum, vitriol of Argile (vitriol of clay) 712 Leibniz’s view of vitriol as a basic principle of metals 219, 721 The ‘tinctura vitrioli’ (Stisser, 1698) 219, 721 China Calendar office in China 117, 791 China missions 48, 754, 822 Religious conversion of the Chinese – Leibniz’s missionary zeal 208, 827f. Jesuit mission 8, 50, 248, 357, 423, 756 Protestant missions 13, 618 Anglican missionary efforts in China – journeys to China by English merchants (1697) 208, 827 Support for the mission from the Berlin Society – along the overland route to the orient 208, 827

Index of Subjects China (cont.) Leibniz’s suggestion (new year 1697) of the use of the dyadic or binary number system in the missions – intended to counteract a pagan or heathenistic philosophy 27, 645f., 753f., 828 His view of the prodigious origin of all numbers out of 1 and 0 – an archetype of the secret of creation – the coming into being of all from God and Nothing (1 and 0) 754 His communication (January / February 1697) to the China Missionary Grimaldi 48, 754 His view of the main use of binary arithmetic in the investigation of the properties of numbers 48, 754 Christian missionary ambitions combined with the advancement of science – propagation of the faith by means of science – an objective of the Berlin Society (1700) 208, 827f. Desired spread of the Christian religion among the (partly) heathenish and still (partly) barbarous – even among barbarian peoples 828 Chinese mathematics. See also Mathematics Acquisition of mathematical instruments in China (1699) 208, 827 Binary Fohy (or FuXi) sequence 50, 756 Chinese figures of Fohy (‘FuXi hexagrams’) 50, 756 Peking (Beijing) – The ‘Tribunale Mathematicum’ 8, 357 Chiromancy. See Medicine, Limbs, Palm Reading Christianity / Christendom 788 Christian Charity 683f. Chrysopoeia. See Chemistry, Alchemy Churches, Christian churches

985 Anglican (Anglo-Catholic) church 116, 208, 827 Anglican anti-Catholicism sentiment 116 The ‘Society for the Propagation of the Gospel’ 208, 827 Catholic (Roman Catholic) church xiii Catholic theology/ theologians – ecclesiastical policy – the Roman Inquisition xiii, 13, 105, 114, 117, 367f., 618, 788 German Catholic dioceses – Cologne – Münster 11 Synods – Synod of Nicæa (Nicene Synod, 325 A.D.) 789 See also: Calendar Reform Foreign missions. See China missions Reconciliation of the Protestant churches 13, 618 Reunification of the Christian churches 14, 745 Clausthal (Clausthal-Zellerfeld / Zellerfeldt) 136, 144f., 226, 344, 384, 566f., 569, 891. See also Mining Combinatorics – Renaissance and modern combinatorics 238, 845 Leibniz’s dissertation on the combinatorial art (1666) 238, 751f., 845 Leibniz’s combinatorial characteristic 18, 284f. Category combinations (combinatorics) Juridical, mathematical, philosophical, scientific categories 238, 845 Systematic categories in botany. See Biology Commonweal, common good (‘bonum commune’) 19, 195, 197, 201, 316, 360, 505, 595, 597, 606, 718, 720, 787, 888 Controversies and disputes Leibniz’s meeting with Boyle (1673) – his disparaging remarks about Boyle and his work – his misgivings about Boyle’s development of the vacuum pump – his insistence on Guericke’s priority over Boyle – his resentment towards Boyle 89–92, 210, 290–293, 331

986 Controversies and disputes (cont.) Boyle’s continuing interest in Leibniz – his expression of affection towards Leibniz 89, 289 Leibniz’s misgivings about the Boyle’s studies of the properties of air – his insistence on the superiority of Guericke’s work 89–91, 210, 290, 293, 331 Leibniz’s mistrust of Boyle’s role in communicating intelligence about Drebbel’s submarine crossing of the Thames (c. 1620) 179, 488f., 585 Misgivings about the discovery and study of phosphorus – Leibniz’s insistence on Brand’s priority over Boyle – his insistence on the superiority of his own process 211, 333, 335 Leibniz’s recollection of other instances of non-recognized discovery claims – Snell van Royen’s law of refraction, wrongly attributed to Descartes and Kepler – Kepler’s priority in explaining gravity on the basis of centrifugal force 91, 301, 383f. Leibniz’s perception of German reticence in claiming success – of preferential treatment being given to foreigners – of prejudice against Germany and Germans 38, 90, 292, 632 Satirization of Leibniz – J. J. Becher’s satirical work (1682) – ridicule of discoveries and projects of contemporaries like Leibniz’s imagined rapid transit system 7, 140, 146, 188, 278, 390, 398, 880. See also Transport, Transportation Leibniz’s discord with Tschirnhaus (1682–84) – following unapproved publication of his quadrature method 19f., 359f. Priority issues in the context of the formulation of the minimal principle of optics (1682–83), following the publication of Leibniz’s principle of optics – his principle of the easiest light path (1682) 120f., 125, 300f.

Index of Subjects Leibniz’s dispute with Vanni (1684–85) – concerning the static moment of a heavy body on an inclined plane 96f., 375 Controversy about the true measure of force (from 1686) Leibniz’s demonstration of Descartes’ ‘remarkable error’– his ‘Brevis demonstratio’ (1686) – reaction of the Cartesians and Papin’s rejoinder (1689) 56–58, 63, 362f., 458, 534, 646 Leibniz’s dispute with the Cartesian Abbé Catelan 18f., 21f., 53, 358, 432, 453 Papin’s opposition (January 1691) to Leibniz’s assault on Cartesianism 57f., 457f., 646 Leibniz’s reassertion of his anti-Cartesian stand (September 1691) 59f., 460f., 647 Leibniz’s support for Corradi in a dispute with Stabe de Cassina – issue of dangerous emissions in chemical processing using vitriol (1689–90) 190, 410 Leibniz’s conciliatory approach (1690– 1695) regarding an explanation of gravity / gravitation – his own vortex theory – theories of Newton and Huygens 106f., 111f., 463f., 547f., 550, 876 Leibniz’s priority claims (1693) regarding winding (or ore-hoisting) machinery in mining – use of an endless rope / cable for weight compensation 134, 138f., 143–145, 386f., 407, 565–567, 569f., 879f. Conflict (1694–95) with the Mining Office over the design of a power supply system for pumping and winding machinery 145f., 567, 571 Public philosophical dispute with Foucher (1692–93) 54f. Dispute with Papin about ‘vis viva’. See also Natural Philosophy The ‘vis viva controversy’ – dispute conducted in articles (published up to 1691), and in private correspondence (from 1692)

Index of Subjects Controversies and disputes (cont.) First phase from January to December 1692 – Papin’s ‘Synopsis controversiae’ (Oct./Nov. 1692) 60, 462 Rekindled correspondence with Papin in 1695 61–63, 526–535 Leibniz’s time-out (two months early in 1697) 68, 656 Papin’s time-out (spring to fall, 1697) 69, 656f. Final phase of the debate (January 1699 to springtime 1700) 78, 873f. Dispute with Papin about action (‘actio’; 1696–1700). See also Natural Philosophy 50, 287, 362, 450, 525, 646, 757 Action 66, 74–81, 85–87, 648, 669–682, 757–762, 772–775 Dispute regarding Papin’s attempts (1696/97) to demonstrate a loss or gain of force in the substitution of bodies 67–70, 459f., 654–659 Leibniz’s final letter to Papin dealing with the measure of force and action (April 1700) 774f. Guglielmini’s dispute with Papin (1691–1697) about the fundamentals of fluid flow and fluvial mechanics – mathematical abstraction versus engineering practice 167, 481f. Huygens’ critique of infinitesimal analysis – dissension between Leibniz and Huygens (1691–1692) about the ‘Leibniz series’ and a similar series of Huygens 24, 437f. Publication of the catenary problem solutions 22, 24f., 432f., 439f., 442, 628, 864f. Exchange of inverse-tangent methods 24, 437 Huygens’ dispute with Renau d’Eliçagaray (1689–1694) – about the method of steering and maneuvering a sailing ship 182f., 588–590 Leibniz’s thoughts regarding the dispute (1694–1695) 183, 590

987 Discussions about the foundations of the calculus Clüver’s criticism of the differential calculus (1694–1695) – its failure to achieve ultimate geometrical precision – example of the relationship of unity to infinity  41–43, 523f., 639, 642 Nieuwentijt’s criticism of the calculus (1694–96) – his ‘Considerationes secundae’ (1696) – Knorre’s review (March 1697) – Leibniz’s ‘Excerpta’ (June 1697) – Johann Bernoulli’s criticism of Nieuwentijt (1697) 31–33, 41–43, 523f., 621, 639–642 Mencke’s role in the dispute with Nieuwentijt 32, 41f., 524, 640f. La Hire’s criticisms and Leibniz’s answers (1697) 34, 43, 623f., 644, 868 Leibniz’s approach to such criticisms – revealed to Clüver (June 1697) – deferment and referment – reliance on the judgement of adepts / experts 43, 642 De Volder’s difficulties with the calculus (1698) – dispelled following Joh. Bernoulli’s explanations 43, 639f., 643 The conflict between Jacob and Johann Bernoulli Drawn-out conflict / the isoperimetric problem (1697) 37f., 630–632 Leibniz’s criticism of Jacob’s behavior – disruption of the correspondence with Jacob (until 1702) 38, 632 The Dispute about the calculus. See also Mathematics, Calculus Questions of independence, priority and plagiarism – the priority dispute 11, 19, 28–30, 34, 38f., 359, 508, 517f., 521f., 624, 632–639, 868 Eminence of continental mathematicians 30, 522, 638 Eminence of English mathematicians 11, 28–30, 500, 508, 517, 519, 522, 753

988 Controversies and disputes (cont.) Leibniz’s publication and conflict management policy – his defense of his discovery claims 19, 48, 359, 450 Correspondence between Leibniz, Oldenburg, Newton (1676) 29f, 40, 519, 638f. Wallis’ focus on Newton’s calculus of fluxions (1693) 30, 39f., 521, 634–639 Wallis’ insinuations / resentment against Leibniz (1695) 41, 47, 626, 639, 752f. Leibniz’s view of Wallis as an English nationalist – his complaint to Burnett of Kemney (1695) – his review of Wallis’ Opera (June 1696) – his criticism of Wallis’ biased, one-sided treatment 30f., 522f. Wallis’ subsequent complaint to Leibniz 523 Beginning of Leibniz’s correspondence with Wallis (1696) – and discussion of priority issues (from December 1696) 634–639 Limited circulation of scholarly results – a factor in priority issues 39f., 636 Joh. Bernoulli’s complaint (August 1696) about Wallis’ failure to acknowledge the differential calculus – his suggestion that the fluxional calculus was built on information received from Leibniz 39, 635 Fatio’s allegation of plagiarism against Leibniz (1697) 34, 624, 868 Critique of Mencke’s editorial policy at the Acta Eruditorum Mencke’s abhorrence of polemical disputes 47, 752 Mencke’s alleged preferential treatment of foreigners – in contrast to the treatment of Germans by foreigners 38, 632

Index of Subjects Skirmish with Mencke concerning David Gregory (1697) – Gregory’s belated solution of the catenary problem – in the Philosophical Transactions (August 1697), and in the Acta Eruditorum (July 1698) 36, 38, 46, 629f., 632–634, 749 Leibniz’s (anonymous) criticism (February 1699) and Gregory’s reply in the Philosophical Transactions (December 1699), and Acta Eruditorum (July 1700) 38, 46, 633, 749 Accusations of censorship against Gregory – Leibniz’s call (January 1701) for Gregory to obtain Newton’s approval – repercussions for the priority dispute 38, 632–634 Fatio’s and Wallis’ accusatory publications of 1699 Fatio’s belated solution of the brachistochrone problem – his apparent desire for recognition and feeling of having been excluded in the announcement of the problem – his rejection of mathematical challenge problems – his allegation of plagiarism against Leibniz and his insistence on Newton’s priority 44–46, 746–749 Derivations of the problem of the solid of revolution of least resistance (Fatio and Joh. Bernoulli) 45–47, 746f., 751f. Wallis’ publication of the Leibniz-Newton correspondence (1676) – ContinentalEuropean support for Leibniz in the competition of methods – supporters like Joh. Bernoulli, L’Hospital, Varignon 25, 29f., 40, 48, 519, 638f. Bernoulli’s view of Wallis as an overeager defender of English glory – his fear of the anger and wrath of Fatio and Wallis 47, 751

Index of Subjects Controversies and disputes (cont.) Leibniz’s two-track reaction to Fatio’s publication Complaint sent to the Royal Society (August 1699) – rejoinders in the Acta Eruditorum (November 1699) – defense of his standpoint (May 1700) – greeted by Joh. Bernoulli (June 1700) 46, 749–752 Wallis’ and Sloane’s condemnation of Fatio (September 1699) – Royal Society’s expression of veneration for Leibniz – Newton’s disapproval of Fatio’s attacks against Leibniz 46, 750, 753 Fatio’s reply to Bernoulli and Leibniz, sent to Mencke (1700) 47, 752 Leibniz’s replacement of the notation of the method of fluxions with that of the differential calculus in Fatio’s reply sent to Mencke 752 Rift in Joh. Bernoulli’s relationship with brother Jacob – Leibniz’s role as a mediator in this dispute – his criticism of Jacob’s behavior towards Johann 37f., 48, 631f. Swiss alliance of Jacob and Fatio directed against Leibniz – Jacob’s correspondence with Fatio (1700– 01) – complaints about a perceived hegemony of Leibniz – Fatio’s reports of English resentment against Leibniz 41, 44, 47, 639, 746, 752 Leibniz’s admission to the Académie des Sciences (1699) 48, 753 French criticism of the foundation of the Leibnizian calculus – powerful opponents alongside supporters at the Académie – Varignon’s role (together with L’Hospital) as defender of the differential calculus 14, 34, 43, 45, 48, 623f., 745, 747f., 753, 868 Rolle’s critique of the foundation of the calculus (1700) – expansion of the dispute (from 1701) 34, 48, 623, 753, 868

989 The Académie Commission set up to settle the conflict (1701) 48, 753 The Burnet diluvian controversy in Leibniz’s correspondence with Büssing (1696–1697) 228f., 583, 723–726, 897f. Ramazzini’s dispute with Schelhammer (1699–1700), about changes of mercury column levels with the weather 100, 776–778 Leibniz’s explanation of the phenomenon – quest for a solution of the problem based on demonstrations / proofs and on mechanical experiments 100, 777f. See also Experiments, Thought Experiments Papin’s high-pressure steam engine (1707–1708). See also Engines, Enginery – design approved by Leibniz, but rejected by Newton and Savery – Savery’s accusation of plagiarism against Papin 149f., 698, 801f. Dispute between animalculists and ovists (ovulists) in the theory of preformation – Leibniz’s meeting with Leeuwenhoek (November 1676) – his Correspondence with Leeuvenhoek (1715–1716) 128, 130, 234, 240f., 301, 379, 726f., 848f., 894 Cosmology. See also Astronomy, cosmological, cosmogenic theories Creation. See Religion Cryptography Cryptographic script or cipher code 173–177, 184, 315, 483–486, 713–715, 862 Concealment of information – encryption / decryption – encoding / codebreaking 174f., 177, 184, 225, 315, 483–486, 715, 840 Contemporary military conflicts – Siege of Montmélian (1691) 175, 486 Copology 174, 484f. Cryptanalysis 175f. Historical development of cryptography 174, 484

990 Cryptography (cont.) Early modern English cryptography 176 17th Century – proximity to algebra – Viète and Wallis 176, 713f. Theory and theoreticians – Practice and practitioners Bodenhausen’s secret-key encryption 225, 840 Wallis’ cryptographic knowledge – his opus on the ‘Art of deciphering’ (1653) – instruction of his grandson (Blencow) 176, 714f. Leibniz’s interest – his unsuccessful attempt to persuade Wallis to share his knowledge – Wallis’ refusal for political reasons – the need for secrecy in conducting state business – the need for royal approval 175, 713–715 Cryptography seen as a clouded pursuit – a method needing continual adaption 177, 715 Leibniz’s cipher machine 175 Steganography Haes’ tract ‘Steganographie nouvelle’ (1693) – his cipher code – its use in diplomatic communications – his system of encryption 173–175, 483–486 Steganology Haes’ technique for hiding / detecting information – use of alphabetical, numerical, and combinatorial tables 174, 484f. Watermarking 174 Curves. See Mathematics, Curves and Surfaces Deluge, diluvian. See Geology Demography, demographics – the science of populations – political arithmetic. See Economics, Political Economy Denmark, Danish xv, 2, 115, 152, 183, 200, 209, 227, 236, 262, 315, 327, 401, 731, 784 Copenhagen 97, 143, 152, 177, 183, 211, 213, 216, 245, 262, 298, 312, 315, 323, 336, 377, 400f., 410, 413, 734

Index of Subjects The Danish court / king 115, 152, 183, 236, 262, 315, 400, 731, 784 Ven, the Island of Ven 97, 298 Discoverers and innovators 132, 683 Disputes. See Controversies Dresden. See Saxony Dutch, Dutch republic. See Netherlands, Holland Dynamica. See Natural Philosophy Leibniz’s planned publication ‘Dynamica’– Bodenhausen’s role in the edition and publication – retrieval and return of Bodenhausen’s manuscripts (1698) – the role of M. G. Block  50–58, 81, 92, 103, 363–365, 375, 451, 453–456, 459, 525, 537, 736f. Dynamics 450, 525 Force in Leibniz’s dynamics. See Force Galilean law of falling bodies 36, 627, 869 Laws of dynamics – metaphysical foundation. See also Natural Philosophy Derivations of the (true) measure of force – a priori and a posteriori derivations 60, 526, 536f. Leibniz’s Descartes critique 54, 455 Reasoning in dynamics. See Reason, Reasoning Science of dynamics 50, 456 Dynasties House of Austria 6, 276 House of Brunswick-Lüneburg 174, 484. See also Hanover House of Este 12, 509 House of Welf (Guelf or Guelph) 7, 9f., 13, 226f., 307, 356, 419, 427f., 430, 499, 508, 566, 610, 618, 892 Dynastic history – Leibniz’s historiographical assignment – his projected ‘opus historicum’ – archival sources 7–13, 52, 356f., 430, 452f., 508f., 566, 618, 892 Earth history (pre-history). See also Geology Earth Sciences. See Geology

Index of Subjects Economics, Economic systems and theory  406, 591 Feudalism, serfdom and slavery 186, 320. See also Slave Trade Mercantilism, mercantile economics, economic policy 184, 191, 315, 406, 496 Mercantile economic projects (1690s). See Projects Mercantile trade / trading / trade wars. See Wars Cameralism, cameral sciences – a German variant of mercantilism – a ‘science’ of government, involving societal reform and economic development 188f., 407, 828 Leibniz’s mercantilist-cameralist conviction – seeking the advancement of German-style cameralism and public administration – having a good police regime with orderliness and supervision 188f., 407f., 828 Economic liberalism – in the guise of a ‘capitalist’ chemist in Hamburg (1699) 221, 833 Economic projects. See also Projects, Economic, Techno-Economic Projects Economic prosperity 184, 316, 328 Leibniz’s interest in economic or trade advancement – entrepreneurial involvement with or without princely or baronial participation 191, 497 Entrepreneurs, entrepreneurial activity 191, 194, 497, 508, 594, 801, 809, 888 Finance and commerce 187, 406 Leibniz’s calculations of interest and discount, of bonds and debentures 16, 187, 281, 406 Evaluation of life annuities and insurance 17, 187, 284, 406 His ‘Meditatio … de interusurio simplice’ (1683) – values of loans and repayment schedules – the method of compound interest (‘anatocismus’) 16, 187, 281, 407 His exchanges with Ferguson (1683–84)  187, 406f.

991 Government economic planning and administration – at state level in Hanover – at Imperial level in Vienna 189, 408 Leibniz’s advocacy (1688) of the establishment of an Imperial mining college or council – the establishment and coordination of the occurrence of mineral and ore deposits – with an associated laboratory and a chamber of arts, for the presentation of mechanical inventions and innovations 189, 408 Purpose of the Imperial mining institution – counteraction of imports of ores and minerals – colonization of regions of Hungary following the re-conquest (1683)  189, 408f. Economic utilization of chemical processes or substances – use as paints 190, 214, 337, 409, 888 Monetary systems – proposals for improvement – Leibniz’s collaboration with Crafft – joint memorandum for the emperor (1688) – discussions with Holeysen in Vienna (1690) 187, 189, 406f. Business ventures, undertakings, processes – cost effectiveness, economic feasibility – economic efficiency of the Hungarian mines – excerpts from Holeysen’s papers 9, 187f., 218, 358, 407, 418 Claims concerning gold extraction processes – discussions with Crafft (1688) – questions of cost-effectivity – costs of related ingredients 188, 208, 328, 407 Salt production processes (salt works) – cost-effective assessments of such ventures – brine, sole, and salina (concentrating house) – exchanges with Mohr (1686) and Heyn (1686– 87) 141, 147, 156, 188, 191, 394, 407, 497, 574, 590, 687, 700 Street illumination with oil lamps – exchanges with Crafft (1689–90) 407

992 Economics, Economic systems (cont.) Improvement of the system of coinage 191, 406, 579 Economic development of kiln technology – ore and glass smelting – glass working for optical equipment 158, 160, 191, 497, 591, 704, 808 Metal refinement or ennoblement – gold, silver and lead production 191, 497 Retort manufacture 158, 191, 497, 706 Pearl cleansing procedures 191, 497 Porcelain manufacture 191, 591 Oil production processes 191, 497 Increase of agricultural production – use of manures 191, 497 Development of silk production – growing of mulberry trees – rearing of silkworms 191, 408, 497 Drapery – clothes (fashion) – linen drapery production 185, 318, 408f., 590 Wallpaper manufacture 187, 191, 322, 590 Improvement of the wine and brandy trade 191, 496 Argument for measures against brandy / cognac imports – projected alternative to French brandy produced from wine 12, 191f., 194–196, 496, 508, 563, 591, 596, 716–718 A projected brandy manufactory at Münden (1693) 192, 591 Development of a new ferment at Hamburg (1693) 192, 591 Production of brandy from native sugar 192, 591 German domestic production of distillates 192, 591, 716 Processes used for distillates in Holland 192, 591 Projected use of sugar solutions – syrup or treacle 192, 195, 591, 596 Negotiations in Hamburg about the process 192, 591 The Leibniz / Crafft brandy project (1693–95) – conceived as economic retaliation against France and a

Index of Subjects French trade monopoly in foodstuffs and merchandising – intended to damage French foreign trade – inflicting long-term damage by means of trade wars – the legitimacy of such trade wars – also in times of peace 12, 192–196, 508, 591–596, 716–718 Contract for the formation of a company – signatories Leibniz and Crafft (1694) – proceeds intended partly for pious, and charitable purposes – for promotion of practical arts 12, 192, 194f., 508, 591, 594f., 716 Projected production of a brandy substitute – further idea of producing vinegar from the residue of the distillation process 192, 591 Intended location of production in England and / or Holland – preparations in Holland – Leibniz’s and Crafft’s journey to, and stay in Amsterdam (November 1694) 11, 192, 194, 196, 508, 591f., 716, 719 Final proposal sent to William III – call for the formation of a company enjoying royal privilege – with monopolist privileges and exclusion of French influence 12, 192, 194, 508, 591f., 594 Project intended to – increase the allies’ power, wealth – promote navigation, plantations – enable expansion in south America 194, 593f. Fate of the project – delays and final demise (1695) – attributed to adverse economic factors – including high sugar / syrup prices in Europe 195, 595f. Crafft’s new proposal (1696) – removal of the fusel oils from fruit and corn liquor by means of distillation with quicklime 195, 596 Crafft’s contact with Baron von Stauff – for Leibniz a dubious and unsavory character – his projected finance plan and continuation of the brandy project – located in Amsterdam

Index of Subjects Economics, Economic systems (cont.) or Vianen – his idea for the presentation of the plan to the ‘States General’ 195–197, 716–718, 720 Leibniz’s accusation of breach of contract – his refusal of any further financial support 196, 718f. Crafft’s fear of a ‘civil death’ (‘civiliter mortuus’) – of insult and humiliation – of his transfer to a charitable institution, a hospital, infirmary, or workhouse 717f. His demise, death and aftermath 195– 197, 718f. Leibniz’s judgement on Crafft – his talents as a chemist and technician – his inability to manage money – his quest for personal fortune and glory – his abhorrence of the pursuit of an ordinary profession – his indifference to the common good 197, 330, 720 Political economy 190, 497 Political arithmetic – the application of mathematics to economic-political matters – to economic welfare issues, and sustentation 191, 497f. English bills of mortality – Petty’s ‘Essays’ (1686–87), regarding the two cities (London, Paris) – their people, housing, hospitals, etc. 191, 498 Neumann’s empirical observations – his theological-political observations – baptismal and mortality registers (in Breslau) 498 Education. See also Projects, Higher Education Ehrenfriedersdorf. See Power, Water Power, Saxony Einbeck, and Sulbeck near Einbeck 141, 146, 394, 398 Elasticity. See Materials, Natural Philosophy, Physics Energy – Energy conversion, storage, transmission. See Power Engineering, engineers – the art of engineering 162, 488, 812 Chemical or process engineering. See Chemistry

993 Civil engineering (‘Civilbaukunst’) Sturm’s civil engineering (‘Der bürgerlichen=Bau=Kunst’) – design and construction of roads and bridges – water-supply and sanitation systems 156f., 702 Historical connection between civil and military engineering – connection between engineer and soldier – 17th-century attenuation of this link 156f., 701 Architecture and civil engineering – architects, civil engineers, master builders 120, 153, 156f., 161, 698, 701f., 808, 861 Mathematicians and engineers, including Goldmann (+1665), Lauterbach (+1694), and Sturm (+1719) 156f., 574, 701f. Sturm’s ambitions – as architect, draughtsman, master builder – as mathematics professor – as poet, preceptor and polymath – as designer of a castle of grief (‘castrum doloris’) 156, 702 Sturm as advocate of the art of civil engineering (‘Civil Bau-Kunst’) in letters to Leibniz (in 1697– 98) 156, 701 Gengenbach as architect – his drawings (1700) of a fortification model – of a pull-out or fold-out table – of an Italian andiron – of carriages and lanterns 161, 808 Engineering enterprises Papin’s contemplated (1696) new machines and inventions – difficulties in their realization 147, 157f., 688, 703f., 829 Leibniz’s own engineering discoveries – similar difficulties in their realization 147, 161, 688, 808 Papin’s petition (1696) for his release from the service of the landgrave of Hesse-Kassel – his desire to return to England – rejection

994 Engineering, engineers (cont.) of the application – granting of concessions (1697) 157f., 704f. Waterworks (in England, France, Saxony) 95, 140, 143, 297, 388, 390–394, 397f. Waterworks in garden design and architecture Garden design (1696) at the electoral gardens at Herrenhausen (Hanover) 153–156, 698–701, 813 Design of waterworks at Herrenhausen – including cascades, waterfalls, ornamental fountains 153f., 156, 698, 700 First contemplated scheme – erection of a vertical water wheel for raising water into a tank reservoir in a tower – intended for the supply of the fountains through pipes – Court decision (August 1696) for this scheme – intended construction on the river of a Persian or scoop wheel of 50-foot diameter – additional construction of a mill, to help offset costs 154f., 698, 700 Second contemplated scheme – erection of a water wheel on a river branch near Hanover’s ‘new town’ district – provision of a fountain water-supply – an additional urban water-supply, using a lengthy system of wooden pipes 154f., 698f. Third contemplated scheme (Leibniz’s preference) – construction of a canal passing through the electoral gardens – connecting two locations on the river – raising water into a tank in a tower – fountain watersupply from the tower – use of a hydraulic flume (on stands) 154f., 698–700 Additional canal benefits – navigation along the canal – creation of a waterway for gondolas between Hanover and

Index of Subjects Herrenhausen – supply of water mills along the course – hydraulics works kept off the main river – no impairment of shipping traffic – reduced exposure to seasonal dangers like river currents and ice formation 154f., 699f. Urban water supply Leibniz’s urban water-supply scheme – establishment of a ‘water-supply network’ 154, 698 Medieval / early modern supply systems – in London and in central and eastern European cities (networking) 154 Thoughts of Leibniz and Du Mont regarding protective measures against flooding – excavation works to build a dike, making use of the excavated earth 154f., 699 Canal construction and navigation – costs / cost factors – cladding of the canal sides – prevention of erosion – protection of the canal and gardens 155, 699 Maintenance of the canal water level – regulation of water flow – building of canal locks – building of cascades 154–156, 699f. Draining of the canal for repair and maintenance works 154, 699 Regulation of the water quantity – for the operation of a water wheel – the water supply for the fountains 154f, 698f. Concrete measures for the waterworks (May 1697) – Linsen’s services offered – his tests of a piston for a water pump 156, 700f. Urban power sources and supply Wind, water, horse power – windmills, water mills / fluvial water mills – horse mills 153f., 572f., 699 Flour mills – envisaged use of watermills by bakers / bakeries – in Amsterdam and other Dutch towns 153, 572f.

Index of Subjects Engineering, engineers (cont.) Water power – pumped storage in elevated reservoirs – reserve supply for watermills 153, 572, 862 Pump forms – circular crosssection (standard) – four-sided (rectangular) section – pump with pyramidal form 153, 571–573 Leibniz’s experiment (1696) – with a quadrangular cross- section pump – its length, width, stroke length 153, 573 Military engineering and engines 3, 151, 157, 399, 574f., 701f. Military architecture – battles, sieges / besiegement 175, 189, 408, 486, 575f. Military academies. See Projects, Scientific and Educational Sturm’s military engineering (‘Der Kriegs=Bau=Kunst’) 157, 702 Ballistae – military engines 151–153, 399–402, 574–578 Cannons, guns, muskets – improvement in the production of canons 5, 152, 273, 323, 399, 577, 809 See also: Metallurgy, Metallurgical Processes Military engineers 150, 153, 156, 496, 698, 802 Military innovations Military bridge tested by the duke of Celle (1683/84) 152, 401 Danish artillery (1683–1687) – military technologies in Copenhagen – howitzers – grenade or artillery shell launchers – Brandshagen’s mortar bombs 152f., 177f., 213, 324, 401, 411 Iron and steel production for military purposes Mass production of steel in Saxony (1686/87) – smelting furnace 153, 402 Damascene steel – production of quality steel since medieval times – of interest at the Danish

995 court (1683/84) – production of damascene blades in Saxony (1687) 401f., 152f. Other military innovations in Saxon production – copper coatings for canon muzzles – grenade throwers – halberds – light armor 153, 402 Danish artillery (1683–1687) – military technologies in Copenhagen – howitzers – grenade or artillery shell launchers 152f., 401 Dutch military technologies – arsenal in Delft – planned demonstration of a repeating firearm at Rijswijk (1694) – subsequent demonstration in Amsterdam 576f. French ballistic mortars – trial of such mortars 152, 401 Fortification – fortification systems, principles, techniques – Teyler’s tract concerning fortification (1679) – fire power / fusillades – fortification arrays 150, 161, 574–576, 802, 808, 882, 894 Fortifications of the town of Breda (1683) – employment of a windpowered water elevator 142, 395–397, 894 The ‘slang-molen’ – a water screw (Archimedean screw) – a rotating wooden spiral, like a helical staircase 142, 395f. The ‘ketting-molen’ – a chain elevator system (or chain mill) – a system of troughs attached to the chain 142, 395f. Fortification works at Neuf-Brisach (Neu-Breisack) – Vauban’s process for transporting earth (1699– 1703) – power sources: manpower and horsepower – drawing / sketch sent by Leibniz to Papin  150f., 802 Comparable works (‘Gazette d’Amsterdam’, 1700) – a machine for transporting a large quantity of sand 151, 802

996 Engineering, engineers (cont.) Mining engineering. See also Mining, Mining engineers Science of engineering – Engineering science 3, 163, 402, 407 Hydromechanics 163, 402, 474, 476f., 882 Hydrodynamics – Torricelli’s efflux law 165, 167, 405, 477, 481, 883 Hydrostatics – hydrostatic pressure – Archimedes principle 164–167, 180, 299, 403, 475–481, 491, 883 Hydraulics (applications of hydromechanics) Engineering hydraulics before Leibniz – Castelli’s continuity law (1628) 164, 403 Vertical velocity distribution in a stream – Castelli’s postulated linear distribution (1660) – increase from the river bed to the surface 164, 403–405, 477, 882 Engineering hydraulics in Leibniz’s time – hydraulic engineer Cornelis Meyer – structure built in the river Tiber (before 1678) – earth wall, levee or dam – Meyer’s tract on fluvial navigation (1683) 164f., 404 Mechanics of fluids (Fluid mechanics) Fundamental laws of fluid mechanics – quest for an exact rule to supersede Castelli’s – Leibniz’s skepticism (1690) 163–165, 403, 405, 882f. Studies of fluid motion in open channels 164–166, 403, 476f., 882f. Consideration of the flow of water around an obstacle in a stream – question of the velocity change downstream from the obstacle – Leibniz’s expectation of a negligible change 164f., 403f. Ramazzini’s experimental investigation (1689–90) – his ‘Tractatus physico-hydrostaticus’ on the springs / wells of Modena (1691) 163–165, 402f., 474–476

Index of Subjects Ground (Geological) structure – ground pressures / temperatures – barometric / thermometric levels 99, 475f., 775 Ground water – water containment – water flows 475 Ascent of waters – artesian aquifers / wells – spring sources / origins  99, 163–165, 403, 474f., 775f. Medical considerations – sources of pure water – water contamination / pollution 475, 501f. Boccabadati’s investigation of fluvial mechanics – based on practical experience in the floodplain near Modena – his observations and measurements (1690) along the Po tributaries Panaro (Scultenna) and Secchia (Gabellus) 164f., 403–405 Guglielmini’s investigation (1689–90) putting the laws of fluid flow on a new foundation – fundamental questions in open-channel flow 164, 167, 403, 476f., 481, 882f. Considerations of canals / channels / flumes – of channel slope – of inclination of the water surface – of water pressure – of upper and lower layers 165–167, 476, 479, 481, 532, 872, 883 Guglielmini’s mathematical considerations – involving only proportions of homogeneous magnitudes – physical entities like gravitation and resistance (friction) not considered 476f. Guglielmini’s work on the measure of flowing waters (1690–91) 480 Leibniz’s reception of the work – his review of the basic tenets – of the postulated parabolic velocity increase from the water surface to the channel bed 165–167, 405f., 477, 481, 883 Laws of fluid flow based on the fall (hydraulic head) of the channel – the slope or inclination of the water surface – the pressure of the water 167, 476f., 481, 883

Index of Subjects Engineering, engineers (cont.) Essentially an abstract mathematical approach – with gravitation and resistance forces not considered 167, 481, 883 The ‘scala fallacy’– based on a false assumption of the applicability of Torricelli’s efflux law in openchannel flow 165, 405, 883 Leibniz’s conclusion of the invalidity of the postulated velocity distribution in real rivers and canals 165f., 403, 406, 477, 883f. Papin’s investigation (1690) of the ‘Wurtemberg Siphon’ – his comparison of the efflux / effluent from an inclined water pipe at the side with that through an orifice in the bottom of a cylindrical container – under the same conditions, with equal cross-sectional areas of the pipe and orifice – the same hydraulic head 178, 478, 487, 886 Papin’s critique (1691) of Guglielmini’s work on fluid flow in open channels – of his fundamental theorem – of his postulated parabolic velocity increase 165– 167, 405, 477, 481, 883 Guglielmini’s réplique (1692) in his ‘Epistolae duae hydrostaticae’ and the ‘Miscellanea Italica physicomathematica’ 166, 478–480, 883 His treatment of Galileo’s laws of falling bodies – of their validity / invalidity in fluid flow – of fluvial flows in layers and the mutual influence of lower and upper layers – of fluid efflux velocities out of orifices, or openings in a cylindrical container – out of a pipe in the side wall or an orifice in the bottom 166f., 476–479, 481f., 883 Papin’s more detailed criticism (1695) – his consideration of analogies and differences between solid bodies and fluids 166, 479f.

997 Guglielmini’s reply to Papin’s criticism (1697) – his postulated parabolic velocity increase, from the water surface to the canal bed – based on Torricelli’s efflux law 165, 167, 405, 477, 481, 883 His consideration of the general applicability of the law to openchannel water flow over both horizontal and inclined canal beds – the general validity of Galileo’s laws of falling bodies in fluvial mechanics 167, 481, 883 His physical-mathematical tract on fluvial flows (1697) reflecting – both conditions in real rivers and canals and engineering practice – not mathematical abstraction 167, 481–483, 884 Issues / parameters of hydraulics / fluvial mechanics (1689–97) Laws of fluid flow – fall or hydraulic head of a channel – slope or inclination of the water surface, channel bed – pressure of the water – gravitation forces – resistance forces 164f., 167, 403, 405, 476f., 481, 882f. Curl or vorticity flows 167, 482 Streamlines – theory of streamlines – hydraulic grade lines – hydraulic / piezometric head variation 163, 402, 476 Engines, enginery. See also Machines, machinery, mechanization Combustion / explosion engines Combustion 160, 182, 212, 246, 413, 585, 710, 805, 850, 862, 878, 880 Explosion 94, 109f., 374, 543–546, 690, 862, 876, 878, 880 Explosion theory of gravity. See Physics Gunpowder (explosion) engine – promptitude of the explosion – receptacle or cylinder – its lack of elastic play – danger of bursting / rupture – comparison of explosion and steam engines 146f., 690, 695, 862, 878, 880f.

998 Engines, enginery (cont.) Papin’s experimental results – revealing that the effect of gunpowder increases with the resistance to be overcome 148, 695, 881 Further research required regarding – the exploding gunpowder conglomerate – the means to control its expansion 148, 695, 881 Papin’s view that with further development the effect produced by a pound of water might exceed that of a pound of gunpowder 148, 693 Engines to power a vehicle and facilitate transport. See Transport Military engines. See Engineering, Military Engineering Mining engines. See also Mining Pneumatic Engine (Vacuum Pump). See Instruments Leibniz’s idea of a vacuum or pneumatic extractor 92, 421 Pneumatic engines or machines Leibniz’s idea of a pneumatic engine to power a vehicle and facilitate transport 148, 881 His idea of a means of the – improvement of the contact between a piston and pump cylinder – making airtight or sealing the contact 148, 691f. His idea of using mercury – similar to the use of water with wooden pumps in the corrosive environment of the Harz mines 148, 692 The air pressure inside the cylinder – arising from the expansion / dilation of water vapor – to be balanced by the mercury 148, 692 Components / parameters involved – the height / length of the Cylinder – the stroke of the piston 149, 692, 697 Mercury lubrication / sealing – reduction of friction losses 148, 691f. Papin’s doubts about the functionality of Leibniz’s pump-lubrication /sealing idea with mercury – with considerable resistance losses anticipated from the

Index of Subjects alternating movement of the three interlaced tubes 148, 694f. Leibniz’s understanding of the resistance effects in relation to pump performance – dependent on the length of the pump cylinder (or the stroke of the piston), the cylinder (or piston) diameter, and the square of the diameter 149, 697 Papin’s steam digester (1679–82) – his ‘engine for softening bones’ (1681) – culinary applications / uses 243f., 348f. Other applications considered. See Medicine, Diseases Steam engines and pumps – superiority over a pneumatic engine: Papin’s experimental test – providing knowledge of the variation of the internal force of the air with heat and time 147f., 690f. His steam pump – for raising water from a depth by the power of steam – capability to pump water only to a height of 70 feet 148, 693 His principle of the atmospheric steam engine (1690) – atmospheric pressure from the condensation of steam 147, 688 His experiments (1698) using the principle of the dilation / expansion of steam – principle of rarefaction more effective than atmospheric pressure accompanying condensation – use of both suction and compressive effects 147, 688f. Agreement with Leibniz regarding Papin’s result that a small increase in the degree of heat leads to a greater effect 148, 693 Leibniz’s explanation of the connection between the strength of the expansion force and the height attained in lifting a body – an adiabatic expansion process, with loss of force through cooling during the expansion of steam 149, 696

Index of Subjects Engines, enginery (cont.) Spirit-of-wine powered engines and pumps – a power source for a twostroke piston engine – a combustion or rarefaction stroke – a compression or condensation stroke 182, 585f., 878, 880 Possible use of spirit of wine as a fuel (1695) – Leibniz’s conjectures – Papin’s experiments 182, 585 Prohibitive costs of the fuel – use of water as a seal over the piston – imperfect impermeability of the engine to water and to the spirit of wine 182, 587 Savery’s steam pump – patent granted by the English Parliament – his tract ‘The miners friend’ (1702) 149f., 698, 801f. Leibniz’s indirect correspondence with Savery (1704) – Savery’s invitation to Hanover 149f., 801 Papin’s high-pressure steam engine – his treatise on the design of the engine (1707) 150, 698 Papin’s design approved by Leibniz – rejected by Newton and Savery – Savery’s plagiarism claims 150 Other applications besides the raising of water – propulsion using steam power. See Transport Expansion of steam like the power of gunpowder – Leibniz’s penchant for gunpowder explosivity. See Power, Gunpowder Expansion of other liquors or vapors – advantages of water vapor or steam – it being less explosive than gunpowder – water being readily available everywhere 147f., 686, 690 England Anglo-Saxon Settlement 231, 841 Cambridge 2f., 119, 795 Cornwall. See also Mining Truro 387 English crown – King’s council / court – Hanoverian accession, succession, court, etc. 4f., 9, 11, 13, 108, 169, 174–176, 199, 232, 271, 274, 313, 428, 484, 486, 508, 540, 715, 737, 790

999 English advances in science and technology 201, 499 English mathematics and mathematicians 11, 28f., 175, 500, 508, 517, 519, 522, 753, 793 English mining, mining engineers – including Kir(c)kby in Saxony 139, 201, 387, 499 English parliament 149, 790, 801 English physicians 90, 201, 247, 258, 265, 292, 350, 499, 738 Great plague of London (1665–66) 225 London Pall Mall 288 Royal mint – Newton’s appointment as warden (1696) 522 Royal Society of London. See Projects, Academies St. James’s palace 89, 289 Whitehall – Garden of Whitehall 580 Overseas Territories – Saint Helena island 782, 794 Oxford 40, 103, 117, 430, 633, 639, 788 Revolution of 1688–1689 192f. Enlightenment xivf., 142, 159f., 774, 885, 888. See also Knowledge Epidemiology. See Medicine Erfurth 224, 838 Ethics xi, xiii, 205, 744, 820 Ethiopia, Ethiopian 285 Ethnography, Etymology. See Peoples and Languages Ethology and animal behavior. See Biology, Zoology Europe, European Continental European rivers – Danube – Leine – Rhine – Rhine-Meuse-Scheldt delta – Po and tributaries Panaro and Secchia 154, 164f., 403, 414, 5016, 663, 698 Evolution. See Biology, and also People and Languages Experiments, experimentation, experimental approach Enlightening experiments (‘experimenta lucifera’) – enriching experiments (‘experimenta lucrifera’) 208, 222, 835, 887f.

1000 Experiments, experimentation (cont.) Experimental approach to complement reason – practical experience or experiment 50, 61, 74, 668, 523, 527, 863, 870 Experimentalist von Guericke – Schott’s ‘Mechanica hydraulico-pneumatica’ (1657) – von Guericke’s ‘New Magdeburg experiments’ (1672) 90, 290f., 293 Experimentalist Boyle – pioneer of the modern experimental method – his experiments measuring the weight and elasticity and (spring) of air – his ‘New experiments physicomechanicall’ (1660) 90, 101, 219f., 291, 780 Real experiments – accumulation of experimental data 88, 288 Engineering experiments – Leibniz’s experiment (1696) with a pump assembly having a quadrangular cross section 153, 573 Newton’s optical experiments. See also Physics, Optics Spectacular experiments – luminescence and refulgence 205, 821f. Light-emitting devices – based on different illuminant or luminescence phenomena 205, 821f. ‘Mechanoluminescence’ – resulting from mechanical action on a solid – sparkle produced using hard sugar 205, 822 Luminescent objects or curiosa – based on Joh. Bernoulli’s demonstration (1700) of glowing mercury vessels (following shaking) 205, 821f. Luminescent insignia – scepters, crowns, and a luminous showcase (‘museolum’) 205, 821 A luminous vial sent by Joh. Bernoulli – his ‘perpetual phosphorus vial’– presented by Leibniz at the Berlin court (1701) 205, 821 Hoffmann’s recipe (1701) for a fiery spirit (‘spiritus igneus’) – presented by Leibniz to the royal family 205f., 822 Thought experiments – pure-thought assumptions 59, 460, 871

Index of Subjects Engineering thought experiments Leibniz’s engineering thought experiment – with force as the product of mass and velocity squared 531f. Weights at the circumference of a horizontal wheel over a stream – powered by an undershot vertical water wheel in the stream – with cog-heel, lantern-pinion gear mechanism 62f., 529–534, 871f. Consideration of – breadth and cross section of the stream – stream depth and inclination or surface area of the radial vanes – specific gravity of the water or other fluid 62f., 532, 872 Model of water consisting of balls or globules 63, 533 Physical / Mechanical thought experiments Papin’s thought experiment – with force as the product of mass and velocity 62f., 532 Weights at the circumference of a horizontal wheel – rotation of the weights powered by falling weights – with rope, pulley (cylindrical drum) transmission 62, 529f. 534, 871f. Variation of the horizontal wheel drive – of the horizontal wheel diameter – of the velocity of the weights carried 63, 534f., 871f. Thought experiments on percussion and elastic spring – on the very nature of percussion and elastic spring – on resilience of elastic spring 59f., 66, 68, 70f., 461, 647, 649, 654, 660f., 872 Physical effects considered where absorbed force is ceded again 647 Substitution and surrogacy. See also Natural Philosophy Papin’s thought experiment (1696) involving the collision of a larger with a smaller body, with an intervening spring – the smaller body is replaced at zero velocity by a much larger surrogate body – the surrogate body absorbs the impact of the larger body,

Index of Subjects Experiments, experimentation (cont.) and the elastic resilience, or recoil of the spring – alleged loss of force following the collision – no total transferability of force – violation of the law of conservation of ‘vis viva’ 67, 651, 872 Leibniz’s interpretation of Papin’s thought experiment – replacement only admissible if the force lodged in the inner spring of the body’s particles be transferred to the surrogate body – complete transfer theoretically possible from a larger to a smaller body 67, 651, 872 Capability of a smaller body of arresting / reversing a larger body 67, 651f., 872 Capability of a smaller body of carrying off a larger body – where the latter is moving more slowly and precedes the former – without loss of velocity 81, 84, 763, 768 Discussion of the mechanism of substitution – practical execution of a substitution – assumption of an (almost) perfect hardness with a total transfer (almost) of force to the spring 67–70, 459f., 651–659 Impact of recoil possibly not central / off-center – resulting in a possible rotation of the body – diminution of resistive potential 68, 652f. Papin’s thought experiments (1697) to demonstrate gain / loss of force in substitutions – equivalence / non-equivalence of a substitution and separate collisions of the bodies involved 68–70, 79, 652–659 Upholding / violation of the conservation of force requirement 69, 657 Leibniz’s explanation of the substitution process based on a ‘vis viva’ 67f., 70, 651, 653, 658 Papin’s explanation of the process based on a ‘vis mortua’ 67, 70, 651, 658f. The dead force concept to establish which bodies bring each other to a standstill 71, 658, 661, 664, 761

1001 The living force concept to establish which bodies produce the same absolute effect 67, 650, 658f., 661 Central points of Leibniz’s interpretation (Dec. 1697) – bodies of different magnitude might have the same quantity of force – a substitution is possible so that the quantity of force of the bodies is conserved 70, 659 Leibniz’s thought experiment (Dec. 1697) about the collision of a body against two other bodies – the first body is then replaced by a wall – each of the other two bodies impacts a side of a spring, whose other side is attached to the wall 70, 660 Each of the other bodies is stopped by the wall even though they have unequal forces – according to Leibniz’s definition of absolute / living force 70, 660 Two-body / three-body collision thought experiments – colliding spheres or balls – instantaneous or momentary collisions – total transfer of the quantity of motion – conservation of the quantity of motion – sum of the quantities of motion 66f., 71–73, 77, 80–85, 648–658, 663–666, 761–770, 872, 874 Head-on collision of two bodies – the larger body (at rest) and the smaller body (in motion) – an apparent contrariety where the smaller body could carry off the larger one 84, 768 Two-body collisions of ‘stronger’ and ‘weaker’– possible linguistic paradoxes 70, 661 Leibniz’s definition of ‘stronger’ and ‘weaker’– the ‘weaker’ yields to the ‘stronger’ – the stronger might be forced into reverse while the weaker continues along its path 70, 659, 661 Collision of two bodies with velocities inversely proportional to their masses – resulting reversal of the motions 66, 649

1002 Experiments, experimentation (cont.) Oblique / diagonal / slanting impact of three bodies – simultaneous or separate impacts of the three bodies – skew angle of inclination of path – change in the direction of oblique impact – oblique impact of a body against two others at rest 64, 66, 73f., 81, 536, 648, 664, 666f., 669, 764, 873 Velocities of the colliding bodies are represented by the sides or diagonal of a square – following the diagonal collision, the first and second bodies move off along the extended sides of the square – the third body comes to rest at the corner – impact with partial or total force transfer 72–74, 78–81, 84f., 655f., 664f., 668f., 757, 759, 761f., 763, 768, 770, 873 Experiment in reverse – the first and second bodies come to rest at the corner – the third moves back along the diagonal 72–74, 664, 667f., 873 Leibniz’s and Papin’s different interpretations of the diagonal collision 65f., 68, 70–73, 79, 81, 652, 658f., 661f., 664, 759, 873f. Papin’s consideration of the resistance encountered in collisions (November 1698) 74, 668 Leibniz’s idea of geometricallycompounded resistances – resolution into components possible (November 1698) 74, 668f. Papin’s consideration of obliquity/ skewness in collisions (December 1698) 74, 669 Leibniz’s idea of a replacement of spheres by long thin cylinders (July 1699) – rejected by Papin 84f., 768, 770, 874 Papin’s explanation of the three-sphere oblique-collision experiment – separate versus simultaneous collisions with the latter impacts being shorter and less forceful – example of a non-simultaneous impact of two elastic spheres against an identical third sphere – one encounters a chord

Index of Subjects rather than a diameter of the third sphere 69, 73, 79, 657f., 667, 759f., 873 Papin’s understanding that there is no total force transfer in the collisions – the striking bodies do not come to rest, but continue in their paths following impact 73, 667 His position opposed to that of Leibniz’s assumption (March 1699) of a perfect hardness – and of an instantaneous collision of the three balls 79f., 759–761 His insistence the total transfer (and conservation) of the quantity of motion, would of necessity result in a ‘perpetuum mobile’ 80, 761f. His view (April 1699) that even assuming a perfect hardness, the sum total of the quantities of motion would, following the collision, be less than before 81, 762 Location and Time – alterations of location and time 77, 681f. Papin’s thought experiment (January 1698) about a two-body collision – as seen by two observers at two different locations in space – firstly, at an air-free and gravity-free location, where equal quantities of motion are observed, and where equal forces are likewise observed – secondly, at a location where a hailstorm is raging – the hail particles are unimaginably small and their velocity is extraordinarily large – the bodies are of equal magnitude, and move against the hail stream before losing their movements and falling back – the traversed distances are found not to be proportional to their quantities of motion – doubling the quantity of motion results in a quadrupling of the traversed distance – for the first observer (Papin) the hailstorm accounts for the result – the second observer (Leibniz) has to introduce a new force to explain the outcome 71f., 662f.

Index of Subjects Experiments, experimentation (cont.) Leibniz’s reply (January 1698) – his interjection on ‘camp thinking’ – his view of Papin’s interpretation as resulting of necessity in a ‘perpetuum mobile’ – with an infringement of the principle of the equality of cause and effect 72, 663f. Leibniz’s own thought experiment – based on the law of ‘vis mortua’ and rules for the composition of movements – his interpretation applicable both in terrestrial gravity, and in a space devoid of gravitational force – his assessment of Papin’s ‘hailstorm’, as being relevant in relation to the quantity of motion – and involving a loss of movement during the ascent, and gain during the descent 72f., 664–666 Ideas of an ultimate decisive physical experiment to settle the controversy between Papin and Leibniz – Papin’s idea of such a physical experiment (August 1698) – Leibniz’s call for an experimental decision (September 1698) – thus an experimental proof to compliment reason – reference to previous agreement of reason and experiment – Papin’s retraction of the experimental option (October 1698) – decision to revert to reason 61f., 73f., 527f., 666–668, 871, 873 Leibniz’s physical thought experiment (March 1700) to explain mercury column changes with the weather. See Instruments, Barometer Leibniz’s and Joh. Bernoulli’s thought experiments – thought and physical models for water and air (1699– 1700) 101f., 781f. Florence. See Italy Force. See Natural Philosophy, Physics France Avignon 324f. Cayenne (French Guiana) 197, 324

1003 Dijon 324f. La Rochelle 236, 732 Neuf Brisach en Alsace (Neu-Breisack)  150, 802 Paris – Académie des Sciences. See Projects, Scientific, Educational Projects Observatoire de Paris 381 River Seine 397f. Saint Germain 397 Versailles 165, 266, 397f. Frankfurt am Main – Location of the German diplomatic conference on reunifications 97, 184, 198, 298, 316, 325, 381 Frankfurt an der Oder 156, 204, 702, 818 Furnaces, forges and kilns Experiments / investigations with melting furnaces Leibniz’s first experiments with melting furnaces – his cooperation with Brand (Summer 1679) in the investigation of phosphorus 159, 707 Investigations with ovens built by Johann Daniel Crafft 159, 707 Papin’s glass-kiln development (1697– 98) 158, 704 His improvement of a newly-developed oven – glass melting process using the ‘Hesse pump’ – scaled-down process and envisaged large-scale version – construction of a laboratory and of a new oven 158f., 704f., 706f. Papin’s series of experiments – his new melting furnace intended solely for the production of iron retorts or alembics – use of an improved centrifugal (Hesse) pump 157f., 706 Leibniz’s view of the importance of glass melting for optics – and the production of polished sheet or mirror glass 158f., 704, 706–708 Tschirnhaus’ laboratory for precious stones (1700) – his grindery or grinding shop for precious stones and jewels – his private laboratory on his estate in Kieslingswalde 160f., 806, 808 Blast, cementation and reverberatory / reverberation furnaces

1004 Furnaces, forges and kilns (cont.) Late 17th / 18th century innovations – used for tempering and annealing bar or rod iron 160, 805f. China or porcelain ovens – also for glass ovens in manufactories 160, 806 Leibniz’s views on engineering innovations in general – the difficulties in realization and implementation – the necessity of large-scale trials to counter a widespread skepticism towards innovations 161, 808 Blast furnaces Papin’s new blast furnace – description and drawing (October 1698) – showing air passage above and below burning fuel (wood), using a centrifugal (Hesse) pump 158f., 706–708 Blast and suck operation by means of a ventilator pump – blast and suction air regulation – blowing flames to the melting crucible – use of a smokestack with suction effect – height-limit of the smokestack (2 feet) 158, 706f. Blast and suction air regulation – simultaneous drawing of flames to the crucible 158, 706f. Heat impact of the fire – use of a heating plate for extraction of glass melt through an opening in the upper oven wall 158f., 707 Glass melt from the furnace – suitable for the production of mirrors, window glass, hollow cylinders, iron products 158, 707 Leibniz’s thoughts regarding the process of glass melting – his assessment of Papin’s innovation 159, 707 Control / regulation of fire intensity attained – possible alternatives or improvements – the use of ordinary bellows – abandonment of a special extraction plate – melting operations possible on such a plate – desideratum of rendering superfluous the polishing of plates, over which the molten glass was spread 159, 707–709

Index of Subjects Leibniz’s doubts about the novelty of Papin’s plates – Papin’s belief in the superiority of his furnace method – based on his observations (in 1681) on the island of Murano (near Venice) – involving the moving of a large stone into an oven – the spreading out of molten glass over the stone using iron spatulas (or palette-knives) – the removal using a draw-plate or drawing die 159, 708f. Papin’s own corresponding method (of 1698) for the production of plate or mirror glass – with molten glass being drawn onto oven plates 159, 707f. His key innovation regarding the heating flame – its passage both above and below the molten material 159, 707f. Reverberation furnaces – contact specifications for processing ores – contact with the fuel prohibited – contact with combustion gases allowed 160, 805 Example of copper smelting at the Falun mine, Sweden – involvement of foreign smelters and chemists 159f., 804f. Levanto and his smelting process – essentially a process for roasting or calcination in a roasting oven or calcination furnace – fueled with wood (twigs or branches) – the production of roasted blende by calcination, and subsequent melting in an air furnace 159–161, 804–806 Failed trials of the process, by both Levanto and Kunckel von Löwenstern 160f., 804–806, 808 Leibniz’s proposal for operation of the two furnaces (1699) – with a gradual powering-up of the air furnace, but dependent on the consistency of the material 160, 806 Galenism, Galenist 252, 741. See also Medicine Gardens. See Engineering, Garden Design and Architecture

Index of Subjects Geography, geographers 231 Cartography, cartographers 10, 430 Geographical explorations of the coasts of the North Sea and the Baltic Sea – reported to Wallis (1699) 229f., 840f. Orient, orientalism, orientalists 10, 208, 231, 430, 811f., 827 Geology, geologists xv, 227 Geological and earth science – geological research and studies – geological, geomorphological, cosmological, and cosmogenic theorizing xiv, 226f., 229f., 277, 344f., 419f., 475, 840, 862, 891f. Geological, geomorphological theories Earth history/ historiography – history and form of the earth 235, 723f. Leibniz’s ideas on earth history – origin and history of the earth – his posthumously-published ‘Protogaea’ 164, 227, 229, 419f., 475, 723, 725, 892 Burnet’s ‘Telluris theoria sacra’ (1681/89) – his ‘Doctrina antiqua de rerum originibus’ (1692) 228, 724f., 897 Büssing’s critique of Burnet’s earth history – a kind of literary history (Büssing’s view) 725, 897 Büssing’s ‘Dissertatio AntiBurnetiana’(1695) 228, 724, 897 Whiston’s ‘New theory of the earth’ (1696) – his postulated role of comets in earth history – his opposition to Burnet’s new theory of the earth 228f., 725, 897 Deluge – the deluge in earth history – Biblical narrative and interpretations – questions of its historical veracity xiv, 229, 726, 898 The Burnet controversy – explanatory models of the deluge – Burnet’s account – Büssing’s scenario 229, 725f., 898 Leibniz’s skeptical view 229, 726 Antediluvian form of the earth – upsurge of subterranean waters 229, 726

1005 Postdiluvian form of the earth – subsidence / settlement of the surface – possible fissures in the crust – possible return of flood waters into subterranean cavities 229, 726, 898 Temporal changes of the earth’s surface 229f., 840f. Geological formation history of coastlines 230, 840f. Leibniz’s interest in the geological formation history of the English channel – intended as a means of establishing temporal changes of the earth’s surface 230, 840f. Geographical / geological interpretations of mythology – Odysseus’ supposed journey in northern Europe – Rudbeck’s hypotheses and rejoinders (1699) 230, 841, 898 Explorations of European coasts – of the North sea and Baltic sea (1699) 229f., 840f. Questions of the geological configuration of the European Atlantic coastline – the coasts near Calais and Dover (1701) 230, 840f. Pre-history/ pre-historical finds – Leibniz’s discovery of fish fossils in shale (1683) 227, 419, 891 His studies / views concerning earth history (1684) – on the formation of rocks and minerals (mineralogenesis) – on subterranean formation of minerals by fire – attributed to spirits trapped in the mines 227f., 420f., 892f. His deviant views to Agricola, Descartes, Steno 227, 420, 892 His critique of Descartes – of the his lack of practical experience in mines – his obsession with written sources 228, 421, 892 Mineral ores from the Ilmenau mines (Heyn, 1690) – shale and limestone with fossilized plants 228, 421, 891

1006 Geology, geologists (cont.) Leibniz’s history of the house of Welf – the geological history of the Welf territories – the natural history of the Harz district 226f., 419, 892 His interest in the cave ‘Baumannshöhle’ (1687) 227, 419, 892 Tentzel’s report on mammoth fossils (1696) – found at Gräfentonna (or Tonna) – having been changed into mineral stone in the wet sand 235, 239, 729f., 846. See also Biology, Zoology Mineralogy, minerals. See also Chemistry Magnetic minerals – Lodestone 549 Mineral crystals / Crystalline materials Amber 211, 226, 334f., 344, 582f., 891 Asbestos mineral 127, 561 Iceland crystal / Iceland spar 121f., 124f., 376f., 468, 554, 556f. Jasper (variety of quartz) 806f. Porcelain (ceramic material) 127, 160, 191, 561, 591, 806 Talc / Talcum (mineral) 127, 416, 561 Mineralogical research / studies 226, 344, 891 Mineral ores – formation of rocks 226f., 343, 420, 891f. Origin and formation of minerals (mineralogenesis) – formation of ore deposits (in mines) 226–228, 343, 420, 891f. Processing procedures for ores 226, 344f., 891 Ores from regions of geological interest – in East India, the Harz mountains, Muscau (near Görlitz, Saxony), regions in Poland 226, 892 Paleontology 225, 342, 419, 723, 840 Fossils – fossils found in mines – animal / body fossils – fish fossils 226f., 231, 419, 730, 891

Index of Subjects Catalog of British fossils (Lhuyd, 1699) 231, 841 Queries about the origin of an amber deposit (1680) 226, 344, 891 About fossilization specimens in Mansfeld slate (1681) 226, 344, 891 About a goldmine on Sumatra (1681–82) 226, 344, 891 Geometry. See Mathematics Germany, German nation – prejudice aginst the Germans 90f., 292 German empire. See Holy Roman empire Integration / Unification 184, 316 Prosperity of Germany 184, 222f., 315f., 836 God, Divine Creator xivf., 48, 229, 726, 753f., 798, 898 Görlitz. See Saxony Gravity, gravitation. See Natural philosophy and physics Greece, Greek – classical mythology – the argonaut Zetes 224, 230, 621, 837, 841, 897 Habsburg dynasty 189, 408 Halberstadt 254, 855 Halle 198, 204f., 262, 325, 574, 605, 820 Leopoldina. See Projects, Scientific, Educational Projects Hamburg 10, 152, 185, 192, 200f., 209f., 221f., 228, 253, 271, 318, 328, 331f., 377, 401, 410, 428, 499, 591, 597, 645, 724f., 831, 833–835, 854, 890, 897 Hameln – the French émigré community 253, 698, 854 Hanau (Town in territory Hesse) 236, 732 Hanover ixf., xiii, xv, xvii, 2, 4–9, 11–13, 15, 17–19, 21, 25, 35, 52–54, 57, 87, 89, 102, 104f., 121, 128f., 134, 142f., 145f., 148–150, 153–156, 162, 165, 168f., 171, 173–175, 185, 187, 189, 192, 195, 197, 200, 202, 208–211, 213, 218f., 226f., 229, 242f., 250f., 253, 275, 278f., 287, 297, 301f., 312f., 322, 327–329, 331, 333, 344f., 347, 356, 358, 365, 367, 376, 395, 398f., 404, 408, 412, 416, 418, 428, 431, 437, 451, 454f., 477,

Index of Subjects Hanover (cont.) 485f., 508f., 562f., 581f., 583, 591, 695, 608, 626, 690, 700f., 786, 801, 853, 863, 880, 885f., 893 Hanoverian court / ducal / dynastic / electoral (1692–1806) 4, 5, 9, 108, 169, 174f., 199, 214, 216, 224, 232, 244, 261, 271–274, 290, 307, 313, 318, 330f., 339, 342, 359, 394, 428, 484, 486, 505, 508, 540, 563, 565, 567, 601, 610, 617, 698, 700f., 725, 737, 744, 775, 801, 839, 853, 897 Electoral gardens at Herrenhausen  153–156, 698–701, 813 Town of Hanover – its ‘new town’ district 154f., 698f. Location Linden, near Hanover 162, 812f. Location Wunstorf, near Hanover 226, 344, 891 Harburg (south of Hamburg) 185, 318 Harz mountains. See Mining Helmstedt – University of Helmstedt (‘Academia Julia’) 14, 92, 171, 201, 212, 216, 219, 235, 242f., 254, 275, 294, 337, 345f., 597, 619, 701f., 721, 729, 744f., 814, 834, 855, 886 Hesse-Kassel, Landgraviate of 58, 147, 161, 157f., 170, 174, 178, 180f., 201f., 207, 484, 487, 492f., 578f., 597, 687, 704f., 802, 829 Kassel 10f., 59, 173f., 178–180, 201, 236, 253, 430, 483f., 487, 490, 492, 508, 597, 713, 732, 853, 886, Library, archivists / librarians in Kassel 10, 173, 430, 483 Marburg 58, 178f., 233, 422, 458, 487f., 490, 646, 886 Hildesheim 10, 156, 428, 700 Heyersum (near Hildesheim) 156, 700 Holstein-Sonderburg-Plön 193, 592 Holy Roman empire 12, 225, 508, 791, 839. See also Vienna Hungary 139, 189f., 388, 408f. See also Economics and Mining Habsburgs’ re-conquest (1683) – colonization of certain regions 189f., 408f.

1007 Hypotheses (in the sciences) 81f., 85, 96, 103, 108f., 119, 123, 228, 230, 234, 264, 266, 366, 375, 383, 421, 466, 469f., 473, 507, 539f., 542f., 547f., 552, 554, 556f., 622, 649, 653, 727, 737f., 743, 763f., 771, 774, 791, 836f., 841, 875–877, 892, 896, 898 Illumination – urban illumination – street illumination with oil lamps 188, 407. See also Economics India, Indian – Indian seed 89, 290 Infinite 28, 42–44, 58, 73, 82, 109f., 224, 234, 438, 478, 516, 542, 546, 554, 623, 638, 640, 643, 646, 666, 727, 738, 746, 764, 838 Infinitely small 31, 36, 44, 66f., 234, 523, 623, 627, 649f., 653, 727f., 746, 869 Infinity 42, 55, 162, 234, 286, 457, 515, 554, 642, 685, 727f., 812, 830, 870 effective infinity and infinite divisibility 55, 457 Infinitesimals. See Mathematics, Calculus Inquisition. See Churches Instruments Astronomical instruments – astrolabes, globes, quadrants, sundials 199 Balances – beam balances – precision balances 96, 100, 293, 374, 778 Barometer Mercury barometer 474, 495 History of the barometer – the Torricellian experiment 100f. Discussions (1697–1700, with Ramazzini, Schelhammer) about the motion of mercury in the Torricellian tube 474, 495, 775–778, 824 Leibniz’s explanation of barometric phenomena – his balance instrument 777f. See also Experiments, thought experiments Constituent parts and operation – horizontal beam balance – water pipe with floating ball – equilibrium state maintenance: Water pipe with sinking ball and equilibrium state infringement 100, 778

1008 Instruments (cont.) Air-pressure measured by the height of fluid column – the pressure-height problem – influence of weather changes on the rise and fall of the mercury column 100f., 776f. Discussion with Hoffmann (1700– 1701) – Leibniz’s explanation of the phenomena and of the operating principle of the barometer in the Torricellian tube 100f., 778f. Hoffmann’s barometric-meteorological observations 206, 823f. Emulation / simulation of rain drops in air 100, 778 Solution of the anomaly / paradox as to why serene air is lighter than pluvial air 294, 778 Other barometer forms Aneroid barometer precursor 100 Portable barometer – construction of a portable barometer (1697/98) 99, 776 Static barometer 91, 293 Hygrometer 99, 258, 299, 500 Optical instruments – Lenses and mirrors Lenses, lens optics – glass lenses 37, 126–130, 158, 160, 187, 302–305, 322, 379, 561f., 704, 807f. Mirrors, mirror optics 126–128, 158f., 306, 331, 378, 471, 561–564, 704, 706–709, 753 Construction and improvement of Copper mirrors 126 Concave mirrors 126–128, 158, 306, 378, 471, 561–564, 704 Convex mirrors – production (Nuremberg, 1695) 128, 564 Tschirnhaus’ lenses and mirrors – his commitment to their improvement / perfection – his concave copper mirrors 126f., 378, 471, 561 Display of a mirror of his at Amsterdam (July 1695) 564 Convex glass lenses (burning glasses) – manufacture of convex lenses 127f., 158, 160, 561–563, 704, 807

Index of Subjects Tschirnhaus’ new machine (1694) 127, 561 His processes for making glass spheres (beads) from paper ashes and vegetable matter – also from molten porcelain, asbestos, talc (talcum) 127, 561 His burning glasses with the capability of burning a mark in wood under water – and of rendering molten materials like pitch, sulfur, colophony (rosin resin) – even of reducing of metals to a glass form – like gold to ruby glass 127, 562 Advantages of his convex lenses over concave mirrors, namely high effectivity – reduced weight and size – easy transportability – more enduring polish or glaze – dirigible / directable refracted rays – their being aimable / directable at fluids and powders 127, 562 Sale of his optical products – proceeds from sales intended for the establishment of a fund for the advancement of the sciences 127f., 562 Demonstrations of his burning glasses (and a concave mirror) – at the court in Hanover (Fall 1694) – in Amsterdam (December 1694) 127f., 563 His meeting with Huygens (1694) 128, 563 Huygens’ preference for glass concave mirrors with a diameter of up to 4 feet – having a coating on the back side and a small plane mirror near the focal point – with rays being directable to combustible material 128, 564 Microscopes and telescopes / Microscopy and telescopy Huygens’ ‘Des telescopes et des microscopes’ 125, 471

Index of Subjects Instruments (cont.) Tschirnhaus’ practice-related optical investigations – his improvement of the illumination of instruments – his envisioned breakthrough in optical instruments – possibly akin to Galileo’s ‘Starry messenger’ (1610) 126f., 472 Limits of resolution capacities of optical instruments – objective of approaching these resolution limits 127, 472 Microscopes, microscopists Desired features of microscopes – enlarged field of view – light weight – magnification 472 Leeuwenhoek’s microscopic observations / investigations – presentation to Leibniz (1676) – his commitment to microscopic research – his reports sent to the Royal Society – his methods and instruments – his (secret) observations – his observational methods and their preservation for posterity – the planned written bequest and their value for medicine and the medical arts 128–132, 301–306, 682–685 Spherical or globular (single lens) microscope – developed by Jan Hudde – improved and employed by Leeuwenhoek – subject of Leibniz’s interest (1678) 130, 304f. Microscope without a lens (Tschirnhaus, 1685) – held in proximity to the observing eye 126, 378f. Observation through a slit (Scheiner, 1619) 126, 379 Compound microscope (with two lenses) 130, 305 Thermometer Construction of the thermometer – thermometer (in Leibniz’s Dynamica) – use in medicine 52,

1009 99, 207, 258, 299, 365, 451, 500, 775f., 824, 826 Vacuum pump – development of the vacuum pump (pneumatic engine). See Engines Invention – the art of invention or discovery (‘ars inveniendi’) 176, 631, 714 Discoveries and innovations 135, 309, 402 Mechanical inventions and innovations 189, 408 Scientific and technical inventions 127, 140, 149f., 158, 177f., 180, 182, 185, 199, 205, 209, 214, 244, 291f., 304, 317f., 323, 327f., 332, 348f., 383, 391, 408, 413, 460, 488, 491–493, 572, 577, 587, 689, 697f., 703, 707, 709, 717, 800–802, 805, 809, 820f. Ireland x, xiii, 193, 231, 288, 291, 332, 841 Cork 288, 291, 780 Donegal (Inishowen peninsula) xiii, 232 Dublin – Dublin Philosophical Society 125, 235, 281, 470, 729–731 Dungarven (County Waterford) 291, 780 Irish Protestant ascendancy xiii Williamite campaign (1690). See Wars, Jacobite / Williamite War Italy 2, 7–10, 21f., 33, 37, 54, 58, 103–105, 141, 163, 166, 200, 220, 244f., 249, 251f., 258f., 263, 327, 356f., 366, 368, 370, 394, 402, 424, 428, 430f., 433, 456, 458, 462, 466, 473, 476f., 480, 499–502, 601, 605, 612, 620f., 630f.,722, 735, 741, 839, 867, 882, 888f. Bologna 8, 131, 164, 260, 357, 403, 425, 473, 477, 504, 882 Ferrara 8, 357 Florence, Tuscany, Florentine court – Grand Ducal Library 8, 10, 12, 23, 33, 52, 54f., 131, 169, 176, 213, 220, 224, 235, 245, 248, 357, 365, 412, 423, 430, 433f., 443, 456f., 473, 483, 509, 525, 560, 582, 620f., 713, 723, 729f.,735, 839 Florentine problem. See Mathematics, Curves and Surfaces Genua 265 Italian Renaissance – art, artists and painters 132, 477, 683

1010 Italy (cont.) Leibniz’ Italian journey (‘iter Italicum’) 2, 7f., 21, 263, 356f., 366, 370, 424, 466 Lombardy 504 Milan 809 Modena 8, 99, 163–165, 190, 201, 206, 255, 258–263, 357, 403f., 410, 425, 474– 476, 500f., 503f., 506, 604, 775f., 858 Measurements in the subterranean springs and wells – barometric and thermometric investigations – barometric and medical ephemerides (1691) 99, 163f., 255, 261f., 403f., 474f., 502–506, 604, 775f. See also: Medicine, Physics, Geophysics Military camp at Spilamberto, near Sassuolo, South of Modena 260, 503 Naples 809 Padua 131, 243f., 246, 425, 601f. Pisa 33, 620 River Po and tributaries (Panaro and Secchia) 164f., 259, 403–405, 501f. Rome 8, 104, 114, 131, 164, 357f., 366f., 424f., 452f., 473, 783, 785 Accademia Fisico-Matematica Romana 104, 367 Pope, papacy, pontifex, pontifical – Papal Calendar Congregation 105, 115f., 368, 783f., 786, 789 Vatican, cardinals, curia 114–116, 783–786 Tiber (River) 164f., 404 Venice (republic of Venice) – Murano (island near Venice) 8, 51, 54, 105, 159, 190, 200, 213, 217, 263, 327, 357, 364, 367, 412, 415, 424f., 455, 709, 737, 807 Sicily 740 Jakarta / New Batavia (Indonesia) 248, 351, 733 Jena 49, 120, 202, 212, 337, 597f., 729, 800 Astronomical observatory 120

Index of Subjects Jesuit order of priests 8, 50, 66, 96, 178, 236, 248, 276, 291, 357, 375, 423, 648, 732, 756 Journals Acta Eruditorum (Leipzig) 7, 16, 19–24, 26f., 30–32, 35, 38f., 41f., 44–47, 55–60, 91f., 95–97, 102f., 105, 107, 109, 112f., 120f., 126, 131, 147, 166f., 170, 176, 178, 187, 204, 226, 228, 243, 257, 280–282, 286, 292, 295, 297, 300, 342, 348, 353, 359–370, 372, 374–376, 378, 406f., 419, 431–436, 438–443, 445, 458–462, 466f., 477–481, 487f., 510–513, 515f., 521–525, 542, 559f., 620, 625, 630, 632–638, 640–643, 645–648, 723f., 747, 749f., 751f., 820, 864, 866, 869, 875, 883, 886, 891, 897 Giornale de’ Letterati (Modena) 33, 621, Histoire des Ouvrages des Savans (Rotterdam) 33, 621, 867 Journal des Sçavans (Paris) 25, 34f., 44, 52, 54f., 123, 153, 178, 198, 235, 243, 281, 325, 453, 457, 510, 572, 622, 730 Miscellanea Curiosa Medico-Physica (Halle) 198, 236, 243, 248f., 260f., 325, 346, 351f., 423, 502, 504, 732f. Nouvelles de la République des Lettres (Amsterdam) 20, 56f., 361, 363, 646, 864 Philosophical Transactions (London) 35f., 38, 46, 88, 91, 129f., 324, 289f., 293, 379f., 624, 629f., 632f., 727f., 750, 868 Jews, Jewish, Judaism – Dutch Jews 186, 320 Jurisprudence, jurist, juror xif., 11f., 145, 275, 508, 567, 571 Kassel. See Hesse-Kassel Kiel 116, 785 Knowledge Theory and practice – Leibnizian perception (principle) – unity of theory and practice (‘theoria cum praxi’) 15, 175, 199, 201, 597, 828 Early-modern consequences for science and technology – a ‘craftsman-scholar cleavage’ – relation of the scholar / scientist to the artisan / craftsman /

Index of Subjects Knowledge (cont.) practitioner – apprentices and students 132, 167f., 198–200, 238, 683, 885 Professional group identities – ‘theoreticus’ (savant, Gelehrter) – ‘practicus’ (artiste, Künstler) – ‘empricus’ (artisan, Handwerker)  167f., 198f., 255f., 885 Mathematical practitioners – practical mathematics and artisanal activity 199, 862 Artisanal enlightenment – artisans’ workshops – instrument makers – minters of coins (moneyers) 9, 143, 199, 358, 565, 885 Physicians and surgeons – practical and artisanal activity – prosthetic technology – making artificial limbs 199f. Universal (pansophist) knowledge 222, 834 Laboratories 57, 158, 160f., 189f., 213, 218f., 221f., 253, 395, 408, 410f., 416, 457, 705, 721f., 735, 806–808, 832–834, 853, 889f. Languages. See Peoples and Languages, Grammar, dialectic, rhetoric Learning – organization of learning 230 Republic of letters – world of learning 47, 272, 684 Academies, academic institutions, universities. See also Projects, Scientific, Educational Projects Outside the academy – non-academic science and engineering – professional scientists and engineers 89, 157, 885, 896 Learned and scientific societies 12, 197, 508 Leipzig. See Saxony Life Sciences. See Biology Light. See Physics Linden. See Hanover Logic xi, xiii, 205, 286, 744, 820 London. See England Lüneburg 99, 139f., 325, 387, 391 See also Dynasties, House of Brunswick-Lüneburg

1011 Machines, machinery, mechanization. See also Engines, Enginery Calculating machines – development as part of a larger project for the mechanization of thought – interdependency of philosophical principles and mathematical and scientific results 169, 314 Conception of a general script to enable (for every topic) calculation and proof – like in algebra and arithmetic – found in Leibniz’s correspondence with English contacts – like Clüver, Haak, Hooke (1673–1680) 169, 314 17th-century calculating devices – calculator of Pascal (‘Pascaline’) – improvements by Grillet 170, 578, 582 Calculating cylinders of Schott and Petit 170, 579 Morland’s machine type and variants – use of slide rules and Napierian logarithms 170, 578 Exemplar in possession of Karl of Hesse-Kassel 170, 578 Machine constructed by Haes himself (1680s) – the Haes adding machine (1695) – adapted for German coinage / accounting 170, 579 Machine made by Cotterell 170, 578f., Tschirnhaus’ machine – gearless machine conceived by him (1694) 170, 579 Leibniz’s calculating machines – his four-function calculating machine – with decimal entry and result positions – with addition / subtraction and multiplication / division functions 168–173, 312f., 483, 578–583, 885 Versions of Leibniz’s machine His three-place wooden demonstration model – presented to the Royal Society (February 1673) – his contact with Moreland (February 1673) 168, 579f. His improved metallic version of the machine – with six entry and twelve result

1012 Machines, machinery (cont.) positions – constructed by Ollivier and presented to the Académie des Sciences (January 1675) – completed in Hanover (mid1680s) 168, 312f., 580f., 885 His ‘older’ machine – with eight entry and twelve result positions – completed by Kölbing in Hanover (1694) – presentation to visitors Tschirnhaus (Fall of 1694) and Burnett of Kemney (April 1695) 578f., 581–583, 814, 885f. Intelligence concerning the machine sent to: France (L’Hospital, Toinard) – L’Hospital’s commission (1694) for a duplicate of the machine 170f., 581f., 885 Holland (Crafft, Huygens) 170, 582, 885 Italy (Bodenhausen) 171, 581f. Difficulties in completing the construction – lack of skilled craftsmen in Hanover – interest (or involvement) of Dutch and French clockmakers 168f., 171f., 312f., 581, 816–818, 886f. Leibniz’s second or ‘younger’ machine – with eight entry and sixteen result positions – report sent to Bodenhausen (1695) – commencement of construction work by Scherp in Hanover (1694/95) 171f., 583, 814–816 Transfer to Helmstedt (March 1700) – construction / repair by Warnecke under the direction of Wagner – with the ‘older machine’ as a model – problems of the interaction of the parts of the ‘younger’ machine 171–173, 583f., 814–817, 886 Wagner’s admiration for Warnecke’s efforts, and disdain for his predecessor Scherp – issues of expenditure, waste, and possible deceit in the overhaul

Index of Subjects and reworking of components – Scherp’s imprecisions, and his machine construction defects 171–174, 814–817, 886 Leibniz’s praise (1701) for his former clockmaker Kölbing 172, 816, 886 Components of the ‘younger’ machine – the carriage, decimal carrying mechanism, pentagonal disks, drawing spindle, rotary disk, upper part of the machine – completion of parts reported (spring time 1701) 172f. 814–817 Warnecke’s efforts for improvement of the ‘older machine’ in Helmstedt (from July 1701) 172, 816 Wagner’s calculation examples – addition and multiplication – removal of errors and incomplete calculations 172f., 816f. Operation of the value transfer mechanism between the setting mechanism (input) and the result mechanism (output) 173, 817 Correction procedure by means of a horizontal positioning of the pentagonal disks – manual through-connection of incomplete positions and a manual rotation of the crank 173, 817 Removal of errors in both machines – by means of precision-engineering alterations 173, 817 Suspension of work on the calculating machines – due to grave illness of the clockmaker – recovery and resumption of the work (end of 1701) 173, 817 Interest of correspondents in Leibniz’s calculating machine – commissioning of duplicates 170f., 581f. Machines as machine-equivalent figures for calculation 151, 283, 882, 884 Mathematical drawing machines – apparatus or machine for drawing mathematical curves 169f., 483

Index of Subjects Machines, machinery (cont.) Pneumatic machines 148, 691f. See also Engines Threshing machines – machine at the location Aerzen (in the Weser Uplands) – Voigt’s drawing of the threshing machine (1699) 161f., 812, 809f. Explanation of its battering or threshing mechanism – its manner of advancing 161f., 809–812 An operator turns a camshaft to move the thresher-cylinders – threshers were attached to a carriage, which was moved or pedaled along the threshingfloor – use of a rack and pinion gear mechanism 161f., 810–812 Leibniz’s suggestion for optimizing the mechanism – replacing the cogged wheel-lantern pinion system with a pulley system 161f., 810f. Leibniz’s idea of making use of water and wind – an alternative power sources to manpower – as a prime mover for the threshing-machine 162, 813 Corresponding requisites – a water raceway – a pumped-storage system with reservoir – availability of a wind mill 162, 813 Another threshing machine reported at the location Linden, near Hanover 162, 812f. Mechanization xiii, 162, 169, 186, 314, 321, 811f. Mechanization of the world picture – mechanization and social change. See also Projects, Economic and Techno-Economic Projects, Manufactories Leibniz’s views regarding social change accompanying technological progress 133, 161f., 862 Leibniz’s reply to Voigt (January 1700), regarding the implications of his threshing-machine – loss of employment due to mechanization – example of the machine at Aerzen – a single

1013 operator could do the work of fifteen laborers 162, 811 Example of the proscription of the ribbon-loom (1685) 161f., 811 Leibniz’s view of the problem of employment loss though mechanization – rejection of the assistance of machines not acceptable with alternative occupations arising through mechanization – only preliminary readjustment difficulties expected for workers 162, 811f. His comparison with the use (in France / Spain) of animals in harvesting – resulting in the saving of human labor 811f. His proposal for remuneration based on performance – recording of completed machine tours or working shifts required 162, 812f. Magdeburg 90f., 262, 291–293, 383, 605 Magnetism. See Physics Mainz – Electorate of Mainz 168, 190, 220, 257, 354, 408, 579, 721, 832, 889 Malacca (Malaysia) 248, 351f. Mansfeld (Harz Mountains) 226, 344, 891 Manufactories, manufacturing. See Projects Marburg. See Hesse-Kassel Materials Strength of materials and its history – history of elasticity – development of the theory of elasticity in the 17th century – elasticity as a structural principle of nature – elastic springs 3, 60, 65f., 92f., 94–96, 296f., 299, 345, 372–374, 461, 538, 647, 649 Hardness, perfect hardness 59, 68f., 80f., 114, 372, 461, 652, 654, 656, 761f., 874 Theory of structures – theories of Galileo, Mariotte, Hooke – their different theoretical assumptions 95f., 296f. Galileo’s assumptions – rigid bodies and sudden breaks – his theory of fracture strength 95, 296f. Mariotte’s work for the royal waterworks – his investigations of aqueducts / conduits – assumption of elastic fibers

1014 Materials (cont.) or filaments – communication of experimental results 95, 296f. Critique of Galileo’s theory of fracture strength – different proportionality factors found by Galileo, Mariotte, Leibniz 95, 297 Development of the ‘Mariotte-Leibniz theory’ – Leibniz’s ‘Demonstrationes novae de resistentia solidorum’ (1684) – Mariotte’s ‘Traité du mouvement des eaux’ (1686) 95f., 297, 374 Leibniz’s theory of strength of materials – elasticity as an explanatory principle – breaking or fracture / rupture strength with elastic tension preceding break or fracture 92, 95f., 296f., 299, 372, 374f. Leibniz’s starting hypothesis (1684) – strain or extension of carrier beam fibers being proportional to tensioning or straining force 96, 374f. Uniform break-proof beams – their form and configuration 96, 374 Profile of a uniform fracture-resistant carrier beam – subjected to its own weight (1684) and an additional attached load (1690) 96, 375 Leibniz’s conviction that the carrier beam problem was only solvable with his infinitesimal calculus 96, 375 Mathematics Algebra 17f., 27, 29f., 39, 169, 176, 200, 279, 283f., 286, 307, 314, 327, 361, 514, 516f., 520, 534, 645, 714 Binomials, binomial development 17, 284 Combinatorial and universal characteristics 18, 284 See also Combinatorics Determinants, determinant theory 17, 284 Non-homogeneous equations 17, 284 Wallis’ ‘Algebra’ (Opera, vols. 1 and 2) – Newton’s gift sent to Mencke (1696) 29f., 176, 520, 714 Analysis, mathematical analysis 20, 24, 27f., 31, 36, 40, 96, 283, 286, 360, 375,

Index of Subjects 439, 445, 448, 514, 516f., 524, 621, 628, 637f., 754 Analysis of the infinitely small. See Infinitesimal Calculus Analytical methods 439 Fundamentals of analysis 448 Infinitesimal analysis. See Infinitesimal Calculus Imaginary and real expressions 17, 284 Ordinary analysis 96, 375 ‘Analysis situs’ 13, 17, 27, 48, 283, 514, 619, 754 Applied mathematics 745, 884 Arithmetic 7, 24, 27, 48f., 169, 191, 203, 279, 281, 283, 285, 314, 437f., 442, 444, 498, 514, 578–584, 599, 637, 645, 754–756, 816, 818, 887 The four arithmetic operations – addition, subtraction, multiplication, division 169 See also: Calculating Machines Exponentiation – exponents and roots – composite roots 16f., 21, 31, 42, 279–282, 284, 362, 444–447, 523, 641, 864 Exponential equations – transcendental exponential equations 21, 31, 42, 279, 362, 445, 523, 641, 864 Exponential expressions or logarithms (inverse function to exponentiation) 441–446 Logarithms (Napierian) 170, 578 Arithmetical tetragonism – the tetragonist method 483, 637 Binary or dyadic arithmetic. See Number Systems Diophantine arithmetic 27, 279, 514 Political arithmetic. See Economics, Political Economy Infinitesimals – arithmetic of infinitesimals 30f., 448 Calculus, infinitesimal calculus ix, 11, 15f., 18, 20f., 27–31, 34f., 43, 64, 95f., 113, 281f., 358, 360f., 372, 375, 431f., 448–450, 508f., 516, 519, 521, 523, 535, 623–625, 643, 645, 863f., 868f.

Index of Subjects Mathematics (cont.) Calculus an expression of reasoning or rational thought 241. See also Reason, Reasoning Foundation and forms of the calculus xii, 11, 31, 40, 48, 444, 508, 517, 523, 636, 639, 753 Epistemological foundations of the calculus 31, 523 Priority issues. See Disputes and Controversies Leibnizian calculus and notation xii. 15, 18, 21, 29, 47, 358, 362, 510, 519f., 523–525, 752, 864 Leibniz’s new method (‘Nova methodus’) 15, 20, 51, 147, 280, 360, 364, 431, 688 Finding maxima and minima, curvature, points of inflexion 16, 280, 282, 514f. Differential calculus 14f., 20, 22–25, 31, 33–36, 39–45, 47f., 51, 113, 121, 280, 283, 301, 359f., 364, 371, 432f., 435–437, 448, 509, 518, 524, 621–623, 625, 628, 635–640, 642–645, 745, 748, 752f., 865–869 Differentials – of first-order, second- and higher-order 15, 31f., 41f., 234, 523f., 640f., 727 Differential equations – of first-, second-, higher order 27, 30, 514f., 520f., 645 Theory of differential equations – attribution to pure quadratures (integrals) 27, 514f. Solution of differential equations – power series method 29f., 514, 521 Exponential equations 21, 31, 42, 279, 362, 445, 523, 641, 864 Differential geometry 27, 514f. See also Geometry Infinite – conception / nature of the infinite / infinitely small 43f., 643, 746 Infinitesimals, infinitely small magnitudes 30f., 448 Conception / nature of infinitesimals 44, 448, 746

1015 Infinitesimal differences – infinitely small changes 32, 67, 653 Discussion between Leibniz and Joh. Bernoulli – their respective conceptions of the infinite / the infinitely small 44, 234, 727f., 746 Questions of rigor of the differential calculus – objections raised against the calculus – proofs less rigorous than those of the ancients 43, 643 The calculus essentially an analytical method for achieving results 43, 439, 643 The integral calculus (Leibniz’s recondite geometry) 18, 20f., 43, 95, 133, 265, 358, 360, 431, 644, 861, 863 Integration theory 27, 514f. Integrals – basic integrals – integrals of known geometrical interpretation 515 More complicated integrals – reduction / transformation using substitutions 514f. Notation / terminology of the Leibnizian calculus – differential / integral symbols – their improvement and unification 29, 47, 519f., 524f., 752 Alleged superiority of the Leibnizian calculus 15, 21, 23, 45, 280, 362, 432f., 439, 444, 747, 864f. The Newtonian calculus 11, 29, 47, 507, 519, 752 Newton’s Calculus of fluxions 28–30, 39f., 47, 518, 520f., 634–639, 748, 752 His ‘De analysi per aequationes … infinitas’ (1669) – seen by Leibniz in London (1676) 28f., 517f. His letters of 1676 (intended for Leibniz) – the ‘epistola prior’ – the ‘epistola posterior’ – Leibniz’s replies 29f., 40, 519, 638

1016 Mathematics (cont.) Gregory’s role in obtaining the letters of 1676 – subsequently published by Wallis (1699) 639 Newton’s calculus / method of fluxions – intended publication (1693) – presentation of the calculus of fluxions in Wallis’ ‘De algebra tractatus’ (1693) 39, 520, 634f. Newton’s calculus – Newtonian notation 29, 47, 519f., 524f., 752 Other forms or methods of the calculus Huygens’ geometrical methods 20, 24, 360f., 376, 435f., 439, 510, 866 Wallis’ tangent method – compared with Leibniz’s differential calculus – equivalence / non-equivalence of the methods 40, 636f. Others methods like those of Archimedes and Fermat – similarities, interdependences, and differences 40, 449, 637f. Questions of nomenclature and notation 28f., 39, 47, 284, 519f., 524f., 636, 752 See also: Controversies and Disputes Transcendental calculus 281f., 445f., 448f. General Mathematics Higher form of general mathematics 515 Clüver’s ‘scientia infiniti’ (1686) 42, 642 Leibniz’s ‘scientia infiniti’– a planned work with participation of other mathematicians – invitations sent (1694) to other mathematicians (Jacob and Johann Bernoulli, Huygens and L’Hospital) – Mencke’s proposed publication of an outline of the conception of the work (1694) 13, 27, 29, 44, 514–516, 520, 619, 644

Index of Subjects Contents of the work – quantities, theory of quantities – finite quantities (algebra) – infinite quantities (infinitesimal calculus) 27f., 516f. Geometry Elementary geometry / mathematics 27, 514 Geometry without tables 283 Euclidean geometry 238, 845 Geometry of Apollonius 449 Geometry of Descartes (Cartesian geometry) 449, 645 Extension to transcendental curves 645 Geometry of Viete 449 Geometrization / mathematization 24 Geometrical methods – those of Huygens – those of Italian mathematicians 20, 23f., 360, 433, 435, 439, 510, 865f. Geometrical precision 42, 642 Graduation – Renaldine circle graduation rule 745 Higher geometry 27, 515 Geometric characteristic (‘characteristica geometrica’) 17, 279, 283 Geometry of location (‘geometria situs’) 17, 283 Practical geometry Ramist geometry (16th / 17th century) – cruder than / inferior to Euclidean geometry – a form of practical geometry which disparaged proofs – figures judged on the basis of their form – focus on benefit or usefulness 238, 845 Quadrature(s) 7f., 17, 19, 24, 42f., 279, 281, 283f., 359, 436–438, 441–445, 448–450, 515, 642f. Quadrature methods 19, 24, 359, 436, 645 Quadratures of circle and hyperbola – reduction of quadratures to those of circle and hyperbola 445, 448

Index of Subjects Mathematics (cont.) Quadrature / squaring of the circle 7f., 17, 24, 281, 283f., 437f., 449 Leibniz’s correspondence with Ferguson (early 1680s) – quadrature of the circle using the ‘witch of Agnesi’ curve 17, 284 Leibniz’s ‘True proportion of the circle to the square’ (1682) 39, 281, 635 Leibniz’s arithmetic quadrature of the circle (1682) – the ‘Leibniz series’ – his ‘trigonometric series or geometry without tables’ – first use of the term ‘transcendent’– his use of term with unknown in the exponent 7, 16, 24, 280f., 283, 437f. Use of the he technical term ‘transcendent (al)’ 16, 23, 279f., 282f., 307, 434, 445f., 448f., 511, 514, 645 Series – theory of series 27, 514f. Leibniz infinite series (1682) 16, 24, 280, 437f. Huygens’ infinite series (1690) 438 [Joh.] Bernoulli series (1694) 515 Power series development 514 Numerical series 645 Curves and surfaces Alhazen’s problem 284 Arc length of a curve (rectification) 24, 436, 441, 443, 513, 645 Area under a curve (quadrature) 24, 436 Quadratures / rectifications expressed algebraically 645 ‘[Joh.] Bernoulli problem’ 23, 434f., 866 Brachistochrone (curve of fastest descent) problem 26, 32–37, 42, 45f., 48, 512f., 619–631, 641, 645, 747–749, 753, 867–870 Announcement / task formulation (1696–97)

1017 Bernoulli (Joh.)’s flysheet about the problem for Dutch, English, French and Italian Mathematicians – his note (February 1697) in ‘Histoire des Ouvrages des Savans’ 26, 32–35, 513, 620f., 624f., 867f. Bodenhausen’s flysheet about the problem for Italian mathematicians 33, 629 Leibniz’s announcement in ‘Giornale de’ Letterati’ (September 1696) and ‘Journal des Sçavans’ (November 1696) 33f., 620–622, 867 Solutions found or published (1696–99) Newton’s solution – achieved in a single day, following receipt of Bernoulli’s flysheet – his anonymous ‘Epistola’, in the Philosophical Transactions (January 1697) – seen by Leibniz as a proof of the effectiveness of the infinitesimal calculus – in form of both the differential calculus and an analogous method 35, 513, 624f. Leibniz’s complaint (April 1697) about Newton’s preemptive publication 625 Leibniz’s own solution – the cycloid or ‘tachystoptata’ – achieved in a single day, while on a coach trip to Wolfenbüttel 625f. L’Hospital’s solution (April 1697) 34, 48, 624, 868 Joh. Bernoulli’s two procedures (direct and indirect) – one based on the law of refraction 26, 36, 512f., 627

1018 Mathematics (cont.) Publications (Philosophical Transactions) – Newton (January 1697) – David Gregory (February 1697) 36, 513, 624f., 629f. Publications (Acta Eruditorum, May 1697) Solutions by Jac. Bernoulli, Joh. Bernoulli, L’Hospital and Newton 513, 627, 641 Contributions by Leibniz (Introduction) and Tschirnhaus (commentary) 35, 37, 45, 625, 629, 747, 869 Aftermath of the publication Joh. Bernoulli’s eulogy (June 1697) of Newton’s achievement – his complaints about Tschirnhaus’ behavior in the contest 37, 626–629 Leibniz’s insistence (1699) on not having had knowledge of Bernoulli’s flysheet being sent to Newton 35, 626 Catacaustic curve 16, 282, 870 Catenary (hanging chain) curve problem 22, 24f., 36, 38, 46, 432, 436f., 439–445, 447, 510, 628, 632, 634, 749, 864–866, 869 Encoded solution of problem (Huygens) 439–441, 443 Construction, features and properties of the catenary curve 439–445 Its surface of revolution – space generated by its rotation – its center of gravity – area between the curve and its axis – rectification of the curve 440f. Evolute / Involute. See also Tractoria / Tractrix Involute of catenary (tractoria / tractrix) – evolute of the tractoria / tractrix

Index of Subjects (catenary) 24, 436, 441, 443, 866 Relation of the catenary to the loxodrome 442 See also: Loxodrome / Rhombic Lines Curvature(s) Curvature center, radius 36, 627 Curvature behavior of curves 515 Curve arrays – properties of arrays 515 Families of curves – investigation using the infinitesimal calculus 515, 645 Different curvatures of a curve – curvature or flexure changes – infinitely small sections – infinitesimal changes 36, 67, 80, 514f., 627, 761 Movement along a flexuous line or curve 80f., 83, 761–763, 766 Constraining force – example of centrifugal / centripetal force – bodies possess this force in order to conserve their state 80f., 761f. Conservation of direction (rectilinear movement) – non-conservation of curvature (curvilinear movement) 80, 83f., 761, 766, 769 Transition from curvilinear to rectilinear movement – essentially a change of state – Papin’s opposite view (1699) 81, 763 Cycloid 26, 32, 36f., 436, 445, 450, 512, 619f., 627, 629, 866f., 869 Properties of the cycloid – obtained analytically 448 Tangent to the cycloid 448 Cycloidal pendulum 17, 24, 284, 866

Index of Subjects Mathematics (cont.) Pendulum clock. See Physics, Applied Physics Cycloidal segment. See Brachistochrone, Solutions Diacaustic curve 16, 282, 870 Drawbridge problem (1692–95) – Sauveur’s problem to find the locus of a moving weight maintained in equilibrium – solution: Limaçon (Snail of Pascal) 26, 512, 866 Elastic curves – studied by Jacob and Johann Bernoulli 95 Families of curves – envelope of a family – orthogonal trajectories – determination methods developed by Leibniz and Joh. Bernoulli (1694) – influence from physics in relation to the Brachistochrone problem, and ‘Huygens’ construction’ (wave theory of light) 37, 437, 515, 630, 870 Geometrical curves Hyperbola – quadrature of the hyperbola 43, 438, 441–445, 448f., 643 See also: Sum of secants of arcs, Huygens’ series Isochrone curve problem 19, 359, 863 Isoperimetric curve problem (1697) – classical isoperimetric problem – variational and extremal task assignments 37f., 513, 619, 630–632 Limiting curves of – the simple tautochrone or isochrone pendulum – the tautochrone or isocrone double pendulum 24, 436, 866 Linear curves – Johan de Witt’s ‘Elementa curvarum linearum’ in Leibniz’s correspondence (1697–99) 193

1019 Loxodrome (Rhumb-line) curve 25, 437, 441–445, 865 Parabola – semicubical parabola (the isochrone) – quadrature and rectification of the parabola 19, 21, 34, 42, 103, 112, 282, 359, 370f., 431f., 441, 443, 511, 624, 642, 863, 868. See also Isochrone Problem Paracentric isochrone problem (Leibniz’s problem) 21, 432, 865 Real-world applications (or origins) of curves – physical influences 25, 37, 437, 630, 865, 870 Secants of arcs – sum of secants – longitudes as a sum of secants – method of finding the sum of secants (Huygens) 444f. Snail of Pascal curve (‘Limaçon’) 26, 512, 866 Solid of revolution of least resistance problem 45–47, 747, 751f. Spiral curves – Archimedean spiral 25, 437, 865 Surface area of a hemisphere – ‘Florentine problem’ (‘aenigma geometricum’) 23, 433, 865 Tangent method, method of tangents / inverse-tangents 17, 21, 24f., 29, 40, 46, 279, 284, 361f., 437, 447f., 514, 520, 636, 749, 864 Leibniz’s method 17, 24f., 40, 279f., 284, 448, 514, 636 Huygens’ ‘equivalent method’ 21, 361f., 440, 864 Inverse-tangent method (Fatio) 28, 46, 437, 447, 518, 749 Inverse-tangent problems (Huygens) – exchange of inverse-tangent methods 24f., 46, 437, 749, 864 Tschirnhaus’ method 16, 279, 282

1020 Mathematics (cont.) Wallis’ (Newton’s) method 29, 40, 520, 636f. Tractoria, tractrix (Involute of the catenary) 24, 436, 866 Transcendental curves – representation by finite equations – transcendental quantities 282, 445f., 448f. Mathematical change (evolution, revolution) xii Mathematical creativity 21, 431 Mathematical discourse 54 Mathematical history and pedagogy x, 32, 193, 645 Mathematical instruments 208, 578–584, 827 Analog equation-solving instrument (‘Constructor, instrumentum algebraicum’) 314 Compass 172, 180, 491, 495, 815 Mathematical instruments in China. See China Protractor 172, 815 Mathematical magnitudes 31, 523 Incommensurables – composite incommensurables 450 Mathematical pedagogy. See Pedagogy Mathematical problems and methods Calculation of annuities, discount, simple interest 16f., 187, 281, 284, 406 Extreme value problems – extremal problems – extremal principles 17, 36, 56, 284, 513, 526 Mathematical contests – challenge questions 19, 21f., 26, 33, 37, 45f., 432, 439f., 510–514, 630, 747, 749, 863–867 Mathematical classification – typological classification 514 Mathematical methods – separation of variables 21, 431, 514 Mathematical principles xiii Mathematical problems rooted in the physical world 37, 630, 870 See also: Brachistochrone Problem, Catenary, Loxodrome

Index of Subjects Mathematical substitution 514f. Mathematical terminology 284, 448 Mathematical textbooks – for the dissemination of mathematical knowledge 44, 645 L’Hospital’s ‘Analyse des infiniment petits’ (1696) – for dissemination of the differential calculus 25, 34, 43f., 509, 623, 644f., 868 Joh. Bernoulli’s reaction to the publication – in view of L’Hospital’s private lessons from Bernoulli (1691–92) 43, 644 Other textbooks – textbook discussed with Vagetius 44, 645 Mathematical sciences 702 Mathematical theorems – application in medical physiology (Guglielmini) 742 The Pythagorean theorem 72, 664, 788 Mathematization of medicine 263, 425, 895. See also Medicine Mathematization of mechanics, engineering and technology 861 Mathematicians Female mathematicians 54, 862 Mathematical practitioners 167, 198f., 327, 862, 884–887 Numbers – investigation of the properties of numbers 48, 754 Number theory 17, 27, 283, 514 Number theoretical applications 49 Reciprocal triangular numbers 17, 284 Science of numbers (Numerology) Characters of numbers 285 Mystery of numbers 754 Properties of numbers 48, 754 Use of numbers 18, 284 Number systems 3, 18, 27, 48f., 285, 514, 645, 753, 755 Binary or dyadic (base 2) 18, 27, 44, 48–50, 204, 285f., 514, 645, 746, 753–756, 818

Index of Subjects Mathematics (cont.) Binary or dyadic arithmetic 27, 48f., 645, 754f. Binary or dyadic calculus 44, 746 Binary or dyadic logic – progression 286 Binary or dyadic progression of numbers – the ‘progressio dyadica’ 49, 285f., 756 Philosophical / Theological interpretations. See also ‘China’, and ‘Religion, Creation’ Binary Fohy (or FuXi) sequence 50, 756 Chinese figures of Fohy (‘FuXi hexagrams’) 50, 756 Decimal or decadic (base 10) 18, 49, 173, 285, 755, 817 Hexadecimal (base 16) 50, 756 Octal (base 8) 50, 756 Other number systems (e.g. base 11 and base 12) 18, 285 Leibniz’s references to binary arithmetic (early 1680s) – letters to Clüver, Ferguson, Tschirnhaus 48, 285f. His later references (around 1700) 746, 753–756 His fear expressed to L’Hospital (1699, 1701) that his ideas might be lost for posterity 48–50, 754–756 His plea (1701) to the Académie des Sciences to undertake investigations on binary mathematics – his efforts (1701) to gain the cooperation of Parent 49f., 755f. His discussion of binary arithmetic with Joh. Bernoulli (1701) – the latter’s reference to Weigel’s work ‘Tetractys’ (1673) – Leibniz’s insistence on the existence before Weigel of number systems other than the decimal – and on The value of his own number theoretical applications 49, 755 Leibniz’s introduction of Dangicourt to dyadics (1700) – continuing co-operation under Leibniz’s

1021 direction – Dangicourt’s publication, in the ‘Miscellanea Berolinensia’ (1710) 49, 756 Leibniz’s communications with Bouvet (1701), with his theological interpretation and his latest results – Bouvet’s adoption of binary mathematics 50, 756 See also: China, Chinese Mathematics Pure mathematics 151, 279, 283, 288, 645, 745, 865f., 882, 884 The mathematical sciences (‘scientiae mathematicae’) 745 The ‘Bernoulli problem’ – Joh. Bernoulli’s problem (1693) and solutions 23, 434f., 866 The ‘problema alterum pure geometricum’ (1697) 645 Matter. See also Natural Philosophy, Dynamica Fluids 94, 127, 163, 166, 228, 246f., 256, 373, 421, 474, 476, 478, 480–482, 562, 747, 850, 852f., 882, 892f., 896 Rarified fluids 45 Theory of matter 92, 223, 372 Sensible / Insensible matter 63, 535, 540, 617, 687, 877 Mechanics. See Physics Mechanization. See Machines Medicine Art of medicine, ‘res medica’, matters medical, medicinalia, medicinal or pertaining to medicine 132, 241, 248–250, 252–255, 422, 425f., 560, 601, 605–611, 613, 615f., 844, 853, 855–857, 895 Concrete and abstract / potential 241, 425f., 895f. Medical science 243, 250, 346, 610 Theoretical medicine 255, 506, 742 Anatomy 235, 237, 239, 242–247, 253, 265, 345–347, 559, 601, 723, 730f., 734, 739f., 845–847, 850–853, 893f., 896 Anatomists xv, 131, 227, 240, 347, 380f., 601f., 848 Anatomical discoveries, insights, observations, reports, studies 235, 242–245, 253, 345f., 601f., 729f., 734, 850, 853

1022 Medicine (cont.) Anatomy of the ear. See also Physics, Acoustics, Aurality / aural experience of sound 93 Problem of identifying a missing entity in the hearing organ (1681/82) – homotonic with every sonorous body 242, 346 Ossicles (‘ossicula’), ossicular chain (middle ear) – stimulation by vibrations / oscillations of the air – production of a corresponding sound in the ear 93f., 372f. Cochlea (inner ear) 93f., 295 Ear drum (tympanic membrane) 94 Otology. See Diseases Anatomy of fluids 246f., 850, 852, 893, 896 Gakenholz’s ‘Epistola’ (open letter, 1701) on the emendation and correct practice of medicine – concerned with human body fluids – blood, serum and vital (or animal) spirits 237, 844f., 850, 852, 893, 896 Special roles of experimental science and chemistry – revealed in the works of nature – the chemical reactions of life – with the seat of most illnesses being found in body fluids 247, 852 Gakenholz’s argument that the human body should be considered as a machine or automaton – the heart being the prime mover of the machine 247, 851 Circulation of the blood – anatomical studies of the vessels emanating from the heart 246f., 850–852 His allegation of the backwardness of medicine – attributed to a superstitious veneration for the ancients and to wrong priorities in medical studies and training 246, 850 His advocacy of an anatomy of fluids in medicine, and of a reform

Index of Subjects of anatomical or postmortem examination 246f., 850–852 His understanding of the body in the context of organs and vessels 246, 850, 896 His focus on the circulation of the blood – arteries, veins, the heart chamber – aorta (the largest artery) – their connectivity and interrelation 246f., 850f. His views regarding incisions and their avoidance 246, 850 His experience with injections and reinjuries of vessels in corpses 246, 850 His thoughts on infusions, blood transfusions, and the value of corresponding experiments with animals – his emphasis of the role of chemistry in medicine, the need for physicians to study chemistry, and to understand the processes in nature – his criticism of the excrescence of chemical pharmacy – his advocacy of the study of plants, with regard to their healing powers, their color, odor, taste, and their combustion or incineration properties – his reference to investigations of the reaction of plant sap with human blood, differences found in the reactions with arterial and venous blood, and the resulting lack of clarity about the effectiveness of such medicaments 246, 850 Published review of Gakenholz’s ‘Epistiola’ (1701), highlighting its particular focus on the – study of blood and other body fluids – anatomy of fluids – study of vessels emanating from the heart – field of anatomy, involving study of the passage of blood from the heart through the aorta, and then through the body to the kidneys – role of experimental science (chemistry in

Index of Subjects Medicine (cont.) particular) – consideration of the structure of plants, animals, and the human body as machines or automatons, with the heart as the prime mover 247, 851f. Blood Blood circulation – blood supply – the passage of blood from the heart through the aorta / the body to the kidneys – arterial and venous blood 233, 246f., 422, 850f. Blood vessels – their form and shape 242, 345 Leibniz’s theoretical considerations – triangular vascular formations 241, 345f. Meibom’s observations (1681–82) 242 Leibniz’s call for microscopic investigation 242, 345 His hydraulic machine model with – elastic blood vessels having a polygonal cross section – irregular entry of blood (machine input) and regular rate of flow (machine output) 242, 345f. His application of trigonal prismatic geometry – blood vessels represented by a circumscribed polygon, with a possible range of multifaceted polygons – from best case (triangular) to worst case (circular) 242, 345 His corresponding physical model – the most simple hydraulic machine to emulate blood flow – consisting of a hollow triangular prism or tube, filled and constantly supplied with water through an orifice 242, 345f. The mechanical problem of reconciling the intermittent or pulsed fluid intrusion (input) with continuous fluid extrusion (output) 242, 345

1023 His more general consideration of elasticity as an explanatory principle in anatomy – with greater flexibility of the multi-faceted polygonal structure being obtained by increasing the side length while reducing the number of sides – optimal structure form being triangular 242, 345f. Bloodletting – Therapeutic Phlebotomy / Venesection Alleged abuse of phlebotomy abroad – in Italy (Bodenhausen) – in France, Spain and Italy (Block) 245f., 252, 735, 741 La Scala’s ‘Phlebotomia damnata’ (1696) 252, 740f. Leibniz’s advocacy (1698) of the moderate application of bloodletting 252, 740 Positive effects of the method found in the treatment of animals 252, 741 Bloodletting might act in the same way as arsenic as an antipyretic – with nature reacting to an artificiallyproduced health threat 252, 740f. Block’s view (1698) of bloodletting as the last resort of the Galenists 252, 741 Possible medical applications of bloodletting with – fever and blood heat – unconsciousness / disturbance of consciousness – blood congestion in the lungs or heart 252, 741 Leibniz’s request for Ramazzini’s opinion (1699) 252, 741 Cannibalism, Medical cannibalism 253f., 853–855 Corpse medicine 253 Anatomical knowledge from postmortem examination of corpses used for – the development of examination and treatment

1024 Medicine (cont.) methods – obtaining medicaments and medicinal or pharmaceutical products 253, 853 Goddard’s drops’ / King’s drops – Charles II’s distillation in his private laboratory – based on a recipe for the liquefaction of material from inside human skulls – wonderful or miracle-like reports about the drops 253f., 853–855 Leibniz’s interest and Papin’s skepticism (1699) 253, 853f. Mumia – a substance obtained from pulverized Egyptian mummies – used as a medicament 253, 854 Use of corpses for therapeutic purposes – a proposed treatment method – by rubbing a sore, swelling or wart with the finger of a corpse – Bouquet’s account (1701) of an unsuccessful trial in Hamburg, and a successful trial and lasting cure there 253f., 854f. Rationale of corpse medicine – medical benefit derived from extended suffering, death struggle, mortal agony – the agonal state of long-suffering patients, tortured and executed prisoners – soldiers in their death throes on a battlefield 254, 855 The corresponding production of substances having curative or immunization effects – serving as ingredients for medication – analogous to bloodletting and the resulting improved defense mechanisms of the body 254, 855 Post-mortem rituals – necromancy (‘necromantia’) and necrophilia 220, 830, 836, 898 Cardiology – Cardioplegia or heartbeat 236, 732 Chemical medicine / Iatrochemistry. See also Chemistry Ramazzini’s acquaintance with iatrochemistry – the diagnostic

Index of Subjects and therapeutic teachings of the chemiatric school 259, 500 Aetiological theories – therapeutic strategies proposed by Ramazzini 259 Chinese medicine – method of diagnosing diseases by pulse observation 247f., 351 Cleyer’s method (1680–82) – his ‘Specimen medicinae sinicae’ (1682) 236, 248, 351, 732 Boym’s ‘Clavis medica’ (1686 ed.) on Chinese Cardioplegia 236, 248, 351, 732 Schröck’s questionnaire for Cleyer (1698) 236, 732 Diseases Asthma – mountainous, mining asthma 857f. Breast diseases – cancer and ulcers 249, 424 Consumption – pulmonary phthisis (‘Hüttenkatze’) 256, 348, 857f. Dysentery – medication against dysentery 248, 250f., 261, 422f., 505f., 606f., 612 Gangrene 606 Gout / Podagra – the ‘Patrician malady’ 195f., 248, 252, 263, 354, 423, 596, 613f., 717 Oncology, Cancers 249, 256, 424, 857 Malignant breast cancer 249, 424 Occupational and environmental lung diseases – pulmonary disease ‘Bergsucht’ (later ‘Schneeberg’) – occupational lung cancer 256, 506, 857 Otology / Diseases of the ear. See Anatomy, Aurality Rachitis or rickets – analogy to Papin’s steam digester or ‘engine for softening bones’ (1681) 244, 349 Schrader’s thoughts (1681) on petrification and induration of visceral organs – his knowledge about the embalming of corpses 244, 350 Rheumatic diseases 252

Index of Subjects Medicine (cont.) Scurvy – remedy for scurvy 163, 713 Spirit of sulfur as a remedy. See Chemistry Epidemiology – epidemics and pestilence 4, 101, 206f., 225, 248, 251, 257–262, 352–354, 423, 500–503, 505, 604, 612, 779, 824, 826, 858f. Bubonic plague – affliction and spread from Vienna to Prague and Leipzig (early 1680s) 225, 257, 352–354 Pronounced spread among the common people (Crafft) 257, 352 Cause of Leibniz’s lingering in Saxony (July 1680) 257, 353 Restriction of the movements of other travelers – Crafft’s inability to travel from Dresden to Berlin (April 1681) – Mencke’s / Pfautz’s stay in Oldenburg and inability to return to Saxony (Spring 1681) 257, 353 Leibniz’s ideas on health care policy – his proposals to combat the spread of the plague / ‘Vorschläge gegen die Pest’ (1681?), including the closure of borders 257, 353 His medical deliberations on the plague – his conviction that the malady resided especially in the body’s humors, above all in the blood 257, 353, 893 His reference (September 1680) to infusional medicine (‘medicina infusoria’) as an effective remedy 257, 353 His suggestion to investigate the cause of the pestilence, by investigating changes in the blood of infected persons 257, 353 Medical ephemerides 202, 261, 502, 505, 604, 822f. Preparation of medical ephemerides. See also Modena Ramazzini as Leibniz’s most important correspondent in Medicine (from 1690) – his role in the dissemination of Ramazzini’s writings 258, 262, 500, 604

1025 Publication of Ramazzini’s first epidemiological work (1690) 258, 500 Use of physical instruments in medicine – the barometer, hygrometer, thermometer 258, 500 Establishment of a relationship between diseases / illnesses and the prevailing weather conditions 258, 500 Introduction of statistical investigations in medicine 258, 500f. Demography, the statistical study of population – the quantitative recording of mortality, morbidity, population development 257f., 500f. Establishment of the causes and prevention of diseases – causes found in the weather, in occupational conditions, and the living environment 258f., 501 Epidemiology – investigation of causes and circumstances of the occurrence of epidemics 258, 501 History of epidemiology in the 17th century 258, 501 The role of Sydenham as an epidemiologist in the Hippocratic tradition – his concept of the ‘constitutio’ 258, 501 The epidemic constitution for a year or season – efforts for the annual publication of such ‘constitutiones epidemicae’ 258–262, 501–506 Ramazzini’s publication of epidemic ‘constitutiones’– his five annual ‘constitutiones’ (1690–94) 258f., 501f. Content, considerations, scope – descriptions of all epidemic diseases occurring in the Modena region – provision of information and data about symptoms, courses of diseases, therapeutics – weather and climatic influences on the occurrence of diseases 259f., 501f.

1026 Medicine (cont.) Health, welfare of farm animals and livestock – welfare of useful or crop plants like wheat, vine 259, 501f. Social, urban, rural sections of the population – the extent affected by a particular epidemic 259f., 501f. Epidemics in the Emilia-Romagna region (1690–94) 259, 501 Malaria epidemics (1690–91) – extreme precipitation and flooding along the Po tributaries (early 1690) – with the accompanying epidemic affecting the rural population 164, 403, 258–260, 501f. Ramazzini’s description of the course in relation to the individual seasons – accompanying ills like cereal / wheat rust and animal diseases 259, 502 Contrasting dry and warm conditions (1691) – with the epidemic primarily affecting the poorer urban population 259, 502 The typhoid epidemics (1692–94) – with different prevailing weather and climatic circumstances 259, 501f. Ramazzini’s attention dominated by typhoid afflictions – the transmission of infectious diseases – his view of the spreading through the air – transmission of the pestilence from Africa by a wind from the south 259f., 502f. Ramazzini’s epidemiological considerations – the plight of the Modenese region (1691–92) considered to have arisen from a series of afflictions – specifically a difficult climatic and epidemic situation, economic decline, threat of war and French intervention, shortages, including difficult provision supply for the Italian and allied Bavarian troops 260, 502f.

Index of Subjects Deployment of troops in the Modena region during war time regarded as epidemiologically innocuous 260, 502 Suspected connection between the epidemics and shortages, and infant malformation and mortality 260, 503f. See also Pathology Leibniz’s influence on the reprinting of Ramazzini’s ‘constitutiones’ by the Academia Leopoldina (1691, 1692) – his revived correspondence with the Academia’s president Volckamer – his further influence on Ramazzini’s appointment as (the 201st) member of the Leopoldina (1693) 260f., 502–505 Leibniz’s insistence on the necessity of collecting medical statistics in Germany, and of the Leopoldina using its influence to promote such undertakings 261, 505 Leibniz’s call for physicians to carry out and publish medical compilations for other regions and time intervals – sent to PellissonFontanier (December, 1692) and to Franck von Franckenau in Wittenberg (January, 1694) – subsequently forwarded to colleagues at other locations, including Berlin, Dresden, Halle, Leipzig, Magdeburg, and Torgau, Zerbst 260, 262, 503, 604f. Bodenhausen’s reference (1695) to an infectious dysentery epidemic in Italy 251, 612 Vagetius’ reference (1695) to the spread of the plague / epidemic disease throughout Germany 261, 604 Interruption (after 1694) of the series of ephemerides published by Ramazzini – Leibniz’s enquiry (1699) about the continuation of the series 262, 856

Index of Subjects Medicine (cont.) Ramazzini’s justification (1700) of the publication interruption – due to data collection having proved cumbersome for physicians, a lack of remuneration, and an absence of any new notable epidemic occurrences 262, 858f. Leibniz’s advocacy (1700) of data collection even in the absence of special occurrences 262, 859 Hoffmann’s ‘Dissertatio’ (1700) – his schediasm on the influence of winds on the human body 778 Leibniz’s and Hoffmann’s project for the annual publication of medical-meteorological observations – under the aegis of the Berlin Society of Sciences (1700) 206, 262, 825, 858 Leibniz’s health – characterized by an overall state of good health for most of his life 251f Problems arising in middle and old age – lower limb or foot ulceration (‘ulcus cruris’) – articular or joint problems like gout 251f. His health and therapy requirements 250f., 610–613 His feeling of health deterioration (1693) – subjectively-felt pressure of work / overwork in connection with the ‘opus historicum’ 250f., 610 His illness pattern (1693–94) with functional health disorders – caused by stress or mental strain 251, 610 His possible psycho-vegetative disorders 251 Bodenhausen’s reaction (1694–95) to Leibniz’s health worries – his attribution of Leibniz’s indisposition to a lifetime of overwork 251, 610f. His recommendations – dieting, exercising, resting 251, 610f.

1027 His diagnosis of Leibniz’s biliousness – revealed though external inflammation (phlogosis), painful urination, and the after effects of medical drinks (lemon juice) 251, 611 His recommendations for the – use of mild acids in fruit drinks – use of drops of vitriol, as a remedy against infectious dysentery – intake of a vitriolic emetic, under the supervision of a physician – avoidance of all exertion 251, 611–613 Leibniz’s reaction to Bodenhausen’s proposals – propensity to try out acidic / vitriolic remedies – reluctance to try out the vitriolic emetic 251, 613 Leibniz’s interest in the health conditions of correspondents 252, 613 Crafft’s fight against gout – his quest for medication to relieve suffering – his reference (1694) to Zipffell’s ‘Podagrischer triumph’  195f., 252, 263, 354, 596, 613f., 717 Leibniz’s interest in medication / medicinal products for relief of gout pains – medicaments obtained from quicklime through the spirit of wine – ‘Schroeder’s spirit’ prepared with quicklime 195, 252, 596, 613f. Haes’ queries regarding Moebius’ ‘teinture aperitive’ (1696) and Hoffman’s ‘spiritum martis volatile striatum’ (1696) 252, 613 Leibniz’s reflections on medicine as an empirical science – a sentiment expressed to Huygens (1694) – the mainstay of medicine being empiricism and practice 263f., 614, 738f, 896 His view of the necessity of observation and applications based on observation 88, 131, 288, 473, 614, 899

1028 Medicine (cont.) His vision of a religious order of friars (Capuchins), embracing medicine as a charitable endeavor 263f., 614f., 895 Medicine (hitherto) primarily an empirical science – a view expressed to Block (1698) – most of its theories and hypotheses having been hardly reliable or useful 263f., 614, 737, 895 His recollection of Meibom’s desire that the discipline be established on an empirical foundation – his greeting of the conjectures of competent physicians 264, 737, 896 Block’s reply and call for the institutions of medicine to reject occult speculation, and be rooted in empiricism – his doubts that medicine could be built up solely on the foundation of experience 264, 738, 896 Leibniz’s view on hypotheses and conjectures – serving as tentative solutions on the way to the establishment of the truth 264, 738, 896 His insistence on the need to separate certain from provisional knowledge 264, 738, 896 Leibniz’s deliberations on medicine as an exact science – his discourse on medical subjects with Italian physicians and scientists (1689–90) – ‘medici’ with mathematical abilities (Guglielmini, Spoleti et al.) 263, 425, 895 His vision of the application of mathematics in medicine – of medicine rooted in calculus, which was essentially a form of expression in the process of reasoning, an application of rational thought – a sentiment expressed to Bodenhausen (1690) 263f., 425f., 614f., 895

Index of Subjects Medical interests of other mathematicians – Joh. Bernoulli’s inaugural dissertation (1694) on the movement of muscles 264, 616 Leibniz’s admonition for him to continue his commitment to medicine 265, 615 Jac. Bernoulli’s sentiments (1696) on the opportunities and benefits of applying mathematics in medicine 616 Limbs – hands and hand analysis – palm reading (palmistry or chiromancy) 220, 830, 898 Medical experiment – role of the experimentalist 131f., 560 Medical observation – role of the observer 131, 473, 560 Medical observations – Pratisius’ medical observations (1691) 261, 505 Medical organization / Organization of medicine – Leibniz’s plea to Jac. Bernoulli (1695) 266, 615f., 742, 850 Medical practice – Stisser’s ‘Dissertatio epistolaris’ (1700) 223, 256, 837 Stisser’s passionate plea for the inclusion of chemistry in medicine / medical studies 256, 852, 896 His view of the omnipresence of chemistry in medicine – addressed to the enemies of chemistry, namely the ‘misochemists’ (‘misochymici’) 256, 852f. His example of foodstuffs like bread, beer, wine being prepared with the help of chemical processes 256, 852 His suggestion that both chemical and non-chemical medicaments were likewise being prepared with the help of chemical processes 256, 852 His argumentation was founded on authorities both past (like Hippocrates) and present – and also on case studies where wrongly prepared medication had brought

Index of Subjects Medicine (cont.) about undesired reactions 256, 852 Leibniz’s reply and complaint about the multiplicity of available pharmaceutical products 256, 852 His endorsement of Stisser’s opinions that – chemical medicaments had great advantages when derived from the natural world – more effective medication against illnesses that affected the body fluids would be found either by chance or as a result of advances in chemistry 256, 852f. Wagner as physician and patient – his reports (1699–1701) to Leibniz about his own ailments – and about the injuries and illnesses he treated – and the therapies he applied 254, 855 His reports about the chronic illnesses and deaths of professors in Helmstedt (1699/1700) 254, 855 Report about the recurring hemorrhages experienced by the hemophiliac J. A. Schmidt (1699) 254, 855 Report about the pleurisy of the medical professor Meibom following infection through contact with the patient and vice rector Wideburg – the failure of a bloodletting therapy and death of Meibom (March 1700) 254f., 856 Reports about the deaths of Ilse Stisser (in childbirth) and of her husband J.A. Stisser (April 1700) 255, 856 Report about the illness and death of Cörber, the professor of eloquence (April 1700) 255, 857 Wagner’s own short but intense illness (April 1700) – his suffering and symptoms – headache, hot flushes, lassitude, states of anxiety and fear of dying 255, 857

1029 His recovery following consumption of large quantities of medicinal beer made from scorzonera 255, 857 Report about the case of a fourteen year old patient (1699) – with hoarseness, coughing, intense headache, and an accompanying fear of asphyxia – treatment methods for headache considered involving the opening of the temporal artery, and use of medicinal leeches (bloodsuckers) 254, 856 Report about the case of a female patient from Halberstadt (1701) with a swelling / tumor on her cheek (1701) – Wagner’s treatment with relief, recovery and setback 254, 855 Medicine as a profession / The medical profession 4, 256, 262–265, 354, 614, 737–739, 895f. Perfunctory / superficial attitudes – accompanying professional status – sentiment expressed to Huygens (1694) 614 Physicians and surgeons 198f., 206f., 243, 246f., 249, 257–259, 262f., 265f., 326, 350, 352, 354, 425, 500f., 604f., 737, 739, 823–825, 850, 884, 897 Practical medicine 239, 608f., 615, 846, 895f. Practical and artisanal activity. See also Knowledge, Theory and Practice Social standing of physicians – social groups and social promotion in France during the reign of Louis XIV 265f., 739f., 862 Unqualified physicians – charlatans, quacksalvers, and the academically unqualified 262, 265, 354, 739 Instances of charlatanry / charlatanism Gedenus’ proposal of onions as an amulet against the plague (Vienna, 1680) 257, 354

1030 Medicine (cont.) Issue of the influence of the moon on the body humors (Schrader, 1681) 263, 355 Scradetzky’s apparent cure for gout (1682) 262f., 354 Instance of a Roman charlatan and his departure from several courts (Scheffer, 1682) 263, 355 Case of an amulet presented to the Elector of Brandenburg (Elers, 1682) – claimed to be effective against pain caused by stone (kidney, ureter and urinary stone) 263, 355 Case of a blacksmith’s laborer – his claim to be able to diagnose diseases by urine observation (Scheffer, 1682) 263, 355 Medical studies and qualifications 246, 850f. Pratisius’ critical report (1685) from Venice about medical practice and practitioners there – his critical sentiments regarding the pharmaceutical system – also about the methods of treatment 263, 424f. Leibniz’s advocacy of a comprehensive scientific training for physicians – his recollection (1698) of a meeting in Paris with the personal physician (Fagon) of Louis XIV – Fagon’s role in the enactment of a law requiring medics to provide evidence of their knowledge of anatomy, botany and chemistry – his efforts for the enactment of a law for the exclusion of charlatans and quacksalvers 265, 739f., 896 Molière’s satirization of French medicine – regarding the repertoire of the treatment methods of French physicians – their limitation to the application of clysters, enemata, purgatives or cleansing enemas, and venesection (phlebotomy) 265f., 739f.

Index of Subjects Gakenholz’s criticism of the existing system of studies and qualification (1701) 246f., 850–852 Occupational or industrial medicine 255, 500 Ramazzini’s investigation (1691) of the working conditions of laborers in the well pits and shafts of Modena – experience of suffocating vapors 255, 506 His tract on the diseases of workers and tradesmen, ‘De morbis artificum diatriba’ (1700) – its announcement to Leibniz 255f., 506, 857 Leibniz’s recollection of Agricola and Stockhausen 256, 857f. Agricola as representative of the medical profession – his works on the ailments of miners and pitmen 256, 857f. Stockhausen, a physician from Goslar – his tract on the lung diseases of miners (1656) 256, 857 See also: Diseases Organs. See also Pathology Internal / deep-seated / visceral organs 260, 349f., 503, 603 Kidneys (nephrology) 198, 243, 245, 247, 260, 263, 325, 346, 355, 503, 735, 851 Diseases of the kidneys – monstrous kidneys – description of an extremely enlarged kidney (1678– 1679) 198, 243, 263, 325, 346, 355 Male organs Conduit or vas deferens – male prowess 894f. Prostate, prostate or prostatic glands, seminal vesicles, testicles 243, 347, 894 Urinary tracts 243, 346 Urethra – external urethral / urinary orifice – the ‘meatus urethrae externus’ 243, 347, 611 Pathology Autopsies, dissections and postmortem examinations 235,

Index of Subjects Medicine (cont.) 244–246, 253, 601–603, 730f., 734–736, 853, 850, 896. See also Cannibalism, Corpse Medicine Bouquet’s anatomical reports from Padua (1695) – two remarkable autopsies, representing a grotesqueness of nature 244f., 601–604 First case: a corpse with an oversized split spleen – an extension of the diaphragm, with one part pressed into the chest or breast area – the other part pressed into the abdomen 244f., 601, 603 Second Case: the corpse of a crippled / maimed man – a school master with two livers – one of normal proportions in the normal location – the other within the coverings of the diaphragm, having the size of two fists, weighing two to three pounds, with an approximately round shape, and a small lobe, and located above the vena cava 244f., 601–603 Similarities with a liver (not the heart) were deduced – based on the form and substance of the organ, the path of the vena cava, and the distribution of other veins and arteries 244, 601f. Other anatomical anomalies – missing organs, in particular the gallbladder and the gallbladder passage to the intestines – organs of the lower abdomen were swollen, or overblown, were pressed together and pushed upwards 244f., 602f. Bouquet’s interpretation of the deformities / monstrosities – a grotesqueness of nature which failed to provide insights into the normal functions and

1031 functioning of organs 245, 604 The postmortem examination of Bodenhausen’s corpse (1696) – Block’s anatomical report from Florence – an abscess of the liver being the cause of his death 245f., 735f. Monstrous births and birth deformities Ramazzini’s report (1692) of the birth to a German woman of stillborn deformed female twins at a military camp near Modena 260, 503f. The twins were conjoined at their breasts and abdomens but were otherwise of normal proportions 260, 503 The presentation of the remains to the ducal authorities in Modena 260, 503 The postmortem examination where the pathologist found that the twins had but a single or shared heart, a single stomach, and a single liver – each individual was found to have its own intestines and internal organs including a bladder, kidneys, spleen 260, 503 The anointment and conservation of the remains among other cimelia – undertaken by Ramazzini 260, 503f. Ramazzini’s intelligence about the occurrence of a similar monstrous birth in Bologna 260, 504 Franck von Franckenau’s autopsy account (1697) – a postmortem examination in Copenhagen of the remains of a dead-born twoheaded girl – with two arms, two legs, and nails – the mother (wife of a schoolmaster) had previously given birth to several children 245, 734f.

1032 Medicine (cont.) Duplicate organs found – trachea or wind-pipe with outgrowths, oesophagus or gullet, stomach, small intestine (with ileus and sac), spine, lungs, ribs 245, 734 Single organs found – a heart, liver, spleen, kidneys, adrenal glands, urinary bladder, uterus, pancreas, mesentery, cunt 245, 734f. Aftermath of the autopsy – an exenteration followed by a public display – preservation of the remains in a fluid of florantibalsam (spiritus balsamicus) – deposition at the Royal Museum (Copenhagen) 245, 735 Pharmacy, pharmacists 209, 236, 246, 250, 328, 732, 850 Pharmacology – pharmacological advances 4, 247, 250, 610 Age-old conflict between physicians and apothecaries – with the production of medication in the hands of the apothecaries – Leibniz’s endorsement of the physicians 247, 350 His complaint to Stisser (1700) about an enormous multiplicity of pharmaceutical products 256, 852 Drugs and medications – adulteration of medication 250, 610. See also Herbs, Paraguayan Herb Antifebrile (antipyretic), febrifugal medicaments 252, 328, 740f. Antiepileptic or epilepsy drug – obtained from the hearts of frogs 247, 350 Antimony preparations 247, 350 Armenian (or white Armenian) bole 248, 423 Cinchona bark 247, 350 Emetics (vomitive agents) – antimonial emetics – vitriolic

Index of Subjects emetics 248, 250f., 290, 423, 606f., 609f., 612f. Ferguson’s skin cosmetic (‘cosmeticum Fergusoni’) 247, 350 Medication against dysentery 248– 250, 423, 505f., 606f. Medication against the pest 257, 353f. Medicinal beer – made from scorzonera (‘Schwarzwurzeln’) 255, 857 Moxa / moxibustion 328 Peru balsam syrup 248, 422 Smelling salts (‘Schlagbalsam’) 248, 422 Sulfur as medication against cough 247, 350 Sweet almond oil 248, 422 White candied sugar 248, 422 Wound healing / sore water 328 Herbs – herbal remedies 248, 261, 414, 421, 423, 506 Proposal (Gedenus, 1680) to use onions as an amulet against the plague 257, 354 An emetic plant from south America for alleviation of nausea or vomiting (1686) 248, 423 A herbal remedy against gout (podagra) – a Chinese plant in Florence (1690) 248, 423 Medicinal cortices or barks – used as emetics and nauseants, and in the treatment of dysentery 250, 607–609 A plant root called ‘Ipecacuanha’ (Justel, 1691) – Leibniz’s ‘antidysentericum’ from America (1696) – a rhubarb-like plant used as a remedy in the treatment of dysentery and as an ‘emetica sine violentia’ – previously used by the French army – Leibniz’s hope that it might also be employed by the allied forces 249f., 261, 505f., 605–609 Volckamer’s alternative recipe (1691) for the treatment of

Index of Subjects Medicine (cont.) dysentery – using vegetable or herbal remedies like sorrel / common or garden sorrel 261, 506 A herb from the Indies (‘herbe des Indes’) for the alleviation of vomiting (1694) – previously recommended by Boyle 251, 290, 610 Other medicinal plants from south America – Cinchona, Peruvian bark (‘Cortex Peruviana/ us’) – the Paraguayan herb (‘herba Paraguay’) – its effectivity as emetic or nauseant 250, 606–610 Other apothecary products (Wagner, 1701): crab’s eyes – dragon’s blood – prepared ‘mumia’ – prepared native cinnabar – diaphoretic antimony 253, 854 Physicians – court / personal physicians 6, 210, 214, 224, 235f., 245, 247, 261f., 265, 275, 331, 339, 350, 394, 505, 731, 739, 896 Physiology 4, 239, 242, 246, 266, 742 Public health – Leibniz’s special interest in public health matters – his proposed project with Hoffmann for the collection and annual publication of meteorological-medical observational data 246, 850f., 897 Rational thought / rationalization in medicine 4, 262, 855. See also Mathematization / Mathematics in Medicine Facets of the rational and critical thought in the reign of Louis XIV – foundation of academies and institutions during his reign 265 Leibniz’s quest for the development of a rational medicine 266f., 742f, 859f., 862, 896 His correspondence (1697) with the ‘medico-mathematicus’ Guglielmini 266, 742f. His expectation for Guglielmini to assist the advancement of a rational medicine, and to help

1033 mathematics find a place in medicine 263, 266, 425, 742f. Guglielmini’s hope of being able to deduce mathematical laws in physiology 266, 742 His skepticism regarding the possibility of the organization of medicine as an exact science – his view regarding the training of ‘medico-mathematici’ – medics were generally not versed in mathematics and not welldisposed to such ideas 266, 742 Leibniz’s belief in the higher value for medicine of rational over speculative thoughts – his opinion that plausible hypotheses should replace less certain conjectures, which were to be taken into consideration only where they were expedient or purposeful 266, 743 The importance for Leibniz of keeping certain and provisional knowledge separate 264, 266, 738, 743 Leibniz’s quest (1699–1701) for the development of a rational medicine – his correspondence with the medical (Cartesian) philosopher Hoffmann – his interest in Hoffmann’s ideas on the mechanism of nature, and the representation of nature 266f., 859f., 862, 896 Leibniz’s insistence on the reduction of composite principles to simpler (or secondary) principles – firm concepts were be chosen and vague terminology avoided 267, 859f. The outcome (after Leibniz’s death) – Hoffmann’s multi-volume work ‘Medicina rationalis systematica’ (1718–34) 267, 860, 896 Sexual reproduction 240, 243, 347, 894f. See also Biology Debate about constituent parts of mammalian semen – positions of

1034 Medicine (cont.) Dutch physicians and professors (van Horne / Hoorn, De Graaf, Swammerdam) 243, 347 Schelhammer‘s result (1680) and Leibniz’s objection 243, 346f. Surgery (‘res chirurgica’) – surgery, surgeons, barber-surgeons 177, 199, 216, 249, 257, 322f., 352, 424 Therapeutics – therapeutic applications against diseases 4, 247, 250, 253, 259, 350, 422, 500f., 606, 854 Chronic diseases – Lister’s ‘Exercitationes medicinales’ (1696) 249, 606 Women’s breast diseases – methods of prevention and treatment – painful operations by barbersurgeons – quest for milder treatment methods (Tschirnhaus, 1683) 249, 424 Universal remedies – cures and panaceas 249, 264f., 423f., 738f. Ledel’s panacea against chronic diseases (1688–90) 249, 423 Block’s belief (1698) in a form of panacea or universal remedy 264f., 738 Leibniz’s reference to the investigations of the English physician Morton – his finding that (in the case of fever patients) a remission often occurred, making it possible for the physician to save the patient – in contrast, with extreme weakness of the body recovery was no longer possible 264f., 738f. Morton’s inability to find a means for the procurement of a remission – Leibniz’s continued adherence to Morton’s vision 265, 738f. Metallurgy, metallurgists, metallurgical processes 133, 142, 152, 187, 394, 407, 857f. American, Spanish-American metallurgy – Barba’s ‘Art of metals’ (1640) 142, 394

Index of Subjects Boyle’s contribution to the study of metals 89, 289 Casting of metals – production of malleable cast iron 5, 151f., 273, 399f. Rupert of the Rhine’s process for tempering iron, and the production of an alloy (Prince Rupert’s metal) 5, 139, 160, 273, 387, 806 Douceur’s cast-iron process (1679– 1684) – his roasting or annealing process – technical details of the process 5, 142, 151f., 217, 225, 273f., 312, 397, 399–401, 415, 809 Tyresson’s (Falkenstjerna’s / Falkenhjelm’s) process for making iron malleable (1699) 225, 809 Foundries, metal foundries 858 Refiners of metals 187, 407 Sheet metal, sheet metal works 408 Production of canons. See Engineering, Military Engineering Metaphors – Leibniz’s metaphor of an evil spirit / little devil 24, 449 Metaphysics. See Philosophy Meteorology 3, 7, 99–102, 278, 299. See also Physics, Geophysics Meteorological history – Drebbel’s tract on the nature of the elements (1608) – wind, rain, storms (thunder and lightning) 190, 410, 824f., 777f. Meteorological instruments. See Instruments Observations – barometric / meteorological ephemerides 99, 204, 474, 775, 818, 823 Weather – rain and precipitation 100, 259, 501f., Weather observations – corresponding simultaneous observations – wind conditions at different locations 99, 324f. Microscopy, microscopes. See Instruments Mineralogy. See Geology Mines and mining – coal mines, copper mines, lead mines, silver mines 150, 199, 201, 226, 343, 500, 802f., 891 Mining in the Harz mountains 133f., 138, 142–144, 146, 148, 151, 162, 256, 273, 275,

Index of Subjects Mines and mining (cont.) 299, 307, 313, 356f., 386, 394f., 428, 566, 813, 857, 878–880 Corrosiveness of water in the pits 136, 311, 878f. Slanting mine pits 151, 800 Variation of slope along the veins 151, 800 Leibniz’s involvement in the Harz ore mines – his ideas for improvement of ore production – his frequent visits and periods of absence 8, 10f., 133–135, 307–310, 357, 428, 508 Brandshagen’s role as supervisor and accountant – costs and payments for labor and materials – tradesmen, smiths, millers, material suppliers 138, 386 Leibniz’s counterparts and opponents in the enterprise Linsen’s role in technical and engineering matters – provider of wooden models for technical designs 134f., 139, 143f., 308f., 386f., 566 Board of mines in Clausthal – local mining authority and mining officials – his main opponent, the juror Pöhler 134–137, 145f., 307–309, 384–387, 567, 569–571, 880 Court chamber in Hanover – his superiors – his reputation and influence at court 4, 11, 13, 135, 143, 145, 273, 309, 508, 565, 567, 617 Engineering techniques, processes, procedures – power supply, pumping, winding, transmission machinery 134f., 137–141, 143–146, 161, 307f., 384–388, 391–393, 407, 565–571, 810, 878–880. See also Power Technology Water-powered and water-raising machines 62, 134–136, 138f., 142, 147–150, 153, 161, 178, 299, 309f., 311, 386–388, 392, 395, 397, 570, 572f., 687–689, 695, 872, 879, 881 Vertical water wheels 62, 144, 154, 309, 312, 532, 567, 570, 698, 872

1035 Use of water wheels for draining the mines – powered by rainwater collected in reservoirs 134, 307 Use of water wheels for hoisting ore – ore production dependent on water supply – reduced in times of drought 134f., 138, 144f., 307–311, 386, 566, 571, 685f., 879f. Winding machinery for hoisting ore 134, 139, 143–145, 386f., 407, 565–570, 879f. Leibniz’s most important innovation in mining – exploitation of wind power – use of windmills 46, 134f., 169, 273, 275, 308f., 311–313, 385, 813, 878; See also Power Technology His use of windmills for draining the mines – at the Dorothea Landskron colliery (1679) – at the Catharina colliery (1680) 136–138, 384–386, 878f. Windmill project for draining mines – idea of using wind power with vertical (or horizontal-shaft) windmills 137f., 385f. Alternative project using horizontal (or vertical-shaft) windmills 137– 139, 142, 311f., 385–387, 396, 813, 878f. Applications of windmills – the ‘immediate’ and ‘mediate’ solutions The ‘immediate’ solution using vertical windmills – direct attachment of pump assembly – preferential trials of the direct system – protracted series of trials, with the employment of new pumps – use of control mechanisms, for more uniform operation – contemplated power transmission using compressed air 137f., 384f., 878 The ‘mediate’ solution using horizontal windmills – employment of pumped-storage techniques to service and replenish reservoirs, especially in times of drought 137, 162, 384f., 813, 878

1036 Mines and mining (cont.) Idea of Hartsinck (Hartzingk) adopted by Leibniz (1680) – deployment at the Zellbach colliery 137, 384f., 878 Trial of horizontal windmill at the Lower Eschenbach pond (1684), but not under full-load conditions – problem of erratic wind supply in the mountainous environment 137f., 385 Aspects of horizontal windmills – horizontal rotation of vanes about a vertical axis – uniform regulation of wind power – lower efficiency and lower construction costs compared with vertical windmills 137f., 385f. Efficiency improvement of vertical windmills – by rotation of windmill sails with direction changes of the wind – by variation of inclination of the sails’ axis with strength changes of the wind 136, 311 Leibniz’s commitment to efficiency improvement – interest in discoveries / innovations – instructions for craftsmen / tradesmen 4, 7, 135–137, 141, 143f., 188, 309, 356, 385, 392, 407, 566, 879f. His regular visits to the mining district 135, 309 Efficiency improvement of pumping systems in the mines 4, 7f., 136, 138, 144, 146, 153, 356f., 384, 386, 407, 565f., 571, 685f., 879 Corrosiveness of water in the Harz pits – corrosion of metal components – detrimental for use of the ‘bucket and chain’ system 136, 311, 878f. Use of pumps with wooden cylinders – arranged in tiers, one above the other 136, 311, 879 Reduction of friction losses with – ‘rag and chain’/‘paternoster’ pumps – piston-pumps with flap

Index of Subjects valves – leather sealing of valvepistons 141, 146, 392f., 571 Power transmission mechanisms – parts of the mechanism and frictional losses between them 141, 393, 879 Later improvement of the pumping machinery (1694– 95) – construction of energy-saving pumps – reduction of friction losses – replacement of leather obturator rings – use of pump cylinders with valves 144–146, 566f., 571, 879f. Improvement of winding / hoisting machinery – closed-loop or endless cable – powered by water wheels 138f., 144, 386f., 566, 879f. Test of practicability and advantage, at pits in the ‘Thurm Rosenhofer’ mountain range (1685) – repair / maintenance work at the pits (1686) – termination of the test series 138, 385f. Proposed venture (BornemannJenisch, 1693) – winding machinery to be powered by horses – employment of an endless cable / rope for weight compensation – postponement following Leibniz’s priority claims 143, 565f. Transmission systems for power supply to the pumping machinery – iron crankshaft component – alternative construction 134, 308 Repair and maintenance work – adverse weather conditions – transport and installation difficulties 134, 138, 308, 386 Role of skilled craftsmen / tradesmen – carpenters, cabinetmakers, charburners, millers, tailors 134f., 138, 143f., 156, 212f., 308f., 386, 412f., 700, 719 Role of Leibniz’s designs – use of cogged wheels engaging lantern pinions with vertical staves – cog

Index of Subjects Mines and mining (cont.) and rung transmission – transfer ratio value 62, 134f., 161, 308, 532, 810f., 872 Projected power transmission system (1682) – making use of compressed air 135, 137, 308, 385 Becher’s report on waterworks, water wheels 140, 391 New power transmission system – a variant of the long-established rod-engine technology – a ‘Stangenkunst’ with rods connected to a double rotary crank mechanism – with regular (circular) motions at the ends, and an alternating linear motion in between 139–141, 391f., 879 Connection of a prime mover – supplying wind, water, or horse power with a distant load 137, 140f., 145, 162, 384, 391f., 569, 813, 879 Leibniz’s theoretical ideas regarding mining His efforts to prove their practicality – theoria cum praxi 15, 828 His time-consuming mining involvement (1680–86 and 1693–96) – aims of improving the efficiency of the mine-dewatering pumps and the ore-hoisting winding machinery 4, 7, 144, 188, 356, 407, 566, 880 Elements of his innovation – replacement of horse power by water power – replacement of an overshot reversible water wheel by a rod-engine transmission system from a remote power source, like a water wheel on a stream 144, 392, 566, 879f. His design of a power supply system for the joint operation of the pumping machinery and the winding or hoisting machinery 144, 566f., 880

1037 Reduction of the overall power requirement – use of a novel tugging / towage mechanism and a switchable pinion-gear mechanism – use of an endless (closed-loop) winding cable 144f., 566f., 880 Transformation of horizontal into vertical linear motion – of above ground alternating rod motion into alternating motion of the piston rods 144, 566f. Transformation of linear into rotary motion – of above ground alternating rod motion into closedloop rotary winding motion 140, 391 Introduction of a switching point along the transmission line – between water wheel and pithead 144f., 566f., 569 Pithead transformation elements – a cross-shaped lever-device for the pumping machinery – a capstan or roller drive for the winding machinery 144f., 566f. Trials of the combined system – supervision / progress reports of the trials (Reimers, Crafft)  144–146, 566–571, 880 Demonstration (February 1694) of the ore-hoisting function – subsequent dysfunctionality 144f., 566–569 Conflict with the mining office – opposition and obstruction from jurors and mining officials 145, 567f. Damage / sabotage to the rod-engine system (April 1694) 145, 567–569 Doubts about the combined system – about its capability to meet simultaneously both requirements – the pumping and ore-hoisting requirements 145, 569f. Issues of meeting costs incurred and suspension of trials (in 1695) 145f., 570f.

1038 Mines and mining (cont.) Other mining districts in Germany Freiberg mining district 141, 391f., 879 Mining in the Erzgebirge / Ore mountains, Saxony 201, 499 Water mill near Ehrenfriedersdorf, Saxony – the water wheel ‘Ehrenfriedersdorfer Radpumpe’ 140f., 391–393, 879 A technically-improved version, consisting of a single prime mover – a horse mill or water wheel – a piston-pump system with two or more pump stages, one above the other – a transmission mechanism with sections – comparable to rodengine sections 141, 392, 879 A Hesse coal mining location – Papin’s employment of his Hesse pump (1699) there with a long wooden air-conduction pipe – serving for mine aeration or ventilation in the coal mine 150, 802f. See also Pumps Breathing difficulties in the pits, and the extinguishing of lamp flames there – attributed by Leibniz to inadequate air supply and circulation 150, 803 Ilmenau mining district – source of mineral ore containing fossilized plants – sent by Heyn (1690) 141f., 228, 394, 421, 891 Other mining districts in Europe and beyond Central European mines – silver mining and minting – the mining boom 199 English mines and mining engineers – accounts of the engineer Heyn (1686–87) – his practical experience in English mining – his familiarity with English mineral ores 139, 201, 387, 499 Cornish mines – the mining district of Cornwall) 9, 139–141, 358, 387–389, 390, 392, 879

Index of Subjects A standard scoop wheel water lifting system – referred to by Heyn (1687) 139, 387f., 879 A novel water wheel-powered pumping machine – with alternative power sources namely water, wind, horsepower, and manpower – constructed at a disused pit – designed by Becher (+1682) and reported to Leibniz by Heyn (1687) 139–141, 387–392, 879 Technical details of the Cornish ‘Taschenkunst’-like machine – a Rag and chain / chain of beads pump system – consisting of a series of pump stages, with similarities to the stages of a rod-engine transmission system – provided with pumps using several pipes / pistons of different measure – operating in perpendicular or inclined shafts at depths up to 100 or more fathoms 139–141, 287–389, 879 Successful operation of the machine over a period of three years – with an investment return of 1100 Taler (250 pounds sterling) for the operating company and investors 140, 389f. Ultimate demise of the machine – machinery at a complete standstill following vein termination and a mining accident – revelation of details of the machine offered by Heyn to Leibniz using a model of the device 140, 390 Hungarian mines 9, 188, 358, 407, 612 Paternoster pumping system – described by Agricola (1556) 139, 388f. Scottish coal mines 136, 310f. Paternoster pumping system with chain and buckets for lifting water from the mine

Index of Subjects Mines and mining (cont.) pit – powered by horse mills – reported to Leibniz by Huygens (1680) – issue raised of investment versus expected return 136, 310 Spanish-American mines and mining – Barba’s ‘art of metals’ 142, 394 Swedish mines and mining 142, 151, 394, 800, 806 Copper mining at Falun – King Charles XI mineshaft (1698–99) 151, 159, 800, 804 See also: Furnaces Machines of the engineer Polhammar (Polhem) – suitable for inclined or slanting pits – used for quarrying out stone – the conveyor system with conveying machinery 151, 800f. The Swedish mining expert Odelius 142, 394f. Welsh mining – silver mine in Wales 201, 500 Monarchy, monarch 152, 400, 497, 617f., Sovereign(s) 8, 11, 13, 143, 156, 177, 200, 309f., 499, 508, 565, 590, 617, 702, 715 Princes 4f., 11, 23, 27, 33, 139, 169, 175f., 183f., 191, 193f., 197, 200, 202, 213, 218f., 244, 272f., 302, 315f., 327, 387, 412, 417, 433, 483f., 497, 508, 514, 598, 601, 621, 701, 704, 713, 802, 829, 865 Subjects 184, 316f., 497 Motion, movement. See Natural Philosophy Münden 192, 591 Münster 11, 193, 508 Muscovy. See Russia Nature Kingdoms of nature – animal, mineral, vegetable realms 222, 890 Secrets / treasures of nature 206, 683f., 721, 825f. Treasures of nature – shared among many bodies / substances – example vitriol 721. See also Alchemy, Chemistry

1039 Natural history 226f., 229, 235f., 239, 419, 484, 504, 723, 729, 732, 892. See also Biology and Geology Natural philosophy xii–xv, 3, 50ff., 52, 57f., 87, 150, 157, 209, 219, 230, 287f., 362ff., 366, 450ff., 452, 458, 525, 646f., 703, 757ff., 870ff., 892 About nature – features, laws, philosophy, science, works of nature 55f., 60, 81, 120, 155, 219, 238, 245, 247, 267, 303, 343, 352, 363, 404, 460f., 525, 544, 604, 684, 700, 763, 798, 845, 847, 852, 859, 890f., 897, 899 Aristotelian (and scholastic) natural philosophy xii Natural philosophy of Descartes – his approach to the vegetal realm – the mechanical life of plants 58, 238, 458 Natural philosophy of Papin 57f., 363, 458f., 757f. Natural philosophy in Leibniz’s correspondence 50–87, 287–307, 362–365, 450–462, 525–539, 646–682, 757–775, 870–874 Core concepts and topics (Leibniz / Papin) Action. See also Bodies, Force, Motion, Movement Action – a continuing state which exists by virtue of the movement of a body – movement per se as a kind of action 74f., 671 Action – a succession of states of a body during a change of location 672 Different terminology for the concepts 61, 65, 75, 79, 527, 648, 671, 759 Action (‘actio’, ‘action’, ‘Wirkung’) 66, 74–80, 646, 648, 669, 757 Actions over equal time intervals – ‘actions contemporaines’ 76, 676 Change, mutation – ‘changement’, ‘mutatio’ 75, 671 Change of location – ‘changement de lieu’, ‘mutationes loci’ 75, 80, 82, 671, 762, 764, 769 Changes of space – ‘changemens des espaces’ 79, 758

1040 Natural philosophy (cont.) Changed spaces – ‘espaces changés’ 79, 758f. Produced changes – ‘mutationes loci productae’ 78, 758 Producing changes – ‘mutationes loci producendae’ 78, 758 Traversed spaces – ‘espaces parcourus’ 78, 677, 758 True action (Leibniz) / Intrinsic movement (Papin) 75, 673 True / veritable action estimated both by its intension (celerity / promptitude), and by its extension (duration) 75, 673 Concepts of change – intensive or temporal change (‘intension’) – extensive or spatial change (‘extension’) 75, 82, 673, 765f. Papin’s proposal to equate action with a perseverance / persistence within the same manner of being – thus its independence of the movement 79, 759f. Multiplication and division of an action – doubling, triplicating / halving, trisecting, etc. – instance of a body moving uniformly through a given space over one, two, three, etc. time intervals – instance of a given space being traversed in half, a third, etc. of a time interval 74f., 669f., 674f. Leibniz’s proposition regarding action Action proportional to – the product of path and velocity – that of time and the square of velocity 76, 674 Actions over equal time intervals proportional to squares of the velocities 76, 676 Absurdities or contradictions arise if actions be made proportional to velocities, traversed paths, times (or reciprocals of times) 76, 676 Leibniz’s principle of action – and its combination with his measure of force by which every exercise of

Index of Subjects force passes for an action – free of absurdity or contradiction 76, 676f. His conclusion regarding his conservation law for force – the quantity of action in the world is conserved 76, 537, 675 The Cartesian interpretation 76, 81 Papin’s conception of action and force – different concept of action to that of Leibniz 75, 77–79, 87, 670f., 678, 757f., 775 Papin’s rejection of Leibniz’s proposition regarding action – his assumption an absolute indifference for every kind of manner of being – a perseverance or persistence within the same manner of being 76, 79f., 675, 761f. The Cartesian measure of force – erroneous for Leibniz due to the confusion of the quantity of action, and quantity of movement 76, 674, 676f., 681f. Papin’s rejection (Nov. 1698) of Leibniz’s quantity of action 77, 681 Leibniz’s two different forms of action – formal (a priori) action, where the acting force is conserved – violent or contingent action, where the acting force is consumed – both forms (‘actions violentes ou contingentes’) yield the same measure of force – essentially a connection of action and force 77, 679f. Action proportional to – the product of force and time (Leibniz) – the product of distance and time (Papin), an embarrassing contradiction (for Leibniz) 77, 86, 679, 773f. Distinction between force and action – action as a resistance-free movement 75, 77, 79, 671f., 681, 758

Index of Subjects Natural philosophy (cont.) Papin’s endorsement withdrawal (Nov. 1698) 77, 681 Force always implies an action (Leibniz) – view rejected by Papin 76f., 675, 680 Papin’s view that all bodies with the same volume – be they in motion or at rest – have the same force 77, 680 Force manifestation involved both with motion with resistance and with motion without resistance, where a body is at rest 75f., 670, 673, 676, 679 Force acts on a body’s own mass – the body rotates around its axis – the exercise of force is conservative 75, 672 Reaction – re-action 75, 670, 682, 758 Leibniz’s action without reaction possible – with a movement that does not surmount any resistance 74f., 669–671, 681f., 758 Papin’s action – no action without reaction – action tantamount to overcoming of resistance 75, 78, 670, 682, 758 Papin’s own notion of change of place / location – more distinct for him than that of action 762 Bodies Bodies in motion. See Motion, Movement of Bodies Collision of bodies – laws of colliding bodies – duration of the event – bodies reduced to a state of (relative) rest – postcollision separation 58, 65f., 71f., 80, 82f., 85, 451f., 647–649, 656, 662–664, 649, 761, 766, 770f, 873 Elasticity of bodies and of their constituent parts – intervening springs between bodies– breaking effect of a spring – elastic resilience of a spring 59–61, 64–68, 70f., 73,

1041 461, 527, 536, 538, 648f., 651, 654, 659–662, 666, 872 Masses and velocities of colliding bodies 69, 656 Essence / nature of bodies – a body’s manner of being – a general inclination for its conservation (Papin’s penchant) – an inherent / intrinsic predisposition of its being present 52, 80f., 452, 761, 763 Essence of a body (Descartes)  458 Extension / physical extension of bodies 52, 452 Forces (and mutual interaction) of bodies – forces associated with corporeal states 55f., 525 Hardness of physical bodies – assumption of perfect hardness – condition / state of perfect hardness – its conceivability without contradictions 59, 68f., 80f., 461, 652, 654, 656, 873f. Leibniz’s view (April 1699) of a transition from movement of a body along a curve to that in a straight line – representation of a change of state 763 Example of the free-fall of a hard ball and rebound from an anvil – the movement in contrast to that along a curve – a small change in height would be scarcely noticeable – changes in the direction of oblique impact would lead to more appreciable obliquity 81, 762, 764, 874 Papin’s view (May 1699) of movement along a curve – as a concatenation of an infinite number of states 82, 764 Leibniz’s view that movement along a curve was indeed a concatenation of states – the

1042 Natural philosophy (cont.) past, future and location change were states that were being conserved – the change of direction represented a further state that was being altered 83, 766 Impact of bodies – laws of impact 64f., 536, 538 Inertia and mass of bodies. See also Entelechy and Inertia below Inertia of bodies – inertia of an essential nature and always existent in a body, both at rest and in motion 81, 763 Mass – mass of bodies 51, 56, 59, 61f., 66, 69–71, 73, 75, 80, 87, 110, 287, 362f., 461, 463, 526–528, 537, 641, 647–649, 656–658, 660, 662–664, 666, 672f., 681f., 760–764, 781, 861, 871–873 Motion of bodies. See Motion, Movement Oscillation and percussion of bodies – centers of oscillation and percussion 65, 93f., 295f., 372f., 538f. Percussion and elastic spring 70, 660f., 872 Properties of bodies – intrinsic and extrinsic properties – possible application to movement 84, 769 States (‘manieres d’être’) of bodies – rest and motion – single and compound states 80–82, 84, 86, 774, 761–766, 769, 873 Papin’s view that both states had the same amount of reality, perfection, force 774 The same amount of force was to be found everywhere and in everything 86, 771 A body in motion acts more strongly in the direction of motion 86, 774

Index of Subjects A body at rest acts more strongly in the opposite or reverse direction 85, 770f. Papin’s incorporation of a weakness in the opposite direction – at variance with Leibniz’s understanding of action 85, 771f. State of motion (Papin’s view) – the movement not stronger, more real or perfect than the state of rest 84f., 770 State of rest – an apparent (or potential) state, or the true (actual or real) state – rest as such regarded as, or similar to inertia 82f., 766 Relation of the state of rest to that of motion – like the relation of zero to the positive numbers 82f., 766 Incompatibility of states (Papin) 83, 85, 766, 770 Resistance – concept of incompatibility or resistance (Papin) – external resistance 83f., 766, 769 Compatible or incompatible states – like rest and motion 82, 764 Leibniz’s distinction between the states of rest and motion 80f., 762 Nature’s (matter’s) penchant or preference for an existing state 81f, 763f. Change of state of bodies – three states of movements – past, future and location change 83, 766. See also Motion Concatenation of states – multiple states – an infinite number of states 82f., 764, 766 Curvilinear motion – a compound state involving changes of direction – no conservation of state 83f., 767, 769

Index of Subjects Natural philosophy (cont.) Internal and external causes – change of location (internal) – change of direction (external) 73, 75, 77, 82, 83f., 667, 671f., 681, 765f., 769 Rectilinear motion – a composite entity, involving a conservation of state 84, 109f., 542–544, 769, 876 Uniform motion – consisting of several states 76, 78, 83, 674f., 678, 758, 766f. Conservation of states of bodies – maintenance of a state of being – actual, real or merely potential – provision by means of an entelechy – motion attributable to the intrinsic force or entelechy 80, 83, 761, 766, 873, 892. See also below: Entelechy Change of location – attributable to an internal cause 84, 769 Change of speed / velocity – attributable to an external cause 83, 766 Change of direction – attributable to an external cause 84, 769 Change of duration – duration and speed / velocity – greater perfection of rapid movement 84–86, 772f., 769 Nature of change – simple change – change of change – end of change as the external cause becomes inoperative 83f., 766 Quantity of change(s) – of changes of location – quantity of changed locations 83, 85f., 767, 772 Papin’s view of quantity of changed locations (or that of changes of location) – manifest as the product of the times and velocities 78f., 85f., 772

1043 Leibniz’s view of an absurdity in Papin’s interpretation of duration and velocity – with mutual compensation or a reciprocal relationship between times and velocities – the entities were not always in such a reciprocal relation 86, 773 Leibniz’s comparison with the relationships between assets and liabilities (debts), possession and deprivation, knowledge and ignorance, darkness and light, states of action and rest 86, 773f. Papin’s recapitulation of the conflicting positions (Spring 1700) – his insistence that all states were like bodies, at rest and in motion – possessing the same degree of force, of perfection, and of reality 85f., 772 Leibniz’s elaboration of his views about the for him still unanswered matters of dispute (April 1700) 86, 774f. Stress – state of stress 60, 461 Substitutability of bodies 58f., 64, 459, 536, 647, 871 Substitution / surrogacy. See Experiments Transferability / transmission between bodies – or a non-transferability / nontransmissibility – of the total force of a body to another – from a body of greater to one of lesser mass – or following replacement of a body by a larger body (or wall) 58–60, 70, 459–461, 647, 656f., 660, 871f. Feasibility of a transfer / transmission between bodies – means of realizing such a transfer – practical execution of a substitution 59, 69, 460, 656f.

1044 Natural philosophy (cont.) The elastic resilience of bodies – spring tension or spring force 61, 66, 68, 527, 649, 654 Cause(s) – cause and effect – principle of the equality of cause and effect – efficient causes (‘causae efficientes’) – final causes (‘causae finales’) 56, 59, 65, 72, 87, 287, 526, 539, 664 Effect (‘effectus’) – quantity of effect 51, 61, 364, 460f., 527 Entities – incomplete entities – substantial or absolutely real entities 56, 362, 461, 762, 770 Dynamics – Leibniz’s dynamics 50– 56, 60, 64f., 87, 96, 183, 230, 363, 364, 451–456, 525f., 535, 538f., 590, 648 Fundamental concepts of his dynamics – abstract Dynamics – concrete dynamics 51, 364f. Parallels to the infinitesimal calculus 63f., 535 Dynamica – Leibniz’s projected work ‘Dynamica’ 50–58, 80, 92, 363–365, 375, 451, 453–456, 459, 525, 537, 736f. Classification of the ‘Dynamica’ – content of the work 51f., 363–365 Versions of Leibniz’s dynamics – manuscript version (‘manuscriptum dynamicum’) – Élémens de dynamique (1692) – Essay de dynamique (1692) 53, 454 Specimen dynamicum (1695) 55, 60, 63, 65, 525f., 535, 538, 648 Entelechy – Leibniz’s concept of an inherent, intrinsic, purposive force – the realization or actualization of that which is merely potential through an entelechy – the concept rejected by Papin 80–83, 85, 761–764, 766, 770, 873, 892f.

Index of Subjects Considerations about inertia and entelechy – Leibniz’s hypotheses regarding inertia and an entelechy – inertia was of an essential nature, and always existent in a body, both at rest and in motion – the entelechy in contrast was of a changeable nature 81, 763 Papin’s view of an obligation for Leibniz to prove his hypotheses regarding inertia and the entelechy 82, 764. See also Inertia below Considerations about the mass of bodies and the entelechy – mass was of an essential nature, the entelechy of a changeable nature 80, 760f., 762f., 873 Leibniz’s distinction between states of rest and motion – his concept of the entelechy being essentially a preference for the existing states of rest and motion 80f., 761–763 For Papin the entelechy meant an added complication – a multiplication of entities 81, 762 Force – ‘force’ – ‘conatus’ – ‘effort’– ‘potentia’ – ‘vis’ 14, 18, 50–87, 96, 101, 103, 106, 108–111, 149, 167, 183, 287, 358, 362, 366, 369f., 375, 383f., 389, 393, 451, 453–455, 458–463, 477, 481, 525–530, 532–538, 542f., 545, 549f., 563f., 589, 646–682, 692, 744, 757f., 760–764, 766, 770–772, 774f., 780f., 861, 863, 871–876, 892f. Conceptions of force 61, 527 Active and passive forces – total and partial forces 53, 56, 453, 525 Internal force (‘vis respectiva’) and outward-operating force (‘vis directiva’) 56, 525

Index of Subjects Natural philosophy (cont.) Metaphysical and physical forces – ‘vis primitiva’and ‘vis derivativa’ 55, 525, 648 Motive / moving forces – force in Leibniz’s Dynamica. See also Dynamics Concept of force – metamorphosis of a concept xiii, 50, 61, 527 Leibniz’s concept of force 55, 65, 538f., 648 Leibniz’s understanding of force – his distinction between force and inertia – Papin’s rejection of the distinction between force and inertia 77f., 80, 681 Force exists only when a body is in motion, and varies with velocity – force an active ability or acquirement – inertia a passive ability (‘potentia’) 77f., 680f. Leibniz’s view of force as the most important property of bodies 52f., 453 Types of force – absolute and relative – living force (‘vis viva’) and dead force (‘vis mortua’) – real force and virtual force 14, 55–57, 61, 64, 66–68, 70–72, 450f., 525, 527, 535, 646, 648–651, 653, 658f., 661, 664, 744, 861, 871–874 Conservation of force – conservation of force requirement 60, 657 Absolute force – that produced where there is a certain determined movement – a living, productive, and spatial force analogous to areas, being the force conserved in nature – the corresponding law of ‘vis viva’ – a collective law of conservation and the principle of its conservation 71, 454, 537, 661f.

1045 Leibniz’s conservation law – product of mass and the square of the velocity – the conservation of this entity (‘vis viva’) 87, 287, 363 Relative force – that produced for the determination / regulation of a body – preventing its advance, forcing its reversal of direction – a dead, disabled, relative, plane force analogous to lines – the corresponding law of ‘vis mortua’ – a distributive law of changes 71, 661f. Leibniz’s other conservation laws – product of mass and directional velocity – his concept of progress (‘progrès’), the counterpart of ‘force morte’– the conservation of progress 70, 660f., 872 Papin’s conservation law – product of mass and velocity – movement, momentum and impulse – the conservation of this entity 56, 62, 71, 362, 662, 871 The conservation of force requirement – violation of the requirement 69, 657 Quantities conserved in all mechanical changes 57, 451 The ‘vis viva’ controversy. See also Controversies and Disputes Consumption of force – the consumption of dead force – accompanying that of living force, but In a different proportion 71, 661 Example of the tensioning of a spring – arising from the dead force – accompanied by the consumption of living force – comparison with changing areas and peripheries in geometry 71, 661 Example of the ascent of a weight against the force

1046 Natural philosophy (cont.) of gravity – similar to the tensioning of a spring 71, 661 Estimation of force – Leibniz’s estimation of force 64, 536, 682, 771 An ‘aestimatio virium’ (‘ars aestimandi’) – auguring additivity, homogeneity, substitutability 64, 535f. His (real) measure of force – proofs for his measure of force, independent of experiment  66, 649 His distinction between force and action. See Action Measure of force – Leibniz’s measure of force – Papin’s measure of force – both rooted in space and time 14, 18, 60, 66, 73f., 76–78, 80, 82, 85–87, 287, 358, 526, 536, 538, 647, 649, 666, 669, 674, 678, 679, 681, 744, 757, 761, 766, 771f., 774f., 863, 871, 873f. True measure of force 18, 60, 66, 73, 78, 85, 358, 526, 649, 666, 757, 772, 863 Measurement of force by number of traversed springs – overcome with equal tension force / stress state of the springs 59f., 461, 647 Quantification of forces, based on the – attained heights of fall of bodies – distance covered by bodies – duration of the motion of bodies – velocity of the bodies – the product of mass and square of velocity 56, 59, 64, 71, 75, 460, 526, 536, 647f., 662, 671, 861 Transfer / transmission of force in collisions – laws of colliding bodies – force transmission between bodies 59–61, 66, 72, 527, 648, 656, 663f. Elastic or tensioned springs – resulting from collisions or

Index of Subjects between colliding bodies 60, 64–66, 461, 536, 538, 647f., 650 Substitutability of bodies – explanation of the substitution process 67–70, 459f., 514f., 651f., 654–659 Papin’s definition of force and force transfer – attributable to very rapid percussions in a massless ether – measured by the resistance to be overcome – expressed as the product of mass and velocity 58f., 61, 71, 75f., 78, 459f., 527, 647, 672, 675, 682, 861, 871f. Force and weakness – a force acting in a particular direction – a corresponding compensating weakness, acting in the opposite direction 84f., 770f. Papin’s and Leibniz’s competing concepts of force, with regard to – dynamic processes – physical phenomena and their interpretation – terminology and the underlying theory 61, 65, 526f., 648 Papin’s and Leibniz’s lack of agreement regarding physical processes like – force transmission from a falling body to other bodies – in collisions of two or more bodies – in tensioning / relaxation of springs 61, 70f., 527, 648, 658, 660f. Papin’s rejection of Leibniz’s proposition regarding – the uniform motion of a body – the concept of action 75f., 674–676 Papin’s understanding of the effect of force in terms of resistance being overcome – with the resistance not being proportional to velocity 59, 75f., 460, 647, 672, 675f.

Index of Subjects Natural philosophy (cont.) Leibniz’s formal counterargument 76, 676 Gravitation, gravity, force of gravity, universal gravity 19, 21f., 26, 51f., 56, 58, 61–65, 71f., 74, 76, 81, 91, 101, 103, 105, 108–111, 167, 183, 293, 358, 363, 366f., 369f., 383f., 432, 438, 441, 453, 458f., 463f., 481, 510f., 512, 526f., 532f., 536, 538–550, 577, 588f., 619f., 646–648, 661f., 665, 669, 676, 678, 762, 861, 863, 865, 867, 872, 874–878, 883 Conceptions / hypotheses of gravitation and gravity Mechanical causes of ellipses 795 Non-uniformity of gravity 108 Cause and properties of gravity. See also Astronomy Motion of a ‘materia gravifica’ 108, 540 Ether percussion as the cause of gravity (Leibniz) 65, 538 Ether vortex – acting with infinite velocity (Papin) – proportional to the traversed distance, and the square of the velocity (Leibniz) – proportional to the elapsed time, and the velocity attained (Papin) 58, 103, 366, 458, 562, 646, 875 Center-of-gravity – center-ofgravity principles 65, 536, 538 Specific gravity 51, 62, 293, 363, 532, 872 Terrestrial gravity – influence of terrestrial gravity 19, 21f., 26, 56, 58, 61, 64, 81, 358, 432, 459, 463, 510–512, 527, 536, 619, 646–648, 762, 764, 863, 865, 867, 874 Fall and rebound of bodies in terrestrial gravity 81, 762, 764, 874 Leibniz’s discussion with Papin about gravity – force experienced by an ascending heavy body due to physical

1047 percussion effects (blows) – force proportional to the product of weight and height 58, 108, 459, 646f. Papin’s alternative explanation – based on philosophical suppositions – force the effect of a resisting insensible fluid 108, 507, 539f., 877 Leibniz’s discussion with Huygens about gravity. See Physics Inertia 73, 76–78, 80–83, 666, 676, 680f., 760–766, 873 Machines – applications of dynamics to machines – section about machines in Leibniz’s Dynamica 51f. Magnitudes – homogenous magnitudes 51, 363 Matter – nature of matter – indifference of matter, e.g. towards states of rest and motion 52, 80–84, 453, 761–763, 767, 873 Media – resisting (resistance of) media. See also Physics Motion in resisting media – problems of resisting media 112f., 372, 438 Resistance (absolute and relative) encountered by bodies in motion – arising from a body’s natural inertia – force required to overcome inertia – aversion / repugnance to such a force 58, 76f., 458, 676, 680 Motion / movement Moving bodies / bodies in motion/ collision of bodies. See also Experiments, and Natural Philosophy, Bodies Communication of movement – laws of communication of movement – Malebranche’s tract (1692) 53, 454 Compound / conjoint movement – compounded movements of bodies in a single body 65, 84, 538, 608, 768

1048 Natural philosophy (cont.) Concept of motion / movement 55, 525, 648 Impetus 51, 364 Laws of motion / movement – systematic laws of movement – laws of extended (or physical) bodies – actual (systematic) physical laws – connection with metaphysical laws – metaphysical foundations or principles 56, 60, 68, 83, 87, 287, 526, 537, 648, 652, 766, 874 Means of estimating moving bodies’ effect as – a body’s gravitational ascent or descent – the overcoming of spring tension / force – the resistance encountered by bodies 58f., 61, 527 Mechanical motion – composition of motion 72, 76, 301, 664, 674, 762, 872 Perpetual motion – ‘motus perpetuus mechanicus’ 58, 81, 133, 287, 459, 762f., 766f., 871, 873 Total motion/ movement in the world – a perpetual, inalterable, or invariable magnitude – an erroneous Cartesian belief (Leibniz’s view) 59, 459 Uniform motion of a body 76, 674f. See also Action, Bodies, above Varying motions – accelerating and decelerating motions 51 Velocity – magnitude of speed or velocity – with greater velocity / faster motion giving greater force, greater perfection, greater reality 84f., 769, 772 Velocity – directionality of speed or velocity 65, 539 Velocity changes or effects – absolute and relative – simple velocity, twofold velocity,

Index of Subjects etc. – infinitesimal changes  61f., 67, 77, 527f., 650, 681, 871 Resistance. See also Media above Absolute resistance – relative resistance 77, 113, 680 External resistance – Internal (intrinsic) resistance 83f., 766, 769 Statics – static moment of a heavy body on an inclined plane 96, 375, 451 General problem (‘problema staticum generale’) 52, 451 Navigation – seafaring, shipping and navigation 108, 157, 179, 182, 194, 587, 704 Development of sea-worthy and precise clocks 182, 587 Portable watches of Leibniz’s invention (1675) – principle of their exactness 182, 587 Huygens’ completion of a new clock (1693) 182, 587 Shipbuilding and sailing – ancient and contemporary shipbuilding – Witsen’s tract ‘Aeloude en hedendaegsche Scheeps-Bouw’ (1671) 146, 398 Methods of steering / maneuvering a sailing ship – Renau d’Eliçagaray’s ‘De la théorie de la manoeuvre des vaisseaux’ (1689) – Huygens’ dispute with the author 182f., 588–590. See also Controversies and disputes Leibniz’s opinion regarding the dispute – his approval of the practical nature of Renau’s tract – his regret regarding the author’s neglect of the center of gravity of the ship 183, 588–590 Matters at issue – force, speed, leeway or windward drift – Leibniz’s belief in a possible determination of a correct rule for leeway through the power of his dynamics 183, 589f. Sailing in a fixed direction. See Mathematics, Loxodrome (Rhumbline Curve) Global circumnavigation and observations – journeys of Dampier and Halley (reported 1701) – Halley’s

Index of Subjects Netherlands, Holland (cont.) astronomical tables formerly used for computations at St Helena – Dampier’s presence at St Helena 98, 782, 794 Kirch’s astronomical table – sent by Leibniz to Sloane and Halley (1701) 118, 794 Netherlands, Holland 2, 9, 11, 20, 28, 33, 40, 43, 86, 116, 127, 129f., 132, 142, 156, 185f., 192–194, 197, 237, 250, 257, 302, 304, 306, 318, 320, 330, 349, 353, 360, 396, 408f., 428, 430, 497, 508, 518, 562, 572, 574–576, 578, 591–594, 606–608, 621f., 638, 643, 684, 702, 716, 733, 775, 786, 802, 867 Amsterdam 2, 7, 32f., 41, 128f., 132, 142, 146, 151, 153, 185, 192, 195–197, 219, 222, 250f., 271, 278, 301f., 304, 306, 318, 330, 347, 396, 398f., 524, 560, 563f., 571–573, 577, 592, 595f., 608–610, 622, 640, 716f., 719f., 802, 834f., 880 House offering medicinal beverage (1694) 610 Renowned apothecary / druggist (1696) 608 Side street / back street (‘Reguliers dwars straet’) 719 St Anthony’s Church cemetery (‘Sint Anthonis Kerkhof’) 719 Antwerp 306 Breda 142, 395–397, 894 Brussels 306 Delft x, 2, 128f., 131f., 241, 301f., 304, 306, 347, 474, 560, 576f., 682–685, 849 Delft’s ‘Burgomaster’ (mayor) and officials – the honor and glory of the town – the ‘Oracle Delphique’ (Hugo Grotius) 132, 683–685 Dutch / Netherlandic – mathematicians, scientists, microscopists, physicians, etc. 6, 31, 91, 108, 128, 132, 137, 142f., 164f., 169, 179, 190, 196, 200, 214f., 224, 243, 249, 272, 283, 301, 312f., 327, 339, 383f., 395, 404, 410, 523f., 560, 574f., 605, 837, 848 Dutch East India company – the ‘Vereenigde OostindischeCompagnie’ (VOC) – the company’s Batavian Society 108, 226, 236f., 344, 732, 891

1049 Dutch republic – Republic of the United Netherlands – Union of Utrecht (1579) – Republic of the Seven United Provinces (1581–1795) – States General of the United Provinces 132, 186, 192–194, 320, 592, 685, 716 Office of the Stadhouder (head of state of the Dutch republic) 192, 592 Reign of stadholder-king William III (1672–1702) – his accumulation of wealth – Leibniz’s and Crafft’s addressee (1694) 192–194, 592–595 Stadtholderless periods (1650–72 and 1702–1747) – Office of the Grand Pensionary of Holland – calamity year / year of disaster (1672) – murders of the de Witt brothers (August 1672) 193 The States-General / Staten Generaal 592 The Dutch slave trade 186, 320 ‘s Gravenhage (The Hague, Den Haag, La Haye) 2, 34, 265, 302, 466, 564, 622, 802 Groningen 32, 116, 250, 607, 786f., 867 Haarlem 2, 185, 318 Harderwijk 33, 622 Leiden 2, 43, 131, 302, 306, 347, 349, 559f., 643 Mastricht 193, 592 Rijswijk 576f. Rotterdam 33, 621, 867 Utrecht 130, 305f., 716 Vianen (‘Free city’) 716f. Norway – Trondheim 236, 731 Numismatics, numismatist 8, 104, 358, 582 Nuremberg (Nürnberg) xii, 97, 120, 128, 168, 198f., 220, 224, 261, 297, 326, 504, 564, 701, 721f., 800, 829, 839f., 884, 889 Alchemy in Nuremberg – alchemical society xii, 220, 721f., 829, 889 Astronomy in Nuremberg – astronomical observatory – astronomical instruments 120, 799f. Convex mirror production in Nuremberg (1695) 128, 564. See also Instruments Master craftsmen and practitioners of Nuremberg 198, 326f., 884f. See also Projects

1050 Observers xv, 71f., 131f., 327, 380, 456, 473, 560, 662–664, 683–685, 800 Observers – their special abilities and assiduity 132, 683 Oldenburg (town) 257, 353 Osnabrück 273, 275 Optics. See Physics Organization of science, learning and education 4, 197–208, 324, 499, 597f., 818. See also Pedagogy, Projects Paleontology and earth history. See Geology Pansophy, pansophism. See Knowledge Paradigms xii, xiv, 88, 233, 288, 878 Paradox(es) 70f., 73, 336, 578, 661f., 666, 774, 778 Paradox(es) in Leibniz’s and Papin’s systems of natural philosophy with their respective concepts of force – apparent or linguistic paradoxes 70f., 661f. Paradoxes as experienced by Papin – regarding two mutually-arresting bodies, one with double the velocity which would produce double the effect – also regarding the ability of a body at rest to bring a moving body to rest without force by virtue of its inertia 73, 666 Paradoxes as experienced by Leibniz – regarding Papin’s interpretations / explanations, which were both paradoxical and absurd, and offended against reason – even leading possibly to a ‘perpetuum mobile’ 73, 666, 773f. Pathology. See Medicine Pedagogy 32, 202f., 598f., 887 Mathematical pedagogy 32 Pedagogical projects. See Projects Pedagogical reform – the Parisian pedagogue Ramus (16th Century) 199, 238, 597, 885, 887 Peoples and languages – origin and relatedness of peoples (and nations) 10, 231, 430, 841, 862 Language dynamics – Leibniz‘s language dynamics – analogy with his

Index of Subjects dynamics in natural philosophy and physics 230 Language evolution – theory of language evolution 230 Protolanguage(s) 10, 230, 430 Sinology / Proto-Sinology 18 Search for a universal language 18 Linguistics – comparative linguistics – historical linguistics 10, 230, 430 Glossography – study of ancient words or languages 231, 841 Interrelationship of languages and alphabets 500 European Languages – history and relationship 232, 843 Matrices or unrelated languages of Europe – Basque, Finnish, Hungarian, Lappish 231, 843 Celtic / Celtic Studies / Celticization – pre-Christian Celticization xi, 230–232, 841, 844 Languages of Great Britain and Ireland – origins of the peoples and languages 231, 841, 862 The Saxon origins of the English – the Anglo-Saxon settlement 231, 841f. Relation of the Welsh to the Germanic tribe ‘Cimbri’ 842 The Scots and Irish of more ancient, and of Continental European origin 842 17th-Century discussions of the development of the Celtic languages 230f., 841 Separation of Irish and Welsh (Scaliger, 1610) 231, 842f. Relatedness of Irish and Welsh (Wallis, 1653/74), and Irish, Welsh and Breton (Wallis) 231, 843 Discussion in Leibniz’s correspondence (from 1694) – his thoughts on ancient ‘Gaulish’ and its Germanic influences 843 His rejection of an Irish-Basque connection 231, 843 His comparison of Irish and Welsh texts – contemporary texts of the Lord’s prayer 231, 843

Index of Subjects Peoples and languages (cont.) Division of the Celtic peoples and languages – Brythonic or Welsh (‘Cymraeos’/ ‘Cambros’) – Goidelic or Irish (‘Scotos antiquos / Hibernos’) – referred to by Leibniz in his correspondence with Wallis (1699) 231, 841f. Lhuyd’s observations regarding Irish Gaelic (1699) 231f., 841f. Similarity between the two linguistic families – P-Celtic (Breton, Cornish and Welsh) and – Q-Celtic (Irish, Manx, Scottish Gaelic) 231, 841 The ‘P-Q split’ of the Celtic Languages – Leibniz’s reference to the split in correspondence with Wallis (1699) – first published in Lhuyd’s ‘Glossography’ (1707) 231f., 841 Toland as an Irish speaker – his influence on Leibniz (1701–1707) 232 Leibniz’s cooperation with Eckhart, and posthumous publication of the ‘Collectanea etymologica’ (1717) – on the history and the relationships of the European languages 232, 843f. Perpetuum mobile 58, 72f., 80, 82–84, 664, 666, 761, 764, 766, 768, 874. See also Power Persia, Persian 155, 236, 388, 700, 733 Pharmacology. See Medicine Philosophy. See also Natural Philosophy Aristotelian philosophy / natural philosophy xii, 80 The Aristotelian entelechy concept 80 Entelechy. See also Natural Philosophy Cartesian philosophy – Cartesian world view – Cartesians xiii, 19, 21, 44, 56f., 59, 63–65, 76, 78, 81f., 85, 87, 105, 131, 233, 267, 271, 283, 287, 349, 359, 363, 369, 422, 427, 431, 451, 458–460, 463, 473, 512, 534f., 537f., 617, 620, 628, 644–647, 675f., 682, 687, 763, 766, 771, 830, 859f., 864, 871, 873–875, 878, 894

1051 Contemplative Cartesian – antonym of a Leeuwenhoekian experimentalist – Leibniz’s critique 131, 473 History of philosophy x Mechanical philosophy – the mechanical view of nature – champions of this novel view (like Boyle) 91, 219, 383 Leibniz’s philosophical interests – his philosophical system – his philosophical works 56, 362, 526 Metaphysics xi–xiv, 80, 205, 267, 647, 744, 820 Leibniz’s Discours de metaphysique (1686) 56, 362 Leibniz’s metaphysical controversy with Joh. Ch. Sturm – Its influence on Hoffmann’s mechanical world picture 266, 859 Metaphysical laws, paradigms, principles xii, 56, 60, 103, 301, 526 Metaphysics and mechanics xiii Metaphysics and physics – confrontation of metaphysics and physics 80 Force conceptions rooted in natural philosophy / metaphysics xii Leibniz’s efforts to establish the overall Metaphysical foundation of the laws of dynamics 60, 526, 648 Physical and metaphysical contexts of the world 647f. Block’s position (1699) regarding metaphysics and the disciples of that art – metaphysics in relation to reason considered by him to be a non-phantasm and non-entity of reason 830 His philosophical standpoint of not being a skeptic, but [rather] a Cartesian – doubting but not negating 830 Philosopher’s stone. See Alchemy Philosophical assumptions, interpretations, thought – Leibniz and Papin Papin’s views essentially shaped by Descartes’ philosophical thought 57, 458

1052 Philosophy (cont.) Leibniz effort to prove that the source of error lay on the side of the Cartesians – example of the philosophical view of many philosophers – namely that the ‘total movement in the world’ was a perpetual, inalterable or invariable magnitude 59, 459 Philosophical interpretation of biological preformation – the generation (and later death) of an animal – a transformation from a state to another state – the Leibniz-Arnauld correspondence (1686–87) 130f., 379f. Reasoning and philosophy. See Reason, reasoning, rational thought, rationalism Science and philosophy – Newtonian influence xiii, 238f. Sophism, sophistry, sophist – pansophism, pansophist 222, 224, 834, 838 Physics Acoustics, sound – theory of acoustics and sound 3, 92 Sound production – tension and string tension – sound generation by string tension 52, 92f., 372f., 451 Sound propagation – for a given string tension, oscillations always isochronous – the same tone pitch is produced – the sound is transmitted at a constant speed 92f., 295, 372f. Sound from a resonating body – manifest as vibrations or oscillations of tiny air particles 93, 295, 372f. Percussion and repercussion – sound produced by a blow to a cushion – straining and state of tension of threads – a striving for restitution of the original state – possible rupture of the cushion 93, 296 Audiology, the science of hearing 93, 372

Index of Subjects Hearing of sound – human experience of sound 94, 373. See also Medicine, Anatomy of the ear Vibrations of tiny air particles carried to the ear – perceived pitch of a sound – constancy of pitch 93f., 295f., 372f. Isochronism of elastic vibrations (oscillations) 93, 296 Different pitches transmitted in air 93, 296 Different sonorous bodies – in simultaneous resonance with the ear 93, 296 Homotony (condition of being homotonic) – being of uniform tension / tonus 242, 346 Sympathetic resonance with parts of the inner ear 93, 295 Sonority – sound level or loudness 93, 295, 372f. Pitch, experience of pitch – related to frequency of received oscillations 94, 373 Ear consonance with all resonating bodies 94, 373 Ear drum – reproduction of corresponding sounds 94, 373 Similarity with a musical instrument, like zither or lute – different stretched strings – rendering of many different sounds – various instruments in mutual harmony 94, 373 Applied physics Pendulum. See also Mathematics, Curves, Cycloid Pendulum Clock – Huygens’cycloidal pendulum – isocrone (double) pendulum – the ‘horologium oscillatorium’ 17, 24, 129, 284, 302, 436, 587f., 866 Richer’s ‘seconds pendulum’ – measurement of its length 197, 324 Experimental physics 204, 820. See also Experiments and Experimentation

Index of Subjects Physics (cont.) Mariotte’s research on the nature of an elastic collision – on the mode of operation of the wedge – on motion in a resisting medium 88, 306 Motion in a resisting medium – thoughts, theoretical considerations – mathematical treatment – experimental investigations 88, 112, 306f., 370 Fall of a body taking account of the resistance of the air 112, 306f., 370f. Motion of a projectile – explanations of Galileo and Descartes – trajectory supposed to be a parabola – resistance of the air disregarded by Galileo and Torricelli 112, 370f. Ballistics / science of ballistics – Blondel’s tract (1683) 88, 112, 306f., 894 Leibniz’s ‘Schediasma’ (1689) on the – resistance of a medium – movement / motion in a resisting medium 21, 88, 112f., 121, 306, 370–372, 376, 406, 431, 439, 466f., 524 Motion of heavy projectiles – issue of the resistance of the air – application of the differential calculus 112f., 306, 370f., 466f. Two forms of resistance – ‘resistentia absoluta’ and ‘resistentia respectiva’ 113, 371 Absolute resistance – proportional to the velocity 113, 371, 680 Relative resistance – proportional to the square of the velocity 113, 371, 680 Combination of the two forms in – Newton’s ‘Principia’ (1687) – Huygens’ ‘Discours’ (1690) 113, 371f. Revision and extension of Leibniz’s Schediasm as an ‘Additio’ (1691) 113, 372, 439, 467

1053 Exchanges with Huygens (1690– 91) – difficulties in reaching an understanding – role of the infinitesimal calculus 113, 372 Different understandings of resistance – as an effect synonymous with the resistance itself (Leibniz) – as pressure of a medium against a body (Huygens and Newton) 113, 467 Related issues – nature of an extended and resisting medium – admissibility of a perfect hardness of matter – existence of atoms in space devoid of air, matter 113f., 372 Studies of fundamental properties of air and water – compressibility (like with steam) – incompressibility (like with water) – partial or total incompressibility 101, 781f. Density / temperature / expansion force of air – their interrelationship and proportionalities involved  101, 780f. Elasticity and ‘heaviness’ of the air 101, 779f. See also Laws of Physics, Boyle’s Law Discussion with Joh. Bernoulli (1699–1701) – thought experiments and physical models 101f., 781f. Bernoulli’s processes – based on proportionalities between densities and weights 101, 781 Discussion about incompressible parts of air – particles resisting compression – very subtle particles and their possible expulsion through the pores of the air pump 101, 781 Leibniz’s call (1700) for further experiments – to decide the matters of expansion by heat, and of contraction by cold 102, 782 Bernoulli’s measuring process – his condensation / compaction methods – differing from

1054 Physics (cont.) attenuation or rarefaction methods 101, 779f. His claim of error reduction, and power-requirement reduction – with 3 or 4 rather than 20 cylinder strokes 779 His ‘Dissertatio’ (1701) on the weight and elasticity of the air 101, 780 Geophysics – practical problems 97, 297f., 782 The shape of the earth – spherical or elliptical – an elliptical-spheroidal shape 107, 465f. An elliptical-spheroidal shape of the earth – postulated excess of mass at the equator (Huygens and Newton) 107, 466 Postulated excess of mass at the poles – Eisenschmidt’s theory (1691) – Leibniz’s critical assessment – Huygens’ overall good impression, notwithstanding some doubts and reservations 107f., 465f. Meridian(s) – line of longitude 25, 120, 381, 437, 441, 799 Meridian circle – construction 120, 799 The longitude problem – solution of the problem 97 Determination of longitude at sea – Huygens’ clocks for these measurements 97, 108 Subterranean measurements – pressure and temperature measurements 99, 476, 775f. See also Modena, Subterranean wells Earlier measurements undertaken by the Académie des Sciences – preparation of barometric ephemerides: Possibility of an antiperistasis in observations – an illusion or false perception 99, 775f. Gravity / gravitation. See also Natural Philosophy Attraction, gravitational attraction 105, 367, 463, 875

Index of Subjects Law of gravity – inverse-square law 105f., 109f., 367, 369f., 463, 540f., 543–545, 547, 549, 875f. Attraction – of lead weights to the earth – of planets to the sun 463 Cause of gravity – an inherent property of matter – mechanical explanation of gravity 52, 58, 103, 108f., 366, 452f., 458, 539–542, 646, 876f. Competing theories to explain gravity – based on assumptions of physical processes 109, 527, 542f., 876 Effects of circular motion (Huygens) 109, 542f., 876 Effects of rectilinear motion (Newton) 109f., 542–544, 876 Huygens’ theory (explanation of gravity) – his discourse on the cause of gravity (1690) – his hypothesis of matter in motion – his interpretation of gravity as a centrifugal force – deficit in the failure to yield an inverse-square law – similarities with his theory, seen by Leibniz 195f., 109f., 367, 369, 541f., 545, 547, 875f. Newton’s explanation / theory of gravity – his ‘Principia’ (1687) – supposition of attraction and trajectory – lack of a law of gravity (Leibniz’s view) 102, 105f., 113, 201, 365f., 369f., 371, 462f., 542f., 548f., 874f. His theory of gravitation – declaration of mutual attraction – the inversesquare law 109, 540f. Constitution of the universe – consisting of empty space (for the most part) 109, 540–542, 876 Fatio’s tract on the cause of gravity (1688–90) – his mechanical explanation of gravity with two forms of matter – terrestrial matter, constituted of the smallest homogeneous particles – and an (almost) infinitely thin form of

Index of Subjects Physics (cont.) matter whose particles were the cause of gravity – subjection of the particles to high-speed rectilinear motions in all directions 108f., 542, 876 Reception of Fatio’s theory – Newton’s approval and Huygens’ objection that matter surrounding the earth would become increasingly dense 100, 109f., 542, 545–547 Leibniz’s counter-argument – suggestion of a dissipation of surrounding matter – analogous to the activity of sun spots 110, 546f. Varignon’s conjectures regarding gravity (1690) 110, 545 Leibniz’s supposition of gravitational attraction, and of rays of attraction 105f., 367, 369, 463, 875 Leibniz’s vortex theory – vortical motion of an ambient fluid 102, 106f., 111f., 463f., 548, 550, 552, 875. See also Astronomy, Planetary Motions Leibniz’s theory based on a circular-motion hypothesis – his conceptions of a rotating ether, and of a centrifugal force of a very subtle fluid 103, 196, 109f., 366, 369, 383, 463, 543, 875f. Orbits of bodies rotating around the sun explained by his theory – based on the principle of equality of active force (being proportional to the square of the velocity) – all planets rotate in the same direction – a model for the derivation of Kepler’s third law, and of the law of gravity 106f., 111, 369f., 464, 548–550, 876f. Other phenomena explained by his theory – water drops / droplets, and their round or spherical forms – the form of the terrestrial globe – parallelism of the axes of the planets with that of the earth 106, 463

1055 Phenomena not consistent with Leibniz’s theory – constant eccentricity of planetary orbits – acceleration / deceleration along paths – movement of comets through vortices 107, 464 The trajectory of a comet – minimal impedance through a rare ethervortex 111, 549, 877 Possible confirmability of Leibniz’s theory – possible harmonization with the other theories 106, 111, 464, 548 Huygens’ rejection of Leibniz’s theory – his insistence on the superiority of his own theory 106f., 464 Leibniz’s alternative theory based on a rectilinear-motion hypothesis 543f., 876 His notion of a fine ether vortex, where the ether particles produce gravity, and contain a compacted fine matter – analogous to a system of little air guns enshrined within a coarser matter 110, 546. See also Magnetism and Electricity Leibniz’s ‘explosion’ theory of gravity – based on a rectilinear motion – with coarse matter enriched with fine matter being attracted to rarefied matter located at the center of attraction 109f., 543, 545, 876, 878 Explosion theory comparable to an incendiary or shattering process – example of the effect of a flame as a center of attraction – and of the effect of the sun as a center of attraction – with the shattering of bodies on impact 109f., 543, 546, 876 The process involving – an explosion or ignition being accompanied by rarefaction – fine matter being expelled to the periphery – realimentation of the coarse material there and the continuation of the cycle or process 109, 543f., 876

1056 Physics (cont.) Comparison with the movement of light – ether particles producing light would contain a compacted fine matter 109f., 544, 546, 876 Explicability of the force of gravity as a centrifugal force – an inversesquare law for gravity – similarity with the photometric inversesquare law 109, 543f., 876 A combination of circular and rectilinear motions – in conformity with nature’s preference for an optimal, or minimum-redundancy solution 109f., 544, 876 Heat – solar heat and radiation (sunshine) 45, 848 Thermodynamics (the science of heat) xi, 149, 696, 862, 881 Leibniz’s theory of heat 94, 373 Processes due to the motion of constituent particles of bodies – evaporation of water over a fire – liquefaction of metals in a furnace – retention of the liquid state by the power of the sun 94, 373 Effects of heat and cold in the human body – also attributed to the motion of particles – feeling of warmth evoked by the flux or movement of these particles – a sensation of cold experienced following the body’s debilitation and attack on its humors 94, 373f. Elasticity as an explanatory principle 95, 242, 345, 372–374 The phenomenon that water in a vessel expands when frozen solid, and may shatter its container – attributed to a lack of convection and to the inability of the air, present in small bubbles, to form larger bubbles and exploit their elastic properties 94, 374 Analogous processes – explosion of gunpowder, by the application of fire, with scattered air pockets and

Index of Subjects the formation of larger bubbles – river flow regulation, using logging / lumbering techniques – use of large tree trunks capable of being swept away by torrential water flows, and sweeping away large obstacles, like bridges 94, 374 Leibniz’s explanatory theory for such processes – based on an assumption of the existence of small elastic particles – these being mutually obstructive while isolated, but with explosive capability when combined 94, 374 Instruments in Physics. See Instruments Laws of Physics Galileo’s law of falling bodies – his two new sciences, mechanics and local motion 36, 88, 296, 627, 869 Boyle’s law of the air’s elasticity – his ‘New experiments physicomechanicall’ (1660) 90, 101, 291, 780 Linus’ / Line’s critique in (1661) 780 Boyle’s defense (1662) of his ‘Doctrine touching the spring and weight of the air’ 101, 780 Boyle’s observation of the role of heat in the expansion of rarefacted / rarefied air 780 Leibniz’s reference (1699) to a ‘casual experiment’ of his own – his proposal for a clarifying experiment 101, 780. See also Experimental Physics, Experiments His interest in Boyle’s literary bequest and his manuscript estate 201 Kepler’s laws 103f., 366, 463, 875. See also Astronomy Law(s) of gravity 106, 110, 369f., 463, 543, 545, 875 Laws of motion 3, 56, 60, 83, 87, 287, 526, 537, 648, 766, 874 Cartesian laws of motion 87, 287. See also Natural Philosophy Newton’s laws of motion 874 Light and optics

Index of Subjects Physics (cont.) Theories of light 121–124 Leibniz’s supposition of a fine ether vortex – the particles of the ether produce light, and contain a compacted fine matter – analogy to a system of little air guns enshrined within a coarser matter 110, 546. See also Magnetism and electricity The corpuscular / particle theory – Newtonian corpuscular theory – Fatio’s corpuscular theory 123, 223, 554 The wave theory – Huygens’ predecessors – Ango, Pardies, Hooke 121–124, 376, 469, 556–558 Huygens’ treatise on light (1690) – ‘Huygens’ construction’ – his explanation of wave propagation – his theory of light propagation – spherical wave propagation – his construction of wave fronts 105, 121, 125, 369, 376, 557 Light rays and waves – path of a ray in homogeneous media – waves orthogonal to rays 36f., 627, 630, 869f. See also Mathematics, Orthogonal trajectories Color(s) of light – theories of color – apparent and fixed colors 120– 122, 124, 300, 376, 468f., 553, 556, 558 Color of blood attributed to refraction (Leibniz) 120, 306 Mariotte’s tract on the nature of colors (1679–81) – hypothesis formulated by Mariotte – no primitive constant colors of light rays – color change following refraction – his hypothesis opposite to Newton’s views 120, 123, 306, 552f. Newton’s ‘Theory about light and colors’ (1672) – his new experiments on the theory of colors – his seminal work ‘Opticks’ (1704) 121f., 124, 376, 468, 555f.

1057 Huygens’ understanding of the nature of colors – his explanation requested by Leibniz 122, 124 Intensity of light – the photometric inverse-square law 106, 109, 369, 543f., 875f. Movement of light – finite speed / velocity of light – Rømer’s demonstration (1676) 123, 554 Path of light – Fermat’s principle of the least time (1662) – supported by Pardies and Ango (1682) – supposition of slower motion in a denser medium 121, 125, 300f., 470 Leibniz’s minimal principle – his principle of the easiest light path (1682) – light follows the path of least resistance 120, 125, 300, 470 Leibniz’s priority over Fermat (Molyneux, 1692) 125, 470f. His ‘universal principle in optics’ – his claim of a shorter proof using the differential calculus – more rapid motion in a denser medium, with greater resistance of the medium leading to a greater velocity 121, 125, 300f. Objections of Ango and Basilius Titel 120f., 300f. Polarization of light – a phenomenon observed but not explained by Huygens 122, 124, 486, 556 Reflection of light – catoptrics – mirrors and waves – laws of reflection – Huygens’ derivation (1690) 121–123, 125, 301, 376, 469f. The catacaustic curve. See Mathematics, Curves Refraction of light – dioptrics 16, 26, 107, 125f., 282, 465, 470f., 558f., 704, 867, 870 Cartesian laws of refraction 87, 287 Snel(l)’s law of refraction – explanation of the law – Huygens’ derivation of the law (1690) 91, 121–123, 376, 383f., 469

1058 Physics (cont.) Knorr’s ‘De refractione luminis’ (1693) 124, 556 Phenomenon of double refraction in Iceland spar – Huygens’ explanation of the phenomenon (1690) – a critical test or an ‘experimentum crucis’ 121–123, 125, 376f., 554 Leibniz’s opinion of Huygens’ treatment – merely a description, not an explanation 122, 376 Experiments with Iceland spar – samples of the mineral obtained by Leibniz – method of polishing the crystal using aqua fortis (nitric acid) 121f., 124f., 376–378, 468, 554, 556f. Dioptrics – lenses and waves 37, 107, 125f., 465, 470f., 559, 704 Diacaustic curve 16, 282, 870. See also Mathematics, Curves Molyneux’s ‘Dioptrica nova’ (1692) – Huygens’ examination and critique 125, 470f. Hartsoeker’s ‘Essay de dioptrique’ (1694) 126, 558 Huygens’ (posthumously-published) ‘Dioptrica’ 107, 125, 465, 559 Optics – mathematical science of optics 37 Leibniz’s ‘De lineis opticis’ (January 1689) 121, 376 Newton’s optical experiments – his planned work on optics 124, 555f. Optical Instruments. See Instruments Visuality and seeing – refulgence or luminescence 205, 822. See also Scientific, educational projects, Berlin Society, Spectacular experiments Magnetism and electricity – phenomena of magnetism and electricity – related phenomena 98, 381 Magnetism – analogy of Leibniz’s vortex theory to this phenomenon 107, 464, 550, 877

Index of Subjects Magnetic curl / rotation 111, 549 Leibniz’s supposition of a fine ether vortex – the ether particles produce magnetism, and contain a compacted fine matter – analogous to a system of little air guns enshrined within a coarser matter 110f., 546, 549. See also Light and optics Terrestrial magnetism 7, 43, 97f., 105, 110f., 278, 326, 369, 381f., 549f., 644, 782, 875, 877 The ‘terrella’, a small magnetized model ball – representing the planet earth 111, 550 Magnetic declination – variation of magnetic declination – gradual / non-abrupt change – spatial variation and temporal variation 97f., 297–299, 782 Law for the variation of declination – Leibniz’s heuristic continuity principle – spatial and temporal continuity 97f., 298 Cause of declination – a randomness in the earth’s make-up and structure (Descartes) – existence of a regularity (Leibniz) 98, 298 Huygens’ account (1679) of his ‘Traité de l’aimant’ 98, 382 Leibniz’s proposal (1681–82) for a system of corresponding terrestrial magnetic observations 198, 261, 325f., 504 Volckamer’s proposal for the creation of a ‘mathematical-magnetic association’ 198, 326 J. C. Sturm’s ‘epistola invitatoria’ (1682) regarding observations of terrestrial magnetic variation 7, 198, 278 Von Guericke’s experiment with a ball of sulfur – his observation of electric sparking – Leibniz’s correspondence with him (1671– 72) 98, 382 Huygens’ electrical experiments and theories 98, 383

Index of Subjects Physics (cont.) Halley’s research journey in the Atlantic – his study of the variation of the magnetic needle 200f., 499 Observations of the variation of the magnetic needle – observations made at sea, during Halley’s maritime journeys (1698–1700) – Halley’s map and observations sent to Leibniz by Sloane (1701) 98, 499, 782 Global circumnavigation and astronomical or magnetic observations. See Navigation Mathematical physics – Leibniz’s paradigm for the advancement of mathematics and physics – organizing / carrying out a system of experiments – accumulation of empirical observations – refining calculations on the basis of experiment 88, 288 Mathematical relations for the physical world – mathematical treatment of physical themes – physical applications of the infinitesimal calculus xii–xv, 18, 25, 37, 88, 288, 306, 358, 437, 630, 863f., 870 Mechanics – celestial mechanics. See Astronomy Mechanical reasoning. See Reason, Reasoning Mechanics and mathematics – mechanics reduced to the terms of pure mathematics 151, 283, 288, 882, 884 Mechanics and physics – mathematical problems relevant for the world of physics and mechanics 271, 286, 870 Mechanics of fluids, hydromechanics. See Engineering, Science of Engineering Newtonian mechanics – mechanistic Newtonian mathematical physics xii

1059 Theoretical physics Leibniz’s ‘Hypothesis physica nova’ (1671) 51, 55, 87, 103, 287, 364–366, 457 Discussion with Foucher (1692– 93) 54f., 57, 214, 412, 451, 456f. Physiology. See Medicine Poland, Polish 17, 161, 226, 276, 345, 808, 892 Political economy. See Economics Population settlement / resettlement 186, 231, 321, 841 Projected new town near Harburg (1680–81) – settlement for emigre Huguenots 185, 318 Potsdam – astronomy in Potsdam 114 Power – power and energy Power generation / energy conversion 133, 861, 878 Power / energy source(s) 134, 144, 147, 307, 391, 566, 686f., 880 Renewable energy / power source 134 Power / energy storage – pumpedstorage 137, 162, 384, 813, 878, 894 Power technology xi, 3, 133, 146, 384, 398f., 565, 685f., 800, 877f., 894 Concept of mechanical power 133 Concept of a power technology 133, 878 Medieval / pre-modern exploration of mechanical power 133, 878 Power-conscious engineers / technicians of the late middle ages 133, 878 View of the cosmos as a reservoir of energies – vision and conception of a ‘perpetuum mobile’ 58, 72f., 80, 82–84, 133, 664, 666, 761, 764, 766, 768, 874 Early-modern development of power technology – accompanying social change 133f., 161, 862, 878 Leibniz’s commitment to the development of power technologies 133, 863 Power / energy transmission – rod-engine transmission 135, 137, 139–141, 144f., 308, 385, 388, 391–393, 566–569, 879f. See also Mining

1060 Power generation (cont.) Power forms Explosion / combustion power 94, 182, 374, 585, 690, 862, 878, 880 Firepower (artillery, firearms) 152, 216, 401, 576f., 894 Gunpowder – experimental investigation of its nature, power, and its constituents – air pockets contained in gunpowder were the cause of the force released in gunfire – pioneering works of Papin (1674 and 1688) – his insight that the effect of gunpowder increases with the resistance to be overcome – the explosive effect of gunpowder attributed by Leibniz (1697) to the compressive pressure of the air 94, 146f., 216, 374, 413, 686f., 695, 880 Muscle power – animal power – manpower 140, 150, 162, 388, 802, 813 Horse mills 136, 141, 144, 310, 392, 566, 573, 880 Steam / fire power. See also Engines, Enginery Steam / water vapor as a power source 148–150, 689f., 692f., 696, 878, 881 Steam engines 146–150, 688, 690, 881 Vapors (other than steam) as a power source – expansion of other vapors – example of spirit of wine 146, 182, 585–587, 686, 878, 880f. Water power. See also Mining Water-powered and water-raising machines – water wheels 62, 134–142, 144f., 154f.,162, 234, 307, 309–311, 384, 386–388, 391–393, 397, 532, 566–570, 698f., 701, 872, 879f. English waterworks – water-lifting machines 143, 397 Water-lifting machines in Copenhagen 143, 312 Water-lifting machines in Paris – the machine of Marley 143, 312, 397

Index of Subjects Wind power. See also Mining Wind power – windmills – horizontal and vertical windmills 4–6, 133–140, 142f., 162, 169, 273, 275, 307–313, 384–388, 391, 396f., 572, 813, 861, 878f., 881 Prime movers. See Engines, Enginery Priority disputes. See Controversies and disputes Projects – the world of projects and projectors – Leibniz as projector 12, 167, 183, 185, 214, 315, 320, 333, 338, 884–888 Leibniz’s philosophy of projects – his desire to overcome the prevailing scholar / tradesman or craftsman cleavage – his proposal (1682) for a dialog between scholars and tradesmen or craftsmen, and for an interaction of artisans, craftsmen, and practitioners with the learned / the world of learning – his desire to counteract the lack of such interaction in Nuremberg – his complaint about a certain sterility, with new and useful annotative expressions of abilities being prevalent in the population, but largely unknown among the learned – his proposal to counteract this sterile state, the practical ignorance of the learned, the bookish erudition of scholars, and the dearth of practitioners’ explanatory notes 167f. 198f., 326f., 884f. Projects / projectors in Leibniz’s correspondence – Defoe’s ‘Essay upon projects’ (1697) 12, 862 Projectors – cooperation (or lack of) between projectors – mutual trust or mistrust – agreement and recommendation, or intrigues, scheming, and withholding of information – use of cryptographic scripts or ciphers, with encrypted and non-encrypted texts – hampering of decryption by other parties, or unintentional confusion or misunderstanding, and use of vague intimations 183f., 314f.

Index of Subjects Projects – the world of projects (cont.) Range of projects Chemical projects – economic utilization of chemical processes 190, 214, 337, 409, 888 Production of a fluid gold paint (Leibniz, 1680) – used for dyeing clothing 190, 214, 338, 410 Production of ruby glass (Leibniz / Hooke, 1680) 127, 190, 214, 338, 410, 562 Preparation of gold and silver from raw materials or chemical precursors (Crafft, Elers, et al.) 190, 214–216, 218, 338f., 410, 418, 888 Efforts of chemists in Dresden to obtain gold from copper, mercury, silver (1680) 214, 339 Adolphi’s chemical secrets offered to Crafft (1680) – processes to obtain mercury from metals, and to separate sulfur and mercury – Leibniz’s intervention 214f., 339f. Becher’s gold from sand project (late 1670s) – failed demonstrations in Amsterdam, Hamburg – witnessed by Stisser (reported 1699) 222, 834 Perfection of pearls (Crafft, Elers, 1681) 190, 214, 338, 410 Production (cementation) of silver from cinnabar (mercury sulfide) through the use of sulfur and lead (Elers, Pratisius, 1681) 214, 339 Ideas of Crafft, Rojas y Spinola, Leibniz (1682) – about obtaining silver from the liquation / segregation of Spanish copper coins 214, 339 Elers’ report to Leibniz (1682) regarding the sale of a process for obtaining gold 214, 339 Economic, techno-economic projects. See also Economics Projects undertaken for national economic benefit – dependent on princely patronage, like financial support, and granting of privileges 183, 315

1061 Futility of entrepreneurial involvement in manufactories without princely or baronial participation – expressed by Crafft (1691) 191, 497 Leibniz’s and Crafft’s brandy project (1694) – for production and marketing of brandy 196, 718 Discussions / negotiation at German and European courts – with court ministers, mercantile communities and interests, estates and social hierarchies 183f., 315 Crafft’s (and Leibniz’s) approach (1680) to the elector of Brandenburg 184, 317 Crafft’s (and Leibniz’s) approach (1680/81) to the emperor, and to imperial privy counsellors – proposals for the establishment of manufactories 184, 315f. Leibniz’s opposition to an anti-French embargo with import barriers for French goods – his expectations for a less expensive production of domestic goods 184, 317 Prospects for export of manufactured goods – silk and wool products – proposed manufactories 184f., 316f. Use of machinery in the manufactories 185f., 317f. See also Machines, Mechanization and Social Change Crafft’s conception of new machines for silk and wool manufacture (1680) – for textile manufacture (1681–82) 185f., 317, 321 The ribbon-loom – the ‘mola limbolaria’ (Bandmühle) – requisite purpose-built building – fabric production – braid and lace 162, 185, 318, 811 Proposed bag cloth and stockings manufactory – associated workhouse and orphanage in Saxony (1680) 186, 321

1062 Projects – the world of projects (cont.) Proposed bag cloth manufactory in Brunswick and Lüneburg (1680) 186f., 321 Proposed steel production in the Harz district (1680) 187, 321 Manufactories considered (by Elers and Leibniz) 187, 322 Diversity of projects in Elers’ sights – a glassworks in the Weser Uplands (1681) for making of burning glasses (lenses) – a new kind of wax bleachery in Dresden (1681) – an invention to make ships unsinkable in Berlin (1681) – wallpaper made of silk, and printed with gold or silver, in Dresden (1681–82) 187, 322 Project for improvement of the luster of pearls (1684) 189, 408 Leibniz’s (and correspondents’) interest in engraving, punchcutting, textile printing (1683), silk and wool manufactories (1683–88), the silk trade, iron and steel production, and the wine trade (1688) 152, 184, 189, 214, 317, 321, 339, 401, 407f. Other techno-economic / chemical projects (1680s). See also Chemistry Dyeing of garments – Leibniz’s historical note (1690) on Drebbel’s discovery of scarlet dye (1608) – history of the discovery of the tincture 190, 410 Production of ruby glass 190, 410 Perfection of pearls 190, 214, 338, 410 Retrieval and extraction of gold, silver 190, 410 Phosphorus production 190, 213, 410, 412 Desalination / desalinization of sea water – Lacy’s desalination plant near Modena (1690) 190, 201, 410, 499 Chemical processing using vitriol (1689) – production of dangerous emissions 190, 410

Index of Subjects Projected utilization of chemical substances 214, 337f., 888 Paints for the conservation of wood and stone 190, 409 Production and application of paints by Crafft, and by Heyn along the river Elbe (1687) 190, 409 Veins of iron and crude ores – yielding fine umbra and brown ocher pigments 190, 409 Projected factory / plant for processing mineral ores 190, 409 Production of paints for building and construction in Hungary and lower Austria 190, 409 Military-related projects 3, 177f. Armor production (1681–1683) 177, 322f. Making mail armor out of silk (Elers, 1681) – incorporating a network of brass wire – similar coats of armor produced in England and Sweden 177, 322 Testing of Swedish armor – resistance to musket balls or shot – tested on a human target, as part of an execution of a soldier 177, 322f. Danish incendiary cannonballs (1682–83) 177, 323 Firearms (1683) – rifled gun, with automatic transfer of powder to the priming pan 177, 323 Ballistic mortars and grenades – mortar made of metal 152, 324 Mortar made of pasteboard – advantages of light weight, and easy transportability 177, 323f. Kindred device – Bonfa’s pendulum (1679), made of pasteboard 177f., 324 Submarine development and navigation. See Submarines Military use – envisaged attacks on hostile vessels 181, 496 Scientific, educational projects – organization of science and education 3, 197, 200, 324, 499, 597, 818

Index of Subjects Projects – the world of projects (cont.) Academies and learned societies – academies of sciences and arts 12, 197, 202, 508, 597, 828 Advancement of knowledge and practical skills – dedicated colleges, institutions and societies 201f., 499, 597f. Pedagogical projects 202, 597, 862, 885, 887 Weigel’s commitment to pedagogy, learning – Leibniz’s approval and political support 202f., 599f., 887 Weigel’s school reform enterprises – his private school project (1683) – his public school project (1690) – his school of virtue, the ‘Kunst-und Tugendschule’ 202f., 599f., 887 Development of teaching / didactic materials 203, 599, 887 Teaching / didactic methods – possible with existing teachers or preceptors 599 Rules and mechanical instruments – a writing rule (‘Schreibregel’) – a reading rule (‘Leseregel’) – an arithmetic teaching aid 203, 599, 887 The core activity concept, with – a floating class (‘Schwebeclaß’) or swaying movements on a suspended platform, giving a common class movement combined with individual rhythmic movements 203, 599f., 887 The dynamic instruction method – a combination of rhythmics and calculation, reading and swinging 203, 599, 887 A traditional syllabus with greater emphasis on mathematics and science – use of the vernacular as a medium of instruction 203, 599 National and international academies Austrian academies – the ‘Collegium Imperiale Historicum’ in Vienna  200, 499

1063 English academies – Royal Society of London xv, 2, 15, 28, 46, 88f., 108, 116, 130, 150, 168, 198, 200f., 207f., 210, 214, 247, 265, 272, 278f., 289, 305, 312, 325, 327, 331, 338, 499, 517, 519, 540, 579, 597, 698, 749f., 787, 790, 802, 828f. Royal Society appointments, membership, financial endowments – contrast with the Académie des Sciences 201, 208, 597, 829 Position of curator of experiments offered to Papin (1699) – Leibniz’s desire (1699) for the reinvigoration of the Society 207f., 828f. French Academies – the Académie des Sciences 6, 34, 43, 48f., 53, 55, 88, 98f., 114, 116–118, 168, 197f., 200f., 208, 211f., 244, 265, 271, 276f., 306, 324f., 327, 336f., 348, 382, 412, 453f., 457, 580, 589, 597, 623f., 644, 753, 755f., 775, 783, 786f., 791f., 793f., 829, 868 Financing of the Académie – meetings of the Académie 14, 197, 324, 745 Laboratory of the Académie des Sciences – Huygens’ appointment – Papin’s assistantship (1673– 1675) 57, 457 Membership and remuneration aspirations (Leibniz, Tschirnhaus) 200, 276, 327 Reform of the Académie – its restructuring (1699) 208, 829 The projects of the Académie – journeys to equatorial regions – French Guiana – journeys for map improvement 197f., 324, 397 German academies and universities – a projected ‘Societas Germana’ – the ‘Collegium Artis Consultorum’ (Weigel’s project, 1694), independent of royal or princely support 200, 202, 499, 597f. Berlin – the Berlin Society of Sciences (1700) – ‘Sozietät der Wissenschaften’, and the Prussian Academy of Sciences 14, 44, 47,

1064 Projects – the world of projects (cont.) 115, 120, 203, 262, 745f., 752, 784, 799, 818–829, 858 Financing of the Society – reputation of the Society abroad 204, 819f. Leibniz’s presidency of the Society 14, 745 Membership of the Society – mathematicians, scientists, physicians – necessity of limiting the number of members, and restriction to the dignified and famous 203–205, 818f., 821 Projects / undertakings – construction of an astronomical observatory (1701–02) – gathering of medical and meteorological ephemerides – the medical ephemerides program – established 1701 and directed by Hoffmann in Halle 204, 206, 818, 822 Leibniz’s efforts (1701) to establish missions in remote regions – intended to help the youth gain knowledge of languages, and receive instruction in mathematics and in medical-surgical doctrines 822 Research on dyadic or binary mathematics – envisaged Journal, the ‘Miscellanea Berolinensia’ (1710–) 49, 167, 204, 209, 214, 328, 413, 481, 756, 818, 820, 883 Leibniz’s efforts to communicate an enthusiasm for science at the Berlin court – by means of spectacular experiments 205, 820f. See also Experiments, Experimentation Joh. Bernoulli’s desire for financial support for his experiments, and access to a journal for publications 204, 820 Projects of the Berlin Society (1701) – a system of fire engines – a calendar monopoly enterprise – the drainage of swamps and

Index of Subjects marshlands – a German technical dictionary project 207, 827 Gießen – University of Gießen (1607) 201, 597 Göttingen – Grammar school 200f., 327, 597 Goslar – center in the Harz mining district – seat of the physician Stockhausen 256, 857f. Halle – University of Halle – Thomasius’ experimental lectures to promote a spiritualistic approach 205, 820 Academia Leopoldina, or the ‘Academia Naturae Curiosorum’, in Halle 97, 198, 201, 206, 236, 249, 260f., 298, 325f., 502, 504f., 597, 605f., 732, 822–824, 884 Hoffmann’s Lectures at the Leopoldina – project of the Berlin Society and the Academia Leopoldina 204, 820 The Medical Ephemerides Program, for annual publications following the example of Ramazzini – the collection of observational data regularly throughout a year – similarity with the joint efforts of theologians and mathematicians in the context of the calendar reform 205f., 261f., 502, 822–824 Hoffmann’s program for recording barometric, hygroscopic, and thermometric data – his goal of understanding the functioning of the barometer, and the link between weather and maladies 100f., 206, 823f. Hoffmann’s explanation of barometric phenomena – his ‘Observationes barometrico-meteorologicae’ (1701) 100f., 206, 779, 824 Leibniz’s proposal (1700) for physicians to establish a system of annual observations – a plan for a system of medical-meteorological observations, under the aegis of the

Index of Subjects Projects – the world of projects (cont.) Berlin Society 206, 262, 822f., 825, 858 Mandate granted (1701) for learned physicians to carry out annual observations in the provinces – a system of observations by physicians to explain the connection with illnesses – to obtain insights into epidemics, their occurrence and prevention 206f., 824–826 Mandate also to explore a possible influence of celestial bodies, or a Keplerian ‘Astrologia meteorologica’, by considering lunar and solar phases (Leibniz) and planetary aspects (Hoffmann) 207, 826 Additional observational data of – weather and illnesses – regional geographical details – living conditions and circumstances of the population – welfare of animals – condition of field crops 207, 825 Observations were to be made ideally by two physicians for purposes of mutual control 207, 825 Optional employment of instruments including barometers and thermometers 207, 825f. Leibniz’s appeal to Sloane for emulation elsewhere (December 1701) 207, 826 Hamburg – Society of Hamburg – the ‘Kunst-Rechnungs-liebende Societät’ 200, 499 Hanover (or Göttingen) – location for Leibniz’s proposed military academy (1680) 200, 327 Helmstedt – University of Helmstedt – the ‘Academia Julia’ (1576– 1810) 14, 92, 201, 212, 219, 254, 275, 294, 337, 345f., 597, 619, 701f., 721, 729, 744f., 834, 855 Jena – University of Jena (1558) 49, 120, 202, 212, 337, 597, 729, 800

1065 Kassel – the ‘Collège de Curieux’ – the ‘Collegium Illustre Carolinum’ (1709) 201f., 597 Wittenberg – University of Wittenberg (1502) 91, 201, 262, 293, 329, 556f., 597, 604f. Wolfenbüttel – Ducal library, the ‘Bibliotheca Augusta Guelfica’– Military academy, the ‘Akademie Rudolph-Antoniana’ 7, 11, 156, 175, 356, 430, 486, 508, 574, 701, 838 Italian academies Rome – ‘Accademia fisico-matematica’ (1677–98) 104, 367 Venice – Sarotti’s scientific academy (1682) 200, 327 Technological projects Technology and technological thought – an 18th-century concept (1777) – a discipline devoted to the systematic description of handicrafts and industrial arts ix–xiv, 188f. Development of technological thought by cameralists (from the late 17th century) xi, 189, 407 Becher as pioneer in the development of technological ideas and thinking – his physical, mechanical, mercantile concepts and propositions (1682) 188f. Technology and engineering sciences – philosophy of technology and the sciences 188 Technological inventions – invention reported by Tschirnhaus (1682) – a chiming repeater clock 187, 323 Proto-industrialization (The early industrial age) xi, 149, 160 Prussia. See Berlin, Berlin-Brandenburg, Brandenburg-Prussia Pumps. See also Mining Types of pump Ancient Greek and Egyptian technology – screw pump – Archimedes’ water-screw pump 138

1066 Pumps (cont.) Force pump – known since Hellenistic times 178 Lift pump – water lifting device – developed in Europe in the late middle ages 178 Suction pump – suction-lift pump 178 Suck and press pump – Reisel’s pump (1684 and 1690) – the ‘Sipho Würtembergicus’ 178, 487, 886 Papin’s centrifugal Hesse pump (1689 and 1695) – the ‘Rotatilis suctor et pressor Hassiacus’ 150, 157f., 178, 487, 494, 496, 704, 706, 803f., 886 Areas of application – air exchange in a submergible vehicle (1691– 92) 150, 179, 181, 490, 493, 803. See also Submarines, Submarine Development Coal mine aeration / ventilation (1699) 150, 803 Seawater desalination 139, 150, 190, 201, 219, 387, 410, 499, 573, 803 Fuel economization in a machine – first successful experiments (1699) 150, 803 Piston pump – pump cylinder and piston – sealing techniques 138, 141, 148, 182, 385, 392f., 587, 691f. Steam pump 146, 149, 686, 697, 801, 880. See also Steam Engine Quedlinburg 90 Reason, reasoning / rational thought xiv, 24, 50, 61, 73f., 76, 91, 131, 229, 241f., 263, 343f., 367, 380, 425f., 466, 468, 473, 515, 527, 556, 593, 595, 649, 666–668, 674, 678, 696, 718, 725, 743, 757, 767, 770f., 778, 790, 806, 830f., 870f., 874, 895, 897, 899 Rationalism – rational scientific thought xv, 863 Rational thought and experimental science xiii Rational thought and medicine – rational medicine 266f., 742f., 859f., 862, 896. See also Medicine

Index of Subjects Reasoning in dynamics 65, 538. See also Dynamics Reasoning / exact reasoning in law, morals, politics 429 Reasoning in mathematics – mathematical reasoning 482 Reasoning in mechanics – mechanical reasoning 225, 343, 890–892. See also Mechanics Reasoning in physics – physical reasoning 482 Reason and experience or experiment 61, 527, 668, 871 Leibniz’s touchstones of form and experiment – formal and virtual; form and experiment; a priori and a posteriori – establishment of a doctrine a priori, independent of sensible bodies 60, 65, 649, 767 Formalization / formalized forms of argumentation 61, 66, 83f., 527, 648, 757, 767, 770 Syllogistic reasoning, syllogisms, syllogism chains 61, 66–68, 76, 78f., 82, 86, 527, 648, 652–656, 674, 678, 757f.,765, 774f. Syllogistic premises – major premise, minor premise, and conclusion 68, 76, 82, 86, 653, 678f., 766, 774f. Leibniz’s syllogistic reasoning 76, 674, 678 His recourse to the method of syllogisms (1696) 66, 648. See also Natural Philosophy, Vis Viva, Action, and Papin’s 13th–17th syllogisms (1696–1697) Regensburg – Imperial Diet / Perpetual Diet (‘Reichstag’) – Protestant imperial estates (‘Corpus Evangelicorum’) 114f., 117, 162, 202, 414, 598, 782, 784, 790, 811 Rhineland district – Rhineish foot (measure) 561 Relativity (Galilean relativity) – absolute and relative 77, 113, 371, 681 Absolute action, force, resistance, velocity 67, 71, 75, 77, 113, 371, 454, 537, 650, 658–661, 673, 680f., 762 Relative action, force, resistance, velocity 66f., 71, 77, 113, 371, 536, 649f., 661f., 680f.

Index of Subjects Religion Biblical studies and scriptural references – the book of Moses 42, 119f., 798f., 898f. Biblical archaeology – Burnet’s ‘Archaeologiae philosophicae’ (1692) 228f., 724f., 897 Biblical narrative – its historical veracity / falsehood xiv, 229 Creation (origin of things) out of ‘God’(1) and ‘nothing’(0) xv, 48, 753f. Leibniz’s ‘new year’s letter’ (January 2/12, 1697) 27, 646 Creationism and Creator – divine creation – wisdom of the creator xiv, 59, 460, 541 Mysticism, mystical theology xv, 899 Obscurantism 798, 899 Religious heresy, heretics xiii, 42, 232, 641 Religious rationalism – faith and reason – deistic, rationalistic theology xiv, 219f. Early modern theorizing about science and religion – cosmological and cosmogenic theories – geological and geomorphological theories xi, xivf. Compatibility of science and religion – interaction between science and religion xi, xivf. Early modern natural philosophy allied with revealed religion – scientisttheologians, or advocates of a physico-theology xv Conflict between science and religion – divorce / separation of science and religion xvf. Relation of science to religion – philosophical and theological issues – reflections of Boyle and Newton 90f., 219 Leibniz’s correspondence with Wedel – objections of the correspondent against heliocentricism – his view of a contradiction of the biblical account of the creation, and the story of genesis from the book of Moses 119, 798, 898f.

1067 Leibniz’s preference for a metaphorical rather than literal interpretation of the biblical narrative 119f., 798f., 898f. Priority for Leibniz of science, reason and rational thought over mysticism, religion and theology 899 Republic of letters. See Learning, Learned Resistance. See Natural Philosophy, Medium, Media Rübeland (Harz district) – nearby cave (‘Baumannshöhle’) 227, 419, 892 Russia – Muscovy / Muscovite Russia / Grand duchy of Moscow 13, 253, 618, 853 Satire, satirical writings – Becher’s satirical work (1682) 7, 140, 146, 188, 278, 390, 398, 523, 880 Savoy / duchy of Savoy (Savoie) – siege of Montmélian (1691) 175, 486 Saxony – electorate of Saxony – Saxon court 6, 19, 141, 153, 160f., 184, 186, 190, 201, 226, 257, 271, 275, 315, 321, 330, 332, 344f., 352–354, 391f., 402, 408, 499, 576, 808, 842, 857, 879, 891 Dresden 6, 146, 152, 160, 186f., 214, 257, 262, 275f., 321f., 330, 339, 352–354, 398, 401, 605, 807f. Ehrenfriedersdorf 141, 391f., 879 Erzgebirge (Ore mountains) 201, 499. See also Mining Estates / orders of social hierarchy in Saxony 184, 315 Freiberg 141, 391f., 402, 879 Görlitz 200, 226, 249, 327, 345, 423f., 891 Kieslingswalde (near Görlitz) 161, 200, 327, 808 Königstein – Fortress Königstein 807 Leipzig – Leipzig spring fair (1697) 16, 22, 36f., 49, 58, 60, 116, 126, 130f., 141, 215, 257, 262, 280, 304, 312, 339, 341, 352, 361, 379, 394, 432, 441, 443, 458, 462, 519, 557, 559, 605, 628f., 785, 864, 869f. Mercantile community in Saxony 184, 315 Muscau (near Görlitz) 226, 891 Schneeberg mining district – Schneeberg disease 256, 857 Torgau 262, 605

1068 Science and the sciences, scientists Advancement of science / the sciences 52, 128f., 132, 197, 208, 324, 452, 562, 626, 685, 827 Abstract / theoretical science(s) or scientific approach 239, 481, 575, 846 Applied /concrete / practical science(s) or scientific approach 87, 89, 92, 131, 239, 290, 294, 328, 846 Exact science(s) 4, 263, 266, 272, 425, 742, 895 Experimental science xiii, 130, 204, 247, 380, 820, 852 Leibniz’s Idea (1701) of a ‘collegium experimentale’, with lessons / lectures on physical-mathematical inventions and experiments – their 100-fold superior value over corresponding lessons in metaphysics, logic, ethics (Leibniz’s words to Hoffmann) 205, 744, 820 Studies in experimental science in Halle – Hoffmann’s lectures on experimental physics (1700– 1701) – issue of their financing / financial support – his advocacy of an empirical science based on a Cartesian mechanical world view 204f., 820 Thomasius’ experimental lectures in Halle – based on a spiritualistic approach 205, 820 History of science x, xii, xiv, 7, 199, 239, 271 Natural science xv, 236, 732 Observational science 131, 473 Observations 7, 57f., 88, 97–99, 117–120, 126, 129–132, 159, 164, 166, 198, 206f., 231, 234f., 237, 241–243, 247f., 258, 261–263, 277f., 283, 288, 294, 298, 300–305, 324–326, 333, 336, 343, 345f., 347, 351, 355, 363, 365, 379, 381f., 403, 458, 465, 473f., 477f., 480, 495, 498, 500, 504f., 557, 602, 604, 614, 646, 683–685, 694, 709, 727–731, 776f., 779, 788, 790–794, 796f., 799, 822–826, 841, 845, 847–849, 851, 858f., 890, 897, 899

Index of Subjects Scientific rationalism. See Reason, Reasoning, etc. Science and religion. See Religion Scientific ideas – transformation of scientific ideas xiii, 103 Scientific revolution(s) xii–xiv, 1, 104, 142, 199, 225, 238 Copernican revolution xii Evolution of classical science xiif. Newtonian revolution xiii, 103 Paradigm of the scientific revolution xii Scientific societies. See Learning, Learned Societies Unity of science xv, 51 Scotland – draining coal mines – water power in Scotland 310f. Shipbuilding and sailing. See Navigation Steering and maneuvering a sailing ship. See Navigation Slate – Mansfeld copper-slate 226, 344, 891. See Mansfeld (Harz) Slavery and serfdom – slave trade / slave traders 186, 320 The Atlantic slave trade – between Africa, the Americas, and Europe – the Dutch and Atlantic slave trade 186, 320 The ‘Brandenburg-African Company’ (1682–1721) 185f., 319f. Elers’ project relating to black Africans (1682) – Elers’ advocacy and Crafft’s rejection / skepticism 186, 319f. Leibniz’s interjection regarding the Dutch slave trade – with total prohibition within the republic itself 186, 320 Elers’ insistence – that black people were being held in Holland, even by Jews there – that black laborers were hardier than their European counterparts 186, 320 Economic and demographic factors considered – demographics of Germany and of north American territories – possibility of relocation and rural settlement of black Africans in Canada 186, 320 Space. See Astronomy Spain, Spaniards, Spanish 14, 142, 214, 220, 252, 339, 607, 723, 741, 746, 811

Index of Subjects Spicery, spices 408 Speyer 414 Steam – steam engine / steam pump. See Engines, Enginery Steganography. See Cryptography Stralsund 264, 738 Strength of materials. See Materials Submarines (submersible vessels) 3, 177–182, 487f., 490–493, 496, 584, 586, 827, 862, 885f. Submarine development and navigation Drebbel’s submersible vessel and his passage across the Thames (c. 1620) – speculation regarding air exchange / renewal – supply of fresh air to the vessel – possibly achieved by chemical means – possible use of a quintessence – possible beneficial effects from the burning of spirit of wine 178f., 488–490, 584–586 Papin’s ‘Navis urinatoria’/ ‘Batteau plongeant’ (1695) 178–181, 488–496, 584–586 His trials of the vessel on the river Fulda at Kassel 150, 488, 803, 885 His first design (June 1691) – vessel crashed and wrecked (August 1691) 179f., 490f., 496 Form and construction details of the vessel – rectangular parallelepiped tinplate box – its wooden hull and iron guide rails 179, 490f. Use of lead ballast for submersion – lockable openings in floor and roof – upper hatch used for entry and exit, and loading of lead ballast 179f., 490f. Bottom hatch used for offloading of lead ballast, and other under water operations 180, 490f. Use of a ventilator pump for air exchange 179, 490, 887 Key features of the air exchange system – intake of fresh

1069 air – expulsion of foul / exhaust air 181, 490, 493 Essential role of air-exchange for the human respiratory system – and for illumination from a lamp flame 179, 490, 887 Key components of the pump system – a roof cylinder connecting inside and outside – tubing for air supply and exchange between vessel and the water surface 179–181, 488, 490–492, 494, 496, 887 Interior section of the roof cylinder – its movement within another moveable cylinder with a downward-opening valve – an up and down movement, for drawing fresh air into the vessel 180, 491 Key parameters – air pressure inside the vessel – atmospheric air pressure – hydraulic thrust 180, 491 Instruments used – a barometer (for pressure measurement) and a compass (for navigation) 180, 491 New series of trials of the vessel at Kassel (second design, springtime 1692) – successful demonstration (June 1692) 180f., 492–495 Form and construction details of the vessel – a wooden hull of oval shape – machine room places for three persons – single (upper) hatch for entry and exit – sealed side openings enabling oar propulsion of the vessel – use of water ballast tanks for submersion 180f., 492–495 Submergence and reemergence – achieved by filling and pumping out of a water tank (‘bucket’) 494f.

1070 Submarines (submersible vessels) (cont.) Key features of air exchange – use of the centrifugal (Hesse) pump, and hoses / tubing for air supply 181, 490, 492, 496 Additional features of the new design – illumination of the machine room – use of instruments for submersion and navigation (barometer, compass) – oar propulsion under water 181, 490, 493–495 Possible military use – envisaged attacks on hostile vessels 181, 496 Leibniz’s idea of using a ‘spirit-ofwine lamp’ for illumination – dangers of the extinguishing of the flame, and of pollution of the air inside the vessel 182, 489f., 585f. Sumatra (Indonesia) 226, 344, 891 Sweden, Swedish kings, court 2, 142, 151, 159, 176f., 220, 246, 264, 322f., 394f., 713, 723, 736, 738, 800, 804, 806, 838 Falun 151, 159, 800, 804. See also Mining Stockholm 224, 395, 800, 839 Switzerland, Swiss 24, 44, 437, 445, 746 Duillier, Municipality (Canton de Vaud) 44, 746 Technology. See also Power Technology, Technological Projects History of technology x, 139, 150 Renaissance (pre-Galilean) technology – the practical-empirical tradition 477 Galilean / post-Galilean technology – the scientific-mathematical tradition 477 Technological thought – project conceptions xi, 314. See Projects, Technological Projects Textbooks – early-modern textbooks 25, 34, 43f., 238, 258, 509, 623, 868. See also Mathematical textbooks Theology, theologians. See Religion, Mystical Theology Therapeutics, therapies. See Medicine

Index of Subjects Thermodynamics. See Physics Thuringia 235, 729f., 846 Gotha – Collegium Medicum 235, 729 Gräfentonna (Tonna) 235, 239, 729, 846 Tiger (panthera tigris). See Biology, Zoology Transport, transportation 133, 146, 148–150, 154, 398, 691–694, 697, 699, 877f., 881 Leibniz’s imagined rapid transit system (before 1682) – travel between Hanover and Amsterdam in six hours – Becher’s satire (1682) on Leibniz’s vision 7, 140, 146, 188, 278, 390, 398, 880. See also Controversies and Disputes Mail-coach, stagecoach – improvement of coaches and carriages 7, 146, 278, 398 Schmid’s ‘schese rolandte’ (1687) 146, 398 Linsen‘s work on a model for a carriage (1697) 156, 700 Leibniz’s ideas for the improvement of transportation – an engine to power a vehicle and facilitate transport – a steam engine or pneumatic engine – Papin’s plea for their publication (1698) in order to be made available for posterity 148, 690–692, 694, 881 Steam-powered transport – Papin’s conception of propulsion using steam power – his model of a vehicle powered by steam and operating on water (1698) – his vision of a marine vehicle powered by steam – its unsuitability for the propulsion of vehicles on land, due to the imperfections of existing roadways 147f., 689, 881 Tübingen 240, 847 Universe, the universe as a whole – force of the universe conservative 75, 109, 541f., 672, 876 Vienna. See Austria Vis, Force – ‘vis viva’ and ‘vis mortua’. See Controversies and Disputes, Natural Philosophy, Physics

Index of Subjects Wales – a silver mine in Wales 201, 500 Wars in Europe (1672–1721) – Franco-Dutch war (1672–1678) – Third Anglo-Dutch war (1672–1674) – War against the Turks (1683–1689) – War of the Grand Alliance against France (1688–1697) – Jacobite / Williamite war in Ireland (1689–1691) – Palatine war of succession (1688–1697) – Denmark-Norway, and the Anti-Swedish alliance (1700) – Great Northern war (1700–1721) – War of the Spanish succession (1701–1714) 14, 104f., 177, 192f., 259f., 319, 323, 367, 502f., 508, 574, 590f., 746, 884 Trade wars – Leibniz’s envisioned trade war with France 12, 194, 591, 593, 716.

1071 See also Economics, Leibniz’s / Crafft’s Brandy Project Weather. See Meteorology Westphalia – Neuhaus 6, 275 Wittenberg 91, 201, 262, 293, 329, 556f., 597, 604f. Wolfenbüttel. See Principality of Brunswick-Wolfenbüttel Wuerttemberg (Wurtemberg) – Stuttgart – ‘Wurtemberg Siphon’ 178, 478, 487, 886. See also Engineering, Mechanics of Fluids Zeitz 120, 800 Zellerfeldt. See Clausthal (Clausthal-Zellerfeld) Zerbst 262, 605 Zoology. See Biology

MEDIE VA L A ND E A RLY MODER N PHIL O S OPH Y A ND S C IENCE

Leibniz’s correspondence from his years spent in Paris (1672-1676) reflects his growth to mathematical maturity, whereas that from the years 1676-1701 reveals his growth to maturity in science, technology and medicine; in the course of which more than 2000 letters were exchanged with more than 200 correspondents. The remaining years until his death in 1716 witnessed above all the appearance of his major philosophical works. The focus of the present work is Leibniz's middle period. The core themes and core texts from his multilingual correspondence are presented in English from the following subject areas: mathematics, natural philosophy, physics (and cosmology), power technology (including mining and transport), engineering and engineering science, projects (scientific, technological and economic projects), alchemy and chemistry, geology, biology and medicine. JAMES G. O’HAR A Ph.D., (1979), University of Manchester, is an historian of science and technology. During his career, he has taught and done research in Delft, Regensburg, Stuttgart, Munich (Deutsches Museum), Hamburg and Hanover. His research interests include the edition of manuscript papers of historical personages in science and technology (17th–19th centuries). Between 1987 and 2013, he co-edited five volumes of Leibniz’s correspondence in mathematics, science and technology at the Gottfried Wilhelm Leibniz Library (Hanover).

9 789004 354906

ISSN 2468-6808

brill.com/memps