Les publications de l'Académie royale des sciences de Paris (1666-1793) (De diversis artibus) (French Edition) 250351197X, 9782503511979

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OPTICS AND ASTRONOMY

DE DIVERSIS ARTIBUS COLLECTION DETRAVAUX

COLLECTION OF STUDIES

DE L'ACADEMIE INTERNATIONALE

FROM THE INTERNATIONAL ACADEMY

D'HISTOIRE DES SCIENCES

OF THE HISTORY OF SCIENCE

DIRECTION EDITORS

EMMANUEL

ROBERT

POULLE

HALLEUX

TOME 55 (N.S. 18)

@

BREPOLS

PROCEEDINGS OF THE XX1h INTERNATI ONAL CONGRESS OF HISTORY OF SCIENCE (Liege, 20-26 July 1997) VOLUME

XII

OPTICS AND

ASTRONOM Y Edited by Gerard SIMON and Suzanne DEBARBAT

@j

BREPOLS

The XXth International Congress of History of Science was organized by the Belgian National Committee for Logic, History and Philosophy of Science with the support of : ICSU Ministere de la Politique scientifique Academie Royale de Belgique Koninklijke Academie van Belgie FNRS

Chambre de Commerce et d'Industrie de la Ville de Liege Club liegeois des Exportateurs Cockerill Sambre Group Credit Communal FWO Derouaux Ordina sprl Communaute fram;:aise de Belgique Disteel Cold s.a. Region Wallonne Etilux s.a. Service des Affaires culturelles de la Ville Fabrimetal Liege - Luxembourg de Liege Generale Bank n.v. Service de l'Enseignement de la Ville Generale de Banque s.a. de Liege Interbrew Universite de Liege L'Esperance Commerciale Comite Sluse asbl Maison de la Metallurgie et de l'Industrie Federation du Tourisme de la Province de Liege de Liege Office des Produits wallons College Saint-Louis Peeters Institut d 'Enseignement superieur Peket de Houyeu "Les Rivageois" Petrofina Rescolie Academic Press Sabena Agora-Beranger SNCB APRIL Societe chimique Prayon Rupel Banque Nationale de Belgique SPE Zone Sud Carlson Wagonlit Travel TEC Liege - Verviers Incentive Travel House Vulcain Industries

© 2001 Brepols Publishers n.v., Tumhout, Belgium

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the publisher. D/2001/0095/60 ISBN 2-503-51197-X Printed in the E.U. on acid-free paper

TABLE OF CONTENTS

Part one STUDIES IN ANCIENT, MEDIEVAL AND PREMO DERN OPTICS

Introduction ...................................................................................................... 9 Gerard SIMON The Methodological Foundations of Ptolemaic Visual Theory .................... 11 A. Mark SMITH What " Euclid Said " to his Arabic Readers : The Case of the Optics ........ 17 Elaheh KHEIRANDISH Euclid's De speculis. Its Textual Tradition Reconsidered ............................ 29 Ken' ichi TAKAHASHI Brahe and Rothmann on Atmospheric Refraction ........................................ 43 Peter BARKER Hieronymus Fabricius d'Aquapendente : De visione, Ending of the Perspectivistic Tradition ........................................................................... 51 Erwin DE NIL - Mark DE MEY Kepler's Critique of the Medieval Perspectivist Tradition ............................ 83 Raz Dov CHEN-MORRIS - Sabetai UNGURU How Galileo's Mind Guided his Eye when He First Looked at the Moon through a Telescope .................................................................. 93 William R. SHEA Reftexions sur " L' optique " de Galilee ...................................................... 111 Philippe HAMOU De Kepler a Descartes : le renouvellement de la problematique de la vision ................................................................................................... 119 Gerard SIMON Descartes and Hobbes on Optical Images ................................................... 127 Antoni MALET

6

TABLE OF CONTENTS

Part two ASTRONOMY

Introduction Suzanne DEBARBAT ................................................................................ 137 Hipparchan Precession-Math Spherical Trig Relics. Manitius' Discernment. Ancient Calculus ? ................................................................ 139 Dennis RAWLINS On the Measurement of Celestial Longitude in Antiquity .......................... 145 Nicholas KOLLERSTROM Astronomical Aspects of Robert Hooke's Scientific Research ................... 161 Hideto NAKAJIMA Dialogue Concerning the Two Astrologies in Coimbra Jesuit's Thought.. 167 Luis Miguel CAROLINO Analisis de un modelo cosmografico presentado en el Colegio Imperial de la Compafifa de Jesus en Madrid ........................................................... 177 Javier BERGASA LIBERAL Entre science et philosophie : la cosmologie dans l'Encyclopedie D 'Alembert et Maupertuis ........................................................................... 185 Martine GROULT Des observations astronomiques vieilles de deux siecles toujours d'actualite - Un exemple relatif a Neptune ................................................. 195 Suzanne DEBARBAT - Simone DUMONT Sir Harold Jeffreys, Pioneer of Modern Planetology .................................. 213 Alexander V. KOZENKO Schuster-Schwarzschild's and Milne-Eddingto n's Viewpoints on the Physical Structure of Stellar Atmospheres ....................................... 217 Leo HOUZIAUX Cosmology and Technology ........................................................................ 229 Gustaaf C. CORNELIS

Contributors .................................................................................................. 237

PART ONE

STUDIES IN ANCIENT, MEDIEVAL AND PREMODERN OPTICS

INTRODUCTION

Gerard SIMON

On trouvera ici les communications qui ont ete consacrees a l' optique au cours du XX" Congres international d'histoire des sciences. Neuf d'entre elles ont ete presentees dans un symposium sur " L' optique antique, medievale et premodeme (avant Newton)" place sous la responsabilite d' A. Mark Smith et Gerard Simon. La dixieme est une conference d'ouverture presentee par William Shea, qui porte sur !'interpretation perspective par Galilee des ombres portees des montagnes de la Lune, observees au telescope. Elle s'inscrit tellement dans notre propos, le raisonnement optique de Galilee y est si bien mis en lumiere, que nous l 'avons integree avec joie a nos travaux, heureux de cet apport remarquable et imprevu. Ces textes presentent une unite thematique qui etait celle du symposium. Apres une etude sur les fondements de la theorie de la vision chez Ptolemee (A. Mark Smith), on y trouvera deux recherches philologiques sur l 'Euclide medieval, l'une Sur la reception arabe de l'Optique (E. Kheirandish), l'autre sur la filiation des manuscrits du De Speculis, traduction en latin de la Catoptrique (Ken'ishi Takahashi). Le reste porte sur la periode modeme. Une communication de P. Barker evoque les discussions qui eurent lieu dans les annees 1580 entre le Landgrave de Hesse Guillaume IV, Rothmann et Brahe sur la refraction atmospherique et sa mesure. On entre deja dans une periode de renovation et de tension, qu'evoquent M. de Mey et E. de Nil en retras;ant la figure d'un grand medecin traditionaliste de la fin du siecle comme Fabricius d' Aquapendente, tandis que S. Unguru et R.D. Chen Morris montrent au contraire en quoi Kepler dans sa theorie de la reftexion se separait au meme moment de la tradition perspectiviste et du conservatisme theorique. Viennent ensuite deux etudes tres complementaires Sur Galilee (W. Shea et P. Hamou), et deux autres Sur le rapport d'une part de Descartes a Kepler (G. Simon), d'autre part de Hobbes et des prenewtoniens anglais de Descartes (A. Malet). Tout ceci tisse une trame assez serree sur la periode, ses oppositions, ses lieux critiques et leurs enjeux.

10

GERARD SIMON

Ce volume aurait du , helas, etre plus riche encore. Parmi les collegues dont la participation etait prevue figurait Wilbur R. Knorr, dont les idees si decapantes ont permis de reposer bien des probtemes que l' on croyait regles, y compris sur la tradition manuscrite de l'optique antique. Nous comptions beaucoup sur lui pour animer et susciter des debats passionnes, en particulier a propos du corpus euclidien sur lequel il m' avait ecrit vouloir intervenir. Malheureusement, la maladie a ete plus forte que ses projets et que nos espoirs. Que ce recueil soit aussi un peu comme un dernier hommage rendu au collegue et a l'ami qu'il etait devenu. Il me reste a remercier tous ceux qui ont permis la tenue et la reussite de nos travaux. Outre les intervenants eux-memes, le professeur A.I. Sabra, avec qui dans un premier temps ont ete discutes le theme et les limites chronologiques du symposium, et avec qui a ete esquissee une premiere liste d'invites. A Mark Smith ensuite, qui a accepte d'en prendre avec moi la responsabilite scientifique. Les organisateurs du Congres bien sur, Robert Halleux et son equipe, qui nous ont permis de debattre a loisir, et sur lesquels porte encore la lourde charge de la publication des actes. Et enfin Mme Thill, secretaire du Centre de recherche "Savoirs et textes" (UMR 8519, CNRS, Universites Lille 3 et Lille 1), qui a assure le suivi administratif du symposium dans toute sa phase preparatoire.

THE METHODOLOGICAL FOUNDATIONS OF PTOLEMAIC VISUAL THEORY 1

A. Mark SMITH

Several years ago I suggested that Greek mathematical optics and astronomy shared essentially the same methodological foundations in that both epitomized the endeavor to " save the phenomena "2 . Accordingly, I argued, both sciences were firmly grounded in the supposition that observed irregularities or anomalies, such as the retrograde motion of planets or the appearance of images behind plane mirrors, were mere illusions. To save the phenomena was therefore to uncover the true regularity behind such illusory appearances. That regularity, in tum, was understood as a function of a saving principle or salvans : perfectly uniform circular motion in the case of astronomy, perfectly rectilinear visual radiation in the case of optics. On this basis, classical mathematical astronomy and optics - both brought to perfection by Ptolemy took shape according to a structure of nesting anomalies and corresponding salvations. In his 1908 study of the theoretical implications of pre-Galilean astronomy, Pierre Duhem contended that " saving the appearances ", as exemplified in the Ptolemaic model of epicycles and deferents, was an essentially positivist undertaking 3 . 1. This paper is an abbreviated version of an article entitled " The Physiological and Psychological Grounds of Ptolemy's Visual Theory: Some Methodological Considerations", which is currently under consideration by the Journal of the History of the Behavioral Sciences. 2. See esp. " Saving the Appearances of the Appearances : The Foundations of Classical Geometrical Optics", Archive for History of Exact Sciences, 24 (1981), 73-100; see also" Ptolemy's Search for a Law of Refraction: A Case-Study in the Classical Methodology of 'Saving the Appearances' and its Limitations", Archive for History of Exact Sciences, 26 (1982), 221-240. 3. This seminal study, :LQZEIN TA ...o ""~

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ofa d_)c-:-1 1 c ~c:; 1) 1 ""lso led 13 VI: al-Ya'qiibi, Ta'rikh (1883), v. 1, p. 139. [Krause (1974), p. 441; Kheirandish (1996, 1998); Rashed (1997), p. 42]. ~ J~ t l....::J 1 3 0~ I c.; l.>..o i f ~>l:s.13 _,..];LI I

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68

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ON THE MEASUREMENT OF CELESTIAL LONGITUDE IN ANTIQUITY

Nicholas KOLLERSTROM

"For Babylonian and early Greek astronomy the beginning points of the signs are rigidly connected, not with the equinoxes, but with the fixed stars " van der Waerden 1

INTRODUCTION How, in the Hellenistic world of late antiquity, was celestial longitude measured ? For over a millennium planetary longitudes were measured with respect to the Vernal Point - as Claudius Ptolemy advocated, writing in the second century AD. However, the zodiac framework of antiquity was inherited from the Babylonians, who used a sidereal reference, with certain fixed stars defining its position. Otto Neugebauer's Greek Horoscopes argued that these Hellenistic charts were using a sidereal reference, but was vague about what this was. Almost nothing is written about this subject in modem histories of science or astronomy. Evidence is here presented supporting Neugebauer's view, based on computer reconstruction of planetary longitudes as given in the 1si_yh centuries AD, and some earlier, showing that a sidereal zodiacal reference continued to be used by Greek sources, comparable to that used by the Babylonians ; and supporting a claim recently made by John Britton, concerning the star f3Gemini as defining zero degrees of Cancer2 . In the fifth century BC, a twelvefold division of the ecliptic into equal intervals appeared, which by the fourth century was clearly subdivided into thirty degrees per sign, and stellar longitudes were thereby defined ; and then, in the third century, planetary degree-longitudes appeared, for distinct moments in time. This not unremarkable evolution remains a largely ignored topic, with lit1. B.L. van der Waerden, Science Awakening II, 1974, 222. 2. J. Britton, Ch. Walker," Astronomy and Astrology in Mesapotamia ",in Ch. Walker (ed.), Astronomy before the Telescope, 1996, 49.

146

NICHOLAS KOLLERSTROM

tle having appeared since the researches of Otto Neugebauer and Van der Waerden earlier in the century. Two books entitled Early Astronomy have appeared recently. One of them, by O'Neill, gave no hint that any issue over zodiac position existed or required discussion 3 ; while the other, by Thurston, posed the question : "Where precisely on the ecliptic were the signs placed ? " a propos of Babylonian astronomy4, but then gave an answer in terms of the equinoctial points: it averred that the signs had been fixed with regard to so many degrees from the solstices and equinoxes. This, however, was far from being the case, as it was in the nature of the Babylonian zodiac that it remained fixed against the stars. The solstices and equinoxes moved round against it, at the rate of precession, viz. one degree per 72 years. Noel Swerdlow's The Babylonian Theory of the Planets has reviewed the manner in which Babylonian scribes computed planetary longitudes, while avoiding any statement as regards what reference was used for such. Its graphs depict planetary longitudes through the zodiac signs, and over thirty tables show planetary ingresses into zodiac signs, but nowhere is a reference indicated whereby these divisions were fixed. Swerdlow even avers that " the division of zodiacal signs into 30 us does not indicate a coordinate of longitude ", and that " we shall, for lack of any alternative term, refer to locations and distances in iis through the zodiac as longitude, and measure them in degrees, but without implying that they are measured along a circular co-ordinate " 5 . This book's strange claim, that the Scribes of Chaldea were unable to measure celestial longitude, has been described by a reviewer as " almost certainly untrue " 6 . The "us" was a time-measurement equal to four minutes of time, or 1/360 of a day. But, to quote Morrisson and Stephenson, " since this unit [the iis] was the interval required for the celestial sphere to tum through 1°, it is customary to translate iis directly as degree " 7 ; just as today, one may add, the terms " minute " and " second " signify degree measure as well as time. STELLAR LONGITUDES

In 1958, Peter Huber published the result of his investigation into the celestial longitude framework utilised in the Babylonian astronomical data, over the period -124 to - 99 8 . He expressed his findings in terms of a single reference, 3. W.M. O'Neill, Early Astronomy from Babylonia to Copernicus, Sidney U.P., 1986. 4. H. Thurston, Early Astronomy, Springer Verlag, 1994, 68. 5. N. Swerdlow, The Babylonian Theory of the Planets, Princeton, 1998, 35. 6. J. Britton, Planetary Theory in Babylon, review of N. Swerdlow, op. cit., Journal for the History of Astronomy, 29 (1998), 381-386. 7. L.V. Morrison, F.R. Stephenson, "Contemporary Geophysics from Babylonian Clay Tablets", Contemporary Physics, 38 (1997), 13-23, 16. 8. P. Huber," Ueber den Nullpunkt der Babylonischen Ekliptic '', Centaurus, 5 (1958), 192208. NB, the year -99 is equivalent to 100 BC.

ON THE MEASUREMENT OF CELESTIAL LONGITUDE IN ANTIQUITY

147

an estimate of what will here be called the sidereal zodiac position (SZP). This refers to the angular distance in celestial longitude between the historic zodiac (which was sidereal, i.e. star-defined) and the modern value computed for the epoch in question (which is tropical, ie equinox-defined). Huber estimated this parameter to be 4 °28' for the epoch of -100 BC. Huber derived that value using merely eleven star-positions, thereby expressing the mean displacement of their stellar longitudes from those of the tropical zodiac, in that year. Six of these had come from a pre-Seleucid (ea 400?) fragment of a star catalogue published by Sachs9 , and five more were added by Huber from his analysis of Almanacs for -122 and -110, i.e. roughly three centuries later, an analysis which also confirmed three of the longitudes found by Sachs (and disagreed with none). The brightest zodiac star is Aldebaran the "Bull's Eye", and in the Babylonian 30° "sign" of the Bull of Heaven, its tropical longitude was 10°34' of Taurus for the epoch of -100 10 , which is 4°26' short of the sign's mid-point, ie 15°. That difference is, for that epoch, a mere few arcminutes from the mean dispacement of the Babylonian zodiac which Huber ascertained. In other words, if a sidereal zodiac were to be defined by adding on Huber's 4°28' to tropical longitudes, for 100 BC, then Aldebaran would have a longitude of 15°02' Taurus. This suggests that they took Aldebaran at 15° Taurus, or something close to it, as a prime reference, though Huber refrained from drawing such a conclusion. No Babylonian tablets have been found specifying a procedure for locating the sign divisions. There are a couple of references from later Hellenistic sources affirming that Antares and Aldebaran were located at central 15° positions, by Kleomedes in the 4th century and Rhetorios in the 6th century 11 . Figure 1 shows the zodiac structure using this as its reference-axis, bisecting the signs of Taurus and Scorpius. The two first-magnitude zodiacal stars Antares and Aldebaran were 180° apart to within a single arcminute over the period 300 BC to 1200 AD 12 ; and that, although they may "never be seen simultaneously in the Mediterranean area ", on some days each year they could be seen together from below the Tropic of Capricorn 13 .

9. A. Sachs," A Late Babylonian Star-Catalogue", Jnl Cuneiform Studies, 6 (1952), 146-150. 10. P. Huber, op. cit., 205. 11. 0. Neugebauer, A History of Ancient Mathematical Astronomy, II, Berlin 1975, 960, assumed that the positions for Aldebaran and Antares given by Kleomedes (1 st century BC) were tropical, but there is no clear evidence either way. Rhetorius gives 16°20' Taurus/Scorpio for these longitudes (5 1h century AD), which are clearly tropical. 12. D. Rawlins, Dio, (Jan 1991), 62 (Rawlins Ed., an independent US history of astronomy journal ; copies in Royal Astronomical Society library, London). 13. K. Pickering, Dio, (April 1992), 15.

148

NICHOLAS KOLLERSTROM

Figure 1. The Sidereal Zodiac (Source: R. Powell & P.Treadgold, The Sidereal Zodiac, 1979), with names of some first-magnitude stars, plus movement of Vernal Point from 5th century BC (Euctemon) to today at 25° of Pisces.

ON THE MEASUREMENT OF CELESTIAL LONGITUDE IN ANTIQUITY

149

About thirty-two reference or normal stars were employed by Babylonians 14, and it may be of interest to view the positions of a few of these, converted to a sidereal zodiac with Aldebaran at 15°00' Taurus in at epoch -100 as shown in Table 1. Table 1 : Key Star-Longitudes, Sidereal (for epoch -100) Aldebaran (a-Taurus) Antares (a-Scorpio) Regulus (a-Leo) Spica (a-Virginis) Other stars near to sign-boundaries: Alhecka (~-laurus) Pollux (f3-Gemini) Deneb Alg. (6-Capricom)

15°00' 15°00' 5°12' 29°06' 00°02' Gemini 28°48' 28°41'

The stars at sign boundaries had names, eg 6-Capricom was called " rear star of the Goat-fish " 15 which names however derived from the constellation rather than the sign. Recently, Britton and Walker have averred that " the norm of the Babylonian sidereal zodiac appears to have been fixed so that the longitude of the bright star f3-Gemini was 90° " 16 , but without giving any evidence for this view. That appears to be the only post-Neugebauer statement concerning the positioning of the star-zodiac of antiquity made by science historians. Relative to the values given in Table 1, a one-degree and twelve arcminute rotation of the zodiac would put Pollux (f3-Gemini) on the Gemini/Cancer boundary. It is unclear as to whether such a shift would have been significant, as we hardly know the extent to which the reference-star longitudes were coherent. One should not assume that such positions at different portions of the ecliptic were meant to be fully compatible. Van der Waerden concluded that the Babylonians positioned the star Spica at 29° of Virgo, " with a possible deviation of 1° to either side " 17 , which gives a fair idea of the accuracy involved. Four of the stars listed above probably denoted sign boundaries, with Pollux placed at 90° as the Gemini/Cancer boundary. Of the first-magnitude stars, 14. A. Sachs, The Place of Astronomy in the Ancient World, Ed. D.G.Kendall et. al., Oxford, 1974, 46; the 32 reference stars are listed with ecliptic coordinates in A.Sachs and H.Hunger, Astronomical Diaries and Related Texts from Babylonia, 1988, 1, 17-19. 15. A. Sachs, op. cit., 46. 16. J. Britton, Ch. Walker, op. cit., 49. 17. B.L. van der Waerden, "History of the Zodiac", Archiv fur Orientforschung, 1953, 16, 216-230, 222. Spica is one of the stars included in both Sach's star catalogue fragment (ref.9) and Huber's almanac analysis (ref.8), in both cases with a longitude of 28°.

150

NICHOLAS KOLLERSTROM

Spica and Regulus were especially useful as being on the ecliptic, having celestial latitudes of 2° and 0° respectively. In contrast with their attention to stellar longitudes, van der Waerden emphasised how little interest the Babylonians had over solstice and equinox positions : " they did not care for exact observation of equinoxes ... the spring equinoxes have errors up to 5 days " 18 . There is a profound contrast here with Greek astronomers who, once they heard about the zodiac later in the fifth century BC, defined it by reference to the Vernal Point, taking the longitude of this at around S0 of Aries. A zodiac thus defined is tropical, and this inquiry is not concerned with such. No Greek astronomer is on record as having measured celestial longitude by reference to fixed stars. Hipparchus of Rhodes " reckoned the seasons from the beginning of the signs " 19 , thereby conceiving the zodiac signs tropically. He may not have used ecliptic longitude for his measurements, but an oblique or right ascension, making it not altogether clear to historians in what way he discovered precession. Assuredly, however, he made a radical break from the ways of the Babylonians, who produced " ... Cuneiform tablets in which the vernal point is put at 10° or S0 of Aries, but never at 0° Aries " 20 . Earlier, the Greek or Tropical zodiac had been used for estimating time in terms of the seasonal course of the year, by astronomers Meton and Euctemon, whereas Hipparchus used it as the basis for cataloguing star-positions. Van der Waerden emphasised how, after the transmission of the Babylonian zodiac to the Hellenistic world of late antiquity, the habit of measuring from a sidereal reference was retained, and that, once the notion of precession came to be accepted, astrologers realised that they only had to add on a certain number of degrees, depending on the year, to convert tropically-computed tables to sidereal. Referring to Theon of Alexandria, who lived in the fourth century, van der Waerden explained his conversion procedure, adding : " Their successors ... living in the era of Diocletianus, still used the same rule, adapted to the new era. Obviously the purpose of the rule was, to reduce tropical longitudes " (taken eg from tables of Apollonius, Hipparchus or Ptolemy) to sidereal longitudes " 21 . Theon of Alexandria in his commentary on Ptolemy's Handy Tables in the fourth century recommended that certain longitudes be measured from the star Regulus 22 . Ptolemy introduced the Tropical reference system for measuring celestial longitude, at a time when the two systems were merely one degree apart. Was 18. Ibidem, 223. 19. 0. Neugebauer, op. cit., I, 278; Hipparchi in Arati et Eudoxi Phenomena Commentarium, Teubner, 1894, Ed. C. Manitius, 5-7, 48. 20. B.L. van der Waerden, Science, op. cit., 126. 21. B.L. van der Waerden, "History ... ", op. cit., 228. 22. 0. Neugebauer, A History .. ., op. cit., 1002; H.T.I. Halma, Commentaire de Theon d'Alexandrie sur le livre III de J' Almageste de Ptolemee, Paris, 1822.

ON THE MEASUREMENT OF CELESTIAL LONGITUDE IN ANTIQUITY

151

Ptolemy thereby reflecting an accepted practice ?23 This question was here investigated by using the collection Greek Horoscopes by Neugebauer and van Hoesen 24 . To avoid misunderstanding, this title did not mean that the horoscopes were made either by Greeks or in Greece, but solely that they were written in the Greek language. They are mainly from Egypt. A TEST

Twenty-one charts were located in this compendium which had planetary longitudes given in degrees (Table 2), one-fifth of the total, and the date of the chart reliably ascertained. These charts spanned the period from AD 40 to AD 497, almost five centuries. Time-of-day information was normally given for each chart, either the hour of day or the zodiac sign rising. It was decided to omit Mercury since, as van der Waerden points out, its longitude values were subject to large errors 25 . Excluding Mercury, at least four planetary (including Sun and Moon) longitudes were required. A couple of obviously mistaken positions were omitted; which was taken to mean, that their SZP differed from the mean of the others by more than twice the standard deviation of the group. The charts were mainly from around Alexandria, and to convert its local time to GMT, two hours were subtracted. GMT was then converted into the Ephemeris time required for the computation by adding on L1T 26 , which was about two hours for the era of Ptolemy 27 . This L1 T factor expresses the gradual slowing down of Earth's rotation due to tidal friction. (Ephemeris Time is a measure of time derived from the uniform motions of the planets, while GMT is defined by the rotational motion of the Earth). Thus there are two steps of time-transformation required, to tum the historically-given times into those used for the computation. Planetary longitudes in Greek Horoscopes were mostly given in degrees only, without arcminutes, in which case they sometimes gave the longitude as being thirty degrees, but never as zero degrees (Table 2). The first degree position (from zero to 59 arcminutes) was being designated as "one", up to their last degree within a single zodiac sign (from 29 degrees, zero arcminutes up to 59 arcminutes) which they called" thirty". Thus, our best estimate of their one 23. J. North, Fontana History of Astronomy and Cosmology, 1994, 67. 24. 0. Neugebauer, H.B. van Boesen, Greek Horoscopes 1959, American Philosophical Society, 1987. 25. B.L. van der Waerden, "History ... ", op. cit., 229; Ptolemy's Mercury theory generated regular errors of up to 6°, whereas for other planets his errors were only a degree or so. CJ. Owen Gingerich, The Eye of Heaven, New York, 1993, 67-68. 26. Explanatory Supplement to the Astronomical Ephemeris, London, 1992, p. K8-K9 gives b.T values from 1620 onwards ; Strictly speaking, Ephemeris Time (ET) became Terrestrial Dynamical Time (TDT) after 1984: The Astronomical Almanac, 1993, p. B4-B7. 27. P.R. Stephenson, "Long-Term fluctuations in the Earth's Rotation: 700 BC-AD 1990 ", Philosophical Transactions, Ser. A, 351 (1995), 165-202.

152

NICHOLAS KOLLERSTROM

degree is 0.5°, etc. Half a degree was therefore subtracted from each given degree-value where no arcminute values were given. Table 2 : Historical planetary longitudes The planetary longitude-values, 0-30°, as given in ancient horoscopes, with the modem-equivalent Julian year and date, in degrees (d) and minutes (m), plus given zodiac signs. Sun

a

Moon

m

a

Saturn

m

a

BABYLONIAN HOROSCOPES 234 June 3 12 30 l 6 199 June 4 15 ~ 10 198 Oct 31 3 -87 Jan 5 5 'l:J' -68 April 15 30 y 18 \/"! 15 GREEK HOROSCOPES 40 April 5 19 y 15 .i+ 120 46 Jan 3 11 30~ 11 y 30 75 July 19 29 30.!!0 12 27 76 Jan 24 5 8 ~ 1 -AA 81 March 31 14 6Y 13 'O' 5 110 March 15 25 81t 16 53 l[ '1 137 Dec 4 13 23 XI 3 6~ 3 260 Sept 29 8 ::!:::> 8 32~ 11 338 Dec 24 9 412 Feb 8 17 29 :Jr 24 440 Sept 29 5 Ba 8 4 Y:J • 25 463 Apr 25 3 'O' 23 V'l. 26 474 Oct 1 27 36l"fi\ 27 478 Aug 29 4 nn_ 11 9* 479 July 14 19 G 16 16 482 Mar 21 29 43* 6 ;!::! 25 483 July 8 18 !!:ii 10 AA" 11 484 July 18 23 ~ 7 11'\11 15 486 March 17 27 ~ 11 26 487 Sept 5 4~ 1 0 Y\'l\ 15 497 Oct 28 4 22 OVI 18 10 'd 24

*

°"'

'*

Jupiter

Mars d m

Venus m d

m

a m

5 l"W\_

18 X" 26 1)\)1 10 \/"i. 27Y 24 )("

24 !:o 10,,, 10 X" 20 J\.. 14 ~

13

]!

6 ~ 19 ~

5 15 14 30~ 19 7 231'111. 28

y

.==-

* ~ :0 8 '>('I

1 -AA 59-it 6 ~ 25-i( 25 18 X' 38 ~ 12 44 y 32 y 3 !YI\. 1 J(1 22-* 23 'O' 24 41 ()' Ti 23 B~r 17 IV)\ f:YI' .!!Q 16 30 tilt IYh. 26 1(1 V'(

v

*

Mercury

4 Y:J 5 JI 4 \/"I'.

H\-

~ 13~

*

22 12 16 3~ 16 4~ 21 1'" 8~ 30 OVi'. 9 54 x7' 8 16 Ill(. 14 6 \If 29 ('NI 29 50-. ·o.

"

•

"

0

f'.:: '

"

-;; Q,)

~ :'S