The Controversy on the Comets of 1618: Galileo Galilei, Horatio Grassi, Mario Guiducci, Johann Kepler [Reprint 2016 ed.] 9781512801453

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Galileo, Grassi, Guiducci and Kepler C O N T R O V E R S Y ON C O M E T S

THE CONTROVERSY ON THE COMETS OF 1618 Galileo Galilei Horatio Grassi Mario Guiducci Johann Kepler Translated by STILLMAN D R A K E A N D C. D. O'MALLEY

PHILADELPHIA

University of Pennsylvania Press

© i960 by the Trustees of the University of Pennsylvania Published in Great Britain, India, and Pakistan by the Oxford University Press London, Bombay, and Karachi Library of Congress Catalog Card Number: 59-10458

Printed in Great Britain at The Curwen Press, Plaistow

CONTENTS INTRODUCTION by Stillman Drake PAGE vii

HORATIO GRASSI On the Three Comets of the Year 1618

Translated from the Latin by C. D. O'Malley PAGE 3

MARIO G U I D U C C I Discourse on the Comets

Translatedfrom the Italian by Stillman Drake PAGE 21

HORATIO GRASSI The Astronomical Balance

Translatedfrom the Latin by C. D. O'Malley PAGE 67

MARIO G U I D U C C I Letter to Tarquinio Galluzzi

Translatedfrom the Italian by Stillman Drake PAGE

133

GALILEO GALILEI The Assayer

Translatedfrom the Italian by Stillman Drake PAGE

151

JOHANN K E P L E R Appendix to the Hyperaspistes Translated from the Latin by C. D. O'Malley PAGE 3 3 7

NOTES by Stillman Drake PAGE 3 5 9

INDEX PAGE 3 7 5

INTRODUCTION ι In the autumn of 1618, three comets appeared in rapid succession. The last was of unusual size and brilliance, remaining visible from November until January of the following year. These events inspired a large number of books and pamphlets, because comets were at that time generally regarded with superstitious dread, and because even among the learned it was still debated whether they were atmospheric or celestial phenomena. Among these many publications, there was one which was destined to arouse the aging Galileo to renewed activity after a decade of discreet silence. The controversy which ensued resulted in his publication of The Assayer ('II Saggiatore'), which has justly been called his scientific manifesto, and which is certainly one of the most celebrated polemic works in the history of physical science. The dispute over comets had consequences of great significance both to Galileo and to science in general, as the favorable reception of his book led him to proceed with the publication of the much more famous Dialogue,1 for which he was later imprisoned by the Inquisition. That fateful event was in turn intimately connected with the rift between Galileo and the Jesuits, which was widened and made permanent, if indeed it did not originate, in the public dispute about comets. Thus the controversy here presented in translation is closely linked with some of the most dramatic events associated with the dawn of our modern era. So far as its strictly scientific content is concerned, The Assayer ranks far below any of Galileo's other treatises on astronomy or physics. Except in Italy, where the book has always been esteemed for its literary merit, it has never been widely read. Yet certain problems which have come to the fore as a result of historical inquiries in recent decades make it singularly appropriate to invite attention now to this relatively neglected work. Apart from literary considerations or the matter of scientific content as such, The Assayer and its attendant polemics deserve study for their bearing upon the origin of modern scientific method. Though this is a field that is relevant to

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the work of scientists, historians of the sciences, philosophers, and cultural historians, it is not strictly the province of any of these; hence, it tends to be left by each to the others, and to be thoroughly examined by none. Yet it probably holds the key to an understanding of the extraordinary success of Galileo in winning converts to his' new sciences,' with profound consequences to the orientation of modern society. For a long time, it was presumed that these sciences were truly new, in the sense that Galileo had no veritable predecessors and that the prompt success of his ideas was accordingly almost selfexplanatory. It is now known that such is by no means the case; many of the results achieved (or borrowed) by Galileo in mechanics, for example, had been known and circulated not only in antiquity but again in the Middle Ages and the Renaissance. Similarly, in astronomy, the notion that the earth moved had been seriously put forth in ancient Greece, tentatively suggested again by philosophers of medieval times, and developed in detail by Copernicus, though prior to the time of Kepler and Galileo it had won few followers. Thus, if a scientific revolution took place about 1600—and hardly anyone questions the fact, though few still support the older view that it came unheralded—it can be explained satisfactorily only in terms of some novel element which intervened about that time. Such an element is found in the emergence of scientific method as a road to truth. The controversy which sprang from the comets of 1618 enables us to see in strong contrast the spirit of traditional philosophy and the spirit of modern science—the former with its emphasis upon authority, dogma, and verbal exegesis; the latter with its stress on observation, skepticism, and mathematical analysis. It enables us to see these engaged, perhaps for the first time, in a struggle whose captains on both sides were by no means mediocre or half-hearted champions of their respective causes, but first-rate scholars, well trained in every stratagem of disputation, and for compelling reasons determined to emerge victorious. On the one side was Horatio Grassi, professor of mathematics at the leading Jesuit college of Europe, a young man committed to the defense of the

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traditional philosophy by the rules of his powerful religious order, but shrewd enough to defend this not blindly but in a form so modified as to escape certain fatal objections created by recent improvements in astronomical observation. On the other side was Galileo, a sort of emeritus professor of mathematics, an elderly man who had become convinced that tradition of any kind merely stood in the way of the discovery of scientific truth, but was willing to content himself with showing its irrelevance in such matters without blindly attacking authority as the ill-fated Giordano Bruno2 had done not long before. The debate between these two men, truly representatives of large and influential groups among their contemporaries, is admirably suited to bring into focus for us an event of profound consequence to our cultural history, namely, the opening of a wide breach between philosophy and science. From the time of Aristotle to that of Galileo, an interval of nearly two thousand years, the study of philosophy had included physics as well as metaphysics. Both subjects were similarly treated. Since it is hardly possible to apply scientific method to metaphysical questions, the general result had been that questions of physics were treated metaphysically. The conclusions reached, however brilliant, remained philosophy, and without some violent wrench could never be transformed into what we think of as science. Admirable insights into physics had been attained by isolated thinkers of great genius in previous times; yet one may say that it was only in Galileo's day, and largely through his efforts, that a clear parting of physics and metaphysics was eventually reached. For a very long while thereafter, the rift between philosophy and science continued to widen, until within the memory of men now living it had become fashionable for physicists to speak scornfully of philosophy, and especially of metaphysics. Only in the present century, with the advent of general relativity theory and a series of queer transformations to which nearly every concept of classical physics has now been subjected, did this fashion begin to die out. Today, it is no longer easy to tell where physics ends and philosophy begins. In this regard, we stand now in much the same position as did Galileo's contemporaries, though at a rather different altitude. And precisely because the breach between science

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and philosophy is once more beginning to heal, we are in a better position than ever before to appreciate the magnitude of the cultural revolution that was ushered in by Galileo. II Considered in the light of Galileo's previous publications, The Assayer (and the Discourse of Guiducci in which, as will be seen, Galileo's dominant role is beyond question) is a very curious production. Since all of Galileo's previous books are mentioned in the opening paragraphs of The Assayer, it will be appropriate and convenient to review them briefly here, and in so doing to set the background against which he entered the controversy over comets. In 1606 Galileo, being then forty-two and having spent fourteen years as professor of mathematics at the University of Padua, published for the use of his pupils and friends a manual of instruction covering the use of a mathematical instrument that he had devised or perfected.3 This treatise was written in Italian with a view to making it useful to engineers and military men. It was promptly plagiarized in Latin by two enterprising scoundrels at the same university, Baldessar Capra and his tutor Simon Mayr. 4 As usual in such cases, the plagiarists accused Galileo in their book of having poached the invention from them. Inasmuch as Galileo had been manufacturing the instruments for nearly ten years and selling them to augment his miserly salary, it was not difficult for him to prove the falsity of this charge and to have the offending book suppressed and its nominal author (Capra) censured.® Three years later, Galileo commenced his telescopic observations of the heavens, and early in 1610 published his first results." Two of his principal discoveries—the mountainous character of the moon and the existence of four satellites of Jupiter—were hotly contested by several authors as false and impossible, if not contrary to Aristotle and the Bible.7 Galileo did not trouble to reply to such writers, being perfectly sure of his own claims and confident that others would be compelled by the facts to concede them. In the summer of 1610, Galileo resigned from the University of Padua and moved to Florence to enter the employ of the Grand

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Duke of Tuscany, with the additional honorary post of chief mathematician at the University of Pisa.8 In 1612, he published at Florence a Discourse on Floating Bodies,e in which he not only set forth a number of theorems and experiments in hydrostatics, but seriously questioned the then dominant Peripatetic philosophy and tentatively supported the atomism of Democritus, who of all philosophers was the most thoroughly rejected by the Aristotelians. This book was quickly attacked by at least four writers at Pisa and Florence, who seem to have been intent upon causing trouble for Galileo at the court where he was employed.10 Even before his book on floating bodies had emerged from the press, Galileo was engaged in composing some studies on sunspots which were published early in 1613. 11 In this book, he spoke out quite openly for the Copernican system, which he had supported in a previous book only by implication. Because the idea that the earth moved was generally considered to be contrary to the Bible and inimical to religion, Galileo soon found himself subjected to attacks and intrigues which he could not safely ignore. He was publicly denounced from the pulpit at Florence by a young Dominican firebrand, and one of his private writings was brought to the attention of the Inquisition at Rome. Knowing that he was not only placed in some personal peril by these machinations, but that the Church was considering an official prohibition of the work of Copernicus, Galileo journeyed to Rome late in 1615 with a view to setting matters straight. He succeeded in clearing his own name, but failed to prevent the prohibition of Copernicus. Accordingly, he was personally admonished by Cardinal Robert Bellarmine, who was acting under instructions from Pope Paul V, not to hold or defend the Copernican doctrines any longer. By this time, Galileo had completed a number of further works which he intended to publish, and had also projected an elaborate treatise on the system of the world. These projects he abandoned in the face of such determined opposition, and for a while he was content merely to discuss his researches with friends and to turn his attention to some non-controversial problems, among them the determination of longitudes at sea. Nevertheless, he felt a good deal

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o f resentment against the enemies w h o had managed to silence h i m , and doubtless was determined, if possible, to thwart them by one means or another. W h i l e at R o m e in 1616, he had written and p r e sented to Cardinal Alessandro O r s i n i " a paper offering an explanation of the ocean tides on the basis o f a double motion o f the earth. T h e explanation was not correct, but it was certainly ingenious and quite original. Early in 1618, it occurred to Galileo to send a c o p y of this paper to the Archduke Leopold o f Austria, brother-in-law o f the Grand D u k e o f T u s c a n y , with some deprecatory remarks to the effect that it was a mere fanciful speculation of his, written before the doctrine of the earth's motion was banned. It is probably significant that he accompanied this gift with a copy o f his Letters Sunspots;

on

those letters had been written in answer to the theories

held by a G e r m a n Jesuit who had been forbidden by his superior to publish them, but the resourceful Jesuit, Father

Christopher

Scheiner, 1 3 had nevertheless contrived to circulate his views by embodying them in a series of letters to a wealthy amateur o f science and friend o f the Jesuits, Mark Weiser. Weiser published the letters on Scheiner's behalf, concealing the author's identity under a pseudonym. Probably Galileo hoped to achieve a similar result w h e n he sent his paper on tidal theory to the friendly archduke. B u t if so, he failed; for all he received in reply was a courteous letter promising to study Galileo's theories when affairs of state permitted, and to master them if he could. 1 4 Scarcely two months later, Galileo received another letter, this time from Rome, which may have had a very important bearing upon events which were soon to follow. Virginio Cesarini, a brilliant young man of letters at whose house Galileo had held several debates and exhibited experiments during his campaign at R o m e to prevent the ban on Copernicus, wrote to tell him that, in the t w o years that had since elapsed, he had felt a great desire for knowledge, ' a n d with the guidance of your discourses I chose a better road to philosophy and knew a surer logic, whose syllogisms, founded either on physical experiments or mathematical demonstrations, open the intellect to a knowledge of truth no less than they close the mouths o f some most vain and pertinacious philosophers whose science is mere

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opinion, and what is worse, the opinion of another man and not their own'. 1 5 Cesarini proceeded to liken Galileo to an insect whose bite is not felt by the victim at the time it is received, but plagues him for a long time afterward. This letter reached Galileo in October, not long before the last of the three comets of 1618 made its appearance. During the weeks which followed, he was confined to bed by a painful illness 1 · and was unable to make any extensive observations of the comets himself. They became, however, the topic of frequent conversations with friends who met at his bedside. Meanwhile, Galileo began to receive from Rome and elsewhere (in particular, from Leopold of Austria) a number of requests for his written opinion on the phenomena. Now Galileo was not in the habit of giving out opinions on subjects concerning which he had no special knowledge, let alone on things he had not even observed. Still less was he disposed to publish such conjectures. Not only was he contemptuous of idle speculation and cautious by nature concerning scientific matters, but experience had made him sensitive to attack from certain quarters.17 It should also be remembered that at this time Galileo already enjoyed a world-wide reputation, and had nothing to gain by hazarding guesses on such matters. He had, moreover, remained on excellent terms with the Jesuits at Rome, and, in view of his somewhat delicate position with regard to the Church, it would seem most imprudent for him to quarrel with them in public. These are only a few of the puzzles which surround Galileo's intervention in the dispute over comets, puzzles which may perhaps be avoided by a hypothesis along the following lines. Galileo had reached certain conclusions about the nature and motions of the heavenly bodies which he was forbidden to defend any longer. He had reached those conclusions, however, by methods of investigation which were themselves under no ban. If those methods were made widely known, they might in time lead others to the same conclusions. For Galileo, a recent and evident example of the effectiveness of this approach had been the case of Cesarini, who was a man of letters and not a mathematician or philosopher. He had heard Galileo's discourses only accidentally, so to speak, and not

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because of any previous interest in the subject; yet, despite the fact that he had not been gready moved at the time, he had taken the trouble two years later to write Galileo and tell him that once bitten he had itched for knowledge ever since. T o accomplish the same effect on a broader scale, all Galileo needed was some pretext for writing on an astronomical topic—preferably some problem that had no direct connection with Copernicus or with the idea of the earth's motion. In the discussion of any such problem, his criticism of traditional notions and his own methods of searching for a scientifically satisfactory theory could be systematically set forth. The required conditions were fully met by the appearance of the comets. Not only that, but an unusually wide audience was assured, since comets were the center of attention everywhere; the eyes of men were riveted on the skies, and people were clamoring for the explanations of astronomers. Whether these were the precise thoughts that crossed Galileo's mind as he lay ill, and whether Cesarini's letter was responsible for them if they were, may be debatable. What is fairly certain, both from the content of Galileo's ensuing writings and from the difficulty of rationally accounting for them at all in any way substantially different from this, is that he designed them primarily to inculcate a certain skepticism and distrust of dogmatic authority, to encourage observation and mathematical analysis in preference to philosophical speculation, and to emphasize the vast extent of the unknown in comparison with the little that men had gained as certain knowledge. It is quite apparent that in these writings Galileo did not claim to set forth, as he had in his previous books, any new scientific discoveries or proofs. And though the absence of such content has caused The Assayer to be neglected by historians of astronomy, it does not mean that this work was inconsequential to the history of scientific thought. Ill The Collegio Romano, known today as the Pontifical Gregorian University, is (as it already was in Galileo's time) the heart and center of Jesuit scholarship. Founded by Ignatius Loyola in 1551, it was

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confirmed in 1583 by Pope Gregory XIII—almost simultaneously with the inauguration of the celebrated reform of the calendar which immortalized his name. The principal mathematician of the Collegio, Father Christopher Clavius (1537-1612), had carried out an important part of the work which led to that reform. From 1616 to 1624, and again from 1626 to 1628, the chair of mathematics at the Collegio was held by Father Horatio Grassi (1583-1654). Grassi was something more than an academic mathematician and philosopher. His architectural ability has its permanent record in the design of the Church of St. Ignatius associated with the Collegio, a monument of baroque architecture for which the cornerstone was laid in 1626. Another instance of his interest in practical affairs was his effort to design an unsinkable boat, a topic on which he corresponded with G. B. Baliani (1582-1666), an able physicist and friend of Galileo. It was Grassi who delivered, and published anonymously in 1619, an address which constitutes the first of the works to be translated here. His Disputation was on the whole a reasonably sensible discourse, and certainly contained nothing deliberately offensive to Galileo. Though Grassi did employ one argument which was based on a misconception of the workings of the telescope, this in itself would scarcely seem sufficient to have evoked Galileo's wrath, as such misconceptions were the rule rather than the exception at that time. It is also true that word reached Galileo from Rome to the effect that the Jesuits were making much over this pamphlet, declaring that its proofs of the celestial location of the comet constituted an utter refutation of Copernicus. But since Copernicus had never discussed the nature or location of comets, and since their celestial nature was generally considered by astronomers to be most damaging to the Peripatetic philosophy and to the solid spheres that had come to be associated with the Ptolemaic astronomy, these claims were rather ridiculous and deserved no answer, least of all a reply from Galileo. Yet it was this pamphlet, selected from scores which had appeared, that Galileo singled out for attention in his remarks. Probably to avoid a direct clash with the Jesuits at the Collegio,

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Galileo's reply appeared in the form of two lectures delivered by his young friend and disciple, Mario Guiducci (1585-1646), and subsequently published in the latter's name. Guiducci had studied first at the Collegio, and afterward at the University of Pisa where he took his degree in law. During this period, he was drawn into the circle of Galileo's friends, and abandoned his diplomatic aspirations to take up the study of science. At the time of the comet episode, he had recently been elected Consul of the Florentine Academy, and he utilized Galileo's opinions as the subject of his inaugural address there. T h e Discourse, second of the works to be translated here, was immediately recognized to be Galileo's own work, and, though for strategic reasons he continued to belittle his own part in it, there is no doubt that he was in fact its true author. T h e evidence for this has been summarized by Antonio Favaro as follows: In Volume X I of Part III of the Galilean manuscripts in the Florentine collection . . . we can distinguish three parts of the codex relating to the Discourse. The pages of the first part, containing a little more than the first quarter of the work, are written in Guiducci's hand but have corrections and additions in Galileo's handwriting. A second part, which includes another long section and constitutes the continuation of the first, is entirely in Galileo's writing. The third part comprises, in Guiducci's hand, another version of one part of that which is to be read in the second from Galileo's, but in this there are corrections by the latter. A careful examination of the manuscripts in their entirety leads definitely to the conclusion that so much of the codex as is read from the hand of Galileo must be his own work, and the additional material occurring in the cancellations, revisions, and marginal additions which are frequently written in those pages by his hand show that we have before us his first version. As to the other parts of the Discourse, taking into consideration that section which is preserved to us in two versions—one in Galileo's writing and the other in Guiducci's—and comparing the two versions with one another and with that definitive text which is represented by the printed version, it seems clear that Galileo's version is the first, and that between this and the printed version is the place for the version in Guiducci's handwriting. From this it follows that some pages of the Discourse which we possess written in the hand of the disciple were nonetheless composed by the master, from which it is legitimate to doubt whether we should not also take away from Guiducci even that part which is preserved only in a single version and in his writing; the more so as

INTRODUCTION xvii this, especially at the beginning, has the aspect of fair copy. So in the last analysis no doubt remains about its paternity, except for those many passages of which we lack any manuscript version. And even this doubt may be but a passing one, it being understood that in all probability even these parts are subject to the same inference that may be drawn for all the rest. In conclusion, therefore, we believe we may affirm with complete confidence that the major—and as to the doctrines set forth, the most important—portion of the Discourse came from the hand of Galileo; if Guiducci had any part in composing it, that must be limited to the initial pages. And it is possible that while Galileo was still convalescing from the serious illness mentioned above, the pupil commenced to write at the teacher's inspiration a work which the latter certainly completed later. In any case even those initial passages passed under Galileo's eyes, and were retouched and improved by his additions, so that the entire Discourse may be said to be essentially his work."

It has already been remarked that Grassi's pamphlet contained nothing offensive to Galileo; similarly it would appear to a modern observer that Galileo's reply through Guiducci's agency contained no severe or personal criticism of the Jesuit or his views. Its principal sarcasms were reserved for the Danish astronomer, Tycho Brahe, 19 whose views the author had undertaken to support, rather than for that author himself. On the whole, it is a calm appraisal of the various ancient theories and a critique of the unproved assumptions underlying the views expressed by the Jesuit. Nevertheless, the Jesuits took great offense at it, and Grassi lost no time in preparing and publishing a rebuttal, this time directing many personal reproaches against Galileo. For a time, Galileo could not believe that Grassi was really the author of this violent answer, which appeared as the Libra Astronomica and is the third work translated here. This book concealed its authorship under the pseudonym of Lothario Sarsi of Siguenza, a slightly defective anagram of Oratio Grassio Savonensi (for Grassi was of Savona and not Salona). But possibly Grassi was not the sole author of this book, or at least not its sole arbiter of tone and style. Well-informed friends of Galileo at Rome advised him at once that the Jesuits were much offended and were at work on a reply, 80 and later that others of the Collegio Romano were far more

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bitter against him than was Grassi himself, who forebore to threaten Galileo's destruction as did the others. 21 And if the Discourse had been temperate in its criticism of Grassi's theory, its opening section, nevertheless, included a very biting allusion to another Jesuit then far from the Collegio. This was Scheiner, who had called himself 'Apelles' in the sunspot letters mentioned previously. T h e Discourse derided those who would style themselves 'Apelles' and yet could not paint. When a copy of this book reached Scheiner in August of 1619, he declared that he would pay Galileo back in his own coin. 22 The astronomer who imparted this information to Galileo had informed him not long before that Scheiner was about to publish a book about the comet. 23 But no such book ever appeared, and it seems likely that Scheiner instead sent his material to Grassi or to others at the Collegio, perhaps with some suggestions concerning the tone of their answer to the Discourse and the inclusion in it of some specific accusations against Galileo. With the appearance of the Libra, the gauntlet was down, and Galileo's friends began to urge him not to let it pass in silence. Guiducci replied for himself in a published letter addressed to Father Tarquinio Galluzzi (1574-1649), his former professor of rhetoric at the Collegio. 21 Galileo began to annotate his copy of the Libra, but took his time about composing a reply. It eventually took the form of a letter to Virginio Cesarini, to whom a copy of the Discourse had been sent immediately upon its publication—facts which also tend to support the hypothesis that it was Cesarini's letter to Galileo that had originally influenced him to enter the dispute over comets in the manner in which he did. The Assay er seems to have been started early in 1621 but written chiefly during the summer and autumn of 1622. In October, the completed manuscript was sent to Rome, where it was read by Federico Cesi (1585-1630), leader of the Lincean Academy, by Cesarini, and by other members of that distinguished group. After they had made a number of suggestions concerning the style and tone of the work, the Academy authorized publication under its sponsorship. T h e task of seeing the book through the press was, however, not undertaken by the Linceans but assigned to an arrogant

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literary controversialist called Tomasso Stigliani. If he read the proofs at all, he did so very carelessly, while with incredible effrontery he inserted in Galileo's text a passage celebrating his own literary works. Only sixteen 'errors of importance which occurred in the printing' were listed by Stigliani on the last page of text, though in fact the number of such errors was enormous. When Galileo received the copies sent to him at Florence for distribution to his friends, he held them up while he had a two-page list of errata containing no less than 209 entries printed for insertion in them.*5 The printing of The Assayer had proceeded rather slowly, a fact which turned out to have important consequences. Just before it was completed, Pope Gregory XV (the successor of Paul V) died, and Cardinal Maffeo Barberini took the tiara under the name of Urban VIII. Barberini was a man of many intellectual interests, very well disposed toward Galileo, and a close friend of many of the Linceans at Rome. One of his first official acts was to appoint Cesarini to a high post at the Vatican. Appropriately, the Linceans decided to dedicate The Assayer to the new pope, and had the title page redesigned at the last minute to include his armorial bearings. The official censor under Gregory XV had already not only approved it, but had written into the imprimatur a handsome eulogy of Galileo. The book quite delighted the new pope, so much so that he had portions of it read to him at table. With all these auspicious beginnings, The Assayer quickly won wide acclaim and was generally accepted as a victorious conclusion to the controversy over comets. Greatly encouraged by the success of his venture, Galileo visited Rome the following year and was granted a number of audiences with Urban VIII. It appears that in this way he secured permission to proceed with his work on the system of the world, provided that he dealt with the Copernican system as a mere hypothesis. Guiducci had accompanied him to Rome, but fell ill while there and remained behind when Galileo returned to Florence, loaded with favors. During his illness, Guiducci was several times visited by Father Galluzzi, who urged him to grant Grassi's expressed wish to talk with him. After much hesitation, Guiducci finally consented. Grassi turned out to be friendly and courteous to the point of embarrassing

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him, and continued to show great respect in his attitude toward Galileo. Guiducci, favorably impressed, entered into a number of scientific discussions with Grassi. On one occasion, the Jesuit listened attentively to the tidal theory previously described, and went so far as to say that if a proof could be found linking the tides to a double motion of the earth, then it would be necessary to reinterpret certain passages in the Bible which speak of the stability of the earth.26 He also showed great interest in Guiducci's presentation of Galileo's experiments and deductions concerning the principle of inertia and the law of free fall. Thus Guiducci, who considered it possible that Grassi would himself eventually embrace Copernicus, began to hope that the young professor would devote himself to such studies and would abandon any further agitation of the question of comets. But before very long, Grassi informed him that a reply to The Assayer was in preparation and asked him if he would mind being named in it. He replied that it made no difference to him one way or the other, but this ended his cordial relations with the Jesuit, who excused his own action on the ground that he was 'forced' to reply to Galileo. The answer to The Assayer was published at Paris in 1626 with the curious title, Ratio Ponderum Librae et Simbellae, and once more the pseudonym of Sarsi was used, its author still pretending to be a pupil of Grassi. The title appears to mean Ά Reckoning of Weights for the Balance and the Small Scale'; the unusual word simbella (a scale used to weigh single coins) may be meant to carry a pun on cimbella (a challenge). The heavy wit with which Grassi thus attempted to deride Galileo's delicate assayer's balance is typical of that which pervades the entire book; thus the author pretends that saggiatore really meant' winetaster' (assaggiatore), and that the appearance of Galileo's book in the autumn months suggested that its author had been imbibing too freely of new wine.27 These sallies were a poor match for the rapier-thrusts which Galileo had dealt out to him in The Assayer, and, as the Ratio dealt mostly with minutiae of the dispute, it made little impression on the public. Galileo enriched his copy with some of the most pungent commentaries he ever penned, but forbore to publish any further refutation.

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In place of the Ratio, we have ended this series of translations with the comments of Johann Kepler, whose name had been drawn into the dispute by both Grassi and Galileo. Kepler's commentary was printed as an appendix to his book, Tychonis Brahei Dani Hyperaspistes ('The Shieldbearer to Tycho Brahe the Dane'). The book was published at Frankfort in 1625, as an answer to a violent attack against Tycho that had appeared in 1621, written by a Peripatetic astronomer named Scipio Chiaramonti (1565-1652). Even though Kepler had never adopted the system of Tycho, he resented unjust criticism of the work of his revered predecessor, with whom he had worked and whose precise observations had given him the key to the perfection of the Copernican system. Kepler's attention had been drawn to the references made to him by Galileo and Grassi just as the Hyperaspistes was about to be published, and he hastily added this candid and impartial critique which deserves attention not only for its relation to this controversy, but also because it contains some very remarkable insights and conjectures by Kepler that are not found in his earlier works concerning comets. IV It remains to set forth some astronomic and philosophic points that will be useful to the reader in assessing the merits of The Assayer. A comet is a cluster of very small particles separated from one another by distances that are enormous in comparison with their own si2e; comets may be likened to clouds of dust which move about the sun in roughly parabolic orbits. There are perhaps 100,000 comets associated with the solar system, making them its most numerous components. The ancients supposed them to be similar in nature to meteors. Though this is not true in the sense they intended, an association does exist between comets and meteors, for many of the belts in which the earth experiences large meteor showers have orbits practically identical with those of known comets. The head of a comet is called the coma, and may range in diameter from perhaps one thousand to five hundred thousand miles. The coma of a comet (unlike the tail) shrinks as it approaches the sun and expands as it moves away again. Generally, there is a bright spot within the coma,

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called the nucleus; there may be no nucleus or there may be several, just as there may be several tails or none. The tiny particles which compose the tail of a comet have diameters comparable in magnitude with the wavelengths of light; hence, they are easily driven by radiation pressure, which causes the tail to point away from the sun. The tail begins to appear when the comet approaches the sun, generally at a distance from it not exceeding that of the earth, and grows as the approach continues. Curvature of the tail is caused by composition of the two motions of these particles—away from the sun, and around the sun in the orbit of the comet. The curvature is most conspicuous when the earth happens to lie well outside the plane of that orbit. When a comet first appears, its light is spectroscopically identifiable as originating entirely from reflection of sunlight, but as it nears the sun its spectrum usually shows emitted as well as reflected light, especially in the region of the tail. The nature of this emitted light is still debated, though like the reflected light it must originate from solar energy. Most comets have very long periods of return to the sun, generally thousands of years, and remain invisible during those periods because of their great distance from us. Most comets, of course, are never visible to the naked eye. The motion of a comet is relatively slow when distant from the sun and rapid when close; for example, Halley's comet varies in speed from about half a mile per second to thirty miles per second. The tail of a comet may stretch out to prodigious lengths (as much as 200,000,000 miles in the case of one seen in 1843), and yet will contain at most a few hundred tons of matter. Nearly all comets are almost perfectly transparent both as to coma and as to tail. Of the foregoing facts, Galileo, Grassi, and Kepler had not the slightest knowledge. They were all guessing, and not one of them guessed altogether correctly. This is by no means astonishing, in view of the fact that very few reliable observations and descriptions of comets had been made at the time, and many of the more significant kinds of observations were not even possible. It is important to remember this, for it is often said that Galileo was wrong and Grassi

INTRODUCTION

xxiii

right on the facts of the dispute. This is an extreme oversimplification. Grassi was right in saying that comets displayed little or no parallax, nor was this ever denied by Galileo, who merely declared that this fact afforded no argument for the location of a comet until one could prove that the comet was a definite physical object whose apparent place did not change with changes in place of the observer. His opponents, of course, were far from being able to prove this; indeed, even after the telescope had been much improved, it was a long time before solutions were found to many of the problems presented by comets. Two generations later, the distinguished astronomer, G. D. Cassini, revived the hypothesis, similar to Galileo's, that comets were reflections in some kind of exhalation emanating from the stars.28 Newton himself offered an incorrect argument in refutation of such theories, for Newton mistakenly believed the bodies of comets to be solid and compact.29 Thus we should not condemn Galileo out of hand for suggesting that comets may be formed by the reflection of sunlight in thin vapors that became visible only after rising beyond the cone of the earth's shadow. Nor should we overlook the fact that if Grassi followed Tycho, he must have believed comets to be self-luminous bodies revolving in rather small circles about the sun. In fact, an enthusiastic supporter of Galileo might declare him to have been much closer to the truth than his opponent, considering that comets are indeed nothing but solar reflections in a kind of vapor; it might be argued that Galileo's only mistake lay in attributing to this vapor a terrestrial origin and a limited area of illumination. Certainly Galileo may be said to be nearer right in implying for comets a continually varying distance from the sun than was his adversary in defending the idea of their circular rotation about the sun. Compared with the views of his opponents, Galileo's thesis is by no means indefensible. It is only so in the light of modern knowledge, whereas at his time no one had a correct idea of the nature, motions, or positions of comets. The philosophy of Galileo as set forth in The Assayer is best characterized by saying that he presented an open system of scientific inquiry in opposition to the closed systems of the schools. His

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parable of the man in quest of the causes of sound illustrates this point. It teaches that scientific knowledge is infinite in scope, that the more one knows the more one learns how much remains to be discovered, and that a well-disciplined skepticism must always be maintained in such matters. But this skepticism is by no means classical skepticism as exemplified by Sextus Empiricus; for it does not include a denial of the existence of any criterion of truth. As their criteria, the traditional schools accepted agreement with authority and consistency within a fixed system of beliefs. Galileo adopted as his criterion a logical unity in the sense of mathematical description. In his hands, this is an esthetic rather than a metaphysical criterion; nature is to be regarded as a great book written in mathematical characters. Unlike the rationalist school which Descartes was soon to found, Galileo's philosophy avoided overt metaphysical assumptions of simple underlying principles. Unlike the empiricist school that was to take form at the hands of Hobbes and Locke, it gave no final authority to the evidence of the senses. Galileo ridiculed his opponent Grassi for believing that the sense of sight could not be deceived, and later he praised Copernicus for having risen above apparent sensory contradictions of his theory and for having put his faith in that overwhelming combination of observational data and mathematical reasoning beside which those contradictions were of trivial significance.30 Thus Galileo was no empiricist in the philosophical sense, even though he anticipated the development of philosophical empiricism when he distinguished primary from secondary qualities in The Assayer and suggested an atomistic theory of sensation. For the philosophical empiricists, logic has continued to present grave difficulties, and they have made many efforts to portray it as a by-product of sensory data. Galileo's view of logic, on the other hand, is peculiarly modern—true demonstration, he says, is to be found only in mathematical works and not in those on logic.31 Yet the Platonic dualism between mathematical and natural objects was rejected by Galileo; for him, the failure of the one to correspond precisely with the other existed only in the mistakes or the incompetence of the calculator.32 One might contend that Galileo's interjection of mathematical

INTRODUCTION

XXV

coherence into nature was a metaphysical assumption on his part; yet even this appears to be not true in any real sense. To Galileo, the universality of mathematical proportion was something discovered in the background when one approached nature by means of experiment; it existed only as a limit. This is markedly different from the attitude of Kepler, to whom a harmonious universal proportion was a metaphysical reality in which one might profitably seek hints about the world of phenomena. Galileo's revival of atomism is a good illustration of his antimetaphysical approach. Where Democritus did not escape endowing his atoms with the very properties they were designed to explain, such as sharpness or roughness, Galileo stripped them of all such qualities and required their motion alone to account for all sensation. The substitution of methodology for metaphysics is the key to the open system which Galileo offered as a rival to the closed systems of the ancient philosophers. It is a key that has not yet lost its usefulness in opening the doors of nature's mysteries.

The text of each work here translated, with the exception of the last, is that of Antonio Favaro's edition of Galileo's works.83 Paginations from the original editions have been indicated, and in a few instances readings have been altered to conform to those editions. For the final work, Frisch's edition of Kepler's works was employed.34 The original edition of The Assayer contains the entire text of the Libra, divided into sections and answered part by part. Here, we have followed the method employed by Favaro, separating the texts and providing cross references. An abridged text of The Assayer was previously published by Doubleday & Co., 36 to whom grateful acknowledgment is rendered for permission to reuse this material.

Galileo, Grassi, Guiducci and Kepler C O N T R O V E R S Y ON C O M E T S

On the Three Comets of the Year MDCXVIII

An Astronomical Disputation Presented Publicly in the COLLEGIO

ROMANO

of the Society of Jesus by ONE OF THE FATHERS OF THAT SAME SOCIETY • ·

R

O

M

E

Jacobus zMascardus,

MDCXIX

With the Permission of the Superiors

ON THE APPEARANCE OF THE COMET

Have you seen the fleering comet with its terrifying tail ? Behold how with its fearsome beard it is carried sky-high. But no longer need you fear that stellar body with its menacing rays, nor is there harm in those stars which delight us by their appearance. Tell me, does this phantom glitter as a better and more favorable omen and does its false light surpass that true fire of the stars?

OF T H E SAME

The vain comet which by its light has disturbed the earth and the heavens begins its harmless journey. With that light bestowed upon it by the creator it shrewdly propitiates the adverse celestial torches by its equal fire. May this comet which alters the heavens with its ready advantage teach me the nature of the stars.

A N ASTRONOMICAL D I S P U T A T I O N ON THE T H R E E COMETS OF THE YEAR 1618 PROLOGUE The human mind, Most Illustrious Ones, is so desirous of novelties that occasionally it grows weary of the long continuance of things which are good and desires to improve upon the situation by the alternation of something which is bad. Thus in song and music, we are less partial to those measures which are accompanied by a constant and unwavering consonance of voices, and music is much more pleasing if it has been composed of dissonant and consonant voices and if by reason of conflicting tones the concord and force of the voices have been weakened and, as it were, broken. Therefore, since for many years the sun and other sidereal lights have travelled in the sky as beacons of good fortune, and since no calamitous fire has gleamed with mournful brightness, no pestilential firebrand has unfolded a comet's tail, and no comet has put forth a beard, we have bewailed the completely empty and unfruitful sky, ill-suited to newborn fires; we have reproached our age as too miserly in fleeting lights, and we have desired—Ο the impatient desires of men—that some portents of this sort should arise which, at least by their novelty, would delight and gratify our eyes now weary of more benign lights. But what of the present ? No longer, like those earlier generations, are we bleary-eyed from continual watching of the stars1 since we know that they are very far removed, and now no part of the sky escapes our glance, {p. 4) nor is the beauty of the moon so great as it was for us formerly. We have been able to distinguish the circular motions of Venus and Mercury, and who does not blush that we see the sun occasionally disfigured ? We have laid bare the stratagems of Mars in approaching the earth, and we have exposed the attendants of Jupiter and Saturn, hitherto hidden away to no purpose.

6

C O N T R O V E R S Y ON COMETS

Thus, only comets have remained aloof from these lynx eyes,2 ifor it was to be hoped that that former contention regarding the place of the comet might now easily be settled. Therefore, it is well that you consider this among the good things which must be counted: last year there occurred fires of a kind prodigious beyond all de:sire, which in the space of not more than three months exposed! for leisurely observation three fiery lights drawing long trains. But, good God, how hard it was to turn our eyes toward these portents. The month of August was already ending when at the hind feet of the Great Bear the first torch was kindled, and then it blazed for the blind since scarcely anyone raised to the sky those eyes which had now for so long been averted from it. Perhaps that torch was too high and small to arouse men bowed down to the earth, and a fire had to be kindled for them in a lower place, one more ample in nnass so that it might easily assail even the unwilling. Nor was this lacking, for now in indulgent November we, although exceedingly few of us, observed a long beam in the form of a sword unfolding itself toward the spirals of the Hydra, for rather whitish, loose-textured, and of no considerable brightness it did not excite many observers. Therefore, sky, you accomplish nothing when you are so miserly of glitter and brightness. Unless I am mistaken, the sky realized this, and finally on the twenty-ninth of November it carried a very bright comet upward from the east, of such brightness that all eyes and minds were immediately turned toward it, and great throngs gathered on mountains and other very high places, with no thought for sleep and no fear of the cold north wind. Suddenly, men had no greater concern than that of observing the sky; if Venus chanced to shine more brightly than usual, it was changed into a comet; if at sunset a cloud did not immediately disappear but formed a cross, it was considered as a monstrous thing. But these were the views of the mass of the people, of less weight than a feather, and in this present gathering of wise men I must consider matters differently. Therefore, mindful that I am supporting the single role of mathematician, on this day I propose to consider those things which do not exceed the bounds of our knowledge, limited solely to that which has been proposed.

ON T H E T H R E E C O M E T S OF T H E Y E A R

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{p. 5) Hence if I explain the position, motion, and magnitude of those fires, I shall be satisfied that I have fulfilled my purpose, for I do not approach you today as the sinister crow or the evil screech owl, the precursor of evils from these comets, forewarning of pestilences, famines, and the wars which they assist. PROBLEM TO I N V E S T I G A T E THE NEARLY TRUE DISTANCE OF T H E C O M E T F R O M T H E E A R T H In order that I may approach the matter more clearly, I shall first give an account of what has occurred, and after I have presented briefly the times and motions of each comet I shall reveal the region of the sky where it shone. In the month of August, news was brought to us from many parts of Italy that during that period a comet was seen licking the hind feet of the Great Bear. But we, knowing that the ignorant mass of the people had considered Venus as a comet, suspected the same on this occasion and considered that those vigilant watchers had been readily deceived. However, advised again and again of the same thing and informed of the comet's motion, finally, although tardily, we desired to make certain; but now it had vanished. Meanwhile, rumor, although as yet unfounded, crept in from other places that a comet had shone, and, when not even this gained any belief from us, we next received letters from our establishments in Germany in which it was stated that the same fire had been seen there at the same time. When the Italian and German observations had been compared, it was discovered that on the twenty-ninth day of August the comet had been between two stars—numbers 22 and 39—of the Grtat Bear, and by its [swift] motion it had reached the forelegs in the space of four days, so that on the second of September it was observed under the exterior stars numbered 33 and 34, and there it finally vanished after having completed a journey of about 12 0 . And what wonder if no fire was able to be of longer duration among the frozen Septentriones ? In magnitude, it was equal to the stature 1

8

C O N T R O V E R S Y ON C O M E T S

of a man; its tail, according to the testimony of all, verged southward whither the brilliance of the sun clearly directed it. {p. 6) All these things which have been described could be observed in the constellation of the Bear. On the eighteenth day of November, to the southeast there emerged a second new fire of that sword-shaped type called xiphuae.% This comet was of a very slight brilliance but of such great magnitude that it formed a visual angle of about 40°. It also was carried from east to west by the motion of the prtmum mobile,4 and as well was carried in that direction by its own motion so that as a resultt in its daily course it outstripped the fixed stars. On that day on which we first saw the comet, it approached close to the stars of the Crater, and on the day after the twenty-ninth of November it was a litttle distance away so that with its point it transfixed the very heart of the Hydra, and although the lower part of it had first touched the shoulder of the Centaur it was then seen under the triangle of the Hydra. Thus its motion had carried it through nearly 24° in the space of eleven days. However, these fires, doubtless from lack of size and lack of brilliance, did not greatly kindle men's minds, frozen at that time by the north wind, and the fires were not considered worthy of very acute observation. Therefore, we shall not have to delay any longer in the examination of these [first two] comets. I hasten on to the third which as it surpassed the others in magnitude of light and daily continuance, so it was outstanding as long as it remained by reason of its course and life, and it drew to itself the eyes of all; as it was but recently extinguished, I seek from you as its mere due this solemn observation of its obsequy and from myself this eulogy of its life. Since I believe that in this duty I ought not deviate from the masters of eloquence, in accordance with their practice, taking the first argument of my discourse from the comet's birth, I have sought its native land and parentage, and I have opened a pathway for myself through the illustrious circle of its subsequently very famous life to the far from obscure character of its death. Moreover, so that among the celestial regions we may know the native region of our comet, something must first be established

ON THE THREE COMETS OF THE YEAR l 6 l 8

9

regarding its natal day, for it is said that it was not first observed by all a t the same time. There are those who assert that it first began to shime on the fourteenth day of November, and there are not lacking those who assert that the first day of its life was the twenty-sixth; finally there are many—indeed, nearly all—who declare that it was not seen before the twenty-ninth. I believe that those who maintain that this Ught came into being on the fourteenth day were readily deceived by the appearance of the other, preceding beam,® especially since they make no mention of such a beam or of any other, earlier irruption; {p. 7 ) thus they believed that the [previous] beam and this comet were the same fire, for almost at the same time that the one began to be seen the other disappeared. Furthermore, this comet in its daily motion ran through almost 3 0 , and thus if it were seen on the twenty-ninth of November under the northern scale of the Balance, on the fourteenth day it ought to have been seen in the neck of the Wolf, which part of the sky came up almost two hours after sunrise. Although it would not have been easily observable in the sun's great brilliance, neither we nor other observers of the stars were so blind that we would not have recognized a very bright torch even though shining in the midst of the sun's light, and especially at that time when we were examining all the sky very intently and measuring the course of the beam. T h e authority of one, or at most of a few, is easily overthrown by the number of others who support our opinion, for scarcely was there anyone in Rome who had observed it before the twenty-ninth, and our colleagues in Milan and in Parma assert the same while this is also reported from Innsbruck in Germany and from France and Belgium. Y e t I believe that by no means ought those be rashly dismissed who have asserted that they saw the comet on the twenty-sixth. According to that reckoning and taking into consideration the motion of the comet, it began in the ecliptic precisely in that place where a little before, that is, on the fourth day of the same month, the sun and Mercury, turning according to the long courses of their routes, lodged together in Scorpio; for it was proper that a very elegant and splendid feast be prepared for such guests and, as well, that a very bright torch be kindled.

10

CONTROVERSY ON COMETS

But, finally, whatever of these dates saw the first light of the comnet, it is Scorpio which was its true native land. On the twenty-sixth dday, it reached the ecliptic nearly 14J0 inside Scorpio, and on the twenntyninth this new foetus was established in Scorpio at a longitude e of about 1 b e t w e e n the two scales of the Balance with a northeErly latitude of almost 7 0 . If anyone now asks me about the parents of the comet, althouugh this is the duty not of the astronomer, whose character I am s u s taining, but that of the astrologer, yet I, a man by no means skilllled in the physiognomic art, may conjecture in so far as possible frcom the appearance and color of the foetus, and I would call it the ooffspring of Mercury. For thus it bore the eyes, limbs, and couuntenance; that is, although when the comet was very near to the suun, this golden Lucifer® almost outshone it, yet when it receded far frcom the sun it at once grew pale and astonishingly changeable aand manifested Mercury in its countenance. Many say that in tthe beginning they recognized in it the color of Mars since it was bornn in ( p . 8) Scorpio, that is, in the principal house of Mars; but an honorable exchange had occurred between Mercury and Mars aand the one then inhabited the house of the other, that is, Mercury w a s in Scorpio and Mars in Virgo. But here I exaggerate. Let astrologers consider these things mcore carefully and as good midwives receive the foetus. They will coonsider the delineation of its countenance very attentively and,, as prophetic Protei, predict for it the various vicissitudes of life aind foretell the final day of its light. I, insofar as I am able, have sougght its native land which, in agreement with all, I declare to have beeen Scorpio. Although, according to the view of astronomers, tlhis region, like all others, extends from the middle of the earth to tthe firmament, and although the comet first looked upon the light of tthe sun spread through it, yet in addition it may be inquired whetther the comet was produced in the lowest or the highest part of tlhis house. T o speak plainly, what is particularly sought at this time; is whether fires of this sort occur in the atmosphere or whetherr a material and a place are to be assigned to them among the enduriing flames. In this regard, I first present to you the following: ir

ON T H E T H R E E C O M E T S OF T H E Y E A R

l6l8

II

anything which has been established between the firmament and the earth is observed from different places, it will correspond to different parts of the same firmament. Let the globe of the earth in the diagram of parallax be Q A C , the firmament H N P , and the object—whatever it may be—be placed between these two at T , equidistant between two cities A and Q_on the surface of the earth. I declare that if the object Τ is observed from these two cities, it will not be seen at the same point of the firmament. For the visual ray from A extending to the object Τ is carried in a straight course into P; but the ray proceeding from Q_ through the same object Τ will terminate at M. Therefore, let there be some star in the firmament, for example N ; to those looking from Q_, the object Τ will seem to be distant from the same star Ν by the whole space of M N ; but to those looking from A, the same object Τ will seem to be distant from Ν by the whole interval P N ; but these intervals or distances differ from one another by the whole arc M P . This, then, is called the parallactic difference or difference of aspect. Moreover, this is diminished in proportion to the greater remoteness of the object seen from the earth. For if the same object is placed at S, the visual rays proceeding to it from A and Q_, and extended further, will lead into L and O; and to an observer at A the apparent distance from the star Ν will be the arc O N , but to one gazing from Q_, the arc L N ; their difference will be the arc L O , much smaller than the above, for the former {p. 9) difference was the arc M P . If, finally, the thing seen is in the firmament itself, or not very distant from it, there will be no difference of aspect, for, from whatever place the star Κ fixed in the firmament is seen, it will always appear at K , and its distance from the star Ν will constantly be the arc K N . Hence, it is clearly deduced that if the comet was observed from different places and compared with the stars of the firmament, and if it preserved the same distance from them, it must be regarded as either in the firmament or certainly not far removed from it. But if it underwent parallax, it must be placed below the firmament in proportion to the amount of the difference of aspect.

12

C O N T R O V E R S Y ON C O M E T S

Now that these things have been set forth, I affirm first that this comet ought by no means to be placed in the uppermost region of the atmosphere, even though that same region may be considered to rise a distance of 100 miles from the surface of the earth, although commonly only 60 miles are attributed to it. For assuming this distance, the very smallest parallax that can occur between observations from Rome and from Antwerp, for example, will be an arc greater than 56°. If on a terrestrial globe Q A C , Antwerp is at A, Rome at C, and the distance between is i2°48', that is 800 of our miles—reckoning, according to Ptolemy, 3579 xex miles as the radius of the earth—and since in an isosceles triangle A B C , the angle Β is understood to be i2°48', and the remaining two will be understood as equal—each as 83°36', the side A C will also be known to be 798 miles. Now, since the smallest parallax in observations from different places first occurs when the thing seen emerges from the horizon, therefore let the visual ray of one observing directly from A, be A E , perpendicular to A B and hence parallel to the horizon; and let Ε be the point of the uppermost region of the air in which the object seen will be placed. Therefore, after the rays A E and C E intersect at E, they extend to the different points Η and I, and the angle I E H will be that of the difference in aspect whose size will be found in this way. Let B A be drawn out to D, and let A D , the distance from the uppermost region to the earth, be 100 miles; then the whole of B D will be composed of one terrestrial radius plus this distance, or 3679 miles. Disregarding the fraction, let this represent the 100,000 parts of the whole sine; A D will be the versed sine of the angle B E D and A Ε the ordinary sine of the same. Therefore, if it is said that 3679 is to the whole sine 100,000 as 100 is to {p. 10) the desired fourth number, it will be found that the versed sine A D equals 2718 parts in the 100,000 parts of the whole sine; from this, by the laws of sines, A Ε will be found to be 23,416 parts. Now if A D as a versed sine is 2718 while A D as a straight line is 100 miles, then the ordinary sine A Ε being 23,416, the straight line A E becomes 851 miles. This granted, then since in the triangle Ε A C the two sides A Ε and A C are known, as well as the angle Ε A C of 6°24' contained by these sides, inasmuch

ON T H E T H R E E C O M E T S OF T H E Y E A R

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13

as it is the complement of the angle C A B of 83°36', the angle C E A may also be known; this is found to be 56°56', and this will be the smallest parallax which can occur between the observations from two given cities [if the comet is 100 miles above the surface of the earth]. The maximum parallax will be i45°50', which occurs when the visual rays intersect each other in the object seen, as for example at T , an isosceles triangle above the base A C . If the distance between places is the same AQ_, and T R is the vertical distance from the earth to the highest region of the air, the visual rays Q T M and A T P will form the angle M T P or ATC^—for these are equal since they are vertical angles—and one skilled in the measurement of triangles will find this to be I45°56'. But upon comparison of our observations with those made at Antwerp, the difference in aspect is found scarcely ever to exceed 1°. Therefore, this phenomenon was not in the highest region of the atmosphere, which is what had to be proved. Second, it seems that it ought not be said even that this same comet was sublunar. T o demonstrate this, I assume the containing sublunar concavity7 to be distant 34 terrestrial radii from the centre of the earth, a little more than Ptolemy assigned, and hence the distance from the terrestrial surface is 1 1 8 , 1 2 5 miles. Therefore, if in the triangle A F C the straight line C F is considered to be this distance of the lunar concavity, since the side denoted C A is 798 miles and the angle F A C is 6°24', the angle C F A will be found to be 3', the smallest lunar parallax, while the maximum of 24' will be found in the triangle ASQ_. But if you compare our observations with those made at Antwerp, sometimes that difference will be greater than 24', sometimes smaller; indeed, on the fifth of December it appeared to be less, that is 16', but in the remaining observations more. Likewise, if one compares them with those made at Parma, a distance which allows of a parallax of about 7', sometimes none will be found there, sometimes more. (p. 1 1 ) For let the comet be observed from both places on the second day of December; there will be no discrepancy between the observations and therefore no parallax; but if the observations of the third day were to be considered, they would give a greater difference of more than 10'.

14

C O N T R O V E R S Y ON C O M E T S

Third, in comparison with the observations made at Innsbruck on the thirteenth day of December, in those the distance of the comet will be found to have been io°53' from Arcturus, while in our observations the same distance was ι o°55'; therefore the difference is only 2', but the distance between Innsbruck and Rome is capable of yet greater parallax, even if the comet were to be placed in the lunar concavity. However, in order that observations of this sort may be made very exactly, instruments are required of such monstrous proportion that not only the degrees but also one minute of a degree may be registered in very large size on them, such as those Tycho Brahe 8 constructed at royal expense. Hence, it necessarily follows that the minute has been less accurately reckoned in these observations of ours since we did not use very large instruments, and this is the particular reason why we have not employed more care in their comparison. I know that the reckoning of these things by which observations of this sort were made in those different places, although on the same day, had to be considered; and, furthermore, the investigation of refractions and other matters required much more careful observations. Therefore, if they seem suspect to anyone, allow me to present one thing in regard to this matter which is not affected by the incapacity of the instruments. At Rome, on the thirteenth day of December, the comet almost concealed the tenth star of Bootes. We hoped that this same phenomenon had been observed elsewhere, for, if at the same time from other regions the same star was also observed very near to the comet, no stronger and clearer argument could be hoped for by which it might be demonstrated that the comet had very little or no parallax, since this could be observed without any instrument and by observation with the unaided eye. It fell out as we hoped, for in the following days the observations of a certain person in Cologne reached us, in which we noticed among other things that on the same day the tenth star of Bootes had been partly hidden behind the comet. Therefore you have it from parallax, however observed, that our comet was not sublunar but clearly celestial. If, nevertheless, anyone feels that little trust ought to be placed in this, and believes that it is less certainly demonstrated, surely he

ON THE THREE COMETS

OF T H E Y E A R

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15

cannot deny the following: since no difference in degrees is found, {p. 12) but only in minutes, then, even if we were to concede that the comet was sublunar, it must be considered to be not very remote from the moon; but in the following way I shall demonstrate that it could not have been sublunar. The distance of the moon from the centre of the earth is 121,704 miles; therefore, this would be the radius of the region of the comet, and then a circle having been described with this radius, it will be found by geometrical rules to be 764,966^ miles in circumference. Since on the twelfth day of December, the comet with its tail claimed 6o° of this circle for itself, corresponding to 127,499 £ miles in the same circle, therefore it must, indeed, be considered of very great length. Since its smallest observed width was 2', that is, 70 f miles, if this is assumed as the diameter of one circle, the area of that same circle will be found to be 2850 square miles; if this area is taken as the base of the cylinder, whose length is equal to the length of the comet, multiplication will produce 490,871,150 cubic miles as the entire volume of that comet. Now if the comet was sublunar, it ought to have been fueled by exhalations from the earth, 9 but, good God, how great an amount of fuel would be consumed by such an immense fire over so long a time. Therefore, it could not be located under the moon. Among other things, the fact that its tail almost always verged toward that direction in which a line may be extended from the sun through the body of the comet persuades me that this body was not fiery and bright by its own light. 10 For when the sun was situated at 7°22' of Sagittarius, the tail was carried to star 15 of Virgo; but when the sun reached 17 0 , the tail was directed to the exterior star numbered 29 of the Great Bear. This also occurred in the first comet of the month of August, which, when the sun was in Virgo, constantly turned its tail to the opposite direction. All those things indicate sufficiently that the body of the comet did not shine by its own light but by that of the sun; and the solar rays, either refracted or reflected, proceeded farther on and formed the tail, for the same reason perhaps, as Kepler 1 1 would have it, by which the rays of the sun falling on a crystalline globe and then being refracted in another direction are collected and shine more brightly.

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A second argument proving the same thing is taken from the motion of the comet. For fiery irruptions have no regular and definite motion, but are carried wherever fuel draws them or {p. 13) wherever they are impelled by the motions of that which is moving about. The motion of our comet was always constant and not unlike the motion of the planets, for, as has been found by many observations, it was moved northward to star 30 of Draco, completing almost 3° each day, although in the final days it moved more slowly; by this motion it very constandy described part of a great circle on the sphere, 12 obviously just as the sun by its motion describes the ecliptic, and the moon and the rest of the planets other great circles contained under the zodiac. And I do not see whence could come such constancy in the elemental region, so that always following a middle and splendid pathway, it was never deflected in any direction and, constantly holding to its purpose, was never deflected from the route which it had taken. Thus I demonstrate that the path of the comet described part of a great circle. That part of the sky which this new fire ran through is described on a plane in that way in which sundials are usually marked. For if some surface A B is conceived of as touching a sidereal globe at C, with the eye placed at the centre of the globe D, the visual rays led through each star on the globe to the plane will mark on it the points at which the same stars ought to be noted. You have a figure of this sort placed before your eyes in which there is a straight meridian line of the same plane I H ; I is the pole of the world, Ν the star Arcturus, the point at which a stylus ought to be placed and of which the length is OP; the straight line cutting the meridian at right angles near star 23 of Virgo represents the equator, and the curved line C N D , the tropic of Cancer. 13 Therefore, let the positions of the comet be found on this same figure, corresponding to the single days of observations; experiment will show that a straight line drawn from the point of the initial to the point of the final observation runs also through the points of the remainder; therefore, positions of this sort are established along one straight line. Moreover, our Clavius 14 demonstrates in the first book of his Gnomonics, in propositions 1 1 and 12, that great circles are represented by straight

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lines and lesser circles by curved lines. Thus you see that on sundials and on our figure the meridian, equator, colures, and all other great circles are represented by straight lines, but the tropics, the polar circles, and other lesser circles are represented by the curved lines C N D and L B G . Therefore, as had to be proved, the motion of the comet was along a great circle, and very much resembled the motion of the planets, {p. 14) Now what is that which the poets have said, that by their motion and pace the usual gods are recognized, so that he who moved in the manner of the gods was considered as a god ? Thus, according to Virgil, Aeneas recognized his mother as Venus. 16 Hence does not this light by its venerable and august pace also reveal a goddess ? that is, not arisen from the dross of this earth into the air but granted a seat among the celestial lights, where in a manner certainly not unworthy of the sky it shone with brief and transitory brilliance— yet so long as it lived in nowise did it display itself unworthy of the sky from which it imbibed its celestial quality. In the third place, I am convinced of the same thing by the fact that when the comet was observed through a telescope, it suffered scarcely any enlargement. Nevertheless, it has been discovered by long experience and proved by optical reasons that all things observed with this instrument seem larger than they appear to the naked eye; yet according to the law that the enlargment appears less and less the farther away they are removed from the eye, it results that fixed stars, the most remote of all from us, receive no perceptible magnification from the telescope. Therefore, since the comet appeared to be enlarged very little, it will have to be said that it is more remote from us than the moon, since when this has been observed through the telescope it appears much larger. I know that this argument is of little significance to some, but perhaps they have given little consideration to the principles of optics which, it must be understood, play a very important part in what we are considering. Thus in order that we may now determine almost the true place of the comet, let us say that it can probably be placed between the sun and the moon. Since for those lights which are excited by particular motions there is an established law according to which the

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more slowly they move the higher they are, and since the motion of our comet was midway between that of the sun and of the moon, it will have to be placed between the two of them. If, therefore, the distance from the centre of the earth is established at 572,728 miles, the circumference for this radius will be fixed at 3,600,0047 miles; and 6o° in that same circle occupy 600,00 miles; using the twelfth day of December for comparison, such will be the length of this comet. The width of 2' occupies 333 miles; if these things are accepted for the diameter of the circle, the area of this circle will be 87,127 miles, and this multiplied by the 600,000 miles of the comet's length, the whole of its bulk becomes {p. 15) 52,276,200,000 cubic miles. The volume of the body alone, with the tail discarded, will be found to be about 19,361,555 cubic miles—in these calculations fractions are usually discarded. Finally, one thing which has tormented some persons for a long time remains to be solved. Since the comet had then been very near to the arctic circle, it ought during the whole night never to have been seen to sink; nevertheless, it was observed that it did not come into sight until after the middle of the night. I believe this occurred because at that time it would have been of very slight brilliance and easily concealed by vapors, denser around the horizon and especially in the northern parts; for we noticed that the same thing happened at that time not only to the comet but also to the stars located in the tail of the Great Bear; indeed, these lie hidden as if extinct among very dense vapors on the nearest horizon, and then they are seen little by little to be lighted again upon emerging from those vapors. Thus you have my beliefs regarding the motion, place, and size of the comet. POSTSCRIPT I have believed that the comet, shining on all directly from the same place and appearing the same from all sides, must be considered as worthy of the heavens and very near to the stars. I hope, most distinguished gentlemen, that I, now enjoying your singular kindness, have demonstrated my efforts to your satisfaction today and that all

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of you will consider the motives of my reasoning to have been directed from that same lofty place, and that I have presented to all of you a satisfactory defense of comets. If I have done this, I remain without envy of the comet, and I rejoice in its good fortune. With my head exalted I shall touch the stars.1'

DISCOURSE on the COMETS BY

MARIO GUIDUCCI Delivered at the FLORENTINE ACADEMY

During his Term as Consul • ·

FLORENCE cMDCXIX

To

THE

MOST

ARCHDUKE

SERENE OF

LEOPOLD

AUSTRIA

I have made bold to dedicate to your Serene Highness this short discourse of mine on comets, heartened by the knowledge that when you rest from affairs of state you reserve no mean place for literature, and in particular for speculation upon celestial matters, that subject above all others being suited to the loftiness of your mind, greater even than that empire through which your august house exercises dominion over such a large part of the earth. I have been further encouraged by the signs of high regard which you deigned in passing through Florence to exhibit toward Sig. Galileo Galilei, his Supreme Highness' chief mathematician and philosopher. T h e main foundation of this essay of mine being his opinions concerning comets, I have not hesitated to appear before you with this little offering concerning a matter in which such an important role has been played by that sovereign intellect so highly esteemed by yourself. And finally, my action has been determined above all by your desire (as shown in your gracious letters to Galileo) to learn his opinion upon this matter. For all these reasons, I have hoped from your beneficence not merely gratitude but protection. Therefore, I beseech your Highness to favor my hopes and to recognize in me that devotion which everyone owes to your heroic power; most particularly we who glory in being subjects and vassals of the Most Serene Archduchess, Grand Duchess of Tuscany, your Highness' worthy sister who, like a bearing tree transplanted into this land of ours, has so happily produced those fruits in whom, young though they are, the high qualities of the royal Austrian line may be recognized. May the Giver of all good continue to prosper that line, together with your Most Serene Highness, for the special benefit of Christianity. This I pray with all my heart, which does the most humble reverence to your Highness. From Florence the eighth day of June 1 6 1 9 Your Most Serene Highness' most humble and devoted servant MARIO GUIDUCCI

DISCOURSE ON THE COMET Learned Academicians, however great the extent to which the marvelous structure of this universal framework lies exposed to the eyes of everyone who wishes to contemplate it—nor has any of us withheld his gaze from so admirable a spectacle—nevertheless there is one part of it more venerable than all others, and to this not all persons are admitted, but only those who can penetrate within it; and such men are exalted to a sublime dignity. That excellent place is the seat of government for all this beautifully contrived expanse, and its contemplation is only for the philosophically initiated. Nor can even they fix their view upon every part of it, much as they wish to; the splendor diffused thence on all sides is so great, {p. 2) and the obscurity which fills it is so profound, that the mind becomes confused and loses much or all of its power. Since freedom to extract any jewel of price from so rich a treasury is thus limited, those who have acquired such a prize should be held in high esteem as fortunate men and wealthy patrons. Likewise, they should be pardoned if the brevity of the time they have been permitted to remain in such a place has prevented them from singling out the better things from the poorer, and if sometimes, in place of the cause of some effect which we have requested from them, they have brought us something else. But just as they amply deserve to be excused, so we must not be blamed if after careful examination of such causes we do not equally approve them all; for gold receives its value not from the hand which proffers it, but from its weight, its color, and those other qualities by which true gold is separated from alchemies, dross, and all other counterfeits. When new or rarely seen things awaken in our minds more wonder than those which are common and ordinary, our desire to learn their causes should be aroused accordingly, and with it our wish to put to test those things reported to us by others or supplied by our own minds. Now several months ago, a new splendor appeared in the sky, and just as it was then a worthy cause for your marvel, so shall it now become a deserving object of your investigation. Hence I shall set forth what has been remarked upon similar

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occasions by ancient philosophers and modern astronomers, and as I weigh their opinions carefully you shall see whether these things satisfy your minds. Afterward I shall bring before you—not {p. 3) positively but merely probably and with reservations, as I think should be done in so obscure and difficult a matter—those conjectures which have taken shape in the mind of your Academician Galileo. I do not doubt that these will be as welcome to you and as valuable as those other conclusions, for they had their origin in that noble and sublime intellect who adorns the present age no less than this native land of his by having discovered so many marvels in the sky. May I be granted the ability to explain them to you vividly, for I esteem more highly the praise of having been a good imitator than I do that other kind which is usurped by those who have attempted to make themselves the inventors of views that are really his, pretending to be Apelleses,1 when with poorly colored and worse designed pictures they have aspired to be artists, though they could not compare in skill with even the most mediocre painters. I say, then, that probably the most celebrated opinions of the ancients,2 besides that of Aristotle, are the three to which he refers; that of Anaxagoras and Democritus, that of some of the Pythagoreans or Stoics, and that of Aeschylus and Hippocrates of Chios (the last two being Pythagoreans also). Anaxagoras and Democritus supposed that comets were groups of several errant stars which joined their light together, confirming this by having observed some stars to appear upon the disintegration of comets.3 Others held a comet to be a single star, coeval so to speak with others and having the same period and ordinary motion, so that its appearance and disappearance would depend upon its extreme approach toward and retreat from us. It is in this way that Mars appears to us at its greater magnitude and then diminishes from this so much as to be lost to view, and sometimes to have given rise to fables of Mars having been exiled from the heavens. {p. 4) Hippocrates of Chios and Aeschylus, both Pythagoreans, believed that such a single star by approaching the earth would attract from it some vapors and moisture; our vision being refracted

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to the sun by this, there would be produced the appearance of a curl.4 Aristotle objects against Anaxagoras and Democritus that it would be necessary always, and not just sometimes, for the dissolution of a comet to show it dividing into stars, which does not occur. Moreover, he says that comets should appear not only in the meetings of planets with each other, but also in the conjunctions of planets with fixed stars, for the occurrence of which he cites the Egyptians; yet he says that he had twice observed Jupiter united with a star in the sign of Gemini so completely as to occult it, without any comet having resulted. Furthermore, to show clearly why this whole position has not even a vestige of probability, he remarks that however much the stars differ in magnitude, they nevertheless appear as indivisible points, and he asks who can fail to see that just as no magnitude can be created by bringing together a great number of indivisible points, so a large number of bodies which look indivisible will not, upon approaching one another, appear to make up any more extension or body than will one of them alone. T o this argument, Anaxagoras and Democritus might reply in the first place that a comet is not always composed of stars large enough to be visible when they are not conjoined. Moreover, since the fixed stars are at such an immense distance beyond the wandering ones, it might be that in such a conjunction these rays would be so united as to appear to us as one continuous stretch of light. Besides, the assumption which Aristotle adopts as being clear and evident is self-contradictory and inconsistent; like Penelope {p. 5) unraveling the cloth with one hand as fast as she weaves it with the other, it defeats in the end the very proposition which it affirms at the beginning. For the first part of Aristotle's enthymeme includes two conspicuous contradictories, since not only the appearance of different magnitudes precludes the appearance of indivisibility, but simple appearance does so alone, that which is indivisible being by no means capable of being seen. But even supposing the proposition he has advanced to be true, his conclusion is nevertheless false. For, given the inability of many united indivisible points to produce a

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real quantity, we cannot legitimately deduce that the same would be true of the appearance presented by a great multitude of bodies which are apparently but not really indivisible when these gather together and become contiguous. Indeed, it may be that appearing indivisible is nothing other than being invisible and not appearing at all. For if at a distance of a thousand yards a tiny grain of wheat is not visible to our eyes, we may call it apparently indivisible; yet it is obvious that if we mass many of these together they will become visible and will loom up as a huge bulk. But let us not wander so far from our own subject. The Milky Way is so much like a comet that Aristotle believed it to be (and wrote that in a manner of speaking it was) sister to one, 5 and that both were generated by the same kind of exhalation. Nevertheless, as has been made abundantly clear by our Academician, the Milky Way is composed and constructed of very many small stars, each in itself invisible to our eyes, though it fills a very large part of the sky. Hence, on behalf of Anaxagoras and Democritus, one might turn the argument back upon the Philosopher in the following way: The Milky Way is so similar to a comet in color and light that by your own admission it consists of the same material. But it is an aggregate of very minute stars. Therefore, in accordance with your {p. 6) reasoning, a comet is composed of many stars. But the incorrectness of Aristotle's objection does not imply the truth of the proposition which he erroneously opposes. For as Seneca says, we often see planets in conjunction; yet we do not then see comets, as we should necessarily do if they were produced in this way. Nor do these conjunctions endure long enough; indeed, they vanish promptly because of the rapid course of the stars producing them, just as eclipses are very brief because the same celerity which causes approach and conjunction likewise separates and disunites the stars. Nor does Aristotle oppose the second opinion any more effectively, bringing against it only the argument that since all the wandering stars are compelled by their nature to perform their revolutions within the zodiac, comets too should appear only in that same circle if they are wandering stars. Against this Seneca exclaims, and

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27

very reasonably: ' W h o places these limits upon the stars? Who encloses divine creations and marvels within such narrow bounds ?' e But let us leave out exclamations. That a comet is not one of the wandering stars which become visible in a manner similar to that of some planet which shows itself now small and now large may, in my opinion, be inferred very plainly from the disparity to be noticed between the growth and diminution of the latter and the appearances and disappearances of the former. Planets become gradually larger upon their approach, until at their closest they appear to us in their greatest magnitudes; then, gradually retreating, they diminish with that same uniformity which they maintained during their growth, being seen to shrink again proportionately. But a comet (j>. 7) is very large when it first appears, and afterward grows little or not at all for a very short time, subsequently diminishing during all its remaining period until, having become very small, it is completely lost by reason of its tenuity. This is a convincing argument that a comet does not descend and approach in a circular revolution from the uppermost regions, where it would be invisible because of its great distance. Besides, considering the length of time a comet is hidden, the brevity of its appearance, and the space which it traverses during its short time in our hemisphere, one would be obliged to assign to it an epicycle 7 incomparably larger than any orb, however vast, of the other wandering stars. For if, indeed, after some determined period the same comet returns, there is no previous comet which could have been the same as ours except that of 1577, since that alone was similar to ours in size and duration. And if so many years are required for it to complete one revolution of its own, then in the forty days during which it was seen by us it cannot have traveled even one degree in its orbit; yet with its apparent motion it passed over more than one-fourth of a great circle in the celestial sphere. Now how many worlds and how many universes will have to be assigned to give it space enough for an entire revolution when one four-hundredth part of its orbit exceeds half of our universe ? T o say nothing of the fact that no way would ever be found to save its great change in magnitude while it remained visible in such a small

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arc of its orbit, which orbit would for us resemble a straight line parallel to our horizon. And if in order to avoid this absurdity someone tries to say that during these few days it had passed as many degrees in its own orbit as would suffice to account for its apparent travel with respect to the firmament, then he will fall into the other difficulty that its return ought to occur after a few months, which is not the case. {p. 8) Against the third army captained by Aeschylus and Hippocrates of Chios, Aristotle directs the same weapons which he used against the second; namely, that comets should not take a course outside the zodiac. But having been blunted by Seneca, these weapons do not strike home. Still, I hear a philosopher rise up against me, and drawing forth a sharp syllogism from the Peripatetic quiver he lets fly at the Pythagoreans, not wishing to see them get off thus without a battle. ' If the comet were a refraction,' he says, ' then it would certainly not be seen in a mirror or in the water; that is, by means of another refraction or a reflection. Yet it was to be seen both in mirrors and in our river, the Arno, as brightly as in the sky. Therefore it was not a refraction.' From this most subtle syllogism, practically hidden in ambush behind the comet in the treatise on the Milky Way, 8 1 confess that I have no shield with which to cover and defend the poor unhappy Pythagoreans. Therefore, humbly committing themselves to the mercy and clemency of Aristotle, let them confess frankly that their comets, being refractions, ought not to have mirrored themselves, but that they did so in imitation of rainbows and of those circles called haloes which sometimes exist around the moon or the sun; of mock suns, and of rods.® These, by Aristotle's own declaration, are also refractions or reflections, but despite this they permit themselves to be mirrored. But it is time for us to hear the opinion of Aristotle himself. Examining it with some diligence, let us see whether he has propped it on some more probable conjecture or whether it totters as badly as those others which he pretends to refute. Aristotle supposes the elemental part of the universe where it touches the celestial region is a hot and dry exhalation10 which,

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29

together with a large part of the air beneath, is carried (p. 9) about the earth by the motion of the sky. It sometimes happens that this vapor, being sufficiently warmed by that motion, catches fire; and thus are created the stars which we call shooting stars. But when in this uppermost region of the air combustible material collects and condenses, and a beginning of fire is added by the motion of bodies above it in such a temperate manner that this material becomes warm but neither so vehement as to burn and be consumed in an instant, nor yet so feeble as to be extinguished, and if close to it there ascends simultaneously from lower places a warm breeze to fan it and feed it, then this material is ignited and makes a comet, having one shape or another according to the arrangement of the burning matter. He then goes on to posit some differences among these comets, basing them upon several considerations which I do not think it necessary to go into; for if, as I expect, his assumptions as to the generation and nature of comets are demonstrably foolish and fanciful, no time need be wasted in rejecting those consequences which merely depend upon the things assumed. I say, therefore, that unless I am mistaken Aristotle's reasoning is filled to the brim with assumptions which if not obviously false stand much in need of proof, whereas that which is assumed in science must needs be perfectly evident. In the first place, I believe that it is not so easy to admit that the hot and dry exhalation bounded within the lunar hollow is carried round by the revolving of the sky, together with a great part of the air contiguous to it—even supposing that this space is filled with such substances, which is very questionable. For, since a most perfect shape must be attributed to the heavenly spheres, and since exhalations consist of a tenuous and very light material, that is not naturally inclined to any motion other than straight, they surely will not be swept along by simply touching the smooth and polished surface of their container. Experiment shows this, {p. 10) for if we cause a concave circular vessel of very smooth surface to revolve about its center with as great a velocity as we wish, the air contained within it will remain at rest. This may be clearly demonstrated by the tiny flame of a little, lighted candle held inside the hollow of the vessel;

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the flame will not only fail to be extinguished by the air contiguous to the surface of the vessel but it will not even be bent, though if the air were moving so swiftly it ought to put out a much larger flame. Now if air does not participate in this motion, still less would some other lighter and more subtle substance acquire it. And if even under the assumption that the celestial orbs revolve, there follows no circulation of the contained exhalation, then what will happen when we deny that revolution as well? Yet this rotation must truly be entirely abandoned, and the motion must be assigned solely to the bare and simple bodies of the stars, in order not to run into difficulties and contradictions which have already become manifest from recent discoveries and observations. 11 But even if we suppose that celestial orbs move, and sweep along with them the uppermost elements, I do not see why that agitation should produce heat and the lighting of fire rather than cold and the extinguishing of fire. I should not like to have Aristotle beguile us into his idea that motion has a property of exciting heat, 12 for that proposition is false. It is indeed true that strong compression and friction of hard bodies is able and sufficient to excite heat and even fire, even when produced by a very slow movement. Thus, both the pulleys and the ropes are burned when a very great weight is being raised with quite a slow motion unless they are cooled by drenching. If we make a large wheel of wood or other material go round with great speed, it does not heat up at all along (p. 1 1 ) its circumference where the motion is most rapid, nor elsewhere in the wheel itself, but great heat is excited in the axle by its rubbing against its supports, though the axle in turn may be very slender and consequently have a slower motion than any part of the wheel. Blacksmiths, compressing iron with a heavy hammer, so heat it in a few blows that they draw fire from it. Compression and friction of solid and hard bodies cannot be produced without motion, but many motions exist without them; and since we see heat excited by compression, however slow, and not by even, rapid, frictionless motion of hard bodies, the heating effect is to be recognized as from friction and not as from motion. Aristotle, relying more upon false and fanciful concepts than upon

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sensible experiences, believed and wrote that the iron tip of an arrow which was shot with great speed would grow hot. I believe the opposite, and I say that to shoot an arrow with a well-heated iron tip would (by the high speed) cool it down much faster than if it were held still. Others, making the same mistake as Aristotle, have believed that a forest might be burned by a furious wind, and some have thought that in a tempestuous sea ships might take fire from the extreme velocity of wind and water. But I had rather believe that the caulking and planks of the ship might be burned by being compressed and rubbed together in the torment of the storm, to which their groaning and creaking bear witness. In a forest of trees, some might be shaken and tossed by the fury of the wind and rubbed together so strongly that flames might arise from them; lighting a fire by the rubbing of two sticks is a common practice in America. And as to the arrow, I strongly suspect that if Aristotle ever got round to putting the matter to a test, he had a powerful archer shoot with a very strong bow (p. 12) at a thick target. Extracting the arrow immediately afterward and finding its tip to be hot, he persuaded himself that it had been heated by the speed of its motion in the air, and it never occurred to him that the iron tip was heated by violent friction in passing through the target. The experiment may be observed every day in drills, which though moved very slowly are much warmed in piercing through anything. Hence, I do not believe that a mere agitation made in water or in air or in any other tenuous and yielding body could excite heat and fire, for no such thing do I see; rather, I see the contrary. If time and space permit me to do what is necessary to explain my own ideas, I should venture to say that from motion, as simple motion, neither heat nor cold nor any other alteration except change of position can be produced by the moving body, any more than if the whole were to remain at rest. For a motion which equally affects the whole and all its parts is as if nonexistent with respect to either, and does not differ from rest, since no alterations take place among the parts, and where nothing is changed nothing is produced. But when motion or compression is attended by a rubbing of the surface of a movable body against another solid body, or by the rubbing of its

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internal parts among themselves, then heat ensues. Moreover, note that friction does not produce heat in all sorts of solid bodies, but only in those of which one or both are consumed or pulverized, so to speak, when they are struck together. For if, either by extreme hardness of the bodies or by their surfaces being smooth and polished, it happens that in their rubbing together no part of them is detached and consumed, all efforts to heat them will be vain. Thus two pieces of very smooth glass or two pieces of highly tempered steel will {p. 13) never warm up by being rubbed together, but, if a piece of soft iron is filed with a very highly tempered file, the iron becomes hot while the file scarcely grows warm—and even that warmth is not from heat excited in it but from its contact with the already heated iron. Diamonds held for many hours rubbing against a rapidly rotated steel wheel do not heat up beyond tepidity, since by reason of their great hardness very little of them is consumed. The body which is to yield heat, then, must undergo dissolution into very fine parts which, moving, penetrate the pores of our flesh; in passing through these, accordingly as the particles are few or many, slow or fast, they produce in us by contact either a certain pleasant feeling which we call gentle warmth, or else by violent dissolution of parts they produce the great pain called scorching or burning. And besides, what material is ever seen to produce heat except when it is being consumed and dissolved into very fine parts ? Wood, wax, oils, and in a word all materials are consumed and burned up in producing heat. But returning to the subject under consideration, perhaps nothing is more conjectural about this sublime burning than to suppose that comets are fires and that they are ignited in the uppermost regions of the air, which amounts to assuming what was to be proved. Besides, if that hot and dry exhalation, together with the contiguous air, is sometimes reduced to parts of such temperament and disposition as to be able to catch fire by contributory agitation from the motion above, it is a great marvel that in so many ages this exhalation has not reached a state in which the whole would catch fire— or at least that part of it which lies between the tropics, where the greater speed of motion and greater efficacy of the sun should

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create more heat than near the poles. Yet shooting stars are seen in that region, and, according to Aristotle, these are produced by the (p. 14) same or similar ignitions. Later on, this philosopher supposes that that kindling of fire which comes from celestial motion and ignites the material of comets is so temperate that they do not burn violently, or even slowly so as to smoulder, but in such a way as to maintain themselves for many days or even months. From this, he seems to me to have taken the view that burning for a short or long time depends largely upon the quality of the fire by which anything is ignited at the beginning.13 In my opinion this is far from true. He would have the fire which burns a combustible material be an external thing and different from that into which this material becomes resolved in burning, so that depending upon the kind of fire applied to a bundle of wood, to a candle, and to a quantity of gunpowder, it might happen that the wood would burn up in one hour, in four, or in twenty; the candle likewise; and the powder, lighted by a slow fire, would last for many days. Now I have always believed the duration to depend solely upon the material which burns, and not upon the material of the fire by which it is started. I am sure that a haystack lighted by ever so feeble a fire would never continue to burn as long as an oaken pyre ignited by a musket flash. I know perfectly well that a stroke of lightning or a petard will burn a plank almost instandy, and that a piece of wood will burn faster in a furnace than upon a little fire of straw. But anyone who tried to defend Aristotle with such experiences and reasoning would not be saying anything relevant. In the first place, one is here concerned only with the starting of a fire which may begin a great quantity of combustible material burning, and not with a large and ample fire surrounding and burning a small quantity of material. In the second place, {p. 15) the Philosopher states that that which ignites a comet is nothing but the movement and agitation of its material, and that this depends upon celestial motion; actually the character of the fire is precisely that of which this material is inherently capable. Finally, suppose someone should assert that the comet's fire depends upon another previous fire, admitting its origin to be

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excited by celestial motion in the hot and dry exhalation which always exists under the hollow of the moon's orb, but then went on to say that this kindles a comet in some other denser and well-heated breeze arising in that region. If he should take such a refuge, I say he would find himself entangled still further, for his kindling fire would now be just the opposite of what Aristotle requires. That is, it would lack slowness and long duration, for it would be that very thing by which Aristotle ignites shooting stars, which are instantaneous fires; comets lighted by that kind of fire should be quickly consumed and finished. It may be added that we do see things which are unquestionably true fires, such as lightning, heat lightning, and certain shooting flames, and we are certain that these are very close to the earth and are of momentary or very short duration. So it is not at all probable that exhalations which rise much higher (and should therefore be considered much lighter and more subtle) should continue burning for months on end, and at a rate so disproportionate as to last a hundred thousand times as long as those mentioned above. T o say that fuel is continually supplied from below by suitable ascending breezes seems to me like putting a pin into a garment to patch it and in so doing to create two or three new rents. For since the fuel and the other material of the comet would all be of the same tenuous and combustible material, I cannot see why it should not all burn up at once near that which ( p . 16) is afire. Moreover, I believe no one asserts that the ascending breeze which feeds this fire leaves from the entire surface of the terrestrial globe rather than from some limited region, if for no other reason than that it would surely not come from the surfaces of the seas; experience demonstrates to us that no exhalations are derived from these. 14 Now assume, for example, that a breeze arises from all Africa to nourish the comet, and let us remember that the latter goes round the terrestrial globe every day. If this nutriment which has its root in Africa and its head in the comet must follow the comet while traversing the Atlantic and Pacific oceans so many times, it must extend infinitely in the form of a very long ribbon with winding upon winding, going round these inferior elements. But if this ribbon is interrupted when passing

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over the oceans, it is very remarkable that it meets the comet so well upon resuming, since the latter changes latitude every day; that is, moves transversely much more than the width of its head; or else it is equally remarkable that new comets are not generated every day by the interrupted breezes. All these and other difficulties occur in the means by which the comet is produced. That a comet is not necessarily a fire is deduced with much probability from its very regular shape and from the fact that it keeps itself with its curl or beard always diametrically opposed to the sun, never altering this by any local movement whatever, a condition which could never be maintained in a tumultuous and wandering fire. That it is not a fire is moreover obviously deducible from experiment, as well as from the statement of the Peripatetics themselves who affirm that no lucid body is transparent. Experiment shows us that a flame, and not only a large one but even the tiny flame of a candle, obstructs the view of objects beyond it. Now what would be the effect of so vast a fire {p. 17) as a comet encased in sticky and viscous material ? What of its immense thickness, which must be many yards or even miles, through which penetrates the image of very minute stars which a thin and rare little cloud is sufficient to conceal? Yet the curl of the comet is easily seen through and is hardly cloudy at all. Finally, it is quite impossible to support the view that a comet is a fire and yet to locate it under the moon, this being repugnant to its small parallax as observed by so many excellent astronomers with extreme care. As a final argument of the impossibility of this view, we may mention a forecast which these men derive from comets. This is that every year in which many large comets are seen will be very dry and hot, for, since a hot and dry exhalation is common both to winds and to comets, numerous large comets would argue a great abundance of exhalation, and consequently the occurrence of winds and arid conditions.16 But if comets involve the burning of such exhalations, then surely whatever quantity is burned will not be left over, as nature has no more violent means than fire for rapid consumption, destruction, and annihilation. Hence, after a multitude of large comets, there ought to follow a less dry and windy season than

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before, because of the great consumption of arid and gusty matter. These, Ο Academicians, are the most celebrated opinions concerning comets that have thus far come to my attention. Among these, I had thought that I might find satisfaction in the Pythagorean view of a comet's origin as a refraction of our vision to the sun, and accept its location far above the moon as having been conclusively demonstrated by astronomers, when some further (p. 18) questions suggested to me by our oft-mentioned Academician entangled me once again in doubts and difficulties. These I shall propound, and if they appear to you as worthy of consideration, as they did to me, then someone who is a better theoretician than I may resolve them for us and remove all uncertainties. The balance of my discourse will therefore deal with the strength of those reasons which at length persuaded the most celebrated astronomers not only to deem comets celestial things, but even to insist that they be necessarily accepted as among the heavenly bodies and to prepare for them tables and ephemerides with perhaps more care and research than plausibility. I shall examine principally the basic assumptions of Tycho Brahe, he having criticized the works of others and dealt with these matters in more detail and with more assurance than anyone else. Later I shall turn my attention to the Professor of Mathematics at the Collegio Romano, who in a recently published tract appears to have subscribed to Tycho's every statement,16 and even to have added some further reasoning in confirmation of that opinion. Speaking chiefly to these authors, then, I say that inferring a great or small distance of objects from the smallness or largeness of their parallaxes has until now been considered an argument so conclusive that not a single person who has fully understood its force has raised any objection against it. Nonetheless, when we consider it more closely, we shall find that this method also leads to error when one attempts to make it serve with respect to all visible objects, for among these there are many whose places and positions cannot validly be determined from this effect. There exist two sorts of visible objects; some are real, actual, individual, and immovable, while others are mere appearances, reflections of light, images, and wandering simulacra which are so

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dependent for their existence upon the vision of the observer that not only do {p. 19) they change position when he does, but I believe they would vanish entirely if his vision were taken away. Parallax operates reliably in real and permanent things whose essence is not affected by anyone's vision; these do not change place when the eye is moved. But parallax does not function in mere appearances. Let me try to explain this better by means of examples. Haloes, which are generated in thin clouds near to us, do not alter their aspect for people who observe them at the same time from places far apart from each other. Since haloes surround the sun or the moon, everyone sees them as having their centers precisely in common with the centers of these bodies, and from this it is obvious that with respect to the stellar sphere they admit of no greater parallax than the sun or moon. Is it not evident that the colored patterns which we call rainbows are seen opposite the sun in such a way that all straight lines from the center of the sun through the eye of any observer go, when extended, so as to strike directly in the center of the bow ? And who does not know that if such lines were produced to the stellar sphere they would exhibit the same parallax as the sun, or insensibly greater, no matter how far apart the observers may be ? But there is no parallax when the observers look at the same rainbow, though, considering the proximity of the phenomenon and the distances separating various observers on the earth, the parallax of a rainbow or a halo ought to be very great. The same is true of parhelia (those triple suns which, to the great marvel of the common people, are sometimes seen in the sky with the same aspect as the sun) which are seen simultaneously by all who observe the event from places many miles apart. But let us speak of things which more resemble comets. Some of you, Academicians, have often seen in the evening, when the sky is cloudy, {p. 20) long rays of sunlight coming through holes in the clouds and descending to the earth. These look brighter and narrower at the apertures where they originate than where, continually widening, they extend a long distance if they do not actually meet the earth. Though the whole horizon may be dotted with similar spotty clouds, these rays appear to our eyes only in the place corresponding

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to the position of the sun; they appear to be confined within a definite angle, and beyond this nothing particularly bright is to be seen. A similar appearance may be easily imagined to be (and indeed is) visible simultaneously from various places far distant to the north or south; yet to everyone the appearance is the same with respect to the sun, so that if anyone wished to recount or remember the spectacle he would say that he had at that time seen very long luminous rays directed through the air toward the sun. And since different apertures occur in the clouds between the sun and various places on the earth, the rays seen by various observers are different. If I am not mistaken, gentlemen, you have sometimes found yourselves in high places not very far from the seashore, the air being in such a state that there was almost no apparent distinction between the sky and the surface of the sea, the two seeming to form one continuous substance. As the sun then commenced to decline toward the west, you have observed a long luminous strip directed toward the sun, produced by its splendor on the surface of the sea. A similar thing is seen by others at the same time from any place facing the same surface, and yet each sees it as pointing toward the sun with no other bright band appearing to his right or left. If compelled to describe what they had seen and no more, they would all agree in saying that they had observed at that time a very bright (p. 2 1 ) light in the direction of the sun, that is, pointing toward the same part of the firmament. In this instance, the sun is above and the surface of the sea is beneath; but if we imagine the sun to be below the horizon and some surface other than the sea's to be elevated above it, we should perceive in this surface a similar reflection of the solar light, everything else remaining indistinct from the sky itself, since even the surface of the sea is sometimes so confused with the sky that no distinction may be perceived between them. What, then, should be said about this matter ? I certainly believe we must say that the whole surface of the surrounding sea is really covered with light in the same way, but that to anyone who looks at the sea from a given place this light remains completely invisible with the exception of that part which is reflected from the water lying directly between the eye and the sun. Similarly, it must be

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said that the sun's light is diffused from all the clouds and their apertures and through all the mists and vapors scattered through the air, but that it is not conspicuous anywhere except around these places in question, directly between the sun and the observer, and sloping at certain definite angles to left and right, beyond which limits nothing is illuminated by that light. All the clouds are covered by the light which produces in them mock suns, haloes, and rainbows, but the eyes of particular observers perceive only that part of the light which faces them. In sum, every eye sees a different rainbow, a different halo, or a particular set of mock suns; those which are seen from different places are not derived from the same rays, the same apertures in the clouds, nor the same parts of the water, but from diverse ones. Now if parallax has no cogency in determining the distances of all these refractions or reflections, images, appearances, and illusions because they change place as the observer moves (and change not only their places but their identities), I shall not believe that parallax {p. 22) has really any place in comets until it is first proved that comets are not reflections of light, but are unique, fixed, real, and permanent objects. And my occasion for doubt is the greater since perhaps there is nothing among real visible objects which so much resembles a comet as do some of these optical images. I do not know of anything which more exactly resembles a comet than those projections of rays through holes in the clouds, and if time permitted I could adduce many analogies between these and comets. And finally, lest our casting doubt be thought captious, or to be done merely to create an objection where none exists, it seems to me that if we will carefully consider what Aristotle tells us about the opinions of the ancients, we shall discover that some Pythagoreans had similar sentiments about comets.17 In assigning causes for the nonappearance of comets between the tropics and beyond the tropic of Capricorn toward the south, they said that between the tropics the attracted moisture in which reflection of vision to the sun would occur is consumed by the sun's heat, and beyond the tropic of Capricorn no comets are formed for us inhabitants of the north not because of any absence there of copious, attracted c

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moisture, but because in the diurnal motion those parallels describe small arcs above the horizon and large ones below, and by reason of this obliquity the vision of us northerners could not be reflected toward the sun. You see, therefore, that they believed comets to be not real objects but mere images and appearances, visible to some people and not to others accordingly as the material in which images were produced was or was not located in a suitable place for reflecting people's vision to the sun. Now inasmuch as parallax is nil in some of the aforesaid images, while in others its operation is very different from its operation on real objects, then in order to have the comet appear as without parallax to all observers and {p. 23) still originate in the elemental sphere, it would suffice for vapors (or other material of whatever sort) to be diffused on high and to be capable of reflecting the sun's light through distances and spaces equal to, or rather somewhat less than, those from which the comet is perceived. For let us imagine straight lines to be drawn from some fixed star or other point of the firmament to places on the earth, taking any and as many such places as you wish and assuming that vapors suitable for reflecting or refracting the light of the sun are spread out on high. Then this vapor cuts across the pyramid represented by those straight lines, and all observers whose lines of vision travel along one or another of those lines would be able to see the comet, and it would appear to all as beneath the same star or the same point in the universe. I do not say positively that a comet is formed in this way, but I do say that just as there are doubts about this, so there are doubts about the other schemes employed by other authors; and if they claim to have established their opinions beyond doubt, they will be obliged to show this and all other positions to be vain and fallacious. These objections throw much suspicion upon arguing from lack of parallax in order to determine the location of the comet. Still weaker, if I am not mistaken, are the reasoning and conjectures based upon the nature of its movement; and completely idle is that which has been understood by some people to have been deduced from the slight enlargement received by the head of the comet from a telescope while the surfaces of other visible objects are magnified

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many hundreds of times. They arrive at this view by supposing that this instrument enlarges objects according to the rule that nearby objects are enlarged very much, and more distant ones less and less in proportion to their greater distance, so that finally the fixed stars receive no sensible enlargement, being very remote, (p. 24) I had not intended to say anything about these two arguments, and particularly about the latter one, since it appeared to me quite incorrect and false, and I did not believe it had gained assent except from persons of so little authority that it would not be worthwhile to consider it. But recently, I have seen in the discourse on this matter delivered at the Collegio Romano how mathematicians there had so high a regard for these arguments as not only to approve them, but to criticize those who had deprecated them, calling them little skilled in the principles of perspective and in the telescopic effects which they themselves had understood and observed by virtue of long experience and from theorems of optics. This made me pause somewhat, and reflect upon the considerations which had persuaded our Academician that this view rested on weak foundations. Long before the appearance of the work mentioned, he had contradicted that reasoning and deemed it worthless; and if he was not the only one to do so, at any rate he did this more positively and more publicly than anyone else. So I have changed my original decision and have decided to set forth our Academician's reflections for you, my listeners, and perhaps for those very learned geometers too if this discourse of mine should reach their ears, in order that either for our benefit its mistakes may be amended, or for the good of the others their errors may be corrected. Thereafter, I shall consider what may be inferred from the character of the comet's motion. Some, then, declare that nearby visible objects are much enlarged by the telescope, farther ones less so, and those most remote little or not at all. I do not know how they explain the fact that the same telescope renders visible innumerable fixed stars of which nothing is seen with the naked eye, for if it does not enlarge these it must illuminate them by means of some still more admirable and undreamt-of prerogative. And if by enlarging their images (which must be admitted), {p. 25) it changes them from invisible to visible—that

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is, if from insensibility to us it renders them quite perceptible—then I do not know why such enlargement ought to be called ' insensible' rather than 'infinite'; for the ratio of something to nothing is infinite. In my opinion, astronomers would not have distinguished the visible fixed stars into various magnitudes unless their inequality made itself perceptibly evident. Indeed, the difference between the smallest stars of the sixth magnitude and the largest of the first magnitude is regarded as so noticeable that between these there are placed five other gradations of inequality. Hence, we should call not merely sensible, but very great, that enlargement by which the telescope makes some of the invisible stars appear to us larger than stars of the first magnitude, though they are perhaps many gradations smaller than visible stars of the sixth magnitude. This effect is nonetheless to be seen among the fixed stars, and would be especially noticeable if we were to observe some of these small stars with the telescope when the sky is still somewhat light; that is, when the largest stars are just appearing. This is beautifully illustrated by the Medicean planets,18 which, being easily found with Jupiter to guide us, are seen at sunset with a fine telescope long before fixed stars of even the first magnitude are seen by the naked eye. And since the Medicean stars are very much less bright than the fixed stars, it would seem that nothing short of a very great enlargement could render them visible; for, on account of their smallness, they are invisible not merely to the naked eye but even through a telescope which magnifies their surfaces less than thirty or forty times. But assuming (as indeed would deceptively appear to be partly true) that the fixed stars are insensibly enlarged by the telescope, I do not know to what extent this ought to be considered an effect of their great distance in the sense that one might conclude conversely that any object insensibly increased {p. 26) by the telescope would necessarily be immensely distant. It seems possible to me that both propositions could be true but that to link them might be false, perhaps in the same way as with regard to the twinkling of these same fixed stars. It is true that the fixed stars scintillate, and it is true that they are very remote, but from these two bare propositions one may not be certain that their excessive distance is the cause of

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their scintillation. Similarly, given that the fixed stars are little enlarged and that they are very remote, it does not thereby follow that their slight enlargement necessarily depends upon their great distance. For if this were really the case, it is certain that all visible objects located at that distance would do the same thing, and hence that not only the fixed stars but also the intervals which separate them should appear the same to us with the telescope as with the naked eye. Yet experiment shows us the contrary. Taking the tube of a telescope with the lenses removed, let us direct it at two fixed stars so far apart that both may just be seen through the tube that is pointed at them. Now replacing the lenses and retaining the same setting, the telescope will not only fail to include both stars in the same field of view, as ought to happen if very remote objects were not enlarged, but in order to pass from one star to the other it will be necessary to move the tube as one would for two objects no more than a mile away from us, since the same ratios of increase hold for celestial distances as hold on earth for objects at small distances. Moreover, if the conclusion in question were true, we should sometimes see a remarkable result follow from it. For suppose we place an object some distance away—a black circle, for instance— and then several times as far away in the same direction we put a white one, just enough larger than the first so that the black one {p. 27) does not quite cover it entirely, but leaves a white rim exposed to view. Next, take the telescope and direct it at the circles; if the closer one is enlarged more than the farther one, then surely the latter will necessarily be entirely covered and hidden, and the white rim will be seen no more. If this effect did occur, then sometimes the nearby moon might amazingly interpose itself between our eyes and the very distant sun, and, eclipsing it only annularly for the naked eye, eclipse it totally for the telescope, so that looking through the latter we should see dark night while others were enjoying the light of day by naked eye. Not only will this fail to occur, but when of the farther of the two circles mentioned above only a fine thread appears to the naked eye, precisely the same is perceived with the telescope—a necessary argument that the enlargement of the two objecto is made in exactly the same ratio.

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By these experiments it seems to me to be plainly demonstrated that the most immense distance of an object does not deprive it of any enlargement at all. But since it is nevertheless seen that stars observed through the telescope appear little larger than when observed unaided, it will perhaps be not irrelevant to look into the true causes of an effect which, arising as it does from the ordinary way in which other visible objects appear to us, may easily deceive anyone who does not consider the matter most attentively. I say, then, that the same telescope enlarges all visible objects in the same ratio at whatever distance they are located, and those who have believed otherwise were mistaken either because they were looking at diverse objects of very unequal size, or because while they thought they were using the same telescope they were actually using very different ones. It is evident (/>. 28) that the stars, and not only the fixed stars but also the wandering ones (except the moon), appear much larger to the naked eye in the darkness of night than in the twilight glow when they first appear. Venus and Jupiter seen in a lighted sky are not even one one-hundredth their apparent size in the dark. But I do not believe that on this account anyone deems their true bodily size— namely, that which is seen by day—to become larger at night, though they do acquire a large irradiation within which the little body of the star remains indistinct. Thus the visible image by night is very different and incomparably larger than by day. Now if, in order to test the power of a telescope, someone should look at a star by night and compare the bare little body as enlarged by the instrument with that seen garlanded with rays by the naked eye, he would indeed be erroneously comparing different objects while supposing that he was considering the same object. No doubt he will fail to find that enlargement which is seen when one looks at the same object, because what is seen with the telescope is the simple and real body of the seen star, while what is perceived with the unassisted eye is the irradiated star, so that the enlargement by the telescope seems very small, sometimes nil, and even sometimes the star may appear to be reduced in size. In confirmation of what I am saying, let the telescope be fixed

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upon the Dog Star, for example, before dawn; it will not appear much larger than if seen without the telescope. Now let us follow it until the sun rises. We shall see it remain the same size through the telescope, but to the unaided eye it will seem gradually to diminish in such a way as to be seen smaller than the least visible of the night stars. And finally, the sun risen, it will be made infinitely smaller and will be completely lost; yet it will still be seen very well through the telescope, {p. 29) looking always the same. Venus, Jupiter and in sum all the stars observed through the instrument appear to us no larger by night than by day, yet the same stars seen with the naked eye are very large in the dark and very small in the lighted sky. This is a sure argument that that which is seen through the instrument is the pure object robbed of its alien rays. The same is deduced from its perfect and bounded shape, sometimes horned in Venus, oval in Saturn, and circular in the other stars. The error, then, depends not upon the immensity of the distance but upon the brightness of the object, and the same thing is seen to occur in our earthly lights when not far off. Thus whoever stubbornly maintains that the argument based upon slight enlargement by the telescope conclusively proves the immensity of distance might readily be made to believe that a lighted candle placed at a height of one or two hundred yards should be among the fixed stars, since it is enlarged very little by the telescope. But I hear it argued, to overthrow all this reasoning, that even non-brilliant objects receive from the same telescope a greater enlargement the closer they are. If, for example, an object seen at a distance of one hundred yards appears to us one hundred times larger, then at ten yards it will appear to be two hundred times enlarged, and four hundred or one thousand or two thousand if placed at distances of two yards, one, or one-half; and in brief that by approaching it we may magnify it indefinitely at will. All this is very true, and has been observed and understood by our Academician, perhaps before anyone else. But indeed at the outset, it appears to me that those who regard this as the effect of approaching the object have not guarded against a mistake. So I should like to learn from them whether, when they tried to see distinctly an object

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placed at a distance of {p. 30) ten yards, they kept the length of the telescope (and consequently the distance between its lenses) the same as when the same object was one hundred yards away. Certainly they will say that they lengthened the tube, and that they extended it much more in order to look through it at a distance of four yards; at a distance of one or one-half yard they would admit lengthening it to double, triple, or even four times that length which sufficed for looking at distant objects. I shall then advise them that they were not observing with the same telescope, but with different ones; and that the cause of greater or less enlargement of the objects does not depend upon getting closer to them, but upon the employment of larger and larger telescopes. That this is true is proved by setting a telescope to view some object placed at a distance of one thousand yards, for instance, and without moving it from place lengthening the tube by only an inch or two. Immediately a noticeable growth of the object will be seen. 19 Yet it has not been moved closer; if anything, it is farther from the eye by that little measure by which the tube has been lengthened. But on the other hand, keeping the instrument fixed and moving the object closer not merely an inch or two but ten, twenty or thirty yards or even one or two hundred, no increase whatever will be seen to take place beyond that which is always achieved by a simple approach of the naked eye. So that if at a distance of one thousand yards the object appears to us through the telescope ten times as large, for instance, as when seen naturally, then at a distance of nine hundred, six hundred, or four hundred it will likewise appear to us with only the same tenfold enlargement. T o sum up, this enlargement will never increase except when the distance between the lenses is increased by lengthening the tube. Now let these men tell whether, when they have been observing the moon, which according to their own statement is very much magnified, (p. 31) they have had to shorten the tube later in order to view very remote objects and even the fixed stars. Certainly not; indeed, not only for the distance of the moon, so many thousands of miles away from us, but not even beyond a distance of half a mile away is there any need to shorten the telescope by a hair's-breadth

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and thus to cause a reduction in the enlargement of things looked at; but when the telescope is employed at a given length, it shows us every object perfectly, and all of them with the same ratio of enlargement. Let us therefore conclude that it is quite true that all objects are enlarged by the telescope in the same ratio, and, if very close objects seem to be more enlarged, this arises from the use of a longer instrument. As to things which are very remote, only shining ones deceptively show themselves as less enlarged, and this is due to the phenomenon of their brightness, not to their very great distance. Since the true cause of this latter effect has not previously been assigned by others, I believe you may be pleased to hear it. For it would appear rather remarkable that the telescope should so greatly enlarge all visible objects for us, but that only those which emit light and are crowned with additional rays at a certain distance should appear to be similarly enlarged only as to their primary light, while this crown, though also a visible object, receives no enlargement. Here it is necessary first that we upset a false opinion about the nature of this same irradiation, if indeed anyone has put faith in what some philosophers have written to the effect that stars, torches, and other luminous bodies of all kinds light up and brighten a part of the surrounding air also, which in turn at a suitable distance shows its splendor more vividly and more definitely, and that this is why the whole torch appears much larger to us. That reasoning is false. The truth is, first, that the air is neither lighted nor brightened; next, that {p. 32) this irradiation is not around the luminous object anyway, but is so close to us that if indeed it is not actually within our eyes, it is at least upon their surfaces; perhaps it is caused by the principal light from the object being refracted in that moisture which is always maintained upon the pupil of the eye by the eyelid. Several things support this. The irradiation appears greater to moist or teary eyes; also, if you partly close and compress the eyelids, the rays appear very long, an evident sign that this brilliance is established in the eye and resides there. And what finally proves it to exist in the eye is that if we interpose our hand or some other opaque body between the eye and the light, and gently move it rather as if we wanted to cut out the light, the irradiation is never completely

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hidden until the actual flame is concealed, but the rays appear quite unaltered between the hand and the eye. This would not occur if the rays were close to the light; that is, between it and the hand. As the hand first begins to cut off part of the actual light, parts of the said rays also commence to disappear, namely, those which seemed to stem from the opposite part of the light. Thus if in raising the hand the lower part of the flame is hidden, those rays will begin to be lost which seem to burst forth from the upper part; and on the contrary, if the hand is placed above the light and is lowered to hide the upper part, then the lower rays will be lost. The same thing is proved by another most evident experiment. If looking at this irradiation we lean our head upon the right or left shoulder and thus tilt our eyes in the same direction, we shall behold this tilt occurring in the rays, but certainly not in the candle flame, which remains fixed—a certain (p. 33) argument that the rays are in our eyes and that the flame is far outside them. Now if this irradiation is in our eyes, as is obvious, then what wonder is there that the telescope does not enlarge it? T h e telescope magnifies only those images which pass through and beyond its lenses, not those which are on the same side as our eye and do not pass through the glasses. Such are our experiments and conclusions stemming from our principles and our reasoning from perspective. If our conclusions and demonstrations shall be false and defective, then our foundations are weak; but if ours true and those of other people are false, let those others be assured that we shall justly pass upon them the judgment which they have wrongly made against us. These things established, I do not see that anything may be inferred about the comet from its slight enlargement by the telescope except that it is luminous, and as such has the property of appearing irradiated and larger at a certain distance from the naked eye. Now we come at last to a consideration of the argument taken from the character of the comet's motion as proving it celestial, which will perhaps prove to be no sounder than the others, as there are many reasons for questioning it. First, let it be said that the assumption of distinct celestial spheres and orbs in which stars are firmly fixed and by whose motion

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alone they are set to turning has at length become so notoriously full of improbabilities and contradictions20 that even many of our most stubborn antagonists have been led to get rid of them by believing the planets to move by themselves. Still, assume that some may wish to assign to comets a sphere and a special heaven where they spring into being and by which they are carried round, it being considered improbable that they are born with enough knowledge and skill to navigate. Then it would be necessary to assume not one single orb, but many, with regards to whose movements with respect to each other in various ways, (ρ. 34) in inclination as well as in speed, there cannot be attributed one motion assigned to any particular sky, whatever that motion may be. I might adduce many examples of this, but for your better understanding and lesser tedium let us consider only the differences which existed between the comet of recent months and that of 1577 which was so carefully described by Tycho Brahe. The comet of 1577 appeared to move in a circle which cut the ecliptic about the twenty-first degree of Sagittarius; the recent one cut it at the fourteenth degree of Scorpio. The circle of the former one was inclined less than thirty degrees to the ecliptic, while the recent one was rather more than sixty degrees. Thus the poles of these two orbs would be quite different and very remote from one another. At the beginning of its appearance, the earlier comet moved in its apparent circle more than five degrees per day; the later one, three. Finally, their movements were diametrically opposite, since the former one moved in the order of the signs and the latter moved against them. These events being incompatible within a single sphere, we should be forced to assume as many spheres as there have been comets in the past, and perchance also in the future. Now this multiplicity of spheres, forever idly waiting in the hope that a comet may come along, God knows when, to turn round in them for a brief time through a small part of its circle, I cannot reconcile with the extreme neatness which nature maintains in all her other works by retaining nothing which is superfluous or idle. Tycho says in effect that such an arrangement of the heavens suffices for such pranks of Nature and playthings of the true stars, for though infirm they have

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a natural inclination to follow every manner and custom of the skies.21 This savors much more of poetic grace than of scientific soundness and rigor, and deserves no consideration from you whatever, as Nature takes no delight (p. 35) in poetry. Then the argument derived from the motion of comets being regular and being executed in a great circle is very defective. As to regularity, the observations and statements of these very people have shown the motion not to be regular because of being continually decelerated in such a way that the comet of 1577 was twenty times as fast at the beginning as at the end, and the recent one was about twice as fast. And although Tycho tries his best to reduce this to uniformity by assigning comets an orb about the sun, nevertheless he cannot gloss over the truth so completely as not to be forced to give it an irregular motion even within its own orb. Also he permits himself to assume for it a non-circular path, now ignoring (in order to indulge this new fancy of his) that one of the principal reasons which caused both him and Copernicus to depart from the Ptolemaic system was the impossibility of saving the appearances by means of motions which are absolutely circular and perfectly equable in their own circles and around their own centers. He also pretends not to see another extravagance: that although it is obvious in every system that all movements belonging to planets are made in the same direction, he allows himself to introduce this orb designed only for comets and destined to move backwards, which is really most improbable. As to the confident statement that the motion of comets is along a great circle, important points are lacking in the demonstration, and their omission gives evidence of defective logic. For although it is true that great circles and motions made along them would appear as straight lines to an eye placed at the center of the sphere, and lesser circles as curved lines, still the converse is not necessarily true as would be required by Tycho and by the author of the Problem. That is, every motion which may appear straight to us is not necessarily made along a great circle; if that were so, a movement actually made along a straight line should appear to be made in a curve, which is false. Therefore, he must (j>. 36) say that to the observer, two sorts of motion appear straight: those which really are

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straight, and those circular motions which are made along great circles. (When I say this I am speaking only of simple motions; speaking generally, all movements made within a plane would appear to be along straight lines to an eye situated in that same plane.) Thus, whoever wanted to prove faultlessly that the movement of a comet was along a great circle would be under the necessity of proving first that it was not really and inherently along a straight line, which has not been done and which would perhaps not be easy to do. For example, in order to prove the movement of the sun from east to west to be circular even though it appears to be made in a straight line, good astronomers argue from its appearing to be the same size in the middle of the sky as it appears to be when it is near the edges, and from its motion appearing uniform to us, assuming that it is also intrinsically uniform. These two conditions are not met with in motion along a straight line, for that, if intrinsically uniform, would appear non-uniform and fastest near the center (being closer to the eye) and slower toward the extremes; also the body would appear larger at the center and smaller near the extremes. But if we wish to reason about the comet from these good hypotheses, it seems to me that it should strike us as much more reasonable that its movement was a continual retreat from us and was made along a straight line; for its apparent size was always diminishing until the comet was totally lost, and its velocity was always apparently slackening. Nor are these the only appearances and data which would favor that opinion; there are still others whose probability is much more evident as they adapt themselves better to lessening the absurdities which it seems must follow from assuming this {p. 37) cometary orb. For a clear explanation of the whole matter, I shall proceed thus. Many ancient philosophers believed the comet to be a wandering star which appeared only when by getting farther and farther from the sun it emerged from its rays, just as Venus and Mercury become visible by a similar elongation, remaining invisible all the rest of the time because of their proximity to the sun. A favorable argument is that comets under very extensive observations usually get farther and farther from the sun after their initial appearances, just as

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happened with these two which principally concern us and of which we have fresh and personal observations of the one and a careful account of the other by Tycho and others who observed it. Now some comets have their origin in the evening, as did that of 1577, while others appear in the morning, as did ours; and it follows from this that in departing from the sun the former must move in the order of the signs and the latter in the opposite direction. This contrariety of motions is a very unhandy thing to be obliged to assume in a single sphere or in different spheres devised for transporting materials which are identical in their nature. But besides the alleged improbability of this view, Academicians, you may note for yourselves the other kinds of absurdity lightly passed over by those who desire too anxiously that physical things shall correspond and accommodate themselves to ideas which they have formed casually. Tycho observed that the comet of 1577 departed from the sun at the outset, that it achieved a certain elongation, and that it then commenced to approach the sun once again. Moreover, it diminished successively after its first appearance, and thus it was supposedly getting farther away from us in imitating the elongations of Venus and Mercury. He thought to introduce competent reasons for each of these effects by assigning his comet a revolution about the sun similar to those of the planets named, but in an orb as much (p. 38) larger than that of Venus as the comet's elongation of about sixty degrees appeared greater than that of Venus, which is only about forty-eight. On the whole, this assumption was not entirely implausible, although as I shall shortly suggest he might have found another simpler and more natural explanation, in my opinion, and one more neatly corresponding to the appearances. The Mathematician of the Collegio Romano has accepted the same hypothesis for this last comet as well; beyond the little which that author has written in support of Tycho's opinion, I am led to affirm this by seeing how much he concurs with Tycho's other fantasies throughout the remainder of the work. If the comet's orb is as these authors depict it, it is a great source of wonder to me that the Fathers at the Collegio have later been persuaded to call the comet the offspring of heaven; being in effect a triple goddess, it would have to

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be made an inhabitant of the heavens, of the elemental regions, and also of hell. Since the elongation of our comet from the sun exceeded ninety degrees, a smattering of geometry suffices to show that if its orb encircles the sun [but not the earth], 22 it must, after running through the sky a long way, traverse the elements and then plunge into the infernal bowels of the earth. For [the line marking] an elongation of exactly ninety degrees being at right angles to the path of the sun, this would amount to its being tangent to the orb of the elongated star, and touching the earth, and passing through the eye of the observers. I cannot believe that the author of the Problem would wish to maintain such a monstrosity; and I know that if in order to sustain his original statement he thinks of attempting to assign the comet a rotation perhaps not around the sun similar to the orbits of Venus and Mercury, but around the earth without encircling the sun, in imitation of the moon, or even one encircling the sun in the manner of the three (ρ. 39) outer planets, he will in every case run into tricky and dangerous shoals if he carefully weighs all the implications. Never having given any place in my thoughts to the vain distinction (or rather contradiction) between the elements and the heavens,*3 there is for me no qualm or difficulty about the idea that the material of which a comet is formed having sometimes invaded these nether regions of ours, and being sublimated here, having surmounted the air or whatever else it is that is diffused throughout the immense reaches of the universe. I am sure it might do so without meeting any resistance or solid obstacle which would impede its journey or even retard it for a brief instant. Indeed, it seems to me that we have often observed such sublimation of smokes, vapors, exhalations, and all other thin and light materials. And I know, Academicians, that many of you will have seen more than once the sky at nighttime illuminated in its northern parts in such a way that its brightness yields nothing to the brightest dawn and closely rivals the sun—an effect which in my opinion has no other origin than that a part of the vapor-laden air surrounding the earth is for some reason unusually rarefied, and being extraordinarily sublimated has risen above the cone of the earth's shadow so that its upper parts are

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struck by the sun and made able to reflect its splendor to us, thus forming for us the aurora borealis. 24 This appearance has a beautiful and probable occasion, as it is seen only (or most frequently) in the summer when the sun is northerly and is thus a shorter distance below the horizon; then the southward tilt of the cone of the earth's shadow is so great that the vapors need to rise much less than at other times in order to emerge from the shadow and become exposed to the light of the sun. In order to {p. 40) theorize more in detail, let us recall that for some days before our comet proper was seen, when the beam 85 was observed in the morning before daylight, all the eastern region was seen to be more than usually filled with luminous vapors which were so little less bright than the comet itself that at the beginning it seemed as if it were distinguished from the rest of the sky by two lateral stripes less lucid than it was, rather than by surpassing in light all the rest of the sky. Besides, it has been proposed and proved by our Academician that kindred smoky patches go wandering through the celestial fields and are generated and dissolved there; this he first did in connection with sunspots, and made us so certain of it that there remains no room for reasonable doubt. And now, to lessen these difficulties that are seen to follow from assigning the comets a sphere, I say that all contradictions are removed very probably and easily by means of a single, simple movement. For we need imagine nothing more than a most simple and equable motion along a straight line from the surface of the earth to the sky. In the first place, this satisfies the appearance of a straight line (as we have remarked) since it actually is one, and this motion though in itself equable will appear to us as continually slowing as it gets farther away; it will show us a diminution in the visible size of the object; and finally, without our having to introduce any contrariety of movements, whether the comet is eastward or westward, morning or evening, it will always appear to us to get farther away from the sun. For a clear understanding of all this, see the figure below. T h e circle A B C is supposed to be the terrestrial globe, with the eye of the observer at A , his horizon being along the straight line A G which points toward the rising sun. It is to be understood that

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toward the eastern region the straight line along which the material of the comet moves (/>. 41) rises perpendicularly toward the sky; let

Fig. ι this be the line D E F , and mark on this several equal segments S O , O N , Ν I, and I F ; these will be the spaces passed over by the comet from day to day. Now let Ο be the place of its initial appearance, it having been invisible previously by reason of being too much under the sun's rays; then on the second day it will be seen at N, on the third at I, on the fourth at F, etc. It is clear that {p. 42) since the comet is closer to the eye at its initial appearance than at any other time, it should appear larger at Ο than at N, and at Ν than at I, except perhaps in so far as at Ο it falls more under the sun's rays and

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the brightness of dawn dims its light there so much that for two or three days it appears to us to continue growing; but later, having emerged from the brightness of the dawn, it will continually decrease. Its apparent motion will be always slower, because the angles O A S , Ν Α Ο , I A N , F A I, etc. (which are the measures of these motions) become successively less and less, as is easily proven. For since in the triangle A S N the angle S is obtuse, the line A N will be longer than A S ; but if the angle Ν A S were cut into equal parts by the line A C , the part of the side opposite N O would be greater than Ο S ; therefore, as they are assumed equal, the angle Ν Α Ο must be less than the angle O A S . In the same way, it may be demonstrated that succeeding angles will always be less than those preceding, which is the cause of the apparent retardation of motion. Furthermore, if first seen in the east, it will appear to us in ascending to approach the sky always toward the west, and its movement will consequently seem retrograde, that is, contrary to the order of the signs, as was the case with the most recent comet. If it first appears to westward, it will seem to us to withdraw toward the east, and its ascent and movement will be forward in the direction of the signs, as happened with the comet of 1577. And in both situations, it will appear to us to move continually farther from the sun, its elongations being measured by the angles O A G , N A G , and I A G , which widen continually from day to day by the addition of the angle of its apparent motion. Now here there occurs a difference worthy of consideration, which is that when the comet {p. 43) is easterly, as the last one was, it will progressively depart from the sun not only because of its apparent retrograde motion but also because of the sun's own motion, which is always in the direction of the signs. But when the comet is westerly and therefore has a forward motion, its own motion will be the same as that of the sun, and it will not continue to move away from the sun except in so far as its own apparent motion happens to be greater than that of the sun. 26 But its own motion continuing to diminish, and {p. 44) that of the sun being constant, it may happen later on that it will no longer increase its distance from the sun but will diminish this progressively. These two events are exactly verified

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in the two comets of which we are speaking, since this last one, being easterly, was always getting farther from the sun while the one of 1577, which was westerly, started by moving about four degrees per day farther away, for by that much was its movement in excess. This later diminished progressively so that in a little more than twenty days it was reduced to a speed equal to that of the sun, and hence no longer moved away. Afterward, the comet being outraced, the sun commenced to reapproach it, and at the last was doing so at a rate of almost half a degree per day. I shall not pretend here not to know that if the material in which the comet takes form has only a movement straight and perpendicular to the earth's surface (that is, from the center toward the sky), the comet should appear to be directed exactly toward the zenith; yet it did not appear so, but declined toward the north. This forces us either to change what has been said or else to retain that, but to add some other cause for this apparent deviation. I cannot do the one, nor should I like to do the other. Seneca recognized and wrote how important it was for the sure determination of these matters to have a firm and unquestionable knowledge of the order, arrangement, locations, and movements of the parts of the universe.*7 In our age we still lack this; hence we must be content with what little we may conjecture here among shadows, until there shall be given to us the true constitution of the parts of the universe— inasmuch as that which Tycho promised us still remains imperfect. And because we have examined with some care so many other details, it will (/». 45) be good to give some consideration to the curvature of the curl or beard of the comet. Concerning this matter, I do not find that anyone but Tycho has written; and he, I believe, no more correctly than of other particulars which depend upon human conjecture. I shall therefore examine so much as he has written, and this being found inconclusive I shall try to produce something possessing more probability. Tycho thinks that the stretch of curl is not really curved in itself, but is straight and merely appears bent and twisted.28 In this, I believe he has judged correctly; the recent comet showed itself sometimes with its curl curved and sometimes with it extended straight.

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But I think that in assigning a cause for this fortuitous appearance, Tycho has deviated more from the truth than the comet has from the straight. He would refer the cause to the comet's extremities being unequally distant from our eyes, and he says that any visible object which is really perfectly straight, but one of whose ends is farther from our eye than the other, happens to appear bent to us and not straight; and he adds that for this effect there are sure proofs from perspective in Yitellio and Alhazen. 2 9 Being sure of the incorrectness of the proposition in the first place, I wanted to see these passages in the authors cited, since it seemed to me strange that writers of that caliber should have strayed so far from the truth as to believe they had proved something which is false and is not susceptible of proof. It seemed incredible to me that such a man as Tycho could have been mistaken in understanding the conclusions of those writers; but I was the more deceived, for surely Tycho failed to understand what had been demonstrated in the propositions cited from Yitellio and Alhazen, {p. 46) who were speaking of quite a different matter. What these authors were investigating in the places cited was the sign by which we recognize when it is that a plane surface seen by us is viewed head on and as it really is, and when oblique and foreshortened. They say that we know its position to be head on when the extremities of the object are equidistant from the eye, and rays fall perpendicularly from there to the center of the object; we then see its right-hand and left-hand parts with equal distinctness because they are precisely the same distance from the eye. But when the same object is obliquely exposed to view, that is, with one end close to and the other far from the eye, then the eye does not find the two points equally distant from it, and since we see the nearer parts distinctly while we see those more distant gradually becoming more confused, our discriminatory faculty judges the former to be close to us and the latter to be remote, which amounts to knowing that such an object is obliquely exposed to view and is foreshortened. So there is nothing written here about a straight object ever appearing crooked, and the word 'oblique' does not mean 'curved,' as T y c h o would require, but simply what we call 'foreshortened' or 'in perspective.' If Tycho's

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conclusion had been correct, one might more readily excuse his having run over these passages superficially and having misunderstood their sense, believing them to relate to his purpose. But the manifest falsity of his conclusion ought not merely to have rendered these passages suspect to him, but should have condemned that conclusion without further trial. Experiences which show us the falsity of the conclusion are so numerous and so frequent that I am quite astonished that anyone of even ordinary intelligence should remain in error. Do we not daily see masts, spears, roads, towers, {p. 47) campaniles, and thousands of other straight objects which never are viewed except in foreshortening, and yet which never look curved ? It is equally false that anything straight could deceive us by appearing curved when one of its extremities is closer to us than the other. For upon experiment, there is no better way for us to ascertain the straightness of a thing than by placing one end of it as near as possible to the eye and the other as far away as possible; it is in this way that a carpenter determines the straightness of a piece of wood by a simple glance. I add, moreover, that Tycho's reasoning is so diametrically opposed to the truth that if a straight line ever could appear bent, then this would be when its two ends were equally distant from the eye. Thus, for example, a very straight wall may appear to us as sloping to right and left when we are opposite its midpoint, for there it will appear higher and broader than toward either of its ends, and for that reason its upper edge will seem to slope down toward the ends. We are certain, then, of the invalidity of Tycho's reasoning. Next I shall suggest what occurs to me on this subject, more to give you occasion for discovering what there is in it of good or bad than to pretend that I definitely consider myself entirely satisfied on the question. I say, then, that it is obvious (and is generally accepted) that the medium surrounding the earth is not pure and simple air, but that up to a certain height this is mixed with fumes and gross vapors which make it noticeably denser and thicker than the remaining aether above, which expands clear and limpid throughout immense spaces. Since these vapors surround a body of spherical shape, the terrestrial globe, they also take on a similar shape, so that their

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external surface is a convex sphere. Therefore, a visible object (p. 48) lying outside this vaporous region, in coming to our eyes which are always situated at the bottom of these vapors, must pass through an additional and dense transparency, and be refracted and altered in apparent shape at its surface. The better to understand this we should first call to mind a general proposition taught to us by masters of perspective: that every refraction is made in the very plane which cuts perpendicularly the transparent body that causes refraction, and that the incident ray which falls on this transparent surface from a point on the object, the point of incidence, the refracted ray, and the eye lie always in this same plane which also passes through the perpendicular erected upon the surface of the refracting medium at the point of incidence. Now granting this, and understanding that we speak of an object having a long shape and extending in a straight line (this being the comet), I say that to the eye placed within the vaporous orb it may show itself in one of two ways. For either the eye is placed in that plane which passing through the length of the object extends also through the center of the vaporous sphere, or else it lies outside that plane. If the eye lies in this plane, it will see the object without alteration of any part so far as shape is concerned; for, cutting the sphere through the center, the surface in which it lies is perpendicularly erect to the sphere. And as the refractions of all points of the object are produced in the same plane, it is represented to the eye as straight. Indeed, if in addition to lying in this plane the eye were located at its center, it would take in all parts of the object without any refraction whatever, for the incident lines from all points of the object would be perpendicular to the transparent medium and hence would be refracted to the center and would reach the eye. But {p. 49) if the eye is outside this plane, it is impossible that the object should appear straight any longer, for the plane which passes through the eye and through the length of the object does not pass through the center of the vaporous orb and no longer cuts its surface perpendicularly. Hence, the refraction of rays coming from points on the object are no longer made in such a plane, and not being made in the common intersection of such a plane with the surface of the vaporous

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orb, but in some other line, they must appear bent to the eye. For none of the lines marked upon the surface of a sphere appear straight except those made by the intersection of a plane surface which passes through the eye. I take this to be a very evident demonstration of the matter in hand, and it may also be seen experimentally by you, Academicians. For if you take a rather large crystal lens, convex on one side and plane on the other, and hold the flat side toward the eye while placing the curved side toward a straight line, as you change the position of your eye and of the object you will see that the line looks now straight and now bent. And you will understand that it appears straight to you whenever the plane through it and through the eye, produced in imagination, cuts the lens at right angles; but when this imaginary plane cuts it more obliquely, the line will be perceived as bent. Now in our case, since the eye is unquestionably not at the center of the vaporous orb, the comet (which in itself is really straight) never appears straight to us except when extended in a plane which would pass through our eyes and through the center of the vapors, which in brief is the same as its being in any circle vertical to us. When it cuts these circles, we shall always see it curved, and more so or less so accordingly as it cuts them more or less transversely. Therefore, when it is located with some of its (p. 50) points at our zenith, it will appear straight because it will be necessarily extended along a vertical, and if it is not far from the zenith it will be insensibly bent although it does cut some verticals; this is because it remains practically parallel to some other one. But dropping toward the horizon and being extended almost parallel to that, it will appear always more and more curved.80 At the horizon, this divergence is a maximum, for the plane which passes through the eye and lengthwise through the comet cuts the surface of the vaporous orb less and less obliquely the more the comet is elevated above the horizon, whereby the incident rays, sloping less from the straight, are conducted to the eye with less refraction and thus alter less the straight shape of the object. And thus, worthy listeners, in my opinion, the road to better philosophizing has been smoothed by what has here been discussed,

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as was not done by Tycho and his adherents. But I do not wish to hold back from extending them a helping hand and drawing them out of another and perhaps greater tangle in which Tycho is also to be found in need of help from a more fortunate if not a braver mathematician. He constantly writes (and he pretends to prove) that the curl of his comet was always opposite Venus and not the sun, 31 and although he corresponded with the greatest astronomers, many of whom declared that the comets which they had diligently observed all had the curl opposed to the sun, he wished rather to throw doubt upon their unanimous testimony and to believe that they all might have been mistaken, perhaps from not possessing instruments so costly as his, than to doubt himself and his own observations. But on the other hand, if the comet had originally {p. 51) to depend upon Venus, it appears somewhat puzzling how the light of that planet, which is but small and of little efficacy, could have made such a reflection or refraction of so great a brilliance. And in regard to the source of this latter phenomenon, he would not have held back from making his comet the offspring of the enormous light of the sun except that then he could not fathom how it could tilt away from direct opposition to the sun. Now in commencing to undo the knot, I say first that the comet is in no way a refraction of the light of Venus, which by its smallness and weakness (being nothing more than a light reflected from the sun by a very small body) cannot make a second refraction so large and bright. Besides, if the light of Venus was refracted in the material of the comet, why was there not simultaneously a refraction there of the sun's light, forming another comet far superior to the first in size and brightness? Surely there was no obstacle interposed between the comet and the sun that could impede the arrival of its rays. And since no more than a single comet was formed, it may be more readily believed that the one depending upon Venus was lacking rather than the one produced by the sun. And finally, whoever wants to maintain Tycho's comet to have been made by Venus must necessarily say that all others have been derived from that same source, and that all the conjectures and observations of other authors who have observed and recognized them as from the sun have been

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foolish and erroneous. The reason for this is quite evident: if some comets have originated from the sun and some others from Venus, then the solar ones surely must have been infinitely more bright than the venusian, as much more so as the sun is more resplendent than Venus. But no notable difference as to brightness has been reported among comets; therefore, if Tycho's was the offspring of Venus, all the rest have also (p. 52) had that origin. This I do not think anyone believes, and much less that Venus, which is always drawn round the sun, has a thousand times met with material disposed to refract its light and form a comet from it while the sun has never had such an opportunity. I shall indeed believe that the rays of the sun, being refracted, form a comet, for whose formation Venus and all other stars remain hopelessly impotent. This unraveled, I come to the other topic. I declare that I am certain Tycho was mistaken in believing and repeating positively many times that the curl of his comet was directly opposite Venus and not the sun. His mistake originated in his not having submitted this to reason, and it seems to me that he too authoritatively and too arbitrarily reduced the curvature of this curl to the direction of a straight line extending from the center of the ends of the hairs through the center of the head, whereas this curvature might have been reduced to the direction of infinite other straight lines drawn through various other points. For one may reduce a curved line to straightness in as many ways as one might bend it if it were straight. Now, one end of a straight line may be left in place and all the rest be curved, and it is in that way that a stick is curved by those who work it on a lathe. Or the center point may be left fixed and the rest of it be sloped to one side or the other, and this is the way a bow is bent. And finally, any point whatever of the line may be fixed and all its other parts may be bent to either side. Thus in restraightening it, we may at will hold immovable any point we choose, moving all others toward the straight. This amounts to saying that a line may be reduced to straightness by all lines tangent to its arc at any point whatever, which lines are infinite and point in every direction. If Tycho had (p. 53) considered this and then had coupled it with the other things he wrote, truly he would have discovered the curl of

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his comet to be directly opposite the sun and not Venus. Together with this is the fact that he first says that its curvature is only apparent and not real, and that it is an optical illusion from one part of the comet being near the eye and the other parts more and more distant, accounting for its appearing curved. Later he says that if the comet were derived from the sun, its head would be distant from and the tip of its tail close to the eye of the observer; and since the curvature progresses as the parts of the curl become more distant from the eye, the incurvation amounts to having the end toward the eye retain its true position and all the remaining parts being successively bent; therefore in straightening it one would have to reduce it to the tangent of the arc at the end toward the eye. Now let us take the same shape which Tycho assumed and draw this tangent, for we shall find it to go striking right at the center of the sun. This true conclusion might have been deduced by Tycho from his principle even though the principle is false as pertains to the cause of the curl's appearing curved (as has been explained above). But since the effect—that is, the curved appearance—is true, and it is also true that the curvature may be reduced to various straight tangent lines, we ought not to remain in doubt that among these there is also one which goes striking at the sun, and which is the true directrix of the curvature. And finally, inasmuch as not all comets always look curved to us, and the same one is even sometimes straight and sometimes bent (as happened with this last comet of ours), accordingly as it is much or little elevated above the horizon and much or little turned toward our zenith, Tycho might have taken his clue from the straight ones, for surely he would have found that they pointed toward the sun. {p. 54) This, gentle Academicians, is as much as I have been able to accomplish in so controversial and puzzling a subject, even though fortified by the labors of others. I know that there should be read before this very learned audience not mere conjectures, but only the soundest arguments and the finest papers; but possessing nothing better at this time I have preferred to present this to you rather than appear before you empty-handed. And in matters of science and of the intellect, I neither approve nor emulate the opinion of Euripides:

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Being poor, I do not wish to offer gifts To you rich, lest you deride the giver And think me by my giving to be begging." Against these poor gifts of mine being derided by you, I am protected by your benevolence. I indeed confess pretending to augment my own little store infinitely with these inquiries, having no other goal today in placing them before you than to have them taken into your clear and lofty intellects as seed in rich and fertile soil, there to acquire strength and germinate to the world in the form of positive demonstrations from which we may come to a full knowledge of that truth Which rolls away the clouds from all our minds."

The Astronomical and Balance on which the Opinions of Galileo Galilei regarding Comets are weighed, as well as those presented in the Florentine Academy by Mario Guiducio and recently published. BY

LOTHARIO SARSI OF SIGUENZA

PERUGIA eMarco Naccarini

MDCXIX

With the Permission of the Superiors

TO THE READER ON THE T I T L E OF THE WORK

When through the ardent globes of the lesser stars the comet displays its beard with fearful light and brandishes a fiery torch in the frozen Bear, what is that which gleams between the balanced scales {Lances) and consecrates the first days of the life of the Balance {Libra) ? I recognize the silent dominion of a new light. It orders its light to be weighed on one scale and the other, and on those scales its tail is tested. We also shall weigh our remarks on them.

FIRST WEIGHING THOSE THINGS WHICH HAS OPPOSED TO OUR

GALILEO

CALCULATIONS

Last year when three fiery brands were shining in the sky with unusual brilliance, there was no one of such limited intelligence and dull vision that he did not from time to time direct his gaze toward them, and no one who was not amazed at that time by that unusual brilliance. But since the mass of the people, despite its great desire for knowledge, is not equipped for investigation into the causes of things, it therefore demanded for itself and as its right, an explanation of such important phenomena from those who are especially concerned with the contemplation of the whole of the heavens and of the world. Hence it was decided that the academies of philosophers and astronomers ought immediately to be consulted. But why was it so readily believed that this Gregoriana of ours, renowned for the many interests of its academicians should be considered as, among other things, the eyes of all, and that it ought especially to be consulted and its answers awaited ? However, since the matter was as yet unexplained, at the least it could but undertake to fulfill its duty and to satisfy the wishes of the inquisitive; and those upon whom this task fell did not perform it badly if you will consult the opinion of even the greatest minds. One person, however, Galileo, disapproved of our explanation, and rather sharply. At first, we were grieved that these matters displeased a man of great reputation, but afterward we were consoled to find that Aristotle himself, Tycho, (p. 4) and others were not considered much more gently by him in this dispute. Therefore, no other apologies need be offered by those academicians for whom it is sufficient that they have made common cause with the greatest intellects; indeed, even with those great men silent, the matter itself would plead their cause before just magistrates. But since it appeared desirable to the wisest men that those arguments by which Galileo attacks what he does not favor, as well as those in which he presents his own views, should be more carefully considered by at least somebody or other,

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I decided that I ought to give some brief consideration to both of them, hoping that thereby I might perform a task pleasing to the many who are unable in any way to approve what Galileo has done. Furthermore, in this discussion, I shall constantly abstain from words which are more indicative of an exasperated and angry spirit than of knowledge, although I readily grant that method of reply to others if they desire it. Consider, therefore, that since Galileo ordered the matter to be discussed through intermediaries and interpreters, he has thereby presented the secrets of his mind to everyone not through himself but through Mario the consul of the (Florentine) Academy. Thus I, too, am now permitted to present those things which I have heard from my master Horatio Grassi about the recent discoveries of that same Galileo, not to the consul but to the students of mathematics, and not merely to one academy but to all of them and to all who understand Latin. Nor need Mario be astonished that I neglect the consul and deal directly with Galileo. For first, in a letter sent to friends in Rome, 1 Galileo clearly indicated that those arguments were his brain-child; then, since the same Mario ingenuously confessed that he, very trustingly, was willing to proffer what he had not discovered but what he had received from, as it were, the dictation of Galileo, I have determined, not without justice, that my dispute about those matters is with the dictator rather than with the consul. First of all, therefore, I am grieved that Galileo complains that he was treated unfairly in our Disputation when we contended that the employment of the telescope produced no increase in the size of the comet and that from this it could be deduced that the comet was very far away from us, for he says that much earlier he had openly {p. 5) asserted that this contention is of no importance. But assuming that he asserted it, would not the winds have immediately borne back his pronouncement to my teacher? The words of great men are frequently able to spread their fame, yet of this remark—what happened to it—not even a syllable has reached us. And despite his pretense in this matter, from the testimony of many he knows the great benevolence of my teacher toward him, immoderate in his praise both in private conversations and in public discussions.

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Certainly Galileo is unable to deny that no reproach was ever made about this to anyone by my master, nor did he specifically allude to it in any words. If Galileo has any doubts, he may recall that he once was honorably received in this Collegio Romano by its mathematicians, and not only at that time when there was a public dispute regarding the Medicean planets and the telescope, he listening and— with what modesty—blushing at their praises, but also at a later gathering in that same place when another person who was discoursing on bodies floating in water complimented Galileo continuously. Therefore I do not know what reason he has for vilifying the good name of this Collegio Romano so that he calls its teachers unskilled in logic and does not hesitate to pronounce our position regarding comets as worthless and supported by false arguments. But lest we waste time on useless complaints, first, I do not understand how Galileo can justly oppose my master and even declare him at fault, presumably because he appears to have sworn by the words of Tycho and to have followed him in all his vain devices. For this is patently false, since, except for the manner and method of calculation by which the location of the comet was sought, Galileo found nothing else in our Disputation, as its very words testify, in which Tycho was followed. Even with his telescope, the lynx-eyed astrologer cannot look into the inner thoughts of the mind. But consider, let it be granted that my master adhered to Tycho. How much of a crime is that? Whom instead might he follow? Ptolemy? {p. 6) whose followers' throats are threatened by the out-thrust sword of Mars now made closer. Or Copernicus ? but he who is dutiful will rather call everyone away from him and will equally reject and spurn his recently condemned hypothesis. Therefore, Tycho remains as the only one whom we may approve as our leader among the unknown courses of the stars. Therefore, why does Galileo become enraged at my master because he did not reject Tycho ? In vain does Galileo here invoke Seneca; in vain does he here mourn the calamity of our time because the true and certain disposition of mundane things is not understood; in vain does he deplore the misfortune of this age, as if there is nothing which may render happier these times which he considers unfortunate. D

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Although here in this introduction to the debate I must confute even these things which seem of little significance, yet truly I would never have expected that that courteous gentleman, such as all know him to be, would shun certain witty and facetious remarks which had been employed in our discourse and that he, with greater severity and dislike than Cato himself, would reply scornfully that nature takes no delight in poetry. 2 But, oh, how far I am from this opinion! I have always considered nature as poetry. Certainly, nature scarcely ever produces apples and other fruits without also putting forth flowers as sources of pleasure. Who would ever have believed that Galileo is so harsh that he would order that pleasant things, as the very spices of grave matters, ought to be far removed from them ? This is the stoic rather than the academician. Nevertheless, he may justly accuse us if we attempt by jests and witticisms to elude rather than to explain more serious affairs; but who objects that the weightiest of reasons may not sometimes be expressed gracefully and wittily ? However, the academician forbids. We do not obey. And what if this urbanity of ours is not to his taste ? We have many erudite friends whom it pleases. Nor was this attitude of his assumed by those men famous in birth and learning who took part in our disputation and who considered that it had been undertaken solely {p. 7) that the comet, commonly looked upon as a sad and unlucky portent, might be considered under the somewhat mitigating influence of calm and comforting words. But, you say, these are slight matters. Such is the case, and therefore they ought to have been treated in kind. Now I come to more serious matters. My master decided that the position of the comet ought to be investigated by three arguments in particular; first, through observations of its parallax; then, from its (manner of) approach and its motion; finally, from those things which may be observed of it by means of the telescope. Galileo attempts to overthrow their credibility one by one and to deprive them of significance. For when from various observations taken from different places we demonstrated that the comet suffered little change of aspect and therefore ought to be considered as beyond the moon, he replied that the argument taken from parallax has no significance

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unless first it has been established whether those things which have been observed are true bodies existing in one place or whether they are unfixed and delusory apparitions. Indeed, he is correct; but his objection was unnecessary in this case. And what if we consider this matter as already determined ? Surely, since our contest would be particularly with the Peripatetics, whose opinion a great many followers hold even now, it would have been meaningless to exclude comets from the number of mere appearances, since we would be concerned with a doubt held by no one. Truly, Galileo himself when he disputes against Aristotle, employs no sharper and stronger argument than that taken from parallax.8 Why, therefore, is it not permitted to us for a wholly similar and identical reason to use freely the same argument ? Furthermore, the opinions ofAnaxagoras, of the Pythagoreans, and of Hippocrates would have to be refuted, yet no one of them affirmed that a comet is a completely vain delusion of the eyes. Anaxagoras said that it is a collection of genuine stars; Hippocrates as well as Aeschylus dissented in nothing from the Pythagoreans; when Aristotle explained the opinion of the Pythagoreans, according to which they said that a comet is one of the wandering stars approaching us very slowly and fleeing very swiftly, he added: 'Those who followed Hippocrates (p. 8) of Chios and his pupil Aeschylus expressed a view similar to theirs; but they say that the beard does not belong to the comet itself which in its wandering sometimes receives the beard by reason of position, when our sight has been refracted by moisture attracted from it to the sun.' 4 But when Galileo in the very exordium of his disputation recounts the conclusions of those same persons, he asserts that they said that a comet is a star which sometimes is very near to the earth and attracts vapors from it, from which it contrives for itself not a head but a beard. Thus, as I may add, he takes little account of the matter since afterward from those same places he also proves that the Pythagoreans believed that the comet exists as the refraction of light; but they believed that nothing in comets is apparent, except the beard. Therefore, he understands that a comet, as regards its head, never seemed to any of them to be a mere apparition. What then is his objection since in this matter everyone up to the

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present has agreed with our reason for removing from this very bright torch its spectral and imaginary brightness and averting from it that reproach which no one whose opinion ought to be considered has brought against it ? Here Galileo seems to be somewhat indebted to Cardan8 and Telesio,® although having attained a sterile and unhappy philosophy they were blessed by no offspring and left to posterity books rather than disciples. Therefore, let it be enough for us and for Tycho, with Galileo as witness, that among the academies of philosophers, numerous as they are and faultless as were their disputations, the comet never incurred suspicion of being a vain and false apparition. But if anyone is found to have taught plainly that these phenomena ought to be placed among pure apparitions, I shall display to him in its place, unless I am mistaken, how far removed the comet is in its characteristics and motions from rainbows, haloes, and coronae. From these arguments, it results that the comet, if you exclude the beard, does not act at the nod and beck of the sun—a characteristic common to all apparitions—but is free {p. 9) to move onward and to be carried about wherever its nature drives and draws it. I must reply for wholly the same reason to those things which have been objected to the argument taken from the comet's motion, because, from the argument that the position of the comet day by day corresponds to a straight line on a plane like a sundial, we have inferred that that motion is necessarily in a great circle. However, Galileo objects that this need not be deduced, because, if the approach of the comet were truly in a straight line, so also its position described in the manner of a sundial would constitute a straight line; yet this motion would not be in a great circle. Although it may be true that motion along a straight line ought to be represented as straight, when, however, controversy was directed against those who did not doubt the circular motion of the comet and who had never considered this straight motion, that is, against Anaxagoras, the Pythagoreans, Hippocrates, and Aristotle, this only was sought, whether the comet which was believed to be driven in an orbit circled in a very large or a very small orbit. From its motion apparently in a straight line, it has been inferred, properly and necessarily, that this motion

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described a great circle, for no one as yet had presented this motion as straight and perpendicular. When previous to Galileo, Kepler in a little appendix on the motion of comets sought to explain that same motion by straight lines, he saw in what kind of difficulties he was involved, and therefore he considered this motion to be not perpendicular to the earth but transverse, and not a constant motion7 but slower at the beginning and end and swiftest in the middle. Furthermore, he believed that it ought to be supported by a circular motion of the earth itself so that this might explain all the phenomena of comets, but these things are in no way permitted to us Catholics. Therefore I decided that that opinion, which may not be held piously and sacredly, ought to be given no consideration, and if later Galileo thought that with a few changes this straight motion (p. 10) could be attributed to comets, he did not demonstrate this correctly, as I shall indicate below. Meanwhile, let him understand that we have in no way sinned against the precepts of logic when from motion which appears to be in a straight line we have deduced that it described (a great circle in) its orbit. For what was the use of excluding that straight and perpendicular motion which it has been declared that comets do not possess ? But, furthermore, in this place, he argues against us: If the comet were driven around the sun, since it would elongate from the sun by a whole quadrant, at some time it would descend as far as the earth.8 Does it not perhaps occur to him that it is not in one way alone that a comet may be driven around the sun ? What if the circle in which it is carried be eccentric to the sun with its larger portion located beyond the sun or verging to the north ? What if the motion be not circular but elliptical, compressed above and below and extended far out on each side? 9 What if it be not even elliptical but entirely irregular—since especially in Galileo's system it would be able to move freely without any hindrance ? In that case, there would be no fear that the earth or Tartarus 10 would ever see the light of comets too close at hand. Since Galileo objects to my master's ignorance of logic, let us see how well he himself has observed the rules of that discipline; but not by many examples, for we shall be content with one or two.

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We said that when stars were observed through the telescope we perceived them to receive a very slight enlargement. But, he says, since a very large number of stars which escape the most observant eye are seen through the telescope, it will have to be said that they receive an enlargement which is not insensible but rather infinite; for nothing and something are separated by an infinite interval. 11 From this fact, therefore, that something may be seen although it was not seen before, Galileo infers the infinite enlargement of the object, (j>. 1 1 ) that is, at least an apparent increase in size. But I consider that neither infinite enlargement nor any increment can be inferred. First, although it may be true that the gap is infinite, at least from one point of view, between that which is seen and that which is not seen, then the two have that proportion which nothing has to something, that is, no ratio at all. Nevertheless, when that which is not begins to be, it is not said to grow or be increased, because all augmentation always presupposes something of prior existence; nor do we say that the earth upon being created by God has increased infinitely, since nothing preceded it; for an object is augmented and becomes larger only when first there has been something smaller. Therefore from that which formerly was not seen as anything but afterwards may be seen, it cannot be inferred that the augmentation is in any ratio whatsoever, let alone infinite. But not to dwell on this matter, let the transit from nonexistence to existence be called enlargement. Yet from the fact that stars which had not formerly been seen were observed through the telescope, Galileo inferred that they had received infinite enlargement, although he ought to have remembered that elsewhere he had affirmed that the telescope increases all things in the same proportion. Therefore, if it enlarges the stars which we see with the naked eye in a certain and determined proportion, let us say a hundredfold, when it brings into view those smallest ones which escape the eye, it will also enlarge them in the same proportion. Therefore, their enlargement will not be infinite, for this does not admit of any proportion. Second, in order that infinite enlargement might occur in a quantity becoming visible from invisible—for the word increment employed by Galileo signifies this—it would be necessary to demonstrate

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that the disparity between the quantity unseen and that seen is infinite; otherwise this infinite enlargement would never be inferred. For suppose one were to argue as follows: What crosses over from the non-visible to the visible is enlarged infinitely; but stars cross over from the non-visible to the visible, therefore they are enlarged infinitely. A distinction {p. 12) would have to be made in the major premise to the effect that they are augmented infinitely in relation to visibility, while it would have to be denied that they are enlarged in relation to size. Therefore the conclusion would also have to be governed by the same distinction, namely, that they are augmented in relation to visibility but not in relation to quantity. From these things it appears that the term 'increment' is not employed in the major premise in the same way as in the conclusion; for in the former it is accepted for the increment of visibility, but in the latter for the enlargement of quantity. Now let Galileo see how well this agrees with the laws of logic. Third, I say that no enlargement can thence be inferred, for it is a law of the logicians that whenever some effect can result from several causes, it is incorrect to infer only one of them from the effect itself. For example, since heat can be considered to result from fire, from motion, from the sun, and from other causes, it is incorrect to infer that when there is heat, therefore it is the result of fire. Thus when something is seen which was not seen before, this may result from many causes, and from that visibility there cannot be deduced only one of those causes. I believe that it is obvious that this effect can be considered to result from several causes; first, with the object itself remaining unchanged if the visual force is increased per se; or if some impediment present in it has been removed, or the same force becomes stronger through some instrument such as the telescope; or if with the force unchanged the object has been either illuminated more brightly or approaches closer to view; or, finally, if its bulk has grown. Any one of these will be sufficient to produce the same effect. When, therefore, it is inferred from this effect that the stars which at first lay concealed seem to have received infinite enlargement, this is scarcely correct according to the rule of the logicians, because other causes from which the same effect can occur have been neglected.

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It is not sound for Galileo to attribute the increment to the telescope, for if he were suddenly to open his eyes which had just been closed, he might equally truly pronounce all things to have been enlarged infinitely, because first the stars were not seen and thereafter they were seen. And if he says that he was speaking only {p. 13) of those things which can be observed through the telescope, and that he admits other causes since here he is considering only the telescope, I reply that that is not sufficient for a correct argument. For the telescope does not bring to view just in one way those things which cannot be seen without it; first, by bringing objects to the eye under a larger angle they are made to seem larger; second, by gathering the rays and images together they are made to act more efficaciously; but it is enough for the moment that those things are seen which formerly escaped sight. Therefore, one may not infer just one of those causes from this result. Fourth, it does not agree with the law of the logicians that if the stars are not enlarged by the telescope they are illuminated by a remarkable property of that instrument. In this regard, Galileo seems to divide the effects of the telescope into only two parts, as if he were to say: The telescope either enlarges the stars or it illuminates them; it does not enlarge, therefore it illuminates. Nevertheless, there is another law of logicians to the effect that in a division all the dividing parts must be included; but in this division of Galileo's not all the effects of the telescope are included, nor are those which are enumerated peculiar to it; for illumination, as he believes, cannot be the effect of the telescope, and the collection of images or rays which are considered peculiar to the telescope are omitted by him; therefore his division is faulty. I shall not add anything further to this matter, but I desired to call attention to these few things, almost all of which may be met with in one place in one's reading; meanwhile others have been omitted so that he may understand that his disputation does not lack that fault which he himself criticizes in others. But what—for I would not omit in this place a thing as yet unheard by Galileo—what, I say, if he did not himself dare to attribute that capacity to his telescope; shall I demonstrate that he ought to have attributed it ? The telescope, he says, enlarges objects, or certainly

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it illuminates them by a hidden and unheard-of force. So it is: the telescope illuminates (p. 14) more brightly all luminous objects. If I demonstrate this, truly, I hope I shall gain the great gratitude of Galileo; while he boasts deservedly of the telescope in respect to its amplification, I shall have provided it also with this unheard-of capacity. Therefore consider: we say that objects are enlarged by the telescope because these objects are carried from it to the eye under a greater angle than they are observed without this instrument. Furthermore, according to optics, whatever things are observed under a larger angle seem larger; but when the telescope collects the images of luminous objects and dispersed rays and gathers them almost into one point, it produces a much more lucid visual cone or luminous pyramid by which the lucid objects are observed, and thereupon it brings the luminous objects to the eye by means of a brighter pyramid; hence with equal reason, the telescope is said to illuminate the stars, just as it is said to enlarge them. Just as the larger or smaller angle under which an object is observed displays the object as larger or smaller, so the more or less luminous pyramid through which the luminous body is observed will show the object as more or less lucid. Moreover, it is sufficiently apparent, and experience and reason demonstrate, that the more lucid optical pyramid arises from the gathering of the rays. Reason teaches that the smaller the space in which a given light is comprised the more it illuminates the space in which it is, and the rays collected into one compress the same light into a smaller space; therefore they illuminate more. But the same thing will be proved by experiment if we expose a burningglass to the sun; for we shall see that not only is wood burned and lead liquified in the rays which are gathered into one point, but the eyes are almost blinded by that light inasmuch as it is very bright. Wherefore I assert that it is as truly said that stars are illuminated by the telescope as that they are enlarged by the same telescope. Therefore happily, by this telescope of ours, I am now able to illuminate more clearly the stars and the sun and their very clear lights. I hasten to the third argument, and I believe that I ought to present it here verbatim; that is, so that all (p. 15) may understand what it was at which Galileo professed himself to be so displeased.

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It is as follows: ' I n the third place, I am convinced of the same thing by the fact that when the comet was observed through a telescope, it suffered scarcely any enlargement. Nevertheless, it has been discovered by long experience and proved by optical reasons that all things observed with this instrument seem larger than they appear to the naked eye; yet according to the law that the enlargement appears less and less the farther away they are removed from the eye, it results that fixed stars, the most remote of all from us, receive no perceptible magnification from the telescope. Therefore, since the comet appeared to be enlarged very little, it will have to be said that it is more remote from us than the moon, since when this has been observed through the telescope it appears much larger. I know that this argument is of little significance to some, but perhaps they have given little consideration to the principles of optics which, it must be understood, play a very important part in what we are considering.' 12 First, I wish to explain to what purpose an argument of this sort was attached to our disputation, for I do not wish it to be considered of greater value to others than to us; nor are we the sort who impose upon purchasers, but we sell our merchandise at its value. When, therefore, from many parts of Europe, the observations of illustrious astronomers were brought to my teacher, there was no one of them who did not add finally that the comet observed by them with a very extended telescope received scarcely any increment; and from this observation they deduced that it ought to be placed at least above the moon. After this, as well as other matters, had been considered in various discourses in crowded gatherings of men, there were not lacking those who plainly and freely asserted that no faith ought to be placed in this argument and that the telescope carries spectres to the eyes and deludes the mind with various images; therefore, it does not display genuinely and without deception even those things which we observe close at hand, much less those (j>. 16) which are far removed from us, except it will show them bewitched and deformed. 13 Hence, that we might seem to have granted something to the observations of our friends and at the same time publicly confuted the ignorance of those for whom this instrument was of no significance, we maintained publicly that this argument ought to be

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presented in third place, and finally those words ought to be added by which Galileo stated that he was displeased, since we hoped that by protecting from invidious calumnies this telescope which, though not his offspring, is certainly his foster child, we might therefore deserve well of him rather than ill. Furthermore, what significance we gave to this argument can, I believe, be sufficiently understood from that fact that it was presented in few words, and its meagreness was due to the fact that all had previously been explained much more precisely and fully in the two other arguments. Nor are these arguments concealed from Galileo if he wishes to admit them. When we learned that he was gravely agitated by this third argument and that he believed that he alone was the target of these words, my master undertook that it be made known to him through friends that it was farthest from his thoughts to harm him in speech or writing; and although Galileo indicated to those from whom he had received this information that his mind was at peace and that he accepted their words, yet afterward he much preferred to lose a friend than an argument. But let us now discuss the matter more clearly. I say that nothing alien from the truth is to be found in this argument, for we assert first that the nearer the objects seen with the telescope the more they are enlarged, and the more remote the less they are enlarged. Nothing is truer, but Galileo denies it. If only he would admit it. For, since he has in his hands that telescope of his, and a very good one it is, I ask him if perhaps he desires to gaze at something within his bedroom or enclosed in the space of his courtyard, does not the instrument have to be greatly lengthened ? So it does, he says. But if with the same instrument he desires to look through his window at something far away, he will say it must immediately be contracted from that great length and made very short. Now if I seek the cause of the contraction from that extension, (p. 17) it will be necessary to return to the nature of the instrument; that is, according to the principles of optics, it is necessary that it be extended for looking at things nearby and contracted for looking at things far away. Therefore, as he himself says, since it necessarily arises that there will be a greater or lesser increment of objects according to the extension or contraction of the telescope, then I may draw this conclusion: those things which

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must be viewed with the telescope extended are necessarily enlarged; and those which must be viewed with a shortened telescope are necessarily less enlarged; but all objects which are near must be looked at with the telescope more extended, and those which are farther away, with the telescope more contracted; therefore all things which are near are necessarily more enlarged, and those which are farther removed are necessarily less enlarged. If the major and minor premises in this argument are proved true, I believe that he will not deny that which must follow from them. Moreover, he admits the first proposition, and the other is also very certain. In regard to those things which are viewed from less than a half mile, no proof is required for him. That those which lie farther away than this are customarily seen with the telescope equally extended comes about not because it ought not be shortened more and more, but because this further contraction would be so slight that it does not matter much if it is omitted, and therefore it is frequently neglected. Nevertheless, if we look at the nature of the thing and if we must speak with geometrical rigor, a greater contraction is always required, clearly for the same reason as if one were to say: be the visible objective whatever it may, the more it is removed from the eye the smaller and smaller the angle at which it is seen; this proposition is very true. Nonetheless, when the object opposed to the eye reaches a certain distance at which it may form a very slight angle of vision, although it may afterward become very remote by a yet greater interval, the same angle is not sensibly decreased, although it can be demonstrated that it will always be less and less. (p. 18) Thus, the angles of incidence of the images at the telescope scarcely vary after the objects have reached a very great distance, for then it is just as if all the rays fell perpendicularly on the lens. Consequently, the length of the instrument need not be varied appreciably. Nevertheless, that proposition ought to be considered as very true which asserts that by the nature of the telescope the more remote the objects the more it must be shortened for seeing them, and therefore that it enlarges them less than those which are near; and even if, as I said, this is required only by great rigor, I affirm that the stars must be viewed through a shorter telescope than the moon.

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But he will say that this is not to use the same instrument, and therefore that if we speak of the same telescope, our position is false; for although the lenses are the same and even the tube is the same, if nevertheless this telescope is now more extended, now more contracted, it will not always be the same instrument. Away with these minutiae. If someone talking with a friend were to speak in a soft voice, that is, so that he might be heard from close by, and then catching sight of another friend far off shouted to him in a very loud voice, would you not say that he had employed his throat and mouth for one and for the other of them, and that in the first instance it was necessary that the vocal organs be contracted and in the latter, dilated ? And when we observe trombonists with their right hand pushing forward and pulling back that curved and bent brass slide, lengthening it for lower notes and shortening for higher, do we therefore consider that they use first one horn and then another ? But let Galileo see that I do not speak contentiously; let the now extended and now contracted telescope be different instruments, and with a few alterations I shall again reach the same conclusion. Whatever things must be observed with a different instrument also take a different enlargement from the instrument. Nearby and distant things are observed with a different instrument, therefore they receive a different enlargement from the instrument. Again these are major and minor premises, and the conclusion {p. 19) necessarily follows. These things having been demonstrated, it seems to me that I have shown sufficiently that hitherto we have said nothing alien from the truth or from Galileo when we said that by this instrument the remote are less augmented than the near, since by its nature the telescope must be contracted for looking at the former and extended for the latter; nevertheless, it can be said not improperly that it is the same instrument, employed in a different way. But he will say: These things are indeed very true if the matter is considered according to the technicalities of geometry which, however, have no place in our affair; and since the telescope is usually employed with no difference of length, at least for looking at the moon and the stars, here also the greater or lesser distance will be considered insignificant for producing a greater or lesser enlargement

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of the object. Therefore, if the stars seem to be increased less than the moon, the reason for this phenomenon must be deduced otherwise than from the remoteness of the object. Granted; unless this telescope differs, it increases the stars less than the moon, and perhaps the argument has less weight. Nevertheless, while it is attributed to this instrument that in addition it polishes away from all luminous things that widespread radiation by which they are, as it were, wreathed, yet it is perhaps as a result of this that from the telescope the stars acquire the same enlargement as the moon, although they seem to be less augmented. For what is observed with the telescope is clearly different from that which was previously seen with the naked eye. Indeed, the naked eye looks at the star together with the brightness diffused about it, but when the telescope is employed only the body of the star is observed. It is also very true that when all those things which concern optics have been considered, the stars receive less enlargement with this instrument, at least as to appearance, than the moon; and sometimes, if you may believe your eyes, they are even enlarged for no reason and, as it pleases God, even diminished; Galileo himself cannot deny this. Therefore, it ceases to be astonishing that we have not sought here the cause of this appearance but the appearance itself, (p. 20) But now let Galileo observe that from those things presented by him in the Starry Messenger it is not foolish for us to infer that the comet ought to be placed beyond the moon. He himself says that among celestial lights some shine by their own light, in which number he places the sun and the stars which we call fixed; but others not having been provided by nature with any innate brilliance, borrow all their light from the sun, and the six remaining planets are usually considered of this sort. Furthermore, he observed that the stars have very greatly enjoyed that vain wreath of light and have been accustomed to nourish it just like an exterior adornment; but the planets, especially the moon, Jupiter, and Saturn, are clothed in almost no brightness of this sort; 14 nevertheless Mars, Venus, and Mercury, although they have been equipped with no brilliance of their own, consume so much light from the propinquity of the sun that somewhat like the stars they imitate their scintillation and

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circumfused rays. Therefore, since the comet, on the authority of Galileo, has a light not endowed by nature but likewise received from the sun, we with other men of no little note believe it to be a kind of temporary planet, and in this regard it had to be considered like the moon and other wandering things. It is their property that the less they are distant from the sun the more brightly they shine; and as a result, clothed with a greater brightness, so when observed with the telescope they seem to be less enlarged, while from this same instrument the comet takes almost the same enlargement as Mercury. We were unable to determine with great probability whether the comet received much more of that circumfused light than Mercury and accordingly whether it was distant from the sun by a greater interval. But, on the other hand, since it was enlarged less than the moon, shouldn't it have been circumfused by a greater light and located closer to the sun ? He will understand from these things that we have spoken correctly: since the comet seemed to be enlarged very little, it ought to be said that it is more remote from us than the moon. And truly, from the parallax which has been observed and also from the fitting and clearly sidereal course of the comet, (ρ. 2i) its place is now sufficiently clear to us. Furthermore, since the telescope gives it almost the same increment as Mercury, certainly there is no reason to persuade us to the contrary, and hence also is derived no slight consideration of moment or weight in favor of our opinion. For although we know that these matters can result from many things, yet from the fact that this luminous body in all its phenomena preserves an analogy with the rest of the celestial bodies, we have therefore considered that we have been greatly assisted by the telescope 15 which gives strong endorsement to this opinion of ours, which as well is strengthened by the weight of other arguments. What remains to be added to the argument are these words: Ί know that this argument was of little moment to others,' etc. 1 ® The purpose for which these words were added was mentioned above clearly and freely; it was against those who, disparaging faith in the instrument and plainly ignorant of the discipline of optics, declare it false and worthy of no trust. Therefore, unless I am mistaken,

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Galileo understands how undeservedly he opposed our opinion regarding the telescope, which he perceives in no way opposed to the truth and, indeed, to his own conclusions; he could have recognized this before if he had considered the matter with a less agitated mind. Why should it ever occur to us that at some time these things which we have considered to be wholly his own would not be pleasing to him ? But since I consider this to be sufficient regarding our opinion, let us undertake to consider Galileo's own conclusions, {p. 22)

SECOND WEIGHING IN W H I C H

GALILEO'S

OPINION

REGARDING

T H E S U B S T A N C E A N D M O T I O N OF IS QUESTION

I. W H E T H E R KIND

COMETS

CONSIDERED

OF

OR N O T

A COMET

IS A

APPARITION

Although up to the present no one has said that the comet ought to be counted entirely among vain apparitions, yet from this it would result that we would not consider it necessary to free it from this reproach of meaninglessness, but because Galileo sought to give another, better, and wiser explanation of the comet, it is desirable that we delay for a careful consideration of this new discovery of his. He was concerned with two things: one, the substance of the comet and the other, its motion. As concerns substance, he says that this light is not produced innately but appears through the refraction of some other light, and it seems that such ought to be called shadows of luminous bodies rather than luminous bodies; of this sort are rainbows, haloes, mock suns, and many other things of this kind. As concerns motion, he affirms that the motions of comets have always been straight and perpendicular to the surface of the earth. These facts having been brought to light, he believes that he can easily destroy the opinions of others. Briefly and without any wordy dissimulation (j). 23)—since adorned or bare the truth is enough for

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him—let us now see how much ought to be attributed to these opinions; and although it is very difficult to comprehend these two remarks singly since they are so interrelated that they seem to depend one upon the other, and one in turn assists the other, we shall nevertheless take care that no suspicion of doubt about this matter remains with the reader. Therefore, contrary to the first statement of Galileo, I affirm that the comet was not a vain figment of light deceiving the eyes of those watching, and I believe that his opinion has no influence on anyone who had once looked at it whether with the naked eye or with the telescope. For it is enough that from its very appearance and by the nature of its light, it displayed itself so that anyone might easily judge through comparison with a true light whether it was true or false. Indeed, when Tycho examined the observations of Thaddeus Hagek, he presented the following remarks from his letter: 'The body of the comet in those days equalled in magnitude the planets Jupiter and Venus, and was provided with a shining light and distinguished brilliance, very fine and beautiful, and its substance appeared too pure for its purity to compare readily to the elemental materials, but it had rather an analogy to the celestial bodies.' Afterward Tycho added to these things: 'And Thaddeus was correct in his perception of this matter, and therefore he was able to conclude clearly that this comet was not in any way elemental.'17 Yet at that time when our comet shone here, Galileo, as I hear, lay bedridden by illness and because of the state of his health was unable, perhaps ever, to observe that pellucid body with his eyes; therefore we were compelled to discuss the matter with him by means of other arguments. Now he says that smoky vapor from some part of the earth was carried upward above the moon and even the sun, and as soon as it had progressed beyond the shadowy cone of the earth it beheld the light of the sun, the light of which the comet received and obeyed; and that the motion or ascent of this sort of vapor appears not be wandering and uncertain but straight and deflected to neither side.18 (p. 24) Thus he; but we refer the weight of these statements to our balance. It is set forth that at first this smoky and vaporous matter ascended

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from the earth, although during those days when a very strong north wind dominated the whole sky it might easily have been dispersed and dissipated, so that it is truly astonishing that such very slight and light little bodies were able to be carried safely upward in the midst of the violence of the raging north winds and maintain constantly that course on which they had started, since not even the heaviest weights committed to the air were at that time able to withstand the wind's driving force. I can scarcely believe it to be possible that with these two contending so with one another that a very light vapor could ascend, at least so directly, in the midst of the unstable shiftings of the air. In addition and also on the authority of Galileo, concretions and rarefactions of smoky bodies of this sort are not absent even from those highest regions of the planets, and accordingly those motions by which they are carried cannot be aimless and uncertain. But finally, despite the winds, let us concede that these exhalations were able to hold the course they had begun, and striving whither they could, were able to receive the direct rays of the sun and send its reflected rays back to us. Why then, since they receive quite the whole of Phoebus, do they display him to all of us only in the smallest part ? Indeed, on the testimony of Galileo himself, when during summer days a not dissimilar vapor is carried to the north, perhaps higher than usual, and opposes itself to our view of the sun, bathed in a very clear light it displays itself in its entirety as very silverywhite, literally resembling the aurora borealis even in nocturnal darkness. It does not appear so avaricious of its borrowed brightness that when it has taken the sun to its bosom it scarcely permits its light to be slipped back to us through one little fissure. Not only during summertime but even in the month of January and four hours after sunset, which is very remarkable, I myself have seen a little cloud gleaming white in appearance and inclining almost over the zenith, 18 so rarified that it did not veil even the smallest stars; {p. 25) and this, which also had received gifts of light from the sun, poured it forth freely on all sides through a wide opening. Finally, all clouds —if they preserve an affinity with the material of comets—when they are so dense and opaque that they do not freely transmit the rays of the sun, at least in that part where they face back to the sun reflect

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it to us by reciprocal generosity, while if they are rare and thin the light easily pervades them everywhere, and they display themselves nowhere obscure but everywhere imbued with a very clear light. Therefore, if the comet does not shine forth from any other material than from smoky vapors of a sort not compressed, as it were, into one globe but, as Galileo himself says, occupying a rather ample space of the sky and everywhere shining from the light of the sun, what finally is the reason that to those watching it always appears to shine from its short and narrow little orb, while the rest of that same vapor which has been lighted by similar light from the sun is never visible ? This is not easily settled by the example of the rainbow, in the production of which the same thing occurs so that it slips back to the eye from only one part of the cloud, although the same diversity of colors is created by its light in the whole space lighted by the sun. For those things and others of this sort rather require material bedewed and moist, already resolving into water; and then it sends back light from that part where the angles of reflection and refraction occur only if this material has been changed into water, like smooth, polished, and transparent bodies such as mirrors, waters, and crystal balls. But if the exhalations that have arisen are rarer and drier, they have neither a smooth surface, as mirrors, nor do they effect much refraction of rays. Therefore, since smoothness of the body is required for the reflections of the body, and density (combined) with transparency for the refraction, these are never taken into account in meteorological phenomena except when there is much water in them, as not only Aristotle ( p . 26) but also all teachers of optics have taught and reason itself effectively persuades. Hence it must follow that exhalations of this sort will by their nature be very heavy and accordingly less suited to those which ascend beyond the moon and even the sun, since Galileo himself confesses that those which fly away that far ought to be very thin and light. Therefore, that shining image of light capable of being reflected to us did not arise from that smoky and rare vapor of little weight, while aqueous vapor, which is very heavy, can in no way be carried upward. Perhaps someone may nonetheless dare to affirm that there is no reason why aqueous and dense vapor may not be carried higher by

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some force and that the refraction and reflection of the comet result from this vapor. Indeed, no other escape seems open to Galileo although it has been found by long experience that the rarer the bodies the more transparent they are and the less they are illuminated, at least as far as appearance; and the more (illuminated) the denser and more opaque they are. Therefore, since the comet shone with so great a light that its brightness surpassed even that of stars of the first magnitude and the planets themselves, it will have to be said that its matter was very dense and opaque in some part—for at the same time we saw a beam, which was very tenuous, gleaming white rather than shining or glittering with any rays. However, if this smoky vapor was so dense that it turned back to us such a notable and great light, and if as Galileo wishes, it occupied a sufficiently large part of the sky, how then did it finally occur that the stars which twinkled through this underlying vapor suffered no unusual refraction, nor did they appear smaller or larger than before ? Since at that time we measured very exactly the distances between the stars existing on all sides about the comet, we found that those distances in no way differed from Tycho's distances. Nevertheless, experience taught us, and Vitellio and Alhazen 20 indicated in their writings, that the magnitudes of the stars and their distances from one another vary {p. 27) through the interposition of vapors of this sort. Therefore it ought to be said either that these vapors were so tenuous and rare that they obstructed none of the light of the stars—which vapors nevertheless have already been proved scarcely suited for producing the light of the comet through refraction—or, what is by far truer, that they did not exist. Furthermore, Galileo asserted that the matter of the comet did not differ from the matter of those little bodies which are moved about the sun in a certain repetitive turning and are commonly called sunspots. I do not disagree, but rather I add that at the time when the comet was seen no spot was observed on the sun for an entire month and that afterward disfigurements of this sort were rarely observed on it. It was not without reason that a poet was able to seize this occasion for fancying that perhaps during those days the sun had washed its very shiny countenance with water more carefully than usual, that the remains of the slops scattered about through

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the sky formed the comet, and that afterward the sun was astonished that its dirt shone much more clearly than the stars. But why do I even now pursue poetic trifles ? T o return to my own considerations, therefore, let the material of the comet and, as I may say, of the solar pox be the same; and since this, about to beget the comet, is carried upward always by a straight and perpendicular motion, what is it that afterward perpetually drives and urges it around the sun in an orbit while it defiles the face of the sun with those spots and is whirled about in the same place through lines parallel to the ecliptic ? For if it is the nature of light things to be carried only upward, why therefore is one and the same vapor driven now upward and now in an orbit by such definite laws ? Perhaps someone may say that all its force is always directed in a very straight course, but where it has approached very close to the sun, yielding to its inclinations, is moved thither under the regal power of the master. I shall then be astonished that the rest of the bodies with the same matter unchanged so avidly encircle the sun, while one comet which was born very close to the sun, contrary to every inclination, departed as far as possible from the sun {p. 28) and preferred to be extinguished in an obscure place in the midst of the frozen Great Bear rather than to cover the sun itself with darkness, although this would have been possible by the interposition of its body among the rays of the sun. But these things are physical rather than mathematical. Now I come to the optical reasons by which it is proved far more effectively that the comet never was a vain apparition, nor did it ever wander as a spectre among the nocturnal shadows, but that it displayed itself to the view of all in one place and that it was always one and the same in appearance. For whatever those things are which through the refraction of light may appear more real than they are, such as rainbows, coronae, and other things of this sort, they are always produced according to a law, and as they exist from the light of a luminous body, whithersoever that light is directed they follow with an obedient and compliant motion. And so the rainbow I H L , with the sun on the horizon A, has the vertex of its semicircle at H ; if the sun is assumed to be raised from A to D , it descends in the opposite direction, and the vertex of its arc Η will decline to the horizon;

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and as the sun is more elevated, the more the vertex Η of the rainbow will be depressed. It is clear from this that the same rainbow is always moved in the direction in which the sun is carried. T h e same thing can be observed in halos, coronae, and mock suns, for when all

these surround the luminous body from which they occur at a certain interval, they are always carried in accordance with the direction of its motion, {p. 29) The same may also be very clearly understood in the case of the luminous image which the setting sun is accustomed

1

Β

D

Ε

Τ

Fig- 4 to cast on the surface of the sea and of rivers; the farther the sun is removed from us, so also the farther the image withdraws, until upon the sinking of the sun it vanishes. Let the surface of the sea be seen at Β I, imperceptibly differing from a flat surface; let the eye be placed on the shore at A, and the sun first at F ; let the radii F D and

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D A be drawn to D, making equal A D Β and F D E , the angles of incidence and reflection at D ; therefore the light of the sun will be seen at D. Now let the sun descend to G , and in the same way as before let two lines be drawn, G from the sun and A from the eye, making equal angles of incidence and reflection with the straight line Β Ε. These coincide nowhere other than at the point E, as is apparent; therefore the light of the sun will appear at E. And with the sun now still more depressed at H, the light will appear at I for the same reason. T h e contrary happens whenever the light from the rising sun is projected upon the water, for then as the sun approaches more toward our vertex so the light appears nearer to the observer; first, for example, it will appear at I, second at E, and third at D. From these things, one may understand that those apparitions are always moved in the same direction as the luminous object by which they are produced and carried. If the comet is produced from the light of the sun, undoubtedly it ought also to follow the movement of the sun, but, if it does not do this, it need not be numbered among the luminous apparitions. Therefore I say that nothing of this sort was ever observed in the case of the comet, for when on the first day on which it was seen, that is the twenty-ninth of November, the sun was found 6°43' in Sagittarius and thence {p. 30) was moving toward Capricorn, on the following days one by one up to the twenty-second of December it ought necessarily to have become more depressed in every culmination. Now if this motion is followed out, the sun was more and more moved southward from the equator; therefore if the comet were a kind of refracted or reflected light, it ought also to have been carried to the south; yet it was so far from having this motion that it sought rather to move to the north. Perhaps by this it announced its freedom to Galileo and showed that it owed nothing more to the sun than men who walk about in the light of the sun but freely go whithersoever their desire directs them. If perhaps at this point someone were to bring forward another rule of reflection or refraction different from the above, I do now know by what occult indications he could believe that it ought to be attributed to the comet, but at least this ought to be established: that once he has introduced a rule of motion let him afterward preserve it exactly. When this is

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understood, let it be as anyone desires. It might be that the comet was moved not by the motion of the sun but by a contrary motion of comets so that when the latter moved to the south the former fled away to the north; therefore when the sun returned to the north these, on the other hand, ought to have been moved to the south for the same reason. When therefore from the twenty-second day of December, that is from the winter solstice, the sun again withdrew into the north, our comet ought on the other hand to have returned to the south whence it had departed; nevertheless, it very constantly maintained always the same course of motion toward the north. From this, it can be well understood that the course of the comet had no relationship to the motion of the sun since, whether the sun was moved in this or that direction, the comet proceeded along the same path on which it had first entered. Furthermore, if the comet were of the number of delusory images, it ought to have been observed (only) at a certain and determined angle; this occurs in the case of a rainbow, a halo, a corona, and other things of this sort. In this respect, Galileo ought to have remembered {p. 31) that he had affirmed that the space of the heavens occupied by vapors of this sort is very large; and if this is so, I say

I Fig- 5 that the comet ought to have appeared as a circle or a segment of a circle. For one may argue as follows: Things observed under a determinate and certain angle are seen in that place where that

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determinate and certain angle is formed, and these having been fixed in several places in a circular line, this determinate and certain angle of the comet is established; therefore the comet will be seen in several places which are disposed in a circular line. The major premise is certain, not requiring proof. I prove the minor as follows. Let the sun be beyond the horizon at I, the site of the smoky vapors around A ; let the comet display itself, for example, at A, and the eye be placed at D ; let the same vapor occupy other parts established around A, as Galileo grants voluntarily. Now let it be understood that a straight line has been drawn through the centre of the sun I, and through the centre seen at D ; from the points I and D to the place of the comet A, the radii I A and D A run together constituting the triangle I A D ; therefore I A D will be that certain and determinate angle under which the appearance of the comet is sent back to us. Now let us imagine that the triangle I A D is moved around the axis I D H ; then let its vertex A describe the segment of the circle in which the direct rays of the sun I A and the reflected rays A D form the same angle I A D . But when in this circumduction of the vertex A many parts of it are touched by the disseminated vapor, in all these there will occur that determinate and certain angle at which the comet must occur; therefore, in the whole segment of the circle Β A C, which touches the vapor, the comet will be visible precisely for the same reason by which it happens that rainbows and coronae occur in moist clouds either as circles or as segments of circles. Since, therefore, nothing of this sort has been observed in respect to the comet, it must not be placed among the number of delusory apparitions since {p. 32) in no way does it display itself similar to them. I hold that this is confirmed from the words of Galileo himself, because he says that perhaps it is also true that this sort of spectres and vain images follows that same law in respect to parallax which the luminous body follows which produces them; thus, if any of them were the effect of the moon, such would have an equal parallax with the moon, but those which occur from the sun obtain the same difference of appearance as the sun. Furthermore, when he disputes against Aristotle and takes his argument from parallax, he maintains the following:' Finally, it is quite impossible to support the view that a

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comet is a fire and yet to locate it under the moon, this being repugnant to its small parallax as observed by so many excellent astronomers with extreme care.' 21 From this I conclude as follows: On the authority of Galileo, whatever mere images are produced from the sun have the same parallax as the sun; but the comet did not have the same parallax as the sun, therefore the comet is not an appearance produced from the sun. If anyone is in doubt as to the minor premise of this argument, let him compare the observations of Tycho with the observations of others concerned with the comet of 1577. From his observations, Tycho finally deduced that the demonstrated distance of the comet from the centre of the earth on the thirteenth day of November was only 2 1 1 radii of the earth, 22 while the sun is placed distant at least 1150 radii from the same centre, and the moon 60 radii. Regarding this matter of ours, if anyone gives consideration to those observations which my master published in his Disputation Held by One of the Fathers, the truth of this proposition will then be very clear to him; for he will find that almost always the parallax of the comet is much greater than that of the sun. Nor can these observations now be suspect to Galileo, since he proclaimed that they had been corrected for astronomical calculations by the efforts of the greatest astronomers, {p. 33) Finally, we ought not omit that one thing which we have considered and which is enough to persuade a man desirous of truth rather than altercation. Daily we experience those things which have no certain and stable form but which delude the eye by vain display of colors and of light; their lives are ended in a very short space of time, and also they change themselves into various shapes in a very brief interval of time; now they are extinguished, now again they are kindled, now they become pale, now they shine with a very bright light; parts of them are now broken away, and now again they join together; never, finally, do they appear for long in the same form. If all these things are compared with the stable motion and appearance of the comet, they indicate how much variation of characteristics and nature there is between the comet and vain apparitions of this sort. If you find the comet to be proven clearly dissimilar to them in every way, why do you not say that it has no affinity of nature or relationship to

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those things ? For the very ancient and greatest philosophers said it, as well as the most erudite of the recent; now one person, Galileo, opposes them; but, unless I am mistaken, the truth seems to oppose Galileo. QUESTION I I . WHETHER THE A P P E A R A N C E OF THE COMET M A Y BE E X P L A I N E D THROUGH M O T I O N W H I C H IS S T R A I G H T A N D P E R P E N D I C U L A R TO THE EARTH

I now come to the motion which Galileo asserts was straight; but I wholly deny this. First, that reason which he clearly professes not to know or does not dare explain persuades me to this; for that reason is so apparent and it is so effective for arguing against this motion, that greatly as he might desire to conceal it he would be unable to do so. For if—these are his words—this motion alone is attributed to the comet (i.e., straight motion), the fact that not only did itapproach more and more toward the vertex (p. 34) but also reached farther toward the pole becomes inexplicable; therefore, either this notable discovery must be discarded, and I cannot do so, or another motion must be added, and I dare not." Ought one not be astonished that a straight-forward and by no means timid man is suddenly seized by : such fear that he is afraid to present his argument ? But I am not one who is acquainted with prophecy. Therefore, I ask whether this other motion by which he could . 40)

QUESTION I I I . WHETHER THE CURVATURE OF THE T A I L C O U L D ARISE FROM R E F R A C T I O N There remains now the hair or beard of the comet, or, if you prefer, the tail, which by its curvature has roused no little interest among astronomers; nevertheless, Galileo clearly considers himself to have triumphed in his explanation of it. But first I must announce to him here that that way of explaining comets, which he ascribes to himself, is nothing new, and that in his disputation he has offered nothing which Kepler did not see much earlier and present very clearly in his writings. When Kepler sought to discover why the tails of comets sometimes seem curved, he said that this does not arise from parallax nor from refraction, 27 and he proved it elsewhere supporting his opinion with much evidence; finally, he said that this phenomenon must be left among the secrets of nature. 28 Therefore I wish this to be brought forward whenever Galileo says that he knows of no one except T y c h o who has written about this matter. Kepler and Galileo differ in this one thing, that the latter gives assent here to these reasons which the former believed not to be of such great weight and therefore decided that the controversy ought to be left undecided. Ε

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But now let us see whether, as Galileo asserted, the curvature of this tail may arise from refraction. For in this matter, he seems not to have held to those laws which he himself prescribed for it; that is, that whenever it inclines to the horizon it is almost opposite to a parallel and intersects many verticals; then only is it curved; but where it looks to our vertex, it is directed higher. For the tail preserved its first curvature scarcely three or four days, and did so whether close to the horizon or whether remote from it. Afterward, it was seen to decline from that line which may be drawn straight through the head of the comet from the sun, but it displayed no curvature, although, nevertheless, very often the course of that tail was tilted with respect to the horizon. But if the matter were {p. 41) as Galileo asserted, it ought to have appeared far straighter in its origin than when it was elevated higher. Very often it ascended from the horizon so that the whole of it existed almost on the same vertical; in its ascent it became more inclined to the horizon and intersected many verticals, as anyone can recognize from the globe itself if, for example, on some celestial globe he were to observe the location of the comet and its tail corresponding to the twentieth day of December. At that time, the tail crossed between the two final stars of the Great Bear, and the head of the comet was distant from Arcturus 200 54', and from the Corona 240 25'. Therefore, if the comet's location were to be found on the globe and the course of the tail described on the rounded surface of the globe, the tail would appear emerging from the horizon in almost one vertical; then, carried higher, it would become almost parallel to the horizon, but not even in this position would it display any curvature. Furthermore, I do not see how Galileo can be so certain that he is able to assert that the vaporous region of the earth is spread out spherically, since while he strives to strengthen his opinion regarding straight motion, nevertheless he teaches very constantly that vapors of this sort are raised higher in some places than in others. Indeed, he asserts repeatedly that comets are formed not otherwise than from these vapors when they have passed beyond the shadow cone of the earth. What then, if in one place the vapor is distant three miles from the surface of the earth, but in another place it extends beyond a

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thousand leagues; will that vaporous region still preserve the shape of a sphere ? Certainly, those who up to the present have propounded the elements of the sphere teach that if the middle part of the air, which is especially formed of vapors, preserves a definite shape, it is spheroidal or oval rather than round, since the vapors are less dissolved by the sun in those parts which lie under the poles and therefore are raised higher than in those regions which lie under the equinoctial circle and the torrid zone where they are very easily dissipated by the heat of the neighboring {p. 42) sun. Therefore, if this vaporous region is not spherical, nor is it everywhere distant from the earth by an equal interval, and does not preserve everywhere an equal thickness and density, the curvature of the tail cannot be caused by a nonexistent rotundity of that region. These things which have been said regarding the opinion of Galileo are among those which immediately concern the comet. For he, who in a very long disputation has presented his beliefs in many and confused words, objects to our saying more and prevents us from presenting many refutations against his position: for how can we divine and refute what he does not offer ? Let us now return to the remaining matters, (p. 43)

THIRD WEIGHING CERTAIN PROPOSITIONS

CONSIDERED

INDIVIDUALLY FIRST PROPOSITION:

AIR AND

EXHALATION

C A N N O T B E M O V E D B Y T H E M O T I O N OF T H E

SKY

Before I undertake, as is now my endeavor, to consider more precisely certain propositions of Galileo, I wish to assert that here my whole desire is nothing less than to champion the conclusions of Aristotle. At present, I shall not delay over the question of whether the remarks of that great man are true or false, but at the moment I seek this one thing, that I may demonstrate that the reasons advanced by Galileo are unsound, that his blows have been ineffectual,

Ιθ6

C O N T R O V E R S Y ON C O M E T S

and to speak plainly that certain propositions on which, like a foundation, the entire mass of his disputation rests display perhaps some appearance of truth, but if anyone inspects them very carefully, he will, I believe, judge them to be false. Therefore, when he attempts to refute the opinion of Aristotle, he maintains among other things that the air cannot be carried around by the motion of the lunar sky; hence it follows that it is not kindled through this motion as Aristotle deduced. ' For since,' says Galileo, ' the shape of the celestial {p. 44) bodies ought to be the most perfect, it will have to be said that the concavity of this sky is a spherical and polished surface and admits of no roughness; neither air nor fire adheres to polished and smooth bodies, wherefore the former will not be moved at the motion of the latter.' He proves all these things by argument drawn from experiment. ' F o r if,' he says, 'some hemispherical vessel, polished to smoothness, is revolved about its centre, the air enclosed in it will not be moved at its motion; this is proved by a lighted candle placed very close to the internal surface of a vessel; for if the air were carried along at the motion of the vessel it would also draw that flame with it.' 2 9 Thus Galileo. Of these matters, you will find that some can be considered as true and some not, while others which are also considered as true may be proved false. First, if anyone denies that remark in which Galileo asserts that the lunar concavity ought to be spherical and polished, in what way or by what reason may he evince the contrary ? For if the celestial bodies ought to be smooth and rotund, that must be especially so lest their motion be impeded, because if the surfaces of those orbits had any roughness that roughness undoubtedly would delay their motion. 30 Furthermore, according to Aristotle, the external surface of the top of the sky requires such rotundity lest, if perchance it contained angles, a vacuum might occur at its motion. However, all these things have no bearing on our problem. For if this concave surface of the lunar sky is neither rotund nor smooth, but rough and protuberant, no absurdity results since the body nearest to it cannot withstand its motion, whether it be air or fire, nor with one body always succeeding to the place of the other does any vacuum result. Furthermore, if this roughness be admitted, it provides much better

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for the connection of all the mobile bodies, for thus the upper elements are moved at the motion of the sky, and from {p. 45) this motion, as we see daily, many things are generated and many are destroyed. But when Galileo asserts that the shape of the most noble bodies must be rotund, will he therefore desire that man, far more noble than the sky, be smooth and rotund ? Yet, according to the oracles of wisdom, we prefer him quadrate. Therefore I would say rather that that shape ought to be attributed to each which is best suited for achieving the purpose of the body. From this, someone may not improperly infer as follows: Since the concavity of the moon must in some way attach and bind these lower things to those very lofty orbits, therefore it ought to have been made rough and tenacious rather than polished and smooth. But why do I seek elsewhere for arguments against Galileo when he himself supplies them abundantly to me ? He has said nothing truer than that the moon not only is rough, but like another earth it has its Alps, Olympus, and Caucasus, is depressed into valleys, is extended into great plains; certainly lunar mountains cannot be lacking to the moon. Is not the moon a celestial and very noble body ? Is it not much more noble than the sky by which it is carried as in a chariot and which it inhabits like a home ? Why therefore is the moon rough and protuberant rather than rounded ? Are not the stars themselves, on the testimony of Galileo, formed in various and angular shapes? What among sublime substances is more noble than the stars ? It may also be added that not even the sun, if you may believe its appearance, attains this very noble shape since certain faculae are observed on it much brighter than the rest of its parts, which show it either to be rough or to be bathed in a light which is not everywhere uniform. Therefore, as Galileo's reasoning is not persuasive, one may admit the roughness of the lunar concavity, and no one, I believe, will deny that the exhalations and air are carried along with its motion. In short, Galileo cannot easily explain away this roughness. It ought to be mentioned here that in his third Letter to Mark Weiser he held that sunspots are smoky vapors 31 (p. 46) carried around by the motion of the body of the sun. Therefore, either the solar body is smooth and polished and will not be able to carry around vapors of

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this sort, or the sun is rough and protuberant, and thus the most noble among the celestial bodies is neither spherical nor polished. Furthermore, in his second Letter to the same Weiser he s a y s : ' T h e sun is rotated about its center with the motion of that which surrounds i t ' ; 3 2 but the surrounding body must be much more tenuous than the air itself. Therefore if the solid solar body is moved at the motion of a circumfused, very rare and tenuous body, I do not see why the solid sky itself by its own motion is unable to carry with it an enclosed body, however tenuous, such as the elemental sphere.

Fig. 8 But, finally, let us concede to Galileo that the interior surface of this orbit is rounded and smooth; I deny that air does not adhere to smooth bodies. A sheet of glass B, although it is very smooth, having been placed in water will float no less than if it were another, rougher material, and the air adhering to it will by its force restrain the water A C from raising itself around the glass lest it flow over and sink the sheet. Why therefore, does not the air depart when pressed by the weight of the water which has been depressed by the glass sheet, but rather clings fast to it and does not yield its place unless driven away by a greater force ? Furthermore, if one were to place on a highly polished stone plate another equally heavy and polished body and then draw the underlying plate here and there, he would at will draw the imposed equal body; and yet if the weight by which that imposed body rests on the plate is lifted away, the latter will not adhere to the former. Therefore, the whole reason which also compels

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the imposed body to be moved at the motion of the underlying plate results from that compression by which that heavy body presses upon the underlying plate. Now, just as in the case of that one of those two bodies which is pressed by the other so that at its motion the other must also be moved, so I assert that the concavity of the moon in a certain way is pressed by the enclosed air or exhalations, if { p . 47) it so happens that they are rarefied, which is always the case. For when they become rarefied, scorning their former cramped quarters, they expand into a wider space and exert very great pressure on all parts of such surrounding bodies as anywhere oppose their rarefaction, and therefore the sky itself. Thus it is not astonishing if from this pressure some adhesion results which, as it were, joins and binds together these two bodies so that both are moved afterward at the same motion. But let us see how true that experiment is which in particular is supported by Galileo: 'If,' he says, 'a flat dish is turned around its central axis, the enclosed air does not readily follow but remaining behind, no part of it is driven around.'®8 I had already heard from certain persons who were on a familiar footing with Galileo that he was accustomed to affirm something of this sort about water contained in a dish of this sort, that is to say, that it is not carried around even at the motion of the container. His evidence was that if some light body such as straw or reed is placed in it, floating in the water very close to the edge of the dish, when the vessel is turned around the reed always keeps the same place. I know that from this and other experiments some have gready commended Galileo's remarkable facility in the explanation of very difficult matters by very simple demonstrations. 34 1 do not wish to lessen this widespread praise of him, but, as concerns the present subject, I have found each experiment entirely false—may Galileo spare me for speaking the truth. Indeed, I believe that at one time or another he twirled around once or twice a flat dish, for that way no motion of the water is perceived; but, if he had proceeded further, then he would have understood whether or not the water is moved at the bottom of the dish, or resists it. For if a reed or bit of chaff which has been placed in the water is not far away from the inner edge of the dish, it is carried

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around very swiftly, and when the dish has been stopped {p. 48) you will see that the water with the bodies in it does not cease to be moved for a long time, but from the impetus received it is driven around with a slower and slower whirling. Lest anyone believe that we tested this negligently and carelessly, we obtained a brass hemispherical

Fig. 9 vessel skillfully hollowed out on a lathe, and we undertook that the axis C E be turned on a lathe and joined to the dish itself so that the axis would pass through its centre as a spherical axis—if it were prolonged. Furthermore, we constructed a firm and stable foot lest it be agitated by the motion of the vessel, and we caused the axis to be drawn through the hole E, erected perpendicularly and fixed in the lower part on a support. Thus, when the axis was twirled about by hand, the dish was necessarily carried around by the same motion. But not only water was carried around by the motion of the vessel, but the air itself, from which especially Galileo took his example. This is shown by the flame of a candle which has been placed very close to the internal surface of the vessel, and which has its slight body deflected to the same direction in which the vessel is moved. It is shown more clearly with a small paper slip suspended on a very

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slender silken thread A, one side of which is very close to the inner surface of the vessel. For if the small dish is moved in one direction, the paper also turns itself toward that same direction; and again if the vessel is turned by a reciprocal revolution in the opposite direction, it also draws with it the paper, with the adhering air, in the same direction. I have no few witnesses to the fact that I say this not more surely than truly; first, many fathers of the Collegio Romano—however, many others were willing to recognize this on the authority of my teacher—and many others as well. I ought not be silent about that one among them whose name is very well known to me not more by birth than by his singular erudition, {p. 49) and who can verify my activities and substantiate my remarks. I speak of Virginio Cesarini 36 who was astonished that a thing that many today hold for certain could ever be proved false; and yet he saw what was done, which many denied could be done. These things are certain from experiment; yet if this experiment were lacking, reason itself would also teach them. For since air and water are humid things, the property of which is to adhere to bodies whether polished or smooth, it can never occur that they do not adhere to the surface of vessels; if this bond of adherence be admitted, it is necessary that the motion of these humid things also be admitted. For that first part which touches the vessel, that is, that which adheres to the vessel, will be moved at the direction of the vessel; then when this part has been moved, it draws another part adhering to itself, and this second, a third. Since this motion is made in a spiral, it is not astonishing if the motion of the water is not perceived at the first or second rotation of the dish, since the first parts of this spiral are very near to the surface of the vessel, and therefore the motion has not yet been transmitted to the remaining interior parts, since they undergo some rarefaction and therefore do not immediately follow the motion of that which is drawing. Nor in these experiments of ours should anyone be astonished that the motion of the air is so slight and of the water so great. For since air compresses and rarefies more easily than water, so that at the motion of the vessel the air adhering to it is very easily moved,

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yet this air does not draw the air very near to it with the same facility, because that is restrained with greater force by the remaining parts of the unmoved air and by its slight compression or rarefaction it is able for a short time to resist the drawing force of the air (in motion). Yet if anyone desires to test more clearly whether a spherical body driven circularly draws the air with it—this globe A, for example, (p. 50) supported by its poles Β and C—let it turn by the handle

θ Fig. 10

D, a piece of paper depending from a very thin thread E, so that it almost touches the globe; for when the sphere is rotated in one direction, the paper F is carried in the same direction by the air which has been moved, especially if the globe is very large and is turned very rapidly. However, from this small movement of air which we experience now in the dish, now in the sphere, it is not correct to infer that the same motion would be very slight in the concavity of the moon. One reason among others why there is no great motion of air in the sphere A and in the dish I, which have been turned about is this: since the whole dish and sphere have been placed in the air, and the circumfused air must be moved by their motion, that which moves is always less than that which is moved. If, for example, upon the motion of the sphere A, the surface of it Β C ought to move the air adhering to

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it, represented by the circle D; then since the latter is greater than the circle B C , the greater will have to be moved by the lesser; and the same occurs when the circle D must draw with it the circle E. But in the concavity of the moon, the situation is the opposite since

that which moves is always greater than that which is moved; for in the circle, £ is the concavity of the moon which must move the circle D, but D must move the circle B C ; the motion of the mover is always greater, and therefore the motion is easier. Although I have no doubts about this, yet someone may consider that I separate the air circumfused about that dish from that which is enclosed within the dish, expecting that surely there would be no doubt that the same air, {p. 51) which before was carried more tardily than the water, afterward would undoubtedly be carried along with equal speed in a circular course by the circumduction of the dish. Therefore, lest the view be impeded, I prepared a transparent plate of Muscovite stone, which we commonly call mica, equal in extent to the orifice of the dish; then I fitted it to that dish with a hole about the size of three fingers—which, however, could be smaller— left in the middle; next I took a copper wire Ε F, considerably shorter than the width of the dish and flattened out and perforated in its middle part I, and led the wire I G through the hole I. I suspended it like a balance from G, and attached two paper wings to the extremities Ε and F ; then when weights had been added to each end, later

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to be removed, I arranged the equilibrium of the copper wire so that the support I was centred under the dish but the wings were at least a quarter of an inch from its surface. When the vessel had been twirled around, I noticed that after a second rotation the wings and

G A

y C

Β

1 ™

Fig. i2 the whole balance were moved in a circular course, first slowly and then more swiftly, but, however, they did not yet equal the motion of the water; therefore I superimposed the transparent plate Α Β , which I had prepared so that the air contained in the dish might be separated from that outside except for the single hole C. Then the balance F seemed to be carried more swiftly at the motion of the vessel, and for a little time it began to be driven so swiftly that the motion of that dish, although very swift, followed it. Thence you may see that whenever the mover was greater than the moved, the motion was far easier; for the lid A B having been placed on the vessel, then it was by the motion of the inner surface of the dish and of the lid at the same time that the air had to be moved, and this was greater than the neighboring air which was being moved, for that surface was the container and the air was the contained {p. 52) Finally, I tried the same thing in a glass sphere A with a similar result in so far as it was able to occur, with only the highest part C perforated for inserting the plate I. For when the same sphere had been placed on the axis B D , and the axis itself had been turned

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around, not only the sphere A, but also the suspended plate I, although far distant from the interior surface of the sphere, were seen to be moved very swiftly. Thus I decided that no industry or labor ought to be spared in order to prove this by many and very careful

Fig- 13 experiments. Those same ones who were mentioned by me earlier saw these final experiments, but I do not consider it necessary that they testify again. However, I decided that it ought to be noted that we had tested all these things in the hot season when the air was warmer and thus drier, approaching therefore more to the nature of fire which Galileo believes is the least suited of all the elements for adherence. From all these things, it may at least be gathered that by the motion of the dish both the air and water were moved, and that air adheres to smooth bodies and is driven at their motion; Galileo constantly denied these things. SECOND P R O P O S I T I O N : N O T M O T I O N BUT F R I C T I O N , BY W H I C H T H E P A R T S OF A B O D Y ARE L O S T , IS T H E C A U S E OF HEAT. AIR CAN N E I T H E R BE W O R N AWAY NOR 36

KINDLED

Aristotle says that motion is the cause of heat; all explain this proposition so that the heat must not be attributed, as it were, to

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motion as its special and intrinsic effect, (j>. 53) for this is attainment of place; but since bodies are worn away through local motion, and heat is aroused by friction, indirectly at least, motion is called the cause of heat; nor did Galileo refute Aristotle on this matter since, as yet, he had offered nothing in disagreement with the remarks of the latter. But when he says that no friction whatsoever can produce heat and that in addition it is necessary that some parts of the bodies be worn away and lost through friction,37 all this is his and nothing is borrowed from another. But why is this consumption of parts required for the production of heat ? Can it be that it is necessary that bodies become rarefied for the reception of that heat, and that the bodies seem to be broken up in all cases of rarefaction, and all the particles fly away in very small pieces ? But bodies can be rarefied without separation of the parts, and therefore no consumption. Or is this breaking up into small pieces required so that first those particles, as they are more suited for the reception of heat, become heated and afterward give heat to the rest of the body ? Not at all, for it may be that the smaller those particles are the more suited they are to the reception of heat, as occurs in the case of iron filings which have been struck often and disappear into fire through friction; yet when first they fly or fall away, they are unable to give heat to the rest of the body to which they do not adhere. But if one desires to seek examples from experiment, what if, with no loss of parts, some body becomes hot from motion ? After a very small bit of copper has been wiped clean of all oxidization and rust so that no little bits adhere, I weigh it very carefully on a precise and very exact banker's scale with the smallest weights—since I may have J J T S of an ounce; then I beat that copper out into a sheet with very strong blows of a hammer, and with two or three strokes and blows of the hammer it becomes so hot that it may not be touched with the hand. But no matter how many times it has been made hot (p. 54) and the same scale and the same weights are employed to discover whether or not it has suffered some loss and sacrifice of weight, yet I have found that the amount is constant; therefore that copper becomes hot through friction with no loss of its parts. Galileo denies this. I have also heard that something similar occurs in the

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binding of books when the binder strikes the folded signatures of paper very hard and for a long time with a hammer; for afterward it is found that they are of the same weight as before although they were greatly heated by the blows and almost burned. If perhaps one asserts here that parts are lost but so minute that even an exact balance does not reveal them, I ask him whence he learned that such parts were lost; for I do not see in what other way I could have examined the matter more properly and more carefully. Then, if this loss of parts is so slight that it cannot be perceived by the senses, why did it excite such heat ? Furthermore, when iron is smoothed with a file it becomes hot, but less or certainly not more than when it is struck very hard with a hammer; and yet the loss of parts is much greater from filing than from hammering. Therefore I believe that much depends on the greater or lesser heating of the bodies worn away and their qualities, that is, that they are more suited to heat or cold, and that this matter depends on many other things which it is not so easy to establish. For if you rub together two wooden sticks of very light and rare substance or employ the friction of some other piece of wood, they will in a short time take fire; this does not occur in the case of other very hard and dense woods even though they are rubbed together vehemently for a very long time and worn away. Indeed, Seneca says, 'Fire from friction occurs more readily in warm air,'88 from which, as he says, it results that there is much lightning in the summer because there is much heat. Furthermore, iron filings cast into a flame take fire, but not marble dust. Wherefore if there is much hot exhalation in the air, (p. 55) it happens that it may be subject to some friction, and I do not see why it could not become hot and even kindled; for at that time, since it is rare and dry and has much heat mixed with it, it is very well suited to receive fire. Although Galileo laughs at and attempts to make a joke of Aristotle's example of the iron tip of an arrow becoming hot through motion, yet he cannot do so; for not Aristotle alone asserted this, but almost innumerable men of great name have presented examples of this sort—undoubtedly from things which they themselves observed or had been told by observers. Does Galileo desire that I

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present here some of the many who assert this not less truly than exactly ? I begin with the poets, satisfied with those whose authority is considered great and is usually presented in very serious matters, because they were very well trained in knowledge of natural phenomena. Ovid, skilled not only in poetry but also in mathematics and philosophy, testifies that not only arrows but leaden balls hurled from Balearic slings have often been kindled in their course. For in the Metamorphoses he says:' It was kindled not otherwise than when a Balearic sling hurls a leaden shot which flying along is heated by its motion and discovers fire in the clouds which it did not know before.' 39 Lucan, very well known for his talent and doctrine says similar things: 'Thence firebrands and stones fly, and shot melted by its passage through the air and fused by its heated weight.' 40 What of Lucretius, no less a philosopher than a poet ? does he not testify the same in many places ? ' . . . a leaden ball also melts whirling on its long course'; 4 1 and elsewhere, ' I n much the same way as a leaden ball often becomes hot in its course, when it loses many bodies of cold and has taken fire in the air.' 4 2 Statius agrees with this when he says: (p. 5 6 ) ' . . . shot which will burn through the empty spaces of the sky.' 4 3 What of Virgil, greatest of poets ? does he not twice affirm this very clearly ? For when he describes the games of the Trojans he speaks thus of A c e s t i s : ' For flying amidst the clouds the reed took fire and traced a path by its flames, and when it was consumed, disappeared into the thin air.' 44 In another place, speaking thus of Mezentius: 'With spears cast aside, Mezentius thrice whirled the sling with tautened thong around his head and split the forehead of his foe with molten shot, stretching him at his length upon the sand.' 45 Water proves that a very hard body can be consumed by a second softer one through attrition, carving out even very hard stones and breaking up and smoothing them off marvelously by daily dripping and by the sharp edge of the dashing wave; also we find that the corners of towers and houses are eroded by the force of winds. Therefore, when the air is condensed and is carried with great force, it wears away even very hard bodies and is in turn worn away by them. T h e whistling which is heard in the agitation of a wave is evidence of the densening of the air, which

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perhaps Statius meant when he said that enclosed air is traced by the whirling of the sling: '. . . and the Balearic wielder of the pliant thong whirls round his weapon with rhythmic motion and with his swing traces a circle in the air.'48 A hailstorm proves the same, for the higher the place from which it falls the smaller and rounder the hailstones; raindrops the same, larger from a lower place, smaller when they fall from higher since they are broken up and worn away in the air. But lest the testimony of poets, or the very name poet itself, seem suspect to anyone—although we know that they speak at least according to the common view of all—I come to other men also of great authority and trustworthiness. Therefore Suidas47 in his Histories under the word Περιδινοϋντες narrates this: 'The Babylonians (j>. 57) whirling about eggs placed in slings were not unacquainted with the rude hunter's diet, and by this method which the solitude of the army required, by that force they also cooked the raw eggs.' Thus he. Now if one seeks the causes of such things let him hear Seneca the philosopher, since he among others is approved by Galileo when he discusses these things philosophically. First in accordance with the opinion of Posidonius, he says: 'In the very air whatever is attenuated is at the same time dried and hot'; 48 and according to his own opinion: 'The course of the air,' he says, 'is not constant, but as often as by its more violent agitation it kindles itself, it has an impulse to flight.' 49 But these things are stated far more clearly elsewhere, when seeking the cause of lightning, ' It happens,' he says, 'that when the air in the clouds has been rarefied it is turned into fire and has not found the strength to extend farther'—now let Galileo hear and consider what follows—'you are not astonished, I presume, if either motion rarefies the air, or extenuation kindles it; thus a leaden slingshot which has been thrown melts, and by the friction of the air falls in drops as if by fire.'801 do not know whether it can ever be said more plainly or clearly. Therefore, whether you believe the best of poets and philosophers and whatever doubt you may have in this matter, you see that the air can be worn away through motion and so heated that even lead is melted by its heat. For who believes that men who were the flower of erudition and speak here of things which were in daily use in military

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affairs would wish egregiously and impudently to lie ? I am not one to cast this stone at those learned men. I shall not conceal what Galileo may object against these things: For perhaps he may say that there never were slingers or archers of such power as to equal the force of cannon or bombard; that if the leaden balls fired by these bombards do not melt, even with the burning of the powder—and by this one thing, if any, they might melt—we may correctly conjecture that those comments regarding examples of melted lead and burned arrows were written by poets. {p. 58) But if Galileo were to object readily to these things, yet not equally easily might he test them, for I know that leaden balls fired by the larger bombards sometimes melt in the air. Certainly Homerus Turtura, a very recent and careful writer on French affairs, says that sometimes the great force of cannon balls, when they were small iron balls made much larger by a coating of lead, was useless for destroying walls. 'For,' he says, 'when they were fired into the walls, the lead having melted in the air, only the internal little ball of iron, like a nut with the husk shed, struck the wall.' 81 Furthermore, I myself have heard from those who had seen this, men of the greatest veracity, that when by chance the round, leaden ball fired from the cannon had struck into the outworks of the enemy's fortification and afterward was extracted from it, it was not round but longish and bore the shape of an acorn; this is also proved daily by examples, such as when musket balls of lead fired by a faulty shot often become entangled among the garments of the enemy and are discovered no longer in the shape they formerly had, but compressed, dented, and even crushed to pieces, (and from this it is apparent that having become rarer from the heat which they had incurred, they struck with weakened force). 51 * But we do not see these things happen daily. Indeed, the authors cited by us do not affirm that whenever the Balearic slinger hurled leaden shot from his sling it was melted by the motion, but only that this had once happened and was so unusual that it seemed almost miraculous. We also said above that a large amount of exhalations is required in air which has been worn out in order to excite fire from it, because drier things ignite more easily. For not rarely do we see

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it occur in cemeteries during the summer that at the approach of some man or other or at the blowing of a very gentle zephyr, the air filled with dry and hot exhalations immediately bursts into flame.82 What friction of very hard bodies is found here ? Yet {p. 59) that very light air ignites from motion and friction. This is what Aristotle meant when he said: ' When, moreover, it is carried and moved in this way, being well tempered it is often ignited by whatever it touches,'68 by which statement he clearly signifies that these things do not occur except under those circumstances which we have enumerated above. Therefore, when the condition of the air was such that it was copiously heated by exhalations of this sort, I say that leaden balls hurled from slings with great force would kindle the air by their motion, and in turn they would burn by that burning air. Therefore, there is no reason for Galileo to seek refuge in experiments, since we assert that in our opinion it would not occur except by chance, and it is a chance which, although you might desire it, yet it would be very difficult to achieve. But if perhaps one were to say that shot fired by cannon is kindled not from friction of the air but from the very strong fire by which it is propelled, although I cannot so easily persuade myself that a huge quantity of lead liquifies by that fire which scarcely touches it for the briefest moment of time, yet it is sufficient for the present to have demonstrated by these examples that no refuge is permitted to Galileo from the testimony of poets and philosophers. But he objects furthermore: Although it may be admitted that exhalations can sometimes be kindled from motion, yet he does not understand how it may happen that immediately upon taking fire they are not consumed, as we see occurring daily in the case of lightning, falling stars, and other things of this sort.84 I believe it can be well understood if, from those fires which the art and industry of men have discovered, one philosophizes that they are similar to those kindled by nature in those highest regions. For ours are of a double nature: some dry, rare, and joined by no cohesive substance, which when they take fire usually burn with a clear and profuse brightness; they are of sudden growth, but transitory and brief, with almost nothing left; others compressed and formed of firmer matter

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and pitchy liquid, endure for a long time and light up the nocturnal darkness for us with a long-lasting flame. Therefore, why not {p. 60) a similar situation in those higher regions ? for either light matter is so rare and dry that it is tied together by no binding moisture, and this is kindled into a sudden and swift brightness dying away in its origin; or it is viscid and glutinous, and if by chance it is kindled does not hasten immediately to its death but through its juices it lives longer, and in its longer life from on high it shines on all sides upon mistrustful mortals. Hence it is sufficiently apparent how it can occur that fires kindled in the highest regions of the air sometimes are not immediately extinguished but blaze for a very long time; it also appears that the air can be kindled, especially if those things are present which greatly contribute to the heat aroused by friction, that is, strong motion, a supply of exhalations, the attenuation of matter and whatever else conduces to the same.

THIRD PROPOSITION:

THE R A D I A T I O N

OF

LUMINOUS

BODIES IS A S E N S A T I O N OF T H E E Y E A N D NOT

ILLU-

M I N A T E D A I R , S I N C E T H E AIR C A N N O T B E I L L U M I N A T E D

When Galileo considers that brightness circumfused by luminous bodies, and which at a distance from those observing is not distinguishable from the luminous body itself, he says, first, that it occurs in the surface of the eye through refraction of the rays in the humor residing there and that it does not truly exist around a star or flame; second, he adds that the air cannot be illuminated; third, if luminous bodies are observed through a telescope, that spacious radiation is removed.66 For investigating the truth of these propositions, that which was put in second place must be considered by us first, that is, whether the air can be illuminated, for the rest depends on this. In this question it must be supposed first, from optics and physics, that light is not seen except with a boundary; but it cannot be bounded except by some opaque body, for transparency does not bound light but {p. 61) gives it a free passage; second, that pure and genuine air is especially transparent and therefore less suited for the boundary of light; but impure air mixed with many vapors can

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both bound and send back light to the eye. The first part of this second supposition is voluntarily conceded by all and by Galileo himself; but the second part is proved by many experiments. For, the dawn at sunrise and the twilight at sunset sufficiently indicate that impure air can be illuminated, and haloes, rainbows, mock suns, and other things of this sort which occur from thicker air testify to it. Galileo seems also to confess this in the Starry Messenger where he placed a kind of vaporous orb around the moon,6® not unlike that which is around the earth, which he asserts is illuminated by the sun; and he seems also to affirm it regarding Jupiter's orb. Furthermore, if one observes the moon before its emergence and when it is lying hidden behind the roof of some house, he will first see the greater part of the air brightened by the light of the moon, like a kind of lunar dawn; he will find this brightness to grow greater and greater the nearer the moon is to visibility. It is ridiculous to affirm that dawn, twilight, and other brightnesses of this sort arise through refraction in the humor residing in the eye. When I gaze upon the moon and sun carried higher and enclosed in a narrow circle, I am no drier in the eyes than when I catch sight of them afterward extended in a broader globe near the horizon. Therefore, it is sufficiently clear from these things that impure and mixed air can be illuminated, as is also proved by reason. For light is bounded by that which has some opacity; but air becomes more condensed and opaque through vapors, and at least in that part where it is opaque the light could be reflected. These things having been thus explained, I return to the proposed question. When many important authors assert that part of the air circumfused in appearance is likewise illuminated by luminous bodies, it ought to be understood that they speak not of pure air unmixed with vapors, (p. 62) but of that air which when it has been made opaque by denser exhalations can halt and restrain the light of the stars so that it does not proceed farther. For when they say that the sun and the moon display themselves to view in more ample form near the horizon than when they are higher, they assert that this occurs through the intervention of vaporous air; from these things it is demonstrated that they speak not of pure air but of

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corrupted and therefore more opaque air. Therefore, that opinion which asserts that air can be illuminated by the stars ought to be accepted rather than rejected—as Galileo orders—since if this matter of impure air is understood it may be proved very true by many experiments. If the air can be illuminated, some part of that luminous garland by which the stars are wreathed could also offer illumination. I do not deny that which had been proposed in the first place: that that radiant halo, distinguished by long rays, and which is moved at each movement of the eye, is a sensation of the eye; from this it occurs that the rays may now be many, now few, now shorter, now more extended, according to the movements of the eye. However, as yet, Galileo will not agree that no part of the light, which we do not distinguish from a true flame, arises from illuminated air; wherefore the luminosity cannot afterward be removed, even through the telescope. Nor does the experiment offered by Galileo oppose this: ' I f , ' he says,' the hand has been placed between a light and the eyes, and you so move it as if you wished to conceal the light, that circumfused brightness is never cloaked unless you conceal the true light, and the rays will nonetheless gather between the hand and the eye; but when you have covered some part of the true light, you will find that an opposing part of the same rays will vanish; for if you have concealed the upper part of the light, the lower rays cease to appear.'87 This is what Galileo says, and I find all these things very true when I consider only the rays themselves. Those rays, I say, I distinguish very well and separately from the true light by the almost constant motion and variation of their light; {p. 63) but when I attempt to conceal that light which I consider true light, if I do not entirely conceal it, at least I diminish and obscure it in that part where I interpose my hand; I obscure it, I say, because luminous objects cannot be concealed by any interposition of the hand so that they may not be seen. For if, as I said, one notices attentively when we attempt by the interposition of the hand to conceal the true flame of a candle some distance from us, even if the hand covers the highest part of the burning pyramid, yet we catch sight of it between the hand and the eye, and when a finger has been interposed that flame

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5

Fig. 14 is seen to burn divided, as it were, into two parts in that way which the finger A demonstrates. Thus I display how it may happen that from this interposition of a finger the appearance of the flame is not hindered. Since the pupil of the eye is not indivisible, but can be divided into many parts, one part of it can be covered while the remainder is uncovered; although the appearance of the opposed light does not reach it when some part of the pupil has been covered;

Fig- 15 if, however, the rest remains open it can reach to those images and light will still be seen. For example, let the light be B C , the pupil of the eye F A , the interposed opaque body D , which does not permit the image of the point C to reach to F ; yet let there be {p. 64)

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another unimpeded ray reaching from C to the part of the pupil A. Therefore, through the ray C A , the apex of the light C will be seen, but it will not be seen as bright as when it filled up the whole pupil with its image; moreover the same apex C does not cease to be seen until the body D covers the whole pupil and the apex C is not carried to it by any rays. If the body D were much smaller than the pupil of the eye—for example, some thick thread—and it were to be somewhat removed from the pupil while the light has been placed at a distance, in whatever way the thread is extended between the eye and the light it impedes no part of the light, nor will any part of the thread be visible when it has been placed between the eye and the flame, but it will seem to have been wholly consumed. This arises from the same reason. For since that thread is smaller than the pupil, if it is not far distant from it, it is unable to impede so that all parts of the flame, at least by some rays, contribute to the effect; therefore at least through them the flame will be seen. Finally, there are many things which also are not easily explained in regard to his third remark in which he says that the stars are despoiled of this accidental brightness when they are observed with the telescope, for if the telescope despoils the stars of this assumed brightness, it ought not to be seen through the telescope; but nevertheless it is seen. And, indeed, among the fixed stars there is none so small that it suffers that brightness to be removed by the telescope, even his own. Galileo seems to confess this when he states that that brightness can never be entirely removed from the Dog Star as well as certain others, for even through the telescope we always observe those twinkling rays in them. But why do I say from the stars ? Even the planets are so tenacious of some of this brightness that they never permit it to be snatched away from them; namely, Mars, Venus, and Mercury which—unless you drive back the light by colored glasses adapted to the telescope—will never be seen denuded of it. And if the true cause of those rays remains in the surface of the eye, that is, in the humor residing constantly in the pupil, if the light of the star, refracted through the glass of the telescope (p. 65) falls on the same humor, and again is reflected although perhaps in a different way, I do not see why that same effect of the light ought not be produced.68

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Now if that is admitted, as must be admitted—as we proved above— then the air also is illuminated, and from this it may result that a star appears larger than it really is; Galileo cannot deny, on this head at any rate, that circumfiised brightness is seen through the telescope, and therefore it ought also be augmented. Indeed, he confesses that all those things which have been placed beyond him are seen through the telescope and are augmented by it; therefore since this brilliance is also beyond the telescope, it will necessarily be observed and augmented by it. I f nonetheless this increment is not perceived in the stars, the reason for such appearance must be sought elsewhere, and not from the fact that this radiation occurs between the telescope and the eye; that is, in the humid surface of the eye. For if we speak not of those roving and distinct rays but of the stable and continuous garland of wider light, this can arise from the illuminated air as is proved by the examples of the sun and moon appearing near the horizon in a wider disc than in the vertex; but if we speak of the rays themselves, since they also are observed in the stars through the telescope, this very small enlargement of those stars could not be referred to the rejection of those rays since they are not rejected. FOURTH P R O P O S I T I O N : NOTHING LUMINOUS IS TRANSPARENT, AND A F L A M E DOES NOT P E R M I T THOSE THINGS TO BE S E E N W H I C H HAVE B E E N PLACED BEYOND IT

But let us see how correctly from Peripatetic doctrine and from experiments Galileo forges arms against Aristotle. 'Moreover,' he says, 'we deduced that the comet was not flame from experiment and from the statement of the Peripatetics (p. 66) in which they affirm that no lucid body is transparent. Experiment teaches that a flame, even the very smallest of one candle impedes the view of objects placed beyond it. Therefore, if anyone says that the comet was a flame, he will have had to say that the stars placed beyond it ought to have been concealed by it; and yet we saw those stars twinkling very brightly through the tail of the comet.' 89 In regard to these matters, I cannot be sufficiently astonished that the man, otherwise

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of great name and a great lover of experiments, can asseverate so plainly these things which are easily and completely disproved by obvious experiments. The statement of the Peripatetics, if correctly understood, is very true; for every body must, as it were, fix and hold the light from fleeing farther away, in order that it may be illuminated or rather appear illuminated; moreover, being transparent, namely, pervious to the light, it cannot bound it, and from this it must be said that any body ought to be illuminated more clearly the more opaque and less transparent it is. Nevertheless, there is no one who denies that bodies are found partly transparent, partly opaque, which bound some part of the light by which they appear lucid, but permit some to pass along freely; of this sort are the rarer clouds, water, glass, and many things of this kind which bound the light on the surface and transmit it at another part. Therefore, there is no reason why Galileo should think that anything of importance has been contributed by his experiments to this statement. His experiments are certainly to be considered false. Therefore I assert that the flame of a candle does not remove passage from the eye to an object placed beyond it, and it is transparent. First, the Sacred Scriptures agree with this statement when they consider Shadrach, Meshach, and Abednego cast into the furnace on the order of the king. For thus the king is represented as saying: ' Lo, I see four men loose, walking in the midst of the fire, and they have no hurt; and the form of the fourth is like the son of God.' 60 And lest anyone consider that this ought to be considered as a miracle, (p. 67) the same thing is again proved from the fact that the lamp wick in the middle of the flame of a candle is seen to remain either blackish or shining. Furthermore, when some huge pile of wood is burned, we readily observe half-burned pieces and burning coals in the midst of the flames, yet often the greatest force of the flames exists midway between the eye and that same wood. Therefore, the flame is transparent. Second, anything opaque which has been placed between the eye and an object impedes the appearance of that object, whether it is distant by a great or small interval; thus, for example, some piece of

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•wood, whether it is near the object, whether it be far removed from it—if, however, it is between that object and the eye—does not permit the object to be seen. This does not happen in the case of a flame, for whatever things are placed beyond it, if they are not very far away, it illuminates the nearby very strongly, but it always permits them to be seen; anyone can easily try this if he places something which is to be read at an interval of only one inch beyond the light, for then he may easily read the type covered over by the flame; therefore the flame is luminous and transparent, which Galileo denies, taking the opposite as an axiom, in opposition to Aristotle. But if anyone inquires why objects placed far beyond the flame are not observed, I reply that an object exerting a force very strongly prevents other objects which are less suited to exert the same force from being seen; all objects, the more lucid they are, exert the force more strongly than other similar ones, and therefore objects placed far beyond the flame are illuminated much less than the flame itself, so that the latter seizes and controls the whole force thus preventing other objects from being seen. Therefore, the nearer the objects are to the flame the more they are illuminated, and so also the more suited they are to exert the force, and {p. 68) therefore they are observed. Indeed, if they have been illuminated by a stronger light, they almost compete with the flame. Thus, if either the flame shines with a duller light or the object placed beyond it is luminous from it, or is illuminated strongly by another light, the interposed flame never prevents its appearance although that object may be very distant from the flame. This may also be confirmed by certain experiments. Let distilled wine, which is commonly called brandy, be burned; its flame, not being very bright, leaves a free route to the eye for the images ot things, so that even the very smallest type may be read through it. The same occurs in a flame rising from burned sulphur which although it is colored and thick, yet it offers scarcely any impediment to those same images of things. Second, a flame may be a very bright and shining light, yet it you place the light of another candle beyond it, you will observe the more remote flame shining through the light of the nearer flame.

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Therefore, since the stars are luminous bodies and far brighter than any flame, it is not astonishing if their appearance cannot be impeded by the interposed flame of a comet; and therefore Aristotle's opinion is not damaged by this argument of Galileo. Third, not only are those luminous things which shine by their own light unable to be veiled by an interposed flame, but not even opaque bodies if they are illuminated by another light. Thus, for example, if you look at something illuminated by the sun, no flame can impede its appearance. Therefore, it is clear beyond doubt that flames are transparent, and this also refutes the idea that the comet cannot be a flame. Also it ought not be omitted that Galileo is overwhelmed by the same argument by which he attacks Aristotle. For he s a y s : ' Flames are not transparent; but the beard of the comet is transparent; therefore it is not a flame.' {p. 69) But against Galileo I say: Luminous things are not transparent; the beard of the comet is transparent; therefore it is not luminous. The stars nowhere hidden by its interposition indicate that it is transparent. Furthermore, when Galileo contends that it is formed of illuminated vapor, he asserts that this beard is luminous, for illuminated vapor is a luminous body. Let him not say that he speaks of luminous things shining by an innate and special light and not of those which receive their light from elsewhere. These also impede the appearance of things placed beyond themselves; for if some glass vessel or jar were filled with wine or some other thing and exposed to the light, it would display the wine only in those parts from which the light did not reflect or gather illumination, but in that part where the light was sent back to the eye it would oiFer nothing to the observer except something lucid and shining. The same thing also occurs in waters illuminated by the sun. Nothing placed beyond that part of them from which the sun is reflected to the eye can be seen, but the remaining parts display the pebbles and plants existing on the bottom. Therefore, it will be seen that illuminated bodies also veil farther objects, and these bodies can also be called luminous. If therefore, according to Galileo, these admit of no transparency, we cannot see the stars through the beard of a comet either luminous or illuminated; yet we were able

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to do so, and therefore the beard of the comet was illuminated and transparent. I was very happy to present all these things so that anyone may understand them easily since they depend not on those trifling lines and angles from which not everyone understands equally easily how to disengage himself; for here, if one has eyes, he has sufficient talent. In addition, Galileo objects that Aristotle wrongly predicted from comets that the year would not be very rainy but rather dry and portended great winds and earthquakes. For, he says, since {p. 70) comets are, according to Aristotle, nothing but fires like monsters, very voracious of exhalations of this sort, if you say that no remains ought to be left by them, you speak very wisely.· 1 But I believe that the matter ought to be considered otherwise. For if in some city a great supply of grain is considered to have been distributed carelessly through the squares and streets, or if perhaps you see the least significant officials and the mean rabble always feasting sumptuously, do you not thence wisely deduce from such abundance of grain and of the whole food supply that in that place no scarcity ought to be feared for a long time ? Clearly such is the case. And the region of the exhalations is enclosed within narrow boundaries like a granary, nor is it easily led to those regions which the voracious flame controls, except when a huge supply of them cannot be kept in the lower region or perhaps they have become very dry and rare and have lost all quality of moisture. Therefore Aristotle not ineptly inferred from comets, that is, in regard to the fire produced from exhalations of this sort, that all these lower regions had not a moderate but a great profusion of them.ea Nor does it follow from this that there are no remains of those exhalations, for the fire consumes only those things which are raised above the rather cramped quarters of the lower regions to the region of the fire. That fire which afterward breaks out not in an alien region but always fixed in its own kingdom acquires for itself those things which approach nearer to it, or, as it were, things which have fled from more moist areas are lacking to it; and therefore Aristotle was able to foretell winds, a very dry climate for the year, and other things of this sort. If anyone

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foretold such things of our comet, he was able to confirm them very well from the outcome. For the year was dryer than usual, and we experienced winds blowing with unusual force, while a large part of Italy was struck by earthquakes, and in some places with no little damage to cities and towns. What then? did Aristotle not speak wisely of these things and many others? {p. η ι) I consider that what can properly be inferred from all these things ought to be heard not from me but from Galileo. When he had presented his experiments he added: 'These are our experiments and our conclusions drawn from our principles and our optical reasons. If the experiments were false, if our reasons faulty, the basis of our remarks would also be infirm and weak.' 63 I believe that nothing need be added to these remarks. These are the things which I considered ought to be said in this disputation because of my respect for my preceptor. I presented these matters, attempting first that just complaints be made to Galileo—and this was the chief purpose of writing—on behalf of my preceptor who always held him in honor; then that in that published Disputation we were able to measure the distance of the comet from the earth through observations of its parallax and motion; that from the fact that the telescope magnified the comet only slightly we gained important confirmation for our theory; furthermore, that Galileo was not justified in excluding the comet from the number of true lights and in prescribing such rigorous laws of very straight motion for it. Moreover, it is clear from these things that the air is moved with the motion of the sky and is worn away and can be heated and kindled; from that motion heat is aroused through friction, and no part of a body which has been worn away is lost; the air can be illuminated whenever it is mixed with very thick vapors, and also bright flames are transparent, which Galileo denies is the case. Finally, those experiments have been considered false by which these almost unitary conclusions are proved. I wished to intimate these things rather than explain them more fully so that it may appear to everyone that no wrong has been done to anyone in our disputation, nor were we influenced by weak reasons in our preference for that opinion which we have presented.

LETTER T o the Very Reverend Father Tarquinio Galluzzi of the Society of Jesus by

MARIO GUIDUCCI In which the latter justifies himself against the imputations made against him by Lothario Sarsi of Siguenza in the

Astronomical & Philosophical Balance

FLORENCE 1620

VERY REVEREND F A T H E R , AND E S T E E M E D

SIR

Had the author of the Astronomical and Philosophical Balance kept himself within the bounds of defending Father Horatio Grassi's opinion about the distance of comets based upon their receiving little or no enlargement from the telescope, which opinion I attacked in my Discourse to the Florentine Academy, and even if he had gone on to refute any other conclusion whatever that I had affirmed in that discussion without going on to make imputations and biting remarks, as he has done, I should gladly have conformed to your judgment, most reverend Father, and terminated this dispute by my silence. For with very tranquil spirit, I should without the least anxiety have left the decision to men of science like yourself, freely renouncing that popular favor which in such literary controversies always proclaims that man the victor who contends the most pertinaciously. But their esteem and applause are much easier for me to deprecate than that opinion which others may have conceived because of Sarsi's reproach that I far exceeded the bounds of politeness and education; hence I am obliged by the duty every man feels toward his own good name (for it is there that I have been stained) to depart from your friendly counsel—but not so far as to lose sight of that moderation which you have urged in me. Though I have been resolved to respond from the beginning, ever since his book appeared, both of my own choice and by the advice of others, still I have deferred until the present so that by the maturity and tardiness of my defense it would the better appear that my action is not blameworthy, nor that I am driven by sudden impulse and hasty anger, like a snappish dog, in an attempt to retaliate and avenge myself. But as those whom Caesar has angered appeal to Caesar not angered (though I have never harbored in my heart any anger toward Sarsi, nor so much as entertained it), I have tried also during my procrastination to justify my own rectitude before the tribunal of my conscience, purged not only of anger but even of that righteous indignation or nemesis which those who favor Sarsi with their inconsiderate plaudits (and perhaps without even having read my essay) F

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might have been able to provoke in my soul; and I leave judgment in this matter to the forum of forums—to yourself and the other reverend Fathers of the Collegio. Meanwhile, I place myself before your Reverence as a defendant, to render an account of the facts and of my intentions in that treatise of mine; taking heart from the purity of my conscience and in the uprightness of your judgment, I do not fear an unfavorable decision, inasmuch as Sarsi in this cause pretends with too much animosity that he has been outraged and offended. T h e Florentine Academy (as I believe you well know, reverend Father) was instituted by our elders to the end that the Academicians should exercise themselves in speaking and should cultivate and increase the beauty of our language. In this sort of exercise, the Academicians have been accustomed to employ themselves from time to time—especially the Consul, and those upon whom the Consul has imposed the duty of so doing. Being at that time placed in that office, my reason for setting myself to compose that treatise was most certainly not to gain fame among the people for giving answers in the manner of an oracle, but to exercise myself, and by my example to incite the youth to employ themselves in this praiseworthy and native talent. Conforming thus to tradition, I undertook to find some subject or other to discourse upon in our mother tongue, both because that was suited to the place and because of the capacity of our language to be understood not only throughout Italy but everywhere else that good literature is valued, being everywhere studied with interest and mastered—and in particular by that serene Prince to whom my Discourse was dedicated, who (to everyone's great admiration) speaks and writes it exquisitely. In this, I did not depart from the example of Sig. Galileo, who has also set forth his marvelous ideas in this idiom—nor has its scant fame concealed or hidden any part of that glory (if Sarsi will permit me so to speak) which he has procured before the world. Therefore, in order to speak of something which would find favor with everyone, I found no subject more appropriate to select than that one which then, because of the recent appearance of the comet, was awakening the minds and filling the mouths of all. Examining in this connection the opinions of the most famous ancient and modern philosophers, I

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placed among these the reverend Mathematician of the Collegio Romano—leaving out many who had written and published on this subject with no less distinction. I never dreamed that to disagree with his opinion could possibly be interpreted as an injury by his Reverence or by any of his followers, especially as I referred to it with the greatest possible honor and respect. And who would ever have believed that in the republic of letters there would be found minds so tyrannical as to want to restrict the liberty of men's intellects to the approval of their own caprices and opinions; men who would organize a crusade against those who did not believe with them, just as they would against the Saracens and infidels? Let Sarsi remain in such slavery if he wishes; but let him not pretend to drive you in his company perforce, nor believe that this practice which he attributes to his master (or which his master attributes to himself) is the rule and standard that is to govern the world of letters by the rod, and to depart from which is to be considered sinful. Too remote from the gentleness and good will that your Reverence has described to me in Father Grassi would it be if to go contrary to his opinions were to be considered an injury by him; too high would be the throne upon which he would be seated if his judgments could not be appealed. But often, the factions and the indiscrete partiality of pupils, through indecent praises and immoderate applause, work prejudice to the masters without any blame falling on the culprits. And who is this that undertakes to speak for a person who, like Father Grassi, makes profession of a religious life—that is, one of humility and modesty—and is not yet eminent in letters by any of his works, if I may speak frankly, but who will presume to write (or at least to permit that others write of him) the following words which occur in the proem of the Balance ? ' In the present year three unusual splendors being seen to shine resplendently in the sky, there was no man so base or so little curious as not to turn his eyes to them, admiring in that time particularly the generous display of unaccustomed lights. But as the common people, though they are eager to know, are equally unable to investigate for themselves the causes of things, they therefore required as their right that those to whom the contemplation of the universe and the

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sky principally belongs should unveil these secrets to them. Therefore, turning to the Academies of philosophers and of astronomers much more than to any others, they had their eyes and minds upon the Gregorian Academy, which, being well supplied with science and filled with valiant and skillful Academicians and therefore being greatly venerated and famous above all others, is easily understood to be the one from which, as from an oracle, the common people awaited the replies to their questions.'1 Although these words appear to relate to the Collegio Romano, as to the giving of replies they are verified in the person of Grassi, the only professor of mathematics at that time in the said Collegio, who alone among those Fathers wrote concerning comets. These praises, Ο Sarsi, are too prejudicial to the master, nor did he certainly accept them. And that noble Collegio, although it well might do so, does not give itself such airs. It has done quite well with its very learned studies; but it is not therefore ambitious. The first thing one learns there is modesty, and everyone is taught the small esteem that should be given to oneself. Thus Sarsi offends with his praises as he does with his imputations. Indeed, the latter appear to me less harmful than the former. Therefore, so far as I am concerned, it will be much easier for me to defend myself against Sarsi's criticism than it will be for Father Grassi to take away from the world the opinion that it is by his consent that others have written in his praise in such a manner. For not everyone is as much a connoisseur of the teachings and the style of these Fathers as am I, who spent a large part of my youth among them. Great virtues excite great emulators who easily persuade themselves that the possessors of those virtues credit themselves with them very strongly, and sometimes more than is proper. But perhaps there will not be lacking to the Mathematician and to the Collegio the means of determining who among them held so false a belief. The thing that affects me is the discourtesy and the mordancy with which the Balance is filled to overflowing. These are of two sorts. One consists in attributing my writing to someone else; the other, in attributing to that writing what it does not say. First of all, I firmly believe that Sarsi was motivated not to let that happy and witty joke about the Consul and the Dictator go to waste.

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He says that Sig. Galileo having openly written to his friends that the Discourse on Comets was his, and I having ingenuously confessed this, it should not appear wrong to me for him to deal rather with the Dictator than with the Consul. In this play on words, I can clearly show Sarsi's little erudition and his small knowledge of Roman history, seeing that those magistracies are not compatible, and there never was a case in which an enemy of the Roman people could leave the Consul in order to combat the Dictator. But I do not wish to go into this; for my discharge, it suffices merely to make manifest how true were those words of mine from which, out of a sincere wish not to advance myself by the inventions of others, has been deduced the subtle and simulated simplicity with which Sarsi finds occasion to mock me. Please note, your Reverence, the courteous credulity of this fellow, and see how far he will go to assume more than I have written. In the proem of my Discourse, I say t h a t ' I shall set forth to the Florentine Academicians that which ancient philosophers and modern astronomers have remarked upon similar cometary events, and examine their opinions diligently so that it may be seen whether these give satisfaction. Then I shall set forth—not positively but merely probably and with reservations, as I think proper in so obscure and difficult a matter—those conjectures which have taken form in the mind of our Academician Galileo.' 2 U p to this point, I spoke not of copying, but rather of recounting the opinions of the ancients and of the moderns, and among them the opinion of Sig. Galileo, to which I incline more than to any other. That which follows and which contains the word 'copyist' has relation and reference to some who have tried to appropriate Galileo's inventions and who call themselves Apelleses, and is plainly seen to be taken metaphorically from painting and coloring the designs of others; when such works come from the hands of excellent masters, they are so distinguished that the most celebrated and superb professors of that most noble art achieve a special glory from coloring and retracing them. This happens especially with the works of that man, as the poet says, . . . ch'a par sculpe e colora, Michel ρϊύ che mortal Angelo divino;*

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whose designs and pictures the famous Jacopo da Pontorno did not disdain to color and to finish. And not only has the coloring of others' designs sometimes been honorable to painters, but copying the canvases of other men has even brought them no less appreciation and fame than the painters of the originals. Thus this is clearly seen in a copy which the famous painter Andrea del Sarto made of a picture by Raphael of Urbino which connoisseurs of art have praised and admired as much as the original. Now just as it would be quite wrong to Jacopo and Andrea to call them copyists, because in their works they show themselves to be exquisitely understanding and to be masters of color and design, so it seems to me that other men are wronged by being called copyists when in treating a philosophical question understandingly they take some idea from one author or another and, as does not happen with those who merely copy the writings of others, make it their own in this way, judiciously adapting it to their purposes in order to prove or disprove some statement. If this were not so, then those who daily publish huge tomes in the various sciences and professions ought to be called copyists, seeing that for the most part these labors of theirs consist in selecting various propositions and arguments from different authors, which, variously divided and arranged, result in those marvelous compositions and very learned books. T o give an unexceptionable example, in this sense Father Cristopher Clavius would have been an egregious copyist, having been so diligent in reviewing and compiling in his very erudite works the opinions and demonstrations of the best and most illustrious geometers and astronomers who had existed up to his time—as seen in his compendious commentary on Sacrobosco,4 and in so many other of his works. A similar attempt to represent as upon a canvas the differing opinions of authors on comets for the savants of the Academy was thought to be worthy of praise and not of derision. And my work was the more welcome to that learned audience because I gave them not only those things which had been written and published by others before me, but also the sketches and thoughts of Sig. Galileo which had been communicated to very few people, or perhaps to no one else. These, tentative and merely probable though they were,

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were nevertheless so highly applauded that I was obliged to put them into print. Wherefore, because I wished to attribute to its own author each of those doctrines that I had made use of in that discussion, Sarsi found occasion in this for his mockery. But let him say what he will. I have always deemed that praise fair and generous which is attributed to Socrates in the Lesser Hippias (and have thought I might manage to deserve the same) of never arrogating to himself the inventions of others, but of always celebrating and exalting the true originators and those to whom they belong.® And if during Plato's lifetime he magnified his gratitude toward his master and honored him in his dialogues by always having him sustain and defend the more reasonable side, why must Sarsi mete out disgrace and blame to me for having studiously sought to emulate the divine skill of that great man ? Let him not reply that the nature of dialogues is such that most of the time the persons introduced into them have never so much as dreamed of that which they are there fated to say, for Plato himself, in his second letter to Dionysius, expressly declares that he has written nothing of his own, and that nothing is to be found which is a work of Plato, but that what he wrote and published came to him from Socrates his master, who was a very brilliant man and illustrious all his life for his virtue as well as his teachings. Now would it not be a great impertinence and a rashness on the part of any man to call Plato a copyist, and to disdain to quarrel with him but to prefer disputing with Socrates as Dictator? And such is my 'ingenuous confession' with regard to having copied that Discourse. Then as to Sig. Galileo having openly written to his friends that he was the author: since I have a great deal more faith in Sig. Galileo who denies this than I have in Sarsi who affirms it, I am confident of the denial, which will be more clearly evidenced by a treatise of Galileo's which is shortly to appear. I pass on to the other point of the accusation—the attribution to the Discourse of that which it does not say. This is in two parts; in one I am strongly attacked for ingratitude because of having spoken without respect of the teachers at the Collegio Romano and having held their dignity and reputation in small esteem; in the other I have been burdened with conclusions and doctrines that I have not held.

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These pricks, though they appear to be directed against Sig. Galileo, come against me when I profess that that discussion was my own. As to the first point, therefore, vain is the long account which Sarsi gives of the honors which at different times and occasions have been paid by the teachers and mathematicians of the Collegio Romano to the inventions and marvelous discoveries of Sig. Galileo by approving these and celebrating them and their author with high praise; and vain is his deduction of Galileo's ingratitude, since the Discourse on Comets is mine. Indeed, this criticism would tacitly turn to wound and transfix me too painfully if I should ever so little recognize that in speaking my opinion too freely I had given any sign of not having deeply at heart the reputation and dignity of the Collegio Romano, in which I was brought up as a youth with incredible and paternal love, and (though because of my incapacity this may not appear) instructed in the highest and most sublime sciences which elevate the mind of man. I am not eager to tell here in my defense how, before making that discourse in the Florentine Academy, I had given it into the hands of many learned men, among whom there were some who were closely connected with the Fathers of the Society not only by friendship but even by kinship, with permission to take out of it anything which appeared to them likely to aggrieve any person, or which seemed to them to be prejudicial to anyone. But I shall here set forth faithfully all that of which Lothario Sarsi complains, and cite the places in the Discourse, for I am assured that your Reverence and every judicious and dispassionate reader will not wish from me any more patent amends or exculpation. He complains in the first place that on page 50 his master has been called ignorant of logic. Here are my exact words: 'As to the confident statement that the motion of comets is along a great circle, important points are lacking in the demonstration, and their omission gives evidence of defective logic.' The reason for this is set forth, and it is chiefly Tycho Brahe that is thus referred to. On page 41, the mathematicians of the Collegio are spoken of with honor, it being said that the argument to prove the comet remote from the earth which is taken from its slight enlargement when seen through the telescope was at first regarded by me as of little or no value, but that

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upon hearing the name of the place from which this argument came, I changed my view, and wavered for a long time over the reasoning by which our oft-mentioned Academician had persuaded me to the contrary. On page 36, likewise cited, I did not say positively that the professor had sworn fealty to Tycho, but merely that he appeared to me to have subscribed to Tycho's statements. On page 52, I said I was induced to believe that the above mathematician had accepted the same Tychonian hypothesis when I saw throughout his writing how much he agreed and accorded with that position and with other Tychonian fantasies. These are the places noted and criticized by Sarsi, and in which he says his master has been so much vilified and outraged. These had been very carefully looked over and considered well by learned and religious men without being criticized for mordancy, nor has anyone recognized wherein consists the reputed sting—unless merely having differed from Father Grassi has been held to be a shame and an injury. But this is absolutely denied by the Fathers, for I have unquestioning faith in what your Reverence signified to me—that every man being free in this sort of matter to adhere to either side, no prudent person would take it ill or deem it a malicious affront for me to dissent from the Problem, provided that I did not exceed the bounds of disputation. As I had punctiliously followed this admonition, I was certain that my oppositions would be not odious but acceptable and welcome to those Fathers, since they might serve to cast some little light upon the determination of the truth (of which in this instance I remained equally dubious and undecided). But Sarsi, not welcoming at all the little bit of light that I offered, has tried instead to obscure it and extinguish it so that others would not benefit by it, and he raises against it various accusations and impostures, and in divers ways he antagonizes the readers against me. On this point, I shall not neglect giving the lie to that lamentation of his on page 72, that denigrating the wit and the words of his master, I have said Nature does not delight in poetry; for anyone who will consult the passage cited will be astounded at the boldness and brashness of this young man in putting forth something which can be so easily refuted, nor will he then be much astonished at the other impostures. Your Reverence, please read

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everything on page 49 of my Discourse, and if there you find a single word which by any stretch of the meaning might be interpreted as having been said by the author of the Problem, I shall admit whatever Sarsi says against me in that Balance of his. Tycho had said (perhaps finding no other way to save the irregularity of the motion of comets) that they are apparently imperfect planets and are like mimes of the true planets, and that being thus obliged to imitate the motion of planets they do not thoroughly acquire such movement, though they are in every way celestial offspring. Against this conception, I write precisely these words: ' T o say with Tycho that some such heavenly condition suffices to those imperfect stars, which, although defective, have a natural inclination to every manner and custom of the skies, savors much more of poetic grace than of scientific soundness and rigor, and deserves from you no consideration whatever, since Nature takes no delight in poetry.' 6 With no greater veracity than in the foregoing, Sarsi saddles me with doctrines and conclusions that I have not held and do not hold to be true, in order then to have a field in which to vanquish them and thus expand the size of his volume. How he schemes to prove that objects visible to us with the telescope and invisible without it do not receive infinite enlargement! But when have I said they did ? Father Grassi declared in his Problem that the fixed stars, being immensely distant from us, receive no magnification at all upon being viewed through the telescope. I said, on the other side, that they increase in the same proportion as do nearby objects. And in proof of the magnitude of such augmentation it was added that we plainly see the Medicean planets and other stars which are sought in vain with the naked eye, nor do I know why that author or others should call such enlargement insensible when it rather would seem to be infinite. It should have been clear to Sarsi that in this argument I had not given credence to such 'infinity', having more than once remarked that the intervals and objects in the sky appear to us to be enlarged in the same proportion as are all other objects on the earth at small distances, which proportion could only be finite. Not unlike this trick is his saying that I affirm[the comet to be not a real thing but only an apparition, and that it moves with a straight

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motion perpendicular to the earth; these two propositions I adduced only dubitatively. As to the first, I said on page 39 'that if in refractions, reflections, images, appearances, and illusions parallax has no efficacy for determining distance, as with any motion of the observer these also are changed, I believe that parallax would not really have any efficacy with respect to comets unless it were first determined that they were not like these reflections of light, but were unique, fixed, real, and permanent.' And here, I went on to show the agreement and analogy between those simulacra and comets, leaving it then to the listening savants to decide upon one or the other alternative. Nor did I affirm more than this of the straight and perpendicular motion of the comet from the earth, saying only that with such motion the obstacles would disappear or be smoothed out which at every step impede those who assume Tycho's cometary orb. It would take me too long, and I should trespass too much upon the common domain of letters, if I were to go along collecting and refuting all the criticisms and imputations put upon me by Sarsi. Therefore setting this aside, I shall put to the test the experiments and doctrines with which he pretends to beat down some of the propositions in my Discourse. Let the first of these be that in which, more than in all the rest of his essay, he has done his best to convince people of the falsity of an experiment which I adopted for proving that the motion of the celestial spheres is not accompanied by any sweeping along of the inferior elements. I said that if a round vessel is rotated with any velocity about its center, it would not sweep round with it the contained air. A manifest indication of this was to hold a lighted candle down inside the vessel; this not only is not extinguished, as ought to happen in a great commotion of air, but preserves its flame erect just as if the vessel were not moving. Such a proof I had already seen in a potter's shop where a clay bowl was placed on the wheel and rotated rapidly; though it was rough and scabrous inside, and not perfectly centered on the wheel, no more than a slight trembling was caused in the flame of a slender candle stub held within it. I believed this small motion to proceed from the roughness of the interior surface and from the approach and retreat

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made alternately by the sides of the vessel, which was revolving eccentrically. Such proof being heard (and later seen) by Sig. Galileo, since he had perhaps formerly thought or written differently, was reputed true by him, as an open-minded man and one who is not excessively devoted to his own opinions; but he indeed told me that this did not assist my purpose in any way. Afterward, it being proved necessarily (which is more than Sarsi can say, with his poets and storytellers) that the production of heat by motion requires a strong rubbing and grinding of two hard bodies, it follows from this that if the motion of the lunar orb should carry with it the lower spheres of fire and of air, as Aristotle has it, there would be no grinding or rubbing at all, any more than in their standing still without rotation. Yet, my desire to produce some new thing (the more so since I had more than succeeded in my intention of showing that the revolutions of celestial bodies could not be the cause of fire) kept me from heeding the counsel I had received. Now, coming to the point, I say that the experiment adopted as true by me and denied by Sarsi is indeed as I have said and not as he gives people to understand; that is, the contained air does follow the motion of the container only insofar as the container moves eccentrically and is not polished and smooth inside. For a proof of this truth, it seems to me that one should first note that if the flame were to be moved with the same velocity and in the same direction as the air, the flame would not bend the other way. Second, the same effect exactly takes place when the air strikes with a given velocity against a fixed and immovable candle as when the flame strikes with equal velocity against quiet and motionless air. Assuming this, I say that an infallible test of what we are investigating will be to fasten a little candle to the bottom of a vessel, placing it (as is shown in Sarsi's diagram) a little distance from the center, and revolving the basin with some speed. If the flame and the air moved at the same speed as the vessel, the flame would be bent very little or not at all in comparison with what would happen if the candle were not fixed to the moving system; in the latter case, the contained air which is driven along would strike against the candle flame which would be stationary. Now a test shows the reverse of this; for in the first case

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(that is, when the candle is affixed to the vessel), not only is the flame bent in the opposite direction from that of the candle's motion, but it is entirely extinguished if the motion is very swift; whereas in the other case, when the candle is not stuck to the moving body, the flame will bend little or not at all even when the motion is very brisk. I might name for your Reverence many witnesses of this if I were concerned lest the reader would be unable to test it for himself, and if it did not seem to me a rather unreasonable and injudicious thing to try to prove by testimony the effects of Nature. Sarsi's experiments are no hindrance to what I have said, they being very fallacious and not free from suspicion of fraud. For as to his idea of covering the basin with mica so that the moving surface should be greater than that of the moved, such a test is very fallacious. Mica being by nature scaly, and this lid being made perhaps of many pieces attached together with glue or white of egg, and consequently being an aggregate of many diversely sloping planes, it is no wonder that when it is revolved it carries much air along with it, and in that way rotates the paper butterfly suspended by a thread inside it. Also very fallacious is the experiment of the glass ball threaded on a spit, which upon being revolved blows upon a thin leaf that is suspended outside and brought close to the sphere; for here the perfect sphericity is very much subject to doubt as well as Sarsi's assurance about his having pierced and threaded it precisely through its center; this being impossible in actual practice, it necessarily reveals the fallaciousness of the proof. I do not wish to leave out mention of the fact that even if Sarsi's experiments were correct (which is denied absolutely), there would still remain for me the question in what manner such a motion of sweeping along could be accommodated to or verified in comets and other exhalations in the air. For from his experiments it is revealed that the contained material is moved more slowly, or no more quickly, than the container; but comets and those other fires move more swiftly than the lunar orb which surrounds them, since they complete and sometimes exceed one entire revolution in twenty-four hours, while the moon lacks fourteen or fifteen degrees of completing one in the same time.

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Such are Sarsi's experiments, and his arguments are no better, as will be evident upon examining two or three of these. T h e rest will be left to the consideration of a much greater man from whose writings, which are soon to be published, Sarsi will discover to his cost how different Sig. Galileo's style is from mine. Among other things that I said about the third of Father Grassi's delicious arguments, one was that a telescope becomes a different instrument when it is lengthened or shortened. Sarsi here exclaims that I am trying to split hairs, and with two examples he attempts to defeat my aim, saying that in this sense the human vocal organs would be made different by raising or lowering the pitch of the voice, and similarly a trombone player would be operating with a different instrument accordingly as this was lengthened or shortened. But these examples of yours do not suit the case, Sig. Sarsi. For the telescope is kept fixed and always of one form in viewing an object, and is not contracted and extended like a trombone, which does not operate in the same manner; nor is the telescope similar to the throat, which continually varies in the articulation of the voice and raises or lowers it. Indeed, the tube of the telescope is not only not lengthened or shortened for viewing a single object, but not even for observing diverse ones at different distances, it being operated in exacdy the same way (as I said at length in my Discourse) for viewing an object placed at a distance of one mile as for viewing most distant objects such as the fixed stars. Void, therefore, are the objections made against me; and those people who would be guided by weighing and by the steelyard would not deny that a very long telescope is quite a different instrument from a shortened one. Here I hear someone say from aside that the Balance was not written for people who deserve so much consideration, and he certainly speaks truly. For otherwise, what sort of judgment would that author have had who undertook to defend Grassi from the oppositions made by me against only a single argument of his when he himself confesses that this third argument, the cause of all this dispute, is of no value ? And how would he have the effrontery to say that even his master considered it ineffective, if he was not relying upon the simplicity of the reader ? The words of the Problem, if I

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remember correctly, are these: 'From the principles of optics it must be understood that this argument plays a very important part in what we are considering.' If Sarsi has the temerity to show that these words signify a low regard for that argument, then I shall allow myself to be persuaded of what he adjoins; namely, that Father Grassi set forth this argument with that additional remark (that whoever did not value the argument was ignorant of perspective) in order to gratify Sig. Galileo—which at present seems to me a threadbare charity. But why did Sarsi not foresee the conclusion that may be inferred from his master's proposition and his own? Father Grassi pronounced that, 'Those who do not value the argument are poorly informed in optics.' Sarsi adds, 'Father Grassi does not value the argument.' The conclusion will be left to the reader. But no more of this. In closing, I wish to relate one argument of Sarsi's which, by the immense authority of its source, seems at first glance to be irrefutable. Instead of responding to it, I wish to adjoin some words from the book cited which he omitted—whether inadvertently or deliberately, I know not. I had said with the Peripatetics that luminous bodies are not transparent; here, against them, I inferred that a comet was not a flame, or any burning thing, as stars could be seen through it. Sarsi opposes this and affirms the contrary; that is, that lucid bodies are transparent; and for a proof of this proposition of his, this is his first argument. 'First, the Sacred Scriptures agree with this statement when they consider Shadrach, Meshach, and Abednego cast into the furnace on the order of the King. For thus the King is represented as saying, " Lo, I see four men loose, walking in the midst of the fire, and they have no hurt." ' This part of the Holy Scriptures, in the third chapter of Daniel, I have very diligently searched and reverently read, and I find that before the three holy youths sang their song of benediction to the Lord and were seen by the King, the Holy History says: 'An angel of the Lord descended with Shadrach and his friends, and put out the fiery flames of the furnace, and made the midst of the furnace like a wind bearing dew.' 7 1 do not mean to place my interpretation upon this, and I defer the matter completely and entirely to the

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declarations and expositions of holy doctors and professors of divinity; let them judge from these words whether it is to be deduced that King Nebuchadnezzar saw the holy ones amid the flame, or amid a cool and dewy wind although they were walking upon the fire; and let them say also whether or not it is praiseworthy to cite Holy Scripture in this manner. I am quite sure, as to my purpose, that the stars do not shine and are not seen through a flame, even the tiny flame of a candle; and anyone at his pleasure may be clear about this if only (as Sarsi says) he has eyes to see. And this is enough to show your Reverence and all those venerable Fathers the loyalty of my spirit and of my behavior toward that virtuous and noble Collegio, and it suffices to defend me from the criticisms and imputations of Lothario Sarsi. And let him bear it with patience if, in order to exculpate my Discourse from deficiencies and defects imputed to it by him, I have sometimes had to recognize those in his Astronomical and Philosophical Balance. I reverently kiss your Reverence's hands, and pray God to increase them with heavenly graces. From Florence, the 20th day of June, 1620. From your Reverence's most affectionate servant, MARIO

GUIDUCCI

THE ASSAYER In which With a delicate and precise scale will be weighed the things contained in The Astronomical and Philosophical Balance of Lothario Sarsi of Siguenza Written in the form of a Letter to the Illustrious and Reverend Monsignore DON V I R G I N I O CESARINI

Lincean Academician Lord Chamberlain to His Holiness BY SIGNOR

GALILEO GALILEI Lincean Academician Gentleman of Florence Chief Philosopher and Mathematician to the Serene Grand Duke of Tuscany •

·

R O M E

MDC XXIII

IMPRIMATUR SI V I D E B I T U R R E V E R E N D I S . P . M A G . S A C . P A L . A P O S T .

A. Episc. Hieracen. Vicesg.

I have read, by order of the Most Reverend Father, Master of the Sacred Palace, this work The Assay er; and besides having found here nothing offensive to morality, nor anything which departs from the supernatural truth of our faith, I have remarked in it so many fine considerations pertaining to natural philosophy that I believe our age is to be glorified by future ages not only as the heir of works of past philosophers but as the discoverer of many secrets of nature which they were unable to reveal, thanks to the deep and sound reflections of this author in whose time I count myself fortunate to be born— when the gold of truth is no longer weighed in bulk and with the steelyard, but is assayed with so delicate a balance. In the College of St. Thomas on the Minerva at Rome, 2 February 1623. F . NICOLO RICCARDI

Imprimatur F. Dominicus Paulaccius Mag. & socius Reverendis. P. Fr. Nicolai Rodulfi Sac. Apost. Palatii Mag.

TO HIS

HOLINESS

POPE U R B A N V I I I

In this universal jubilee of literature and of virtue itself, when the whole Gty and especially the Holy See is more resplendent than ever from the placing there of Your Holiness by celestial and divine disposition,1 every heart in veneration is inflamed to praiseworthy studies and worthy actions. Imitating so eminent an example, we come to appear before you, mindful of infinite obligation for the benefits continually received from your benign hand and full of joy and contentment to see on so sublime a throne such an exalted Patron. As evidence of our devotion and as a tribute from our true fealty, we bring you The Assayer of our Galileo, the Florentine discoverer not of new lands but of hitherto unseen portions of the heavens, containing investigations of those celestial splendors that usually attend great wonders. This we dedicate and present to Your Holiness as to one who has filled his soul with true ornaments and splendors and has turned his heroic mind to the highest undertakings, and we hope that this discourse upon unusual torches in the sky will be to you a sign of our live and ardent passion to serve Your Holiness and to merit your grace. Meanwhile, humbly inclining ourselves at your feet, we supplicate you to continue favoring our studies with the gracious rays and vigorous warmth of your most benign protection. At Rome, the 20th of October, 1623 From Your Holiness' most humble most devoted servants, THE LINCEAN

ACADEMICIANS

JOHANN FABER LYNCEAN OF BAMBERG, R O M A N AND P O N T I F I C A L

TO GALILEO

PHYSICIAN

PHARMACIST

GALILEI

LYNCEAN OF F L O R E N C E , P R I N C E OF

MATHEMATICIANS

OF OUR AGE, DISCOVERER OF MARVELOUS IN THE SKY T H R O U G H T H E

THINGS

TELESCOPE

THE NEW EYE OF N A T U R E

Porta possesses the first claim; you, German, may have the second. The third claim, Galileo, rests on your labor. 2 But you, Galileo, surpass the others by as great a distance as the celestial stars are separated from the earth. With the telescope they may measure a few miles of the earth and venture at sea; you surpass them by an infinite distance in the art of observation with the telescope while you ascend the famous Olympus. Yield, Vespucci, and let Columbus yield; let each take his course through the unknown sea; yet the land of the antipodes was not unknown to the ancients; nor did each pole flee former astronomers. But you were the one who gave the succession of the stars and the new constellations of the heavens to mankind. Hail to your telescope, Galileo; as it approaches the stars so mortals of city and state love you. Did you perhaps with marvelous skill so fit spectacles to an aging world that with mind still sound but eyes dimmed and body weakened it might see through two glasses? Through them new progeny of stars descend from the celestial heights as well as the coundess ones which are in the Milky Way. By them also cold Saturn, marvelous to see, is observed with twin ears; horned Venus shines at night, a new Diana; Jupiter is surrounded by four companions. By them, you also, the brightest lights of the great universe, Sun and your sister, change your appearances. You, Sun, who shine so very brightly as the pure orb, appear marred by strange spots. And that smooth, round Moon in which we have believed, behold, this globe is conspicuous for its swollen mountains. With this Eye, we see bright stars, once called nebulae, shining in

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the sky. Nor yet is the limit reached; shining through the tail of the Comet, by this Eye, they settle in a better-known place. Under a learned appearance, Aristotle deceived minds when he approved an aerial home for those torches; and he believed that the comet, a wholly harmless brightness, when it kindled the air was to be dreaded. Which, if yet you may believe, speaking with fateful countenance, it announces the destruction of its spectators; I fear it portends a sterile year alone for him for whom the greedy fire devours the sceptre of mathematics. But Galileo smooths all; the leveller of the telescope teaches what the comet is; observing with the eye of the lynx he has exposed the phenomena and the meaningless nonsense believed by princes of learning. Ο bold deed, to have penetrated the adamantine sky and walls of crystal with such fragile aid. It is granted to your mind that by this tube of yours, Galileo, you are able to illuminate the happy citadel of the gods.

CONTROVERSY ON C O M E T S

TO THE

ABOVE-MENTIONED

SIGNOR

GALILEI

FROM S I G N O R

FRANCESCO LINCEAN

STELLUTI

ACADEMICIAN

Unlike other things alive— Birds that wing their way through air Fish that in chill waters dive Beasts that tread the earth and leave their footprints there Man, by reason made aware, Solely judges and discerns; Man approaches angels by the things he learns. Nature models tasks for man; Things by her to him denied He by artifice and plan Creates, as wonders numberless have testified. Man has mind to serve as guide; Dextrously his work begun Master artists beautify what he has done. If he would some beast portray Or himself, in image true Man can make this so it may Move its eyes and hands and feet as creatures do. Once Archytas made and flew Wooden doves that soared in air Seeming then to have both life and senses there.

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Then a sage is famous who (Called 'the Great' by all men still) Did by wondrous art endue Lifeless lips with speech and storytelling skill. Geverly he forms at will Other artificial birds Giving them sweet songs to carry and make heard. Other men have made of glass Models of the universe And around these cause to pass All our many girdling heavens so diverse; Tiny planets thus rehearse All the motions of the world Rolling starlike just as those on high are whirled. Overhead, to our alarm In the spaces of the sky Sometimes lightnings threaten harm, Loud and fearful thunders crash and terrify. Man makes also flames that fly; Thunder never louder roared Than when man shoots lead through tubes in iron bored. Some men dare to turn their backs On the Gates of Hercules Sailing where there are no tracks Hollow wood their home, impelled by ocean's breeze Seeking roads through high-piled seas Storming palisades of cold Sailors add a new world to the world of old.

CONTROVERSY O N COMETS

Braver yet in leaving land Bold beyond all human kind Daedalus with skillful hand Wings of feathers made, upon his back to bind; Boldly hoping he would find Means of flight, he did indeed Cleave the moist and salty air with birdlike speed. You, when I consider well, Vigorous and proud must be, So to feast your sight, and tell Things transcending human thought that you can see Lynxes blind as moles are we, G A L I L E O , without you; Argus eyeless is beside you, Linceans too. But your piercing rays of sight Do not owe their strength alone To that great resplendence bright Lent by glassy lenses you have made your own, For a finer light has shone Gathered there within your mind; This light conquers vision, leaves it far behind. Thus what Nature has concealed In her breast from others' view By your gaze serene revealed Now is opened wide for other men by you. Some believe they know this, too From the sage old Stagirite, Who but saw it dimly, as a shadowed sight.

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That which you now teach of it Did not come from pages old Nor from new books filled with wit— No, and you have not by friendly stars been told; Labors long and vigils cold Proofs and searches, studies deep These are what aroused such powers from their sleep. Scarce a man can understand Though he use his senses well How our touch is in our hand How our eyes see sights, ears hear, and noses smell This we ask you now to tell, Though the tongue can scarce relate How it knows the varied flavors on a plate. Any man would gladly know How both cold and heat are felt How the sky for us below Makes the wonders that are seen in heaven's belt— Riddles that your soul has spelt; Nothing near or far from you Ever keeps its secrets from your piercing view. Once an ancient sought the cause, Near to Chalcis so men tell, Why Euripus' wave no pause Made in ebb and flow as tides now rose and fell; Had you told him what so well You have proved of your belief He would not have plunged into those waves from grief.

CONTROVERSY ON C O M E T S

Of those persons long since dead— Wise Hipparchus and his kind— It respectfully is said They share high and starry thrones with your great mind; Yet they never thought to find That celestial lights on high Numbered many thousand stars within the sky. They would not have turned the back With a show of mannered grace Nor have strayed from truth's straight track Nor established seven in some special place Nor would they have tried to trace Sites and bounds improperly For those errant stars with golden hair we see. Further planets you did place High among the starry ways Where in far celestial space Mighty Jupiter benignly sheds his rays; Where the slowest planet stays Through new forms you see him run, Likewise her whose rapid course outstrips the sun. Of the fixed stars with their rays You have seen so many turn Through those vast and distant ways That to number these the eye can scarcely learn; Stars so countless we discern It would seem that they must be Numbered as the sands on shores beside the sea.

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Glory must be yielded by Daring modern Tiphyses Celebrated to the sky Having charted unknown shores and new-found seas; You, however, unlike these Add not just some new lands here But new stars in skies sublime you make appear. It is news to us when these Find new lands in any place; Not to aborigines— Paths they found across the ocean's briny face And arrived before our race. You discover, far more sage, Orbs to all men new and to our very age. For these objects, new indeed, Men are much in debt to you; Your frail glasses lend us speed Lightly soaring up to heaven with our view, And the sky's your debtor too For this brighter beauty there And for more and larger lights in regions bare. Had your eyes not soared on high Spying out wide heaven's ways, All that is within the sky Would have been just as it was before our days; You these globes with golden rays Veiled from us and hid to fame Dressed, and gave their motion, glory, place, and name.

CONTROVERSY ON

COMETS

Therefore if from present view Of these lights by you perceived Heaven gains much glory new She will not by death's oblivion be bereaved; You from whom she much received Shall, so long as heaven turns, Shine as bright as any glorious star that burns.

THE

ASSAYER BY

G A L I L E O GALILEI Lincean Academician Chief Philosopher and Mathematician to the Most Serene Grand Duke of Tuscany Written in the form of

A LETTER TO THE MOST I L L U S T R I O U S AND REVEREND S I G . DON V I R G I N I O CESARINI

Lincean Academician Lord Chamberlain to His Holiness

I have never been able to understand, your Excellency, how it comes about that every one of my studies which, in order to please or to be of service to others, I have seen fit to place before the public has occasioned in many a certain animus to detract, steal, or deprecate that modicum of esteem to which I had thought I was entitled, if not for the work, at least for my intention. In my Starry Messenger were revealed many new and marvelous discoveries in the sky that ought to have pleased all lovers of true science. Y e t it had scarcely been printed when men arose on all sides who envied the praises due to the discoveries thus made, and those were not lacking who merely to contradict what I said did not scruple {p. 2) to cast doubt upon things they had seen at will again and again with their own eyes. M y Lord the Most Serene Grand Duke Cosimo 11, of glorious memory, once ordered me to write my opinions on the causes of things floating or sinking in water, and in order to comply with this command I set down upon paper everything beyond the teachings of Archimedes

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that occurred to me, which perhaps is as much as may be truly said about the facts of this matter. And behold! immediately the whole press was filled with attacks upon my Discourse. My opinions were contradicted without the least regard for the fact that what I had set forth was supported and proved by geometrical demonstrations, and such is the strength of men's passions that they failed to notice that the contradiction of geometry is the bald denial of truth. How many men, and under what disguises, combatted my Letters on the Solar Spotsl The material contained therein, which should have opened to the mind's eye so much room for admirable speculation, was completely scorned and derided by many who either disbelieved it or little appreciated it; others, not wanting to agree with my conceptions, advanced ridiculous and impossible opinions against me; and some, conquered and convinced by my reasons, attempted to rob me of that glory which was mine by pretending not to have seen my writings and subsequently trying to make themselves the original discoverers of such impressive marvels. I say nothing of some of my private discussions, proofs, and propositions (many of them not published by me) having been seriously impugned or deprecated as worthless; yet even these have sometimes been chanced upon by others who have then exerted themselves with admirable adroitness to appropriate these honors as inventions of their own ingenuity. Of such usurpers I might name not a few, but I shall pass them over now in silence, as it is customary for first offenses to receive less severe punishment than subsequent ones. But I shall not remain silent any longer about a second offender who has too audaciously tried to do to me the very same thing which he did many years ago by appropriating the invention of my geometric compass despite the fact that (p. 3) I had many years previously shown it and discussed it before a large number of gentlemen and had eventually publicized it in print. May I be pardoned this time if, against my nature, my habit, and my present intentions, I show resentment and cry out, perhaps with too much bitterness, about a thing which I have kept to myself these many years. I speak of Simon Mayr of Guntzenhausen; 3 he it was in Padua, where I resided at the time, who set forth in Latin the use of the said compass of mine and, appropriating

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it to himself, had one of his pupils print this under his name. Forthwith, perhaps to escape punishment, he departed immediately for his native land, leaving his pupil in the lurch as the saying goes; and against the latter, in the absence of Simon Mayr, I was obliged to proceed in the manner which is set forth in the Defense which I then wrote and published.4 Four years after the publication of my Starry Messenger, this same fellow, desiring as usual to ornament himself with the labors of others, did not blush to make himself author of the things I had discovered and printed in that work. Publishing under the title of The World of Jupiter, he had the temerity to claim that he had observed the Medicean planets which revolve about Jupiter before I had done so. But because it rarely happens that truth allows herself to be suppressed by falsehood, you may see how he himself, through his carelessness and lack of understanding, gives me in that very work of his the means of convicting him by irrefutable testimony and revealing unmistakably his error, showing not only that he did not observe the said stars before me but even that he did not certainly see them until two years afterward; and I say moreover that it may be affirmed very probably that he never observed them at all. Although from many places in his book I could draw the most evident proofs of what I say, I shall adduce but a single one, reserving the rest for some other occasion in order not to become excessively diffuse and be distracted from my main purpose. In the second part of his World of Jupiter, under the sixth phenomenon that he considers, Simon Mayr writes of having diligently observed that the four satellites of Jupiter are never found in a straight line parallel to the ecliptic except at their greatest elongations from Jupiter, and {p. 4) that when they are outside of these they always tilt with a noticeable deviation from the said line. He says they always tilt northward from this when they are nearest us in their orbits, and conversely slope toward the south when farthest away. To preserve this appearance, their orbits would be inclined to the plane of the ecliptic toward the south in the upper regions and toward the north in the lower. Now this doctrine of his is full of fallacies which openly show and testify to his fraud.

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In the first place, it is not true that the four orbits of the satellites incline from the plane of the ecliptic; rather, they are always parallel to it.® Second, it is not true that they are never exactly mutually aligned except when they are located at their maximum elongations from Jupiter; indeed, it sometimes happens that any distances— maximum, mean, or minimum—they are seen in a perfectly straight line and fall in with one another; also, when two of them have opposite movements and are very close to Jupiter, they meet so exactly that the two appear one. And finally, it is false that when they [apparently] slope from the plane of the ecliptic they always tilt toward the south when in the superior half of their orbits and toward the north when in the inferior. Rather, at some times only do they have their tilts in this fashion, while at other times they tilt the other way; that is, toward the north when they are in the upper semicircle and toward the south when in the lower. But Simon Mayr, from not having understood or observed this affair, has inadvertently disclosed his error. Now, the facts are as follows. The four orbits of the Medicean planets are always parallel to the plane of the ecliptic, and, since we are located in that same plane, it happens that whenever Jupiter has zero latitude (lying also in the ecliptic), the movements of these stars appear to us to be made along the same straight line, and their conjunctions at any place will always be made bodily and without deviation. But when Jupiter lies outside the plane of the ecliptic and its latitude is {p. 5) north from that plane, the four orbits of the satellites remaining parallel to the ecliptic, those parts of them which are farthest from us (we being always in the plane of the ecliptic) show themselves as tilted to the south with respect to the closer parts of these orbits, which to us appear more northerly. Conversely, when Jupiter's latitude is southerly, the farther parts of the same little orbits seem to us more northerly than the closer parts, and thus the tilting of the stars is seen in the opposite manner when Jupiter's latitude is northerly from what happens when Jupiter is southerly. That is, in the former case, they will be seen to tilt toward the south when they are in the upper parts of their orbits, and toward the north in the lower parts, but in the latter case they will tilt the contrary way; to wit, toward the north

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in the upper half and toward the south in the lower. And this tilt will be greater or less accordingly as the latitude of Jupiter is greater or less. Now Simon Mayr writes of having observed that the said four stars always slope toward the south when in the upper half of their orbits; hence his observations were made at a time when Jupiter had a northerly latitude. But when I made my first observations, Jupiter was southerly, and it remained so for a long time, nor did it become northerly until after more than two years. Thus the latitudes of the four stars could not have appeared as Simon writes of them until more than two years later, so if he ever saw and observed them it was not until two years after me. Behold him, then, already convicted by his own depositions of lying about having made such observations before me. But I shall go further and say that it may be much more probably believed that he never made them at all, inasmuch as he affirms that he has not observed or seen them mutually arranged in a precise straight line except when they were at their greatest elongations from Jupiter. The truth is that for four months together, from the middle of February to the middle of June, 1611, in which time Jupiter had little or no latitude, the disposition of these four stars was always along a straight line in all their positions. Next, notice the craft with which he tries to show himself prior (p. 6) to me. I wrote in my Starry Messenger of having made my first observation on the seventh of January, 1610, continuing then with others on the succeeding nights. Along comes Simon Mayr, and, appropriating my very observations, he prints in the title of his book and again in the opening part of the work that he had already made his observations in the year 1609, trying to give people the idea that he was first. Now the earliest observation that he produces as made by him is the second one made by me; yet he announces it as made in the year 1609. What he neglects to mention to the reader is that since he is outside our church and has not accepted the Gregorian calendar, the seventh day of January of 1610 for us Catholics is the same as the twenty-eighth day of December of 1609 for those heretics. So much for the priority of his pretended ο

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observations. He also attributes to himself falsely the discovery of their periodic movements, found by me after long vigils and wearying labors, and revealed in my Solar Letters and again in the treatise which I published on things placed in water. That my book was seen by the said Simon may be clearly deduced from his book, and from mine he undoubtedly extracted those movements. But I find that I have allowed myself to run on in too long a digression beyond what was required by the present occasion. Therefore, getting back to the discussion we have begun, I shall go on to say that after such very clear proofs there remained to me no longer any room for doubt of the ill feeling and stubborn opposition against my works. I had considered remaining perfectly silent about it, in order to save myself further occasion for the unpleasant sensation of being a target for such frequent sharpshooting, as well as to remove from others any matter capable of exciting such reprehensible talents. Certainly I have not lacked opportunities to put out other works of mine, perhaps no less surprising in the philosophical schools and no less consequential in science than those hitherto published. But the reasons recited above were so effective that I was content merely with the opinions and judgment of some gentlemen, my real and sincere friends, to whom I communicated my thoughts and in discussion with whom (p. 7) I have enjoyed that pleasure which accompanies the privilege of imparting what the mind gradually brings forth, at the same time avoiding any renewal of those stings which I had previously felt with so much vexation. These gentlemen, my friends, demonstrating in no small way their approval of my ideas, have managed with various reasons to change my mind about the resolutions thus made. In the first place, they tried to persuade me not to be concerned about these obstinate attacks, saying that in the end these would in fact rebound upon their authors and would render my arguments more vivid and attractive, becoming a clear proof of the uncommon nature of my compositions. They pointed out to me the common maxim that vulgarity and mediocrity receive little or no consideration and are left behind; the mind of man turns only on that which reveals marvels and transcendent things, and it is this which in turn gives rise in ill-tempered minds to envy and defamation.

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These and similar arguments, coming to me upon the authority of those gentlemen, nearly destroyed my resolve to write no more. Yet my desire to live tranquilly and without such disputes prevailed, and thus fixed in my purpose I believed I had silenced in this way all the tongues which previously had shown such eagerness to contradict me. But it was in vain that I had reached this frame of mind, nor have I been able by remaining silent to avoid my persistent fate of having always to concern myself with those who write against me and quarrel with me. It was useless for me to forbear from speaking, for those people who are so anxious to make trouble for me have had recourse to making mine the writings of other men. In thus stirring up a fierce fight against me, they have been willing to do something which in my opinion never occurs without clearly indicating a spirit impassioned beyond all reason. Surely Sig. Mario Guiducci, in carrying out the requirements of his office, should have been allowed to lecture in his Academy and then to publish his Discourse on Comets, without Lothario Sarsi, a completely unknown outsider, having jumped upon me for this, and, without the slightest regard for that fine man, {p. 8) having made me the author of this Discourse, in which I had no part beyond the regard and honor done me by Sig. Guiducci in his concurrence with my opinions—an agreement he had expressed in the said discussions held with those gentlemen, my friends, with whom he was pleased to meet frequently. And even if the entire Discourse on Comets had been the work of my hand (an idea which could never occur to anyone wherever Sig. Mario is known), what kind of behavior would this be, for Sarsi to reveal my face and unmask me so zealously after I had shown my wish to remain incognito ? Upon this action, finding myself constrained by such unexpected treatment of so unusual a kind, I come to break my previously established resolve not to publish my writings any more. I shall do what I can to see that the impropriety of his action shall not escape unnoticed, in the hope of discouraging anyone who will not let sleeping dogs lie, as the saying goes, and who stirs up trouble with men who would hold their peace. Now I am aware that this name Lothario Sarsi, which has never

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before been heard in the world, serves as a mask for someone who wants to remain unknown. It is not my place to make trouble for another man by tearing off his mask in the fashion of Sarsi himself, as this does not seem to me an action deserving emulation or one which can in any way bestow aid or favor upon my writing. Indeed, I think that to deal with him as an unknown person will be to gain a wider field in which to make my arguments plainer and explain my ideas more freely. I am taking into account the fact that many times those who go masked are either low persons who try in this guise to gain esteem among gentlemen and scholars and to utilize for some purpose of their own the dignity which attends nobility. Again, they may be gentlemen who, thus unrecognized, lay aside the respectful decorum accorded to their rank and make free use (the custom in many cities of Italy) of speaking openly about anything with all and sundry, getting as much pleasure as anyone can in this raillery and contention devoid of all respect. And I believe that it must be one of these latter {p. 9) whom this mask of Lothario Sarsi hides, for if he were one of the former it would have been in poor taste for him thus to have tried to impose upon the public. Consequently, I believe in addition that just as he, thus unknown, has allowed himself to say some things against me which to my face he would perhaps not say, so it ought not to be taken amiss if I, availing myself of the privilege accorded against masqueraders, deal with him quite freely. Nor should he or anyone else suppose me to be weighing my every word when perhaps I may speak rather more frankly than will please him. I wanted your Excellency above all to be the first witness of this reply of mine, for, as a most understanding man of the noblest quality and devoid of any partiality of spirit, you will righdy understand my cause and will not fail to reprove the audacity of those who, not ignorantly but in passion (for the ignorant matter but little), try evilly to distort my arguments before the common people who do not comprehend. And though upon first reading Sarsi's essay it was my intention to include my answer in a simple letter to your Excellency, when I came to the task I found that the matters contained in his essay which required some attention multiplied under my hands, and I have been compelled to pass far beyond the bounds of a letter.

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I have nevertheless adhered to my original decision to address myself to your Excellency, however extended my reply may be. It has been my thought to call it The Assayer, restricting myself to the metaphor employed by Sarsi; but since it seemed to me that he used too crude a steelyard in his weighing of Sig. Guiducci's propositions, I have elected to employ an assayer's balance precise enough to detect less than the sixtieth part of one grain. Using this with all possible care and neglecting not a single proposition set forth by him, I shall put every one to the test. I am going to distinguish these weighings, denoting each by a number, and thus if they are ever seen by Sarsi and he wishes to respond he may the more easily do so (j>. 10) without omitting anything. Coming at last to particular considerations, perhaps it will be well for me to say something about the title page of the work, in order that nothing may escape weighing. Sig. Lothario Sarsi calls this The Astronomical and Philosophical Balance. After the title, in the subjoined epigram, he gives the motive which induced him so to name it, which is that this comet mysteriously hinted to him by originating and appearing in the sign of Libra that he should balance and weigh on accurate scales the things contained in the treatise on comets published by Sig. Mario Guiducci. I note that Sarsi confidently begins altering things to suit his purposes at the very first opportunity, a style maintained thereafter throughout his essay. He chanced to think up this pun on the correspondence between his balance and the celestial Balance, and, since it seemed to him that his metaphor would be considerably enhanced if the comet had first appeared in Libra, he freely asserted that it arose there. He felt no concern about contradicting the truth, nor even in a certain way himself, for he contradicts his own master, who on page 10 of his Disputation draws this conclusion: 'But finally, whatever of these dates saw the first light of the comet, it is Scorpio which was its true native land.' And a dozen lines farther on, . . it was born in Scorpio, that is, in the principal house of Mars'; and a little later,' I, in so far as I am able, have sought its native land which, in agreement with all, I declare to have been Scorpio.' Hence, much more appropriately (and more truthfully, when we consider what Sarsi has actually written), he

ΐΗΖ

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might have entitled his work, 'The Astronomical and Philosophical Scorpion'—that constellation which our sovereign poet Dante called the . . . figure of that chilly animal Which pricks and stings the people with its tail;® and truly there is no lack of stings here for me. Much worse ones too than those of scorpions; for the latter, as friends of mankind, do not injure unless first offended and provoked, whereas this fellow would bite (p. 1 1 ) me, who never so much as thought of offending him. But as luck will have it, I know the antidote and speedy remedy for such stings, and I shall crush the scorpion and rub him on the wounds where the venom will be reabsorbed by its proper body and leave me free and sound. I Now we come to the treatise, and the first weighing shall be performed upon some words of the proem; namely, the sentence beginning, 'One person, however . . .' But let us set forth this proem in full, precisely as in the printed text of which we do not wish to leave out one iota: FIRST

WEIGHING

OF T H O S E T H I N G S W H I C H W E R E OPPOSED

BY GALILEO ΤΟ OUR

Disputation

'Last year when . . . and rather sharply.' (p. 69,1. 4 to 1. 23). In these final words, he affirms that we have sharply criticized his master's Disputation. To this, I do not see at the moment that anything must be replied, inasmuch as his statement is absolutely false. Diligently searching in Sig. Mario's treatise, I have been unable to find any such place, and Sarsi does not cite one. But we shall have more to say about this later. II Next follows—and this is to be the second weighing—'At first, we were grieved . . . (p. 12) before just magistrates.' (p. 69, 1. 24 to 1-31)·

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Here he says that from the first he has felt pain that the Disputation displeased me, but he adds that he has since been consoled by seeing even Aristotle, Tycho, and others criticized with the same severity, so there was no need of additional defenses for those accused when they took the same side as the most eminent minds; their very cause would speak for itself should they remain silent, and would defend itself in the minds of the just. From these words, I gather that to Sarsi's mind those who impugn authors of the most eminent intelligence should be held in little esteem, for he takes no account of the fact that some people do spring to the defense of those who are attacked, even when the bare authority of the latter suffices to maintain their credit in the eyes of the learned. Here, I should like your Excellency to note how Sarsi, whether by choice or through inadvertence, muddies the reputation of his teacher, Father Grassi, whose chief aim in his Problem was to attack Aristotle's opinion about comets. This is clearly seen in his book, and Sarsi himself here repeats and confirms it on page 73. So if the assailants of great men should be ignored, then Father Grassi should be also. Now we have not only not ignored him but we have given him the same consideration as the most eminent minds, placing him in a class with them, so in this regard he is as much exalted by us as he is debased by his pupil. I do not see what Sarsi can offer in his own excuse unless it be that his meaning was that one ought to ignore the vulgar among the opponents of eminent geniuses, while on the other hand one should esteem those who happen also to be very eminent, and that among the latter he meant to include his master while the rest of us fell among the common herd. But then in this (p. 13) regard, we are reproached for doing that which it was suitable for his master to do. Ill Next follows, and this is to be the third weighing: 'But since it appeared . . . brief consideration to both of them . . (p. 69,1. 31 to p. 70,1.2). T h e sense of these words, continuing that of the above, seems to me to imply that while one need not take account of people who contradict the most eminent geniuses but may rather pass them over in

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silence, still if they must be answered then this task should be given to inferior persons rather than otherwise. Thus in our case the wisest men have deemed it proper that not Father Grassi or someone of equal importance should reply to Galileo, but saltern aliquts—just anyone. Here I have nothing to say or reply except that knowing and confessing my lowly estate, I bow my head to the sentence of such men. Indeed, I marvel not a little that Sarsi should of his own volition choose to be that mere anybody who would tuck up his sleeves and welcome a task which, in the judgment of the wisest men (and himself), should not be given to any but the meanest servant. Nor can I well understand, since it is the natural instinct of every man to attribute to himself much merit rather than little, why this Sarsi should now lower his position so greatly as to be induced to pass himself off as a mere anybody. The improbability of this has aroused in me some suspicion, and in the end has made me think that in these words there may be a slight misprint, and that where it says that,' somebody should consider the argument of Galileo more carefully,' it should read,' somehow the argument of Galileo should be considered more carefully.'7 This reading I consider to be the correct one, inasmuch as it fits in with all the rest of the treatise while the other reading accords but ill with the regard which I still like to think Sarsi entertains for himself. Your Excellency will see, as you go along examining his essay with me, how true it is—as I say here—that of the things {p. 14) written by Sig. Mario he has merely made an examination 'somehow,' or even just 'anyhow,' attending to some minutiae which have little bearing upon the main topic and passing over the chief conclusions and reasons. He has done this because in his heart he knew that he could not fail to approve the latter and confess them to be true, and this would have run counter to his main purpose of only condemning and refuting them—as he himself writes on page 105 in these words:' These things which have been said regarding the opinion of Galileo are among those which immediately concern the comet. For he, who in a very long disputation has presented his beliefs in many and confused words, objects to our saying more and prevents us from presenting many refutations against his position. For how can we divine and

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refute what he does not offer ?' In these words, I note two things in addition to his exclusive intention to refute. One is that he pretends not to have understood many things because of their being (he says) obscurely written, though these turn out to be the things for which no counterattack was discovered. The other is that he says he has been unable to confute things which I have not set forth and which he has not been able to divine. Yet your Excellency will see that as a matter of fact most of the things he undertakes to refute are not set forth by me but are divined (or better, let us say imagined) by him. IV . . hoping that thereby... (p. 15) than with the consul' (p. 70, 1. 2 to 1. 23). In all this remainder of the proem, I note first that Sarsi claims to have done with his impugnations something welcome to many people; and perhaps he may have done so for people who happen not to have read Sig. Mario's essay. But if they have taken Sarsi's word for it, given privately and confidentially, this will have departed a good deal from what is written, since in his own printed and published work he does not refrain from setting forth as written by Sig. Mario a great many things that were never in his essay nor even in our imaginations. He then adds that he wants to abstain from words that would indicate an exasperated and angry spirit rather than a scientific one. We shall see as we go along how well he has adhered to this; for the present I merely take note of his confession of being inwardly exasperated and angry, for, if he were not, his giving expression to this intention of abstaining would have been I shall not say erroneous, but superfluous; abstinence has no place where there is not an inclination and a disposition. As to what he writes next, of wishing to serve as an intermediary in relating things concerning my latest discoveries which he has heard from Father Horatio Grassi, his teacher, I certainly do not believe any such thing. I am sure that the said Father would never have spoken or thought or willingly have seen Sarsi write such fantastic things, far removed in every respect from the doctrine taught

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in Father Grassi's college, as I hope I shall make clearly recognized. Indeed, without proceeding a step further, let me ask who on earth, merely knowing the prudence of those Fathers, could be induced to believe that one of {p. 16) them would have publicly written that in private letters to friends at Rome I had openly declared myself the author of Sig. Mario's treatise ? This is not true, and if it were its publication could not fail to reveal some pleasure in sowing seeds of dissension among close friends. And what sort of behavior is it to take the liberty of printing the private statements of others ? It is best that your Excellency should be informed of the truth of this matter. During the whole time that the comet was being seen, I was confined by illness to my bed, where I was often visited by friends. Discussions frequently took place there, during which I had occasion to voice some thoughts of mine which raised considerable doubt about the doctrines previously held on this subject. Among my other friends, Sig. Mario was ofttimes present, and one day he told me that he had considered speaking on comets before the Academy, and that if it pleased me he would there cite what he had learned from me, along with things which he had gathered from other authors or had thought of himself, inasmuch as I was in no condition to write. The courtesy thus offered I regarded as my good fortune, and I not only accepted but I thanked him and expressed my indebtedness to him. Meanwhile from Rome and other places, insistent requests to know whether I had anything to say on this matter came from other friends and patrons who perhaps did not know of my indisposition. To these I replied that I merely had several questions which I was unable to set down on paper because of my infirmity, but that I hoped these ideas and doubts of mine might shortly be seen inserted in a discourse by a gentleman who was a friend of mine and who in order to do me honor had taken the trouble to collect these and insert them in a treatise of his. That is all that was given out by me, as has also been written in several places by Sig. Mario himself. Hence there was no call for Sarsi to embellish the truth by introducing my letters, nor should he assign to Sig. Mario such a small part in the Discourse (with which he had much more to do than I) as to pass him off as a copyist.

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But since he is pleased to have it this way, let it be so; and meanwhile let Sig. Mario (p. 17) accept my defense of his treatise in return for the honor he has done me. V Returning to the treatise, your Excellency may reread the following words:' First of a l l , . . . by false arguments.' (p. 70,1.24 to p. 71,1.13). Concerning these particular writings, I say in the first place that I have never lamented over being maltreated in the Disputation of Father Grassi, in which I am sure that his Reverence never thought to offend me. Yet if, for the sake of argument, I had held the view that Father Grassi intended to include me in criticizing those who held a low opinion of the argument taken from the slight enlargement of the comet, Sarsi should not think that on that account there was cause for me to take offense and to lament. Perhaps there might have been, had my position been false, and had it been publicly revealed to be so. But since my statement was quite correct, (p. 18) and the other one was false, the multitude of my opponents (and especially of those as worthy as Father Grassi) could only cause me pleasure and not pain, inasmuch as there is more delight in victory over a valiant and numerous host than over few and feeble opponents. News arrived from many parts of Europe, going (as Sarsi writes) to his master, but some people in passing this way enabled us also to hear how generally all the most celebrated astronomers were taking a great interest in that argument. Nor were there lacking even in our region and in our very city men who held the above opinion. As soon as I learned of this, I let it be very plainly understood that I deemed the reasoning quite vain. Many people made a joke of this, the more so when there appeared on their side authoritative support and confirmation from the mathematician of the Collegio Romano, nor shall I deny that this caused me a bit of trouble. Finding myself placed under the necessity of defending my statement against so many opponents (who, strengthened by such assistance, rose up against me still more imperiously), I did not see any way to contradict them without including Father Grassi too. So it was through a necessary though fortuitous circumstance and not by choice that I pointed my

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opposition in the direction which I least wished to. But I never pretended, as Sarsi says, that my opinion was certain to be swiftly carried by the winds to Rome as usually happens with the words of great and celebrated persons; this really far exceeds the bounds of my ambition. It is certainly true that reading the Balance has made me marvel somewhat that what I did say should not have penetrated to Sarsi's ears; is it not surprising that so many things have been reported to him which I never said nor even thought (of which a large number are set down in his discourse), while not a single syllable has reached him of other things that I have said over and over again ? But perhaps the winds that blow the clouds and those chimeras and monsters which tumultuously take shape therein had not the strength to carry solid and weighty things. From the words (p. 19) which come next, I seem to gather that Sarsi would attribute to me a great defect in not having equaled the courtesy of the Fathers at the Collegio by returning the compliment they had paid to me in public lectures upon my celestial discoveries and my ideas about bodies placed in water. And what was I supposed to do ? T o praise and approve the Disputation of Father Grassi, replies Sarsi. But since dealings between you and me are to balance, Sig. Sarsi, and must be businesslike, as they say, then I ask you whether those reverend Fathers consider my ideas to be true or take them to be false ? If they recognize my ideas as true and praise them as such, then it is at exorbitant interest that you demand payment of what was lent when you expect me to extol with equal praise things I know to be false. But if they regard my ideas as foolish and still praise them, then I may indeed thank them for their urbanity, but I should have been much more grateful if they had lifted me out of my error and had shown me the truth, for I regard much more highly the utility of accurate correction than I do mere pomp and ceremony. And since I think that the same is true for all good philosophers, I feel no obligation in either case. Perhaps you will tell me that I should have remained silent. T o this I reply first that Sig. Mario and I were already too deeply obligated to let our ideas be known before Father Grassi's essay was published, so that to have remained silent would have been to invite

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upon ourselves contempt and almost universal derision. I add that I should have asked and perhaps even entreated Sig. Guiducci not to publish his Discourse if there had been in it anything prejudicial to the dignity of the famous Collegio or any of its professors. But if all the opinions opposed by us were held by others before they were by the mathematician and professor of the Collegio, I do not see how his Reverence's merely having lent his assent to them placed us under any obligation to ignore the truth and conceal it in favor of the perpetuation of an error. Hence, any criticism of being a poor logician falls upon Tycho and the others who have committed the equivocation in the argument. This equivocation was revealed by us not to single anyone out or to blame them, but merely to remove others from error and to make evident {p. 20) the truth, and I do not know that actions of this sort can ever be reasonably blamed. Sarsi has, therefore, no reason for saying that I am guilty of contempt for the dignity of the Collegio Romano. Quite the contrary; for if Sarsi's voice does emanate from the Collegio, I have reason to suspect that my doctrine and my reputation have been in bad odor there not merely at present but all along, inasmuch as in this Balance none of my thoughts are approved. Nothing is to be read there except opposition, full of accusation and blame, and, if one may believe the rumors, there is in addition to what is written an open boast of power to annihilate everything of mine.8 But as I do not believe this, nor that any of these ideas exist at the Collegio, I must suppose that Sarsi's philosophy is such as to give him the right equally to praise or to blame, confirm or refute the same doctrines accordingly as benevolence or wrath may move him. In this he reminds me of a teacher of philosophy in my time at the University of Padua, who, being angry at one of his colleagues (as frequently happened), said that if the latter did not mend his ways he would send someone to spy secretly on the opinions he voiced in his lectures, and in revenge would always maintain the contrary. VI Now, your Excellency, read: 'But lest we waste time . . . (p. 21) which he considers unfortunate.' (p. 71,1. 14 to 1. 36).

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From what Sarsi writes here, I may guess that he has not read carefully enough Sig. Mario's Discourse or even that of Father Grassi, since from both the one and the other he adduces propositions which are not to be found in either. It is indeed true that he would have needed such things to have been written in order to get an opening through which he could somehow brand me a Copernican, so in their absence he has attempted to supply them himself. First, in Sig. Mario's essay it is not thrown in Father Grassi's teeth and attributed to a deficiency on his part that he has sworn fealty to Tycho and followed his foolish fabrications in every detail. Here are the places referred to by Sarsi. On page 3 6 , ' Later I shall turn my attention to the Professor of Mathematics at the Collegio Romano, who in a recently published tract appears to have subscribed to Tycho's every statement, and even added some further reasoning in confirmation of that opinion.' And the other place, on page 52: ' The Mathematician of the Collegio Romano has accepted the same hypothesis for this last comet as well; beyond the little which that author has written in support of Tycho's opinion, I am led to affirm this by seeing how much he concurs with Tycho's other fantasies throughout the remainder of the work.' Now you may see, your Excellency, whether anything is here attributed to deficiency and omission. Moreover, it is perfecdy clear that nothing is under consideration in the whole work except phenomena relating to comets, about which Tycho wrote a large volume. T o say that the Mathematician of the Collegio agrees with other fantasies of Tycho does not extend to other views than those which pertain {p. 22) to comets. So I do not see that this is an appropriate place to call into comparison with Tycho such men as Ptolemy and Copernicus, who never treat of hypotheses concerning comets. Sarsi then says that in the writing of his master nothing is to be found in which he has followed Tycho except the demonstrations for finding the location of the comet, but this is not true, with all due respect to Sarsi. Rather, nothing is less to be found there than such demonstrations. God forbid that Father Grassi should have imitated Tycho in these without noticing that Tycho, in his manner of investigating the distance of a comet by observations made from

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two different places on the earth, shows himself needful of attention to the very first elements of mathematics. And so that your Excellency may see that I do not say this without grounds, reconsider the demonstration which begins on page 123 of Tycho's treatise on the comet of 1577, which is in the last part of his Progymnasmata.9 In this, he wants to prove that the comet was not below the moon by means of comparing the observations made by himself at Uraniborg with those made by Thaddeus Hagek at Prague. Drawing the chord A B of the arc of the terrestrial globe passing through the two places named, and sighting from the point A at a fixed star at D , he assumes

F

Fig. 16 the angle D A B to be a right angle, which is not even possible. The line A B being the chord of an arc of less than six degrees, as Tycho himself declares, it is necessary in order for the said angle to be a right angle that the fixed star D should be less than three degrees from the zenith of A. But this is false, since its minimum distance is more than forty-eight degrees, since according to Tycho himself the declination of the fixed star D , which is Aquila (or let us say Altair), is 7°52' north, while the latitude of Uraniborg is 55°S4'. He writes further that the same fixed star is seen from the two places A and Β at the same place in the eighth sphere because the whole earth—let alone the small (p. 23) part AB—has no perceptible magnitude with respect to the immensity of the eighth sphere. Pardon me, Tycho; the largeness or smallness of the earth has nothing to do with the

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case. Seeing the same star in the same place from all parts of the earth depends upon the star's truly being in the eighth sphere, and upon nothing else, in exactly the same way as the letters on this page will never change their apparent positions with respect to the page no matter how much you may change the position of the eye with which you look at it. But an object placed between the eye and the page will vary its apparent place with respect to the letters as the text is moved, so that the same letter is seen now to the right, now to the left, now higher, and now lower. It is in this way that the apparent places of the planets change in the stellar orb when seen from different parts of the earth, because that orb is very far beyond them. What the smallness of the earth does in this case is this: the planets more distant from us making a lesser change and the closer ones a greater, ultimately, for a very remote one, the size of the earth would not suffice to make its change perceptible. Then when Tycho adds that what takes place is in obedience to the laws of arcs and chords, your Excellency may see how far he is from those laws and even from the first elements of geometry. He says that the two straight lines A D and B D are perpendicular to A B , which is impossible, since only the straight line that falls from the vertex is perpendicular to the tangent and its parallels, while these lines do not come from the vertex at all, nor is A B the tangent or parallel to it. Besides, he requires them parallel and then he says that they eventually meet at the center, whereas (in addition to the contradiction between meeting and being parallel) these lines if prolonged pass far from the center. And he finally concludes that coming from the center to the circumference at the points A and B, they are perpendiculars, which is impossible inasmuch as among the lines drawn from the center to all points of the chord A B , only that one which falls at its center is perpendicular to it, and those which fall at its extremities are the most inclined and oblique of all. Thus your Excellency may see to what and (p. 24) to how many absurdities Sarsi would have lent his master's assent if what he had asserted in this statement were true; that is, that the latter had followed Tycho's reasoning and method of proof in seeking the location of the comet. Sarsi himself may see also how much better than

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he, and, even without employing astrology or telescopes, I have penetrated I shall not say into the inner sense of his mind, for to spy that out I have neither eyes nor ears, but the sense of his writing, which is so clear and manifest that there is no need for the lynx eyes so gallantly brought in by Sarsi as a jest at our Academy. Since your Excellency and other princes and great gentlemen are involved with me in this jest, I shall profit from Sarsi's instruction and shall give little heed to his witticisms, taking shelter under your shadow; or, to put it better, I shall illuminate my shadow with your splendor. But getting back to the point, you see how once more he will have it that I deemed it a great defect on the part of Father Grassi to have adhered to Tycho's doctrine, and he asks resentfully: 'Whom then should he have followed? Ptolemy, whosedocrine has been revealed to be false by the recent observations of Mars? Or perhaps Copernicus? But he must rather be rejected by everyone, in view of the ultimate condemnation of his hypothesis.' Here I note several things, and I reply first that it is quite false that I have ever criticized anyone for following Tycho, even though I might very reasonably have done so, as will indeed at last become clear to his adherents from the Anti-Tycho of the distinguished Chiaramonti.10 Hence, so far as this remark is concerned, Sarsi is very wide of the mark. Even more irrelevant is his introduction of Ptolemy and Copernicus, who are never to be found writing a word relative to the distances, magnitudes, movements, and theory of the comets, which (and which alone) are here under consideration. He might with as much reason have brought in Sophocles, Bartoli,11 or Livy. It seems to me that I discern in Sarsi a firm belief that in philosophizing it is essential to support oneself upon the opinion of some celebrated author, as if when our minds are not wedded to the reasoning of some other person they ought to remain completely barren and sterile. (j>. 25) Possibly he thinks that philosophy is a book of fiction created by some man, like the Iliad or Orlando Furioso— books in which the least important thing is whether what is written in them is true. Well, Sig. Sarsi, that is not the way matters stand. Philosophy is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood

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unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth. Sarsi seems to think that our intellects should be enslaved to that of some other man (I shall disregard the fact that in thus making everyone, including himself, an imitator, he will praise in himself what he has blamed in Sig. Mario), and that in the contemplation of the celestial motions one should adhere to somebody else. But even allowing this assumption, I do not see why he selects Tycho and sets him before Ptolemy and Nicholas Copernicus, for both of these have constructed and followed out to the end, with the greatest skill, complete systems of the universe. This I cannot see that Tycho has done, unless indeed Sarsi thinks it is enough for Tycho to have rejected the other two systems and promised us a new one, though failing afterward to carry out his promise. I wish that besides having convicted the other two of error, Sarsi had recognized something of Tycho's; for, as to the system of Ptolemy, neither Tycho nor other astronomers, nor even Copernicus, could clearly refute it, inasmuch as a most important argument taken from the movements of Mars and Venus stood always in their way. Since the disc of Venus shows itself in its two conjunctions and elongations from the sun to vary but little in magnitude, and that of Mars at perigee is scarcely three or four times larger than it is at apogee, one could never be persuaded that the former really shows itself forty and the latter sixty times as large in one position as in the other, as required if their revolutions were about the sun in accordance with the Copernicus system. Yet I have demonstrated this to be true and to be apparent to our senses, and (p. 26) by means of a fine telescope I have made it palpably evident to anyone who wished to look. Then as to the Copernican hypothesis, had not the most sovereign wisdom removed us Catholics from error for our own good and illuminated our blindness, I do not believe that this grace and benefit could have been derived from the reasons and experiences embraced by Tycho.

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Thus the two systems being surely false and Tycho's being null, Sarsi should not reprehend me for desiring with Seneca the true constitution of the universe. The request is a large one, and though such knowledge is greatly desired by me, I do not (as Sarsi writes) deplore the misery and misfortune of our age amidst lamentations and tears, nor is there any trace of such a complaint to be found anywhere in Sig. Mario's essay. But Sarsi, under the necessity of camouflaging and supporting some ideas of his which he wished to explain, went about preparing and supplying attacks himself which have not been made against him by anyone else. And even if I did deplore this misfortune of ours, I fail to see how Sarsi could properly say that my complaints had been voiced in vain because I had no means of power to remove the distress. It seems to me that this is precisely what would give me cause for regret, and that on the other hand there would be no occasion for mourning if I were able to remove the misfortune. VII Now, at length, let your Excellency read this: 'Although . . . ( / . 27) . . . treated in kind' (p. 7 2 , 1 . 1 to 1.26). Hurrying over in a few words what is written here, I say that Sig. Mario and I are not so austere as to be revolted by jokes or poetic graces. As evidence of this there are the various charming things inserted very airily by Father Grassi in his treatise of which Sig. Mario has not breathed a word in reproach. It is indeed delightful to read of the birth, the cradle, the dwellings, and the funeral of the comet, and of its having been lighted to illuminate the supper meeting of the sun with Mercury. It has given us no offense that these lamps were lighted twenty days after the supper; still less, that we know that where the sun is, candles are superfluous and useless, and that this was no supper but merely luncheon; that is, a feast by daytime and not by night, which time of day is unknown to the sun. All these things were passed by without question because, spoken as they were, they left nothing to be desired as to the truth of the concepts underlying these jests which was in itself so well known and obvious that it needed no other and more profound demonstration.

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But now, in a fundamental and very difficult question, Sarsi tries to persuade me, all joking aside, that there exists in nature a particular celestial orb for comets, and whereas Tycho was unable to untangle himself in his own explanation of the irregularity of his comet's apparent motion, Sarsi expects my mind to be satisfied and set at rest by a little poetic flower which is not followed by any fruit at all. This is what Sig. Mario rejects when he quite correctly and truly says that nature takes no delight in poetry. This proposition is quite true, even though Sarsi shows that he does not (p. 28) believe it, and pretends not to recognize either nature or poetry and not to know that fables and fictions are in a sense essential to poetry, which could not exist without them, while any sort of falsehood is so abhorrent to nature that it is no more possible to find one in her than to find darkness in light. But it is time for us to get on to more important matters; therefore let your Excellency read the following. VIII 'Now I come . . . the same argument?' (p. 72, 1. 27 to p. 73,1. 13). In order to recognize just how important are the things written here, it will suffice to review briefly what it is that Sig. Mario says and what is raised against him here. Sig. Mario writes in general: 'Those who wish to determine the place of the comet by means of parallaxes need first to establish that it is a fixed and real thing and not a vague appearance, inasmuch as the reasoning from parallax is indeed conclusive for real objects but not for apparent ones.' This he exemplifies in many ways, and then he adds that absence of parallax renders incompatible the two {p. 29) propositions of Aristotle that a comet is a fire, which is a real thing, and that it is located in the air very near the earth. Here Sarsi rises up and says, 'All very well, but this is beside our purpose. For we are arguing against Aristotle, and it would be a waste of time to prove that the comet was not an appearance when we agree with him to the extent of its being a real thing. And taking it as a real thing, our argument from parallax is conclusive. And,' he adds, 'our adversary himself does

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not employ any more valid an argument against Aristotle; now if he does not, then why may not we freely use it in the same cause ?' Well, here I do not know what Sarsi is asserting nor in what he thinks he is impugning Sig. Mario, seeing that both are saying the same thing; that is, that reasoning from parallax does not hold for mere appearances but holds very well for real objects, and consequently holds against Aristotle when he would have the comet be a real thing. If Sarsi will permit me to be frank, nothing more need be said here than that he has tried to dress up Sig. Mario's remark so as to dazzle the reader's vision and leave him with the idea that Sig. Mario had made a blunder. In order for Sarsi's objection to have any force, it would be necessary for Sig. Mario, instead of saying generally to everyone: 'Whoever wishes the argument from parallax to bear upon comets must first prove that comets are real things,' to have said specifically: ' I f Father Grassi wants the argument from parallax to operate against Aristotle, who takes comets to be real things and not apparent only, then he must first prove that comets are real things and not apparent ones.' In that way Sig. Mario would truly have been guilty of a bad error, as Sarsi wants to make it appear that he was. But Sig. Mario never wrote or thought any such foolishness. IX 'Furthermore the opinions... { p . 3 0 ) . . . drives and draws it.' (p. 73, 1.14 to p. 74,1.19). (p. 31) Once more trying to show that the general question advanced by Sig. Mario was vain and superfluous, Sarsi says that no author worth considering, ancient or modern, ever supposed a comet capable of being a mere appearance; and for that reason that his master, who was disputing only with such men and who aspired to victory over them alone, never had any need to remove comets from the company of mere images. T o this I respond that in the first place Sarsi might for this very reason ignore Sig. Mario and me also, since we are outside the number of those ancient and modern authors against whom his master was disputing. We intended to speak only with those men, whether ancient or modern, who try in all their studies to

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investigate some truth in nature, completely avoiding those who merely engage ostentatiously in noisy contests in order to be popularly judged and pompously praised not as discoverers of truth but merely as victors over others. Nor need he have gone about so anxiously overthrowing something which is not prejudicial either to himself or to his master. In the second place, he should have considered that a man may be much more readily excused who expresses a belief and happens not to think of some detail pertaining to it (especially one which had not occurred to a thousand others who have expressed the same belief) than may one who thinks up something foolish and useless on the subject. Thus he could, and should, confess that it had never passed through his master's mind or occurred to any of his predecessors that a comet might be an appearance, rather than call the consideration which occurred to us foolish. For the one course, without giving any offense to his master, would have indicated candor and frankness, while the other, necessarily damaging my reputation (if he had succeeded in it), betrays instead a spirit moved by some passion. Sig. Mario, in the hope of doing something profitable and welcome to men studious of truth, proposed with all humility that henceforth it would be good to consider the essence of the comet, and whether it might not be a mere appearance rather than a real thing, {p. 32) He did not criticize Father Grassi or anyone else who had not previously done this. Sarsi now rises up and passionately strives to prove the suggestion to be beside the point and obviously wrong. Still, in order to be prepared for anything (lest it should appear worthy of some consideration), he robs me of any possible credit by calling it an old notion of Cardan and Telesio, disparaged by his master as a fantasy of feeble philosophers who have no following. Under this pretense, and without any shame for his disrespect, he robs and strips them of their reputations in order to cover up a very small blemish in his master. Well, Sarsi, though you represent yourself as a pupil of these venerable Fathers in natural philosophy, make no such claim as to moral philosophy, for you will never be credited. I have not seen what Cardan and Telesio wrote, but from other indications which will presently appear I may readily guess that Sarsi did

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not catch their meaning. At the moment, I cannot neglect, for his benefit and in their defense, to show the improbability of his deduction that their science was poor from the small number of followers they have. Sarsi perhaps believes that all the hosts of good philosophers may be enclosed within walls of some sort. I believe, Sarsi, that they fly, and that they fly alone like eagles, and not like starlings. It is true that because eagles are scarce they are little seen and less heard, whereas birds that fly in flocks fill the sky with shrieks and cries wherever they settle, and befoul the earth beneath them. But if true philosophers are like eagles, and not like the phoenix instead, Sig. Sarsi, the crowd of fools who know nothing is infinite; many are those who know very little of philosophy, few, indeed, they who truly know some part of it, and only one knows all, for that is God. To say plainly what I am trying to hint, and dealing with science as a method of demonstration and human reasoning capable of pursuit by mankind, I hold that the more it shall partake of perfection, the smaller the number of conclusions {p. 33) it will promise to teach, and the fewer it will demonstrate; hence the less attractive it will be, and the smaller will be the number of its followers. On the other hand, magnificence of titles and grandeur and number of promises attract the natural curiosity of men and hold them perpetually involved in fallacies and chimeras, without ever offering them one single sample of the sharpness of demonstration, by which the taste might be awakened to the insipidity of its ordinary fare. Hence these will keep an infinite number of men occupied, and that man will be very fortunate who, led by some unusual inner light, shall be able to turn from the dark and confused labyrinths within which he might have gone forever wandering with the crowd and becoming ever more entangled. Therefore, in the matter of philosophy, I consider it not very sound to judge a man's opinion by the number of his followers. But though I think the number of followers of the best philosophy may be very small, I do not conclude conversely that therefore those opinions and doctrines are necessarily perfect which have few followers, for I know very well that some men may hold opinions so erroneous as to be rejected by everyone else. Now from which of

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these two sources is derived the scarcity of followers of the two authors named by Sarsi as sterile and derelict, I do not know; I have not studied their works sufficiently to judge. Returning to our subject, I say that it seems to me Sarsi is a trifle tardy in his attempt to persuade us that the reason his master made no mention of the idea that the comet might be a mere simulacrum to which the argument based on parallax does not apply was not that it had not occurred to him but that it had been dismissed by him as a foolish notion. This excuse comes late, I say, because his master had written in the Problem: 'Anything established between the firmament and the earth, if observed from different places, will correspond to different parts of the same firmament.'12 This clearly shows that there had not occurred to him the matter of rainbows and haloes, mock suns, and other reflections that are not subject to that law, which he should have mentioned and excepted—especially since he himself, forsaking Aristotle, inclines toward Kepler's opinion that the comet (p. 34) might be a reflection. But to continue, I see that Sarsi makes a great distinction between the head of the comet and its beard or curl. He holds that, as to the curl, this might truly be an optical illusion and an appearance (as was believed also by those Pythagoreans whom Aristotle mentions), but as to the head, he thinks that this must be a real thing and that nobody has ever thought otherwise. Now here, I should like a welldefined distinction between what Sarsi means by real and what he takes as apparent, and what his standard is for calling something real or apparent. If he calls the head real because it exists in a real substance and material, then I say that so is the curl real; for if anyone should take away those vapors in which our vision is reflected toward the sun, this would likewise remove the curl, just as removing the clouds takes away rainbows and haloes. And if he requires the curl to be unreal because it would not exist without the reflection of vision toward the sun, then I say that the same would follow for the head. The head no less than the curl is nothing but a reflection of rays in some material, whatever that material may be, and though as reflections they are merely appearances, as to the material they are real. If Sarsi admits that a change of position on the part of the

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observer makes (or may make) a change in the place where the curl is generated in the material, I say that this may follow in the same way for the head, nor do I believe that those ancient philosophers thought otherwise. If, for example, they had thought that the head was inherently a consistently shining star while the tail alone was an appearance, then they would have said that when because of the obliquity of the sphere there was no reflection of our vision toward the sun, the curl would no longer be seen, while the star—that is, the head of the comet—would be seen as well as ever. This they did not say; they said that the whole comet was not seen, a clear indication that the generation of both head and curl is identical. And whether or not the ancients said this, it is now brought under consideration by Sig. Mario with very reasonable grounds for raising the question; this may be weighed, as is done by Sig. Sarsi, and in the proper place (p. 3 5 ) we shall consider what he has written about it. X Meanwhile let your Excellency proceed to read this: Ί must reply . . . {p. 3 6 ) . . . comets do not possess ? ' (p. 7 4 , 1 . 2 0 to p. 7 5 , 1 . 2 0 ) . Sig. Guiducci, with the very honorable intention of smoothing the road for seekers of truth, had brought into consideration the fallacy of those who argued that because the comet appeared to move in a straight line its movement was along a great circle. He averred that although it was true that motion along a great circle would always appear straight, it did not necessarily follow that motion which appeared straight was necessarily along a great circle, as assumed by those who had inferred from the comet's apparent straight motion that it moved along a great circle. Among these was Father Grassi, and, perhaps resting on the authority of Tycho (who had first equivocated thus), he neglected something which he might not have overlooked if his predecessor had not done so. T o me this makes Father Grassi's small error quite excusable, though I believe from what Sig. Mario says that the Father made much of this and held it in high esteem. N o w comes Sarsi, continuing in his predetermined course and contriving to make the remark appear as an inadvertence of trifling importance, believing he can rescue his master in this way;

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but it seems to have the opposite effect (if the Father lends his assent to Sarsi's excuses and defenses), for in trying to save a single error he will run into many more. First, still reputing it vain and superfluous to heed things which neither he nor others have noticed, Sarsi says that since his master was disputing against Aristotle and the Pythagoreans who never brought up a straight motion for the comet, it would have been beside the point to have attempted to dispose of this. But careful consideration shows that this excuse has not assisted the Father at all, for neither did the same adversaries ever mention a cometary motion along lesser circles, and hence it was equally superfluous to prove that comets move along great circles. Therefore Sarsi must either find that the ancients wrote that comets moved along lesser circles, or confess that it was as (p. 37) redundant for his master to consider the motion to be along a great circle as it would have been for him to have considered it straight. T h e second point is that under Sarsi's own rule it was a still greater defect to omit consideration of straight motion, inasmuch as it was Kepler who had attributed this to comets, and he is named by Sarsi himself. Nor does the excuse he puts forth seem to me at all sufficient —that since this opinion was deduced by Kepler as a consequence of the earth's motion, a proposition that cannot be piously and religiously held, Sarsi has therefore deemed it worthless. Why, this must be so much the more motive for destroying it and demonstrating its impossibility; surely it is not a bad idea to prove also by physical reasons, if possible, the falsity of those propositions which have been declared repugnant to the Holy Scriptures. Third, Sarsi's excuse is also defective because not only motion which is truly straight would appear to be made along a straight line, but any other motion, as long as it occurred in the same plane as that in which the observer's eye is located. This is even hinted by Sig. Mario; hence Sarsi will have to find some other way to persuade us that no movement except the circular has ever occurred to anyone as suitable to assign to comets. I do not see how he could entirely succeed in this, since, if nobody else had mentioned one, Sarsi himself did so in writing a few lines later, when, in defense of an

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elongation from the sun of more than ninety degrees, he allowed a non-circular motion and admitted motion along an oval line, and even required the motion along this line to be irregular. Hence, it is necessary either for the movement in question to be now circular and now oval and now completely irregular, according to Sarsi's necessities, or for him to confess his defense of his master to be defective. Fourth, what if I admit the motion of the comet to be circular, and not merely by popular opinion, but truly and necessarily ? Will Sarsi perhaps suppose that it is conclusively proved to be along a great circle by its motion having appeared to his master and others as along a straight line ? I know that Sarsi has believed this until now, but he has been mistaken; and (p. 38) if I thought it would not annoy him, I should remove him from error. In order to do this, I should ask him which circles in the sphere he calls great circles. I know that he would answer me, 'Those which passing through its center, which is also the center of the earth, divide it into two equal parts.' Then I should say, ' S o the circles described by Venus, Mercury, and the Medicean planets are not great circles at all, but rather are quite small ones, the last named having Jupiter for their center, and the others having the sun for theirs. Yet if one observes how their movements appear, these will be found to be along a straight line.' This comes about because our eye is located in the same plane as that in which lie also the circles described by the stars mentioned. We conclude from this that nothing may be deduced from a motion appearing to be straight except that it is made in the plane which passes through the eye (that is, in the plane of a great circle); not that it is along the circumference of a great circle any more than a smaller one. In itself, this motion might be made in a circular line, or in some other line as irregular as you please, and still appear straight. Thus the two propositions already examined by us are not equivalent, and to take one for the other is an equivocation and an error in logic. If I might rest assured that Sarsi would not take it ill, I should like to compare this fallacy with another and similar one which I see has been overlooked by some very great men, and upon which perhaps

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Sarsi himself has not reflected. I should not wish to cause him displeasure by showing him that I have not also overlooked it, as have so many other people more perspicacious than myself, but, be that as it may, I shall impart it to your Excellency. It has been noted by very sharp observation that the tip of the tail, the head of the comet, and the center of the sun's disc are always perceived along the same straight line, and from this it has been very strongly conjectured that the tail is a refraction of the solar light extended diametrically opposite to the sun. Up to the present, as far as I know, no one has considered that the sun and the whole length of the comet appearing in a straight line does not necessarily prove that the straight line drawn from the tip of the tail to the head of the {p. 39) comet would, if prolonged, terminate in the sun. In order that three or more points may appear in a straight line, it is sufficient for them to be located in the same plane as the eye; thus, for instance, Mars or the moon is sometimes seen in line between two fixed stars, but the straight line joining the two stars would not for that reason pass through Mars or the moon. Hence nothing can be necessarily concluded from the tail of the comet appearing directly opposite to the sun, except that these are in the same plane as the eye. Now, in the fifth place, let there be noted what I may call a certain inconstancy in the words toward the end of the passage just examined by your Excellency and me. Sarsi undertakes to show later how incorrectly I (that is, Sig. Mario) have attributed straight motion to the comet; then, three lines below, he says that there is no need to disprove straight motion, it being certain and evident that this has never been found in comets. But if the impossibility of this motion is certain and evident, to what purpose has he undertaken to disprove it ? And in what way is this certain and evident if, according to Sarsi's statement, no one yet has so much as considered it, let alone refuted it ? Such motion, he says, has been taken into consideration by Kepler alone. But Kepler does not refute it; rather, he introduces it as possible and true. It seems to me that Sarsi, feeling himself unable to do anything else, tries to get the reader tangled up. But I shall endeavor to undo the knots.

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XI 'But, furthermore, in this place . . . (p. 40). . . comets too close at hand.' (p. 75,1.2itol. 33). Here, first of all, if I accept Sarsi's imputation of negligence because various motions that might have been attributed to the comet did not occur to me, then I do not see how he can exculpate his master from the same criticism for not having considered its possible straight motion. If he excuses his master by saying that such a consideration would have been superfluous on account of this movement's not having been introduced by any other author, I fail to see why I deserve to be criticized; I may be granted the same pardon, since no other author has introduced these alien motions which Sarsi now names. Besides, Sig. Sarsi, it was up to your master and not to me to think of these movements by which suitable reasons might be rendered for such great elongations of the comet. If any movement lends itself to such a requirement, you ought to have named it and accepted that one alone; you should not have passed it over in silence and adduced with Tycho a simple circular motion about the sun (which is quite unsuitable for saving the appearance in question), and then pretended that not he but we were in the wrong for not divining that he might have given inward assent to ideas very different from those he had written. Moreover, Sig. Mario never said that nature afforded no way to save the elongation of ninety degrees; indeed, if such an elongation took place it is perfectly clear that there was also a way in which it did so. What he said was that in the hypothesis accepted by the Father there could be no such elongation without the comet's touching the earth and even penetrating it. Sarsi's excuse is vain, then, up to this point. But perhaps he pretends that any trivial excuse is allowable for his master, while for me even the strongest one remains invalid. If that is it, I gladly hold my peace and freely concede him the point in question. In the second place, I am going to produce another excuse on behalf of myself disguised as Sig. Mario. Naively confessing my never having thought of movements along eccentrics or oval lines or any other irregularities, I say that this was because it is not my

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habit to give ear to conceptions which have nothing to {p. 41) do with the matter in hand. And why does Sarsi want to introduce an oval motion round the sun in order to have the comet elongate ninety degrees ? Does he perhaps believe that by stretching the shape in one direction and compressing it in another he can succeed in his design ? Surely not; not even if he could stretch it to infinity.13 And the same impossibility exists for the eccentric which has its smaller part beneath the sun. For Sarsi's information, should your Excellency ever meet him, you may suggest to him two straight lines A B and C D , C D being perpendicular to AB, and say to him that supposing

C

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A Fig. 17

the straight line D C to be that which goes from the eye to the sun, then that by which the comet would be seen at an elongation of ninety degrees would necessarily be either D A or D B , it being generally conceded that the apparent motion of a comet is in the plane of a great circle. Entreat him then for our edification to describe the eccentric or oval designated by him, along which the comet in its motion may get down far enough to be seen along the line A D B , as I confess I do not know how to do this. Thus far, two of the proposed means are excluded; there remain the other eccentric (with its center removed to the right or left from the line DC), and the irregular path. As to the eccentric, it is true that it is not entirely impossible to draw this on paper in such a way as to create the elongation sought; but I say to Sarsi that if he would

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set himself to draw the sun with the orbs of Mercury and Venus around it, and also the earth encircled by the orb of the moon, both of which must be provided for, and then should attempt to fit in this eccentric for the comet gracefully, I feel certain that confronted with such absurdities and monstrosities he would be afraid to rescue his master by means of such a makeshift even if he could. A s to irregular lines, there is no doubt that by them not only this appearance may be saved, but any other; yet I warn Sarsi that the introduction of such lines, far from helping his master's cause in any way, (ρ. 42) would only prejudice it more seriously; not only because he never mentioned them, and on the contrary accepts a circular line, the most regular that exists, but because it would be very frivolous to propose this. Sarsi himself may understand this if he will consider what is meant by an irregular line. Those lines are called regular which, having a fixed and definite description, have been susceptible of definition and of having their qualities and properties demonstrated. T h u s the spiral is regular, and its definition originates in two uniform motions, one straight and the other circular; so is the ellipse, which originates from the cutting of a cone or a cylinder; and so on. But irregular lines are those which have no determinacy whatever and are indefinite and casual, and hence indefinable; no property of such lines can be demonstrated, nor in a word can anything be known about them. Hence to s a y , ' Such events take place by reason of an irregular line' is the same as saying,' I do not know why they occur.' T h e introduction of such lines is in no way superior to the sympathy, antipathy, occult properties, influences, and other terms employed by some philosophers as a cloak for the correct reply, which would be: Ί do not know.' T h a t reply is as much more tolerable than the others as candid honesty is more beautiful than deceitful duplicity. Father Grassi was therefore much more prudent in not proposing irregular lines as a means of fulfilling his needs than his pupil was in mentioning them. If I may say frankly how it looks to me, I certainly believe that Sarsi himself understood well enough the inefficacy of his answer and how ill-founded it was. I judge this from his having hurried quickly over it, though the point was most important in the matter

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under consideration, and the difficulty raised by Sig. Mario was quite serious. Sarsi himself serves as my best witness to this when on page 81, in speaking of a certain argument used by his master, he writes:' Furthermore, what significance we gave to this argument can I believe, be sufficiently understood from that fact that it was presented in few words, and its meagreness was due to the fact that all had previously been explained much more precisely and fully in the two other arguments.' The brevity and simplicity {p. 43) with which he has touched upon this may be seen, among other things, from his not having made a diagram of the eccentrics and ellipses introduced to save the whole. Yet farther on, we shall meet with a sea of diagrams introduced into a long discourse designed to corroborate an experiment which in the end fails to achieve the slightest assistance for the main point under consideration there. But without my saying any more, your Excellency may embark upon the following ocean of distinctions, syllogisms, and other logical paraphernalia, and see how high an opinion Sarsi entertains for something which, frankly, I consider to be so much woolgathering. XII 'Since Galileo . . . [pp. 44-45] (p. 46) . . . their very clear lights.' (P· 75,1-34 to p. 79,1- 33)· Here, as your Excellency sees, in exchange for the equivocation into which Father Grassi had run by following (as Sig. Guiducci remarks) in the footsteps of Tycho and others, Sarsi wants to show that I have erred as much or more in logic when (p. 47) I argued in the following way to show that the magnification of the telescope is the same for the fixed stars as for other objects, and is not imperceptible or nonexistent as Father Grassi had written.' Many stars completely invisible to the naked eye are made easily visible by the telescope; hence this augmentation should be called infinite rather than nonexistent.' Here Sarsi gets up in arms and in a series of long attacks does his best to show me to be a very poor logician for having called such enlargement 'infinite.' At my age, these altercations simply make me ill, though I myself used to plunge into them with delight during my childhood, when I too was under a schoolmaster. So to

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all this I answer briefly and simply that it appears to me that Sarsi openly reveals himself to be just what he tries to prove me to be; that is, little cognizant of logic, since he takes as absolute something which was meant relatively. It has never been asserted that the enlargement of the fixed stars is infinite. Rather, the Father having written that it is nil, and Sig. Mario having noted that this is not true because a great many completely invisible stars are rendered visible, it was added that such enlargement ought rather to be called infinite than nil. Now who is so simple as not to understand that if we call a profit of one thousand upon a capital of one hundred' large,' and not 'nil,' and the same gain upon a capital of ten 'very large,' and not 'nil,' then the acquisition of one thousand upon a capital of nothing should be called 'infinite' rather than 'nil'? When Sig. Mario has spoken of the absolute enlargement, even Sarsi knows (and has written in several places) that he has said it is the same as that of all other objects seen through the same instrument. So when in this place he tries to tax Sig. Mario with a short memory, saying that he ought to remember having said at other times that the same instrument increases all objects in the same ratio, the accusation becomes foolish. And even if Sig. Mario had called it infinite, without any relative term, I should never have expected such carping criticism as this attack, since using the word 'infinite' in place of 'very large' is a manner of speaking which is employed every day. Here indeed Sarsi has a large field for showing himself to be a better logician than all the other {p. 48) authors in the world, in whom I assure him that he will find the word 'infinite' chosen nine times out of ten in place of'very large.' Nor is that all, Sarsi. If the Preacher should confront you and say, 'The number of fools is infinite,' 14 what would you do then ? Would you perhaps dispute with him and maintain his statement to be false ? You could prove on equal scriptural authority that the world is not eternal, and that having been created in time there cannot have been and cannot be infinite men; and since foolishness reigns only among men, the proposition in question could never be true even if all men, past, present, and future, were fools; for there could never be an infinite number of human individuals even if the world were to endure eternally. Η

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Getting back to the point, what shall we say of the other fallacy so subtly detected by Sarsi in our calling 'enlargement' that which takes place when an invisible object is made visible by the telescope ? This cannot be called 'enlargement,' he says, because enlargement presupposes some quantity, and enlarging is nothing but making greater from less. I really do not know what to say to this in excuse for Sig. Mario, except that he was speaking everyday language, as it is called. Believing that the property of the telescope by which it shows us these objects which we cannot discover without it was the same as that by which things already visible are shown to us much larger, and, feeling that this is generally called an enlargement of the image or of the visible object, he permitted himself to transfer this name in the same sense to something which Sarsi now declares to us should be called not 'enlargement' but 'passage from nonexistence into existence.' Hence, for example, when the telescope enables us to read from a great distance some writing of which we should see only the capital letters without it, to speak logically one should not say that the telescope enlarges the capitals, but causes the small letters to pass from nonexistence into existence. But if the word 'enlargement' cannot be correctly used when nothing actual is presupposed (p. 49) to receive the enlargement, perhaps it is no more justifiable for Sarsi to appropiate the word 'passage' or 'transfer' where there do not exist two end points, one from which something leaves and another to which it passes. And who knows ? Perhaps Sig. Mario held and holds the opinion that from very distant objects the pure images reach us only under such acute angles as to remain imperceptible to our senses, and are as if nonexistent, though they really do exist. If I may give my opinion, I think that if they were truly nothing, all the telescopes in the world would not suffice to make them become something. Thus the images of invisible stars, no less than those of the visible ones, are spread throughout the universe, and hence enlargement may be predicated of them also, with all due respect to Sarsi and without any error in logic. But why should I go on raising questions about something for which I have sensate and conclusive proof? There is a supplemental radiance seen by us which is not really located around the stars, but

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is in our eyes; only the bare and sharply bounded image comes from the star. We know positively that a nebula is nothing but an aggregate of many minute stars which are invisible to us; yet the field which they occupy does not remain invisible. It shows itself in the aspect of a little whitened patch, coming from the conjunction of the separate radiances that crown each of these little starlets. But since these irradiations exist only in our eyes, it must be that each image of each starlet exists really and distinctly in our eyes. From this, one may deduce another doctrine—that the nebulae and even the Milky Way do not exist in the sky but are a pure sensation (affezione) of our eyes, in the sense that, if our vision were so acute as to distinguish those minute stars, there would be neither nebulae nor a Milky Way in the sky. These conclusions not having been previously voiced by others, I suppose they will not be admitted by Sarsi, and he would still have it that Sig. Mario sinned by calling 'enlargement' that which according to him should be called 'passage from nonexistence into existence. ' Well, be that as it may, I have permission from Sig. Mario (in order not to engage in (p. 50) new battles) to concede to Sarsi the entire victory in this skirmish, as well as in the one which follows, in which Sarsi agrees that the revealing of invisible fixed stars may be called enlargement in relation to visibility but not in relation to quantity. All this is conceded to him if only he will grant to us that both the invisible and the visible stars (let them be increased in relation to whatever he pleases) are ultimately increased in such a way as to render completely false the doctrine of his master, who wrote that they were not increased in any way at all. It was upon that statement that he founded the third of those arguments by means of which he undertook to prove the primary thesis of his treatise; namely, that of the location of the comet. But what shall we reply to still another error in logic which Sarsi would attribute to us ? Let us first hear it, and then we may decide on the most appropriate reply. Not content with having shown that the disclosure of invisible fixed stars ought not to be called an infinite enlargement, Sarsi goes on to prove that saying that their disclosure results from the telescope is a grave error in logic, whose laws require

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that when one effect may be derived from several causes we cannot correctly infer from it one particular cause. In order to show clearly that many causes may exist (in addition to that of the telescope) for something becoming seen which was not seen at first, Sarsi names these one by one, saying that it is necessary to eliminate them all and show that they have no part in causing invisible stars to be seen through the telescope. Hence, in order to escape Sarsi's imputations, Sig. Mario would have to show that first, bringing the telescope to the eye would not in itself and by itself increase the visual power (for this, indeed, is a cause that might make something visible which was not seen previously); second, he would have to show that this act would not be a removing of clouds, trees, roofs, or other intervening obstacles; third, that it was not a mere use of ordinary spectacles (I am simply enumerating the causes set down by Sarsi himself, your Excellency, without altering anything); fourth, that it was not an improved illumination of the object; fifth, that it was not (p. 51) a bringing of the star down to earth or a venturing forth on our part into the sky, by which the interval between would be diminished; sixth, that it did not make the stars swell up so as to enlarge and become more easily visible; seventh and last, that it was not an opening of closed eyes. Each of these—and especially the last—is sufficient to make us see what we did not see before. I do not know what to say to you, Sig. Sarsi, except that you reason very well. The only thing that dissatisfies me is that all these imputations fall back upon your master without so much as touching Sig. Mario or me. I ask you whether any of these causes which you produce as capable of making us see what we would not see without them (as, for example, bringing things closer, interposing vapors or lenses, etc.)—I ask you, I say, whether any of these causes can produce the effect of enlarging visible objects in the way in which the telescope produces that effect. I believe that you will answer yes. Then I shall add that you have openly accused your master of being a poor logician too. For he, speaking generally to everyone, would recognize the enlargement of the moon and of all other objects by the telescope alone, without bothering to exclude any of the other causes, as in your opinion he would be obliged to do. But that obligation

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does not fall upon Sig. Mario at all; he was speaking only to your master, and not to everyone; and he was attempting to show that what your master had said about the effect of the instrument was false. Hence, he considered the matter in the way in which his adversary had considered it, and was not obliged to do so in any other way. Indeed, your charge of being a poor logician falls the more heavily upon your master inasmuch as he has transgressed against this very same rule on another most important occasion—I mean by inferring revolution in a great circle from motion apparently straight. For the same effect might be caused by motion truly straight, or by any other motion in the same plane as the eye. Very acute men might inquire into all three of these cases with good reason, and according to your statement your master himself did not refuse to accept motion along an oval line or even an irregular one. But I do not believe it would ever occur to any but the most simple-minded to raise a question whether any of your seven causes as set forth above could {p. 52) possibly bear upon the disclosure of invisible stars when they are observed through the telescope, if I may speak frankly. I do not mean to place Sarsi in the ranks of the simple-minded because he has allowed himself to get into this position, your Excellency, for it is clear that he has not spoken from inner conviction; ultimately he very nearly concedes that, since nothing but the telescope is being considered, these other causes may be set aside. Yet such an open concession had as its consequence the vacuity of his previous accusation, and nullifies the idea that I am a poor logician which it might have impressed upon some of his readers. T o obviate all this, he adds that not even the above suffices for good reasoning, because it is not in one way only that the telescope renders visible what was not seen before, but in two. The first is by bringing objects to the eye under a greater angle, which makes them appear larger; and the other is by uniting the rays and images so that they act more strongly. And since either of these suffices to render visible that which was not perceived, one may not infer a single one of these causes from the effect. Such are his very words, whose inner sense I must admit I cannot fathom, inasmuch as they are a bit too general.

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It seems to me that it would have been more to the point for him to have expressed himself more specifically, for his proposition may be understood in several ways. Perhaps the first of these to come to mind is one which contains within itself a manifest contradiction, for to bring objects under a greater angle represents an effect contrary to that of compressing together the rays and the objects. Since the rays conduct the images, it is hard to understand how during their passage they are compressed together and at the same time form a larger angle; an angle is formed by lines running together, so it would seem that by restricting them the angle should become more acute rather than wider. But if Sarsi had conjured up some other way in which (p. 53) the rays, uniting, might form a larger angle (and I do not deny that such might be found), then he ought to have stated it and distinguished it from this other, so as not to leave the reader in the midst of doubts and equivocations. Assuming for the moment that there are two ways for the telescope to work, I should like to know whether it always operates both ways at once, or sometimes one way and sometimes the other, separately, so that when it is used to enlarge the angle it desists from restraining the rays, and when restricting the rays it preserves the angle always at its original size. If it always operates with both these methods, then Sarsi is acting with great simplicity when he criticizes Sig. Mario for not having designated and accepted one and excluded the other. But if it operates with one only, then it is Sarsi who has erred in not designating that one and excluding the other—showing, for example, that the telescope works by enlarging the angle when we look at the moon, which enlarges very considerably, but that when we look at the stars it merely unites the rays and does not increase the angle. So far as I can say with confidence, in the infinite—or I should say in the very many—times that I have looked through the instrument, I have never noticed any difference whatever in its mode of operation, and so I think it works always in the same way. Moreover, I believe that Sarsi thinks so too; and in that case, it must be that the two operations of enlarging the angle and restricting the rays always coincide, which accordingly puts Sarsi's objection completely and entirely beyond the pale. For it is certainly true that an

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error is committed by anyone who infers a particular cause from an effect which may depend upon several separate causes; but if the causes are always inseparable, one may at will infer from the effect whichever cause suits him best, inasmuch as every time the effect is present that cause must necessarily be present also. Thus, to give an example, whoever may s a y : ' So-and-so has lighted the fire, hence he made use of a burning-glass' would err, for fire might be lighted by hammering an iron, by tinder and spark, by rubbing two flints together, or in other ways. But he who says: Ί have heard my neighbor striking fire' and adds [p. 54) 'therefore he has a flint' would be criticized unreasonably by anyone who would argue against him that, since in that operation, in addition to flint, there are steel, tinder, and sulphurous material as well, he could not in good logic infer flint with certainty. And thus if the enlargement of the angle and the union of rays always concur in the operations of the telescope, and one of these makes the invisible become seen, then why should one not infer from the effect whichever he likes of the two ? I think I see somewhat into Sarsi's mind; if I am not mistaken, he would have the reader believe what he himself certainly does not believe—that perceiving stars which previously were invisible depends not upon the enlargement of the angle but upon the union of the rays, and that the stars are made visible not because their images become larger but because their rays are strengthened. But he did not want to come out into the open because the other arguments raised by Sig. Mario, of which Sarsi had said nothing, would burden him too heavily—especially the argument that the intervals between stars are perceived to be enlarged in the same ratio as objects here below, which intervals ought not to increase in size unless the stars do, since they are as distant from us as the stars are. But to sum up, I am sure that if Sarsi would explain himself as to how he understands these two operations of the telescope (I mean of restricting the rays and of enlarging the angle), it would be obvious that not only are they both performed together but that they are one and the same thing, so that the rays are never united without the angle being enlarged. In order to hold a different opinion, he would be obliged to show that the telescope sometimes unites the

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rays without enlarging the angle, but that this happens only when the fixed stars are being observed. This he will never show to the end of time, for it is a most foolish fiction, or, to be blunt, a falsification. I did not expect to spend so many words on this trifling, your Excellency, but since the more has been done the less remains to do. Now for this other charge of violating the laws of logic. In Sig. Mario's division of the effects of the telescope, he is said to have included an effect which does not exist and to have left out one that {p. 55) should be given. For when he said, 'The telescope renders stars visible either by enlarging their images or by illuminating them,' 1 6 Sarsi will have it that he should have said instead, 'by enlarging them or by uniting the images and the rays.' I reply that Sig. Mario never had any intention of dividing what is one, and, so far as he and I are concerned, such is the manner of the operation of the telescope in representing objects to us. When he says, 'if the telescope does not render stars visible by enlarging them, then by some unheard-of means it must illuminate them,' he does not introduce illumination as an effect to which he subscribes, but he counterpoises it against the other as an obvious impossibility, with the intent of making still more evident the truth of this other. This is quite a customary manner of speaking, as when one says:' If our enemies did not scale the fortress, they must have rained here from the sky.' Now if Sarsi thinks he can win acclaim by impugning this way of talking, then another door is open to him (in addition to the one regarding 'infinite') for winning a logical battle against all the authors in the world. But in trying to show himself off as a great logician, let him beware lest he appear an even greater sophist. I seem to see your Excellency grin, but can I help this ? Sarsi took it into his head to write in opposition to Sig. Mario's treatise, and he has been forced to grasp at sky hooks, as they say. For my part, I not only excuse him but praise him, for it appears to me that he has accomplished the impossible. Returning to our subject, we have already seen that Sig. Mario did not seriously suggest illumination as a property of the telescope. Nor is that all; Sarsi himself confesses that this was put forth as impossible. Hence, illumination is not one of two alternatives;

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rather, as I have remarked, so far as we are concerned, there exists no alternative at all. As to the union of the images and rays recorded by Sarsi as an alternative omitted by Sig. Mario in his division, it would be well for Sarsi to specify how this second operation differs from the first. Up to this point, we have understood them to be the same thing, but when we are assured that they are two distinct and different operations, we shall understand how we have erred. Even then, the error will not be one of logic in listing alternatives, but one of optics in not having adequately fathomed all the effects (p. 56) of the instrument. When Sarsi says in conclusion that he does not at present wish to linger and note down other errors than those few found thus casually in a single place, and will omit the others, I first thank him for his compassion toward us. Next I rejoice for Sig. Mario, who may be sure that throughout his entire treatise he has not committed the slightest error in logic; for though Sarsi seems to hint that there are many more, I, at any rate, shall believe that he chose as the worst these which he has singled out and criticized. I leave it to you to judge by implication the quality and importance of the rest. I now come to consider this final part, in which Sarsi as a special favor to me attempts to ennoble the telescope with the admirable property of illuminating as well as enlarging the objects which are viewed through it. However, before I proceed, I wish to thank him for his courtesy, as I question whether this effect will put me under much obligation once we have considered the strength of the demonstrations brought forward to prove his point. And since in his own explanation it seems to me that for some unknown reason the author rambles around repeating the same proposition over and over again, I shall try to extract the meat of it. This appears to me to be as follows: 'The telescope represents objects as larger because it brings them to us under a larger angle than that under which they are seen without the instrument. Also, restricting almost to a point the images of luminous bodies and their scattered rays, it renders much more lucid that cone (or rather, luminous pyramid) by which objects are seen; and thus shining objects are represented as enlarged and also as illuminated by greater light. That the optic pyramid is rendered

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brighter by restriction of the rays is proved by reason as well as by experience. Reason teaches us that light collected in a smaller space must illuminate more, and experience shows us that a glass lens placed beneath the sun will not only burn wood where the rays come together, but will liquefy lead and blind the sight. From all this it may be concluded that it is as correct {p. 57) to say that the telescope illuminates the stars as to say that it enlarges them.' In return for Sarsi's courtesy and good will in exalting and ennobling this admirable instrument, the least I can do at present is to give complete assent to all the above statements and experiments. Yet it grieves me that in a sense they are more prejudicial to him by being true than they would be by being false; for the principal conclusion that they are supposed to prove is utterly false, and I do not think we can maintain that those who draw a false conclusion from true premises do not seriously transgress in logic. It is true that the telescope enlarges objects by bringing them under a greater angle, and it is quite true that they come to us in perspective. No less true is it that the closer uniting of the rays of the luminous pyramid renders them brighter, and consequently does the same for the objects viewed. The reason Sarsi assigns for this is correct, that the same light reduced to a smaller space illuminates better. And finally there is nothing wrong with his lens experiment of burning and blinding by uniting the solar rays. But it is quite false that luminous objects are represented to us as brighter through the telescope than without it; indeed, the truth is that we see them much more dimly. If Sarsi, while looking at the moon through the telescope, had ever opened his other eye and with it looked directly at the same moon, he could without any trouble have made a comparison between the splendor of the huge moon seen through the instrument and that of the small one seen with the naked eye. Having made this observation, he surely would have written that the light of the moon looked at directly appears a good deal brighter than that of the other one. The falsity of the conclusion is thus quite evident; it now remains for us to show the fallacy in its deduction from true premises. Here, it seems to me that Sarsi did not consider what would happen to a merchant who in looking over his account books should read only

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the credit side, and in this way persuade himself that he was solvent or even rich, which would be a true conclusion if there were no debits on the other side. It is true, Sig. Sarsi, that the lens—that is, the convex glass—would unite the rays and thus multiply (j>. 58) the light and favor your conclusion; but where have you left the concave glass ? This counterpart of the lens in the telescope is its most essential part, since it is held near the eye and the ultimate rays pass through it; it corresponds to the final balancing and settlement of accounts in the ledger. Do you not see that though the convex lens unites the rays, the concave glass expands them and forms an inverted cone ? If you had tried to catch the rays which pass through both the glasses of a telescope, as you have done in observing those refracted by a single lens, you would have seen that whereas the latter meet in a point, the former go on expanding infinitely (or to speak more properly, through an immense distance). This is very clearly seen experimentally by receiving the sun's image upon a sheet of paper, as when one is tracing the sunspots. In proportion as the end of the telescope is moved farther and farther away, a larger and larger circle is described upon such a sheet by the cone of rays, and the larger this circle is made the less bright it becomes in comparison with the remainder of the sheet which is struck by the direct rays of the sun. And if this and all other experiments had been unknown to you, it would still be hard for me to believe that you had never even once heard of the fact that the larger an object shows itself through a concave glass the darker it appears. Then how can you expect the telescope to brighten anything while enlarging it ? Sig. Sarsi, give up trying to exalt this instrument with these admirable new properties of yours unless you wish to throw it into utter disrepute among those who up to the present have had little enough regard for it. Also, note that in this accounting I have passed over as true one entry which is false; this is that the strengthening of light by the uniting of rays renders more luminous the object seen. That would be true if the light were going out to meet the object, but here it is coming toward the eye and produces a contrary effect. For in addition to offending the eyes, it renders the medium brighter; and a brighter medium, as I believe you know, makes objects

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appear darker. It is for precisely this reason that the stars appear more brilliant as the sky (p. 59) becomes dark at night and look dimmer when the heavens brighten. These things, as your Excellency sees, are so obvious that I cannot believe Sarsi was unaware of them; he induced himself to prove a paradox in order to show the liveliness of his wit rather than because of any inner conviction. His ultimate conclusion confirms me in this opinion when, I believe to show that he was speaking in jest, he follows with these words: Ί therefore affirm that the telescope may be as truly said to illuminate the stars as to enlarge them.' Your Excellency knows that both he and his master have always said, and go on saying, that it does not enlarge them at all. We shall see that Sarsi is forced to maintain that conclusion in the things which follow. XIII Read, therefore, your Excellency: ' I hasten to the third (p. 60). . . than an argument.' (p. 79,1. 34 to p. 8 1 , 1 . 17). Regarding what is here written, I must consider in the first place what reason Sarsi can possibly have for writing that I have been quite unhappy over Father Grassi, inasmuch as there is no trace of any lament of mine in Sig. Mario's treatise, nor have I ever (p. 61) complained to anyone else, or in my own heart. I have no reason to complain; it would seem to me very foolish for anyone to lament that men of high reputation were opposed to his position when he had easy and obvious ways of showing it to be correct, as I am sure I have. All that occurs to me is that under this pretense Sarsi has attempted to hide, I know not why, those ulterior motives which have impelled him to be angry with me—a thing I regret, as I had much rather have employed this time in some other study more congenial to me. I wish Sarsi would believe that Father Grassi had no intention of offending me when he criticized as uninformed those people who belittle the argument derived from the slight enlargement of the comet by the telescope. But if I personally have ever been declared to be among these, I should have been permitted to produce my reasons and defend my cause, especially when it is just and true. Also I want to concede to Sarsi that his master's intentions were

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good when he set himself to sustain that opinion, thinking to preserve and increase the repute and esteem of the telescope against the calumnies of those who claimed that it was a fraud and a deceiver of vision and thus attempted to rob it of its wonderful value. In this act the Father's intention seems to me as praiseworthy and good as the choice and quality of Sarsi's defenses appear to me poor and harmful, when against the impostures of its maligners he tries to cover the true effects of the telescope by attributing to it false ones. This does not seem to me to be a good place to argue the nobility of the instrument, and meanwhile may Sarsi kindly pardon me if I do not acknowledge my obligation to him in as much profusion as might perhaps suit him, or confess my debt for the new merits and honors showered upon the telescope. He cannot reasonably pretend that I should increase my debt and my affection toward people who make silly and false attributions and who threaten me with loss of their friendship because I reveal their errors by speaking the truth. Immediately after this, though perhaps not very opportunely, he is induced to (p. 62) call the telescope my foster child and to reveal at the same time that it is not my offspring in any other way. Now how is this, Sig. Sarsi ? When you are busy placing me under great obligations for benefits showered upon this supposed child of mine, must you go on to tell me that it is only a foster child ? Is this rhetorically sound ? I should have thought rather that on such an occasion you would have tried to make me believe it my own child even if you had been certain that it was not. The part which I played in the discovery of this instrument, and whether I may reasonably lay claim to it as my offspring, I set forth long ago in my Starry Messenger. I wrote that in Venice, where I happened to be at the time, news came that a Hollander had presented to Count Maurice [of Nassau] a glass by means of which distant things might be seen as perfectly as if they were quite close. That was all. Upon hearing this news, I returned to Padua, where I then resided, and set myself to thinking about the problem. The first night after my return, I solved it, and the following day I constructed the instrument and sent word of this to the same friends in Venice with whom I had been discussing the subject the previous day. Immediately afterward, I applied myself

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to the construction of another and better one, which I took to Venice six days later; there it was seen with great admiration by nearly all the principal gentlemen of that republic for more than a month on end, to my considerable fatigue. Finally, at the suggestion of one of my friendly patrons, I presented it to the ruler in a full meeting of the Council. How greatly it was esteemed by him, and with how much admiration it was received, is testified by ducal letters still in my possession which reveal the munificence of that serene ruler in recompense for the invention presented to him, reappointing and confirming me for life to my professorship at the University of Padua at double my former salary, which was then more than triple that of some of my predecessors. These acts did not take place in some forest or desert, Sig. Sarsi; they happened in Venice, and if you had been there you would not dismiss me thus as a simple schoolmaster. But (p. 63) by the grace of God, most of those gentlemen are still living there, and by them you may be better informed. Perhaps someone will say, however, that in the discovery and solution of a problem it is of no little assistance first to be conscious in some way that the conclusion is true and to be certain that one is not attempting the impossible; and hence that my knowledge and certainty that a telescope had already been made were of so much help to me that without this I should perhaps not have made the discovery. T o this I shall reply by making a distinction. I say that the aid afforded me by the news awoke in me the will to apply my mind to it, and without this I might never have thought about it; but beyond that I do not believe that such news could facilitate the invention. I say, moreover, that to discover the solution of a known and designated problem is a labor of much greater ingenuity than to solve a problem which has not been thought of and defined, for luck may play a large role in the latter while the former is entirely a work of reasoning. Indeed, we know that the Hollander who was first to invent the telescope was a simple maker of ordinary spectacles who in casually handling pieces of glass of various sorts happened to look through two at once, one convex and the other concave, and placed at different distances from the eye. In this way, he observed the resulting effect, and thus discovered the instrument.

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But I, incited by the news mentioned above, discovered the same by means of reasoning which, easy as it is, I wish to reveal to your Excellency. Recounting it thus where it is to the purpose, I may by its simplicity render less incredulous those people who, like Sarsi, may wish to diminish whatever praise there is in it that belongs to me. My reasoning was this. The device needs either a single glass or more than one. It cannot consist of one alone, because the shape of that one would have to be a convex (that is, thicker in the middle than at the edges), or concave (that is, thinner in the middle), or contained between parallel surfaces. But the last named does not alter visible objects in any way, either by enlarging or reducing them; the concave diminishes them; and the convex, while it does indeed increase them, shows them very indistinctly and confusedly, (p. 64) Therefore, a single glass is not sufficient to produce the effect. Passing next to two, and knowing as before that a glass with parallel faces alters nothing, I concluded that the effect would still not be achieved by combining such a one with either of the other two. Hence I was restricted to trying to discover what would be done by a combination of the convex and the concave, and you see how this gave me what I sought. Such were the steps in my discovery, in which I was not at all assisted by the conception that the conclusion was true. But if Sarsi and others think that certainty of a conclusion extends great assistance in the discovery of some means for realizing it, let them study history; there they will learn that Archytas made a dove which could fly, that Archimedes made a mirror which kindled fires at great distances (as well as constructing other remarkable machines), that other men have kindled perpetual fires, and a hundred more conclusions that are equally amazing. By reasoning about these, they may easily discover, to their great honor and profit, how to construct such things. Or if they do not succeed, they will at least derive some benefit in the form of a clarification of their ideas about the help which they promise themselves from foreknowledge of the reality of the effects, which will be much less than they have imagined. I return now to what Sarsi has to say. He is careful not to reduce himself to asserting that the argument taken from the slight enlargement of very remote objects is worthless, for that is not true, but he

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says that he and his master have never held it in great esteem. This he shows by the fact that his master has written very little about it, while his other two arguments are seen to be expanded and amplified without sparing words. To this I reply that it is not the number of words but their effectiveness which allows us to deduce other people's regard for what they say. Everyone knows that there are demonstrations which by their very nature cannot be explained except lengthily, while others exist in which length would be entirely superfluous and tedious. Now if one attends to the words here, the argument is conducted with as many as would suffice for a clear and complete explanation. Besides, Father Grassi himself writes {p. 65) that the argument, being necessarily implied by optical principles, has very great force in proving his point. This gives us a clear enough indication of the esteem which he at any rate has tried to establish for it, but which I am willing to believe with Sarsi was very small in his own eyes. I am persuaded of this not by the brevity of the argument but by another and much sounder conjecture. This is, that while the Father put up an appearance of demonstrating the comet to have been very distant because it behaved like the fixed stars in receiving little magnification from the telescope, when he went on immediately to determine this location more specifically he put it below certain objects which receive a very great magnification from that same instrument. As a matter of fact, he puts it beneath the sun, which, as the Father and Sarsi well know, is magnified hundreds or thousands of times. But Sarsi failed to penetrate the clever device by which his master attempted to give courteous approbation to his friends without at the same time alloying the pleasure they felt over the invention of the new argument, meanwhile secretly showing himself very acute and well informed to those who are more intelligent and less emotional. In this, he was imitating the gallant act of that great gentleman who discarded his flush in order not to disturb the ecstasies of the young prince, his opponent, occasioned by the prospect of winning heavily with the 'fifty-five' he had just revealed and laid down on the table.16 But Sig. Mario, a trifle severely perhaps, has tried to state his ideas and to reveal the nullity and falsity of this argument with all his cards on the table. He was governed by a

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different end [than courtesy], which was to try to remedy defects and correct errors with some compassion for the afflicted rather than to foment mistakes and magnify them in order not to incur displeasure. At the end, Sarsi writes that his master had no thought of offending me in criticizing those who caviled at the argument. T o this it is not necessary for me to reply further, since I have already said what I think and what I have never heard contradicted. And I wish that Sarsi would believe that neither did I, when proving the argument wrong, have {p. 66) any intention of offending his master; rather, I intended helping anyone who was in that error. Nor can I well understand what occasion there is here for my being taxed as one who had rather lose a friend than a jest; I do not even see how saying 'this argument is incorrect' can be regarded as particularly witty. XIV Now let your Excellency continue by reading: 'But let us now . . . (p. 6 7 ) . . . than the moon.' (p. 81,1. 18 to p. 82,1. 36). Sarsi, as you see, is preparing here with admirable boldness to maintain by means of acute syllogisms that nothing can be more true than the frequently advanced proposition that objects seen through the telescope are the more enlarged the closer they are, and the less so the more distant; and such is his self-confidence that he almost promises that I shall admit this though at present I deny it. I believe that in the course of weaving this cloth he is going to get himself so entangled in it (more than he supposes now, when he is laying the warp) that in the end he will voluntarily confess himself vanquished. This will be apparent to anyone who will pay attention to the fact that he will end by saying precisely the same {p. 68) things that Sig. Mario wrote—though disguised in such a way, and fitted in piecemeal among such a variety of wordy ornaments and arabesques, or displaced and foreshortened at such angles, that perhaps those who consider them less carefully will at first think them somewhat different from what they essentially are. Meanwhile I add, in order not to discourage him, that if what he is attempting is correct, then the argument supported by this proposition which is utilized by his master and his other astronomer friends

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for finding the location of the comet is not only the most ingenious and most conclusive argument of all, but that this effect of the telescope far surpasses all others because of the important consequences which follow from it. And I cannot help being astonished that Sarsi, who knows it to be true, should have said a little while ago that he and his master had less regard for it than for the other two arguments —the one taken from circular motion and the other from smallness of parallax—which, if he will allow me to say so, are not fit to be handmaids to this one. Your Excellency, if this thing is true, the road is paved for Sarsi to the making of admirable inventions which many others have attempted but no one has ever achieved. Not only might any distance on earth be measured from a single place, but the distances of the heavenly bodies may be established without error. For once we had observed a circle one mile away which, when observed through the telescope, appeared to be thirty times as large in diameter as when seen with the naked eye, then as soon as we saw the height of a tower to be magnified ten times we could be sure that it was three miles distant. If the moon's diameter were three times greater than when seen with the naked eye, we could say that it was ten miles away, and the sun would be fifteen if its diameter merely doubled. Or, if we should see the moon enlarged three times by some fine telescope, and it is more than one hundred thousand miles away as Father Grassi well says, then the ball upon a cupola one mile away would increase in diameter more than a million times. Now (p. 69) to add what I can to so astounding a venture, I shall proceed to set forth a few trifling questions that arose in me as Sarsi went along. Should your Excellency choose, you may show these to him at some time so that by answering them he may establish his whole position more solidly. Sarsi, then, wishes to persuade me that the fixed stars receive no appreciable enlargement from the telescope. He commences with objects inside the room, and he asks me whether I need to lengthen the telescope very much when I look at these; and I answer, yes. Now he passes to objects outside the window at a great distance, and he tells me that in order to see them it is necessary to shorten the instrument considerably, which I affirm. Next I concede to him that

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this comes about from the nature of the instrument, as he says, which requires a longer tube in order to show objects which are very close, and a shorter one for those more distant. Moreover, I confess that the longer tube shows the objects larger than does the shorter one, and finally I grant him his whole syllogism for the present, the conclusion of which is that, in general, nearby objects increase more, and farther ones less. Adapting this to the particulars named, this means that the fixed stars, which are distant objects, are less enlarged than things placed within a room or in a courtyard—for it appears to me that Sarsi includes within such limits those things which he calls 'close,' he not having specifically removed this boundary to any greater distance. But the statement thus far seems to me a long way from satisfying Sarsi's requirements. For next I ask him whether he places the moon in the class of nearby objects, or in that of distant ones ? If he puts it with the distant ones, he will conclude the same for it that he does for the fixed stars, namely, slight enlargement. But this is a direct contradiction of his master, who in order to situate the comet above the moon requires that the moon be one of those objects which are greatly enlarged, and he even writes that the moon does grow greatly and the comet but little. Yet if Sarsi puts the moon among close objects (which are those that grow greatly), I shall reply to him that he should not at the outset have restricted the boundary of close objects to the walls of a house, but should have extended ( p . 70) them at least to the sphere of the moon. Now having extended this boundary that far, let Sarsi return to his original question, and ask me whether I need to lengthen the telescope very much in order to see close objects—that is, those which are not beyond the orb of the moon. I answer, no; and here the archer's bow is broken and the shooting of syllogisms is over. If we go back and consider his argument better, we find it to be defective. It takes as absolute that which must be understood relatively, or takes as bounded that which is unbounded; in a word, an incomplete dichotomy (as the error is called in logic) has been created when Sarsi divided visible objects into far and near without assigning boundaries and limits between closeness and remoteness.

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He has made the same mistake as a person who might say, 'Everything in the world is large or small.' In this proposition, there is neither truth nor falsity, nor is there in saying, Objects are either near or far.' From indeterminacy of this sort, it comes about that the same things may be called very near and very far; the closer may be called distant and the farther close; the larger may be called small and the smaller large. Thus one might say,' This is a very small hill,' and 'This is a very large diamond.' A courier calls the trip from Rome to Naples very short, while a great lady grieves that the distance from her house to the church is too great. In order to avoid this equivocation, if I am not mistaken, Sarsi needed to give his division at least three parts, saying:' Of visible objects some are near, some far, and others are situated at a medium distance,' so that something would stand as a limit between the near and the far. Nor could he stop even there; he should further add an exact determination of the distance of this limit, saying for example:' I call medium, a distance of one league; far, that which is more than one league; near, that which is less.' I fail to understand why he did not do this, unless it was that he perceived his case would be stronger if he furthered it by cleverly juggling equivocations before the simpleminded than it would be if he reasoned (p. 71) it soundly before the more intelligent. And truly it is a great advantage to have one's bread buttered on both sides and to be able to say,' Because the fixed stars are distant, they enlarge very little, but the moon enlarges very much because it is close,' and then again, as the need arises, to say: 'Objects in the room, being close, increase a great deal; but the moon, because it is distant, does so but little.' Second, Father Grassi does indeed give only a single reason for objects seen through the telescope appearing now more and now less enlarged; this is the lesser or greater distance of these objects; nor does he touch upon the lengthening or shortening of the instrument by a single word. Now Sarsi says that this is quite true; yet when he is constrained to demonstrate it, the great or little distance of the object is not sufficient for him and he has to adjoin the greater or lesser length of the telescope. He frames his syllogism as follows: ' T h e closeness of the object is the cause of lengthening the telescope;

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but this lengthening is the cause of greater enlargement; therefore the closeness of the object is the cause of greater enlargement.' Here it seems to me that instead of rescuing his master, Sarsi makes him worse off, having him equivocate from per accidens to per se. It is thus that they err who would put avarice among the rules of hygiene, saying: 'Avarice is a cause of living soberly; sobriety is a cause of health; therefore avarice keeps one healthy.' Here avarice is an occasion, or at best a very remote cause per accidens, of health; health ensues outside the main intention of the miser as miser, whose end is thrift alone. What I say is so true that I shall with equal cogency prove avarice to be the cause of illness, thus: 'The miser, from thrifting at home, goes frequently to the festivities of friends and relatives; frequency of festivities causes many illnesses; therefore avarice is a cause of illness.' From such arguments, it ultimately appears that avarice, as avarice, has nothing to do with health. Nor does the closeness of an object have anything to do with its greater enlargement; the reason for lengthening the telescope when looking at nearby objects (p. 72) is to remove the confusion with which those objects are tinged, and this is removed by the lengthening. But since the lengthening is followed by a greater enlargement quite outside the main intention, which was to clarify the object and not to enlarge it, the closeness in this case cannot be called anything more than an occasion, or at best a very remote cause per accidens, of the greater enlargement. Third, if it is true that only that may be properly called a cause which is always followed by the effect, and which when removed takes away the effect, then only the lengthening of the telescope may be said to be the cause of greater enlargement. Let the object be at any distance whatever; upon the slightest lengthening there will follow a noticeable enlargement. But on the other hand, so long as the instrument is kept at the same length, you may move the object as much closer as you please, reducing it even from a distance of a hundred thousand paces to but fifty, without the magnification of its naked-eye appearance thereby becoming one whit greater in the nearer position than in the farther. It is indeed true that bringing it closer at very small distances, such as four paces, or two, or one, or

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one-half, makes the image of the object always cloudier and dimmer, so that in order to see it clearly and distinctly one must lengthen the telescope more and more; upon this lengthening there then follows a greater and greater enlargement, but, inasmuch as such enlargement depends only upon the lengthening and not upon the approach, it must be governed by that and by that alone. And since at a distance beyond half a mile there is no need to alter the instrument at all in order to see objects clearly and distinctly, no changes occur in their magnifications, and all take place in the same proportion. If the surface of a ball seen through the telescope at a distance of half a mile increases a thousand times, then so will the moon's disc increase a thousand times and no less; so will that of Jupiter, and finally that of a fixed star. Nor is there any such occurrence as that which Sarsi wishes to split hairs about and to review with all the rigor of geometry, (p. 73) When he has finished mincing it and reducing it to atoms and has taken every advantage to himself, his gain will not equal that of a man who has carefully gone about inquiring which gate of the city one should use in order to reach India most quickly. In the end, Sarsi will have to confess (as indeed he seems partly to do toward the close of the passage just read by your Excellency) that treating the telescope with every severity it would have to be shortened less than a hair's-breadth in order to look at the fixed stars instead of the moon. But from all this severity, what eventually emerges to uphold Sarsi? Absolutely nothing; all that he can harvest from it is that if, for example, the moon is enlarged a thousand times, the fixed stars are enlarged nine hundred and ninety-nine. But for his defense and that of his master they should not even double, for doubling is not an imperceptible thing, and they speak of the fixed stars as not increasing perceptibly. I know that Sarsi understood these things very well, even in the reading of Sig. Mario, but he wants to keep his master alive as well as he can by means of a quintessence of syllogisms subtly distilled; we may put it thus because Sarsi will shortly call 'too minute' some points of Sig. Mario's which are actually fat when compared with these of Sarsi's. But to conclude my objections at last, it occurs to me to say something about the example which Sarsi has borrowed from

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objects seen naturally. He says that as these are removed farther from the eye they are seen under constantly diminishing angles, but that after they arrive at a certain distance where the angle becomes very small, then even if an object is removed much farther the angle is not thereby sensibly diminished; still, he says, it can be proved that it becomes smaller. If the sense of this example is what it appears to me to be, and indeed as it must be if it is to square with the concept exemplified, I hold a very different opinion from Sarsi. For to me it appears that in effect he wants the visual angle to continue diminishing with the departure of the object, but always in a successively smaller ratio, {p. 74) so that beyond some great distance the object may be farther removed with little more diminution of the angle. I am of the contrary opinion, and I say that the diminution of the angle is made in a continually greater ratio the more the object is removed. T o explain this more simply, I note in the first place that the apparent magnitude of visible objects may be correctly determined by the size of the angles under which they are represented to us, [that is,] when we are dealing with parts of the circumference of a circle in whose center the eye is located; but in dealing with all other objects this is incorrect. For then it is the apparent magnitudes not of the visual angles, but of the chords of the arcs subtended by such angles, which must be determined; and these always diminish in just the opposite ratio to the distances. The diameter of a circle seen at a distance of one hundred yards appears to me as just one-half that which it would appear to me from a distance of fifty, and seen at a distance of one thousand yards it will appear twice what it will at two thousand, and so on for all distances, and it never happens that at some enormous distance it will appear so small as not to appear halved at double that distance. But if we still want to determine the apparent magnitudes of the angles, as Sarsi does, the facts will turn out still more unfavorable to him, for such angles diminish not in proportion as the distance increases, but in a smaller ratio. And that which contradicts Sarsi's statement is that, comparing the angles with one another, they diminish progressively in a greater ratio for larger distances than for smaller. If the angle of an object

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placed fifty yards away is to the angle of the same object placed at a distance of one hundred yards as 100 is to 60, then the angle at a distance of one thousand will be to that at two thousand as, say, 100 is to 58; at a distance of four thousand it will be to that at eight thousand as 100 is to 55, and at a distance (p. 75) of twenty thousand the ratio will be as 100 is to 52. Thus the diminution of the angle will proceed in greater and greater ratios, without ever becoming interchangeable with the ratio of the distances. Sarsi writes that the visual angle, made very acute by great distance, does not continue to diminish at extreme distances in as great a ratio as it did at lesser distances. If I am not mistaken this is utterly false, and the diminution actually proceeds in an increasing ratio. XV Read now, your Excellency,' But he will say . . . and then another ?' (p. 83,1. ι to 1. 15). Sarsi, as you see, here represents me as at length convicted through the force of his syllogisms and as snatching for protection at some very feeble support by saying that if it is true that the fixed stars do not receive enlargement as do nearby objects, then at any rate this is not using the same instrument, since for very close objects the telescope must be lengthened; and he adds with a 'get thee hence' that I am seizing at trifles. But it is not I, Sig. Sarsi, who need recourse to 'at any rate' and to minutiae. You indeed have needed these before now, and you will again as we proceed. You needed to say that in the very subtle concepts of geometry, at any rate, the fixed stars (p. 76) require more shortening of the telescope than does the moon; from this it later developed, as I have remarked before, that were the moon to increase one thousand times the fixed stars would increase nine hundred and ninety-nine, whereas to maintain your statement you would require that they grow not even twice. This is indeed reducing yourself to an 'at any rate,' Sig. Sarsi; it amounts to taking that to be a serpent which, scotched and trampled, no longer has any life in it outside the tip of its tail, which still goes on twitching in order to make the passers-by believe that it is yet alive and strong.

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To say that the lengthened telescope is a different instrument from what it was before is quite essential to the point of what we are saying, and it is as true as can be. Nor would Sarsi have thought otherwise if he had not equivocated from the subject matter of what we meant to the form or figure of our argument, when he passed judgment upon us, as may readily be shown without even forsaking his own example. I ask Sarsi: Inasmuch as the pipes of an organ do not all sound in unison, why do some render deeper tones and some higher? Will he perhaps say that this comes about because they are of different materials ? Surely not. They are all of lead, but they sound different notes because they are of different sizes; as to the material, that has no part whatever in the formation of the sound. Some pipes are made of wood, some of pewter, some of lead, some of silver, and some of paper; but all sound in unison when their lengths and sizes are equal. On the other hand, with the same quantity of material—that is, with the same few pounds of lead— there may be made now a larger and now a smaller tube, and different notes may be formed from it. With regard to the production of sound, those instruments are different which are of different sizes, and not those which are of different materials. Now, if by melting down one pipe and recasting the same lead one may make another and longer tube, and consequently one of lower pitch, will Sarsi refuse to say that this is a different pipe from the first ? I think he will not. But if someone were to find a way to make the second, longer tube without melting down the first, would this not be the same thing? Surely it would. Now the method will be (p. 77) to make it of two pieces, one inserted in the other. This may be lengthened and shortened at will and made into diverse pipes which will produce various notes, and such is the construction of the trombone. The strings of a harp are all of the same material, but they render different sounds because they are of various lengths. A single string on a lute will accomplish what many do on the harp, because in playing this instrument the sound is drawn now from one part of a string and again from another part, and this is the same as lengthening and shortening it, and in a word altering it into different strings so far as the production of sound is concerned. The same may be

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said of the tube of the throat, which, varying in length and breadth, accommodates itself to the formation of various voices and may correctly be said to become various tubes. And since a greater or lesser enlargement depends not upon the material of the telescope but upon its shape, in such a way that the longer shows things as larger, just so does the tube constitute different instruments when the same material is preserved but the interval between the lenses is altered. XVI Now let us hear the other syllogism which Sarsi frames. 'But let Galileo . . . a different way.' (p. 83,1. 16 to 1. 30). I concede this argument in its entirety, but I do not see that it proves anything detrimental to Sig. Mario's cause or favorable to Sarsi's. It is no advantage to Sarsi that nearby objects seen {p. 78) through a long telescope are more enlarged than distant ones seen through a short one. Such is the conclusion of his syllogism, though it is quite different from Sarsi's original project, which was to prove two main points. One of these was that objects as far off as the moon, and not merely those within a room, enlarge very much indeed, while the fixed stars enlarge not merely little but insensibly when viewed through the same instrument. T h e other was that the difference between these enlargements stems from the difference in distances of these objects and is in proportion to the distance. These things he will never prove in all eternity, since they are false. As to the present syllogism, so far as it concerns the matter in hand, let our evidence of its vapidity be that I shall proceed in his very footsteps and conclusively prove the exact opposite, thus: Objects requiring to be viewed through the same instrument receive from it the same enlargement; all objects from one-quarter of a mile to a distance of thousands of millions of miles require to be viewed through the same instrument; therefore all these receive the same enlargement. Yet Sarsi must not conclude that he has not written anything here that is foreign to the truth or to me; as to me, at any rate, I assure him that he has concluded something contrary to my meaning.

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At the end of this section, he says that a telescope which is now long and now short may be called the same instrument though differently applied. If I am not mistaken, there is some equivocation here; to me it seems that matters stand quite the other way, and that it is the instrument which is varied while its application remains precisely the same. The same instrument is said to be differently applied when it is put to different uses without suffering any alteration; thus the anchor was the same when applied by the pilot to secure the ship and by Orlando to catch a whale, 17 but it was differently applied. Our case is just the reverse, for the use of the telescope is always the same, it being always applied to looking at visible objects, while the instrument itself is diversified by its alteration in one essential respect, which is the interval between its lenses. Thus Sarsi's quibble is made manifest, (p. 79) XVII But let us proceed: 'But he will say . . . the appearance itself.' (p. 83,1. 31 to p. 84,1. 21). Here, your Excellency, note first of all how my previous prediction under X I V , above, (p. 215) commences to be verified. First Sarsi belligerently maintained that nothing could be more true than that objects seen through the telescope are the more enlarged the closer they are, and the less so the farther off; whence the fixed stars do not increase much, being very distant, but the moon does, being close. Now we begin to see here a full retreat and an open confession. First, diversity of the distances of objects is no longer the real cause of diverse enlargements, but recourse is required to the lengthening and shortening of the telescope, something (p. 80) not mentioned or even hinted at (and perhaps not so much as thought of) by them until it was brought up by Sig. Mario. Second, not even this takes place in the present case, inasmuch as no alteration is made in the instrument. So this refuge fails, and the argument based upon it is completely invalid. In the third place, I see that he goes back to causes very remote from those he introduced at the beginning as the true and only ones; he says that the slight enlargement apparent in the fixed stars no longer depends upon either their great distance or

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the shortness of the instrument, but that it is an optical illusion. He says that the naked eye sees the stars with a large unreal irradiation, and that because of this they appear large to us, while through the telescope the bare body of the star is seen, and this, though enlarged like all other objects, does not appear very great in comparison with the same star seen by the naked eye, in relation to which the enlargement appears very slight. From this, he concludes that at least as to appearance the fixed stars still exhibit a very slight enlargement, so that I must not be astonished that he and his master have said what they did, as they do not require any cause for such an appearance but merely the appearance itself. Pardon me, Sig. Sarsi; in attempting to remove my astonishment, you not merely fail to take it away from me, but you increase it a good deal with your new reasons. First, I marvel not a little to see you introduce this discourse in a doctrinaire manner, almost as if you were trying to teach it to me, when you have learned it word for word from Sig. Mario. Moreover, you add that I do not deny these things, with the intention (I believe) of leaving the reader with the idea that I had the solution of the difficulty right in my hands but could not recognize it or avail myself of it. I marvel in the second place that you should say that your master does not seek the cause of the insensible enlargement of the fixed stars but merely the effect itself, whereas he more than once repeated that this cause was the enormous distance. But in the third place, what multiplies my astonishment a hundredfold is that you do not perceive that if this is true, you quite wrongly represent (j>. 81) your master as lacking even that common sense by virtue of which everybody, even the merest idiot, correctly reasons and reaches his own conclusions. T o make palpable the truth of what I say, take away any consideration of the cause and set forth only the effect, since you affirm that your master requires not the cause but only the effect; then reason thus: 'The fixed stars enlarge insensibly; the comet enlarges insensibly; therefore . . Therefore what, Sig. Sarsi? What do you conclude from this ? You had better reply,' Nothing,' if you want to make the best of a bad job, for if you pretend to be able to infer one conclusion, I shall claim to infer a thousand equally well connected

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with the premises. If you think one may say, 'Therefore the comet is very distant, because the fixed stars are also very distant,' then I shall say with no less right, 'Therefore the comet is incorruptible, because the fixed stars are also incorruptible,' and next I shall say, 'Therefore the comet twinkles, because the fixed stars twinkle,' 1 8 and with no less reason I might s a y , ' Therefore the comet shines by its own light, because the fixed stars do.' But if I should draw these conclusions you would smile at me as a logician devoid of logic, and you would be quite right. You would courteously point out to me that from these premises I cannot infer anything about the comet except such things as have an essential connection with the insensible enlargement of the fixed stars. Since this enlargement does not depend upon and has no connection whatever with incorruptibility or with twinkling or with intrinsic light, none of these conclusions may be drawn with regard to the comet. A n d he who wishes to infer from the premises that the comet is very distant must first have established conclusively that the insensible enlargement of the stars depends causally upon great distance, for otherwise the converse would not be available; that is, that those objects which enlarge insensibly must necessarily be very remote. N o w you see what errors in logic you have unworthily saddled upon your master; I say unworthily because this error is yours, and not his. {p. 82) XVIII N o w , your Excellency, read to the end of this First Weighing: ' B u t now let Galileo .. .{p. 83) . . . Galileo's own conclusions.' (p. 84, 1. 2 2 to p. 8 6 , 1 . 8). In the first place, we have here an argument patched, so to speak, upon the old one. It consists of diverse fragments of propositions designed to prove that the comet was between the moon and the sun. Sig. Mario and I may concede this whole thing to him without prejudice, since we have never affirmed anything about the location of the comet nor denied that it might be above the moon; we have only said that the demonstrations so far introduced by other authors are not immune from objections. Sarsi accomplishes nothing in the way of removing these objections by adducing new demonstrations here

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to prove the conclusion true (even if these were conclusive and rigorous), inasmuch as it is possible to argue incorrectly and to commit paralogisms and fallacies even about true conclusions. Still, since I like to have hidden things come to light and since I desire to win to true conclusions, I shall proceed to advance a few considerations touching this discourse, and for clearer understanding I shall first (p. 84) reduce it to the shortest exposition I can. He says, then, that he has it from my Starry Messenger that the fixed stars, shining with their own light, are much irradiated with a fulgor which is not real but only apparent. T h e planets, having no light of their own, are not thus irradiated, particularly the moon, Jupiter, and Saturn, which are seen to be almost barren of any such splendor. Venus, Mercury, and Mars, though lacking any light of their own, are nonetheless irradiated because of their proximity to the sun, whose rays touch them the more brightly. He goes on to say that in my opinion the comet receives its light from the sun, and he adds that he himself, with other reputable authors, has regarded the comet as a temporary planet, and that thus it may be reasoned about as are the other planets, of which those that are closer to the sun are more irradiated and consequently are less enlarged when seen through the telescope. And since the comet was enlarged little more than Mercury and much less than the moon, it would be reasonable to conclude it to be not much farther from the sun than Mercury is, and very much closer to it than the moon. Such is his argument, and it fits so smoothly and assists his needs so neatly that it is as if the conclusion had been framed before the premises and the latter depended upon the former instead of the other way round. It is as if the premises had not come from Nature's bounty but had been prepared for the conclusion by the preciseness of the subtlest art. And now let us see how conclusive they are. First, it is quite false that I wrote in my Starry Messenger that Jupiter and Saturn have little or no irradiation, but that Mars, Venus, and Mercury are grandly crowned with rays; it was the moon alone that I thus sequestered from the rest of the stars, fixed and wandering alike. 19 Second, in order to make the comet a quasi-planet and as such to dress it in the properties of the other planets, I am not so

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sure that it is sufficient for Sarsi, his master, and the other authors to have regarded it as one and to have named it so. If their opinions and their voices have the power to call into existence the things they have considered and named, why then I beg them to do me the favor of considering and naming 'gold' a lot of old hardware that I have about my house. But names aside, what {p. 85) condition induced them to deem the comet a temporary quasi-planet ? That it shone like a planet, perhaps? But what cloud, what smoke, what wood, what wall, what mountain touched by the sun does not shine equally ? Has not Sarsi seen it demonstrated in my Starry Messenger that the terrestrial globe itself shines more than the moon does? And why do I speak of the comet shining like a planet ? For my part I do not hold it impossible that the comet's light might be so weak and its substance so thin and rare that if anyone could get close enough to it he would lose it completely from view, as happens with some fires which emerge from the earth and are seen at night and from afar, but which are lost when close at hand. 80 In the same way, we see distant clouds sharply bounded, which later from nearby show only a little misty shadowiness so indefinitely bounded that a person entering into them may almost fail to distinguish their bounds or to discriminate them from the surrounding air. And those projections of solar rays through rifts in the clouds, which so resemble comets, are never seen except by people who are far from them. Or must the comet be included with the planets by reason of motion ? But what thing separated from the elemental parts (which would obey the terrestrial condition) is there that does not move in the diurnal motion along with the rest of the universe ? And if the longitudinal (traversale) motion is meant, this has nothing to do with planetary motion, being neither in the same direction, nor uniform, nor perhaps even circular. And, apart from these matters, does anyone believe that the substance and material of a comet are similar to those of the planets ? The latter may be said to be most solid, for the moon in particular convinces us of this quite palpably, as does in general the sharply bounded and unchanging shape of all the planets. The substance of the comet, on the other hand, may be believed to dissolve within a few days, and its shape, which is not circularly

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bounded but confused and indistinct, gives us an indication that its material is rarer and more tenuous than fog or smoke. In a word, the comet more resembles a toy planet than the real thing. Third, I do not know how completely he may have compared the comet's irradiation and (j>. 86) enlargement with those of Mercury, which he surely did not see and could not have seen during all the time the comet was visible; the occasions Mercury gives for being observed are quite rare, and during that period it was always quite close to the sun. So I think I may safely believe that Sarsi did not make such a comparison at all, difficult and uncertain of accomplishment as it is, but that he speaks thus because it would better serve his cause if it were so. That he did not get round to this test is indicated to me also by the fact that, in referring to observations of Mercury and the moon, with which he compares those made of the comet, he seems to me to be somewhat confused. To prove the comet to have been farther from the sun than Mercury is, he needed to say that it was less irradiated than Mercury and more enlarged when seen through the telescope; yet he wrote this down in reverse, saying that it was not much more irradiated than Mercury and that it received almost the same enlargement, which amounts to saying that it was more irradiated and less enlarged than Mercury. Next, comparing the comet with the moon, he writes the same (although he speaks of writing the opposite); that is, that it was enlarged less than the moon and was more irradiated. Yet later, in concluding, he draws contrary conclusions from identical premises, saying that the comet is closer to the sun than the moon is, and farther from the sun than Mercury is. Finally, since Sarsi professes to be a very precise logician, I do not know why, in his classification of luminous bodies which are much or little irradiated and which in consequence receive a lesser or greater enlargement when seen through the telescope, he has omitted our elemental lights. For candles shine, and blazing torches seen from a distance, and some pebbles, and bits of wood or other small bodies, and even the leaves of plants or drops of dew struck by the sun; and from certain viewpoints these are irradiated as much as the most refulgent star, and when seen through the telescope they

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show the same type of enlargement that stars do. So there is no help from this source for those people who promised themselves that by means of the telescope they could transport the comet to the sky and remove it from the (p. 87) elemental sphere. Meanwhile, let Sarsi stop thinking he can rescue his master, and learn that to try to maintain one error is to be forced to commit a hundred, and, what is worse, to be defeated in the long run. I also beg him to stop repeating, as he still does at the end of this section, that these doctrines of his are mine; for I never wrote any such thing, nor said it, nor thought it. So much for the First Weighing. XIX Now let us proceed to the Second. 'Although up to . . . (p. 88) in any way elemental.' (p. 86,1. 15 to p. 87,1. 23) Previously Sarsi went along arbitrarily shaping premises fitted to the conclusion he intended to prove; now it seems to me that he proceeds to shape conclusions in order to oppose them as ideas belonging to Sig. Mario and me, though they are quite different from those set forth in Sig. Mario's Discourse, or at least differently construed. That the comet is beyond doubt a mere image and a simple appearance has never been positively affirmed; it has merely been raised as a question, and offered for consideration by philosophers, together with such reasons and conjectures as appear suitable to convince them that such might be the case. Here are Sig. Mario's words in this connection: Ί do not say positively that a comet is formed in this way, but I do say that just as there are doubts about this, so there are doubts about the methods used by other authors; and if they claim to have established their opinion beyond doubt, they will be under obligation to show this and all other positions to be vain and fallacious.' 41 With similar distortion, Sarsi represents us as having definitely declared that the motion of the comet must necessarily be straight and perpendicular to the earth's surface, something which is not proposed in that way but is merely brought under consideration in that it would explain the changes observed in the comet more simply and in better agreement with the appearances. The idea is so temperately proposed by Sig. Mario ι

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that ultimately he says these words: 'Hence we must content ourselves with what little we can conjecture thus among the shadows.' 22 Yet Sarsi has tried to represent these opinions as being the more firmly believed by me as he has imagined himself able the more effectively to annihilate them—which (p. 89) if he does, I shall hold myself obliged to him, as in the future I shall have one less opinion to consider when I set my mind to philosophizing about such matters. But since it seems to me that there is still a little life left in Sig. Mario's conjectures, I shall proceed to make a few remarks about the strength of Sarsi's objections. Attacking the first conclusion with great boldness, he says that to anyone who had once looked at the comet no other argument would be necessary to prove the nature of its light; for compared with other true lights it showed itself only too clearly to be true and not spurious. As your Excellency will note, Sarsi has such confidence in the sense of sight that he deems it impossible to be deceived any time that a spurious object may be set beside a real one. I confess that I do not have such a perfect discriminatory faculty, but resemble the monkey that firmly believed he saw his mate in a mirror, and so live and real did the image seem to him that he did not discover his error until he had run behind the mirror two or three times to catch her. Assuming that what Sarsi sees in his own mirror are not true and real men at all, but are mere images like those which the rest of us see in ours, I should like to know what those visual differences are by which he so readily distinguishes the true from the spurious. For my part, I have countless times been in some room with closed shutters and have seen on the opposite wall the reflection of sunlight coming through some tiny hole, and as far as vision could tell I have judged it to be a star, no less bright than Venus or the Dog Star. When we walk over a field toward the sun, in how many thousands of straws and pebbles, a little polished or moistened, will the reflection of the sun be seen in the aspect of the most splendid stars? Sarsi has but to spit upon the ground, and undoubtedly he will see the aspect of a natural star from that point toward which the sun's rays are reflected. Furthermore, any body placed at a great distance and struck by the sun will appear as a star, particularly if it is placed

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so high as to be seen by night as the (/>. 90) other stars are seen. And who could distinguish the moon seen in daytime from a cloud touched by the sun, were it not for differences of apparent shape and size ? Surely, no one. Finally, if simple appearances can determine the essence of a thing, Sarsi must grant that the suns, moons, and stars seen in still water or in a mirror are true suns, real moons, and actual stars. But Sarsi had better change his mind about this, and not suppose that he can improve his position by citing the authority of Tycho, Thaddeus Hagek, or others—except insofar as having such men for company makes his own error the more excusable. XX Continue to read, your Excellency: ' Y e t at that t i m e . . . aimless and uncertain.' (p. 87,1. 24 to p. 88,1. 14). (p. 91) Neither Sig. Mario nor I ever wrote that fuming vapors rise from some parts of the earth to the moon and even to the sun, and that having got outside the cone of the terrestrial shadow they are impregnated by solar rays and give birth to the comet, though Sarsi would attribute this to me. What Sig. Mario did write is that he does not consider it impossible that sometimes there may be raised from the earth exhalations and other such things so much subtler than usual that they would ascend even to the moon, and might be material for the formation of a comet; and that sometimes there occur unusual sublimations of the twilight material, as exemplified by the aurora borealis. But he does not say that this is identical with the material of comets, which must necessarily be much rarer and thinner than the twilight mists and the material of the aurora borealis, since the comet shines much less than the aurora. Thus if the comet appeared to the east in the whiteness of dawn while the sun was no more than six or eight degrees from the horizon, no doubt the comet would not be discerned, for it would be less bright than the surrounding field. Likewise, straight motion upward is attributed to the same material only with probability and not with certainty. This is said not to retreat in fear of Sarsi's objections, but merely to let it be seen that we are not departing from our custom of declaring nothing as certain except what we know beyond doubt, as our philosophy and

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mathematics teach us. Now, it being granted that we have not said the things with which Sarsi burdens us, let us hear and examine his objections. His first objection is founded upon the impossibility of vapors leaving by a straight line toward the sky when a swift north wind is distorting the air and everything within it. Such a wind was felt by him for many days after the appearance of the comet. The objection is really very ingenious, but it loses a good deal of its force through our having reliable information that there was not the slightest disturbance of the air in either Persia or China during those days, so I shall believe that the comet's material arose from one of those regions unless {p. 92) Sarsi proves to me that it came not from thence but from Rome, where he felt the northerly blast. And even if the vapors had left from Italy, who knows but that they had set out before those windy days? For many days would have passed before their arrival at the orb of the comet, this being some 470,000 miles away according to Sarsi's master. After all, such a journey takes time, and not a little of it. The ascent of vapors as observed from the earth falls a good deal short of the speed of a bird in flight, so that not even a few years would suffice for such a journey. But assuming that such vapors were to move during a windy season, a man who has complete faith in storytellers and poets should admit that the commotion of the wind does not rise more than two or three miles high, for there are mountains whose summits transcend the windy regions. 23 Hence the most that might be concluded would be that within that space the vapors would not go vertically but would fluctuate in their course, while beyond this there would be no interference which would twist them from a straight path. XXI Now, your Excellency, continue: (First argument)' But finally, . . . [ p . 93](/>. 94). . . be carried upward.' (p. 88,1. 15 to p. 89,1. 34). Long experience has taught me that with regard to intellectual matters, this is the status of mankind: T h e less people know and understand about such matters, the more positively they attempt to reason about them, and on the other hand the number of things

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known and understood renders them more cautious in passing judgment about anything new. There once lived, in a very solitary place, a man endowed by nature with extraordinary curiosity and a very penetrating mind. He raised many birds as a hobby, much enjoying their songs, and he used to observe with great admiration the happy contrivance by which they would transform at will the very air they breathed into a variety of sweet songs. Qose to his house one evening, he chanced to hear a delicate sound, and, being unable to imagine what it could be except some small bird, he set out to capture it. Arriving at the road, he found a shepherd boy who was blowing into a kind of hollow stick and moving his fingers about on the wood, thus drawing from it a variety of notes similar to those of a bird, though by quite a different method. Puzzled, and led on by his natural curiosity, he gave the boy a calf in exchange for his recorder and retired to solitude. Realizing that if he had not chanced to meet the boy he would never have learned of the existence of two methods for forming musical notes and very sweet songs, he tried traveling far from his home in the hope of meeting with some new adventure. The very next day he happened to pass near a small hut, and, hearing a similar tone within, he went inside to find out whether it was a recorder or a blackbird. There he found a boy holding a bow in his right hand and sawing upon some fibres stretched upon a concave piece of wood. The fingers of the left hand (which supported the instrument) were moving, and without blowing the boy was drawing from it various notes, and most sweet ones too. Now, you who are participating in this man's mind and sharing in his curiosity, judge his astonishment! Finding himself to have two unexpected new ways of forming tones and (p. 95) melodies, he began to believe that still others might exist in nature. His wonder increased when upon entering a certain temple he glanced behind the gates to learn what it was that had sounded, and perceived that the noise had emanated from the hinges and fastenings as he had opened the gate. Again, impelled by curiosity, he entered an inn expecting to see someone lightly bowing the strings of a violin, and instead saw a man rubbing the tip of his finger round the rim of a goblet and drawing forth from it a very sweet sound. And later he observed that wasps, mosquitoes,

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and flies did not form separate notes from their breaths, as did his original birds, but made steady tones by the swift beating of their wings. In proportion as his amazement grew, his belief diminished that he knew how sounds were created; nor could all his previous experience have sufficed to make him understand or even believe that crickets, which do not fly, could draw their sweet and sonorous shrilling not from breath but from a scraping of wings. And when he had almost come to believe that there could be no further ways of forming notes—after having observed in addition to what has been recounted numerous organs, trumpets, fifes, stringed instruments of various sorts, and even that little iron tongue which when placed between the teeth makes strange use of the buccal cavity as a sounding box and of the breath as a vehicle of sound—when, I say, he believed that he had seen everything, he found himself more than ever wrapped in ignorance and bafflement upon capturing in his hand a cicada, for neither by closing its mouth nor by stopping its wings could he diminish its strident sound, and yet he could not see it move either its scales or any other parts. At length, lifting up the armor of its chest and seeing beneath this some thin, hard ligaments, he believed that the sound was coming from a shaking of these, and he resolved to break them in order to silence it. But everything failed until, driving the needle too deep, he transfixed the creature and took away its life with its voice, so that even then he could not make sure whether the song had originated in those ligaments. Thereupon his knowledge was reduced to such diffidence that when asked {p. 96) how sounds are generated he used to reply tolerantly that although he knew some of the ways, he was certain that many more existed which were unknown and unimaginable. I might by many other examples make clear the bounty of nature in producing her effects by means which we would never think of if our senses and experience did not teach us of them, though even these are sometimes insufficient to remedy our incapacity. Therefore I should not be denied pardon if I cannot determine precisely the manner in which comets are produced, especially as I never boasted that I could, knowing that it may occur in some way far beyond our

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power to imagine. The difficulty of understanding how the cicada's song is formed even when we have it singing to us right in our hands is more than enough to excuse us for not knowing how a comet is formed at such an immense distance. Let us therefore stop at Sig. Mario's and my primary purpose, which is to set forth those questions which have appeared to us to throw doubt upon the opinions previously held, and to propose some new considerations. Let us examine and consider whether there is anything that can give us light in any way and can pave the road for the discovery of truth, as I go on to consider the arguments which Sarsi has raised against us and which made our conceptions appear improbable to him. Sarsi proceeds and grants to us that if there were no dispute about the existence of vapors or other material suitable for the formation of a comet, difficulties would occur in their rising from earth and ascending to the uppermost regions where they could receive the solar rays directly and reflect them to us. How is it that if the whole of them is illuminated, only the reflection of a single part comes then to us? Why is the reflection not made as in those vapors which display the aurora borealis, which are lighted all over and show themselves to us so ? He adds that he has beheld a marvelous thing in the middle of night, that is, a little coud near the zenith, illuminated all over and sending its splendor to us most liberally from every part. And, he continues, all dense and opaque clouds send sunlight to us from all {p. 97) [those] parts [which are] seen, while thin ones are penetrated by the light and look bright to us without having any shady part. So if the comet is formed as Sig. Mario says in such misty vapors, widely extended and not collected into a spherical figure, and if these are touched all over by the sun, why do we receive the reflection of only a little globe and not that of the equally illuminated remainder ? Even though the solutions to this objection are fully set forth in Sig. Mario's Discourse, I shall nevertheless proceed to answer them here in proper order, with the addition of some further considerations as the counter-arguments occur to me step by step. First, Sarsi should have no difficulty whatever in conceding that in all the material sublimated by a comet, the reflection of the sun's light to

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the eyes of a particular observer may be made from only one particular place even though the whole is equally illuminated. In support of this we have a thousand experiences for every one that may seem to contradict it; indeed, among those produced by Sarsi as contradicting this position we shall readily find that the majority favor it. No doubt exists that of any plane mirror exposed to the sun the whole surface is illuminated, and the same is true of every marsh, lake, river, sea, and in a word every smooth surface of whatever material. Yet to the eye of a particular person the reflection of solar rays is made only from one particular place on this surface, and that place changes with the moving of the observer's eye. The external surface of thin clouds diffused over a wide space is all equally illuminated by the sun, yet haloes and mock suns display themselves to a particular eye as only at a particular place, which likewise changes location with every movement of the eye. Sarsi says, 1 That thin sublimated material which sometimes produces the aurora borealis is nevertheless seen as entirely illuminated, as in fact it is.' But I ask Sarsi how he can be sure of this. He can reply to me only that he does not see any part which is not illuminated, {p. 98) while he sees all the rest of the surfaces of mirrors, waters, and marble slabs, over and above the small portion which renders the live reflection of the sunlight. True; but I should call his attention to the fact that if the material were similar in color to all its surroundings, or if it were transparent, then he would not distinguish anything except that single bright reflected ray, as sometimes happens when the surface of the sea cannot be distinguished from the air but the reflected image of the sun may be discerned. Thus, placing a thin piece of glass at some distance, we can see only that single part in which a light is reflected while the rest remains invisible on account of its transparency. Sarsi's error here is like saying that no criminal may ever rest assured that his crime will remain hidden, while ignoring the incompatibility which exists between remaining hidden and being known. Doubtless anyone by whom two registries were kept, one for offenses which remain concealed and the other for those which are discovered, would never have anything at all registered and noted in the former. So I say

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that one may believe without any inconsistency that the material of the aurora borealis is diffused through a very great space and is uniformly lighted by the sun, but since only that part is revealed and made visible to me from which refractions come to my eyes, the rest remaining invisible, I seem to see the whole. Besides, is not one hemisphere of the twilight vapors which surround the entire earth always equally illuminated by the solar rays? Surely it is; yet that part which lies directly between us and the sun looks much brighter than the more distant parts. This effect, like the others, is but an appearance and an illusion of our eyes, since wherever we are we always see the solar body as the center of a luminous circle which loses brilliance gradually as the distance from this center increases to one side or the other. But to people farther north than we, the part which is brightest for me would appear darker and what looks darkest to me would be brighter for them; thus we might say that there exists around the sun a huge perpetual {p. 99) halo traced upon the convex surface which bounds the vaporous sphere. This halo changes place according to the movements of the observer in the same way as do those haloes which are sometimes formed in thin clouds. As to the little cloud which Sarsi says he has seen so bright in the darkest night, I might ask him how he was sure that it was not likewise larger than what he saw—especially since he says that it was in a sense transparent, as it did not veil even the faintest of the fixed stars. For that very reason, there could be no way for him to be sure that it did not extend invisibly far beyond the limits of its observed lighted part, it being quite transparent; hence it remains in doubt whether this was not also one of the appearances which alter with an alteration of the position of the eye. Besides, there is no reason why it could not all appear luminous and still be a mere apparition, as would happen if it were not larger than the space occupied by the image of the sun. Thus if the image of the sun occupies one finger's-breadth in a mirror, and we cut away the rest of the mirror, there is no doubt that this little bit remaining could appear to us bright all over. Furthermore, if the mirror were smaller than the image, it not only might be seen bright all over, but the image in it would not appear to move with every movement of

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the eye, as it does in a large mirror; rather, since the mirror would be inadequate for the sun's entire image, it would follow that upon moving the eye the reflection would be now of one part and now of another part of the solar disc, and thus the image would appear immovable until the eye arrived at some place to which the image was not directed and would therefore be entirely lost. Hence, it is very important to consider the size and quality of the surface in which the reflection occurs, for accordingly as this surface is less smooth, the image of the same object will appear larger and larger, and sometimes the eye must travel a long way before the image completely runs off the mirror, {p. 100) and this image will appear fixed although it is actually mobile. The better to explain a point which is of the utmost importance and which may perhaps give someone (I shall not say Sarsi) a new idea, let your Excellency fancy himself at the seashore at a time when the water is quite tranquil and the sun is already declining toward the west. You will see a very bright reflection of the sun in the surface of the sea near the vertical line passing through the solar disc. This will not spread over a large area; indeed, if the water is very peaceful as I said, you will see a pure image of the solar disc bounded as in a mirror. Next let a light breeze spring up and ruffle the surface of the water, and simultaneously your Excellency will see the sun's image begin to break into many parts and spread and extend into a larger space. If you were close by, you might be able to distinguish the broken pieces of the image from one another, but from a greater distance you would not see this separation because of the narrowness of the intervals between the pieces, or because by their great brilliance the shining parts would mix together and behave as do several fires close together which from afar appear to be one. Now let the ruffling proceed into greater waves, and that multitude of mirrors from which the image of the sun will be reflected to the eye according to the various slopes of the waves will extend into wider and wider intervals. Next, withdraw to a greater distance and climb a hill or some other prominence in order to see the water better, and the lighted field will appear one and continuous. From a very high mountain about sixty miles from the

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Bay of Leghorn, on a clear and windy day about an hour before sunset, I have seen a very bright strip spreading to right and left of the sun and occupying a length of tens and perhaps hundreds of miles which was the same kind of reflection of sunlight as those just mentioned. Now let Sarsi imagine most of the sea on both sides to be removed so that there remains only a breadth of two or three miles {p. 101) at the middle, pointing toward the sun. This surely would all be illuminated, and it would not be movable with every motion of the observer to one side or the other—unless perhaps he were to move several miles, for then he would begin to lose the left side of the image (if he moved toward the right) and the bright image would become constricted until it was made very thin and even vanished entirely. But it is not in this way that the image would actually move with the motion of the observer; rather, we should continue to see it entire, though all of it would move so that its center would always correspond with the direction of the sun, which for other people observing it at the same time would correspond with various other points on the horizon. Here I wish to tell your Excellency something that has occurred to me as the solution of a maritime problem. Experienced sailors sometimes recognize that a wind will come to them from a certain part of the sea before long, and they say that a sure sign of this is to see the air in that direction more bright than it would ordinarily be. Consider, your Excellency, whether this might not arise from a wind disturbing the waves over there already. From such waves, as from many mirrors spread over a wide area, there would originate a much brighter reflection of the sun than would exist if the sea were calm. Then that part of the vapor-laden air may be made brighter by this new light and by the diffusion of that reflection. This air, being high, sends also some reflection of light to the eyes of the sailors, while they, being low and far off, would not be able to receive the primary reflection from that part of the sea which is already being ruffled by the wind twenty or thirty miles away. And that is how they perceive and predict a wind from afar. But pursuing our original idea, I say that the solar rays do not

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impress the image of the sun with the same size in all materials, or I should say upon all surfaces. In some, namely those which are plane and smooth like a mirror, the solar disc is shown to us as bounded and as equal {p. 102) to the actual sun; in smooth convex surfaces it appears smaller to us, and in concave ones it appears sometimes smaller and sometimes larger and sometimes even the same, in accordance with the different distances between the mirror, the object, and the eye. If the surface is not even but is wavy and full of elevations and depressions (composed, as we might say, of a great multitude of little mirrors placed at varying tilts and exposed to the eye in thousands of ways), then this same image of the sun, divided into thousands of pieces, will meet our eye as thousands of parts spread over a large space. Thus it will impress us as a collection of many little bright patches. The number of these will make it appear from a distance as a single continuous luminous field, stronger and more vivid in the center than toward the edges. At the edges the light becomes languid, and finally it vanishes mistily when the obliquity of the eye to this surface no longer causes the visual rays to find any waves to reflect them toward the sun. This large image is also capable of moving with a movement of the eye, provided the surface where the reflection takes place continues beyond the limits of the image. If the material occupies a small space (smaller than that of the whole image), it will continue to appear bright until the eye arrives at that boundary beyond which the obliquity of incident rays upon the material causes the reflections to be no longer directed toward the sun, when the light vanishes and is lost. Now I tell Sarsi that when he saw a cloud hanging in the sky, sharply bounded and lighted all over—and remaining so even though the eye might change its position through some distance—he could not thereby be sure that that illumination was a thing any more real than haloes, mock suns, rainbows, and reflections in the sea. I tell him that its consistency and apparent stability may depend upon the smallness of the cloud, or this may make it incapable of receiving the entire expanse of the sun's image, which would broaden out through a space many times larger (p. 103) than the cloud if there were no lack of material. And if it were seen entire at a time when other

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fields of clouds extended beyond it, I say that the movement of the eye would also cause it to move in its entirety. A conclusive argument of this for us is our often seeing at sunrise or sunset many little clouds suspended close to the horizon; those nearly in line with the sun show most splendidly and look almost like fine gold. Of those to the side, the ones less distant from the sun are of medium light and are brighter than those more distant, and by degrees they show themselves continuously less lighted, until finally those that are very remote have little or no brilliance—to us, that is; but to anyone so situated that they came between his eye and the place of the setting sun, these would be the brightest. Therefore, let Sarsi understand that if the clouds were not scattered but formed one continuous stretch, it would come about that to each observer that part which was at the center for him would look most lighted, and at the sides it would appear less bright according to the distance from the center; thus what is the summit of splendor for me is its terminus for others. Here someone might say that since that bit of cloud remained fixed, and the light in it was not seen to move with every change of place by the observer, this should be sufficient to make parallax acceptable for determining its altitude; and, the same thing being possible for the comet, it is proper for those people to utilize parallax who seek to determine its location. T o this it is replied that this would be correct if one first demonstrated that the comet was only a part of an entire image of the sun and not a whole one. Then not only all the material in which the comet was formed would be illuminated, but the image of the sun would pass beyond its edges and would suffice to illuminate a much larger area if there existed material there disposed to reflect light. Now this not only has not been demonstrated, but one may very reasonably believe the contrary; namely, that the comet is an entire image and not a mutilated or truncated one, for this is argued by its regular shape which is designed with such beautiful (p. 104) symmetry. 24 From this may be drawn a simple and apt reply to Sarsi's objection when he asks how one can imagine (in accordance with Sig. Mario's statement) the comet's being in a material extending through a wide space above,

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without this material being entirely illuminated, but with only a small circle of it sending the reflection back to us. Let me ask the same question of him or of his master, who will not have the comet be a fire, but (if I am not mistaken) who inclines to the belief that at least its tail is a refraction of solar rays. I ask him whether he believes that the material in which such a refraction is made is cut exactly to the measure of this tail, or that here and there it extends beyond it ? If it extends beyond, as I believe he will reply, then why is this material not seen, since it is touched by the sun ? One cannot say here that the refraction occurs in the substance of the aether, which being most transparent has no refracting power; still less does it occur in other material, for if there were anything suitable for refracting it would also be suitable for reflecting the solar rays. Besides, I do not see what right he has to call the head of the comet a ' little circle' when his master, by profound calculations, has found it to contain 87,127 square miles. Perhaps no cloud has ever achieved such proportions. Resembling our man of a short time ago who was of the opinion that sound could be produced in but a single way, Sarsi goes on to say that it is impossible for the comet to be generated by reflection in smoky vapors, and that the example of the rainbow does not reduce the difficulty even though it really is an illusion of sight. For the generation of rainbows and other such things requires a moist material which is already resolving into water and which only then acts essentially like smooth and polished bodies, reflecting light from those parts where there are the proper angles of reflection and refraction required for the production of such an effect, as happens in mirrors, water, and crystal balls, while in thin and dry things not possessing smooth surfaces like mirrors, not much refraction takes place. Thus there is required for this an aqueous material, and (p. 105) consequently a heavy one incapable of rising above the moon and the sun (where in my opinion also nothing can go except things which are in the nature of very light exhalations), and hence, a comet cannot be produced in those smoky vapors. A sufficient reply to all this reasoning would be to say that Sig. Mario has never limited himself as to the precise material in which a

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comet takes shape, nor said whether this is moist or smoky or dry or smooth, and I am sure that he would not blush to say that he does not know. But seeing that in vapors, in thin non-aqueous clouds, and in those which do resolve into tiny drops; in stagnant waters, in mirrors, and in other materials there occur various illusions of diverse images which take shape by means of reflections and refractions, he has deemed it not impossible that there exists in nature still another material, designed to render us one more image different from all the rest, and that this image is the comet. Such a reply, I say, is adequate to the objection, if indeed any part of the objection were valid. Yet, as I have said before, my desire to pave the road for the investigation of truth induces me, so far as I am able, to make some remarks about certain particular things in the foregoing reasoning. First, it is true that the illusion of the rainbow takes place in an effluvium of very tiny drops of water, but I do not believe that conversely no similar illusions can take place without such an effluvium. A triangular crystal prism brought close to the eye shows us all objects as tinted with the colors of the rainbow, and rainbows are often seen in ' d r y ' clouds without any rain whatever descending to the earth. Are not the same varicolored illusions seen in the feathers of many birds when the sun strikes them in certain ways ? And that is not all; let me tell Sarsi something which is perhaps new—if anything new can be said to him. Let him take any material, whether stone or wood or metal, and holding it up to the sun gaze at it most intently. There he will see all colors appearing in most minute specks; and if in looking at this, he will make use of a telescope set for looking at very near objects, he will see what I mean very much more distinctly and without any need of these bodies being resolved into dew or moist vapors. Besides, those little clouds that {p. 106) look so bright in twilight and reflect the sun to us so vividly that it almost dazzles us are among the thinnest and driest which exist in the atmosphere, while those which are moist look the darker the more pregnant with water they are. Haloes and mock suns occur without rain and without moisture in the thinnest and driest clouds (or rather fogs) which occur in the air.

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Second, it is true that smooth and well-polished surfaces such as those of mirrors render a strong reflection of the sun's light to us, so much so that we can hardly look at them without injury, but it is also true that a reflection is made from surfaces not so smooth, though a less powerful one in proportion as the polish is less. Now your Excellency may see whether the splendor of the comet is among those which dazzle the vision or among those which by reason of their feebleness do not offend at all. From this you may judge whether there is required for its production a surface resembling a mirror, or whether a surface much less smooth suffices. I should like to show Sarsi a method of representing a reflection very similar to that of a comet. Take a very clean carafe, your Excellency, and holding a lighted candle not far from it you will see in its surface a tiny image of this light, very bright and sharp. Then take upon the tip of your finger a small quantity of any slightly oily material that will adhere to the glass, and oil it as thinly as you can at the place where the image is seen, so that the surface becomes a little dimmed. Immediately you will see the said image become dim. Next turn the glass so that the image emerges from the oily spot and just touches its edge, and rub once with your finger straight across the oily part. Instantly you will see a straight ray formed in imitation of the comet's tail, and this ray will cut transversely and at right angles across the rubbing you have made with your finger; if you rub across this once more, the same ray will be led away in another direction. This happens because the skin on the ball of the finger is not smooth, but is marked with certain twisted lines utilised by the sense of touch for feeling the most minute distances in (p. 107) tangible things, and in moving the finger over the oily surface these leave some very thin tracks, in the edges of which the reflections of light take place. These being many and being regularly disposed, they form a light stripe at whose head may be placed, by moving the glass, that first image which was made in the unoiled part. The head will then be seen as brighter than the tail, and the tail as somewhat less brilliant. The same effect will be seen if the glass is fogged by breathing upon it instead of using oil. If you should ever suggest this little diversion to Sarsi, and if he protests specifically and at length, I beg your

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Excellency to tell him that I do not mean to imply by this that there is a huge carafe in the sky, and someone oiling it with his finger, and that a comet is thus formed, but that I merely offer this example (and I could offer others, while perhaps there are still others unthinkable to us) as an illustration of nature's bounty in her variety of methods for producing effects. Third, I say that it is not true at all that reflections and refractions can be made only in meteorological materials and forms which inherently contain much water (because only then are the surfaces smooth and polished), or that these are necessary conditions for producing those effects. As to the necessity of polish, I say that even without it there would occur unique and distinct reflections of the image. I say so because the image occurs, broken and confused, when the entire surface is as rough and uneven as you please; for the image of a colored cloth, which is distinctly perceived in a mirror facing it, is seen to be confused and broken when thrown back to us by a wall, from which there is only a certain hint of the color of the cloth. But if your Excellency will take a stone or a wooden ruler not smooth enough to render images to us directly, and expose this obliquely to the eye as if you wished to determine whether it is flat and straight, then you will distinctly see upon it the images of objects that are brought close to the other end of the ruler—and so distinctly that if you held a manuscript there you might easily read it. And if you will place your eye close {p. 108) to the end of some very long straight wall, the first thing you will see is a perpetual concourse of exhalations toward the sky, especially when the wall is struck by the sun, so that all objects seen through them appear to tremble. Next if you will have someone approach the wall slowly at the other end, you will see that when he is very close to it his image will come out toward him from these ascending vapors, which are not in the least moist and heavy but rather very dry and light. Nor is this all. Hasn't Sarsi ever heard all the talk that was spread, especially by Tycho, about refractions that are made in exhalations and vapors that surround the earth, even when the air is most calm, most dry, and farthest from any rain or moisture ? And he need not cite to me, as he does, the authority of Aristotle and of all teachers of perspective,

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because all he will accomplish is to declare me to be a more careful observer than they—something which I believe is diametrically opposed to his intention. So much in reply to Sarsi's first argument; let us get on to his second. XXII 'Perhaps someone . . . (p. 109) . . . that they did not exist.' (p. 89, 1. 35 to p. 90,1. 26). There are many things to be considered in this argument which in my opinion vitiate it a good deal. First, neither Sig. Mario nor I ever went so far as to say that aqueous and dense vapors were attracted on high to produce a comet; hence all objections founded upon the impossibility of this idea fall to the ground and disappear. Second, that bodies appear illuminated less and less in proportion as they are rarer and more transparent, and more and more as they are denser, which Sarsi says he has observed from long experience, I hold to be quite false. A single experience convinces me of this; namely, seeing a cloud illuminated as brightly as if it were a mountain of pure marble, though the material of the cloud is somewhat thinner and more transparent than that of the mountain. So I do not see the necessity of Sarsi's saying that the material of the comet is denser and more opaque than that of the planets, and it is this that he seems to be saying if I have correctly construed his words. T h e more so as I do not think it evident that the comet was brighter than first-magnitude stars and the planets. But if indeed it was, then what is the point of bringing up this density of the material, when we see twilight mists shine much brighter than the stars and the comet? And when one small golden cloud is a hundred times brighter ? Third, assuming that the comet was generated in a thick and dense vapor, it need not follow that because of refraction within this vapor there would be a noticeable discrepancy in the intervals between one star and another, as he pretends. That would be in discord with Tycho's measurements, no difference having been observed by him although he measured them with great accuracy. Frankly, ( p . n o ) there are two things here that displease me very

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much. One is that I can find no way to credit what Sarsi says without refusing to credit his master, since the one speaks of having measured the distances between stars with great precision, while the other ingenuously excuses himself for not having had the opportunity to make such observations with the required accuracy, not possessing large and accurate instruments like those of Tycho. For that reason, he even hoped that others would not be overly concerned with his instrumental observations. And the other thing is that I find no way to inform your Excellency with due modesty and reserve how I fear that Sig. Sarsi failed to understand exactly what sort of thing refractions are, when they take place, and how they accomplish their effects. Therefore, please tell him some time (for I know you can do so with infinite courtesy) how the rays which come from the object to the eye at right angles to the surface of the transparent material in which refraction must occur are not refracted at all; their refraction is nil, and since stars near the zenith send their rays to us perpendicular to the spherical surface of the vapors that surround the earth, these suffer no refraction. But in proportion as they incline more and more toward the horizon and consequently cut the said surface more and more obliquely with their rays, they are more and more refracted and show their position with greater and greater error. Next tell him that because the boundary of this material is not very high, since the vaporous sphere is not much larger than the terrestrial globe on whose surface we are located, the incidence of the rays coming from points close to the horizon is quite oblique. This obliquity becomes always less the more the surface of the vapors is raised, so that if it were many terrestrial radii distant, the rays coming to us from any point in the sky might cut the said surface with very little obliquity and behave as if tending toward the center of the sphere, which is the same as saying that they would be perpendicular to the surface. Now since {p. h i ) Sarsi places the comet very high above the moon, no perceptible refraction need occur in vapors extended to such a height, and in consequence no sensible appearance of difference in position would exist in the fixed stars. Hence, Sarsi had no need to thin out the vapors in order to excuse the lack of refraction,

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muchj less in such a way as to remove it entirely. Others have fallen into this same error when they thought they could demonstrate that the celestial substance is no different from the nearby elemental substance, and that the former cannot be given a multiplicity of orbs because in that event great differences would arise in the apparent places of the stars from refraction in so many different transparent substances. This argument is idle, since even if all these orbs were of differing diaphanous materials, their very size would prevent any refraction for our eyes which repose right at the center of such orbs. XXIII Now let us pass to the third argument. 'Furthermore, Galileo . . . {p. 112) . . . rather than mathematical.' (p. 90, 1. 27 to p. 91, 1. 23). Sarsi continues, as remarked before, to form conclusions at will and attribute them to Sig. Mario and me in order to refute them and in this way to make us the authors of absurd and false opinions. Sig. Mario speaks of the aurora borealis in order to illustrate the possibility that tenuous and thin materials might rise very far from the earth, but Sarsi pretends that he means the comet also to be of this same material. Not content with this, since he himself holds the opinion that reflection of light could not occur in any meteorological substances except moist and aqueous ones, he attributes a little farther on to Sig. Mario and me the statement that aqueous and heavy vapors would rise into the sky to form a comet. Now he will have it that we have stated that the material of the comet is the same as that of the sunspots, which were mentioned by Sig. Mario only to explain why he thinks that some materials may possibly be generated, move, and dissolve amidst the celestial substance, and not at all to affirm that comets are produced from these. Hence, your Excellency may see more clearly that my protest a short time ago was not entirely unnecessary or beside the point when I disavowed the idea that the comet took shape on an immense oiled carafe. [In the first place, in order to reply to everything, I say that Sarsi did not need to repeat so often his reproach against us for abhorring poetry, for as I have already said we do not abhor it at all. Rather,

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we might add that it is not unknown to us that because of the interwoven relationship which exists among all the arts, not only may the philosopher be permitted sometimes to intersperse poetic fancies in his treatises (p. 113) as Plato and many others have done, but it is also occasionally permissible for the poet to seed his poems with scientific speculations, as has been done by Dante among our ancient poets in his Divine Comedy and by the noble Stigliani among the moderns in his New World. Next I say, getting back to our dispute, that] 26 1 have never declared comets and sunspots to be of the same material, but I surely realize now that if I had not needed to fear any stronger opposition than what Sarsi produces here, I should not shrink from affirming this and I daresay I could make it stand up. Sarsi discovers a great contradiction in the possibility of a thin material going straight toward the body of the sun and then being set in rotation upon its arrival there. But why does he refuse to pardon this assumption on the part of Sig. Mario, as well as in Aristotle and all his school who make fire ascend straight upward to the lunar orb and there transform its straight motion into circular ? How can Sarsi maintain it to be impossible that a piece of wood cast from a high place vertically into a swift river should commence being carried round the terrestrial globe as soon as it strikes the water? His other objection would truly be more valid; namely, that while all other materials similar to the comet strive eagerly to embrace the sun, the comet alone has fled, withdrawing toward the north. This objection would be more binding, as I say, had he himself not untied it a short time before—if, in having Apollo wash his face and then throw out the water for the comet to spring from, he had not declared to us his opinion that the material of the sunspots departs from the sun and does not return there. XXIV Now let us hear the fourth argument.' Now I come ...[/>. 1 1 4 - 1 1 5 ] . . . it had first entered.' (p. 91,1.24 to p. 94,1.14). (p. 116) We have already seen how much significance there is in the last three arguments, and I think that even Sarsi did not esteem them highly, because the arguments drawn from physics, as he calls the

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following ones taken from optical demonstrations, he considers to be far more conclusive and effective than what has gone before; a clear indication that he has not received complete satisfaction from the reasoning drawn from nature. But he had better pay attention to his cause, and consider that to a person who wants to convince others of something which, if not false, is at least very questionable, it is a great advantage to be able to use probable arguments, conjectures, examples, analogies, and other sophisms, and to fortify himself further with unimpeachable texts, entrenching himself behind the authority of other philosophers, scientists, rhetoricians, and historians. T o reduce oneself to the rigor of geometrical demonstrations is too dangerous an experiment for anyone who does not thoroughly know how to manage these, for just as there is no middle ground between truth and falsity in physical things, so in rigorous proofs one must either establish his point beyond any doubt or else beg the question inexcusably, and there is no chance of keeping one's feet by invoking limitations, distinctions, verbal distortions, or other fireworks; one must with but few words and at the first assault become Caesar or nobody. This geometrical strictness will enable me more briefly, and with less tedium for your Excellency, to disentangle the ensuing proofs—which I shall call optical or geometrical more to pacify Sarsi than because I find in them, or in his diagrams, much of perspective or of geometry. As your Excellency sees, Sarsi's intention in this fourth argument is to prove that the comet does not belong among merely apparent, simulacra caused by reflection and refraction of solar rays through the relation existing between the comet and the sun, because this relation to the sun {p. 1 1 7 ) is different from those preserved by things known certainly to be mere appearances, such as rainbows, haloes, mock suns, and reflections from the sea. All these, he says, move with the sun's movement in such a way as to go always in the same direction as the sun, whereas the opposite happened in the case of the comet, which therefore was not an illusion. It would be quite adequate here to reply that there is no obvious necessity for the comet to follow the pattern of haloes, rainbows, or the other illusions named, since it differs from a rainbow, a halo, and the

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others. Nevertheless, I wish to concede here something more than I am obliged to, if only Sarsi will not try to take advantage of me later by calling futile for me some mode of argument which must be accepted as conclusive for him. I therefore ask Sarsi whether or not he considers as conclusive the argument derived from the contrariety of patterns in the comet and in mere images, the former opposing and the latter copying the sun's motion ? If he says not, then all his argument is vain and I have nothing further to say. But if he says it is conclusive, then justice demands that in proving the comet to be an illusion it shall be just as valuable to me to prove that it does follow the pattern of some empty appearance in regard to following or opposing the sun's motion. But in order to find such an appearance, I need not even stray from one of those produced by Sarsi himself in order to show us simply and clearly that the comet goes opposite to this image; for to me it appears not opposite but precisely the same. Therefore, take his third diagram,ae your Excellency, in which he draws an analogy between the comet and the reflection of the sun made on the surface of the sea. When the sun is at H, its image is seen by the eye at A along the line A I ; when the sun gets to G , the image will be seen along the line A E ; and being at F , its image will appear along the line A D . Now as the sun appears to us {p. 118) to move in the sky along the arc H G F , it remains to be seen in what direction its image likewise appears to us to move with respect to the sky, which is where Sarsi observed the motions of the comet and the sun. For this, we must produce the arc F G H L M N and extend the lines A I, A E, and A D to L , M, and Ν ; then we say: When the sun was at H, its image was seen along the line A I, which corresponds in the sky to the point L ; when the sun came to G, its image was seen along the line A Ε and it would appear to be at Μ ; finally, when the sun reached F, its image would appear at N. Hence, the sun moving from Η to F, its image would appear to move from L to N. But this is to appear to move contrary to the sun, Sig. Sarsi, and not in the same direction, as you believed—or rather, as you attempted to make other people believe. I put it this way, your Excellency, because I cannot believe that

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he should have equivocated in so obvious a matter. Besides, one may see also that in explaining himself he makes use of some very inappropriate and unusual ways of speaking, merely to accommodate something to his requirements which cannot be so accommodated, as there is nothing in it. Thus, he sees that as the sun passes from Η to G and from G to F, its image comes from I to Ε and from Ε to D . This progress I E D is a true and real approach toward the eye at A , and since Sarsi needs to be able to say that the image and the sun move in the same direction, he decides to say flatly that the motion of the sun along the arc H G F is an approach toward the point A, and that going toward the zenith is the same as going toward the center! Moreover, he has to pretend not to notice another very grave absurdity which he would be {p. 119) adopting by maintaining that the image imitates the movement of real

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objects. If it did, it would likewise be true conversely that the object should copy the image; let your Excellency consider what would follow from this. From the end of the diameter O, draw the straight line OR which falls outside the circle and forms some angle with BO, and produce D F , E G , and I Η to this at the points R, Q_, and P. It is obvious that if the real object moved along the li^e PQ_R the image would go along I E D , and since this is an approach toward the eye at A, and according to Sarsi the image does whatever the object also does, then the object in moving from the point Ρ to the point R approaches the point A. But it is actually departing, and hence the absurdity. Notice, moreover, that when Sarsi here considers what would happen as between a real object and its image, he is assuming that the material in which the image must be formed remains motionless and that only the object moves; for if he meant that the material also moved, then various other consequences would follow with regard to the appearances of the image. And therefore from what Sarsi adds about the comet's not having returned upon the return of the sun, nothing can ever be inferred unless one determines first the movement or rest of that material in which the comet is produced. XXV I pass on to the fifth argument. 'Furthermore, if the comet . . . (p. 120). . . similar to them.' (p. 94,1. 15 to p. 95,1. 27). My astonishment remains and even grows at seeing how frequently Sarsi pretends not to see things that are right before his eyes, perhaps in the hope that his pretense will give birth in others not to a feigned but to a real blindness. At present, he wants his argument to prove that if the comet were a mere appearance it would show itself in the shape of a circle, or part of a circle, because such is the case with rainbows, haloes, coronae, and various other images. I do not know how he can maintain this, having been reminded a hundred times of the sun's reflection in the sea, as well as of those projections of rays through apertures in the clouds that appear as straight stripes very similar to a (p. 121) comet. But perhaps he persuaded himself that without further trouble his point for the comet is

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proved by the optical demonstrations he adduces for this, which I greatly question. Unless I am mistaken, his procedure is mutilated and he lacks a principal part of the data, which is a serious defect in logic, and this is the spatial disposition with respect to the eye of that material surface in which the reflection must take place. T h a t point never comes under consideration by Sarsi, for which I cannot suggest any more moderate excuse than that it escaped his attention; for if he noticed it but pretended not to in order to keep his readers in ignorance, that would seem to be a much graver defect. N o w a consideration of that disposition is the whole point; hence Sarsi's demonstration is completely inconclusive except when the surface of the vapor around the point A in his diagram is directly opposite the eye at D , so that the axis I D Η falls perpendicularly upon the plane in which this surface is extended. For then, the triangle I D A being turned round the axis I H , the point A would lie continually in this surface and would describe the circumference of

I

Fig. 19 a circle. But if the said surface were exposed obliquely to the eye, the angle A would not touch it except in a single point, and upon turning the triangle the same angle A would either penetrate beyond this surface or would fall short of it. In sum, to have the comet appear circular it would be required that the surface upon which it was generated should be plane, and exposed to the eye perpendicularly to the line passing through the eye and the sun. Such an

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arrangement could occur only in diametrical opposition or in lineal conjunction of the vapors with the sun, and thus rainbows are always seen in opposition to and haloes or coronae in conjunction with the sun so as to appear circular; but as to comets, I do not know if they are ever seen either in opposition to or in conjunction with the sun. If in composing this demonstration it had ever occurred to Sarsi to think of that material which he represents around the point A as sea water instead of as vapors, (p. 122) he would have perceived that his own argument, conducted in the same way and with the same words, would prove that the reflection in the sea would necessarily have to extend in a circular line. Then, thanks to the fact that his senses would show him the contrary, he would have discovered the fallacy in his syllogism. XXVI Now let us hear the sixth argument. Ί hold . . . the greatest astronomers.' (p. 95,1. 28 to p. 96,1.21). It is quite false that either Sig. Mario or I ever wrote or said that (p. 123) images produced by the sun maintain the same parallax as the sun, as Sarsi here declares as a foundation for his syllogism. Rather, Sig. Mario names and discusses many such images, and afterwards adds this:' Now inasmuch as parallax is nil in some of the aforesaid images, while in others its operation is very different from its operation on real objects . . .' 27 Nor is it to be found in Sig. Mario's essay that he declares the parallax to be the same as that of the sun or moon except in haloes; in the others, including rainbows, it is assumed to be different. Therefore, the first proposition of the syllogism is false; now let us see how true and conclusive the second is, assuming that the parallax of all mere images does have to be equal to that of the sun. Sarsi wishes to prove on the authority of Tycho and of his master, as indeed he must, that the parallax observed in the comet is greater than that of the sun; but he then abstains from producing the specific observations made by Tycho and many other reputable astronomers upon the comet's parallax, so he does not let the reader see how widely these vary among themselves. Well, whatever they

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may be, they are either correct or incorrect; if correct, so that complete faith may be placed in them, one must conclude either that the comet was simultaneously below the sun and above it, and even in the firmament, or else that, because it was not a fixed and real object but a vague and empty one, it was not subject to the laws of fixed and real things. If the observations were incorrect, then they lack authority and nothing whatever can be determined from them. Tycho himself, among so many disparities, chose those observations which best served his predetermined decision to assign the comet a place between the sun and Venus, as if these were the more reliable. As to the other observations supplied by Sarsi's master, they differ so much among themselves that the latter judged them to be unfit for establishing the position of the comet, saying that they were taken with inexact instruments and without due consideration of the time, of refraction, and of other circumstances, (p. 124) Thus he himself does not oblige others to set much store by them, and he reduces himself to a single observation which requires no instrument and is capable of being carried out quite accurately by simple vision alone; and he puts this ahead of all the others. It relates to the exact conjunction of the head of the comet with a certain fixed star, which conjunction was seen simultaneously from places very distant from one another. Well, Sig. Sarsi, if that happened, it is completely contrary to your requirements, since from this it may be deduced that the parallax was nil, whereas you adduced this authority to confirm your proposition that this parallax was greater than that of the sun. See now how the very authors you have called up testify against your cause. As to what you say about our having confessed the observations made by great astronomers to have been most precise, I reply to you that if you will better consider where and when that was said, you will understand that these might be called 'precise' even if they differed among themselves much more than they did. They were called precise and sufficient to refute Aristotle's opinion when he would have the comet be a real object very close to the earth. Did you not know that your master himself proves that the mere distance between Rome and Antwerp could cause in a real object located in

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the highest region of the air a parallax greater than fifty, sixty, one hundred, or even one hundred and forty degrees ? And if so, could not those observations be called exact and conclusive which, being each less than a single degree, differ among themselves by a few minutes ? XXVII Now read the last argument, your Excellency: ' Finally, we ought n o t . . . (p. 1 2 5 ) . . . to oppose Galileo.' (p. 96,1. 22 to p. 97,1. 4). Sarsi thinks so highly of this argument that to him it seems alone sufficient to prove his point; yet I see in it no efficacy for persuading me when I consider that in producing these vain images the sun enters as the efficient principle and the clouds or vapors as the material principle. Now since the efficient is everlasting, then when the material is not lacking, rainbows and haloes and mock suns and all other appearances should be perpetual; hence, attention should be paid to the long or short duration of the establishment and position of the material. Nothing dissuades us from thinking that above the elemental regions there might be some material of longer duration than clouds or mists or rain falling in small drops, or other elemental materials; so that a reflection or refraction of the sun in this would show itself to us for a longer time than do rainbows, mock suns, or haloes. But without leaving the elements, do we not have perpetual appearances in auroras, which are refractions of solar rays in the vaporous region, and in those reflections on the surface of the sea ? For if the observer, the sun, the vapors, and the surface of the sea remained always in the same arrangement, the aurora or the brilliant stripes in the water would be seen perpetually. Besides, from less or greater duration, one does not conclusively infer an essential difference. Even among comets, without our going further afield, some are seen to last ninety days or more while others are dissipated on the third or fourth day. And since it is observed that the more enduring comets show themselves much larger than the others even when they first appear, who knows but that there are some, and perhaps many, which (p. 126) last not merely less than a few days, but even not many hours, and which are not observed by

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reason of their smallness ? And comets themselves give us assurance that in the place where they are formed material is generated which is better suited to maintain itself than are our elemental clouds or mists, for they are produced from material (or in material) that is neither celestial and eternal nor yet necessarily dissipated in very brief times. Hence the question remains whether that which is produced in this material is a pure and simple reflection of light (and in consequence an empty image) or something else which is fixed and real. Hence Sarsi's argument is inconclusive, and will so remain until he demonstrates that the cometary material is unfitted to reflect or refract the sunlight. For as to its being fitted to endure many days, the duration of the comets themselves more than amply proves this to us. XXVIII N o w let us pass on to the second question of this Second Weighing. (First argument) ' I now come . . . acquainted with prophecy.' (p. 97, 1. 8 to 1. 2i). Here, before I go on, I cannot suppress some resentment toward Sarsi for his completely unmerited imputation of hypocrisy on my part. T h i s is far from justified, for I frankly confess (as I always have) that I am vanquished and almost totally blind when it comes to penetrating the secrets of Nature, (p. 127) I certainly desire to achieve some small knowledge of those secrets, but nothing is more contrary to such an intention than hypocrisy and feigning. Sig. Mario in his essay has never feigned anything, nor has he needed to do so, since whatever he has adduced that is new has always been set forth conjecturally and with reserve. He has not sought to make others accept as proved that which he and I take as questionable or at most as probable, and which we have arrived at and opened to the consideration of people more knowing than we in order to have their help either in drawing confirmations of some true conclusion or in completely excluding some false one. A n d just as Sig. Mario's writing is honest and sincere, Sig. Lothario, yours is equally filled with pretense. In order to clear the path for your opposition, nine times out of ten you have feigned not to understand what Sig. Mario

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wrote; you prepare your material arbitrarily, giving his writing meanings very far from what he intended, and frequently adding to it or deleting from it. The reader, crediting what you then put forth by way of rebuttal, remains in the belief that we have written a lot of foolishness which you have acutely exposed and refuted. This has already been noted by me in the foregoing, and in what is left it will be no less so. Let us come to the point. What is Sarsi's motive in writing that we have failed in what we wanted above all; namely, in our pretense that the comet moves in a straight line; for in that case it would have to go always toward the zenith without any deviation? Now who apprised you of that consequence but Sig. Mario himself, who mentions this? He might indeed have perpetrated a pretense on you, and you in your grace would then have pretended not to detect his pretense. Nor is that all. Only two lines above, you wrote that I have naively confessed my inability to solve (or my disinterest in solving) the very argument which I introduced, and you add that what I chiefly wanted was to feign ignorance of it. Now what kind of selfcontradiction is this? A man brings forth and naively publishes a proposition, and then you charge him with having greatly {p. 128) desired to hide it and to feign ignorance of it! Really, Sig. Lothario, you require of your readers great simple-mindedness and small attention to business. Now let us see whether this statement, in which no pretense of ours is to be found, contains any pretense on the part of Sarsi. And there is certainly more than one such to be found. First, he makes me say things which were never said or written, in order to open the road for showing me to be so ignorant a geometer as to have failed to understand consequences whose proof requires no higher knowledge than certain trite propositions from the first book of Euclid. When we say that if the comet moves with straight motion, it will appear to us to move toward the zenith, he tries to make us say that by so moving it will arrive at the zenith. Here Sarsi must confess either that he did not understand the meaning of the phrase 'to move toward a place' or that he tried by feigning and dissimulation to attribute a false proposition to us. I do not believe the first is

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possible, for otherwise he would have to suppose that saying to ' sail toward the pole' or ' throw a rock toward the sky' meant that a ship arrived at the pole and a rock at the sky. Hence it follows that he pretended not to understand the true proposition which we wrote, and attributed to us the false one in order to have a chance to subject us to his unwarranted remarks. Moreover, he does not quote Sig. Mario's words faithfully in another regard either, for where the latter says that it is either necessary to abandon the straight motion attributed to the comet or else, retaining that, to add some other cause for its apparent deviation, Sarsi wilfully changes the words ' some other cause' to ' some other motion' in order to deduce, quite apart from any intention of mine, a motion of the earth, and to produce more fireworks and foolishness here. He finally concludes by saying that he is not one of those who can read minds; yet he often sets himself to penetrate the inner meanings of other people. XXIX Now let your Excellency continue. 'Therefore, I ask . . . (p. 129) pious and religious.' (p. 97,1. 22 to p. 98,1. 20). Here, as you see, he is at some pains to show that no other motion which may be attributed to the comet or to any other world body can suitably support the straight motion adduced by Sig. Mario and at the same time explain its apparent deviation from the zenith. This argument is superfluous and vain, since neither Sig. Mario nor I ever wrote that the cause of such deviation depended upon any other motion, either of the earth or of the heavens or of any other body. Sarsi (p. 130) has introduced this as a caprice, so let him answer it himself. He should not pretend that others are obliged to support what they have not said or written, nor perhaps so much as thought —and indeed Sarsi admits this himself when he plainly says that he does not believe it ever entered my head to introduce motion of the earth to rescue this deviation, he having always known me to be a very pious and religious man. Now if that is so, why did you bring this up? To what end did you try to prove it unsuited to this requirement ? But we had better proceed.

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XXX Read on, then, your Excellency. 'But lest I . .. (p. 1 3 1 ) . . . never reach R.' (p. 98,1. 21 to p. 99,1. 15). As your Excellency sees, Sarsi once more alters Sig. Mario's writing, pretending that he has said that motion perpendicular to the earth would finally conduct the comet to the zenith point; this is not to be found in the book, though Sig. Mario does indeed say that such motion would be toward the zenith. In my opinion, Sarsi does this in order to create an occasion for bringing in his geometrical proof, based upon no more profound a foundation than the mere understanding of the definition of parallel lines. From this action, some people might deduce a proposition not very complimentary to Sarsi, for he regards this conclusion of his and his proofs of it either as very ingenious, and not for ordinary men, or as trifling and suited for mere children. If he thinks this a childish thing, he may be sure that neither Sig. Mario nor I happen to be in such a sad state of ignorance as to have fallen into error from lacking such information. But if he considers it a subtle and important matter, then I must judge his state sad indeed, and him in need of returning to his master for further instruction. It is true, then, that a thing moved perpendicular to the earth's surface would never arrive at the zenith (unless that thing should depart from the exact place of the observer, which Sarsi may have overlooked), (p. 132) but it is also true that we did not say it would arrive there. XXXI (Third argument) 'Furthermore, since . . . {p. 133) . . . rules of trigonometry.' (p. 99,1. 16 to p. 101,1. 9). I should have thought from Sarsi's foregoing proof that he might at least have seen, and possibly have understood, the first book of the Elements, but what he writes here makes me gravely doubt whether he has any mathematical skill at all. From the diagram drawn by himself to his own taste, he wants to deduce the rate of retardation of speed attributed to the comet by Sig. Mario. First he shows that he has not noticed that in all books by mathematicians no attention κ

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is paid to diagrams so long as there is anything said in writing; and in astronomy particularly it would be little short of impossible to preserve in diagrams the ratios which motions really have to one another, let alone the distances and magnitudes of the celestial orbs, whose proportions are altered (without any prejudice to doctrine whatever) in such a way that a circle or angle which ought to be thousands of times the sLze of another is reduced to only two or three times. Sarsi's second error may also be seen; for he fancies that the same movement ought to appear to have the same inequalities from all places from which it is observed, {p. 134) and at all distances or altitudes at which the moving body is located. Yet the truth is that in straight perpendicular motion, if we mark off many equal spaces, then apparent movements of four units close to the earth will imply alterations of much greater inequality among themselves than those of four units located farther away, and ultimately at great distances those inequalities will remain imperceptible which would be very great at lower places. Likewise, the same retardations will appear to

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be in different ratios when the observer is near the beginning of the line of motion and when he is far from it. Yet, finding that in his diagram the arcs G F , F I and I L (which are apparent motions) decrease rapidly and much more than what is observed in the movement of a comet, Sarsi is persuaded that on no account could a similar motion be adapted to the latter, and he has not noticed how these decreases may appear less and less unequal accordingly as the altitude of the moving body is assumed to be greater. Yet he does know that the proper proportions are not preserved in the diagram,

though it does not matter that they are not. He assures us of his having noted this by his ensuing diagram, in which he proves the angle D E A to be only one and one-half degrees, though in the diagram it is more than fifteen degrees; and the radius of the moon's orbit D E is scarcely three times the terrestrial radius D B , though he calls it thirty-three times as large. This alone was surely enough to show him how simple-minded anyone would be who tried to deduce the mentality of a geometer by measuring his diagrams with a pair of compasses. Therefore, Sig. Lothario, I say that in the same straight and uniform motion there might be a great diminution, a middling one, and also a small, a tiny, and an imperceptible one; and if you wish to prove that none of these would correspond to the motion of the comet, you will have to do something a little more artistic than measure the picture. I assure you that in writing thus,

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you will not secure applause from anyone except those (and here I do not mean either Sig. Mario or yourself) who crown with victory the one who talks the most and has the last word. Now let us hear, your Excellency, what Sarsi produces at the end. I believe {p. 135) that from what he adds about the smallness of the apparent motion he wants to prove that straight motion, so often mentioned, does not in any way belong to the comet. I say that I believe this, and not that I am sure of it, for the author, after all his demonstrations and calculations, does not draw any conclusion at all. He assumes for this purpose that the comet at its first appearance was more than thirty-two terrestrial radii distant from the earth, and that the observer was located sixty degrees from that point on the earth's surface which lay perpendicularly under the line of the comet's motion. These two things assumed, he determines the quantity of apparent motion which would bring it to the sky at an angle of scarcely one and one-half degrees. Here he stops, without applying the statement to any purpose or drawing from it any conclusion. Since Sarsi did not bother, I shall draw two conclusions from it; the first is that which Sarsi would have had the simple reader infer by himself, and the other is that which may be deduced from it as a true consequence—but not casually and by the simple-minded. Here is the first:' Therefore, Ο reader, in whose ear still resounds that which was written above (that is, that the apparent motion of our comet crossed the sky by scores of degrees), form now the idea and hold it as certain that Sig. Mario's straight motion does not help him at all, for by it only a single degree and one-half may be crossed, and that with difficulty.' This is the consequence for the simpleminded; but whoever possesses the flower of natural logic will, by uniting Sarsi's premises to the conclusion to which they lead, form this syllogism: 'Assuming that the comet at its first appearance was at an altitude of thirty-two terrestrial radii, and that the observer was sixty degrees removed from its line of motion, the quantity of its apparent motion could not exceed one and one-half degrees; but it actually exceeded scores of degrees; therefore (and now comes the true conclusion) at the time of the first observation our comet was

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not at an altitude of thirty-two radii from the earth and the observer sixty degrees distant from its line of motion.' Let Sarsi frankly admit this conclusion, which destroys his very assumptions. Yet {p. 136) his syllogism is defective in another respect, too, for it has no validity against Sig. Mario. He openly wrote that a simple straight motion could not be sufficient to satisfy the apparent deviation of the comet, and that one would have to add some other cause for that; this condition, omitted by Sarsi, completely vitiates the latter's inference. I note further another error in logic, and not a trifling one, in this discourse of his. From the great change in location of the comet, Sarsi wants to prove that Sig. Mario's straight motion could not be suitable to it because the alteration which follows from such motion is small. The truth is that there might follow from such motion small alterations, middling ones, or quite large ones, accordingly as the moving body was higher or lower and the observer farther from or closer to the line of this motion. Sarsi, without asking his opponent at what altitude and distance he assumes the moving body and the observer to be, puts them both at places suited to his requirements and ill-assorted for those of his adversary, saying: Assume that the comet at the beginning was thirty-two radii high and that the observer was sixty degrees away. But my dear Sig. Lothario, if the adversary shall say that it was not at that distance by many thousands of miles, and that the observer likewise was much closer, what will you do then with your syllogism ? What will you conclude from it ? Nothing. It would be necessary that we, and not you, should have attributed such distances to the comet and the observer; then you might have run us through with our own weapons. Or, if you had still wished to transfix us with your own, you would first need to prove them actually to have been at such distances (which they were not in fact), and not assume this arbitrarily and choose the distances most prejudicial to your opponent's case. This circumstance alone inclines me somewhat to believe that something may be true which until now I have refused to believe; namely, that you may have been a pupil of him whom you now impersonate. For if I am not mistaken, he falls into the same error

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when he attempts to prove false Aristotle's opinion and that of others who have believed a comet to be elemental and to be domiciled in the elemental region, (p. 137) He raises against them, as a great difficulty, the enormous bulk which a comet would have to possess, and the incredibility of the earth's furnishing it with food and nourishment. Then, to show it to be an enormous framework, he places it (without permission from his opponents) in the very highest part of the elemental sphere, that is, at the very arc of the moon's orbit. Then, from its appearance to us, he sets about calculating its volume and finds this to be little less than five hundred million cubic miles—and let the reader note that one cubic mile is a space so large that it would hold more than one million ships, which is perhaps more than there are in the world. Such a framework would truly be indecent and dishonest, and it would be too great an expense for the human race to send it alms for its food and nourishment. But Aristotle and his adherents would reply, ' Good Father, we tell you that the comet is elemental, and that it may be fifty or sixty miles distant from the earth, or perhaps less; not one hundred twenty-seven thousand seven hundred and four, as you make it upon your own authority alone. So its body is not, by thousands of miles, as large as you believe, nor is it insatiable and incapable of being pastured.' Here there is nothing for us to do except shrug our shoulders and remain silent. If Sarsi is to convict his adversaries, he must confront them with their own most favorable assertions, and not with those most prejudicial to them; otherwise he allows them to escape every time, leaving their enemies feeling stunned and foolish—as Ruggiero felt at the disappearance of Angelica. 28 XXXII Now let us hear what follows; read this fourth argument, your Excellency. ' N o w although the earth . . .(p. 1 3 8 ) . . . motion of the comet.' (p. 1 0 1 , 1 . 10 to p. 102, 1. 2). Here he wants to prove that not even by assuming that motion of the earth which Copernicus assigned to it can this straight motion and that deviation from the zenith be explained and maintained. For if, indeed, from the earth's motion there follows an apparent declination

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of the sun now to the south and now to the north, still, in the space of forty days during which the comet was observed, this declination did not amount to more than three degrees, so that of the comet could not appear to be much more. Adding to this the mere degree and one-half which might come from its own straight motion, we still remain far from that very great motion which was seen in it. Since we did not affirm that the cause of that apparent deviation was any movement of any other body, and least of all of the terrestrial globe (which Sarsi himself admits he knows we hold to be false), it would clearly appear that he has capriciously introduced it in order to swell the size of his book. No obligation falls upon us to reply in support of what we have not said. But I do not wish for that reason to omit remarking that I much question whether Sarsi has even formed for himself any correct idea of the motions attributed to the earth, or of the many and varied appearances which would have to be perceived in other world bodies as a result of it. I perceive that he thinks that any deviation which might appear in the solar body located in the center of the ecliptic should be perceived equally (or little differently) in any other visible object wherever {p. 139) situated in the universe, whether inside or outside the ecliptic, within or without the orbis magnusto the north or south, or near or far with respect to the earth. All this is far from correct, nor is there any contradiction in this change appearing to be three degrees in the sun while it might appear to be ten, twenty, or thirty degrees in other objects because of their different positions. And in conclusion I may add that if the movement attributed to the earth (which I, as a pious and Catholic person, consider to be most false and vain) lends itself to yielding explanations for so many widely diverse appearances observed in the heavenly bodies, then I should not be sure that so false a thing might not deceptively correspond with the appearances of the comet, unless Sarsi will descend to more specific considerations than those which he has thus far produced. XXXIII Now, your Excellency, read the fifth argument. 'This is if the motions ... (p. 1 4 0 ) . . . motion of the comet.' (p. 102,1. 3 to p. 103,1.13).

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Here Sarsi thinks he can confirm his statement by various other changes occurring in other comets and described by other authors. But what I have written above answers this too, nor do we need more. First, Sarsi's generalities are too broad, and he does not get down to specific considerations of particular states of these comets as to their being high, low, southern, northern, or their having appeared at the time of the solstices or that of the equinoxes. These conditions omitted by him are most necessary in such judgments, as he himself will be able to understand whenever he gets round to giving closer attention to this theory. XXXIV I now pass on to the last question of the present weighing:' Whether the curvature . . .(p. 1 4 1 ) . . . left undecided.' (p. 103,1. 14 to p. 103, 1· 33)· Only too clearly does Sarsi reveal himself desirous of stripping me and entirely despoiling me of every ornament of glory. Not content with revealing as false and inconclusive the reason produced as mine by Sig. Mario for the tail of the comet sometimes appearing to us as bent in an arc, he remarks here that nothing new was achieved by me in this, it having all been published long before and refuted as false by Johann Kepler. Hence in the reader's mind (if he stops at Sarsi's recital), there will remain an idea of me as not only a thief of other people's ideas, but a petty miserable thief at that, who goes about pilfering even things that have been refuted. But who knows; perhaps in Sarsi's eyes the pettiness of the theft does not render me more culpable than I would be if I had more hardily set myself to search out books by some noble author not so well known in these parts; and if having found some I had attempted to suppress his name and attribute his entire work to myself, perhaps that enterprise would appear to Sarsi to be as grand and heroic as the other seemed to him cowardly and abject. Since I do not have the nerve for this, I freely confess my cowardice. But though I am poor in both bravery and power, I am at least an upright man, Sig. Lothario, and I do not want to remain with this undeserved scar (p. 142) on my face; I wish to write frankly and reveal what you left out, and, since

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I cannot divine from what passion it may have originated, I leave it to you to specify this later in your apology. Tycho indeed tried to assign the cause of this apparent curvature, reducing it to some propositions proved by Vitellio, but Sig. Mario showed that this did not exist among the things written by that author, which were far from serving the purpose of this curvature. Sig. Mario then added something that appeared to him and to me to be its true cause and demonstrable reason. Up jumps Sarsi, and in his attempt to refute this and to show in addition that it belonged to Kepler, he falls into the same pit as Tycho and reveals himself as having understood nothing of what Kepler and Sig. Mario wrote. At any rate, he pretends not to have understood either of them, and would have it that both write the same thing when they say quite different things. Kepler wants to give a reason for the curvature such that the tail is really curved, and not just apparently; Sig. Mario supposes it to be really straight, and seeks a cause for its apparent bending. Kepler reduces this to a diversity of refractions of rays, themselves solar, occurring in the same celestial material in which the tail itself is formed. He says that this material (in that part of it only which serves for the production of the tail) is more dense in proportion to its proximity to the comet, and since thus various refractions are made, from the final composition of all these there results an overall refraction which is extended not in a straight line but in an arc. Sig. Mario introduces a refraction not of the sun's rays but of the image of the comet itself, and not in the celestial material belonging to its head but in the vaporous sphere surrounding the earth. Thus, for each, the cause, the material, the place, and the manner of production are all different, and no correspondence exists between these two authors beyond this single word' refraction.' Here are Kepler's exact words: Ν on refractio potest esse causa inflextonis huius; nisi nescio quid monstri confingamus, materiam aetheriam certis gradibus propinquitatis ad hoc sidus magis magisque crassam, nec nisi ex una sola parte in quant cauda vergit.30 (' Refraction cannot be the cause of this bending; nor am I unaware what monsters we construct, the aethereal material becoming denser and denser at a certain rate in the vicinity of that star, but only from a single place in which the tail bends.')

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{p. 143) Is it possible, Sig. Lothario, that you have allowed yourself to be so transported by the desire to obscure my name in the field of science, whatever it may amount to, as to disregard not only my reputation but even that of many of your friends ? With errors and fictions, you have attempted to make them believe your teachings to be sound and sincere; by such means you have acquired their applause. But later, if they should ever happen to see this writing of mine and thereby come to understand how often and by what tricks you have treated them as simpletons, they will consider themselves to have been shabbily dealt with by you, and the esteem and grace which you hold in their hearts will change its state and condition. T h e argument introduced and refuted by Kepler is something quite different, and, as he has always been known to me as a person no less frank and honest than he is intelligent and learned, I am certain that he would admit our statement to be completely different from the one he refuted, and would say that just as that one deserved rebuff, so this other deserves assent. For it is true and demonstrable, even though Sarsi may do his best to refute it. XXXV But let us examine the strength of his refutations. (First argument) ' But now let us see . . . (p. 1 4 4 ) . . . display any curvature.' (p. 104, 1. ι to 1. 27). Sarsi's attack here is too ineffective to confute a necessarily conclusive proof from optics. He wants others to neglect the latter in favor of assertions of his which are capable of being freely altered and accommodated to his purposes—let Sarsi forgive me this suspicion, since he himself gives us frequent occasion for suspecting the credibility of what he sets forth. Indeed, what faith may be reposed in a man's reports of things long past, of which nothing is any more to be seen, when in speaking of permanent things which are present, public, and printed, the same man does not refrain from altering nine out of ten of these in the telling, transforming them into a contrary sense ? I return to my remark that the demonstration published by Sig. Mario is purely geometrical, complete, and logical. First Sarsi needs

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to understand it thoroughly, and then if it does not appear conclusive to him he must point out its fallacy either in the falsity of the assumptions or in the steps of the demonstration; but of this he has done little or nothing. Our demonstration proves that if the object seen is extended in a straight line and is situated outside the vaporous sphere in the vicinity of and oblique to the horizon, it must necessarily be seen as curved by an eye placed far from the center of this vaporous sphere; but if it is vertical to the horizon or elevated high above it, then it will be seen as quite straight or as imperceptibly curved. During the first few days the recent comet was seen, it was low and oblique, and was also seen as curved; afterward, having risen high, it was straight, and so it remained because it continued to stay at a great (p. 145) elevation. The comet of 1577, which I saw continually,31 remained always low and much tilted, and therefore was always seen noticeably curved. Other smaller ones which I have seen very high have always been quite straight, and thus the effect will be found to conform to the demonstrated conclusion, provided one has a correct account of the latter. But let us hear what Sarsi opposes to our demonstration, and see how significant his objections are. XXXVI (Second argument) ' Furthermore, I do not see . . . the remaining matters.' (p. 104,1. 28 to p. 105,1. 20). As your Excellency sees, Sarsi begins opposing the demonstration as being established upon a false (p. 146) foundation—that the surface of the vaporous region is spherical—which he thinks he can disprove in several ways. First he says what we ourselves repeatedly affirm, that such vapors rise much higher in one place than in another. But this proposition is found in no different form in Sig. Mario's book; indeed, some vapors do happen to rise higher than usual, but this is rare and of brief duration, so that in this regard it is quite arbitrary for Sarsi to say that the shape of the vaporous region is not round. He then adds another falsehood—that we have said the comet is formed of those same vapors which rise above the cone of the earth's shadow to produce the aurora borealis, a thing which is not to be found in Sig. Mario's book. In the third place, he goes on to

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say: 'If that vapor were elevated three miles in one place and a thousand leagues in another, may I ask whether you take the shape to be spherical even under those conditions ?' No indeed, Sig. Sarsi; anyone who would say such a thing would in my opinion be a great fool. But I do not find that anybody ever did say it, and I doubt if anyone has ever dreamed of doing so; suppose you name an author who has. In the fourth place, he says that those who teach the first rudiments of spherical astronomy say that this vaporous region is oval rather than round. T o this I respond that Sarsi need not be surprised that he knew this and I did not, for I learned astronomy not from those rustic teachers but from Ptolemy, and so far as I can remember he states no such conclusion. But finally, if it were definitely true that this shape is oval and not round, what would you deduce from that, Sig. Lothario? Merely that the curl of the comet would be bent in an oval line and not in a circular arc. I might concede this to you without the slightest prejudice to our meaning and our method of demonstrating the cause of this apparent curvature, but not what you attempt to deduce when you conclude: 'If therefore this vaporous region is not spherical, nor everywhere equidistant from the earth, nor uniformly dense in all its parts'—a proposition repeated three times iii different words in order to overwhelm the simpleminded—'then the {p. 147) curvature of the curl cannot derive from a kind of sphericity which does not exist in nature.' I say that this conclusion does not follow in good logic, and that the most that might follow is that the curvature is not circular but oval, so this would be the extent of your miserable and unhappy gain even if you could be sure that the vaporous region is ovate and not spherical. Whether in fact the curvature has the shape of a circular arc, or an ellipse, or a parabolic line, or a spiral, or something else, I believe could not be determined in any way, as in an arc of at most two or three degrees the differences of such curvatures would be entirely imperceptible. It remains for me to consider his final words, from which I shall oracularly deduce various considerations and hidden senses of Sarsi. First, it is very clearly understood that he puts them into Sig. Mario's writing not with an impartial mind as to criticizing or praising them,

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but with a firm resolution to impugn them, as I also remarked at the beginning. He says, 'And how have I been able to refute things set forth by him which I could not divine?' The truth is quite the opposite; namely, that he has for the most part refuted other things which Sig. Mario did not state and which Sarsi has assigned himself the task of divining. At the same time, he says that Sig. Mario wrote in obscure and tangled words, and that in quite a long disputation his meaning is incomprehensible. To this I reply that Sig. Mario had a different intention from that of Sarsi's master, who (as may be inferred from the introduction to Sarsi's treatise) wrote for the common people and with the purpose of teaching them by his replies what they could not have fathomed for themselves. But Sig. Mario wrote for those better informed than ourselves, and not to teach them but to learn; therefore he always set forth his statements questioningly and never with magisterial certainty, and left the decisions to those who are more learned. And if our writing appeared obscure to Sarsi, then before he censured it he ought to have had it explained to him, instead of setting out to contradict what he did not comprehend, at the peril of finishing without a leg to stand on. If I may say frankly {p. 148) what I think, I really believe that the reason Sarsi did not challenge most of the things Sig. Mario wrote was not a failure to understand them, but on the contrary that they were all too clear and true, and he considered it more judicious to say he did not understand them than to approve and praise them against his wishes. Now I come to the Third Weighing. Here Sarsi does his best to make us appear poorly informed by means of four propositions taken here and there from more than a hundred which appear in Sig. Mario's Discourse. He cloaks in silence all the rest, which are much more important than these, and he accommodates these to his purpose by adding to or deleting from them, or twisting them into senses other than those in which they were proffered. XXXVII Now see, your Excellency: ' T H I R D W E I G H I N G polished and smooth.' (p. 105,1. 21 to p. 107,1. 13).

149) . . .

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Here, right at the outset, are Sarsi's usual tricks. First of all, it is not to be found in Sig. Mario's essay that we have ever said that neither the air nor fire adhere and attach themselves to smooth and polished bodies. Sarsi imputes this falsehood to us {p. 150) at his own caprice in order to pave the way for speaking of a certain glass plate a little later on. Besides, Sarsi pretends not to see that when we say the hollow of the moon's orb is a perfectly polished and smooth spherical surface, this is not because that is our opinion but because Aristotle and his followers would have it so, and we would argue against them ad hominem.32 Pretending to find in Sig. Mario's book that which is not there, he feigns not to see what is written there repeatedly and plainly; that is, that we would not admit the multiplicity of solid orbs formerly believed in, but we suppose a very subtle aethereal material to be diffused through the vast reaches of the universe, through which solid world bodies go wandering with their own movements. But what am I saying ? I have at this moment recalled that he saw and criticized this before, on page 98, where he writes: ' For since Galileo does not hold with the celestial orbs of Ptolemy, and in Galileo's system there is nothing to be found of solid sky . . .' Here, Sig. Sarsi, you can never hide your having understood perfectly well that we said the hollow of the moon's orb is perfectly spherical and smooth not because we believed it, but because Aristotle considered it so, and against him we would dispute ad hominem. Had you believed it to be uttered as our own sentiment, you would never have pardoned us such a contradiction as first to deny the distinctness of orbs and their solidity, and then to admit both the one and the other—an error of much greater consequence than all the others taken together which you attribute to us. Quite vain, then, is all the remainder of your argument in which you do your best to prove that the lunar hollow must be wavy and rough rather than smooth and polished. It is idle, and does not oblige me to make any reply; still I prefer to Let gentlemanly strife prevail between us,33 as the great poet says, and I shall consider the strength of your proofs.

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You say, Sig. Sarsi:' If anyone should deny that the surface of the lunar hollow is smooth and polished, by what method or with what reasons would the contrary be proved?' You then add as a proof brought forth by your opponent, an argument fabricated in your own way {p. 151) and easily resolvable. But suppose the opponent were to reply to you,' Sig. Lothario, assuming that the material of the celestial orbs is solid, and is distinct from that contained within the lunar hollow, I say to you with assurance that this concave surface would have to be called as polished and smooth as any mirror. For if it were wavy, the refractions of the visible images of the stars would execute an infinity of vagaries in coming toward us, precisely as happens when we look at external objects through a glass window in which some panes are flat and smooth while others are crudely made. Whether we or the objects move, their images receive no alteration either as to place or as to shape in passing through the smooth panes, but in coming through the crude panes their extravagant alterations beggar description. That is how it would be if the lunar concave were wavy, and it would be a wonderful thing to behold the many transformations of shape, movement, and situation which would appear from one moment to the next in planets as well as fixed stars, accordingly as their images passed to us now through one and now through another part of the lunar orb beneath them. But no such distortion is perceived; therefore the hollow is quite smooth.' What would you say to this, Sig. Sarsi ? You would have to work hard to persuade people that there was nothing new for you in this argument, that you had passed it by as superfluous, that it belonged not to me but to somebody else, that it had already been dismissed as stale and mouldy, and in addition that you could ultimately overthrow it. Then let the above be my argument for proving the lunar concave is smooth and not wavy. Now let us hear what you say to prove the contrary, remembering that our dispute is whether the uppermost elements are swept round by the celestial motion (for the title you give to the conclusion you are opposing is: 'Air and exhalation cannot be moved by the motion of the sky'), and that I have denied this, proving my point by the uniformity of the refractions. You, to show

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the contrary, w r i t e : ' If the hollow is assumed wavy, the connection of all moving bodies is much better preserved, for thus (p. 152) the uppermost elements are moved by the sky's motion.' But Sig. Lothario, this is the error which logicians call' begging the question,' for you are taking as granted that which is in question and which I deny; that is, that the uppermost elements are moved. Here are four conclusions, two being mine and two yours. Mine are ' the hollow is smooth,' and ' therefore the elements are not swept along.' I prove that the hollow is smooth by means of stellar refractions, and my conclusion is perfectly valid. Yours are, first,' the hollow is rough,' and second,' therefore the elements are swept along'; then you prove that the hollow is rough because thus the elements are swept along by its motion, and you leave your opponent right where he was in the first place; you have accomplished nothing, and he will be neither more nor less insistent that the hollow is not rough and the elements are not swept along. In order to escape from this circle, you must prove one of your two points by some other means. And don't tell me that you have sufficiently proved the irregularity of the surface when you say that lower things are in this way better linked with the higher, for simple contact is sufficient to connect them, and you yourself later admit the same adherence and union to exist even if the hollow is smooth and not rough, so your proof is quite frivolous. Nor would it be any more cogent if you were to pretend to have proved the sweeping along of the higher elements because generations and corruptions are produced down here by such a motion, or perhaps because the higher air and the element of fire would be driven down by this motion, these being mere fantasies and airy nothings. It would take us a long while to get warm if we had to wait for the expulsion of fire toward the earth, especially as you yourself are shortly to say that fire is forced upward, and that for this reason it thrusts, and, by thrusting, becomes overcharged in some way so as to adhere more solidly to the celestial surface. Surely these are puerile ideas and arguments, which now support and now refute the same things in accordance with the childish inconstancy of what they say.

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XXXVIII But let us hear by what other means he proves the same conclusion in the second argument, which follows. ' B u t why do I 153) . . . as the elemental sphere.' (p. 107,1. 14 to p. 108,1. 9). Before resuming, I once more reply to Sarsi that it is not I who want the sky to have the noblest shape on account of its being a most noble body; it is Aristotle himself, against whom Sig. Mario argues ad hominem. A s for me, never having read the pedigrees {p. 154) and patents of nobility of shapes, I do not know which of them are more and which less noble, or which more and which less perfect. I believe that all of them are, in a way, ancient and noble; or, to put it better, that there are none which are noble and perfect or any that are ignoble and imperfect, except in so far as for building walls the square shape is more perfect than the circular, while for rolling or for moving wagons I deem the circular more perfect than the triangular. N o w let us get back to Sarsi. He says that abundant arguments have been supplied by me for proving the roughness of the concave surface of the sky, because I will have it that the moon and other planets (bodies which are also celestial, and much more noble and perfect than the sky itself) are of mountainous, rough, and uneven surfaces, and, if this is so, why should that unevenness not be found also in the shape of the sky ? Here Sarsi may put down for an answer whatever it is that he would reply to a man who tried to prove that the sea ought to be bony and scaly because whales, tunas, and other fish which inhabit it are. T o his interrogation concerning the reason for the moon not being smooth and polished, I reply that the moon and all other planets being inherently dark, they shine only by illumination from the sun. Hence it is necessary for them to have rough surfaces, for if they were as smooth and polished of surface as a mirror, no reflection of light would reach us from them and they would remain entirely invisible to us. Consequently they would have no actions upon the earth and reciprocally upon each other, and, in brief, each of them being in itself as if nonexistent, they would be for others as if they did not exist in the universe. And on the other hand, almost as much

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disorder would ensue if the heavens were of a solid substance and bounded by a surface which was not most perfectly polished and smooth; for, as I have remarked before, on account of the refractions being continually disturbed in a wavy surface, neither the movements of the planets, nor their shapes, nor the projections of their rays toward us (and consequently their appearances to us) would be found to be anything but most confused and irregular. There, Sig. Sarsi, is a sufficient {p. 155) reason in response to your question. In payment for it, please cancel in your writings those words where you say that I have often written that the stars are of various and angular shapes. You know very well that this is not true, and that I have never written any such proposition; the most that you may have read is that the fixed stars are of such live and brilliant light that their tiny bodies cannot be perceived as distinct and bounded among their splendid rays. As to that which Sarsi writes in conclusion about the sun and the smokiness that is generated and dissolved in it and in its surroundings, I have never stated positively whether the latter revolves because of the motion of the former or vice versa, because I do not know. Perhaps neither the surrounding smokiness nor the solar body is swept round, but both naturally possess equally that rotation of which I am certain because I see that these spots revolve in about four weeks. But even if our knowledge about this were complete, I do not see of what use it would be in the present contest; here we are arguing ad hominetn and ex suppositione on a basis of other assumptions which are certainly false, about matters quite different from the sun and its surroundings, and it is being asked whether the lunar hollow, if smooth and hard (which it certainly is not in actuality), rotating (which is still another falsity), sweeps along with it the element of fire (which perhaps does not even exist). Add also this other fiction to which Sarsi says he cannot see any objection, and which he even calls an identity—that one might equally well say, with the same ease and naturalness, that a fluid body contained within the hollow of a spherical solid might be swept along by the latter if it were set in rotation, as to say that this would take place when the thing contained was a solid sphere and the surrounding substance was a liquid. This amounts to believing that just as a ship

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is carried and swept along by the motion of a river, so the water in a stagnant pond ought to be swept along by the motion of a boat, which is utterly false. First, as to experience, we see the ship—or even a thousand ships filling a whole river—to be moved by the river's motion, while on the other hand the course of a ship driven at any speed (/>. 156) is not followed by any water at all. The reason for this should not be very abstruse; no force can be brought against the surface of a ship which is not similarly brought against its whole framework, whose parts, being solid, are firmly attached together and cannot be separated or parted in such a way that some parts yield to the impetus of the external surroundings while others do not. Such is not the case with water or any other fluid, whose parts have hardly any perceptible cohesion or adherence to one another, and are thus readily separated. Hence a very thin veil of water which touches the body of a ship is forced to obey its motion, but other more distant parts forsake the closer ones, and those in turn the ones they touch, so that at a very short distance from the ship's surface they are entirely freed from its force and will. Moreover, the impetus and the motility impressed are preserved much more strongly and for a longer time in solid and heavy bodies than in light and fluid ones. Thus we see a great weight suspended by a cord conserve for many hours the impetus and motion communicated to it by a single push; but you may agitate the air enclosed within a room as much as you like, and no sooner will the impetus which caused the commotion cease than the air will be totally stilled, nor does it retain any of that agitation. So when the surrounding and moving thing is liquid, and it exerts its force against a solid, massive and heavy thing contained in it, it is impressing its mobility upon a subject inherently suited to retaining and conserving this for a long time. Hence the second supervening impulse meets with the motion already impressed by the first; the third impulse finds the impetus conferred by the first and the second; the fourth adds to the operations of the first, second, and third; and thus, step by step, the motion of the movable body is not merely conserved but is augmented. But when the body to be moved is liquid, light, and subtle, and in consequence is impotent to conserve the impressed movement

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but loses what is impressed as fast as it gets it, then trying to impress speed upon it is as vain a task as trying to fill the sieve of the Danaides,34 for it empties out as fast as it is repoured therein. Behold, Sig. Lothario, (p. 157) the enormous difference proved to exist between these two operations which seemed to you to be the same. XXXIX Now let us pass on to the third argument. ' But, finally, let us . . . the same motion.' (p. 108,1. 10 to p. 109,1. 14). Sarsi continues with this fantasy of his, still pretending that I have said that the air does not adhere to smooth and polished bodies, a thing which is not to be found written either by Sig. Mario or myself. Besides, I do not quite understand what sort of thing he means by this' adherence.' If he means a coupling which completely resists separation and parting between the surfaces so that they no longer touch, I (p. 158) say that such 'adherence' exists and is very great. The surface of water, for instance, may be detached only by immense force from that of a plate of copper or other material, and in this case it does not matter whether the latter surface is polished and smooth or not; a close contact suffices. And this holds bodies united so firmly that perhaps the particles of solid and hard bodies have no other cement than this to attach them together. But this ' adherence' is of no use to Sarsi. Now if he means a conjunction such that the two bodies (I mean that of the solid and that of the liquid) cannot move upon each other even by slipping—which would fit in with his requirements—then I say that there is no such ' adherence' not only between a solid and a liquid, but not even between two solids. Thus we see that in two slabs of marble which are quite level and smooth, the first' adherence' is such that if we lift up one slab the other follows, while the second' adherence' is so weak that, if the surfaces in contact are not perfectly horizontal but are tilted even a hair's-breadth, the lower slab will immediately slip away in the direction of the tilt. To sum up, the moving of the one surface upon the other will meet with no resistance, however great may be the resistance to an attempt to detach and separate them. Thus, in the contact of water

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with the boat, though the resistance to detaching and separating one surface from the other may be great, the resistance is only a minimum in the moving of one surface upon the other as they rub together. And as I have remarked above, the swiftly moved ship does not take along with it anything but that veil of water which is in contact with it, and perhaps it is continually robbed even of this and reclothed successively with one after another. And I know that Sarsi will grant me that if a ship is put into the sea moistened with wine or with ink, it will not have plowed the waves more than half a mile before there will remain not the least trace of the fluid which originally encased it. This makes it very likely that the same thing may reasonably be imputed to the water which touches the ship; namely, that this is continually changing. And certainly the tallow with which a ship is smeared, though very firmly attached, (/>. 159) is nevertheless carried away in a short time by the water that slips over it in its course, which would not happen if the water that touched it remained always the same without changing. As for the glass plate which stays afloat between the little ridges of water, I say that these ridges do not sustain themselves because of the adherence of the air to the plate preventing the water from running over the plate; if this were so, the same thing ought to happen if one placed in the water a similar plate somewhat moistened, for it is incredible that the air would adhere less to a wet surface than to a dry one. Yet we see that when the plate is wet no ridges form, and the water runs swiftly over it. The maintenance of the ridges, therefore, has some other cause than the adherence of air to the surface of the plate. And quite frequently we see large particles of water sustain themselves in convex shape and in relief very much higher than the little ridges which surround the floating plate; for instance, upon the leaves of cabbages. In his final proof, Sarsi would have it that pressure or weighing down is sufficient to make one body follow another without any other ' adherence.' He illustrates this by two well-polished slabs of stone, placed one upon the other. The upper one, pressing down, follows the motion of the lower when that is pulled in any direction. I concede him the experiment, but I do not see that it has anything

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to do with our problem, first because we are dealing with a thin and liquid body whose parts are not connected together; otherwise the motion of one part would move the whole, as happens in a solid body. And second, Sarsi is too careless about his proof that fire, air, and the exhalation contained within the lunar hollow push and bear against the surface of this hollow. He sets forth as the cause of this compression a continuous rarefaction of these substances which, dilating, and therefore seeking always greater space, exert force against their container and thus in a way attach themselves to it so that they follow its motion. This reasoning is really very careless, for where Sarsi positively affirms that the contained substances (p. 160) are continuously rarefying and dilating, his opponent with no less reason (I say 'no less' because Sarsi adduces none at all) might say that they are continuously condensing and shrinking. But even assuming that they continually rarefy, and that from this rarefaction there originates an attachment to the hollow and eventually a sweeping along, it may be believed that hundreds and thousands of years ago, before the rarefaction had reached anything like the limits it has today according to Sarsi's doctrine, this sweeping along would not have existed, there having been lacking any cause for its taking place. Indeed, nothing prevents my saying to Sarsi that this continually occurring rarefaction of his has not yet reached that degree at which it would exert force against and would press upon the hollow of the moon, and that it might attain this some two or three years hence, at which time I concede that the highest elemental sphere will commence to be moved, but in the meanwhile let him concede to me that it is not being moved today. I do not want Sarsi to burst out laughing, if perchance he thinks these and other similar replies are really ridiculous, for it is he who gave me occasion for producing this by having let it slip from his tongue and later from his pen that some material substances do perpetually rarefy and dilate. But in order to assist him I wish to teach him a point in his favor by telling him that this eternal rarefaction with pressure against the lunar hollow is superfluous, since he is able to show that the air is swept along by a bowl upon which it does not press or weigh at all, being located in the very region of the air.

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XL (Fourth argument) 'But let us see . . . [pp. 161-164] {p. 165) . . . denied these things.' (p. 109,1. 15 to p. 1 1 5 , 1 . 14). Sarsi now enters into a very abundant apparatus of experiments in order to confirm his statement and refute ours; these, since they were performed in your Excellency's presence, I submit to you as something in which I ought rather to defer to your judgment than to interpose my own. Therefore, if you will, reread the remainder up to the end of the passage, and I shall touch only piecemeal upon some details concerning various minor points. First, what Sarsi attempts to attribute to me at the beginning of his experiments is quite false; namely, that I have said that the water contained in a bowl remains as motionless as air when the vessel is moved. I do not marvel that he has written this, however, since it may be permissible for one who continually reverses the sense of things written and printed by others to alter that which he merely says he has heard. Still, it does not seem to me to be entirely within the bounds of good breeding for a man thus to print and publish what he has heard from his neighbor; the more so when (either from not having understood very well, or by his own choice) his report is very different from what was actually said, as happens in the present case. It is my affair to print my things and publish them to the world, Sig. Sarsi, and not yours or anyone else's. And when at times in the course of arguing, a man may have said something foolish (as indeed sometimes does happen), why must you immediately rush into print with it and thus deprive him of the benefit of time for thinking it over better and amending his error by himself, changing his opinion {p. 166) and, in a word, preserving his own mastery over his mind and pen ? What Sarsi may have heard (but, from what I see here, did not understand very well) is a certain experiment which I exhibited to some men of culture there in Rome, perhaps in the very chambers of your Excellency, partly in explanation and partly in refutation of a third motion attributed by Copernicus to the earth. T o many people, this third motion which he assigned to the terrestrial globe round its own center and contrary to all other celestial

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movements seemed a most improbable thing, and one which greatly disturbed the whole Copernican system. For all the celestial motions, whether of epicycles or of eccentrics—including Copernicus' diurnal and annual motions of the earth itself—are made in the orbis magnus from west to east, and this one alone was made by the earth from east to west, counter to its own two other movements and against all motions of the planets. I used to remove this difficulty by showing that such an event was not only not improbable, but was in accord with nature and was indeed almost necessary; for any body placed and supported freely in a tenuous and liquid medium will, when transported along the circumference of a large circle, spontaneously acquire a rotation about itself which is contrary to its larger motion. This effect was seen by taking in one's hands a bowl full of water and placing in it a floating ball, turning about on the toe with one's arm extended; the ball was seen immediately to turn upon itself in the opposite direction and to complete its rotation in the same time as one's own was finished. Thus the wonder ceased, and one would marvel rather how it could happen otherwise with the earth, if, being a body suspended in a thin and fluid medium and being carried about the circumference of a large circle in the space of one year, it should not have naturally acquired a similar annual rotation about itself opposite to the other. I spoke thus to remove the improbability attributed to the system of Copernicus, and I later added that anyone who would reflect more profoundly would recognize that Copernicus had falsely attributed to the earth a third motion which {p. 167) would not be a motion at all, but a non-motion and a state of rest. For it is certainly true that to him who holds the bowl, the ball placed within it will appear to move with respect to himself and to the bowl, and to be turning. But the same ball compared with the wall of the room and with external things does not turn at all and does not change its tilt; whatever point upon it was originally directed toward some external mark on the wall, or some other more distant place, points always in that same direction. Now this is what had been asserted by me, and as your Excellency sees it is very different from what Sarsi relates. This experiment, and perhaps some other, might give occasion for someone who was often present

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at our discussions to attribute to me that which Sarsi recounts in this place; namely, that by a certain natural talent of mine I used sometimes to explain by means of a few simple and evident things some others which were more difficult and abstruse; this praise Sarsi does not entirely deny to me, as you see, but partly grants. I must acknowledge this concession as coming rather from his courtesy than from his inner feelings, since so far as I can see he is not one to be easily persuaded of my talent—for deeming Sig. Mario's essay to be mine, he said at the end of the previous weighing that it was written in very obscure terms whose sense he had been unable to divine. As I said, your Excellency, I submit these experiments to you, who have seen them; and my only reply against them all will be something already written by Sig. Mario in his Letter.85 But first I shall pay a little attention to a certain argument which Sarsi combines with his experiments, but which I should really have much preferred had not been mentioned, for the sake of his own reputation as well as that of his master—if it is true that he was a pupil of the teacher he pretends to. Alas, Sig. Sarsi, what is this extravagance that you write here ? Unless there has been a ghastly printer's error, these are your words: 'Thence you may see that whenever the mover was greater than the moved, the motion was far easier; for the lid AB having been placed on the vessel, then it was by the motion of the inner surface of the dish and of the lid at the same time that the air had to be moved, (ρ. i68) and this was greater than the neighboring air which was being moved, for that surface was the container and the air was the contained.' Please tell me, Sig. Sarsi, with what you are comparing this surface of the bowl and of its cover; with the surface of the contained air, or with the air itself— that is, with the body of the air ? If with the surface, then it is false that the former is larger than the latter; rather, they are precisely equal, as you are taught by the Euclidean axiom, Quae mutuo congruunt, sunt aequalia ('Things mutually congruent are equal'). But if you mean to compare the containing surface with the air itself, as your words actually say,'then you are making two enormous errors. The first is in comparing two quantities which differ in kind and are therefore not comparable, as said in one of Euclid's definitions:

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Ratio est duarum magnitudinum eiusdem generis (' Comparison is of two magnitudes of the same kind'). Do you not know that a man who says,' This surface is larger than that volume' is no less wrong than one who might say, Ά week is larger than a tower,' or ' Gold is heavier than the key of C ' ? The other error is that if one could compare a surface with a solid, the case would be quite the contrary of what you say; not only would the surface fail to be greater than the solid, but the latter would be more than a hundred million times greater than the former. Do not let yourself be taken in by such monstrosities, Sig. Sarsi, nor yet by the general proposition that the container is greater than the thing contained, even when the two partake of mutually comparable quantities. Otherwise, you will have to believe that the outermost winding of a ball of yarn is larger than the yarn within it, since the latter is the contained and the former is the container; and that since they are of the same material, the husk will have to weigh more, being larger. I much suspect that you have taken with some such equivocation a statement that is quite true when accepted in its plain sense, namely, that the container is greater than the contained whenever' container' is taken to mean both it and its contents. Thus a square described about a circle is greater than the circle, provided one takes the whole square; but if one wished to take only the remainder of the square after deducting the circle, it would not be larger at all (p. 169) but would be very much smaller than the circle, even though it surrounded and included it. But alas! time flies, and I am wearing myself out over these puerilities. Now to counter all Sarsi's experiments, let your Excellency make the bowl rotatable upon its axis, and in order to make sure whether the air which it contains goes along when it is spun rapidly, take two lighted candles; attach one inside the bowl an inch or two from its top, and hold the other in your hand inside the bowl at a like distance from the top. Then make the bowl rotate rapidly; if after a while the air also goes round with it, then since the bowl doubtless moves the contained air and the attached candle with equal speed, the little flame of the first candle will not bend at all, but will remain as if the whole were stationary. This is what happens when a man

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runs with a lantern which encloses a flame—this is not blown out or even bent, inasmuch as the air which surrounds it moves with equal speed. The same effect is seen even more clearly in a rapidly sailing ship, for lights which are placed below decks make no movement whatever, but remain in the same state as if the ship were at rest. But the little candle which is held fixed will give a sign of the circulation of the air which, blowing upon it, will cause it to bend. If the result is the opposite—that is, if the air does not follow the motion of the bowl—the fixed flame will remain straight and quiet while the other one, which is carried rapidly by the bowl, will bend by being pushed against the quiet air. Now whenever I have seen the experiment, it has always happened that the little stationary candle has remained burning with a straight flame while the one attached to the bowl has always been much bent and frequently blown out. And surely your Excellency will see the same, or anyone else who wishes to put it to the proof. Thus you may judge what must be said about the action of the air. From Sarsi's experiments, the most that may be deduced is that a very thin layer of air no more than one-quarter of an inch thick and contiguous to the bowl is carried round. This suffices to produce all the effects of which he writes, ( p . 170) and a sufficient cause for them would be the roughness of the surface, or any little cavities or prominences greater in one place than another. But finally, if the hollow of the moon should carry along the contained exhalations up to a thickness of one inch, what does Sarsi expect to accomplish with this ? Let him not believe that if a bowl carries along half an inch of air, then a larger bowl must carry more; for I think it likely that this would transport less. Neither do I believe that the high speed with which the lunar hollow completes its rotation in twenty-four hours need have any greater effect. Indeed, I shall go so far as to say that I rather suspect it would achieve less rather than more than what would be accomplished by a bowl which made but a single revolution in twenty-four hours. Yet let us assume and grant to Sarsi that the lunar hollow sweeps along with it as much of the contained exhalations as mentioned above; what then ? What follows from this that is unfavorable to Sig. Mario's main point ? Does the material of the

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comet perhaps take fire by this motion, or is it true that this will not take fire, whether moving or non-moving? T h e latter is what I believe, for if the whole remains fixed it will not excite fire, for which Aristotle requires motion; and if the whole moves, then there will be no friction or rubbing, without which there will be kindled no heat, let alone fire. Now here you see a great expenditure of words by both Sarsi and me to determine whether the solid hollow of the lunar orb (which does not exist in nature), moving round (which it has never done), sweeps along with it the element of fire (which we do not know to exist), and thereby the exhalations, which accordingly kindle and set fire to the material of comets (of which we do not know whether it is there situated, and are certain that it is not combustible). Here Sarsi reminds me of the saying of that most witty poet: By Orlando's sword, which they have not, And perhaps which they never shall have, These blows of the blind have been given.3® It is now time for us to come to the second proposition; yet before we pass on to that, since at the end Sarsi repeats that I have constantly denied that water moves with the motion of the bowl and that air and other tenuous bodies adhere {p. 171) to smooth ones, let us reply once more that he does not speak truly, as neither Sig. Mario nor I have ever said or written any such thing. Sarsi, finding nothing to hold on to, goes along manufacturing handles for himself. XLI N o w let your Excellency pass on to the second proposition. 'Aristotle says t h a t . . . do not adhere.' (p. 115,1. 18 to p. 116,1. 22). A t the outset of this dispute Sarsi wants to make Sig. Mario and Aristotle agree, and to show that both have announced the same conclusion when one says that motion is the cause of heat and the other says that it is not motion, but the brisk rubbing of two hard bodies. And since Sig. Mario's proposition is true and needs no comment, Sarsi interprets the other one by saying that if indeed motion, as motion, is not the cause of heat, (p. 172) but rubbing is,

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still such friction is not made without motion, so that we may say at least derivatively motion is the cause. But if that is what Aristotle meant, why did he not say friction ? When one may say definitely what he means with a simple and very apposite word, I cannot see why he should make use of an inappropriate one requiring limitations and being finally transformed into something quite different. Besides, assuming that this was Aristotle's meaning, it is still different from Sig. Mario's; for to Aristotle the rubbing of any bodies is sufficient, even of thin and tenuous ones or of the air itself,37 while Sig. Mario requires two solid bodies and considers that trying to pulverize and thin out the air is as great a waste of time as the proverbial grinding of water in a mortar. I am of the opinion that the original proposition might be quite true, taken in the simplest sense of its words; perhaps it came from some good school of antiquity, but Aristotle, not having properly fathomed the minds of the ancients who set it forth, later deduced from it a false conception. And this may not be the only proposition which in itself is true but which is understood in the Peripatetic philosophy in a sense which is not true. I shall touch on this somewhat later. Now let us follow Sarsi, who (against Sig. Mario's statement) will have it that heat is excited without any consumption of the bodies that are rubbed together and heated, and who goes about proving this first by reason and then by experiments. So far as reason is concerned, I can dispose of all his instances very briefly; for he addresses interrogations to Sig. Mario and then replies for him and refutes these replies. Hence I say that if Sig. Mario does not respond in that way, Sarsi will have to fall silent. And really, taking this first reply for example, I do not believe that Sig. Mario would say that in order to become hot, bodies would first have to be rarefied, and that rarefaction diminishes them, and the thinner parts would fly away, as Sarsi writes; from such a reply I think I may say that he is out of accord with Sig. Mario's thinking. In this action, {p. 173) one must consider the body which is to generate the heat and that which is to receive it. Sarsi thinks that Sig. Mario would require the excitation and the consumption of parts to take place in the body which is to receive the heat, while I

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believe he would have the body which generates heat be the one that is diminished. In a word, it is not the receiving but the conferring of heat which causes diminution in the conferring body. I should therefore like very much to have seen explained more specifically how it is possible to rarefy bodies without any separation of their parts, and how this affair of rarefaction and condensation proceeds, of which Sarsi seems to speak with great confidence; for to me, it is one of the most recondite and difficult questions of all physics. It is also manifest that Sig. Mario would not have made the second reply—that such consumption of parts is necessary so that these more minute parts may first be heated, and then by these the rest of the body may become warmed. For in this way, the diminution would still affect only the body which is to be heated, whereas Sig. Mario gives this property to that body which does the heating. One must note, however, that it often happens to be the same body which produces heat and receives it; thus, in hammering a nail, those parts of it which are violently compressed excite heat, and that which is heated is this same nail. What I have tried to say thus far is that the consumption of parts depends upon the act of producing heat and not upon that of receiving it, as I shall explain more in detail farther on. Meanwhile, let us hear the experiments by which Sarsi thinks he has revealed the possibility of producing heat by friction without anything being consumed. XLII ' B u t if one desires . . . ( / > . 174) . . . than from hammering.' (p. 1x6, 1. 23 t o p . 1 1 7 , 1 . 1 3 ) . I can well believe that Sarsi has not detected any diminution of weight in a little piece of copper beaten and heated many times, even by using the most precise balance. But I do not think for that reason that there was no diminution, since it may very well have happened that the reduction was so little as to remain imperceptible in any balance whatever. I ask Sarsi, first, whether he believes that any difference would be noticeable if a button of silver were weighed, gilded, and then weighed again. He must say no, because we see gold reduced to such thinness that it will even sustain itself upon the

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quiet air, dropping with extreme slowness, and with such gold leaf one may gild any metal. Moreover, this same button may be used two or three months before the gilding is consumed, but since it is ultimately consumed it is clearly diminishing every day and even every hour. Again, take a ball of amber, {p. 175) musk, or some other odoriferous material; carry it with you for a fortnight, and it will fill with odor a thousand rooms and a thousand streets, and in fact every place that you visit. This will not happen without some diminution of material, for without that there would doubtless be no odor; yet if you weigh it after this time, no sensible diminution will be found. Thus there are revealed to Sarsi insensible diminutions of weight occurring from consumption over a period of months on end, which is quite a different matter from the few minutes that he may have kept hammering at his bit of copper—and just that much more accurate is the assayer's balance than the philosopher's steelyard. Notice also that it might very well be that the attenuated material which produces heat should also be still more subtle than the substance of odors, for remember that the latter can be enclosed in glass or metal through which it does not leak out, but the substance of heat makes its way through every body. Here Sarsi raises an objection, saying: ' I f a test with the balance does not suffice to show us a consumption so small, how will you have it known ?' The objection is ingenious, but not so ingenious that a little natural logic has not revealed the solution to us, and here are its steps. Of bodies which are rubbed together, Sig. Sarsi, there are some which are absolutely and certainly not consumed at all, others which are quite sensibly much consumed, and still others which are consumed indeed, but insensibly. Our senses show us that those which are not consumed at all by being rubbed, such as two very smooth mirrors, are not heated. We are certain that those which are noticeably consumed are heated, as is iron upon being filed. Therefore, for those of which we stand in doubt whether or not they are consumed upon being rubbed, if we find by the senses that they are heated, we ought to believe that they are also consumed; and only of those which are not heated may it be said that they are not consumed either.

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Before going farther, for Sarsi's instruction I should like to add something to what I have said above. T o say, 'This body has not lost weight in the balance, and therefore no part of it has been consumed,' {p. 176) is very fallacious reasoning, since it is possible for some part of it to be consumed and yet for it not to lose weight but to gain it. This will always be the case when that which is consumed has less specific gravity than the medium in which it is being weighed. Thus, for example, it may happen that a very knotty piece of wood taken from near the root will sink to the bottom when it is placed in water. Under water let it weigh four ounces, say. Upon filing away some of it—not the knotty parts, but the lighter part which has less specific gravity than water and thus which partly sustained the whole mass—it may happen, I say, that the remainder will weigh more than the original mass did in the same medium. Likewise, it may be that in filing or rubbing together two pieces of iron, or two stones, or two sticks, some particles of matter less heavy than air are parted from them, and if this alone is removed it will leave the body heavier than before. What I say here is said with some probability, and not merely as a flight and retreat to leave the adversary some trouble in refuting it. For let your Excellency make careful observations in breaking glass or stones or some other material, and at every fracturing you will see some easily perceptible fume emerging which will ascend high in the air, a necessary argument that it is lighter than air. I first observed this in glass, when with a key or some other piece of iron I was knocking the corners off it and rounding it. Besides the many little pieces of various sizes that flew off and fell to the ground, a subtle fume was seen always ascending. The same thing is seen to occur upon breaking any stone in a like fashion. Besides what is evident to sight, the odor gives us a very clear argument and sign that in addition to the said fumes there may be ascending other more subtle sulfurous and bituminous parts which are invisible but which make themselves evident by their smell. Let Sarsi perceive now how superficial and how far from profound, apart from appearance, is his philosophizing. He need not think that he can reply with limitations, distinctions; with per

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accidens, per se, and mediate·, with primary, secondary, {p. 177) and such idle talk; for I assure him that in maintaining one error he will commit a hundred more serious ones and will produce ever greater follies in his camp. Greater, that is, than these which remain for me to consider at the end of the present matter, where he first marvels that what is consumed, being imperceptible to the balance, could nevertheless produce heat, and then he adds that much iron is consumed when filed—much more than when beaten with a h a m m e r — and yet filing produces no more heat than hammering. T h i s reasoning is quite vain, for thus one would measure by weight the amount of something which has no weight, or which is so light as to rise rapidly in the air. And if that which is converted under strong friction into hot material was but a small part of that solid body, it should not be astonishing that a very small quantity of this might be rarefied and expanded into a very great space. L e t Sarsi consider into how great a bulk of hot and blazing material a little stick is resolved; and of this, the visible flame is the smaller part, since that which is insensible to sight but perceptible to touch is a great deal larger. A s to his other point, this objection would have some plausibility if Sig. Mario had ever said that all the iron consumed in filing would become calorific material, for then it would appear reasonable that the iron consumed by the file would heat up much more than that beaten with a hammer. But it is not the filings which accomplish the heating; it is another substance, incomparably subtler. XLIII L e t us proceed.' Therefore I b e l i e v e . . . {p. 1 7 8 ) . . . suited to receive fire.' (p. 1 1 7 , 1 . 14 to 1. 30). Here it seems that Sarsi is preparing to bring forth a sounder doctrine and a better explanation of the difficulties being dealt with, but I do not see that much new is introduced, or anything very prejudicial to Sig. Mario. Sarsi says that the hot or cold quality of bodies rubbed together corresponds closely with their heating much or little, and that the business depends upon many other things which are not so evident. T h i s I know only too well, but it does not seem to get us any farther. T h e second clause is too mysterious and L

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the first is too obvious and well known, inasmuch as he tells me in effect nothing except that those bodies which are more calorific (or more disposed to heat up) become more heated, and those which are more frigific become less so. I likewise believe what comes next— that a fire is lighted more readily by rubbing together lighter and less dense sticks than hard and dense ones, even if the latter are rubbed together more briskly and for a longer time; but I fail to see that this accomplishes anything against Sig. Mario, who has not said the contrary. And I knew before now that a distaff of hemp will take fire more quickly in a slow fire than a piece of iron will in the most ardent furnace. He next adds (and supports with the testimony of Seneca) that more lightning occurs during the summer when the air contains a greater quantity of dry exhalations. I admit this, but I question whether such exhalations take fire together with the air, and whether this happens by friction caused by some motion. I should accept as true what ( p . 179) Sarsi has written if he had first assured me that nature had no other way of starting a fire besides these two—namely, by touching combustible material with an actually burning fire, as when we set fire to a torch with a lighted candle, and by the friction of two non-burning bodies. But since other ways exist, such as the reflection of solar rays in a concave mirror or the refraction of the same rays in a ball of crystal or of water, and when straws and other thin bodies are sometimes seen to take fire in the street by reason of excessive heat without any commotion or agitation, even when the air is quite tranquil (and if it were agitated and blown by wind perhaps no fire would occur)—since, I say, there are these other methods, then why should I not believe that there may be still others different from these, and that exhalations in the air and between the clouds take fire because of them ? Why must I attribute this to vehement motion when I see first that fire is not excited without the rubbing of solid bodies, which do not exist among the clouds, and when in addition no commotion is discovered in air or in clouds when lightning and heat lightning are most frequent ? I think that saying this has inherently no more truth than when the same philosophers attribute the great rumbling of thunder to a tearing apart of

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clouds, or to their knocking against one another, though in the brilliance of the greatest lightning flashes, while the thunder is being produced, not the slightest movement or change of shape is discovered in the clouds, when this ought to be very great in such a rending. I neglect the fact that when the same philosophers are dealing with sound they require the percussion of solid bodies for its production, and say that the striking of wool or hemp will not make any noise, while later on, when they need to do so, they say that mists and clouds striking together will render the loudest sound of all. A tractable and benign philosophy this, which so complaisantly and readily adapts itself to our needs and wishes! ( p . 180) XLIV Now let us pass on to examine the experiment of the arrow shot by the bow, and of the leaden ball thrown by the catapult, these being set on fire and melted by the air as confirmed by the authority of Aristotle, many great poets, philosophers, and historians. 'Although Galileo laughs . . . ( p . 181) . . . in the air.' (p. 117,1. 31 to p. 119,

1-7). It is quite false that Sig. Mario or I would laugh and joke at the experience adduced by Aristotle, there being not the slightest hint of derision in Sig. Mario's book. He merely wrote that we do not believe that a cold arrow shot from a bow can take fire; rather, we believe that if a burning one were shot it would cool down more quickly than it would if held motionless. Now this is not derision, but simply the statement of an opinion. Sarsi next adds, since this experience has failed to convince us, that not only Aristotle but many other great men have believed and written the same. T o this I reply that if it is true that in order to refute Aristotle's statement we are obliged to represent that other people have not believed it ( p . 182) or written it, then neither Sig. Mario nor I nor anyone on earth will ever refute it, since it can never be the case that those who have believed it and written it did not believe it or write it. But I must say that it is news to me that anyone should actually wish to place the testimony of men ahead of what is shown by experience. Adducing such witnesses serves no purpose, Sig. Sarsi, since we

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have never denied that many people have written and believed such things. We did indeed say that the thing is false, but as to authority yours alone is as cogent as that of a hundred men in making the effect true or false. You take your stand upon the authority of many poets, and against the experiments which we produce. I reply by saying that if those poets were to be present at our experiments, they would change their opinion, and without any revulsion whatever they might say that they had written hyperbolically or might confess themselves to have erred. Although it is not possible to have present your poets (who, I say, would yield to experience), yet we have at hand archers and catapulters; and you may see for yourself whether by citing your authorities to them you are able to strengthen them to such an extent that the arrows and lead which they hurl will take fire and melt in the air. In this way you will find out how great is the force of human authority upon the facts of nature, deaf and inexorable as she is to our vain wishes. You tell me that there is no longer an Acestes or a Mezentius or a similar skillful paladin. I shall be content if you shoot an arrow not with a simple longbow but with a very stout steel crossbow and catapult drawn with levers and windlasses which could not be bent by the strength of thirty Mezentiuses; shoot ten arrows, or a hundred; and if it happens in a single instance that the steel tip of one takes fire or its shaft is burned, nay if its feathers so much as tan slightly, I shall have lost the battle—and your respect, which I so highly regard, into the bargain. Now then, Sarsi, I do not want to keep you in suspense; you shall not take me to be so wayward as not to wish to yield to the authority and testimony of so many admirable poets, or to disbelieve that the burning of arrows and the {p. 183) melting of metals have not sometimes occurred. But I do say that the cause of such marvels is very different from that which philosophers have attempted to maintain when they have reduced it to attritions of air, or of exhalations, and such chimeras which are all foolishness. Do you want to know the real cause ? Then listen to the peerless poet commenting upon the encounter of Ruggiero and Mandricardo, and the breaking of their lances:

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The shafts, ascending, to the heavens came; And Turpin, writing here with truth entire, Says two or three fell back again in flame, These having mounted to the sphere of fire.38 Do you think that the great Ariosto raised no question about the truth of this when he bolstered it with Turpin's testimony ? Everyone knows how veracious Turpin is, and how far one is obliged to believe him. But let us leave the poets in their proper place and return to those who reduce this cause to friction of the air. I deem that opinion false, and I shall consider what you, Sarsi, set forth in trying to show that very hard bodies may be consumed by friction with others that are softer. You say that this is seen plainly in water and in wind too, the latter wearing away and consuming the corners of the most solid towers, while the former by a continual distillation and constant beating can dig away marble and most solid reefs. I concede all this to you, for it is quite true, and I add more—I do not doubt in the least that arrows and not only leaden balls, but balls of stone and even of iron ejected from a cannon, are consumed more by striking the air at their consummate speed than are reefs or walls by the striking upon them of water and of wind. And I say that if to make a perceptible corrosion or peeling of reefs or towers there are required two or three centuries of beating by water and wind, then for the erosion of arrows or cannon balls it would suffice for them to remain in the air only two or three months. But I still do not see how a time of two or three pulse beats could have any noticeable effect on them. In addition to this, there are two other difficulties for me in applying this truly ingenious conception of yours to our purpose. One (p. 184) is that we wish to discuss liquefaction and melting by heat, and not consumption by percussion. The other is that in making your case you require that not the solid body but the soft and subtle body be the one which is pulverized and made thinner—that is, the air, which must take fire thus. Now the experiences put forth prove that rocks, and not air or water, receive the friction; and truly I believe that the air and water, let them strike as they may, are not thereby made any thinner than they were in the first place. So I

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conclude that there is little aid and assistance for your cause to be derived from these things or from that which you add about hail and raindrops. I concede to you that these become smaller in falling from on high. I grant this to you not because I believe that the opposite of what you say might not also be true, but because I do not see that in either case this has anything to do with the matter under discussion. That the sling with its hissing and popping is an argument of the air being condensed by its agitation, I leave to you to do with as you please; but note that it will be a contradiction of your position and a disaster to your case, since until now you have always said that strong agitation and commotion make friction, rarefaction, and finally an ignition of the air, whereas now you want condensation in order to give reasons for the whistling of the sling—or else to make sense of the very obscure words of Statius. Thus, that same commotion which rarefies the air in order to serve for melting and burning now condenses it in order to serve the slingers and Statius. But let us pass on to hear the testimony of the historians. XLV 'But lest the testimony . . . (p. 185) . . . at those learned men.' (p. 1 1 9 , 1 . 8 to p. 120,1. 2). I cannot help wondering that Sarsi still wishes to persist in proving to me by means of witnesses that which I can see at any time by means of experiment. Witnesses are examined in doubtful matters which are past and impermanent, not in those which are factual and permanent. Thus it is necessary for a judge to seek by means of witnesses to determine whether it is true that Peter injured John last night, but not whether John is injured, for this he is able to see and to make the visu reperto. Furthermore, I say that even in conclusions of which one may attain a knowledge only by reasoning, the testimony of many men is worth little more than that of few, it being certain that the number of those who reason well in difficult matters is much smaller than the number of those who reason badly. If reasoning were like carrying burdens, where several horses will carry more sacks of grain than one alone, I should agree that several reasoners (p. 186) would avail more than a single one; but reasoning

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is like running and not like carrying, and one Arab steed will outrun a hundred pack horses. So when Sarsi brings in such a multitude of authors, it does not seem to me that he strengthens his conclusion, but that he ennobles Sig. Mario's cause and mine by showing that we have reasoned better than many men of great reputation. If Sarsi wants me to believe from Suidas that the Babylonians cooked eggs by whirling them rapidly in slings, I shall do so; but I must say that the cause of this effect is very far from that which he attributes to it. To discover the truth I shall reason thus: 'If we do not achieve an effect which others formerly achieved, it must be that in our operations we lack something which was the cause of this effect succeeding, and if we lack but one single thing, then this alone can be the cause. Now we do not lack eggs, or slings, or sturdy fellows to whirl them; and still they do not cook, but rather they cool down faster if hot. And since nothing is lacking to us except being Babylonians, then being Babylonians is the cause of the eggs hardening.' And this is what I wished to determine. Is it possible that Sarsi in riding post has not observed the coolness brought to his face by the continual change of air ? And if he has indeed felt this, can he prefer to believe things which happened two thousand years ago in Babylon, as related by others, rather than present things which he himself experiences ? I beg your Excellency to have him see some time how wine is frozen in midsummer by means of rapid agitation, without which it would not freeze at all. And I leave it to you to judge the reasons which Seneca and others arrive at for this effect, when the effect itself is false. I willingly yield to Sarsi's invitation to me to listen attentively to Seneca's conclusion, and to his, then demanding whether anything could be said more clearly or more subtly; and I confirm that no falsehood could be told more subtly or plainly. But I should not like to have him place me beyond the bounds of good breeding (as he tries to do) by being compelled to believe what (p. 187) I deem false lest by denying it I give the lie to men who are the flower of literature— and what is more dangerous, to valorous soldiers. For I think that they believed they were speaking the truth, and hence their falsehood carries no dishonor. But when Sarsi says that he does not want

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to be one to give affront to wise men by contradicting what they say and refusing to believe them, I say that I do not want to be among those ignoramuses and ingrates toward nature and toward God who, being given senses and reason, should wish to defer such great gifts to the mistakes of one man, or to believe blindly and stupidly what I wish to believe and subject the freedom of my intellect to anyone who is just as liable to error as I am. XLVI Ί shall not . . . ( / > . 188) . . . with weakened force.' (p. 120, 1. 3 to

1-29)· Sarsi continues in the style in which he began, trying to establish by the stories of others what actually exists and may be seen every day by experiment. And as he has found very distinguished men to confer authority upon ancient archers and slingmen, so he has found a modern historian no less worthy of credit (nor a whit less authoritative than any ancient) to render credible the melting of modern cannon balls and musket shot. But it does not detract from the credit or dignity of an historian to submit a wrong reason for a physical effect, the historian being concerned only with the effect while the cause is the province of the scientist. So I believe with Sig. Homer Tortora that a cannon ball covered with lead had little effect in breaking down the enemy's walls, but I have courage enough to deny his reason for this borrowed from common philosophy. I hope that this same historian, just as he has previously believed what he has found written by many other great men whose authority has been sufficient to win his faith in everything they have said, will now listen to my reasoning, whether he changes his opinion or merely grasps the idea of wishing to see experimentally what the truth of the matter is. I believe Sig. Tortora in that the iron ball covered with lead in the Corbel battery had little effect, and that the iron core was found to be spoiled by the lead. I do not believe the other part, pertaining to science—that the lead would be liquefied and it is on that account that the iron ball was found to be stripped of it. I believe that attaining the extreme impetus given by a cannon to a ball shot at a wall, the lead covering on that side which was

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compressed between the external wall and the internal iron ball was crushed and torn to pieces, and that practically the same thing was true of the opposite side, this being flattened against the iron; and that all the lead, tattered and distorted, {p. 189) blew in all directions. Afterward, covered with rubbish and therefore resembling the other fragments in the ruins, it was not easy to find. And perhaps it was not even looked for with that care which curiosity would demand of anyone who wanted to find out whether it was destroyed or merely lacerated. T h e lead would serve almost as a protection and a pillow for the iron ball, as a result of which the ball would give a weaker percussion; and in ungrateful payment for this the lead was left torn and so badly ruined that not even its corpse was found among the slain. Now since I understand that Sig. Homer is there at Rome, should he ever chance to meet your Excellency, I pray you to read him this little that I have written here—and the remainder which I am about to write on this subject—because I should highly value gaining the concurrence of a person who is justly esteemed by our age. I say, then, that if we consider how much time elapses while the ball is going from the cannon to the wall, and what would have to take place within such a short time to cause lead to melt, it will be remarkable if anyone persists in the opinion that such an effect nevertheless does ensue. This time is much shorter than one pulse beat, within which time the friction of the air must occur which in turn is to set fire to it and finally to liquefy the lead. But if we imagine the same lead ball to be put in the midst of a fiery furnace, it will not be destroyed in even twenty pulse beats. It now remains for Sarsi to persuade people that the air ignited by rubbing had a heat incomparably greater than that of a furnace. Besides, experience shows us that a ball of wax shot from a musket will pass through a plank, which argues that such a ball is not destroyed while in the air, so Sarsi will have to furnish reasons for air liquefying lead but not wax. Moreover, if the lead does liquefy, it will surely strike but a slight blow upon arriving against a corselet; hence it is very astonishing to me that musketeers have not thought of making iron pellets which

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would not be so easily destroyed. Instead, they go on shooting with lead pellets which few iron plates can resist, and in those which do stand up to them there is found {p. 190) quite a deep dent—and the shot, too, is found, flattened, but not liquefied. In birds slain with small shot, there are found grains of lead of unaltered shape; it is up to Sarsi to supply a reason why pieces of lead weighing fifteen or twenty pounds are melted, but not those which run thirty thousand to the pound. Since pellets of distorted shape are to be found any day among the clothing of soldiers, I shall believe that some were shot into breastplates and remained among the cloths, others may have run slantwise into a helmet and have been lengthened in that way, dropping harmlessly into someone's clothes and remaining there without injuring him, and in sum a thousand accidents may happen in a skirmish without any melting taking place. For if melting did occur, it would be necessary (as Sarsi is aware) that lead falling very rapidly from high places should disperse itself into smaller drops than those of water, and be lost entirely, so that nothing of it might be found. I say nothing of the fact that the arrow and the ball accompanied by fiery air ought to show a brilliant track like that of a rocket in flight, especially at night, as Virgil writes that the arrow of Acestes marked its path in flame. This effect is not to be seen except in poetry, though nocturnal events such as lightning and shooting stars are made quite conspicuous by their bright light. XLVII 'But we do not see . . . (p. 1 9 1 ) . . . poets and philosophers.' (p. 120, 1. 30 to p. 1 2 1 , 1 . 24). This melting of the lead ball, which a few lines above Sarsi says is confirmed by daily examples, he next says happens very rarely; for it is so unusual that it has become regarded almost as a miracle. Now this sudden retreat of his assures us still further that he recognizes his own need of defenses and escapes, and this he proceeds to confirm by his own inconstancy, now wanting this and now that. He says that the disturbance of a little breeze suffices to ignite the air; even the mere arrival of a live man at a cemetery of the dead. At

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another time (as he has said above and repeats at the end of this passage), he wants a vehement motion, a copious amount of exhalations, great attenuation of matter, and if anything else it would be something akin to these. To this last requirement, I subscribe more than I do to all the others, being quite certain that not only these ignitions but any other effect, however marvelous and recondite, would follow if such requisites for it were to exist. I should like to know apropos of what it is that Sarsi, after having told (p. 192) of the flame which is lighted over a cemetery by the mere arrival of a man or a light breeze, asks me what friction of hard bodies there is here. I have said that friction capable of exciting fire is derived only from solid bodies. Now I do not know by what logic Sarsi pretends to deduce from that statement the conclusion that I would have it that wherever there is fire there can be no other cause for it than such friction. Hence I reply to Sarsi that fire may be excited in many ways, among which is the vigorous rubbing of two hard bodies; and since such friction cannot be produced by subtle and fluid bodies, I say that comets, lightning, shooting stars—and now I add the cemetery flames—are not lighted by friction of the air nor of winds nor exhalations, but indeed that each of these most frequently occurs during the greatest tranquillity of air and when the wind is quite still. Perhaps you ask me what, then, is the cause of these burnings ? In order not to enter into new battles, I reply that I do not know; but I do know that neither water nor air is ever ground apart or catches fire or burns, being material incapable of being ground, and being incombustible. Lighting a single straw or one strand of flax is followed by a fire which does not stop until all the straw or flax is burned even if there are a hundred million cartloads of it. If a little stick takes fire the whole house will burn—and, unless protection is quickly given, the whole city and all the wood in the world that may touch the first burning stick. Then what would become of the air, so subtle and with all its parts in contact, if ever a particle of it were to catch fire ? Would not the whole of this burn, too ? Sarsi is ultimately reduced to saying with Aristotle that if the air ever happened to be abundantly filled with those warm exhalations in the presence of these requisites mentioned, then balls of lead

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would be melted; and not only those from cannons, but those from muskets and those thrown by slings. This, then, must have been the state of the air at the time the Babylonians were cooking their eggs; thus it was, (p. 193) to the great good fortune of the besiegers, when they razed the city of Corbel; and when it is thus, things go very pleasantly for people who are being shot at. But since finding such a condition is a matter of chance, and one that does not occur any too frequently, Sarsi says that one must not have recourse to experiment, these miracles being performed not at our will but at a chance which is very difficult to meet with. So, Sig. Sarsi, even if experiments are performed thousands and thousands of times at all seasons of the year, and in any place you like, without ever once producing what these poets, philosophers, and historians have mentioned, this will mean nothing; and we ought to believe their words rather than our own eyes. But if I find for you a condition of the air having all these requisites which you say are necessary, and still the egg is not cooked nor the leaden balls destroyed, what would you say then, Sig. Sarsi ? But alas! I should be offering you too much, for there would always remain a retreat by your saying that some necessary condition was lacking. You are extremely prudent in taking a secure position when you say that there is needed for this effect a violent motion, a great quantity of exhalations, a well-attenuated material, 'and whatever else conduces to it'; this 'whatever else' is what dismays me and gives you a heaven-sent anchor, a safe harbor, a sanctuary wholly secure.— What I had in mind was to suspend the discussion and sit quietly by until some new comet should come along, imagining that while it lasted you and Aristotle would concede to me that just as the air was then properly disposed for setting it afire, so it would be also for melting lead and cooking eggs; for it seemed to me that you would require the same disposition for both results. Then I would have had us set to work with slings, eggs, bows, muskets, and cannons to clear up the truth of this affair for ourselves. And even without waiting for a comet, the time ought to be right in midsummer when the air is flashing with lightning, since all such ignitions are assigned to the same cause. But when (p. 194) you did not see a melting of

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balls or even a cooking of eggs at such a time, I question whether you would not nevertheless refuse to give in, saying that there was lacking this 'whatever else conduces to it.' If you will tell me what sort of thing this 'whatever else' is, I shall endeavor to provide it; but if not, I shall relinquish my idea. Yet I believe it would undoubtedly go against you; if not completely and without exception, at least to the following extent: When we seek the natural cause of some effect, you are reduced to an attempt to satisfy me with an event so rare that you yourself finally name it among the miracles. But neither by whirling a sling nor by shooting a bow nor by means of muskets or cannons do we ever see these effects which you mention so often; or, if the event ever does take place, it is so rare that we ought to consider it a miracle and accordingly believe in the stories of others rather than seek to test it by sight. And since matters stand thus, I say you should be content to concede that ordinarily comets are not ignited by friction of the air and be willing to accept such an event as a miracle, if people grant to you in return that once in a thousand years a comet may be ignited by such friction in the presence also of all those circumstances which you require. As to the objection raised and resolved by Sarsi, that some may perhaps say that musket balls and cannon balls are destroyed not by the friction of the air but by the fire with which they are so violently shot, in the first place I am not one of those who would make that objection since I say that they are not destroyed either in one way or in the other. Then as to the reply to this objection, I do not know why Sarsi has not put it in the clearest way, saying that balls and arrows driven by a sling or a bow—where there is no firing—plainly show the emptiness of this objection. This seems to me a much more direct answer than Sarsi's, which is that the time during which the ball is accompanied by the fire is too short for melting so large a chunk of lead. This is true enough, but it is also true that a still briefer time (p. 195) is spent in its journey through the air where it is to be melted by friction. I do not know what to reply to the ultimate conclusion which he draws from this, since I simply do not understand what he means

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when he says that it is enough for him to have shown that in these instances I have no retreat whatever for escaping from the testimony of the poets and philosophers. This testimony being written in a thousand books, I have never attempted to escape from it, and indeed anyone who should undertake such a thing would appear to me to be quite bereft of reason. I have certainly said that these attestations are false, and they still appear to me to be so. XLVIII 'But he objects . . . conduces to the same.' (p. 1 2 1 , 1 . 25 to p. 122, 1. 15). {p. 196) Now, your Excellency, read on to the end of this section, with regard to which there remains little for me to say as I have said a good deal already. I shall merely bring into consideration the way in which Sarsi tries to maintain that the burning of the comet may endure for many months, while other things in the air such as lightning, shooting stars, and the like are momentary. In order to do this, he invents two kinds of combustible materials, some light, rare, dry, and without any accompanying humidity; others viscous, glutinous, and allied with moisture. Of the first, he would make the momentary combustions; of the second, enduring fires such as comets. Here I detect a manifest contradiction; for in that case, lightning, being made of rare and light material, should occur in the highest regions, while comets, being ignited in a more glutinous, and denser and consequently in a heavier material, would occur in lower places. Yet the contrary happens, since lightning does not occur more than a third of a mile above the earth, as we are assured by the small interval of time between our seeing the lightning and hearing the thunder when the latter reaches us from directly overhead. That comets are undoubtedly incomparably higher we know by their daily movement from east to west, similar to that of a star, even were there no other evidence. This is enough concerning these experiences. It now remains, in accordance with the promise made above to your Excellency, for me to tell you some of my thoughts about the proposition, 'Motion is the cause of heat,' and to show in what sense

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this may be true in my opinion. But first I must give some consideration to what we call 'heat,' for I much suspect that in general people have a conception of this which is very remote from the truth, believing heat to be a real attribute, property, and quality which actually resides in the material by which we feel ourselves warmed. 39 Therefore I say that upon conceiving of a material or corporeal substance, (j>. 197) I immediately feel the need to conceive simultaneously that it is bounded and has this or that shape; that it is in this place or that at any given time; that it moves or stays still; that it does or does not touch another body; and that it is one, few, or many. I cannot separate it from these conditions by any stretch of my imagination. But that it must be white or red, bitter or sweet, noisy or silent, of sweet or foul odor, my mind feels no compulsion to understand as necessary accompaniments. Indeed, without the senses to guide us, reason or imagination alone would perhaps never arrive at such qualities. For that reason I think that tastes, odors, colors, and so forth are no more than mere names so far as pertains to the subject wherein they reside, and that they have their habitation only in the sensorium. Thus, if the living creature (Vanmale) were removed, all these qualities would be removed and annihilated. Yet since we have imposed upon them particular names which differ from the names of those other previous real attributes, we wish to believe that they should also be truly and really different from the latter. I believe I can explain my idea better by means of some examples. I move my hand first over a marble statue and then over a living man. Now as to the action derived from my hand, this is the same with respect to both subjects so far as the hand is concerned; it consists of the primary phenomena of motion and touch which we have not designated by any other names. But the animate body which receives these operations feels diverse sensations according to the various parts which are touched. Being touched on the soles of the feet, for example, or upon the knee or under the armpit, it feels in addition to the general sense of touch another sensation upon which we have conferred a special name, calling it ticklings this sensation

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belongs entirely to us and not to the hand in any way. It seems to me that anyone would seriously err who might wish to say that the hand had within itself, in addition to the properties of moving and touching, another faculty different from these; {p. 198) that of tickling—as if the tickling were an attribute which resided in the hand. A piece of paper or a feather drawn lightly over any part of our bodies performs what are inherently quite the same operations of moving and touching; by touching the eye, the nose, or the upper lip it excites in us an almost intolerable titillation while in other regions it is scarcely felt. Now this titillation belongs entirely to us and not to the feather; if the animate and sensitive body were removed, it would remain no more than a mere name. And I believe that many qualities which we come to attribute to natural bodies, such as tastes, odors, colors, and other things, may be of similar and no more solid existence. A body which is solid and, so to speak, very material, when moved and applied to any part of my person produces in me that sensation which we call touch; this, though it pervades the entire body, seems yet to reside principally in the palms of the hands and especially in the fingertips, by means of which we sense the most minute differences of roughness, smoothness, and hardness, these being not so clearly distinguished by other parts of the body. Of these sensations, some are more pleasant to us and some less so, and they are smooth or rough, acute or obtuse, hard or yielding, according to the differences of shape which exist among tangible bodies. This sense being more material than the others and having its rise in the solidity of matter, it seems to be related to the earthy element. And since some bodies continually dissolve into minute particles of which some are heavier than air and descend, while others are lighter and rise on high, perhaps herein lies the origin of two other senses, accordingly as these particles strike us upon two parts of our bodies which are very much more sensitive than the skin and which feel the invasion of such subtle, tenuous, and yielding matter. T h e tiny descending particles are received upon the upper surface of the tongue, penetrating and mixing with its moisture; and their substance gives rise to tastes, sweet or unsavory accordingly as the shapes of these

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particles differ, as they are few or many, and as they are fast or slow. The other particles, ascending, enter by our nostrils and strike (ρ. 199) upon some small protuberances which are the instrument of smell; and here likewise their touch and passage are received to our liking or our dislike accordingly as they have this or that shape, move quickly or slowly, and are few or many. The tongue and the nasal passages are indeed seen to be providently arranged for the above as to location; the former extends from below to receive the incursions of descending particles, while the latter are accommodated for those which ascend. Perhaps the excitation of tastes may be likened with a certain analogy to fluids, which descend through the air, and odors to fires, which ascend. Next the element of air remains available for sounds; these come to us indifferently from below, from above, and from all sides, since we are situated in the air and its movements within its own domain displace it equally in all directions. And the situation of the ear is most fittingly accommodated to all positions in space. Sounds are created and are heard by us when—without any special 'sonorous' or 'transonorous' property—a rapid tremor of the air, ruffled into very minute waves, moves certain cartilages of a tympanum within our ear. External means capable of producing this ruffling of the air are very numerous, but for the most part they reduce to the trembling of some body which strikes upon the air and disturbs it; waves are thereby very rapidly propagated, and from their frequency originates a high pitch, or from their rarity a deep sound. I do not believe that for exciting in us tastes, odors, and sounds there are required in external bodies anything but sizes, shapes, numbers, and slow or fast movements; and I think that if ears, tongues, and noses were taken away, shapes and numbers and motions would remain but not odors or tastes or sounds. These, I believe, are nothing but names, apart from the living animal—just as tickling and titillation are nothing but names when armpits and the skin around the nose are absent. And as the four senses considered here are related to the four elements, I believe that vision, the sense which is eminent above all others, is related to light, but in that ratio {p. 200) of excellence which exists between the finite

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and the infinite, the temporal and the instantaneous, the quantity and the indivisible; between darkness and light. Of this sense and the matters pertaining to it, I pretend to understand but a trifle, and since a long time would still not suffice for me to explain that trifle— or even to hint at its explanation in writing—I pass this over in silence. Returning now to my original purpose, and having already seen that many sensations which are deemed to be qualities residing in external subjects have no real existence except in ourselves, and outside of us are nothing but names, I say that I am inclined to believe that heat is of this character. Those materials which produce heat in us and make us feel warmth, which we call by the general name fire, would be a multitude of minute particles having certain shapes and moving with certain velocities. Meeting with our bodies, they penetrate by means of their consummate subtlety, and their touch which we feel, made in their passage through our substance, is the sensation which we call heat. This is pleasant or obnoxious according to the number and the greater or lesser velocity of these particles which thus go pricking and penetrating; that penetration is pleasant which assists our necessary insensible transpiration, and that is obnoxious which makes too great a division and dissolution of our substance. T o sum up, the operation of fire by means of its particles is merely that in moving it penetrates all bodies by reason of its great subtlety, dissolving them more quickly or more slowly in proportion to the number and velocity of the fire-corpuscles (;ignicoli) and the density or rarity of the material of these bodies, of which many are such that in their decomposition the major part of them passes over into further tiny corpuscles (ignei), and the dissolution goes on so long as it meets with matter capable of being so resolved. But I do not believe at all that in addition to shape, number, motion, penetration, and touch there is any other quality in fire which i s ' heat'; I believe that this belongs to us, and so intimately that when the animate and sensitive body is removed, 'heat' remains nothing but a simple (p. 201) vocable. And since this sensation is produced in us by the passage and touch of the tiny corpuscles through our substance, it is obvious that if they were to remain at

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rest their operation would remain null. Thus we see that a quantity of fire retained in the pores and narrow channels of a piece of quicklime does not warm us even when we hold it in our hands, because it rests motionless. But place the quicklime in water, where the fire has a greater propensity to motion than it has in air—because of the greater gravity of this medium, and because the fire opens the pores of water as it does not those of air—and the little corpuscles will escape; and, touching our hand, they will penetrate it and we shall feel heat. Since, then, the presence of the fire-corpuscles does not suffice to excite heat, but we need also their movement, it seems to me that one may very reasonably say that motion is the cause of heat. This is that motion by which arrows and other sticks are burned and by which lead and other metals are liquefied when the little particles of fire penetrate the bodies, being either moved by themselves or, their own strength not sufficing, being driven by the impetuous draught of a bellows. O f these bodies, some resolve into other flying particles of fire and some into a most minute powder; some liquefy and become as fluid as water. But I hold it to be foolish to take that same proposition from the common point of view—that a stone or a piece of iron or a stick must heat up if moved. T h e rubbing together and friction of two hard bodies, either by resolving their parts into very subtle flying particles or by opening an exit for the tiny fire-corpuscles within, finally set these in motion and, upon their encountering our bodies and penetrating and coursing through them, our conscious mind (anima sensitiva) feels that pleasant or obnoxious sensation which we have named heat, burning, or scalding. And perhaps when the thinning and attrition stop at or are confined within the tiniest particles (i minimi quanti), their motion is temporal and their action is calorific only, but, when their ultimate and highest resolution into truly indivisible atoms is reached, light is created 40 which has instantaneous motion—or let us say instantaneous expansion and diffusion (p. 202)—and is capable of occupying immense spaces by its—I do not know whether to say by its subtlety, its rarity, its immateriality, or yet some other property different from all these, and nameless.

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I do not wish, your Excellency, to engulf myself inadvertently in an infinite ocean from which I should never get back to port, nor do I desire in trying to remove one difficulty to give rise to a hundred more, as I fear may in part have occurred by my sailing but this little distance from shore. Therefore, I shall desist until some more opportune occasion. XLIX 'THIRD PROPOSITION . . .[pp. 2 0 3 - 2 0 5 ] . . . they are not rejected.' (p. 1 2 2 , 1 . 16 to p. 1 2 7 , 1 . 20). [p. 206) Let your Excellency now pass on to the third proposition. Read and reread it attentively; I say attentively so that you may the more plainly recognize afterward how craftily Sarsi still continues in his style of altering, deleting from, adding to, and even diverting the argument and mixing with it things that are alien to the subject, trying thus to confuse his readers' minds so that in the end there may remain with them, among things but obscurely understood, the opinion that Sig. {p. 207) Mario did not establish his doctrine in such a way that others have been unable to find means of opposing it. Many people have held the opinion that a small bright flame appears much larger at a distance because it sets fire to, and thus renders of equal brilliance, the surrounding air; from afar the ignited air and the actual flame both appear then to be a single light. Sig. Mario, refuting this, says that the air is neither ignited nor illuminated, and that the irradiation which makes the enlargement is located not around the flame but upon the surface of our eyes. Sarsi seeks to oppose this correct doctrine, and instead of thanking Sig. Mario for having taught him something he had not previously known, he proceeds to try to prove that the air is illuminated in contradiction to Sig. Mario's assertion. In this enterprise, he seems to me to have erred in several ways. First, where Sig. Mario in countering what is said by these philosophers declares that the air is neither ignited nor illuminated, Sarsi suppresses all mention of ignition and deals only with illumination. Sig. Mario might reasonably say to Sarsi that while he was talking about one thing, Sarsi undertook to refute something else; that is,

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Sig. Mario spoke of the air surrounding the flame and of the illumination which might arise from this air taking fire, whereas Sarsi has spoken of the illumination which occurs in vaporous air in the absence of fire, when such air is located at a distance from the illuminating object. Besides, Sarsi says at the outset that transparent bodies are not illuminated, and at first he places the air among these; then later he adds that the air is indeed illuminated when it is mixed with gross vapors capable of reflecting light. Well then, Sig. Sarsi, it is the vapors which are illuminated and not the air. You remind me of a man who says that some wheat has made him dizzy and light-headed, when in fact it was mixed with cockleweed; now it is the cockleweed that makes one suddenly ill, and not the grain. Are you trying to teach us that it is vaporous air which illuminates the dawn, which thousands of others have said, and as Sig. Mario himself had written in half a dozen places (p. 208) before you ? And this is not all. You yourself, in this very passage, say that I admit this phenomenon with regard to the moon and Jupiter. Then all your proofs and experiments relating to dawn, haloes, mock suns, and the moon hidden behind some wall are quite superfluous, since we have never questioned (let alone denied) that vapors diffused through the air, or clouds, or mists are illuminated. But what is it that you wish to do next with this illumination, Sig. Sarsi? T o say, perhaps, as in effect you do, that on its account the primary illuminating objects appear larger ? Surely you should perceive that if such were the case the sun and moon would have to look as large as the whole dawn— or as their entire haloes—since the vaporous air which is made to participate in their light would be of such dimensions. You have found it written (I say this because you cite philosophers and authorities on optics to confirm and certify these propositions) that the vaporous region is brightened, and that the sun and moon appear larger by reason of that vaporous region when they are close to the horizon than when they are high in the sky, and hence you are convinced that their apparent enlargement depends upon that illumination. Both propositions are true—the vaporous air is illuminated, and the sun and moon do appear larger when close to the horizon as a result of the vaporous region—but it is false that there is any

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connection between the two propositions or that the enlargement depends upon the illumination of that region. You are much deceived; put away this mistaken opinion, for these objects appear larger than usual not because of the light in the vapor but because of its spherical outer surface, and because of the greater distance of this surface from our eyes when those objects are closer to the horizon. Not only luminous bodies, but any bodies placed beyond this region will behave in the same way. Place between your eye and any object a convex crystalline lens, at various distances. You will see that when this lens is close to the eye it increases but little the size of the object viewed, but moving it farther away you will see that enlargement (p. 209) progressively grow. And since the vaporous region terminates in a spherical surface not much elevated above the convexity of the earth, all the straight lines drawn from our eyes to that surface are unequal, the one toward the zenith being the shortest of all and the others being gradually longer the more they point away from the zenith and toward the horizon. Let it be remarked in passing that here one may easily deduce the cause for the apparently oval shape of the sun and moon when they are near the horizon by considering the great distance of our eyes from the center of the earth, which is also the center of the vaporous sphere. Whole books have been written about this appearance, as I believe you know, though the entire mystery requires no doctrine more profound than to understand why a circle seen straight on looks round to us, while looked at in foreshortening it appears oval. Now getting back to our subject, I fail to see Sig. Sarsi's purpose in saying that it is ridiculous to assert that dawn and twilight and other similar splendors are generated in the moisture spread over our eyes, and that it would be no more ridiculous to say that when we look toward the zenith our eyes are drier than when we look at the horizon, and that it is for that reason that the moon and sun should look smaller to us in the former position than in the latter. Not having discovered anyone who has ever said such a thing, I do not know why Sarsi introduces this foolishness. But as Sarsi represents us as too simple-minded, let us see whether that accusation would not apply better to him than to us.

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We are dealing now with that adventitious irradiation, crowned with which the stars and other lights look much larger than they would if their little bodies were seen without such rays. These rays are much less lucid than the true and primary flame, and in the midst of them the little body remains indistinct so that both it and the irradiation appear to us as a single, large, and resplendent object. Sarsi wants to relate this irradiation and enlargement to the light which is produced by refraction in the vaporous air, and he will have it that for this reason the sun and moon look (p. 210) larger near the horizon than on high. What is worse, he pretends that many other philosophers have believed the same, which is false; they never made such a bad mistake. Sarsi should see at once that this is a great error by considering the enormous difference perceived between the light of the sun or moon and the diffused brightness which surrounds either, and within which each is discerned as incomparably brighter and more sharply defined. This is not true of the irradiation of the stars, in the midst of which the little body of a star remains indistinct and is clothed with a brightness identical to its own. But I hear Sarsi answer by saying that this large sun or moon is not actually a bare and plain body, but an aggregate composed of a small real body and an irradiation of equal brilliance which crowns it and encloses it in the center, resulting in the large and uniformly bright apparent disc. Now if this is so, Sig. Sarsi, why does not the moon appear equally large when it is in the center of the sky, too ? Is there no vaporous air above, suitable for being illuminated ? I do not know what you would reply; I cannot even guess; for a truth may be assailed only with fallacies and fictions, and since these (as you know) are infinite, I cannot divine what your choice would be. But to put an end to the matter and if possible to lift you and others out of error, it suffices to make it clear to you that that huge moon which you see on the horizon is plain and bare and is not enlarged by any adventitious circumfused light. For this purpose, it should be enough to note that the spots spread out over its whole surface, right out to its extreme edges, are seen precisely the same as when the moon is in the center of the sky. If matters stood as you believe,

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then the spots in the low, large moon should be seen collected in its central parts, leaving the surrounding crown bright and spotless. Therefore the sun and moon appear larger when low than when high not because of an additional bright region, but from an enlargement of the whole image by refraction at the distant vaporous surface. Behold, Sig. Sarsi, how easy it is to defeat the false (p. 2 1 1 ) and to sustain the true. Abundant evidence of the falsity of many propositions to be read in your book prevents my believing that you remain ignorant of it, and I think it may be that you recognized in your heart the validity of the correct reasons, but were ultimately reduced to trying whether the opponent might not be forced to retreat and yield by being taken in by things you yourself knew to be false. You have thus boldly introduced these things in imitation of the gambler who, seeing from the cards on the table that he has lost the stakes, attempts by offering a larger bet to make his opponent believe that his hand is much stronger than what he himself can see it to be, hoping he will be overcome with fright and will yield. Since I see that you have got rather tangled up among these primary lights refracted or reflected in vapors or in the eye, it is appropriate for you as a pupil that I, as a professor and an old hand at teaching, should somewhat disentangle you. Know, then, that the sun, the moon, and the stars—all of them brilliant bodies located far beyond the vaporous region—send out a brilliance which perpetually lights one half of that region. Of this illuminated hemisphere, the western extremity sends to us the morning dawn, and the opposite edge gives us the evening twilight; but neither of these illuminations increases or enlarges or in any way alters the apparent size of the sun, the moon, or the stars, which lie always in the center (or let us say at the pole) of this vaporous hemisphere which they illuminate. The parts which lie between our eyes and the sun or moon look brighter to us than those other parts which are by degrees removed from there, and whose brightness gradually diminishes, and it is this light which gives sign of the moon's approaching appearance when it is hidden behind some roof or wall. A similar illumination occurs near a little flame which is located within the vaporous sphere, but in this case it is so weak and languid

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that if we hide a light behind some wall at night and then start moving (p. 212) so as to see it, we shall perceive scarcely any circumfused splendor, nor do we see any light until the flame itself is discovered. Now this very weak light does not enlarge the visible image of the little flame at all. But there is another illumination here, made by refraction in the moist surface of the eye, and by this the real object appears to us to be surrounded by a luminous circle very inferior in brightness to the primary light. It is seen to extend through a greater or lesser space, not merely in proportion to the greater or lesser quantity of this moisture, but also according to the condition of the eye itself. I have observed this in myself, for as a result of a certain affliction I began to see a luminous halo more than two feet in diameter around the flame of a candle, capable of concealing from me all objects which lay behind it. As my malady diminished, so did the size and density of this halo, though more of it has remained with me than is seen by perfect eyes. This halo is not hidden by interposing the hand or any other opaque body between the candle and the eye, but remains always between the eye and the hand so long as the light of the candle itself is not cut off. But it does not enlarge the image of the little flame, and it is much less bright than that is. Now there is a third very vivid splendor here, almost as bright as that of the original light itself; this is produced by reflection of the primary rays in the moisture at the edges of the eyelids, and it extends over the convexity of the pupil. That it is thus produced is clearly shown by changes in the position of the head, for accordingly as we incline the head, raise it, or hold it straight toward the luminous object, we see the latter irradiated only in the upper part, only in the lower, or in both. But we never see rays appear from left or right, for reflections made near the angles of the eye can never arrive over the pupil, as these angular parts of the eye lie beneath the horizontal line across the pupil on account of the bending of the eyelid over the sphere {p. 213) of the pupil. And if by pressing with a finger upon the eyelid one widens the eye and removes the edges of the eyelid from the pupil, one will no longer see rays above or below, since the reflections made in the edges do not then alight upon the pupil.

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This, and this alone, constitutes that irradiation by which small lights appear large and radiant to us, and within which the little real flame remains swallowed up and indistinct. That other illumination has nothing, Sig. Sarsi, nothing whatever, to do with enlargement, for it is so far inferior in brightness to the primary light that one would indeed be completely blind not to see the boundaries, confines, and distinctions between the one and the other. Besides, as I have said before, if the discs of the sun and moon were enlarged by this illumination, they ought to appear as large as the immense circles of their dawning. If you would say that you do not deny this radiant crown to be a sensation of the eye, but that I have not thereby proven that some part of it does not depend upon the illumination of the surrounding air, I beg you to desist from such miserable begging for niggardly assistance. What is it that you want to do with that very feeble light, mixed with those extremely bright rays reflected from the eyelid ? You would be adding about as much as a torch at noon would add to the sunlight. Of this light diffused through the vaporous air, I am happy to concede to you not only that little which you ask for, but all that is embraced in the entire dawn and twilight and the whole vaporous hemisphere. Nor do I ask that the luminous body be robbed of this by the telescope or by any other means; for your complete satisfaction I even want to have it enlarged by the telescope as are all other objects, so that it will not merely equal the whole dawn but will occupy a thousand times as much space—if so much space may be embraced by the telescope. But none of these things will help you or your master one bit, for in order to maintain your chief conclusion (which is that because of their distance the fixed stars do not receive any enlargement from the telescope), you would need to have the star and its {p. 214) irradiation be one and the same thing, or at least you would need to have the irradiation located around the star. Neither of these things is the case, for the irradiation is in the eye, and the stars receive just as much enlargement as any other object seen through the same telescope, as Sig. Mario very correctly writes and proves. These other little diversions of yours about illuminated vaporous air and about high and low suns and moons are mere palliatives, so

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to speak; they are attempts to get away from school and to divert the reader from the main point. Among these various diversions, two are quite correct—this one in which you attempt to show by a long argument that the interposition of a finger does not impede one's view of a candle, and that other one which deals with a thin thread and the interposition of a body smaller than the pupil; but I note that they have nothing to do with the matter in hand. I see that in your heart you too have recognized this, inasmuch as, when the time came for applying these things to the subject and drawing some conclusion, you stopped short, and, leaving them dangling, you passed on to another proposition, still trying to prove by reasoning something that is contradicted by a hundred evident experiences. And although you may see by looking through the telescope that Saturn is sharply bounded and is of a very different shape from the other stars, the discs of Jupiter and Mars (especially when close to the earth) are perfectly round and well defined, Venus is from time to time horned but is very exactly delimited; the little globes of the fixed stars, particularly the larger ones, are quite distinct, and finally a thousand little candle flames situated at a great distance are outlined as if they were close at hand. On the other hand, the naked eye distinguishes none of these shapes without the telescope, and all are seen encumbered with alien rays in the same radiant shape. Yet despite all this, you insist that the telescope does not show them shorn of rays, being persuaded by certain of your own arguments. Well, I am not obliged to reveal all the fallacies in these, having experiences which contradict them; still, for your benefit, I shall briefly hint at them. In order to throw the most light upon my meaning, I ask you, Sig. Sarsi, how {p. 215) it comes about that Venus, so strongly surrounded by these extra alien rays among which its true shape is lost, has been crescent-shaped thousands of times since the world began without ever once being seen so by any living person, and had always appeared constant in shape until I first discovered her alterations by means of the telescope ? It did not happen thus with the moon, whose changes of shape are displayed to the naked eye with no perceptible interference from adventitious irradiation. D o not

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say that this occurs because of the great distance of Venus and the proximity of the moon, for I shall tell you that what happens with Venus takes place also with the flames of the candles, the shape of which becomes confused among the rays and gets lost at a distance of only a hundred yards, no less than does that of Venus. If you wish to reply correctly, you must say that it comes about from the smallness of Venus' body in comparison with the apparent size of the moon, and you must picture to yourself the length of these rays produced in our eyes as, say, four diameters of Venus, which would not be one-tenth the diameter of the moon. Now imagine the tiny crescent of Venus crowned with a wig which spreads and extends out around it a distance of four of her diameters, and at the same time think of the huge crescent of the moon with a wig no larger than one-tenth of the moon's diameter. It should not be very difficult to understand how the shape of Venus is completely lost under this coiffure while that of the moon will be altered very little. What happens here is precisely what would happen if you were to dress an ant in the hide of a lamb—the ant's tiny members would be completely lost in the length of the hairs, and the resulting appearance would be merely that of a fleece of wool, but the lamb is large enough so that its members may be clearly discerned under the same clothing. I shall add that when the luminous object receives the brilliant coiffure which resides in the eye, its spreading is less limited by the size of the object than by the constitution of the {p. 216) eye itself. This we see by compressing the eyelid so that very long rays appear to surge from the luminous object, for those which come from the moon are not perceived as longer than those from Venus or from a torch or lantern. Fancy to yourself some definite size for the wig, and in the center of this imagine a very tiny luminous body. The shape of this will be lost, being crowned by excessively long hairs. But if you now imagine a larger and larger body, its real image will eventually be able to occupy so much of the eye that the wig will extend beyond it little or not at all. Thus the image of the moon, for instance, may occupy more space in the eye than does the usual irradiation. This being so, suppose the actual disc of Jupiter to occupy in your

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vision a little circle whose diameter is one-twentieth the breadth of the radiant wig; in this great space, the tiny actual circle remains indistinguishable. Now I bring a telescope to bear upon it, and this magnifies for me the image of Jupiter by twenty diameters; but it does not magnify the irradiation, as that does not come through the lenses; hence I shall see Jupiter no longer as a very small star, but as a round moon quite large and well defined. If the star is much smaller than Jupiter but shines very vividly and brightly (as does the Dog Star, for example, whose diameter is not one-tenth of Jupiter's, but whose irradiation is little less), then the telescope, by enlarging the star but not the wig, makes the tiny disc which originally was imperceptible in the midst of so broad a light four hundred or more times as large, so that its shape may be well distinguished. If you will establish your reasoning upon such foundations, you may get rid of all difficulties by yourself. Next I reply to your objections against our statement when Sig. Mario and I say that the telescope robs the stars of their resplendent crown. This statement was not put forth in the expectation of its being called to account by so punctilious a person as you, who, when you have nothing else to take hold of, (j>. 217) declaim at length against people who employ the ordinary term 'infinite' in place of 'very great.' If we said that the telescope robs the stars of this irradiation, we meant that it operates upon them in such a way as to cause their bodies to appear bounded and shaped as if they were bare and shorn of that obstacle which conceals their figure from the naked eye. Is it not true, Sig. Sarsi, that Saturn, Jupiter, Venus and Mars reveal to the naked eye no difference in shape, and that none of them show much variation in size from one time to another? Yet with the telescope Saturn is seen as in [the first figure of] the adjoining diagram; Jupiter and Mars in this way always [as in the next two figures]; Venus is seen in all these shapes [at the bottom]— and what is more remarkable, with the indicated differences in size— so that when crescent-shaped she looks forty times as large as when round. Mars looks sixty times as large at perigee as at apogee, though the naked eye shows this as only four or five times. You cannot deny these things, because they are visible and permanent; nor can you

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hope by means of syllogisms to make {p. 218) people believe that things fall out otherwise. Now what we meant by saying the telescope ' robs the stars of irradiation' (for the mere words here are of no moment or consequence) is that it operates upon these stars in such a way [as to circumvent] 41 the irradiation which disturbs the naked eye and impedes precise perception. T h i s action is most momentous, and has remarkable and weighty consequences, but if our words offend you, who are still a pupil, you may alter them to suit yourself—just as you have previously changed o u r ' enlargement' into your ' passage from nonexistence into existence.' Y o u think it reasonable to suppose that as the lucid image comes through the medium free of irradiation produced at the eye, so it should continue to do while passing through the lenses of the telescope. I reply by freely granting this to you, and I tell you that exactly the same thing happens to objects seen through the telescope as to those seen without it. T h e disc of Jupiter, for example, when

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seen with the naked eye remains lost within the spread of its irradiation by reason of its small size; but that of the moon does not, for it occupies in our pupil so much larger a space than its radiant circle that it is seen as shorn, and not as hairy. In the same way, using the telescope to bring Jupiter's disc to my eye six hundred or a thousand times larger than its simple image, will, by reason of this amplitude, cause it to swallow up its coiffure of rays, and makes it look similar to the full moon. But the very tiny disc of the Dog Star, though enlarged a thousand times by the telescope, cannot equal its irradiated size so as to appear completely shorn. Yet since the rays near the outer edge are somewhat weak and separated, the disc is visible and the continuity of the little globe of the star is very easily seen amid the discontinuity of the rays. The more the telescope enlarges this, the more distinct and the less irradiated it appears. That is how matters stand, Sig. Sarsi, and we chose to call this ' robbing Jupiter of his crown'; if the words do not (p. 219) please you, you certainly have license to alter them as you will, and I give you my word that in the future I shall profit by your correction. But do not wear yourself out trying to alter the fact, because you will never succeed in doing that. Since at the end you repeat that it is still necessary to grant that the surrounding air is illuminated and that the star appears larger for that reason, I reply to you once more that the circumfused vapors are indeed illuminated, but that it is not for this reason that the luminous body is enlarged. The light of the vapors being incomparably less than the primary light, the lucid body if large remains barren, and if small it is still sharply bounded, including the irradiation occurring at the eye, and is quite distinct from the very weak light of the vaporous air. And I repeat also to you, since you give me so many occasions for doing so, that you must completely abandon your false idea that the sun and moon when close to the horizon look larger because of a garland of illuminated air adjoining their discs; for this is very naive, as I have stated and proved above. And in order not to leave out anything that may lift you from error and enable you to understand this affair, I shall answer your closing words; there you say that these luminous rays around the star must

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come through the telescope, so one cannot take away that small enlargement caused by them simply by saying that they are lost, for they are not lost. I reply that the enlargement is very great, as it is in all other objects, and that your error (as stated repeatedly) lies in comparing the star taken together with its irradiation when seen with the naked eye to the body of the star alone when seen with the telescope and distinguished from the irradiated region. Sometimes it appears larger than the latter, and sometimes equal, according to the size of the actual star and the power of the telescope; but even when it is seen smaller than this irradiation, the disc will still be perceived within the edges of the coiffure, as I have said. A very simple proof that great enlargement takes place as in all other objects is to pick out Jupiter with the telescope before dawn and then to follow it until sunrise and after, (p. 220) With the telescope, its disc will be seen as always of the same size, but as seen by the naked eye it will progressively shrink as the dawn brightens. Near sunrise, Jupiter—which in the dark surpassed all stars of the first magnitude— is reduced to a smaller appearance than a star of the fifth or sixth magnitude, and finally at sunrise it is reduced to an indivisible point and becomes completely lost. Yet after it has disappeared to the naked eye, it continues to be seen through the telescope large and round all day; I have an instrument which shows Jupiter to me when it is near the earth as large as the moon is when seen with the naked eye. So there is not here a small enlargement or none at all, but a great one, just as in all other objects. If I cannot catch you on the run, Sig. Sarsi, I shall try to wear you out. D o you want another proof that objects at all distances increase in the same ratio? Listen, then, to this one. Let us place several visible objects at varying distances in such a way that all are seen in the same straight line, with the closest one hiding the others. Now keeping the eye in the same place and looking at these objects through the telescope, do you see them still placed in a straight line, or does the closest one no longer hide the rest from you, allowing you now to see them ? I believe that you will reply that they appear to you in a straight line, since they are actually arranged that way. Now this being the case, imagine several straight rods placed parallel to one

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another and at various distances from the eye; these rods are to be of unequal lengths, the most distant being the longest and the closer ones being progressively shorter in such a manner that their ends appear to be placed along two straight lines, one to your left and one to your right. Now take up the telescope and look at them through it. By your previous concession, the ends to the right and left will be seen along two straight lines as before, though the angle between the lines will open more widely. But how can this be, Sig. Sarsi? Among geometers it is required that all such lines shall increase (p. 221) in the same ratio; not that the closer ones shall grow more than the farther ones. Therefore yield, and be silent.

L ' F O U R T H P R O P O S I T I O N ...[p. 222] {p. 2 2 3 ) . . . cannot be a flame.' (p. 127,1. 21 to p. 130,1. 11). Your Excellency, it is time that we bring this long discourse to a close, so let us pass on to this fourth and last proposition. Here, as you see, Sarsi says that he cannot contain his astonishment that I, having some reputation as a prudent observer and a man quite familiar with experiments, should be reduced to affirming things that can be very easily refuted by plain and simple experiments. He then adduces (p. 224) many of these, making himself appear to be as careful and honest an experimenter as I am an imprudent and mendacious one. Well, first, I shall mention briefly what it was that persuaded Sig. Mario to write and me to agree that if the comet were a flame it ought to conceal the stars from us. Then I shall consider Sarsi's examples and arguments, and finally I shall leave it to your Excellency to judge which of us is the more deficient and imprudent in his experimenting and reasoning. We considered transparency of a body to be nothing but its permitting objects beyond it to be seen; hence we were convinced that the less visible a transparent body was, the better it might be seen through. Thus the very transparent air is completely invisible, and limpid water or well-polished glass is scarcely to be seen when placed between ourselves and visible objects, and it appeared to us u

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that one might readily infer from this conversely that the more visible a thing was, the less transparent it should be. Now since flames would not seem to be the least among things inherently visible, we judged that they should be but little transparent, and we were confirmed in this opinion when the authority of Aristotle and the Peripatetics was added to this reasoning. With respect to that authority, I note that Sarsi tries to give a different interpretation from that which the words will easily bear; he says that he knows perfectly well that it is true, but that its sense is that bodies may not be transparent in so far as they illuminate, and not that lucid bodies are not transparent. Of course, if Sarsi takes the proposition in this sense because the proposition thus appears true to him, he is abandoning the other because that appears to him to be false; yet as to the words themselves, they are better adapted to the latter sense than to the former. And he himself, a little farther on, not only affirms, but proves by experiments, that luminous bodies impede the view of things placed beyond them, when he writes: ' These also impede the appearance of things placed beyond themselves, ' and what follows there. But returning to the original argument, I say that beyond the authority of the Peripatetics we were still further confirmed in this by finally observing by experience that a heated glass {p. 225) very much impedes the view of objects which a cold glass allowed to be seen distinctly. T h e flame of a candle has the same effect, especially its upper part, for this is brighter than the lower part around the wick, where there are fumes that are not well ignited by the real flame. We observed, moreover, that the thickness of a body was quite significant even when the body was intrinsically not very opaque. Thus, for example, a cloud which did not prevent a tree trunk being seen at a thickness of twenty or thirty yards, when increased to two or three hundred cut off the visibility of the sun itself. So we thought it would be reasonable to believe that a flame could never be so little opaque as to be unable to impede our view of tiny stars, if this flame were increased in thickness to hundreds and hundreds of yards. From this we concluded that if the curl of the comet were a flame, its thickness (which may not be seventy

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miles as Sarsi and his master say, but should at any rate be that many yards) ought to hide the stars from us; and since it did not do so, this appeared to us quite a conclusive argument against its being a fire. Now Sarsi, caring little or naught for the main point of this very reasonable argument and seizing hold of Sig. Mario's single statement that a candle's flame is not transparent, became convinced that victory was his because he could prove that such a flame was somewhat transparent. He says that if one will hold some writing so close to it as almost to touch it, and will then take great pains to read the letters, he will be able to do so—to which I add, 'provided that he has perfect vision'; for I, not being near-sighted, can scarcely see things that close even if I make use of spectacles. It is true that Sarsi adduces many other experiments besides the foregoing. Among these I should consider first, out of reverence and piety and because it is derived from the supreme authority, that one which Sarsi himself puts in first place and which he takes from the Holy Scriptures. Here Sig. Mario and I call attention to the scriptural words immediately preceding (j>. 226) those selected by Sarsi; these appear to me to say that, before the King saw the angel and the three young men walking through the furnace, the flames had been removed from it. This seems to me to be the sense of the words of the Sacred Text, which are these: Angelus autem Domini descendit cum Azaria et sociis eius, et excussitflammamignis de fornace, et fecit medium fornacis quasi ventum roris flantem ('But the angel of God went down with Azarius and his companions, and he drove the flame of the fires out of the furnace, and he made the midst of the furnace like the blowing of a wind bringing dew'). I note that the Scripture, by saying flammam ignis, seems to distinguish between 'flame' and 'fire'; and when one reads later that the King saw four persons walking, there is mention of fire but not of flame: Ecce ego video quatuor viros solutos et ambulantes in medio ignis ('Behold, I see four men unbound and walking in the midst of the fire'). But since I might be much mistaken in fathoming the true sense of matters which far transcend the powers of my mind, I leave such determinations to the care of doctors of divinity, and simply go on reasoning about these lesser doctrines, declaring that I am always prepared to

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accept every decree of the superiors despite any demonstration or experiment which might appear contrary thereto. 42 Returning to Sarsi's experiments for making us see different objects through various flames, I say that I may freely concede all this to him as true. But it is of no help to his cause; it is insufficient for that purpose to interpose a flame one inch thick between objects as close as one inch to it, with the observer not much farther away, or to speak of objects inside the flame itself, and in its lower part, too, which is the least bright. Unless Sarsi is to be left behind, he must make it evident that a flame hundreds of yards thick, and very distant both from the observer and from the visible objects, does not impede their view—which is as much as to say that he must prove that the flame presents much less impediment than it would if it were so much cloud. Now the nature of a cloud is such that when interposed to the extent of several yards, let alone an inch, it introduces no impediment whatever, while at a thickness {p. 227) of one or two hundred yards it hides the very sun, to say nothing of the stars. And finally, I cannot resist returning for a moment to Sarsi's amazement at my hopeless ineptitude in the use of experiments. You reproach me, Sig. Sarsi, as a poor experimentalist, and yet you yourself err as badly as a man can in that same employment. You must show us that counter to our assertion the interposed flame was insufficient to hide the stars, and in order to convince us by experiences you say that if we try to look at people, firebrands, coals, writings, and candles placed behind flames we shall see them quite plainly. Did it not enter your head to tell us that we might try looking at stars ? Why, for heaven's sake, did you not tell us at the outset: ' Interpose a flame between the eye and some star, and the star will become neither more nor less visible'; surely stars are not lacking in the sky. Is this to be a skillful and prudent experimentalist ? Let me ask you whether the comet's flame is like our flames or whether it is of a different nature. If of a different nature, experiments made with our kind of flame have no conclusive force; if like ours, then you might at once have made us look at the stars through our flames, leaving out firebrands, candle-snuffs, and such things, and, instead of saying that letters may be perceived through a

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candle's flame, you might have asserted that a star is thus perceived. Anyone who wished to do business with you in the marketplace with an honest and sensitive balance, Sig. Sarsi, would say that you are under obligation to kindle a very distant flame as large as a comet and to make us see the stars through that, inasmuch as the size of the flame and its distance from the eye are very important in this matter and must be taken into account. But to give you every advantage and to put you at your ease, I will content myself with much less, and shall prepare for you a much more convenient means for your needs. First of all, since proximity to the eye is significant in seeing objects well, instead of placing the fire as far away as the comet I shall be content with a distance of only one hundred yards. Next, because the thickness (j>. 228) and density of the medium is also very important, in place of the thickness of a comet—which as you know is many hundreds of yards—merely ten yards will satisfy me. Furthermore, since the object which is to be seen derives a great advantage from being bright, as you declare, I shall be content that this object shall be one of those stars which was seen through the curl of our comet—for those stars, according to your statement here, are far brighter than any flame. And now, with all these preparations which are so advantageous to your cause, if you can make the star visible through the transparency of this bonfire I want to confess myself vanquished, and to place you among the most prudent and subtle experimenters in the world. But if you do not succeed, I desire no more from you than silence, by which you will put an end to this dispute, as indeed I hope you will. For if you should ever happen to see this essay of mine—and it rests with the gentleman to whom I write to show it to whomever he pleases—you will see what a man ought to do when he undertakes the task of attempting to examine the remarks of others; that is, he should pass over nothing without giving it consideration and should not go about, as you have done, like a blind chicken poking its beak into the ground now here and now there, hoping to find some grain of wheat to bite and peck at. T o conclude this section, you cannot deny that you yourself have understood and admitted that from the interposed flame some

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impediment occurs even for your eye, for if absolutely no obscuration had taken place you would have said boldly (and without all these warnings and cautions about objects being farther from or nearer to the flame, or this flame being generated by sulfur or brandy rather than straw or wax):' Let the flame and the object be what they will, no impediment occurs for me; I see freely as through pure air.' Besides, a little later, in speaking of things which are not self-lucid, like a flame, but are illuminated by something else, you say that these also impede the view of objects; now this word 'also' shows {p. 229) that you concede some impediment to the flame. Nor is that all. If a flame gave no hindrance, who would ever have thought of saying that it was not transparent ? So even for you there is some small sensible beclouding (for you, I say, because for the rest of us the impediment is very great), and your experiments are made around so small a flame that surely the impediment from a cloud of equal size would be completely imperceptible. It follows that your flame is more of a hindrance than an equivalent cloud; but a cloud as thick as a comet would completely veil and remove from sight the sun itself; hence if the comet were a flame, it ought to be sufficient to hide the sun from us; and since it did not conceal the stars, let alone the sun, it was not a flame. T h e resources for sustaining a falsehood are scarce indeed, but for the establishment of a truth supporting truths abound; I wish to hint to your Excellency a certain particular which seems to me to confirm the falsity of Aristotle's opinion. Inasmuch as nature directs upward all flames known to us while their source and origin remain toward the bottom, if the beard of the comet were a flame and its head were the material from which it took its origin, the curl would have to be pointed straight toward the sky. From this, two things would follow. Either the curl would be seen always in the guise of a garland around its head, which would be the case if the comet were situated very high, or else, if it were near the earth, at its birth the tip of its beard would appear first and the head last; then, as it rose toward our zenith, the beard would appear shorter, and at the zenith itself it would either disappear or would closely surround the head. And finally, as it went toward the west, the beard would necessarily

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appear turned the opposite way so that the head would be seen to incline toward the west before the rest did. For if the beard should go first, as at its birth, {p. 230) it would be necessary for the flame to point down, contrary to its natural tendency and in contradiction of what it did when it was westerly. But such events are not observed in comets and their movements; hence comets are not flames. LI (Sixth argument) 'Also it ought n o t . . . has sufficient talent.' (p. 130, 1. 12 to p. 131,1. 7). (p. 231) Here, as you see, Sarsi tries to twist my own argument against me, but let us briefly examine how happily he has succeeded. First, I note that in order to carry out this intention of his, he runs into some self-contradictions; and what is more remarkable, does so without any need to. Previously, because it accorded with his case, he made every attempt to prove that flames are transparent so that stars might be seen through them. Here, to conquer me with my own weapons, he requires luminous bodies not to be transparent, so he sets about proving this by means of several experiments. From this it appears that he wants luminous bodies to be transparent and not transparent according to his necessities. He falls into this inconvenience without any need, since without incurring a shadow of contradiction from trying now to prove what he denied a little while ago, it was sufficient for him to say without attempting any proof that we ourselves have affirmed in general that luminous bodies are not transparent. Nor had he any occasion to fear that I would bring up distinctions between that which is luminous in itself and that which is lighted by something else, for I have always held that such devices are of service only to those who do not know how to express themselves clearly in the first place. If Sig. Mario had made any distinction between these, he would have declared so at the outset, and would not have waited for his adversary to call attention to his deficiency. I say, then, that it is quite true that any illumination, whether intrinsic or external, would impede the transparency of a luminous body. But you need not understand by our saying this, Sig. Sarsi,

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that we mean to imply that the body must become as opaque as a wall from receiving some tiny light. In proportion to the greater or less brightness, it would lose more or less of its transparency, and thus at the commencement of dawn, in proportion as the vaporous region begins to acquire a little light, the lesser stars become lost. Later, the splendor increasing, (ρ. 232) the larger stars are also lost, and finally at full illumination the moon itself is almost veiled. Furthermore, when through some rift in the clouds we see those long rays of the sun descend to earth, you will by taking pains perceive a noticeable difference in seeing the parts of a mountain you are facing; for those parts which lie behind the luminous rays are more obscured than those which lie off to the sides and which are not seen through these diagonal rays. Likewise, when a ray of sunlight descends through a small window into a darkened room, as it is sometimes seen to do where some small pane is broken in a church, all the objects beyond the path of the ray are seen less distinctly—at least when the observer is situated where he may plainly see the luminous ray, which is not true of every position. All these things being true, I say (and have always said) that the material of the comet may be very much more subtle than the vaporous air and much less suited for illumination. I am persuaded of this by our seeing the comet disappear at dawn and twilight, when the sun lies well below the horizon. As to brightness, there is no more reason for the comet to hide the stars from us than for the vaporous region to do so. Then as to depth, the vaporous region is many miles thick, so we need not assume an immeasurable thickness for the beard of the comet, not having determined the diameter of its head, nor whether it is round, nor what its distance is. Despite all this, if anyone wished to assume it to be even eight or ten miles thick, this would not cause any difficulty; for even the vaporous air allows us to see the stars despite its being much thicker than the beard of the comet, and as much illuminated. LII ' In addition, Galileo objects ...(/>. 2 3 3 ) . . . many others ?' (p. 1 3 1 , 1. 8 to p. 1 3 2 , 1 . 6)

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The example in virtue of which Sarsi believes he can defend Aristotle and show Sig. Mario's objection to be invalid does not appear to me to agree very well with what it is supposed to exemplify. Seeing a great quantity of oats along the roadside and in the markets would very reasonably argue a greater abundance of oats than when these things are not seen, for it lies within the owners' power to expose it or conceal it; and besides, oats are not consumed or diminished in the least by being seen. These two circumstances have no counterparts in the matter of the comet, (p. 234) Perhaps this is a more apt example. That the island of Cuba abounds in cinnamon is strongly argued by the knowledge that the islanders are continually burning it. The reasoning is conclusive, for it is within their control whether they burn it or not, and if they were short of cinnamon they would use it only as a condiment, as do we. But now suppose news to arrive that some months ago the cinnamon forest was attacked by a great fire through some accident, and that the islanders were far from the place and therefore could not extinguish the flames, so the forest was irreparably burned. Then if someone were to try to predict to our spice merchants that there would be an extraordinary abundance, and based this upon that unusual accident in which, where ordinarily they burn fagots of cinnamon, this time a whole forest was burned, I believe that he would be accounted a very foolish man. And anyone who should rejoice upon seeing flames devour the mature oats in his possession, and promise himself that because oats were burning by the bushel he would fill his granary much better than usually, would be considered completely crazy, I think. T h e material of which the comet is made is either the same as that which produces the winds, or it is different. If it is different, one may not argue from the one material an abundance of the other— any more than a man might promise himself a great store of oil from seeing plenty of grapes. And if the material is the same, then the whole would burn when attacked by fire.

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LIII ' I consider t h a t . . . (j>. 2 3 5 ) . . . which we have presented.' (p. 132, 1. 7 to 1.36). Here Sarsi makes two points, as you see; the first contains implicitly the judgment men should make of the fundamental weakness of our doctrine which he pretends to have proved to be supported upon mistaken experiments and defective reasoning. In the second place, he gives a catalogue and summary of the conclusions contained in Sig. Mario's Discourse which are impugned and refuted by him. In reply to the first, I imitate Sig. Sarsi and freely refer whatever judgment is to be made about the soundness of our doctrine to those who have attentively pondered the reasoning and the experiments on both sides. I hope that my cause will be not a little favored for my having examined point by point every reason and experiment adduced by Sarsi and replied to all, whereas he has skipped over the greater number of those given by Sig. Mario, and the most conclusive ones. (p. 236) I had thought of reviewing all these here in exchange for Sarsi's catalogue; but though I set myself to the task, I lacked the spirit and the strength, seeing that I should have to transcribe all over again little less than Sig. Mario's entire treatise. Hence, to save both your Excellency and myself this tedium, I have decided instead to refer your Excellency to a rereading of that Discourse.

APPENDIX TO THE

HYPERASPISTES OR

Gleanings from the cAssayer ofQalileo •

·

BY JOHANN KEPLER [1625]

APPENDIX TO THE HYPERASPISTES At that time when I obtained Chiaramonti's Anti-Tycho, I happened also to glance at Galileo's book, written in Italian and directed against Lothario Sarsi's little book on the comets of 1618 which was published under the title of The Astronomical Balance. In this last book there is frequent mention of Galileo who, in turn, replied in a little book entitled The Assayer. A passage was pointed out to me on pages 22-23 of Galileo's book in which there is reference to the false diagram of Tycho Brahe, a remark to which I made reply in the Hyperaspistes, II, xiii, 26.1 The possessor of the book was in passage and time was not granted to me to read through the whole of it; yet, upon turning the leaves here and there, I saw that the names now of Tycho, now of Kepler occurred frequently. Therefore, after I had arrived in Vienna, although the Hyperaspistes had had to be relinquished to the printer [at Frankfort], yet I did not neglect to seek out this Assayer in order to read through it at my convenience. From this reading, it sufficed for me to append, in passing, to my Hyperaspistes this gleaning for which I ask the reader's indulgence. In regard to the controversies which took place between Sarsi and Galileo, I make no judgment because that matter extends beyond the scope of my purpose, but, wherever Galileo touches upon the case of Tycho, his remarks will have to be considered by me lest I appear to undertake the defense feebly or improperly. i. Therefore, in regard to the false diagram, I demonstrated in that place {p. 186) mentioned above that those little errors are implied within the limits of the title; it is nothing other than a diagrama pseudes, that is, a diagram originally prepared for a very different purpose and then violently distorted from that purpose. The difficulty of this application forced childish and unusual utterances from Tycho, and if they are examined and weighed too carefully and exactly by Chiaramonti and Galileo, they will indeed be literally opposed to elementary principles of geometry. But it is incredible that a man who wrote whole books of geometrical demonstrations would have been ignorant of things of no great cleverness

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which are well known to boys and that he would have presented such obvious errors. Even if it must be granted that in addition to numerical errors, he was unable to explain his calculations when condensed to fit an irrelevant diagram, yet because his purpose is subject to condemnation only within his own expressed limitations, he proceeded without hesitancy, in expectation of doing so with impunity. I consider that Galileo may be justifiably excused for reproaching those things not to Tycho, and as a matter of great importance affecting the trustworthiness of Tycho's doctrines, but rather to his own adversary Sarsi, of whom Galileo complains; it seems to him that Sarsi allowed his own understanding to remain in bondage to that of others, as for example to the works of Tycho. Sarsi not unreasonably rejects this charge of servility as well as that condemnation which has been advanced against Tycho's book. Galileo's praise of Chiaramonti, the opponent of Tycho, page 24, was uttered, I believe, upon the first report of the published Anti-Tycho. Unless I am mistaken, Galileo will regret this praise when he has ascertained how badly the matter was handled by Chiaramonti.* 2. Sarsi, page 20, assumes that Mars becomes nearer to the earth than the sun itself, as demonstrated by Tycho; that is, he maintains something common to Tycho and to Copernicus, that the course of Mars is arranged eccentrically around the body of the sun. But fifteen years ago in my Commentaries on the Motion of Mars,3 I revealed a certain mistake which had been thrust upon Tycho by his calculators when he desired them to compute {p. 187) the parallax of Mars from observations; but they, departing from Tycho's wishes, computed it from a Copernican diagram. For this task, it is said, a manuscript was employed in which the parallax of the sun was assumed as demonstrated with the greatest certainty to be 3', and therefore the parallax of Mars was placed at about 6'. But from those same observations which Tycho had proposed, I computed the parallax of Mars at opposition to be not more than 2'; nevertheless the situation is not altered, and from a parallax of 2' the planet Mars becomes nearer than the sun itself, since the greatest parallax of the latter does not extend so far as 3' as was formerly believed.

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In the consideration of the eclipses of the moon, frequently either no parallax or a parallax of only 1' is produced, while at other times the parallax is enormous, according to the conditions of the shadow, physical circumstances, the terrestrial atmosphere, and the ethereal substance diffused about the sun. The variation greatly confuses the very subtle calculations of the distance of the sun from the centre of the earth and its parallaxes, as I testified in the Epitome ofAstronomy published three years ago.4 However, if anyone seeks very carefully into the method which Ptolemy employed for establishing the distance of the sun, he will very greatly praise the singular ingenuity of the demonstration; but he will pronounce those things which Ptolemy accepted as very suspect, as if provided for the purpose of demonstrating that which Ptolemy had taken from the ancients.5 T o balance this condemnation, from the observation of solar eclipses I have extracted the parallax of the sun, and this, although it satisfies many eclipses, is not greater than 1'. I confirm the altitude of the sun as a little less than triple what was formerly believed, and I confirm this, I say, by original arguments which at least completely satisfy me although I do not know if they will satisfy others. Thus a solar parallax of 3', granted too heedlessly by the ancients and accepted by Tycho, has through powerful considerations been reduced by me to 1'. However, the parallax of Mars in Cancer at opposition to the sun was observed by Brahe to be about 2' and thus greater than the solar parallax. When these things have been posited, it follows that the course of Mars is arranged around the sun, and Sarsi took this from Tycho's hypothesis. (p. 188) In turn, if anyone for other reasons accepts the hypothesis of Tycho, or even of Copernicus, in this matter, from the 2' parallax of Mars at opposition, he will demonstrate the parallax of the sun to be not greater than 1'. I used this kind of argument in the Epitome· and elsewhere. When these things have thus been deduced, the parallax of the sun is rather more from hypothesis than hypothesis from parallax; nevertheless, I believe that Galileo does not desire to deny this result of our skill. When the abominable Orcus deprived Orpheus of his Eurydice and thrust upon him other Thracian girls, Orpheus in hatred of the entire sex is said to have cried out even

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against Eurydice, by no means deliberately but overwhelmed by the bitterness of grief. 3. On page 25, Galileo establishes the following comparison of hypotheses. For Ptolemy and Copernicus the system of the world is a whole, constructed and brought to completion with the greatest artifice; Galileo does not consider Tycho's system to be of this sort. No reason is given for this, and propriety forbids that I recommend Tycho's hypothesis in particular to Galileo, for my opinion in this matter is apparent to him as well as to others. However, because this comparison which Galileo has published may seem to hinder others from enjoying the fruit of Tycho's hypothesis despite the weightiness of his reasoning, these matters ought to be examined a little more carefully. First, if Galileo desires integrity in the system, he will be unable to deny under questioning that the system of the world according to Tycho is also a whole. The immobile earth is at the center, and around it the moon, sun, and the sphere of fixed stars, separated from one another by such intervals that between the sun and the fixed stars the remaining five planets are able to preserve the same arrangement and proportion in their orbits as exist among them according to Copernicus; that is, the three superior moving in very wide circles always enclose that region in which the earth and the sun are located, and the two inferior planets pass between the earth and the sun in more constricted circles, cutting off the former from the latter. The transference of motions is an analogy to the aforesaid orbits. Thus the integrity of the Tychonic system is deducible from the Ptolemaic and Copernican. {p. 189) As concerns those imaginary spheres, the ninth and tenth, and if we are to consider every foolishness, the eleventh,7 Tycho on the example of Copernicus leaves them to Ptolemy. Nevertheless, Tycho hoped that a place might be found for their inclusion in the system already described which would be in accordance with observations. And just as in a house there may be a place for a clock, so the system of Tycho ought not be considered incomplete with the ninth and tenth spheres lacking any more than a house should be considered incomplete for lack of a clock. But Galileo might say that this has not yet been accomplished by

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Tycho and that it is this of which he was speaking in the words written above; that even if it were done now, the argument would fall back either upon those supernumerary orbits of the Ptolemaics or upon certain motions of the earth assigned by Copernicus. Perhaps, I say. But what if the representation of those effects is unnecessary ? What if the discussion of such observations among the ancients was meaningless ? What if the system of Tycho as described above is not defective but rather those of Copernicus and the Ptolemaics which retain these minutiae are extravagant ? But let us put aside this aspect of astronomy in which everything that Galileo desires to have supplied may be demonstrated as superfluous; as long as Tycho or some other genuine astronomer does not explain these things fully, so long will others remain unconvinced of those things which have been presented by Galileo. 4. Let us turn to another part of the comparison. Galileo recognizes the greatest ingenuity in Ptolemy and Copernicus. If you ask whether one is equal to the other, he will deny it and give greater support to Copernicus than to Ptolemy. But parts of the Tychonic system were gathered from the Ptolemaic, which is not of the greatest ingenuity, and parts from the Copernican, which is; nor is Galileo opposed to the Ptolemaic system because of its possession of inferior parts, and therefore he should be less opposed to the Tychonic since it draws somewhat more from the completeness of the Copernican. 5. But Tycho has not yet brought his system to completion; that is, as I understand it, he has not yet applied numbers and calculation to the orbits. This is no reason why the Tychonic system should be less acceptable, (p. 190) For, as is demonstrated in my Commentary on Mars,6 all the Ptolemaic and Copernican numbers, as well as mine, can be applied to all three systems, insofar as they are general systems, with freedom left to us equally to change the details of the orbits and their sizes, or in accordance with geometry even to transfer orbits for physical reasons. 6. Therefore, if Galileo pronounces Tycho's system as no system, page 26, because there is nothing in it which is not, in fact either from Ptolemy9 or from Copernicus, I cannot deny this. For even if

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Tycho ought to be believed completely when he affirms that he had developed his hypotheses not from consideration of the Copernican system but through his own efforts, yet there is no reason why each should not, in fact, agree with the other. Let Copernicus be our example of this. Who will deny that his system, making the earth mobile among the planets, was discovered by Copernicus entirely unaware of the conception of Aristarchus ? 10 Yet the supposition of each was exactly the same, as can be proved from Archimedes, Plutarch, and Aristotle himself who refuted it. 11 This harmony and agreement of the two men, separated from one another by so many centuries, is not the result of a great and persuasive argument between them which brought about agreement. Thus, just as the system of Tycho is nothing, so that of Copernicus is nothing; indeed, Copernicus has less of his own to boast about than does Tycho, since the whole system which Copernicus offers is solely from Aristarchus while Tycho has composed his from individual parts of the different systems of Ptolemy and of Copernicus. 7. In the same place, Galileo denies that the Ptolemaic hypothesis could be refuted by Tycho, Copernicus, or others, and says that it was refuted only by Galileo through the use of the telescope for observation of the variation of the discs of Mars and Venus, the latter being forty times and the former sixty times larger at perigee than at apogee; for it is in this way that the arrangement of their orbits around the sun is proved. Nothing is more valuable than that observation of yours, Galileo; (p. 191) nothing is more advantageous for the advancement of astronomy. Yet, with your indulgence, if I may state what I believe, it seems to me that you would be well advised to collect those thoughts of yours that go wandering from the course of reason and memory in that vastness of many interrelated things. This observation of yours that those planets circle around the sun does not refute the very distinguished system of Ptolemy nor add to it. Indeed, this observation of yours refutes not the Ptolemaic system but rather, I say, it refutes the traditions of the Ptolemaics regarding the least difference of planetary diameters, traditions resulting from observation with the naked eye, upon which Maestlin 12 in his

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Epitome and, if I am not mistaken, Regiomontanus left their marks. Your own observation of the discs confirms the proportion for the eccentric to the epicycle in Ptolemy, as it does the orbit of the sun in Tycho or of the orbis magnus in Copernicus; finally, the circuit [of Venus] around the sun, which is common to Tycho and Copernicus, is confirmed not by your observation of the sizes of the diameters, but by that other observation which elsewhere you freely communicated to us, of the phases of Venus rivaling those of the moon.18 And that phase of Venus attenuates such an appearance of breadth, but Mars in opposition to the sun displays his full diameter to us and does not have any gradual diminution of phases whereby he would fail to appear sixty times greater to the naked eye than in conjunction. Thus an excuse was found in phase for that tradition of the Ptolemaics regarding Venus, but such was not found for Mars. However, in both instances, this excuse is sufficient; that the ancients were unaware of the use of the telescope. I believe that attention ought to be called to those things, Galileo, not as if you who have taught them to us were unaware of them, or as if you were unable to make the effort without my assistance, but that the reader of your book may either employ me as a guide in grasping securely what it is that you desire in the passage mentioned, or that he may decide to await your statement if he considers me less trustworthy. Nevertheless, you may congratulate yourself on having Tycho himself as your companion in such reveries in that passage mentioned by you which I considered first in this appendix. 8. On page 26, Galileo adds that he does not believe that the favor {p. 192) and assistance which come to philosophers from a supernatural light—that is, to see the error of following Copernicus —can be obtained from Tycho's reasoning or experience. Here, I cannot be a witness for Galileo, and I consider that through a narrow fissure a little of that supernatural light has shone upon Tycho himself and turned his eyes from the very bright star of the Copernican system to his own system, that is, to that one constructed from the Copernican and the Ptolemaic. Galileo himself provides evidence of this regarding Tycho for those who prefer to follow Ptolemy's hypothesis, but for those who have somewhat firmer eyesight [than

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theirs] the rest of the stars do not immediately vanish at the rising of the sun, especially if they will look separately at the sun and at those stars, whatever may be their region and their zone. 9. On pages 33-34, Galileo remarks regarding Sarsi, that when the latter has discarded Aristotle he inclines to Kepler's conjecture to the effect that the comet may be a reflection. Galileo speaks obscurely of my conjecture; nevertheless his phrase 'that may be' is lenient. In the Optics twenty years ago, I taught how to make a representation of a comet against a wall. 14 This is done through a simple reflection from a glass globe, either solid or filled with water, against a white wall in a closed room, so that with the light of the sun shining through a single, very narrow opening, part of the ray strikes the wall and part is intercepted by the outer margin of the glass object. This manual experiment was then proposed by me, but it was not applied to true comets themselves seen in the sky. But if anyone wishes to apply this, then he must set up in the open spaces of the universe some real object which has the nature of a glass globe and something else to take the place of the wall. For reflection alone would not form a comet. 10. In the same book, I discussed the motion of the comets, 15 and in another place the formation not of a comet but of its tail; 16 mention of this passage was also made in the Hyperaspistes, II, xxxi. 17 Concerning this passage, I usually distinguish first between reflection and refraction, both of which are commonly called reflexion (reflexio). And first, little is seen through reflection; but in that passage in the Optics mentioned by me, the tail of a true comet (p. 193) is represented as formed through the refracted rays of the sun in the transparent head of the comet. This is correctly called a conjecture by Galileo, nor did I propose it there under another name; indeed, I immediately abolished it when my opinion was turned to that which is truer. For I considered that if the tail of the comet were formed through such refraction, it would be necessary that the material behind the head of the comet be very dense and the rest, like a nebula, should be either the upper air or aether since the sun's rays do not adhere in pure and dry aether but become invisible there. However, material of this sort was extremely unsuitable for

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representing as well the bending and curvature of the tail, and it results from these arguments that this conjecture of mine is mine no longer, but exposed at its birth it has been shunned by me, and I have adopted a contrary view which I now both acknowledge and present as mine. It establishes the comets themselves—as well as the beards, hair or rays, and bodies—according to the degree of their density or rarity, differing among themselves and differing from the very pure substance of the aether. The head is like a conglobate nebula and somewhat transparent; the train or beard is an effluvium from the head, expelled through the rays of the sun into the opposed zone, and in its continued effusion the head is finally exhausted and consumed, so that the tail represents the death of the head.18 11. On page 35, and in reference to the words of Sarsi, 19 another passage from my Optics,80 regarding the true motion of the comet, is examined. Therefore, let Sarsi's words be in turn examined by me. Sarsi: Although Kepler sought to explain that motion of the comet by straight lines, yet he saw in what kinds of difficulties he was involved. Kepler: That conception of a straight path occurred before the numbers were tried. I was cautious in my choice of words since I was placing myself intentionally in the snares of this proposition, yet so that I might also extricate myself. I did not see, but I feared, the difficulties of establishing uniform motion along a straight line. Sarsi: Therefore he considered this motion to be not perpendicular to the earth, but transverse. Kepler: Not because a straight course would present certain difficulties in comparison to a circular one, but because it was objected in advance that the comet's motion is maintained throughout its course (p. 194) and its course leads away from the earth. Among the reasons why I attributed a straight course to the motion of the comet was this. It was formerly held that the comet did not proceed from the earth but was carried beyond the earth, approaching through one zone and receding from the earth into another. Sarsi: Therefore, he did not desire uniform motion of passage. Kepler: I said that this was not because I foresaw difficulties, but because I feared them; and that I might have at hand those increases

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and decreases—arranged in order—by which, if required, I might free myself from difficulties. But I had less fear of difficulties regarding the comets of the years 1472, 1577, 1580, 1585, 1590, 1607, and 16x8 than I had at that time when I published the Optics and the little book On the New Star.21 Sarsi: He desired the motion to be slower at the beginning and end, and swiftest in the middle. Kepler: At that time, this was not because of certain geometrical demonstrations from observations of the comet, but from mere contemplation of a meteor or those artificial fires which we Germans call rockets. For at the beginning when the flame has not yet fully developed, these are retarded and put themselves into motion slowly, and at the end of their duration they again become feeble. We observe similar things also in falling stars, especially in the autumn when some ofthat feebleness, usually toward the end [of their fall], can be examined optically. Now that we have considered the aforesaid comets, I find as yet no strong reason for establishing this straight motion as slower at each end, and so I leave this non-uniformity of motion in doubt. Sarsi: Furthermore, he believed that this straight motion ought to be supported by the circular motion of the earth itself. Kepler: This is as if one were to say the same regarding Tycho's circular motion—that he believed that it ought to be supported by the daily motion of the whole [celestial] machine. It is not false but improper to speak of covering a guest with a bolster and then in addition by the roof of the house, for he who receives a guest has shortly before received him under his roof. Thus I have assigned space in the Copernican system for the passage of the comet along a straight line, but in that system, because of the comet, the ship (p. 195) which carries the observer of the comet also travels with a circular motion. Do you see what I mean, Sarsi ? Sarsi: So that this might explain all the phenomena of comets. Kepler: To be sure, I believe this: that the reason for certain appearances in the latitude of the comet cannot be rendered from the position of simple, circular motion in one and the same plane, but is able to be rendered from the former, posited motion of the

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spectator, commonly affecting all stars even if no new origins are placed along the straight course. And you know the law of philosophizing alone approved by Plato:' I pursue this one on one path and many paths, following its tracks as the tracks of a god.'" Sarsi: But these things are in no way permitted to us Catholics. Kepler: Perverse and querulous at best, servile at the worst. Miserable condition of things subjected to the circumstances of the time, which tears apart those things which belong together and completely adhere. For certainly these matters were in no way forbidden to the Catholic Copernicus when he wrote to Paul III, nor to me when in the years 1604 and 1605 I wrote along the same lines. But let Perillus teach his ox to bellow.23 And unless every conjecture deceives me, the inept Aegle herself dreads the brow of Silenus which she paints with minium.24 Sarsi: Therefore I decided that that opinion, which may not be held piously and sacredly, ought to be given no consideration. Kepler: I am pleased that I may rightfully consider as of no significance that which I hold as of no significance. There is no reason, Sarsi, why you may not enjoy that dislocation under Tycho's system if there seems to be elegance in a straight passage for the comet. For, despite your objection, a straight passage from the earth was supported by me, and Tycho will support it equally firmly by systematic motion of the accompanying passage. He would seize upon the straight passage even if oak and triple brass were girdled about his breast25 for believing such things. See the conclusion of the Hyperaspistes, and II, xx, 21. 24 Nevertheless, it seems fair for Galileo to ask on page 37 that you destroy what you believe should be considered of no significance, so that such propositions which have been declared to oppose the Sacred Scripture may be demonstrated as impossible and false, and if possible also by natural reasons. 12. I return to Galileo who on page 36 attributed equivocation, as he calls it, to Tycho (p. 196) for holding that progress under a great circle and progress along a straight course are the same thing. I doubt if I quite understand what the fault is. There was no necessity for Tycho to say that all things which advance in a straight course

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are seen from all places on the earth under the same great circle. This would certainly be false with regard to those things which had such motion close to the earth. Nor did Tycho mean that those things which seem to advance under a great circle are truly moved by circular motion. This, he said, requires no rigorous demonstration, and he believed the conjecture to be at least probable, as well as the converse. See I, iv.27 13. On page [s 87-] 88, Tycho is adduced as subscribing to Hagek who argues from the purity of light to a celestial condition of brightness.28 However much we are of the opinion that the light of the comet's body is its own, this is merely a laudable conjecture. But if it is revealed that the light is nothing but reflected brightness, then whatever was gained through that argument, the sun makes itself the primary source of all reflected brightness. Tycho does not busy himself with the same ends as Galileo, and so Tycho gets the brunt of it, page 90, while Galileo and Sarsi, struggling with one another, would [each] compel Tycho to adapt himself to a hair. 14. On page 1 1 1 , Galileo rejects Tycho's argument that there are no celestial orbs with definite surfaces because there are no refractions of the stars, except perhaps only very slight ones near the horizon. Rays reach the earth perpendicular to the spheres, says Galileo, and perpendicular rays are not refracted. But oh, Galileo, if there are orbs, it is necessary that they be eccentric. Therefore, no rays perpendicular to the spheres reach to the earth except at apogee and perigee. Hence, Tycho's argument is a strong one, if you are willing to listen, you who deny these solid orbs on page 129. 15. First, on pages 122 and 123, there seems to be a passage of Galileo against my Hyperaspistes, in which Galileo, granting to Sarsi the authority of Tycho regarding the distance of the comet, replies almost in the manner of Chiaramonti29 by saying that Tycho and other astronomers of whatever reputation differed much among themselves. But he is on the horns of a dilemma; if all the observations are correct, the comet becomes (p. 197) an empty appearance; if false, they have no authority. In determining the true place of the comet from various observations, I have chosen those by Tycho which are useful for the purpose.

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Even if the reply from the Hyperaspistes is sufficient for these exceptions, nevertheless the authority of Galileo requires that something be said to his readers. Galileo is here defending not his book but that of Guiducci, and even if that does contain many of Galileo's conclusions, yet Guiducci presented and considered them according to his own judgment. Now what else may Galileo, his defender, do than to follow in the tracks of Guiducci and say those things which will be in agreement with his remarks ? Certainly so far as Galileo is concerned, he, if anyone, is a skilled contributor of geometrical demonstrations and he knows how genuine money differs from counterfeit,30 and what a difference there is between the incredible observational diligence of Tycho and the indolence common to many others in this most difficult of all activities. Therefore, it is incredible that he would criticize as false the observations of all mathematicians in such a way that even those of Tycho would be included. But if not all of them are false, I fail to see who may be considered by Galileo as more important than Tycho. Nor will he say that if many men's observations are incorrect, then those of all men are, and that therefore those of Tycho have no authority. If we regard Tycho as an individual, he is one of many, and therefore his authority will be somewhat blemished because of the prevalence of error; but if his authority has developed over a long time on the basis of his behavior and the circumstances of his whole training, who will be so confident as to wish to pit any of the other mathematicians against Tycho ? Tycho did not base his teaching regarding the celestial location of comets upon the observations of other men, but at the same time he refrained from criticizing others; and he chose their observations only on the basis of agreement with his own and appraised them by the same tokens by which he distinguished his own from the indiscriminate observations of others. When these things have been considered, I hope that the readers will judge that Galileo in his argument did not attack his adversary Sarsi in such a way as to exhibit himself as very envious of Tycho's authority {p. 198) and to desire or hope to be able to defraud Tycho of that authority. 16. On page 129, 81 again according to Sarsi, Galileo timidly whispers in his ear I do not know what little deception regarding the

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motion of the earth, but to the effect that, this having been admitted and the solid orbits overthrown, straight motion need not be ascribed to the comet. Ο unworthy suggestion if false; yet Galileo is suspected of giving heed to clandestine opinion, and, if these whispers were scarcely audible, nevertheless Sarsi's ears were wide open. Ο truly timid trickster if he decided to offer to Sarsi as the truth that which is adaptable to belief; finally, a crafty one who foresaw that those things which are discordant would grate on the ears so that he spoke them in a lowered voice. On page 137, 3 2 you might consider that Sarsi is among the watchdogs set to guard the gates of truth and that he is very desirous and cautious that it be protected from injury. Your agitation is unnecessary, Sarsi; if the motion of the earth is displeasing to anyone, let him adjust this appearance so that when eccentric orbits have been marked out for all the planets, the comets may also advance with a straight impulse. Therefore, in its place, you may add to the straight motion of the comet that real motion of its accompaniments offered by Tycho whom you follow here, just as the same real motion is considered to be adjusted to the circular motion of the planets; if you approve Tycho's system, there is no necessity within the limits of that system to take away the straight motion of the comet and to assign it circular motion. You see this point to be made frequently in my Hyperaspistes in regard to the three comets, in II, xx, 21, and xxv, 2 33 —and you can do the same in regard to all of them. 17. On pages 139 and 140, 34 that same comet of Regiomontanus regarding which I wrote much, III, xvii, page 332, 3 6 is misused by Sarsi. I see that Sarsi has read in the original neither the whole description by Regiomontanus nor the views of Ziegler. I see those same errors which Cruger acknowledged and rejected, as if Pontanus wrote of a different comet than that of Regiomontanus. In addition, Sarsi adds that the comet was swift at the end, which cannot be refuted from the ambiguous words of the poem, unless it is compared with the prose of Pontanus, and Sarsi argues incorrectly from these ambiguous words. 18. Just as I noted above that Tycho had received blows from both Sarsi and Galileo {p. 199) in the contest between them, so the

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same must be said of me on pages 141 and 143 of Galileo's book; I am dragged between the mutually opposed factions of detraction and defense: nay more, constituted as arbiter, I was ordered to give my opinion, but with the common fate of arbiters I satisfied neither party. Sarsi wrote that when Tycho from some optical reason considered that the tail of the comet of 1577 had appeared curved, I first made mention of what I know about refraction;3® indeed, I denied that the curvature could occur through parallax, nor could it occur through bare and simple refraction of the sun's rays on the body of the comet, by which the tail is imagined to be formed. The refracted [rays] can be represented by a curved appearance only if one determines that after the first reflection of the rays is made in the head many other refractions may occur behind the head in the ethereal substance in the same region where the curvature occurs, and that the refraction may even increase throughout the continuous extent of space, so that with every increment beyond the head of the comet the substance of the aether is always condensed more and more. But this presumption cannot be squared with the laws of optics, nor can it be understood how that which is a surface is not a surface— a surface because bent to the rays going forth from the head, which it has the power to refract; not a surface because continuous throughout itself as the result of densening, and not separated. For these reasons, I say, such refraction as the effect which is required for curving the tail, as the monstrous portent of a chimera, is shattered. Galileo promptly understood the words of my supposition and declared that it must be rejected; Sarsi also immediately stated that it ought to be rejected by me. Nevertheless, I did not decide that the question ought to be left unsettled, and upon the first opportunity, that is, in a little book on the comets of the years 1607 and 1618, I said clearly what I believed about the formation and the curvature of the tail.®7 No less positively Galileo says that these words of mine ought not be applied to that particular refraction which occurs in our atmosphere; I have never given consideration to this manner of curvature although it may be very true and was well known to Tycho from another effect. For it is thus that the arc of each diurnal circle of a star is curved for us so that even though the star moves on the

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equator itself, yet {p. 200) its descending or ascending line appears curved on the horizon if the star remains wholly visible through some space of its altitude. Nevertheless, it must be added that each seeks his own advantage in the contention between the two, while the point is not clear to me since I have not seen Guiducci's book; certainly, that curvature will be extremely slight; indeed, by it the head and the extremity of the tail do not bend more than a half degree from the whole length of the line of the tail. The bend is always upward toward the zenith and does not exist except when the head is very near the horizon, nor is this curvature ever a half degree except when almost the entire tail has been projected on the plane of the horizon in such a way that at the rising and setting of the head the end of the tail does not achieve an altitude of 20°. If one considers the brevity of the occurrence, he will understandably doubt whether that refraction of the rays in our air achieves anything in respect to the curvature of the comet's tail, which curvature is usually very broad, very marked, and also very unchanging at different hours of the day. Certainly this was not the cause of the curvature of that southern comet of the year 1618, so notable that that which occupied the farthest [southerly] regions was, for this reason, compared to a Persian scimitar. 19. Furthermore, the reader's attention may be turned to another thing of which I was advised by that recent little book of Wilhelm Schickardt, 38 mentioned in the Hyperaspistes, III, xviii, 18. I admit that I was not entirely correct in denying that those things which are straight may appear in the sky as curved without refraction, whether or not they show parallax. When I wrote this, I had in mind projections of visible things upon a surface, and my denial had reference to graphic or observable examples which, having whatsoever variety of straight relationship of their borders, likewise always dispose traces of that straightness in a straight line on the surface of a picture. But our vision has no surface like that of a painting on which it may look at the picture of the hemisphere {p. 201) but only that surface of the sky above in which it sees comets, and it imagines a sphere by the natural instinct of vision. But if a picture of things is

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355

extended in straight lines into a concave sphere, and if our vision is in the center of this, the traces of those things will not be straight lines but, by Hercules, curved ones; that is, great circles of the sphere, as is taught regarding the projection of circles in the astrolabe. I say that we must grant this curvature of the tail of the comet, which is curvature in arcs of great circles. But remember, on the other hand, that there is no question among astronomers about this latter curvature as that which corresponds to the straightness of a string extended against the celestial appearance; but we are speaking of that curvature which exceeds the limits of the arc of a great circle and which we note by its disagreement with the applied string. In this regard, it is true, as I wrote in the Opticsf* that those things which are truly straight cannot be bent by any parallax into this sort of curvature, (p. 202) These, therefore, are the passages which I met with while reading Galileo's book and to which I had to give consideration either on behalf of Tycho or of myself. I look very favorably upon the rest of the book, and, just as it has been recommended to many for the extraordinary care of its calculations and experiments, so it finds praise and favor among students of philosophy.

NOTES

NOTES TO INTRODUCTION 1 Dialogo . . . sopra i due massimi sistemi del mondo, Tolomaico e Copernicano (Florence, 1632). English translation by Thomas Salusbury in Mathematical Collections and Translations (London, 1661); revised version edited by G. de Santillana in Dialogue on the Great World Systems (Chicago, 1953); new translation by S. Drake, Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican (Berkeley, 1953). The last-named is hereafter referred to as Dialogue. 2 Giordano Bruno, born at Nola in 1548, was burned at the stake for heresy in Rome on February 17, 1600; he was an enthusiastic supporter of Copernicus and an uncompromising foe of authority. * Le operazioni del compasso geometrico, e militare (Padua, 1606). 4 Usus et fabrica circini cuiusdam proportionis . . . opera & studio Balthesaris Caprae (Padua, 1607). 5 Difesa contra alle calunnie et imposture di Baldessar Capra (Venice, 1607). 6 Sidereus nuncius magna, longeque admirabilia spectacula pandens ... (Venice, 1610). English translation by E. S. Carlos, The Sidereal Messenger (London, 1880); by S. Drake, 'The Starry Messenger' in Discoveries and Opinions of Galileo (New York, 1957), pp. 21-58. Herein cited as Discoveries. 7 The chief printed attacks were by Martin Horky and Francesco Sizzi; another which remained unpublished was written by Lodovico delle Colombe. 8 Galileo's official Court appointment was as chief mathematician and philosopher of the Grand Duke; since a question has been raised whether it is proper to apply the adjective 'chief to each office separately, it may be pointed out that the legal authorities who reviewed the appointment in 1629 clearly considered that this was intended. Le Opere di Galileo Galilei (Edizione Nazionale [ist ed.; Florence, 1890-1909]) X I X , 487. Hereafter referred to as Opere, the second edition (Florence, 1929-39) being so designated when cited. * Discorso ... intorno alle cose che stanno in su I'acqua, 0 che in quella si muovono (Florence, 1612). English translation by T. Salusbury (London, 1663), op. cit., tome ii (London, 1665). 10 The opponents, all of whom dedicated their books to members of the ruling family at Florence, included three who were officially connected with the University of Pisa. u Istoria e dimostrazioni intorno alle macchie solan (Rome, 1613). English translation, abridged, in Discoveries, pp. 86-144. 19 Cardinal Orsini (1593-1626) inadvertently precipitated the decision against Copernicus by speaking too warmly in favor of Galileo's position to Pope Paul V, who decided there and then to call for an official ruling and who probably influenced personally its unfavorable outcome. " Scheiner (1573-1650) became an implacable foe of Galileo after publication of The Assayer, and there is reason to regard him as the probable prime mover in Galileo's final trial and condemnation. His role in the discovery of sunspots is described in Discoveries, pp. 81-83. 14 Dated 11 July, 1618 (Opere, X I I , 397-98). N*

360 "Ibid.,

NOTES 413·

" Galileo suffered from a very severe arthritic condition that confined hiin to bed periodically for many years; he had also a serious double hernia that required the wearing of a heavy iron truss. 17 See, for example, his remarks in connection with the writing of the sunspot letters (Opere, V , 94-95; Discoveries, p. 90) and the Letter to Christina (Ο fere, V , 310; Discoveries, p. 176). 18 Amici e Corrispondenti di Galileo Galilei, XXXVII, Mario Guiducci, in Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, L X X V , ii, pp. 1368-70 (Venice, 1916). Favaro's conclusions are further supported by the results of later documentary discoveries by Professor Pietro Pagnini (Opere [2nd ed.], vi, 667 ff.). " T y c h o Brahe (1546-1601) had made extensive observations of the great comet of 1577, as a result of which he ascribed to comets circular orbits about the sun in the vicinity of Venus. Galileo was antipathetic to all of T y c h o ' s work, perhaps because T y c h o ' s planetary system offered a convenient alternative to the Ptolemaic and Copernican systems for those who, like the Jesuits, were too well informed to adopt the former and were forbidden to support the latter. Opere, X I I , 466. Ibid., 499. 22 Ibid., 489. 23 Ibid., 484. 1 4 Favaro raised the question whether Galileo might not also have had a part in composing this letter, as he had had in writing the Discourse (Opere, V I , 6). T h i s seems very unlikely, partly because of notable differences in vocabulary and style, and partly because Galileo intended from the beginning to reply himself to Grassi even though he was slow in preparing his answer. T h e additional Guiducci documents uncovered by Pietro Pagnini do not settle this point finally, however. 20 21

85 A t the risk of dwelling too long here on the apparently mere physical characteristics of this book, it may be pointed out that they afford grounds for some deductions concerning Galileo's true feelings about a rival claimant to the invention of the telescope. Galileo sent copies of his lengthy errata sheet to R o m e for'use there, but Stigliani asserted most of the additional errors to be trivial. In compromise, a second issue of the book was run off with the final page reset in smaller type, allowing the inclusion of 136 errata on the verso. T h i s second issue appeared without the preliminary poems in praise of Galileo, which are alsoTfound to have'been deliberately removed from many copies of the firstTissue.jOne'is led to suspect that Galileo was much annoyed by the recognition given injthe'firstjof these poems to the claimsjof G . B. Porta (15351615), a senior colleague of Galileo in the Lincean Academy, of priority in the matter of the telescope. Although no written evidence supports the idea, it is probable that'Galileo suggested the omission of these poems in their entirety (to avoid giving offense'to either author) in order to get rid of this tribute to Porta in his own book. It would have been rather unusualjfor anyone in Rome to take the liberty of deleting this material without Galileo's authority.

*· Opere, X I I I , 202-3.

NOTES

361

" Opere, VI, 380-81. " Abrege des observations sur le Comete de 1680, p. rsxi (cited by Lalande, Abrege tfAstronomie [Paris, 1774], p. 398). 2 ' Mathematical Principles of Natural Philosophy, tr. Α. Motte (London, 1729), II, 360; ed. Cajori (Berkeley, 1934), p. 521. 30 Dialogue, 334, 339. »l Ibid., 35. " Ibid., 207. ** See reference source for note 8, above. li Joannis Kepleri Opera Omnia, ed. Ch. Frisch (Frankfort, 1858-71). 15 See Drake reference for note 6, above.

NOTES TO THE DISPUTATION 1

The ensuing references to advances in astronomy, which had been made principally by Tycho, Galileo, and Kepler, include: (1) the introduction of the telescope, removing much of the strain of observation, revealing new portions of the heavens, and showing the moon to be mountainous; (2) the identification of the relative placements of the orbits of Mercury and Venus, which had been disputed for ages; (3) the discovery of sunspots; (4) the analysis of Mars' orbit, on which see further under note 1 1 to the Discourse; (5) the discovery of four satellites of Jupiter; and (6) observations of Saturn which had led Galileo to believe that planet to have two large satellites. 1 Grassi's initial reference to the Linceans seems sincerely'complimentary, and devoid of the sarcasm that he later employed (cf. p. 7 1 , 1 . 21). 8 The ancients, classifying comets according to their shapes, had given them a variety of names. Respecting xiphiae, Grassi cited a passage in Pliny (Naturalis Historia, ii, 25): . . pointed like a sword, very pale throughout, and without any rays.' 4 In the classical cosmology, the primum mobile was a fanciful crystalline sphere lying beyond the seven planetary spheres and that of the fixed stars; it was supposed to impart the diurnal rotation to all heavenly bodies. See further under note 7 to the Hyperaspistes. 5 The word 'beam' had a variety of uses, among which was the appearance of the tail of a comet when the head was too close to the sun to be observed; cf. Newton, The System of the World, ed. Cajori (Berkeley, 1934), pp. 601-2. But the same word was applied to the zodiacal light and to other phenomena of similar appearance, and even to the aurora borealis. The ambiguity of the term leads to considerable confusion among the early writers; cf., for example, Seneca, Quaestiones Naturales, I, 15, iv; VII, 4; VII, 5 (English translation by John Clarke under the title Physical Science in the Time of Nero [London, 1910]). * Lucifer was the ancient name for the morning star. It is applied here to the comet because this first made its appearance in the eastern sky before sunrise. 7 The moon was supposed to be embedded in a solid transparent sphere which revolved about the earth, within which were contained the elemental materials

362

NOTES

(earth, air, water, and fire); beyond the sphere of the moon lay the cclestial substance or aither. See also Discourse, p. 53, and note 23 thereto. 9 Tycho was particularly renowned for the construction of massive and accurate astronomical instruments which enabled him to make observations of extraordinary accuracy; it has been remarked that he achieved a precision which it is impossible to surpass without the use of lenses. • This was a part of Aristotle's theory, later set forth in more detail in the Discourse·, cf. pp. 29 and 34. 10 And hence was not a kind of fire. 11 Ad Vitellionem paralipomena quibus astronomiae pars optica traditur . . . (Frankfort, 1604), p. 267 (ed. Frisch, I I , 297 η.). On the point in question, see Kepler's reply, §18. 18 By here introducing the concept of a great circle, Grassi seems to imply a circular motion for the comet about the earth. In that case, Guiducci and Galileo would be wrong in accusing him of adhering blindly to Tycho's system (pp. 36), for Tycho placed comets in orbits about the sun; cf. pp. 52, 195. 13 T h e previous sentence referred to the frontispiece figure near the center at the bottom, while the discussion which ensues refers to the large figure at the right. Here the eye is supposed to be situated at the center of a celestial sphere of radius Ο Ρ which is projected upon a plane that touches it at Ν directly overhead. T h e argument that the positions of the comet represent a straight line on this plane—and that therefore the comet moved along a great circle—would be valid if the comet were presumed to move among the fixed stars or in some concentric sphere; cf. note 12, above. 14 Gnomices libri octo, in quibus non solum horologiorum solarium sei aliarum quoque rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometrice demonstrantur (Rome, 1583) has been called the most comprehensive treatise on dialling ever compiled. 16 Aeneid, i, 405. 18 Horace, Carmina, I, i, 36.

NOTES TO THE DISCOURSE 1

Christopher Scheiner; see Introduction, p. xii. T h e views of these ancient writers are outlined by Aristotle, Meteorologica, i, 6. A detailed account of opinions concerning comets in antiquity will be found in Hellman, The Comet of 1577: Its Place in the History of Science (New York, 1944), pp. 1 3 ff. Aristotle mentions the following authors: Anaxagoras of Clazomenae (in Asia Minor), born about 500 B.C. He lived for many years at Athens, where he was finally accused of impiety for teaching that the sun was a hot stone and the moon an inhabited globe—the very charges leveled by Meletus against Socrates (cf. Plato, Apology, 26). Though defended by Pericles himself, he was convicted and imprisoned. Afterward, he migrated to Lampsacus, where he died in 428 B.C. Democritus of Abdera, born 459 B.C., the most learned man of his age and 2

NOTES

363

founder of the atomistic philosophy. Aristotle violently opposed his views, which Galileo revived in The Assayer to the irritation of his Peripatetic opponents (pp. 310 ff.). Hippocrates of Chios, in no way connected with his near contemporary Hippocrates of Cos, the Father of Medicine. Born 460 B.C., this geometer is said by Aristotle to have been cheated out of a fortune because of his simplicity in practical matters. Aeschylus (not the dramatist, but a pupil of Hippocrates), born about 435 B.C. ' It had long been debated whether or not comets ever broke into parts at their disappearance. Seneca ridiculed Ephorus for asserting that they did (jQuaes. Nat., VII, 16). Kepler accepted the possibility after observing the great comet of 1618 (De cometis [Augsburg, 1619], bk. i, ch. i; ed. Frisch, VII, pp. 76-^77). In recent times, the phenomenon has often been observed, notably in Biela's comet in 1846. This, however, throws no light upon their nature or origin, as the ancients supposed it would. 4 Galileo employs the word chioma for the tail of a comet. With but one or two exceptions, this has been translated 'curl', as distinguished from Aristotle's word 'beard' and Kepler's modern term, 'tail'. 5 Meteor., i, viii, 346b, 1-3. * Quaes. Nat., VII, 23, 3-4. Seneca believed comets to be among nature's permanent creations (VII, 22), and though he did not see any reason to suppose that a given comet ever returned, he seems to recognize the possibility of orbits too vast to have permitted such returns to have been observed. 7 In connection with this remark, it is essential to recall that all the great astronomers from the earliest Greeks to the time of Kepler had taken it as an axiom that motions of the heavenly bodies must be explained in terms of uniform rotation in perfectly circular paths. The superposition of circle upon circle in the form of epicycles (circular paths whose centers lay upon the circumferences of other circular paths) had enabled astronomers to account for planetary motions within the requirements of this axiom. Guiducci's objection was therefore quite valid under any of the prevailing systems—Ptolemaic, Tychonic, or Copernican, excluding of course Kepler's modifications of the latter. But Kepler's elliptical orbits had not gained any followers at this time, and not even their inventor had attempted to apply this notion of non-circular paths to comets. See further, Balance, p. 75, and note 9 thereto. 8 This appears to be a reference to Aristotle's remark that the Milky Way, being capable of reflection at night in water, cannot itself be a reflection (Meteor., i, viii, 345b, 27 ff.). * Haloes are pale or weakly colored circles sometimes seen around the moon, the sun, or a bright star, caused by refraction in tiny ice particles suspended high in the air. Mock suns or parhelia, which have a similar cause, are bright patches resembling the sun in shape and brilliance, occur always in pairs spaced symmetrically beside the sun, and are seen only when the latter is close to the horizon. ' R o d s ' seems to refer to those displaced parhelia which may appear when the sun is somewhat higher, and which have the shape of vertical flames. Aristotle discusses such phenomena in Meteor., bk. iii, chs. ii, iii, and vi. Ν

364 10

NOTES

As these debates contain many references to exhalations and vapors, it should be noted that Aristotle distinguished between the two in the following words: 'Vapor is naturally moist and cold, and exhalation hot and dry; and vapor is potentially like water, exhalation like fire.' (Meteor., i, iii, 27 ff., trans. H. D. P. Lee [Harvard University Press, 1952]). 11 Tycho's observation that Mars is sometimes closer to the earth than the sun is, and at other times farther away, had demolished the then prevalent form of the Ptolemaic system in which the various heavenly bodies were supposed to be embedded in solid spheres of crystal. The existence of such physically solid spheres had become a dogma of the Peripatetics. 11 De caelo, ii, 7, 289a.; Meteor., i, iii, 341a, 19 if. 11 Meteor., i, vii, 344a, 16 ff. The imputation is not quite fair to Aristotle; although he requires moderation in the 'fiery principle' in this case, he also specifies 'fuel of a suitable quality.' 14 Meteor., i, ix, 346b, 3 1 : 'The exhalation from water is vapor'; cf. note 10, above. 14 Meteor., i, vii, 344b, 19 ff. 1β Cf. Disputation, note 12. 17 Meteor., i, vi, 343a, 8 ff. 18 Galileo's name for the four satellites of Jupiter which he discovered, conferred on them in honor of the ruling house of Tuscany. 18 Here it would appear that Galileo misinterpreted or misrepresented as a further enlargement the creation of an image slightly out of focus. 20 Cf. note 1 1 above. 21 De tnundi aetherei recentioribus phaenominis (Uraniborg, 1588), II, 8, p. 194 (ed. Dreyer, IV, Part I, p. 162). 22 The words in square brackets have been inserted by the translator. Galileo is here concerned solely with the device employed by Tycho to account for the elongation of the comet of 1577, giving it an orbit similar to that of Venus and slightly larger. Galileo is correct in asserting that for a comet (or other heavenly body) having a maximum elongation of precisely 90° this could not be done without involving the catastrophe he describes. But he is not right in suggesting that the same reasoning would hold for the comet of 1618-19, which achieved a still greater elongation and then vanished. 23 This distinction was vital to the Peripatetic philosophers, and was a favorite target for Galileo's sarcasm; see, for example, the Dialogue, pp. 37, 42, 47. 69· 21 Aristotle had attributed the aurora to condensation and ignition of the air (Meteor., i, v); Galileo's conjecture was a step forward, though still far from correct explanation. 25 Cf. note 5 to the Disputation. 28 That is, the sun's annual course through the zodiac. 27 Quaes. Nat., VII, 31. The concept of suspended judgment coupled with faith in the progress of science was most alien to the spirit of the schools. 28 De mundi aetherei, p. 181 (ed. Dreyer, p. 150). 28 Vitellio, Optica, iiii, 3 1 ; Alhazen, Opticae Thesaurus, ii, 28 (pp. 132 and 44 respectively in Risner's edition of 1572, which is cited by Tycho). Tycho also

NOTES

365

cites in this connection Johannis Pisani Angli (John Peckham, 1240 ?~92), Perspectiva communis (Tr. I, Prop. 69 in Hartmann's edition [Nürnberg, 1542]). Vitellio (Witelo) was a thirteenth-century Polish mathematician who resided principally in Italy. Alhazen, upon whose work Vitellio wrote a commentary, was a leading Arab mathematician and astronomer of the eleventh century. Galileo should have perceived (and very likely did) that if this argument had any merit there would be a very great distortion of the alignment of stars in a constellation as it passed from horizon to zenith and back. " De mundi aetherei, pp. 164 ff. (ed. Dreyer, pp. 139 ff.). " Euripides, Fragment 969 (ed. Nauck). " Dante, Divina Commedia, Purg., c. 28, 81, in which for obvious reasons Guiducci has substituted 'our' for 'your'.

NOTES TO THE BALANCE I On June 29, 1619, Galileo had sent similar letters to Cardinal Maffeo Barberini at Rome and Cardinal Federigo Borromeo at Milan which read in part:' The comet recently seen has tempted many persons to compose discourses about it, which effect it had also on me. But during the entire time that it was visible, I remained ill in bed, and a gentleman of this city, Sig. Mario Guiducci, a man of great culture, thought to honor me by making a discourse concerning it which he delivered publicly at the Academy and later sent to be printed. And because the kindness of your illustrious Reverence to me has frequently evinced your liking for things of mine—even though of slight merit—I did not wish to neglect to send you a copy. I take occasion at the same time to remind you that I am your humble servant, reverently kissing your hem and praying God that the greatest felicity shall be yours.' (Opere, XII, 461-62.) * Discourse, p. 50. * Discourse, p. 35. 4 Meteor., i, vi, 342b, 36 ff. 5 Jerome Cardan (1501-76), an erratic genius who wrote copiously on mathematics, astrology, and medicine. Cardan discussed comets in his De subtili täte, bk. 4, and in De rerum varietate, bk. 1, ch. 1 and bk. 14, chs. 69-^70. * Bernardino Telesio (1509-88) was an anti-Aristotelian philosopher who argued in favor of reliance upon the senses as the source of all certain evidence. His books, placed on the Index soon after his death, included one which dealt with comets: De cometis et circulo lacteo. 7 Ad Vitellionem paralipomena, p. 335 (ed. Frisch, II, 339-40.) * Cf. Discourse, p. 53. * Here Grassi was momentarily closer to the truth than Galileo. The concept of non-circular orbits, suggested by Tycho for comets, was however developed properly only by Kepler for planets, and in application to the heliocentric system which Grassi abhorred. 1 0 Tartarus (Hades) was supposed to be located at the earth's center. II Discourse, p. 42.

366

NOTES

" Disputation, p. 17. 11 This is an echo of the first attacks launched against the validity of Galileo's early telescopic discoveries. 14 Grassi here misinterprets what had been said in the Sidereus Nuncius. Compare Galileo's comments, p. 228; but see also note 19 to The Assayer. 15 That is, by the telescope argument just presented. 18 Disputation, p. 17. " De mundi aetherei, pp. 321-22 (ed. Dreyer, p. 262). Thaddeus Hagek (15251600), a professor of mathematics and later the imperial physician at Prague, was a careful observer and an open-minded astronomer who at first believed the comet of 1577 to be sublunar, but was subsequently convinced by Tycho that it was not. 18 Cf. Discourse, pp. 53-57. 19 It is possible that Grassi alludes to the gegenschein when he speaks of a 'gleaming white cloud' which hung 'almost over the zenith.' He does not appear to mean literally a cloud, but some recurring phenomenon which was best seen in summer and late at night. The nature of the gegenschein is still not entirely certain. Svante Arrhenius (1859-1927) considered it to be the effect of looking longitudinally through a very tenuous sort of cometary tail belonging to the earth itself. If so, then it is ironical that Grassi should have first called attention to the phenomenon in the present context. 20 Refraction is considered in Vitellio, op. cit., prs. 5 1 - 5 2 and in Alhazen, vii, 52-54; cf. note 29 to the Discourse. 21 Discourse, p. 35. 22 De mundi aetherei, p. 201 (ed. Dreyer, p. 171). 23 Cf. Discourse, p. 57; Grassi's misquotation here was castigated by Galileo in The Assayer, X X V I I I , as well as by Kepler, Appendix, §16. 24 Jovianus Pontanus (1426-1503), an eminent literary figure of the Italian Renaissance, wrote a section on comets in his poem Meteororum Liber. The pasages cited occurs at f. i3or in the Opera (Venice, 1583) and is quoted in Cardan's Commentarium in Ptolemaeum de astrorum iudiciis, bk. i, t. liv (Opera [Lyons, 1663], V, 209). See further in Hyperaspistes, §17. 25 Johannes Müller of Königsberg (1436-76), known as Regiomontanus, a celebrated German mathematician and astronomer who, in addition to numerous important original contributions, translated into Latin certain works of Ptolemy, Apollonius, and Archimedes. He suggested the utilization of parallactic observations to determine the location of comets, but did not have instruments sufficiently reliable to establish the result. (The quotation cited here occurs in Cardan, at the place mentioned in note 24, above.) 28 Cf. Hyperaspistes, §17. 27 Ad Vitellionem paralipomena, pp. 265-66 (ed. Frisch, p. 296); cf. Assayer, p. 270 and Hyperaspistes, §10. 28 Ibid., pp. 323-24 (ed. Frisch, p. 332). 2 " Cf. Discourse, pp. 29-30. 30 De caelo, ii, 4, 287a, 1 1 ff. 31 Opere, V, 230; Discoveries, p. 140. 32 Opere, V, 135; Discoveries, p. 1 1 3 .

NOTES 33

367

Cf. Discourse, p. 29. 34 The demonstration meant is identified in The Assayer, p. 286; a further description of it and its application appears in the Dialogue, pp. 398-99. " Cesarini had apparently misunderstood the purpose of the experiment exhibited by Galileo and described in the Dialogue; see previous note. 38 Cf. note 1 2 to the Discourse. 3 ' Cf. Discourse, p. 32. 38 Quaes. Nat., ii, 57. " Metamor., ii, 727-29. 40 Pharsalia, vii, 5 1 2 - 1 3 . 41 De rerum natura, vi, 178-^79. " Ibid., 306-«. 43 Thebaid, τ, 533. 44 Aeneid, ν, 525-27. "Ibid., ix, 585-88. 48 Achilleid, ii, 420-22. 47 Suidas was a Greek lexicographer who flourished in the latter half of the tenth century. 48 jQuaes. Nat., ii, 54. «Ibid., ii, 58. »Ibid., ü, 57· 51 Homero Tortora, Historia di Francia . . . sotto Francesco II, etc. (Venice, 1618), bk. 16. 51a This passage in parentheses is omitted in Favaro's edition. " The phenomenon of cemetery flames was not uncommon at the time. They were caused by spontaneous combustion of phosphine accumulating from decomposing bodies buried without caskets. 53 Cf. Meteor., i, iv, 341b, 19 ff. " Cf. Discourse, p. 34. 66 Cf. Discourse, p. 47. 56 Cf. Opere, III, Part 1, pp. 73, 96; Discoveries, pp. 39, 58. Of this supposed lunar vapor and an analogous atmosphere of the planets, Galileo never wrote further, though in the latter of the passages cited above he promised to do so in his book on the system of the world. But when the Dialogue finally appeared it contained instead an implied denial of any lunar vapors; see Opere, V I I , 126; Dialogue, p. 100. " Cf. Discourse, p. 48. 88 This is a potent argument which Galileo was obliged partly to grant and partly to evade; cf. Assayer, p. 326. The light of a star reaches us as a luminous point to which the telescope, especially if imperfect, may give the appearance of a disk. This is not a magnification, but merely the result of failure to focus in a precise point. T o the extent that this affects a larger area of the retina, the effects o f ' irradiation' and twinkling are reduced; there are also numerous other factors involved, both physical and physiological, of which Galileo was quite unaware. " Cf. Discourse, p. 35. 80 Daniel 3:92 in the Challoner-Douay text; cf. King James version, 3:25.

368

NOTES

11

Cf. Discourse, pp. 35-36. 41 Meteor., i, vii, 344b, 19 ff. " Cf. Discourse, p. 48.

NOTES TO THE L E T T E R 1

Quotations from the Discourse and the Balance are frequently reworded by Guiducci in the Letter, and have therefore been translated anew. 1 Cf. Discourse, pp. 23—24. 2 'Who is equal in sculpture and painting, divine Michelangelo, beyond any mortal.' (Ariosto, Orlando Furioso, c. 2, 33.) 4 Sacrobosco (John Holywood) was of English birth. Little is known of him beyond the fact that he taught at the University of Paris in the first half of the thirteenth century. His elementary treatise on astronomy, The Sphere, went through countless editions and was widely used as a text until late in the seventeenth century. An English translation has been published, with commentaries, by Lynn Thorndike (Chicago, 1949). 5 The Dialogues of Plato, tr. Jowett (Oxford, 1892), II, 449-50. • Cf. Discourse, pp. 49-50. The precise words are not repeated here, at least so far as the printed edition is concerned. 7 Daniel 3:49-50 in the Challoner-Douay text; these passages are omitted from the King James version.

NOTES TO THE ASSAYER 1 Maffeo Barberini (1568-1644) was elected to the papacy in August of 1623 and received the tiara on September 29. The relation of these events to the appearance of The Assayer has been mentioned in the Introduction. 2 See note 25 to the Introduction. The original is in verse form. 3 Simon Mayr, or Marius (1570-1624), was a pupil of Tycho and Kepler at Prague before going to Padua in 1601 to study medicine. In 1605, he returned to Guntzenhausen to become court mathematician. Galileo was amply justified in attacking his pretended invention of the compass and discovery of Jupiter's satellites. The book mentioned here is his Mundus Jovialis anno 1609 detectus ope perspicilli belgici . . . (Nürnberg, 1614), of which an English translation by A. O. Prickard was published in Observatory, Nos. 504-7 (Sept.-Dec. 1916). * In the Difesa of 1607, there is a suggestion that Galileo at that time suspected Mayr of being the true culprit. Cf. Opere, II, 519. 1 This statement is as erroneous as the assertion by Mayr which Galileo is engaged in criticizing. Galileo's mistaken belief that the satellites moved in (or parallel to) the ecliptic may have originated in the coincidence mentioned below, p. 167, when he describes the position of Jupiter and its satellites during the second quarter of the year 1 6 1 1 .

NOTES

369

•Dante, Divina Commedia, Purg., c. 9, 1 1 : 5-6. The traditional cure for scorpion stings mentioned below is from Pliny, Nat. Hist., xxix, 29. 7 Galileo's suggestion is that the words, ut esset saltern aliquis qui Galilaei disputationem . . . [paulo] diligentius expenderet should be replaced by ut esset qui saltern aliqua in Galilaei disputatione paulo diligentius expenderet. • On December 9, 1619, sending a copy of the Balance to Galileo, his friend Giovanni Ciampoli had written: 'Father Grassi deals with you much more leniently than would many of the other Fathers, among whom the word "annihilate" is quite common.' (Opere, XII, 499.) * Opera, ed. Dreyer, IV, Part 1, p. 107. The ensuing criticism of Tycho is quite gratuitous; see Kepler's remarks on pp. 339-340. Tycho had stated quite clearly that his analysis was approximate only, and that the star D was assumed to be near A's zenith. But Galileo seldom neglected an opportunity to ridicule Tycho. 10 Scipio Chiaramonti (1565-1652) was a particularly stubborn defender of the old astronomy, and an opponent of both Tycho and Copernicus. At this period he taught mathematics at Perugia, later becoming professor of philosophy at Pisa. Galileo's attitude toward him altered completely in later years— just as Kepler predicted (cf. p. 340). See Dialogue, pp. 280 ff. 11 Barthole of Sassoferrata (1313-56) was the most famous jurist of the dialectical school, noted for his Resolutiones Bartoli in which the knottiest questions are solved with majestic finality. 11 Disputation, p. 1 1 . " Here it must be recalled that Galileo was considering only the notion of Tycho that comets, like the planet Venus, went round the sun but not the earth; cf. note 22 to the Discourse. 14 Ecclesiastes 1 : 1 5 m the Challoner-Douay version. (The King James version renders this passage quite differently: 'That which is wanting cannot be numbered.') 15 Cf. Discourse, p. 41. " The game referred to here is primiera, a lineal ancestor of draw poker. The deck was stripped of eights, nines, and tens, and four cards were dealt to each player. Four cards of one suit constituted flussi ('flush'), the only hand which could beat cinquantecinque (fifty-five); this consisted of die three highest cards in any suit. 17 Ariosto, Orlando Furioso, c. xi, 37-38. 'Catch a whale' is the literal rendering of Galileo's phrase, but what Orlando did with the anchor was to wedge open the sea-monster's mouth in order to enter and kill it. 19 This is a jibe at Aristotle, who believed that twinkling was dependent upon distance; cf. De caelo, ii, 8, 290a, 18 ff. 19 Opere, III, Part 1, p. 75 (Discoveries, p. 47). Galileo, though literally correct, is quibbling. Grassi doubtless referred to a statement of Galileo's in the' Continuation of the Sidereus Nuncius,' published by Kepler in his Dioptrice; Opere (2nd ed.), III, Part 2, p. 922; The Sidereal Messenger (London, 1880), p. 109. 80 That is, ignes fatui. 81 Cf. Discourse, p. 40. " Ibid., p. 57.

370

NOTES

28

Another direct attack on Aristotle; cf. Meteor., i, iii, 340b, 36 ff. In reading this passage, Grassi made the plausible error of supposing that Galileo referred to the circular shape of the head of a comet, and so treated the point in his Ratio Ponderum. Galileo, commenting upon this in a marginal note in his copy, asserts that he meant the comet as a whole, though the term 'symmetry' seems scarcely to fit this idea (Opere, V I , 425). 24

85

The material enclosed in brackets is that which was inserted by Stigliani; see Introduction, p. xix. It is curious that Galileo did not mention this in the extended list of errata prepared by him, though he noted it in the margins of some copies of the book. 84 See p. 92 of the Balance. 27 Discourse, p. 40, but cf. p. 37 28 Orlando Furioso, c. xi, 7. 28 Orbis magnus was the term applied by Copernicus to the earth's orbit, equivalent to the path of the sun about the earth in the Ptolemaic system. He called this orbit' great,' not in reference to its size, but to its role in explaining the planetary appearances. 80 Ad Vitellionem paralipomena, ch. 6, sec. 13 (ed. Frisch, p. 296). 81 At that time, Galileo was but thirteen years of age. 82 The phrase ad hominem as used here refers not to the fallacy commonly known by that name, but to the fact that the argument is to be directed only against views known to be held by a particular opponent (or group of opponents), so that its conclusiveness will be limited in application to those who hold such views. 33 Orlando Furioso, c. xxiii, 81. 34 The Danaides were the daughters of King Belus who, in punishment for murdering their husbands at his command, were condemned to draw water perpetually in sieves. 86 The reference is to the rotation of a bowl containing a lighted candle; see p. 288, and compare the Letter, p. 145. 88 Boiardo, Orlando Innamorato, I I I , vi, 50, 3-5. 87 Cf. Meteor., i, iii, 341a, 19 fF.: ' W e see that motion can rarefy and inflame air, so that, for example, objects in motion are often found to melt.' Grassi is on strong ground in this argument, however, for Aristotle (in De caelo, ii, 7, 289a, 1 9 fif.) definitely introduces the role of friction in the production of warmth. 88

Orlando Furioso, c. xxx, 49. Turpin was Archbishop of Rheims toward the close of the ninth century. Ariosto occasionally introduced him into his romantic poetry as though to lend verisimilitude to his tale, but the manner of his doing so was such as to justify this sarcasm of Galileo. 39 The ensuing discussion has been noted by historians of philosophy as an anticipation of the principles later developed by John Locke into the empiricist philosophy, which has been closely associated with the rise of experimental science. 40 This speculation by Galileo is very striking in the light of modern physics. It should be noted that his 'truly indivisible atoms' correspond not to what are today called atoms, but to the supposed ultimate constituent particles of matter.

NOTES

371

Our 'atoms' correspond rather to Galileo's minimi quanti of a few lines previously. The conjecture that light might originate from a truly ultimate subdivision of matter has deen dramatically vindicated by nuclearfission.As to the instantaneous propagation of light, Galileo later abandoned this idea and suggested an experiment for determining the velocity of light; see Opere, VIII, 87-89 (English translation by Crew and de Salvio, Two New Sciences, pp. +2-44). 11 The words in square brackets have been inserted by the translator as essential to the sense, but they do not occur in the original text or in any of the contemporary lists of corrections to it. " Galileo had learned by bitter experience that he should not attempt to expound the theory of scriptural interpretation.

NOTES TO THE APPENDIX 1

All page numbers in the text refer to the original pagination of The Assayer. The passage of the Hyperaspistes here mentioned is further explained below

(§0. 2

Kepler's prediction was borne out by subsequent events. A few years later, Galileo wrote very critically of the Anti-Tycho (Dialogue, pp. 52, 57), and condemned Chiaramonti severely for another book; see further under note 29, below. * Astronomia nova . . . de mottbus stellae Mortis (Prague, 1609), ch. 11 (ed. Frisch, III, 219). The incident was one of great importance in the history of astronomy and is described in several places by Kepler. In the chapter cited he says, in part: When in the year 1582 Mars was in Cancer, in opposition to the sun, the observations (as I found) were carried out with unusual precision; in Tycho's handwriting one might find written out an ' Investigation of the parallax of M a r s b u t from this only a very small or nonexistent parallax could be calculated Since Brahe had assured the learned world that from his proceedings in that year he would give a parallax for Mars and that it would be appreciably greater than that of the sun, I looked through the whole book with the greatest care in order to be better grounded in his observations and procedures. I found indeed the [above] title which announced the proceedings for the determination of the parallax of Mars from observations of that year. But how unexpected was what I found next I For [his assistants] had taken the observed places of Mars in conjunction with a very carefully prepared Copernican diagram. They had gone to a great deal of trouble to solve all the triangles formed by the introduction of double epicycles on the concenter, carrying these out to several places; at length they had concluded their calculations, and decided that the parallax of Mars had been actually far greater than that of the sun. These assistants had solved a very different problem from the one Brahe had given them. He wanted them to determine the parallax of Mars from a comparison of the observations taken morning and evening, but they had sought to determine what parallax would follow from the Copernican diagram. Whether Brahe spoke of this parallax only from reliance upon his helpers, I do not know.' (The final remark applies to Tycho's Progymnasmata, Part 1, pp. 414, 661.) Among the many benefits to astronomy which resulted from Kepler's detection of this lapse and his recalculation of the data was a considerable improvement

372

NOTES

on the ancient underestimation of the distance of the sun, on which see further under note 5, below. 4 Epitome astronomiae Copernicanae . .. (Linz, 1620), bk. 4, Part 1 (ed. Frisch, VII, 327). s Ptolemy, Almagest, bk. 5, ch. 15. Ptolemy's determination placed the sun at a distance of 1,210 terrestrial radii, scarcely more than one-twentieth its true distance from the earth, in agreement with the estimate made by Hipparchus in the second century B.C. Copernicus re-examined the assumptions in Ptolemy's calculation but failed to improve upon the result; indeed, he made it slightly more deficient (De revolutionibus orbium coelestium, Book 4, ch. 19). It was Kepler who made the first substantial correction, based upon an estimate of parallax, though even he fell short of the correct distance by a factor of six. • For instance, in the Epitome, bk. 4, Part 1, iv, and bk. 6, Part 5, viii (ed· Frisch, VI, 326, 508). 7 In the ancient cosmology, eight spheres had sufficed; one for each of the 'planets' (moon, Mercury, Venus, sun, Mars, Jupiter and Saturn) and one for the fixed stars. Medieval astronomers put the primutn mobile (note 4 to the Disputation) in the ninth position. Still later, the fancied discovery of a variation in precession ('trepidation') inspired still another sphere, moving the primutn mobile out to the tenth place in the schemes of some astronomers. Finally, an erroneous belief about a variation in the obliquity of the ecliptic induced some astronomers to bring the total to eleven. Cf. De revolutionibus, bk 1, ch. 1 1 , last paragraph; also bk. 3, ch. 1. 8 Astronomia nova, chs. 1-6, especially ch. 6. "Here the original edition incorrectly reads 'Tycho' (corrected by Frisch). 10 Aristarchus (ca. 300-230 B.c.) is reported to have described a heliocentric theory in a book which is now lost. It is known (on the authority of Archimedes) that he placed the sun immovable in the center of the heavens and made the earth revolve about it; very probably he gave a similar treatment for the several planets. 11 This passage is somewhat misleading, as it was not Aristarchus who was refuted by Aristotle (which would have been anachronistic), but certain Pythagoreans; cf. De caelo, ii, 13. Copernicus and Kepler attributed to the latter a heliocentric system, but the 'central fire' about which the Pythagoreans in question had attributed a revolution of the earth was not the sun. 12 Michael Maestlin (1550-1631) was professor of mathematics at Heidelberg and later at Tübingen. He was Kepler's teacher and lifelong friend, but had a poor opinion of Galileo. The work referred to here is his Epitome Astronomica (Heidelberg, 1582). 13 Galileo's discovery of the phases of Venus confirmed his Copernican views and had great propaganda value in favor of that system. Copernicus himself had been much troubled by the apparent absence of the phenomenon, and, though he tentatively cited the suggestion of others that Venus might be translucent {De revolutionibus, Book 1, ch. 10), he gave no explanation of his own. Actual existence of the phases was disclosed by the telescope, and Galileo first announced this discovery in an anagram which much puzzled Kepler until it was

NOTES

373

explained by Galileo; hence the ironical reference here to Galileo's 'free' disclosure. 14 Ad Vitellionem paralipomena, p. 267 (ed. Frisch, II, 297 η.). " Ibid., p. 235 (ed. Frisch, pp. 339-40). 14 Ibid., pp. 265-66 (ed. Frisch, p. 296). 17 Ed. Frisch, VII, 235. 1 8 Here Kepler sets forth a remarkably prescient conjecture about the cause of cometary tails and the reason for the eventual extinction of a comet, though he supposed a comet to become exhausted of material in this way during a single appearance rather than over a period of many returns. 1 9 The passage cited occurs in the Balance, p. 75. 1 0 Cf. note 15, above. 11 De Stella nova in pede Serpentarii (Prague, 1606). " T h e reference here has not been identified. Perillos made for the tyrant Phalaris a brazen bull in which criminals were to be executed by roasting alive. It was provided with acoustic tubes which would cause the cries of the victim to sound like the roaring of a bull. Phalaris proceeded to test the invention by roasting the inventor in it. 1 4 See Virgil, Bucolics, Ec. vi, 13-20. " Horace, Carmina, I, iii, 40. ** Hyperaspistes (ed. Frisch, p. 221): ' B u t even if I cannot demonstrate the line of the course of the comet unless supported by my position, I might gain knowledge of it from certain documents. Nevertheless I can easily transpose into the Tychonic hypothesis that which has already been revealed. And, in so far as it is fitting, I shall do so at present. In this way, because I have undertaken to defend Tycho in this place, I may appear to have also increased the number of his arguments by the addition of one that is my own, so that up to a certain point the Tychonian arguments may be seen through his hypothesis.' Hyperaspistes (ed. Frisch, p. 269): ' N o w I declare that unless Chianunonti henceforth displays himself to be better informed in our science there will be no need for me to publish any book in defense if he undertakes to attack Tycho or to attack me and the mathematical books I have published. Even, so to speak, if Jove himself were to take up his thunderbolt and menace m e , . . . the hypotheses which I follow will fully satisfy astronomers, equivalences having been demonstrated in my Commentaries on Mars, strengthened in my Harmonics [Harmonices Mundi, 1619], and employed in the present booklet. These mathematicians seek some red rag which they may wave at that blundering bull so that in testing its strength against this it may lose out on the splendid and untouched fruits of that knowledge. M a y this be an amulet against hovering plagues of that kind, and an antidote for them if they invade at any point.' 27 Apparently a misprint in the original; the reference seems to be to Hyperaspistes, ii, iv, and especially to sec. 21 (ed. Frisch, p. 173), in which Tycho's position is explained at length. 28 T h e passage intended may be found in the Balance at p. 87 in this edition. (It occurs in The Assayer on pp. 87-88 in the original edition as quoted from the Balance.)

374

NOTES

" One of the favorite devices of Chiaramonti was to attack the data of astronomers as inaccurate because they were never in exact agreement. On this pretext, he would throw out all the observations which did not suit his purposes. He employed this method of argument again in his De tribus novis stellis (Cesena, 162$) to the exasperation of Galileo, who finally took him to task for it; see the Dialogue, beginning of the ' Third Day.' 30 Cf. Horace, Εpp. I, vii, 23. 31 The passage was quoted from Sarsi on p. 129 of The Assayer; see p. 98. 32 P. 101. 33 Cf. note 26 above. In the second passage cited in the text, Kepler asserts that the cornels of 1585 and 1590 followed straight paths; in the latter case the path was nearly parallel to the orbit of the sun and hence the comet appeared to follow a great circle. 31 Pp. 102-103. 35 That is, Hyperaspistes, iii, 17 (ed. Frisch, VII, 249-57). 3 · Ad Vitelltonem paralipomena, pp. 264 ff. (ed. Frisch, pp. 295-96). 37 De cometis libelli tres (Augsburg, 1619) bk. 2 (ed. Frisch, V I I , 110): ' I t is evident, then, that the tails of comets are curved. But it is impossible that the rays of the sun be curved in free aether. For in [our] Optics we teach that the rays of luminous things are not arcs, but straight lines. Therefore, since it is nonetheless evident that the tail of the comet is formed by the sun's rays, it is reasonable that the material which the sun's rays drive out from the body of the comet is present in the tails or beards of comets. And when the material flux has been located, the curvature of the tail in various directions away from the straight line opposed to the sun may be derived.' 36 Wilhelm Schickhardt, Liechtkugel... ein Teutsche Optica (Tübingen, 1624). Schickhardt asserts that the curvature of the tail is merely an optical effect and not a real property, arguing that all lines, even perfectly straight ones, which do not pass through the axis of the eye, must appear somewhat bent. He adduces the instance of a very long corridor in the center of which the observer stands; at either end the walls, ceiling, and floor appear to him to converge. Yet the walls form no angles at the points directly opposite him; therefore, so far as appearance is concerned, they must be very gradually bent. 39 Ad Vitellionem paralipomena, p. 265 (ed. Frisch, II, p. 296); also ch. 9, sec. 6 (ed. Frisch, p. 332).

INDEX

INDEX Notes are indexed by number in italics, preceded by letters indicating the work to which the notes apply: I, Introduction; DN, Disputation·, DS, Discourse; B, Balance; L, Letter; A, Assayer; H, Appendix to Hyperaspistes. Acestis 118 adhesion io8ff, 276, 278, 281-84, 290 Aeneas 17 Aeschylus 24, 28, 73, DS 2 Albertus Magnus 157 Alhazen 58, 90, DS 29, Β 20 America 31 Anaxagoras 24, 25, 73, 74, DS 2 Andrea del Sarto 140 Apelles xviii, 24,139; see also Scheiner Archimedes 157, 163, 213, 344, Β 25, Η ίο Archytas 213 Ariosto 299, L 3, A 17,38 Aristarchus 344, Η ίο, 11 Aristotle: on comet theories, 26, 28-29, 73,258, DN 9; other theories, 115,121, 279, 290-91, 335, A 18, 37; opposed, 29-35. 173. 187. A 23; supported, 105-7, 131; mentioned, 24, 25, 30, 33, 69, 74, 89, 117, 127, 129, 130,159, 173, 190, 192, 297, 305, 306, 332, DS 2, 8, 9,10,13, 24, Η Ii Arrhenius, Svante Β 19 arrows, heating of 31, 117-18, 297-99 astrology 10, 183 atomism xi, xxv, DS 2 aurora borealis 54, 88, 233, 237-38, 250, 259. 273, DN 5 authority and evidence 121, 298, 300-1, 306-8 Babylonians 119,301,306 Baliani, G. B. xv Barberini, Maffeo xix, Β ι, A 1; see also Urban VIII Bartoli (Barthole) 183, A 11 beam 6, 9, DN 5 Bellarmine, Robert xi Bible cited 128, 149, 199, 329 Borromeo, Federigo Β I Brahe, Tycho; see Tycho Btuno, Giordano ix, I 2

Capra, Baldessar χ Cardan, Jerome 74, 102, 188, Β $, 24,2$ Carlos, Ε. S. 16 Cassini^ G. D. xxiii Cato 72 celestial orbs xv, 29-30,48-49,98,106-7, 145, 186, 250, 2768; DN 4, 7, DS 11, Η 7; denied, 53, 75, 350 cemetery flames 121, 305, Β Cfsarini, Virginio xii-xiii, xiv, xviii, xix, i n , 151, 163, Β 35 Cesi, Federico xviii Chiaramonti, Scipio xxi, 183, 339, 340, 350, A 10, Η 2, 26, 29 Ciampoli, Giovanni A 8 Clarke, John DN 5 Qavius, Christopher xv, 16, 140 Collegio Romano xiv-xviii, 3, 36, 41, 52, 69, 71, h i , 136, 137, 138, 141-2, 150, 176-80 comet: of 1475, 102, 352; of 1577, 27, 49-50, 52, 57, 62-63, 96, 100, 181, 273, 348, 353, 1 19, DS 22, Β 17; of 1585, 100, 348, Η 33; of 1618, vii, viii, xiv, 8, DS 22; Halley's, xxii; Biela's, DS 3 comets: ancient theories of, 24-29, 3940, 73; compared with planets, 27, 49, 51, 144, 228-9; curvature of, 57-64, 103-5, 270-4, 347, 353-5; dread of, vi, 4, 5,7,68, 72; fueling of, 15-16,33-35, 122, 131, DS 13; light of, 17, 87, 228, 232; location of, 11-15, 17-18, 84-85, 135, 214; material of, 57, 86, 87-91, 190, 233, 237, 244-5, 248, 250-1, 260, 273, 346; motion of, 16, 49-52, 54-57, 74-75, 86, 97-103,145,191 ff, 231, 233, 261 ff, 346ff, I 19, DN 12, DS 6, 7, Η 33; nature of, xxi-xxiii, 231, DS 6; shapes of, 8, 255, 354, DN 3, DS 3, A 24; tails, direction of, 15, 62-64, Η i8, 3J, 38; telescopic appearance of, 17, 76-84, 135, 144; transparency of, 35, 90, 130, 329; weather affected by, 35-36, 131-2, 335

378

INDEX

C o p e m i c a n system xi, xv, xx, 7 1 , 180, 183-4, 268. 285-6, 342-5. 348-9» 352.

119, H i Copernicus, Nicholas viii, xi, xii, xiv, x v , 5 " . 7 1 , 101, 180, 183, 184, 268-9, 3 4 1 - 5 , 3 4 9 , 1 2 , 1 2 , A 1 0 , 2 9 , Η 5, ii, ij coronae 74, 9 1 , 94, 95, 255 D a n t e 172, 251, D S 33, A 6 D e m o c r i t u s xi, xxv, 24, 25, D S 2 Descartes, R e n e xxiv Dialogue vii, I 1, Β 34, 56, Η 29 earth, motion o f viii, 98, 101, 192, 262, 268-9, 285, 348, 352 Euripides 64, D S 32 experiment: o f carafe, 2 4 6 - 7 ; o f floating ball, 109, 2 8 5 - 6 ; o f hammering metal, 1 1 6 - 1 7 , 293, 295; o f ship, 289; of spinning vessels, 2 9 , 1 0 6 , 1 1 0 - 1 5 , 1 4 5 - 7 , 285, 2879·, A 35; optical, 43, 45-48, 6 1 , 124-5, 247, 326-8, 346; role of, 1 2 1 , 293-4,301-2,306-7,327,330 Faber, Johann 154 F a v a r o , Antonio xvi, xxv, I 17, 24 fire 30-35, 77, 128, 1 3 1 , 149, 205, 296, 298, 305, 3 1 2 - 1 3 , 329-31 floating bodies xi, 7 1 , 108, 163-4, 283 F l o r e n c e x , xi, xix, 22 Florentine A c a d e m y xvi, 21, 67, 70, 136, 137, 1 3 9 , 1 4 0 , 169, 176, Β ι fluid motion 2 8 i f f friction 30-32, 1 1 5 f r , 146, 291, 296,

G r e g o r y X V xix G u i d u c d , M a r i o x , x v i - x x , 68, 70, 169, 1 7 1 , 176, 179, 3 5 ' , 354, I 24, D S 7 , B i , L I H a g e k , T h a d d e u s 87, 1 8 1 , 233, 350, Β 1 7 halo o f candle 3 1 9 haloes 28, 3 7 , 74, 86, 92, 94, 123, 190, 238, 242, 2 4 5 , 2 5 2 , 257, 259, 315, D S 9 heat and m o t i o n 30-32, 7 7 , 1 1 5 - 2 2 , 132, 146, 290 fr, 308 ff, A 37 Hellman, C. Doris D S 2 H i p p a r c h u s 160 Η 5 Hippocrates o f C h i o s 2 4 , 2 8 , 7 3 , 7 4 , D S 2 H o b b e s , T h o m a s xxiv Horky, Martin I 7 illumination: b y flame, 1 2 8 - 3 0 ; by telescope, 4 1 , 7 8 - 7 9 , 2 0 6 - 1 0 ; o f air, 4 7 , 1 2 2 - 3 , 132, 239, 3 1 4 - 2 6 ; o f vapors, 5 3 54, "23, 237, 3 1 5 f r impetus, conservation o f 281 ' i n f i n i t e ' 42, 76, 144, 198-9, 206, 323 Inquisition vi, xi irradiation 44, 4 7 - 4 8 , 84-85, 1 2 2 - 7 , 228, 230, 3 1 7 - 2 6 , Β 5 «

290, 178,

135,

299,

3 ° 5 , A 37 G a l i l e o v i i - x x v p a s s i m ; 22, 2 4 , 4 1 , 45, 54, 6 9 - 1 3 2 passim; 136, 139, 1 4 1 - 2 , 146, 152-62, 339-55 passim; I 8, 12,16, 19, 24, 2S, D N i, 12, D S 4,19, 22, 23, 24, 30, Β ι , 9,13, 3S, s6, 58, A 3, s, 7, 8, 9, 10, 13, 17,19, 24, 31, 38, 40, 42, Η 2, 12, 13,29 G a l l u z z i , T a r q u i n i o xviii, xix, 133 gegenschein 88, 237, 239, Β 1 9 Grassi, Horatio viii, xv, x v i i - x x i , xxiii, 36, 52, 70, 135, 137, 138, 143, 144, 149, 1 7 3 - 8 0 passim; 197, 210, I 24, D N 12, Β 9,19, A 8,19, 24 G r e g o r i a n a , see Collegio R o m a n o G r e g o r y X I I I xv

Jacopo da P o n t o m o 140 Jesuits vii, xiii, x v - x v i i i , I 19 Jupiter 5, 42, 44, 45, 84, 97, 123, 1 6 5 - 7 , 228, 315, 3 2 1 - 6 ; satellites of, see M e d i c e a n stars K e p l e r , J o h a n n xxi, xxii, x x v , 15, 75, 103, 190, 192, 194, 2 7 0 - 2 , D N I, 11, D S 2, 4, 6, 7, Β 9, A 3, 9,10,19, Η 3, n, 12, 13, 18, 33 L e o p o l d of Austria Letter to Christina Letters on Sunspots

xii, xiii, 22, 136 117 xi, xii, 107, 164, I I I ,

17 light, origin o f 313, A 40 lightning 17, 33, 34, 1 1 9 , 296, 297, 305, 306, 308 L i n c e a n A c a d e m y xviii, 6, 7 1 , 153, 158, 183, I 25, D N j L o c k e , John xxiv, A 39 L o y o l a , Ignatius x i v L u c a n 118 Lucretius 118

INDEX Miestlin, Michael 344, Η 12 Mirs 5, io, 24,71,84,102,126,184,194, 228, 321, 323, 340-1, 343, 344, 345, DN /, DS i i , H j Miyr, Simon x, 164-5, '67-8, A 3, 4, 5 Medicean stars 42, 71, 144, 165-8, 193, DN 1, D S 18, A 3,5 melting of metal 118-20, 299, 302-7, A 37 Mercury 5,9,10, 52,53,84-85,126,185, 193,228,230, D N / Mezentius 118 Michelangelo 139, L 3 Milky Way 26, 28, 154, 201, DS 8 mock suns 28, 37, 39, 86, 92, 123, 238, 242. 245, 315, DS 9 moon: appearance near horizon, 315-17; spots on, 317; surface of, 107,154,279, DN/ motion: irregular, 50, 75, 195, 197, 203; relativity of, 31, 289 nebulae 201, 346 Newton, Isaac xxiii, D N 5 odor 293, 294, 310-11 Orlando 183, 225, 290, A 17 Orsini, Alessandro xii, 1 1 2 Ovid 118 Padua x, 164, 179, 211 Pagnini, Pietro I I J , 24 parallax 11-14, 36-39, 72-73, 85, 95-96, 103,145,181-2, i86ff, 243,257-9,353. Β 2$\ of Mars, 340, Η 3 ; of the sun, 37, 96, 257. 34'» Η 3 parhelia, see mock suns Paul III 349 Paul V ri, xix, 1 1 2 Peckham, John D S 29 pendulum 281 Peripatetics xi, xv, 28, 73, 127-8, 291, 328, DS //, 23; see also Aristotle philosophy viii-x, xxiii-xxv, 183-4, 'SBgo, 252,291, 297, 309 ff, A 39 Pisa, University of xi, xvi, 1 1 0 , A 10 Plato xxiv, 141, 250, 349, D S 2 Pliny DN 3, A 6 Plutarch 344 poetry and science 50, 72, 91, 143, 144, 185-6, 250-1, 290, 297-9 Pontanus, J. J. 102, 352, Β 24

379

Porta, G. B. della 1 5 4 , 1 2 5 Posidonius 119 Prickard, Α. Ο. A 3 primary qualities xxiv, 309-13 primum mobile 8, DN 4, Η γ Ptolemy, Ptolemaic system xv, 12,50,71, 98, 180, 274, 276, 341-6, 1 1 9 , DS 1 1 , Β 25, A 29, Η $ Pythagoreans 24,28,36,73,74,190,192, Η ii rainbows 28, 37, 39, 86, 89, 91 ff, 123, 190, 242, 244-5, 252, 255. 257, 259 Raphael 140 Ratio Ponderum xx, xxi, A 24 refraction 15, 36, 60-63, 73. 86. 89-91, 103-4, 122, 194, 244, 247, 249, 252-9, 271, 277, 280, 350, 353-4. Β 20 Regiomontanus 102, 345, 352, Β 25 religion and science xi, xx, 71, 75, 184, 192, 262, 269, 329, 345, 349, 352, A 42 rockets 304 rods 28, D S p Rome xi, xii, xiii, xix, 9, 12, 14, 70, 139, 176,178,218,234,258,285,303,125 Sacrobosco 140, L 4 Salusbury, Thomas 1 1 , 9 Santillana, G. de I / Sarsi, Lothario (pseudonym) xvii, xx, 169 ff, 339 ff; see also Grassi Saturn 5, 84, 102, 154, 228, 321, 323, DN/ Scheiner, Christopher xii, xviii, 1 1 3 ; see also Apelles Schickhardt, Wilhelm 354, Η 38 scientific method vii-viii, ix, xiv, xxv Scorpio 9, 10, 171 Seneca 26, 57, 71, 117, 119, 185, 301, DN 5, DS 2, 6 sensations 309 ff Sextus Empiricus xxiv shapes, excellence of 279 Sidereus Nuncius see Starry Messenger Socrates 141, DS 2 sound 223, 234-7, 297. 3 » specific gravity 294 Starry Messenger 84, 123, 163, 165, 167, 211, 228, 229,16, Β14 stars: invisible, 41, 198, 200, 201; shapes of, 279-80; twinkling of, 279-80 Statius 118,119,300

INDEX

38ο

Stigliani, Thomas xix, 251, I 25, A 25 Suidas 119, 301, Β 47 sunlight: between clouds, 37-39, 229; reflected on water, 38,92,240-1,253-4, 257 sunspots and faculae xi, xii, 5, 54,90-91, 107, 154, 164, 250, 251, 280

taste 310-11 telescope: discoveries

made

with,

x,

154-62, 165-8, 184, 3 4 4 - 5 , D N I , Β i s , Η / } ; invention of, 2 1 1 - 1 2 ; properties of, xv, 17, 4 0 - 4 7 , 7 6 - 8 6 , 124^7, 148-9, 198fr, 209, 214fr, 320ff,

D S 19, Β j8; mentioned, xxiii, 70, 71, 7 2 , 122, 132, 144

Telesio, Bernardino 74, 188, Β 6 Thorndike, Lynn L 4 tides xii, xx, 159 Tortora (Turtura), Homer 120,302, Β 5 / touch 310 Turpin 299, A 38 Tycho: system of, 57, 71, 100, 184-5, 340, 348, 349, I IJ», D N 12, D S 11, Η 26; theory of comets, 49-50, 52, 5 7 - 5 8 , 62, 87, 96, 144, 145, 181 ff, 186,

195, 271, 1 1 9 , D N 12, D S 22, Β 9, ιγ, A 9,13; o p p o s e d , 5 1 - 5 3 , 58-59, 6 3 - 6 4 , 144, 182, 2 5 8 ; s u p p o r t e d , 257, 3 4 0 - 5 5

passim; mentioned, xvii, xxi, xxiii, 14, 3 6 , 4 9 , 6 9 , 7 4 , 9 0 , 103, 1 4 2 - 3 , 1 7 3 , 179, 180, 183, 185, 191, 198, 248-9, 3 3 9 - 4 ° .

D N 1,8, D S 2 9 , A 3,10, Η 3 Tycho's comet see comet of 1577 Urban VIII xix, 153 Venice 211, 212 Venus (goddess) 17 Venus (planet) 5, 6, 7, 44, 45, 51, 52, 53, 62, 63, 64, 84, 8 7 , 126, 154, 184, 193, 228, 232, 258, 344, I 19, D N i , A 13, Η 1 3 ; phases of, 45, 3 2 1 - 3 , 345

Virgil 17, 118 visibility through flame 35, 127-30, 132, 149-50. 327-34 Vitellio (Witelo) 58, 90, 271, D S 29, Β 20 Weiser, Mark xii, 107; Letters to, see Letters on

Sunspots

Ziegler, Jacob 352