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diff --git a/43877-0.txt b/43877-0.txt index aac97fc..aba8725 100644 --- a/43877-0.txt +++ b/43877-0.txt @@ -1,39 +1,4 @@ -The Project Gutenberg EBook of The Life of Galileo Galilei, with -Illustrations of the Advancement , by John Elliot Drinkwater Bethune - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. 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You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org - - -Title: The Life of Galileo Galilei, with Illustrations of the Advancement of Experimental Philosophy - Life of Kepler - -Author: John Elliot Drinkwater Bethune - -Release Date: October 3, 2013 [EBook #43877] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK THE LIFE OF GALILEO GALILEI *** - - - - -Produced by David Garcia, Bryan Ness, Eleni Christofaki -and the Online Distributed Proofreading Team at -http://www.pgdp.net - - - - - - - - - -Transcriber's Note. - -Variable spelling and hyphenation have been retained. Minor punctuation -inconsistencies have been silently repaired. The author's corrections, -additions and comments have been applied in the text. Changes made by -the transcriber can be found at the end of the book. The original text -is printed in a two-column layout. Formatting and special characters are -indicated as follows: - - Letters in superscript are presented ^{like this}. - _italic_ - [Greek] - - - - -[Illustration: Galileo Galilei] - - - - - THE - LIFE - OF - GALILEO GALILEI, - WITH - ILLUSTRATIONS OF THE ADVANCEMENT - OF - EXPERIMENTAL PHILOSOPHY. - - MDCCCXXX. - - LONDON. - - - - -LIFE OF GALILEO: - -WITH ILLUSTRATIONS OF THE ADVANCEMENT OF EXPERIMENTAL PHILOSOPHY. - - - - -CHAPTER I. - - _Introduction._ - - -THE knowledge which we at present possess of the phenomena of nature and -of their connection has not by any means been regularly progressive, as -we might have expected, from the time when they first drew the attention -of mankind. Without entering into the question touching the scientific -acquirements of eastern nations at a remote period, it is certain that -some among the early Greeks were in possession of several truths, -however acquired, connected with the economy of the universe, which were -afterwards suffered to fall into neglect and oblivion. But the -philosophers of the old school appear in general to have confined -themselves at the best to observations; very few traces remain of their -having instituted _experiments_, properly so called. This putting of -nature to the torture, as Bacon calls it, has occasioned the principal -part of modern philosophical discoveries. The experimentalist may so -order his examination of nature as to vary at pleasure the circumstances -in which it is made, often to discard accidents which complicate the -general appearances, and at once to bring any theory which he may form -to a decisive test. The province of the mere observer is necessarily -limited: the power of selection among the phenomena to be presented is -in great measure denied to him, and he may consider himself fortunate if -they are such as to lead him readily to a knowledge of the laws which -they follow. - -Perhaps to this imperfection of method it may be attributed that natural -philosophy continued to be stationary, or even to decline, during a long -series of ages, until little more than two centuries ago. Within this -comparatively short period it has rapidly reached a degree of perfection -so different from its former degraded state, that we can hardly -institute any comparison between the two. Before that epoch, a few -insulated facts, such as might first happen to be noticed, often -inaccurately observed and always too hastily generalized, were found -sufficient to excite the naturalist's lively imagination; and having -once pleased his fancy with the supposed fitness of his artificial -scheme, his perverted ingenuity was thenceforward employed in forcing -the observed phenomena into an imaginary agreement with the result of -his theory; instead of taking the more rational, and it should seem, the -more obvious, method of correcting the theory by the result of his -observations, and considering the one merely as the general and -abbreviated expression of the other. But natural phenomena were not then -valued on their own account, and for the proofs which they afford of a -vast and beneficent design in the structure of the universe, so much as -for the fertile topics which the favourite mode of viewing the subject -supplied to the spirit of scholastic disputation: and it is a -humiliating reflection that mankind never reasoned so ill as when they -most professed to cultivate the art of reasoning. However specious the -objects, and alluring the announcements of this art, the then prevailing -manner of studying it curbed and corrupted all that is free and noble in -the human mind. Innumerable fallacies lurked every where among the most -generally received opinions, and crowds of dogmatic and self-sufficient -pedants fully justified the lively definition, that "logic is the art of -talking unintelligibly on things of which we are ignorant."[1] - -The error which lay at the root of the philosophy of the middle ages was -this:--from the belief that general laws and universal principles might -be discovered, of which the natural phenomena were _effects_, it was -thought that the proper order of study was, first to detect the general -_cause_, and then to pursue it into its consequences; it was considered -absurd to begin with the effect instead of the cause; whereas the real -choice lay between proceeding from particular facts to general facts, -or from general facts to particular facts; and it was under this -misrepresentation of the real question that all the sophistry lurked. As -soon as it is well understood that the general _cause_ is no other than -a single fact, common to a great number of phenomena, it is necessarily -perceived that an accurate scrutiny of these latter must precede any -safe reasoning with respect to the former. But at the time of which we -are speaking, those who adopted this order of reasoning, and who began -their inquiries by a minute and sedulous investigation of facts, were -treated with disdain, as men who degraded the lofty name of philosophy -by bestowing it upon mere mechanical operations. Among the earliest and -noblest of these was Galileo. - -It is common, especially in this country, to name Bacon as the founder -of the present school of experimental philosophy; we speak of the -Baconian or inductive method of reasoning as synonimous and convertible -terms, and we are apt to overlook what Galileo had already done before -Bacon's writings appeared. Certainly the Italian did not range over the -circle of the sciences with the supreme and searching glance of the -English philosopher, but we find in every part of his writings -philosophical maxims which do not lose by comparison with those of -Bacon; and Galileo deserves the additional praise, that he himself gave -to the world a splendid practical illustration of the value of the -principles which he constantly recommended. In support of this view of -the comparative deserts of these two celebrated men, we are able to -adduce the authority of Hume, who will be readily admitted as a -competent judge of philosophical merit, where his prejudices cannot bias -his decision. Discussing the character of Bacon, he says, "If we -consider the variety of talents displayed by this man, as a public -speaker, a man of business, a wit, a courtier, a companion, an author, a -philosopher, he is justly the object of great admiration. If we consider -him merely as an author and philosopher, the light in which we view him -at present, though very estimable, he was yet inferior to his -contemporary Galileo, perhaps even to Kepler. Bacon pointed out at a -distance the road to true philosophy: Galileo both pointed it out to -others, and made himself considerable advances in it. The Englishman was -ignorant of geometry: the Florentine revived that science, excelled in -it, and was the first that applied it, together with experiment, to -natural philosophy. The former rejected with the most positive disdain -the system of Copernicus: the latter fortified it with new proofs -derived both from reason and the senses."[2] - -If we compare them from another point of view, not so much in respect of -their intrinsic merit, as of the influence which each exercised on the -philosophy of his age, Galileo's superior talent or better fortune, in -arresting the attention of his contemporaries, seems indisputable. The -fate of the two writers is directly opposed the one to the other; -Bacon's works seem to be most studied and appreciated when his readers -have come to their perusal, imbued with knowledge and a philosophical -spirit, which, however, they have attained independently of his -assistance. The proud appeal to posterity which he uttered in his will, -"For my name and memory, I leave it to men's charitable speeches, and to -foreign nations, and the next ages," of itself indicates a consciousness -of the fact that his contemporary countrymen were but slightly affected -by his philosophical precepts. But Galileo's personal exertions changed -the general character of philosophy in Italy: at the time of his death, -his immediate pupils had obtained possession of the most celebrated -universities, and were busily engaged in practising and enforcing the -lessons which he had taught them; nor was it then easy to find there a -single student of natural philosophy who did not readily ascribe the -formation of his principles to the direct or remote influence of -Galileo's example. Unlike Bacon's, his reputation, and the value of his -writings, were higher among his contemporaries than they have since -become. This judgment perhaps awards the highest intellectual prize to -him whose disregarded services rise in estimation with the advance of -knowledge; but the praise due to superior usefulness belongs to him who -succeeded in training round him a school of imitators, and thereby -enabled his imitators to surpass himself. - -The biography of men who have devoted themselves to philosophical -pursuits seldom affords so various and striking a succession of -incidents as that of a soldier or statesman. The life of a man who is -shut up during the greater part of his time in his study or laboratory -supplies but scanty materials for personal details; and the lapse of -time rapidly removes from us the opportunities of preserving such -peculiarities as might have been worth recording. An account of it will -therefore consist chiefly in a review of his works and opinions, and of -the influence which he and they have exercised over his own and -succeeding ages. Viewed in this light, few lives can be considered more -interesting than that of Galileo; and if we compare the state in which -he found, with that in which he left, the study of nature, we shall feel -how justly an enthusiastic panegyric pronounced upon the age immediately -following him may be transferred to this earlier period. "This is the -age wherein all men's minds are in a kind of fermentation, and the -spirit of wisdom and learning begins to mount and free itself from those -drossie and terrene impediments wherewith it has been so long clogged, -and from the insipid phlegm and _caput mortuum_ of useless notions in -which it hath endured so violent and long a fixation. This is the age -wherein, methinks, philosophy comes in with a spring tide, and the -peripatetics may as well hope to stop the current of the tide, or, with -Xerxes, to fetter the ocean, as hinder the overflowing of free -philosophy. Methinks I see how all the old rubbish must be thrown away, -and the rotten buildings be overthrown and carried away, with so -powerful an inundation. These are the days that must lay a new -foundation of a more magnificent philosophy, never to be overthrown, -that will empirically and sensibly canvass the phenomena of nature, -deducing the causes of things from such originals in nature as we -observe are producible by art, and the infallible demonstration of -mechanics: and certainly this is the way, and no other, to build a true -and permanent philosophy."[3] - - -FOOTNOTES: - -[1] Ménage. - -[2] Hume's England, James I. - -[3] Power's Experimental Philosophy, 1663. - - - - -CHAPTER II. - - _Galileo's Birth--Family--Education--Observation of the - Pendulum--Pulsilogies--Hydrostatical Balance--Lecturer at Pisa._ - - -GALILEO GALILEI was born at Pisa, on the 15th day of February, 1564, of -a noble and ancient Florentine family, which, in the middle of the -fourteenth century, adopted this surname instead of Bonajuti, under -which several of their ancestors filled distinguished offices in the -Florentine state. Some misapprehension has occasionally existed, in -consequence of the identity of his proper name with that of his family; -his most correct appellation would perhaps be Galileo de' Galilei, but -the surname usually occurs as we have written it. He is most commonly -spoken of by his Christian name, agreeably to the Italian custom; just -as Sanzio, Buonarotti, Sarpi, Reni, Vecelli, are universally known by -their Christian names of Raphael, Michel Angelo, Fra Paolo, Guido, and -Titian. - -Several authors have followed Rossi in styling Galileo illegitimate, but -without having any probable grounds even when they wrote, and the -assertion has since been completely disproved by an inspection of the -registers at Pisa and Florence, in which are preserved the dates of his -birth, and of his mother's marriage, eighteen months previous to it.[4] - -His father, Vincenzo Galilei, was a man of considerable talent and -learning, with a competent knowledge of mathematics, and particularly -devoted to the theory and practice of music, on which he published -several esteemed treatises. The only one which it is at present easy to -procure--his Dialogue on ancient and modern music--exhibits proofs, not -only of a thorough acquaintance with his subject, but of a sound and -vigorous understanding applied to other topics incidentally discussed. -There is a passage in the introductory part, which becomes interesting -when considered as affording some traces of the precepts by which -Galileo was in all probability trained to reach his preeminent station -in the intellectual world. "It appears to me," says one of the speakers -in the dialogue, "that they who in proof of any assertion rely simply on -the weight of authority, without adducing any argument in support of it, -act very absurdly: I, on the contrary, wish to be allowed freely to -question and freely to answer you without any sort of adulation, as well -becomes those who are truly in search of truth." Sentiments like these -were of rare occurrence at the close of the sixteenth century, and it is -to be regretted that Vincenzo hardly lived long enough to witness his -idea of a true philosopher splendidly realized in the person of his son. -Vincenzo died at an advanced age, in 1591. His family consisted of three -sons, Galileo, Michel Angelo, and Benedetto, and the same number of -daughters, Giulia, Virginia, and Livia. After Vincenzo's death the chief -support of the family devolved upon Galileo, who seems to have assisted -them to his utmost power. In a letter to his mother, dated 1600, -relative to the intended marriage of his sister Livia with a certain -Pompeo Baldi, he agrees to the match, but recommends its temporary -postponement, as he was at that time exerting himself to furnish money -to his brother Michel Angelo, who had received the offer of an -advantageous settlement in Poland. As the sum advanced to his brother, -which prevented him from promoting his sister's marriage, did not exceed -200 crowns, it may be inferred that the family were in a somewhat -straitened condition. However he promises, as soon as his brother should -repay him, "to take measures for the young lady, since she too is bent -upon _coming out_ to prove the miseries of this world."--As Livia was at -the date of this letter in a convent, the last expression seems to -denote that she had been destined to take the veil. This proposed -marriage never took place, but Livia was afterwards married to Taddeo -Galletti: her sister Virginia married Benedetto Landucci. Galileo -mentions one of his sisters, (without naming her) as living with him in -1619 at Bellosguardo. Michel Angelo is probably the same brother of -Galileo who is mentioned by Liceti as having communicated from Germany -some observations on natural history.[5] He finally settled in the -service of the Elector of Bavaria; in what situation is not known, but -upon his death the Elector granted a pension to his family, who then -took up their abode at Munich. On the taking of that city in 1636, in -the course of the bloody thirty years' war, which was then raging -between the Austrians and Swedes, his widow and four of his children -were killed, and every thing which they possessed was either burnt or -carried away. Galileo sent for his two nephews, Alberto and a younger -brother, to Arcetri near Florence, where he was then living. These two -were then the only survivors of Michel Angelo's family; and many of -Galileo's letters about that date contain allusions to the assistance he -had been affording them. The last trace of Alberto is on his return into -Germany to the Elector, in whose service his father had died. These -details include almost every thing which is known of the rest of -Vincenzo's family. - -Galileo exhibited early symptoms of an active and intelligent mind, and -distinguished himself in his childhood by his skill in the construction -of ingenious toys and models of machinery, supplying the deficiencies of -his information from the resources of his own invention; and he -conciliated the universal good-will of his companions by the ready good -nature with which he employed himself in their service and for their -amusement. It is worthy of observation, that the boyhood of his great -follower Newton, whose genius in many respects so closely resembled his -own, was marked by a similar talent. Galileo's father was not opulent, -as has been already stated: he was burdened with a large family, and was -unable to provide expensive instructors for his son; but Galileo's own -energetic industry rapidly supplied the want of better opportunities; -and he acquired, under considerable disadvantages, the ordinary -rudiments of a classical education, and a competent knowledge of the -other branches of literature which were then usually studied. His -leisure hours were applied to music and drawing; for the former -accomplishment he inherited his father's talent, being an excellent -performer on several instruments, especially on the lute; this continued -to be a favourite recreation during the whole of his life. He was also -passionately fond of painting, and at one time he wished to make it his -profession: and his skill and judgment of pictures were highly esteemed -by the most eminent contemporary artists, who did not scruple to own -publicly their deference to young Galileo's criticism. - -When he had reached his nineteenth year, his father, becoming daily more -sensible of his superior genius, determined, although at a great -personal sacrifice, to give him the advantages of an university -education. Accordingly, in 1581, he commenced his academical studies in -the university of his native town, Pisa, his father at this time -intending that he should adopt the profession of medicine. In the -matriculation lists at Pisa, he is styled Galileo, the son of Vincenzo -Galilei, a Florentine, Scholar in Arts. His instructor was the -celebrated botanist, Andreas Cæsalpinus, who was professor of medicine -at Pisa from 1567 to 1592. Hist. Acad. Pisan.; Pisis, 1791. It is dated -5th November, 1581. Viviani, his pupil, friend, and panegyrist, declares -that, almost from the first day of his being enrolled on the lists of -the academy, he was noticed for the reluctance with which he listened to -the dogmas of the Aristotelian philosophy, then universally taught; and -he soon became obnoxious to the professors from the boldness with which -he promulgated what they styled his philosophical paradoxes. His early -habits of free inquiry were irreconcileable with the mental quietude of -his instructors, whose philosophic doubts, when they ventured to -entertain any, were speedily lulled by a quotation from Aristotle. -Galileo thought himself capable of giving the world an example of a -sounder and more original mode of thinking; he felt himself destined to -be the founder of a new school of rational and experimental philosophy. -Of this we are now securely enjoying the benefits; and it is difficult -at this time fully to appreciate the obstacles which then presented -themselves to free inquiry: but we shall see, in the course of this -narrative, how arduous their struggle was who happily effected this -important revolution. The vindictive rancour with which the partisans of -the old philosophy never ceased to assail Galileo is of itself a -sufficient proof of the prominent station which he occupied in the -contest. - -Galileo's earliest mechanical discovery, to the superficial observer -apparently an unimportant one, occurred during the period of his studies -at Pisa. His attention was one day arrested by the vibrations of a lamp -swinging from the roof of the cathedral, which, whether great or small, -seemed to recur at equal intervals. The instruments then employed for -measuring time were very imperfect: Galileo attempted to bring his -observation to the test before quitting the church, by comparing the -vibrations with the beatings of his own pulse, and his mind being then -principally employed upon his intended profession, it occurred to him, -when he had further satisfied himself of their regularity by repeated -and varied experiments, that the process he at first adopted might be -reversed, and that an instrument on this principle might be usefully -employed in ascertaining the rate of the pulse, and its variation from -day to day. He immediately carried the idea into execution, and it was -for this sole and limited purpose that the first pendulum was -constructed. Viviani tells us, that the value of the invention was -rapidly appreciated by the physicians of the day, and was in common use -in 1654, when he wrote. - -[Illustration: Instrument No. 1, No. 2, No. 3] - -Santorio, who was professor of medicine at Padua, has given -representations of four different forms of these instruments, which he -calls pulsilogies, (_pulsilogias_,) and strongly recommends to medical -practitioners.[6] These instruments seem to have been used in the -following manner: No. 1 consists merely of a weight fastened to a string -and a graduated scale. The string being gathered up into the hand till -the vibrations of the weight coincided with the beatings of the -patient's pulse, the length was ascertained from the scale, which, of -course, if great, indicated a languid, if shorter, a more lively action. -In No. 2 the improvement is introduced of connecting the scale and -string, the length of the latter is regulated by the turns of a peg at -_a_, and a bead upon the string at _b_ showed the measure. No. 3 is -still more compact, the string being shortened by winding upon an axle -at the back of the dial-plate. The construction of No. 4, which Santorio -claims as his own improvement, is not given, but it is probable that the -principal index, by its motion, shifted a weight to different distances -from the point of suspension, and that the period of vibration was -still more accurately adjusted by a smaller weight connected with the -second index. Venturi seems to have mistaken the third figure for that -of a pendulum clock, as he mentions this as one of the earliest -adaptations of Galileo's principle to that purpose;[7] but it is -obvious, from Santorio's description, that it is nothing more than a -circular scale, the index showing, by the figure to which it points, the -length of string remaining unwound upon the axis. We shall, for the -present, postpone the consideration of the invention of pendulum clocks, -and the examination of the different claims to the honour of their first -construction. - -At the time of which we are speaking, Galileo was entirely ignorant of -mathematics, the study of which was then at a low ebb, not only in -Italy, but in every part of Europe. Commandine had recently revived a -taste for the writings of Euclid and Archimedes, and Vieta Tartalea and -others had made considerable progress in algebra, Guido Ubaldi and -Benedetti had done something towards establishing the principles of -statics, which was the only part of mechanics as yet cultivated; but -with these inconsiderable exceptions the application of mathematics to -the phenomena of nature was scarcely thought of. Galileo's first -inducement to acquire a knowledge of geometry arose from his partiality -for drawing and music, and from the wish to understand their principles -and theory. His father, fearful lest he should relax his medical -studies, refused openly to encourage him in this new pursuit; but he -connived at the instruction which his son now began to receive in the -writings of Euclid, from the tuition of an intimate friend, named -Ostilio Ricci, who was one of the professors in the university. -Galileo's whole attention was soon directed to the enjoyment of the new -sensations thus communicated to him, insomuch that Vincenzo, finding his -prognostics verified, began to repent his indirect sanction, and -privately requested Ricci to invent some excuse for discontinuing his -lessons. But it was fortunately too late; the impression was made and -could not be effaced; from that time Hippocrates and Galen lay unheeded -before the young physician, and served only to conceal from his father's -sight the mathematical volumes on which the whole of his time was really -employed. His progress soon revealed the true nature of his pursuits: -Vincenzo yielded to the irresistible predilection of his son's mind, and -no longer attempted to turn him from the speculations to which his whole -existence was thenceforward abandoned. - -After mastering the elementary writers, Galileo proceeded to the study -of Archimedes, and, whilst perusing the Hydrostatics of that author, -composed his earliest work,--an Essay on the Hydrostatical Balance. In -this he explains the method probably adopted by Archimedes for the -solution of Hiero's celebrated question[8], and shows himself already -well acquainted with the true principles of specific gravities. This -essay had an immediate and important influence on young Galileo's -fortunes, for it introduced him to the approving notice of Guido Ubaldi, -then one of the most distinguished mathematicians of Italy. At his -suggestion Galileo applied himself to consider the position of the -centre of gravity in solid bodies, a choice of subject that sufficiently -showed the estimate Ubaldi had formed of his talents; for it was a -question on which Commandine had recently written, and which engaged at -that time the attention of geometricians of the highest order. Galileo -tells us himself that he discontinued these researches on meeting with -Lucas Valerio's treatise on the same subject. Ubaldi was so much struck -with the genius displayed in the essay with which Galileo furnished him, -that he introduced him to his brother, the Cardinal Del Monte: by this -latter he was mentioned to Ferdinand de' Medici, the reigning Duke of -Tuscany, as a young man of whom the highest expectations might be -entertained. By the Duke's patronage he was nominated, in 1589, to the -lectureship of mathematics at Pisa, being then in his twenty-sixth year. -His public salary was fixed at the insignificant sum of sixty crowns -annually, but he had an opportunity of greatly adding to his income by -private tuition. - - -FOOTNOTES: - -[4] Erythræus, Pinacotheca, vol. i.; Salusbury's Life of Galileo. Nelli, -Vita di Gal. Galilei. - -[5] De his quæ diu vivunt. Patavii, 1612. - -[6] Comment, in Avicennam. Venetiis, 1625. - - - - -CHAPTER III. - - _Galileo at Pisa--Aristotle--Leonardo da Vinci--Galileo becomes a - Copernican--Urstisius--Bruno--Experiments on falling - bodies--Galileo at Padua--Thermometer._ - - -NO sooner was Galileo settled in his new office than he renewed his -inquiries into the phenomena of nature with increased diligence. He -instituted a course of experiments for the purpose of putting to the -test the mechanical doctrines of Aristotle, most of which he found -unsupported even by the pretence of experience. It is to be regretted -that we do not more frequently find detailed his method of -experimenting, than occasionally in the course of his dialogues, and it -is chiefly upon the references which he makes to the results with which -the experiments furnished him, and upon the avowed and notorious -character of his philosophy, that the truth of these accounts must be -made to depend. Venturi has found several unpublished papers by Galileo -on the subject of motion, in the Grand Duke's private library at -Florence, bearing the date of 1590, in which are many of the theorems -which he afterwards developed in his Dialogues on Motion. These were not -published till fifty years afterwards, and we shall reserve an account -of their contents till we reach that period of his life. - -Galileo was by no means the first who had ventured to call in question -the authority of Aristotle in matters of science, although he was -undoubtedly the first whose opinions and writings produced a very marked -and general effect. Nizzoli, a celebrated scholar who lived in the early -part of the 16th century, had condemned Aristotle's philosophy, -especially his Physics, in very unequivocal and forcible terms, -declaring that, although there were many excellent truths in his -writings, the number was scarcely less of false, useless, and ridiculous -propositions.[9] About the time of Galileo's birth, Benedetti had -written expressly in confutation of several propositions contained in -Aristotle's mechanics, and had expounded in a clear manner some of the -doctrines of statical equilibrium.[10] Within the last forty years it -has been established that the celebrated painter Leonardo da Vinci, who -died in 1519, amused his leisure hours in scientific pursuits; and many -ideas appear to have occurred to him which are to be found in the -writings of Galileo at a later date. It is not impossible (though there -are probably no means of directly ascertaining the fact) that Galileo -may have been acquainted with Leonardo's investigations, although they -remained, till very lately, almost unknown to the mathematical world. -This supposition is rendered more probable from the fact, that Mazenta, -the preserver of Leonardo's manuscripts, was, at the very time of their -discovery, a contemporary student with Galileo at Pisa. Kopernik, or, as -he is usually called, Copernicus, a native of Thorn in Prussia, had -published his great work, De Revolutionibus, in 1543, restoring the -knowledge of the true theory of the solar system, and his opinions were -gradually and silently gaining ground. - -It is not satisfactorily ascertained at what period Galileo embraced -the new astronomical theory. Gerard Voss attributes his conversion -to a public lecture of Mæstlin, the instructor of Kepler; and later -writers (among whom is Laplace) repeat the same story, but without -referring to any additional sources of information, and in most -instances merely transcribing Voss's words, so as to shew indisputably -whence they derived their account. Voss himself gives no authority, -and his general inaccuracy makes his mere word not of much weight. The -assertion appears, on many accounts, destitute of much probability. -If the story were correct, it seems likely that some degree of -acquaintance, if not of friendly intercourse, would have subsisted -between Mæstlin, and his supposed pupil, such as in fact we find -subsisting between Mæstlin and his acknowledged pupil Kepler, the -devoted friend of Galileo; but, on the contrary, we find Mæstlin -writing to Kepler himself of Galileo as an entire stranger, and in -the most disparaging terms. If Mæstlin could lay claim to the honour -of so celebrated a disciple, it is not likely that he could fail so -entirely to comprehend the distinction it must confer upon himself as -to attempt diminishing it by underrating his pupil's reputation. There -is a passage in Galileo's works which more directly controverts the -claim advanced for Mæstlin, although Salusbury, in his life of Galileo, -having apparently an imperfect recollection of its tenor, refers to -this very passage in confirmation of Voss's statement. In the second -part of the dialogue on the Copernican system, Galileo makes Sagredo, -one of the speakers in it, give the following account:--"Being very -young, and having scarcely finished my course of philosophy, which I -left off as being set upon other employments, there chanced to come -into these parts a certain foreigner of Rostoch, _whose name, as I -remember, was Christianus Urstisius_, a follower of Copernicus, who, -in an academy, gave two or three lectures upon this point, to whom -many flocked as auditors; but I, thinking they went more for the -novelty of the subject than otherwise, did not go to hear him; for I -had concluded with myself that that opinion could be no other than a -solemn madness; and questioning some of those who had been there, I -perceived they all made a jest thereof, except one, who told me that -the business was not altogether to be laughed at: and because the man -was reputed by me to be very intelligent and wary, I repented that I -was not there, and began from that time forward, as oft as I met with -any one of the Copernican persuasion, to demand of them if they had -been always of the same judgment. Of as many as I examined I found not -so much as one who told me not that he had been a long time of the -contrary opinion, but to have changed it for this, as convinced by the -strength of the reasons proving the same; and afterwards questioning -them one by one, to see whether they were well possessed of the reasons -of the other side, I found them all to be very ready and perfect in -them, so that I could not truly say that they took this opinion out -of ignorance, vanity, or to show the acuteness of their wits. On the -contrary, of as many of the Peripatetics and Ptolemeans as I have -asked, (and out of curiosity I have talked with many,) what pains they -had taken in the book of Copernicus, I found very few that had so much -as superficially perused it, but of those who I thought had understood -the same, not one: and, moreover, I have inquired amongst the followers -of the Peripatetic doctrine, if ever any of them had held the contrary -opinion, and likewise found none that had. Whereupon, considering that -there was no man who followed the opinion of Copernicus that had not -been first on the contrary side, and that was not very well acquainted -with the reasons of Aristotle and Ptolemy, and, on the contrary, that -there was not one of the followers of Ptolemy that had ever been of -the judgment of Copernicus, and had left that to embrace this of -Aristotle;--considering, I say, these things, I began to think that -one who leaveth an opinion imbued with his milk and followed by very -many, to take up another, owned by very few, and denied by all the -schools, and that really seems a great paradox, must needs have been -moved, not to say forced, by more powerful reasons. For this cause I -am become very curious to dive, as they say, into the bottom of this -business." It seems improbable that Galileo should think it worth while -to give so detailed an account of the birth and growth of opinion in -any one besides himself; and although Sagredo is not the personage who -generally in the dialogue represents Galileo, yet as the real Sagredo -was a young nobleman, a pupil of Galileo himself, the account cannot -refer to him. The circumstance mentioned of the intermission of his -philosophical studies, though in itself trivial, agrees very well with -Galileo's original medical destination. Urstisius is not a fictitious -name, as possibly Salusbury may have thought, when alluding to this -passage; he was mathematical professor at Bâle, about 1567, and several -treatises by him are still extant. According to Kästner, his German name -was Wursteisen. In 1568 Voss informs us that he published some new -questions on Purbach's Theory of the Planets. He died at Bâle in 1586, -when Galileo was about twenty-two years old. - -It is not unlikely that Galileo also, in part, owed his emancipation -from popular prejudices to the writings of Giordano Bruno, an -unfortunate man, whose unsparing boldness in exposing fallacies and -absurdities was rewarded by a judicial murder, and by the character of -heretic and infidel, with which his executioners endeavoured to -stigmatize him for the purpose of covering over their own atrocious -crime. Bruno was burnt at Rome in 1600, but not, as Montucla supposes, -on account of his "Spaccio della Bestia trionfante." The title of this -book has led him to suppose that it was directed against the church of -Rome, to which it does not in the slightest degree relate. Bruno -attacked the fashionable philosophy alternately with reason and -ridicule, and numerous passages in his writings, tedious and obscure as -they generally are, show that he had completely outstripped the age in -which he lived. Among his astronomical opinions, he believed that the -universe consisted of innumerable systems of suns with assemblages of -planets revolving round each of them, like our own earth, the smallness -of which, alone, prevented their being observed by us. He remarked -further, "that it is by no means improbable that there are yet other -planets revolving round our own sun, which we have not yet noticed, -either on account of their minute size or too remote distance from us." -He declined asserting that all the apparently fixed stars are really so, -considering this as not sufficiently proved, "because at such enormous -distances the motions become difficult to estimate, and it is only by -long observation that we can determine if any of these move round each -other, or what other motions they may have." He ridiculed the -Aristotelians in no very measured terms--"They harden themselves, and -heat themselves, and embroil themselves for Aristotle; they call -themselves his champions, they hate all but Aristotle's friends, they -are ready to live and die for Aristotle, and yet they do not understand -so much as the titles of Aristotle's chapters." And in another place he -introduces an Aristotelian inquiring, "Do you take Plato for an -ignoramus--Aristotle for an ass?" to whom he answers, "My son, I neither -call them asses, nor you mules,--them baboons, nor you apes,--as you -would have me: I told you that I esteem them the heroes of the world, -but I will not credit them without sufficient reason; and if you were -not both blind and deaf, you would understand that I must disbelieve -their absurd and contradictory assertions."[11] Bruno's works, though in -general considered those of a visionary and madman, were in very -extensive circulation, probably not the less eagerly sought after from -being included among the books prohibited by the Romish church; and -although it has been reserved for later observations to furnish complete -verification of his most daring speculations, yet there was enough, -abstractedly taken, in the wild freedom of his remarks, to attract a -mind like Galileo's; and it is with more satisfaction that we refer the -formation of his opinions to a man of undoubted though eccentric genius, -like Bruno, than to such as Maestlin, who, though a diligent and careful -observer, seems seldom to have taken any very enlarged views of the -science on which he was engaged. - -With a few exceptions similar to those above mentioned, the rest of -Galileo's contemporaries well deserved the contemptuous epithet which he -fixed on them of Paper Philosophers, for, to use his own words, in a -letter to Kepler on this subject, "this sort of men fancied philosophy -was to be studied like the Æneid or Odyssey, and that the true reading -of nature was to be detected by the collation of texts." Galileo's own -method of philosophizing was widely different; seldom omitting to bring -with every new assertion the test of experiment, either directly in -confirmation of it, or tending to show its probability and consistency. -We have already seen that he engaged in a series of experiments to -investigate the truth of some of Aristotle's positions. As fast as he -succeeded in demonstrating the falsehood of any of them, he denounced -them from his professorial chair with an energy and success which -irritated more and more against him the other members of the academic -body. - -There seems something in the stubborn opposition which he encountered in -establishing the truth of his mechanical theorems, still more stupidly -absurd than in the ill will to which, at a later period of his life, his -astronomical opinions exposed him: it is intelligible that the vulgar -should withhold their assent from one who pretended to discoveries in -the remote heavens, which few possessed instruments to verify, or -talents to appreciate; but it is difficult to find terms for -stigmatizing the obdurate folly of those who preferred the evidence of -their books to that of their senses, in judging of phenomena so obvious -as those, for instance, presented by the fall of bodies to the ground. -Aristotle had asserted, that if two different weights of the same -material were let fall from the same height, the heavier one would reach -the ground sooner than the other, in the proportion of their weights. -The experiment is certainly not a very difficult one, but nobody thought -of that method of argument, and consequently this assertion had been -long received, upon his word, among the axioms of the science of motion. -Galileo ventured to appeal from the authority of Aristotle to that of -his own senses, and maintained that, with the exception of an -inconsiderable difference, which he attributed to the disproportionate -resistance of the air, they would fall in the same time. The -Aristotelians ridiculed and refused to listen to such an idea. Galileo -repeated his experiments in their presence from the famous leaning tower -at Pisa: and with the sound of the simultaneously falling weights still -ringing in their ears, they could persist in gravely maintaining that a -weight of ten pounds would reach the ground in a tenth part of the time -taken by one of a single pound, because they were able to quote chapter -and verse in which Aristotle assures them that such is the fact. A -temper of mind like this could not fail to produce ill will towards him -who felt no scruples in exposing their wilful folly; and the watchful -malice of these men soon found the means of making Galileo desirous of -quitting his situation at Pisa. Don Giovanni de' Medici, a natural son -of Cosmo, who possessed a slight knowledge of mechanics on which he -prided himself, had proposed a contrivance for cleansing the port of -Leghorn, on the efficiency of which Galileo was consulted. His opinion -was unfavourable, and the violence of the inventor's disappointment, -(for Galileo's judgment was verified by the result,) took the somewhat -unreasonable direction of hatred towards the man whose penetration had -foreseen the failure. Galileo's situation was rendered so unpleasant by -the machinations of this person, that he decided on accepting overtures -elsewhere, which had already been made to him; accordingly, under the -negotiation of his staunch friend Guido Ubaldi, and with the consent of -Ferdinand, he procured from the republic of Venice a nomination for six -years to the professorship of mathematics in the university of Padua, -whither he removed in September 1592. - -Galileo's predecessor in the mathematical chair at Padua was Moleti, who -died in 1588, and the situation had remained unfilled during the -intervening four years. This seems to show that the directors attributed -but little importance to the knowledge which it was the professor's duty -to impart. This inference is strengthened by the fact, that the amount -of the annual salary attached to it did not exceed 180 florins, whilst -the professors of philosophy and civil law, in the same university, were -rated at the annual stipends of 1400 and 1680 florins.[12] Galileo -joined the university about a year after its triumph over the Jesuits, -who had established a school in Padua about the year 1542, and, -increasing yearly in influence, had shown symptoms of a design to get -the whole management of the public education into the hands of their own -body.[13] After several violent disputes it was at length decreed by the -Venetian senate, in 1591, that no Jesuit should be allowed to give -instruction at Padua in any of the sciences professed in the university. -It does not appear that after this decree they were again troublesome to -the university, but this first decree against them was followed, in -1606, by a second more peremptory, which banished them entirely from the -Venetian territory. Galileo would of course find his fellow-professors -much embittered against that society, and would naturally feel inclined -to make common cause with them, so that it is not unlikely that the -hatred which the Jesuits afterwards bore to Galileo on personal -considerations, might be enforced by their recollection of the -university to which he had belonged. - -Galileo's writings now began to follow each other with great rapidity, -but he was at this time apparently so careless of his reputation, that -many of his works and inventions, after a long circulation in manuscript -among his pupils and friends, found their way into the hands of those -who were not ashamed to publish them as their own, and to denounce -Galileo's claim to the authorship as the pretence of an impudent -plagiarist. He was, however, so much beloved and esteemed by his -friends, that they vied with each other in resenting affronts of this -nature offered to him, and in more than one instance he was relieved, by -their full and triumphant answers, from the trouble of vindicating his -own character. - -To this epoch of Galileo's life may be referred his re-invention of the -thermometer. The original idea of this useful instrument belongs to the -Greek mathematician Hero; and Santorio himself, who has been named as -the inventor by Italian writers, and at one time claimed it himself, -refers it to him. In 1638, Castelli wrote to Cesarini that "he -remembered an experiment shown to him more than thirty-five years back -by Galileo, who took a small glass bottle, about the size of a hen's -egg, the neck of which was twenty-two inches long, and as narrow as a -straw. Having well heated the bulb in his hands, and then introducing -its mouth into a vessel in which was a little water, and withdrawing the -heat of his hand from the bulb, the water rose in the neck of the bottle -more than eleven inches above the level in the vessel, and Galileo -employed this principle in the construction of an instrument for -measuring heat and cold."[14] In 1613, a Venetian nobleman named -Sagredo, who has been already mentioned as Galileo's friend and pupil, -writes to him in the following words: "I have brought the instrument -which you invented for measuring heat into several convenient and -perfect forms, so that the difference of temperature between two rooms -is seen as far as 100 degrees."[15] This date is anterior to the claims -both of Santorio and Drebbel, a Dutch physician, who was the first to -introduce it into Holland. - -Galileo's thermometer, as we have just seen, consisted merely of a glass -tube ending in a bulb, the air in which, being partly expelled by heat, -was replaced by water from a glass into which the open end of the tube -was plunged, and the different degrees of temperature were indicated by -the expansion of the air which yet remained in the bulb, so that the -scale would be the reverse of that of the thermometer now in use, for -the water would stand at the highest level in the coldest weather. It -was, in truth, a barometer also, in consequence of the communication -between the tube and external air, although Galileo did not intend it -for this purpose, and when he attempted to determine the relative weight -of the air, employed a contrivance still more imperfect than this rude -barometer would have been. A passage among his posthumous fragments -intimates that he subsequently used spirit of wine instead of water. - -Viviani attributes an improvement of this imperfect instrument, but -without specifying its nature, to Ferdinand II., a pupil and subsequent -patron of Galileo, and, after the death of his father Cosmo, reigning -duke of Florence. It was still further improved by Ferdinand's younger -brother, Leopold de' Medici, who invented the modern process of -expelling all the air from the tube by boiling the spirit of wine in it, -and of hermetically sealing the end of the tube, whilst the contained -liquid is in this expanded state, which deprived it of its barometrical -character, and first made it an accurate thermometer. The final -improvement was the employment of mercury instead of spirit of wine, -which is recommended by Lana so early as 1670, on account of its equable -expansion.[16] For further details on the history and use of this -instrument, the reader may consult the Treatises on the THERMOMETER and -PYROMETER. - - -FOOTNOTES: - -[7] Essai sur les Ouvrages de Leonard da Vinci. Paris, 1797. - -[8] See Treatise on HYDROSTATICS. - -[9] Antibarbarus Philosophicus. Francofurti, 1674. - -[10] Speculationum liber. Venetiis, 1585. - -[11] De l'Infinito Universo. Dial. 3. La Cena de le Cenere, 1584. - -[12] Riccoboni, Commentarii de Gymnasio Patavino, 1598. - -[13] Nelli. - -[14] Nelli. - -[15] Venturi. Memorie e Lettere di Gal. Galilei. Modena, 1821. - -[16] Prodromo all' Arte Maestra. Brescia, 1670. - - - - -CHAPTER IV. - - _Astronomy before Copernicus--Fracastoro--Bacon--Kepler--Galileo's - Treatise on the Sphere._ - - -THIS period of Galileo's lectureship at Padua derives interest from its -including the first notice which we find of his having embraced the -doctrines of the Copernican astronomy. Most of our readers are aware of -the principles of the theory of the celestial motions which Copernicus -restored; but the number of those who possess much knowledge of the -cumbrous and unwieldy system which it superseded is perhaps more -limited. The present is not a fit opportunity to enter into many details -respecting it; these will find their proper place in the History of -Astronomy: but a brief sketch of its leading principles is necessary to -render what follows intelligible. - -The earth was supposed to be immoveably fixed in the centre of the -universe, and immediately surrounding it the atmospheres of air and -fire, beyond which the sun, moon, and planets, were thought to be -carried round the earth, fixed each to a separate orb or heaven of solid -but transparent matter. The order of distance in which they were -supposed to be placed with regard to the central earth was as follows: -The Moon, Mercury, Venus, The Sun, Mars, Jupiter, and Saturn. It became -a question in the ages immediately preceding Copernicus, whether the Sun -was not nearer the Earth than Mercury, or at least than Venus; and this -question was one on which the astronomical theorists were then chiefly -divided. - -We possess at this time a curious record of a former belief in this -arrangement of the Sun and planets, in the order in which the days of -the week have been named from them. According to the dreams of -Astrology, each planet was supposed to exert its influence in -succession, reckoning from the most distant down to the nearest, over -each hour of the twenty-four. The planet which was supposed to -predominate over the first hour, gave its name to that day.[17] The -general reader will trace this curious fact more easily with the French -or Latin names than with the English, which have been translated into -the titles of the corresponding Saxon deities. Placing the Sun and -planets in the following order, and beginning, for instance, with -Monday, or the Moon's day; Saturn ruled the second hour of that day, -Jupiter the third, and so round till we come again and again to the Moon -on the 8th, 15th, and 22d hours; Saturn ruled the 23d, Jupiter the -24th, so that the next day would be the day of Mars, or, as the Saxons -translated it, Tuisco's day, or Tuesday. In the same manner the -following days would belong respectively to Mercury or Woden, Jupiter or -Thor, Venus or Frea, Saturn or Seater, the Sun, and again the Moon. In -this manner the whole week will be found to complete the cycle of the -seven planets. - -[Illustration: Cycle of the seven planets.] - -The other stars were supposed to be fixed in an outer orb, beyond which -were two crystalline spheres, (as they were called,) and on the outside -of all, the _primum mobile_ or _first moveable_, which sphere was -supposed to revolve round the earth in twenty-four hours, and by its -friction, or rather, as most of the philosophers of that day chose to -term it, by the sort of heavenly influence which it exercised on the -interior orbs, to carry them round with a similar motion. Hence the -diversity of day and night. But beside this principal and general -motion, each orb was supposed to have one of its own, which was intended -to account for the apparent changes of position of the planets with -respect to the fixed stars and to each other. This supposition, however, -proving insufficient to account for all the irregularities of motion -observed, two hypotheses were introduced.--First, that to each planet -belonged several concentric spheres or heavens, casing each other like -the coats of an onion, and, secondly, that the centres of these solid -spheres, with which the planet revolved, were placed in the -circumference of a secondary revolving sphere, the centre of which -secondary sphere was situated at the earth. They thus acquired the names -of Eccentrics or Epicycles, the latter word signifying a circle upon a -circle. The whole art of astronomers was then directed towards inventing -and combining different eccentric and epicyclical motions, so as to -represent with tolerable fidelity the ever varying phenomena of the -heavens. Aristotle had lent his powerful assistance in this, as in other -branches of natural philosophy, in enabling the false system to prevail -against and obliterate the knowledge of the true, which, as we gather -from his own writings, was maintained by some philosophers before his -time. Of these ancient opinions, only a few traces now remain, -principally preserved in the works of those who were adverse to them. -Archimedes says expressly that Aristarchus of Samos, who lived about 300 -B. C., taught the immobility of the sun and stars, and that the earth is -carried round the central sun.[18] Aristotle's words are: "Most of those -who assert that the whole concave is finite, say that the earth is -situated in the middle point of the universe: those who are called -Pythagoreans, who live in Italy, are of a contrary opinion. For they say -that fire is in the centre, and that the earth, which, according to -them, is one of the stars, occasions the change of day and night by its -own motion, with which it is carried about the centre." It might be -doubtful, upon this passage alone, whether the Pythagorean theory -embraced more than the diurnal motion of the earth, but a little -farther, we find the following passage: "Some, as we have said, make the -earth to be one of the stars: others say that it is placed in the centre -of the Universe, and revolves on a central axis."[19] From which, in -conjunction with the former extract, it very plainly appears that the -Pythagoreans maintained both the diurnal and annual motions of the -earth. - -Some idea of the supererogatory labour entailed upon astronomers by the -adoption of the system which places the earth in the centre, may be -formed in a popular manner by observing, in passing through a thickly -planted wood, in how complicated a manner the relative positions of the -trees appear at each step to be continually changing, and by considering -the difficulty with which the laws of their apparent motions could be -traced, if we were to attempt to refer these changes to a real motion of -the trees instead of the traveller. The apparent complexity in the -heavens is still greater than in the case suggested; because, in -addition to the earth's motions, with which all the stars appear to be -impressed, each of the planets has also a real motion of its own, which -of course greatly contributes to perplex and complicate the general -appearances. Accordingly the heavens rapidly became, under this system, - - "With centric and eccentric scribbled o'er, - Cycle and epicycle, orb in orb;"[20] - -crossing and penetrating each other in every direction. Maestlin has -given a concise enumeration of the principal orbs which belonged to this -theory. After warning the readers that "they are not mere fictions which -have nothing to correspond with them out of the imagination, but that -they exist really, and bodily in the heavens,"[21] he describes seven -principal spheres belonging to each planet, which he classes as -Eccentrics, Epicycles, and Concentrepicycles, and explains their use in -accounting for the planet's revolutions, motions of the apogee, and -nodes, &c. &c. In what manner this multitude of solid and crystalline -orbs were secured from injuring or interfering with each other was not -very closely inquired into. - -The reader will cease to expect any very intelligible explanation of -this and numberless other difficulties which belong to this unwieldy -machinery when he is introduced to the reasoning by which it was upheld. -Gerolamo Fracastoro, who lived in the sixteenth century, writes in the -following terms, in his work entitled Homocentrica, (certainly one of -the best productions of the day,) in which he endeavours to simplify the -necessary apparatus, and to explain all the phenomena (as the title of -his book implies) by concentric spheres round the earth. "There are -some, not only of the ancients but also among the moderns, who believe -that the stars move freely without any such agency; but it is difficult -to conceive in what manner they have imbued themselves with this notion, -_since not only reason, but the very senses, inform us that all the -stars are carried round fastened to solid spheres_." What ideas -Fracastoro entertained of the evidence of the "senses" it is not now -easy to guess, but he goes on to give a specimen of the "reasoning" -which appeared to him so incontrovertible. "The planets are observed to -move one while forwards, then backwards, now to the right, now to the -left, quicker and slower by turns; which variety is consistent with a -compound structure like that of an animal, which possesses in itself -various springs and principles of action, but is totally at variance -with our notion of a simple and undecaying substance like the heavens -and heavenly bodies. For that which is simple, is altogether single, and -singleness is of one only nature, and one nature can be the cause of -only one effect; and therefore it is altogether impossible that the -stars of themselves should move with such variety of motion. And -besides, if the stars move by themselves, they either move in an empty -space, or in a fluid medium like the air. But there cannot be such a -thing as empty space, and if there were such a medium, the motion of the -star would occasion condensation and rarefaction in different parts of -it, which is the property of corruptible bodies and where they exist -some violent motion is going on; but the heavens are incorruptible and -are not susceptible of violent motion, and hence, and from many other -similar reasons, any one who is not obstinate may satisfy himself that -the stars cannot have any independent motion." - -Some persons may perhaps think that arguments of this force are -unnecessarily dragged from the obscurity to which they are now for the -most part happily consigned; but it is essential, in order to set -Galileo's character and merits in their true light, to show how low at -this time philosophy had fallen. For we shall form a very inadequate -notion of his powers and deserts if we do not contemplate him in the -midst of men who, though of undoubted talent and ingenuity, could so far -bewilder themselves as to mistake such a string of unmeaning phrases for -argument: we must reflect on the difficulty every one experiences in -delivering himself from the erroneous impressions of infancy, which will -remain stamped upon the imagination in spite of all the efforts of -matured reason to erase them, and consider every step of Galileo's -course as a triumph over difficulties of a like nature. We ought to be -fully penetrated with this feeling before we sit down to the perusal of -his works, every line of which will then increase our admiration of the -penetrating acuteness of his invention and unswerving accuracy of his -judgment. In almost every page we discover an allusion to some new -experiment, or the germ of some new theory; and amid all this wonderful -fertility it is rarely indeed that we find the exuberance of his -imagination seducing him from the rigid path of philosophical induction. -This is the more remarkable as he was surrounded by friends and -contemporaries of a different temperament and much less cautious -disposition. A disadvantageous contrast is occasionally furnished even -by the sagacious Bacon, who could so far deviate from the sound -principles of inductive philosophy, as to write, for instance, in the -following strain, bordering upon the worst manner of the -Aristotelians:--"Motion in a circle has no limit, and seems to emanate -from the appetite of the body, which moves only for the sake of moving, -and that it may follow itself and seek its own embraces, and put in -action and enjoy its own nature, and exercise its peculiar operation: on -the contrary, motion in a straight line seems transitory, and to move -towards a limit of cessation or rest, and that it may reach some point, -and then put off its motion."[22] Bacon rejected all the machinery of -the _primum mobile_ and the solid spheres, the eccentrics and the -epicycles, and carried his dislike of these doctrines so far as to -assert that nothing short of their gross absurdity could have driven -theorists to the extravagant supposition of the motion of the earth, -which, said he, "we know to be most false."[23] Instances of extravagant -suppositions and premature generalizations are to be found in almost -every page of his other great contemporary, Kepler. - -It is with pain that we observe Delambre taking every opportunity, in -his admirable History of Astronomy, to undervalue and sneer at Galileo, -seemingly for the sake of elevating the character of Kepler, who appears -his principal favourite, but whose merit as a philosopher cannot safely -be brought into competition with that of his illustrious contemporary. -Delambre is especially dissatisfied with Galileo, for taking no notice, -in his "System of the World," of the celebrated laws of the planetary -motions which Kepler discovered, and which are now inseparably connected -with his name. The analysis of Newton and his successors has now -identified those apparently mysterious laws with the general phenomena -of motion, and has thus entitled them to an attention of which, before -that time, they were scarcely worthy; at any rate not more than is at -present the empirical law which includes the distances of all the -planets from the sun (roughly taken) in one algebraical formula. The -observations of Kepler's day were scarcely accurate enough to prove that -the relations which he discovered between the distances of the planets -from the sun and the periods of their revolutions around him were -necessarily to be received as demonstrated truths; and Galileo surely -acted most prudently and philosophically in holding himself altogether -aloof from Kepler's fanciful devices and numeral concinnities, although, -with all the extravagance, they possessed much of the genius of the -Platonic reveries, and although it did happen that Galileo, by -systematically avoiding them, failed to recognise some important truths. -Galileo probably was thinking of those very laws, when he said of -Kepler, "He possesses a bold and free genius, perhaps too much so; but -his mode of philosophizing is widely different from mine." We shall have -further occasion in the sequel to recognise the justice of this remark. - -In the treatise on the Sphere which bears Galileo's name, and which, if -he be indeed the author of it, was composed during the early part of his -residence at Padua, he also adopts the Ptolemaic system, placing the -earth immoveable in the centre, and adducing against its motion the -usual arguments, which in his subsequent writings he ridicules and -refutes. Some doubts have been expressed of its authenticity; but, -however this may be, we have it under Galileo's own hand that he taught -the Ptolemaic system, in compliance with popular prejudices, for some -time after he had privately become a convert to the contrary opinions. -In a letter, apparently the first which he wrote to Kepler, dated from -Padua, 1597, he says, acknowledging the receipt of Kepler's Mysterium -Cosmographicum, "I have as yet read nothing beyond the preface of your -book, from which however I catch a glimpse of your meaning, and feel -great joy on meeting with so powerful an associate in the pursuit of -truth, and consequently such a friend to truth itself, for it is -deplorable that there should be so few who care about truth, and who do -not persist in their perverse mode of philosophizing; but as this is not -the fit time for lamenting the melancholy condition of our times, but -for congratulating you on your elegant discoveries in confirmation of -the truth, I shall only add a promise to peruse your book -dispassionately, and with a conviction that I shall find in it much to -admire. _This I shall do the more willingly because many years ago I -became a convert to the opinions of Copernicus_,[24] and by that theory -have succeeded in fully explaining many phenomena, which on the contrary -hypothesis are altogether inexplicable. I have arranged many arguments -and confutations of the opposite opinions, _which however I have not yet -dared to publish_, fearing the fate of our master Copernicus, who, -although he has earned immortal fame among a few, yet by an infinite -number (for so only can the number of fools be measured) is exploded and -derided. If there were many such as you, I would venture to publish my -speculations; but, since that is not so, I shall take time to consider -of it." This interesting letter was the beginning of the friendship of -these two great men, which lasted uninterruptedly till 1630, the date of -Kepler's death. That extraordinary genius never omitted an opportunity -of testifying his admiration of Galileo, although there were not wanting -persons envious of their good understanding, who exerted themselves to -provoke coolness and quarrel between them. Thus Brutius writes to Kepler -in 1602[25]: "Galileo tells me he has written to you, and has got your -book, which however he denied to Magini, and I abused him for praising -you with too many qualifications. I know it to be a fact that, both in -his lectures, and elsewhere, he is publishing your inventions as his -own; but I have taken care, and shall continue to do so, that all this -shall redound not to his credit but to yours." The only notice which -Kepler took of these repeated insinuations, which appear to have been -utterly groundless, was, by renewed expressions of respect and -admiration, to testify the value he set upon his friend and -fellow-labourer in philosophy. - - -FOOTNOTES: - -[17] Dion Cassius, lib. 37. - -[18] The pretended translation by Roberval of an Arabic version of -Aristarchus, "De Systemate Mundi," in which the Copernican system is -fully developed, is spurious. Menage asserts this in his observations on -Diogen. Laert. lib. 8, sec. 85, tom. ii., p. 389. (Ed. Amst. 1692.) The -commentary contains many authorities well worth consulting. Delambre, -Histoire de l'Astronomie, infers it from its not containing some -opinions which Archimedes tells us were held by Aristarchus. A more -direct proof may be gathered from the following blunder of the supposed -translator. Astronomers had been long aware that the earth in different -parts of her orbit is at different distances from the sun. Roberval -wished to claim for Aristarchus the credit of having known this, and -introduced into his book, not only the mention of the fact, but an -explanation of its cause. Accordingly he makes Aristarchus give a reason -"why the sun's apogee (or place of greatest distance from the earth) -must always be at the north summer solstice." In fact, it was there, or -nearly so, in Roberval's time, and he knew not but that it had always -been there. It is however moveable, and, when Aristarchus lived, was -nearly half way between the solstices and equinoxes. He therefore would -hardly have given a reason for the necessity of a phenomenon of which, -if he observed anything on the subject, he must have observed the -contrary. The change in the obliquity of the earth's axis to the -ecliptic was known in the time of Roberval, and he accordingly has -introduced the proper value which it had in Aristarchus's time. - -[19] De Coelo. lib. 2. - -[20] Paradise Lost, b. viii. v. 83. - -[21] Itaque tam circulos primi motus quam orbes secundorum mobilium -reverâ in coelesti corpore esse concludimus, &c. Non ergo sunt mera -figmenta, quibus extra mentem nihil correspondeat. M. Maestlini, De -Astronomiæ Hypothesibus disputatio. Heidelbergæ, 1582. - -[22] Opuscula Philosophica, Thema Coeli. - -[23] "Nobis constat falsissimum esse." De Aug. Scient. lib. iii. c. 3, -1623. - -[24] Id autum eò libentius faciam, quod in Copernici sententiam multis -abhinc annis venerim.--Kepl. Epistolæ. - -[25] Kepleri Epistolæ. - - - - -CHAPTER V. - - _Galileo re-elected Professor at Padua--New star--Compass of - proportion--Capra--Gilbert--Proposals to return to Pisa--Lost - writings--Cavalieri._ - - -GALILEO'S reputation was now rapidly increasing: his lectures were -attended by many persons of the highest rank; among whom were the -Archduke Ferdinand, afterwards Emperor of Germany, the Landgrave of -Hesse, and the Princes of Alsace and Mantua. On the expiration of the -first period for which he had been elected professor, he was rechosen -for a similar period, with a salary increased to 320 florins. The -immediate occasion of this augmentation is said by Fabroni[26], to have -arisen out of the malice of an ill wisher of Galileo, who, hoping to do -him disservice, apprized the senate that he was not married to Marina -Gamba, then living with him, and the mother of his son Vincenzo. Whether -or not the senate might consider themselves entitled to inquire into the -morality of his private life, it was probably from a wish to mark their -sense of the informer's impertinence, that they returned the brief -answer, that "if he had a family to provide for, he stood the more in -need of an increased stipend." - -During Galileo's residence at Padua, and, according to Viviani's -intimation, towards the thirtieth year of his age, that is to say in -1594, he experienced the first attack of a disease which pressed -heavily on him for the rest of his life. He enjoyed, when a young man, a -healthy and vigorous constitution, but chancing to sleep one afternoon -near an open window, through which was blowing a current of air cooled -artificially by the fall of water, the consequences were most disastrous -to him. He contracted a sort of chronic complaint, which showed itself -in acute pains in his limbs, chest, and back, accompanied with frequent -hæmorrhages and loss of sleep and appetite; and this painful disorder -thenceforward never left him entirely, but recurred intermittingly, with -greater or less violence, as long as he lived. Others of the party did -not even escape so well, but died shortly after committing this -imprudence. - -In 1604, the attention of astronomers was called to the contemplation of -a new star, which appeared suddenly with great splendour in the -constellation Serpentarius, or Ophiuchus, as it is now more commonly -called. Maestlin, who was one of the earliest to notice it, relates his -observations in the following words: "How wonderful is this new star! I -am certain that I did not see it before the 29th of September, nor -indeed, on account of several cloudy nights, had I a good view till the -6th of October. Now that it is on the other side of the sun, instead of -surpassing Jupiter as it did, and almost rivalling Venus, it scarcely -matches the Cor Leonis, and hardly surpasses Saturn. It continues -however to shine with the same bright and strongly sparkling light, and -changes its colours almost with every moment; first tawny, then yellow, -presently purple and red, and, when it has risen above the vapours, most -frequently white." This was by no means an unprecedented phenomenon; and -the curious reader may find in Riccioli[27] a catalogue of the principal -new stars which have at different times appeared. There is a tradition -of a similar occurrence as early as the times of the Greek astronomer -Hipparchus, who is said to have been stimulated by it to the formation -of his catalogue of the stars; and only thirty-two years before, in -1572, the same remarkable phenomenon in the constellation Cassiopeia was -mainly instrumental in detaching the celebrated Tycho Brahe from the -chemical studies, which till then divided his attention with astronomy. -Tycho's star disappeared at the end of two years; and at that time -Galileo was a child. On the present occasion, he set himself earnestly -to consider the new phenomenon, and embodied the results of his -observations in three lectures, which have been unfortunately lost. Only -the exordium of the first has been preserved: in this he reproaches his -auditors with their general insensibility to the magnificent wonders of -creation daily exposed to their view, in no respect less admirable than -the new prodigy, to hear an explanation of which they had hurried in -crowds to his lecture room. He showed, from the absence of parallax, -that the new star could not be, as the vulgar hypothesis represented, a -mere meteor engendered in our atmosphere and nearer the earth than the -moon, but must be situated among the most remote heavenly bodies. This -was inconceivable to the Aristotelians, whose notions of a perfect, -simple, and unchangeable sky were quite at variance with the -introduction of any such new body; and we may perhaps consider these -lectures as the first public declaration of Galileo's hostility to the -old Ptolemaic and Aristotelian astronomy. - -In 1606 he was reappointed to the lectureship, and his salary a second -time increased, being raised to 520 florins. His public lectures were at -this period so much thronged that the ordinary place of meeting was -found insufficient to contain his auditors, and he was on several -occasions obliged to adjourn to the open air,--even from the school of -medicine, which was calculated to contain one thousand persons. - -About this time he was considerably annoyed by a young Milanese, of the -name of Balthasar Capra, who pirated an instrument which Galileo had -invented some years before, and had called the geometrical and military -compass. The original offender was a German named Simon Mayer, whom we -shall meet with afterwards arrogating to himself the merit of one of -Galileo's astronomical discoveries; but on this occasion, as soon as he -found Galileo disposed to resent the injury done to him, he hastily -quitted Italy, leaving his friend Capra to bear alone the shame of the -exposure which followed. The instrument is of simple construction, -consisting merely of two straight rulers, connected by a joint; so that -they can be set to any required angle. This simple and useful -instrument, now called the Sector, is to be found in almost every case -of mathematical instruments. Instead of the trigonometrical and -logarithmic lines which are now generally engraved upon it, Galileo's -compass merely contained, on one side, three pairs of lines, divided in -simple, duplicate, and triplicate proportion, with a fourth pair on -which were registered the specific gravities of several of the most -common metals. These were used for multiplications, divisions, and the -extraction of roots; for finding the dimensions of equally heavy balls -of different materials, &c. On the other side were lines contrived for -assisting to describe any required polygon on a given line; for finding -polygons of one kind equal in area to those of another; and a multitude -of other similar operations useful to the practical engineer. - -Unless the instrument, which is now called Gunter's scale, be much -altered from what it originally was, it is difficult to understand on -what grounds Salusbury charges Gunter with plagiarism from Galileo's -Compass. He declares that he has closely compared the two, and can find -no difference between them.[28] There has also been some confusion, by -several writers, between this instrument and what is now commonly called -the Proportional Compass. The latter consists of two slips of metal -pointed at each end, and connected by a pin which, sliding in a groove -through both, can be shifted to different positions. Its use is to find -proportional lines; for it is obvious that the openings measured by each -pair of legs will be in the same proportion in which the slips are -divided by the centre. The divisions usually marked on it are calculated -for finding the submultiples of straight lines, and the chords of -submultiple arcs. Montucla has mentioned this mistake of one instrument -for the other, and charges Voltaire with the more inexcusable error of -confounding Galileo's with the Mariner's Compass. He refers to a -treatise by Hulsius for his authority in attributing the Proportional -Compass to Burgi, a Swiss astronomer of some celebrity. Horcher also has -been styled the inventor; but he did no more than describe its form and -application. In the frontispiece of his book is an engraving of this -compass exactly similar to those which are now used.[29] To the -description which Galileo published of his compass, he added a short -treatise on the method of measuring heights and distances with the -quadrant and plumb line. The treatise, which is printed by itself at the -end of the first volume of the Padua edition of Galileo's works, -contains nothing more than the demonstrations belonging to the same -operations. They are quite elementary, and contain little or nothing -that was new even at that time. - -Such an instrument as Galileo's Compass was of much more importance -before the grand discovery of logarithms than it can now be considered: -however it acquires an additional interest from the value which he -himself set on it. In 1607, Capra, at the instigation of Mayer, -published as his own invention what he calls the proportional hoop, -which is a mere copy of Galileo's instrument. This produced from Galileo -a long essay, entitled "A Defence of Galileo against the Calumnies and -Impostures of Balthasar Capra." His principal complaint seems to have -been of the misrepresentations which Capra had published of his lectures -on the new star already mentioned, but he takes occasion, after pointing -out the blunders and falsehoods which Capra had committed on that -occasion, to add a complete proof of his piracy of the geometrical -compass. He showed, from the authenticated depositions of workmen, and -of those for whom the instruments had been fabricated, that he had -devised them as early as the year 1597, and had explained their -construction and use both to Balthasar himself and to his father Aurelio -Capra, who was then residing in Padua. He gives, in the same essay, the -minutes of a public meeting between himself and Capra, in which he -proved, to the satisfaction of the university, that wherever Capra had -endeavoured to introduce into his book propositions which were not to be -met with in Galileo's, he had fallen into the greatest absurdities, and -betrayed the most complete ignorance of his subject. The consequence of -this public exposure, and of the report of the famous Fra Paolo Sarpi, -to whom the matter had been referred, was a formal prohibition by the -university of Capra's publication, and all copies of the book then on -hand were seized, and probably destroyed, though Galileo has preserved -it from oblivion by incorporating it in his own publication. - -Nearly at the same time, 1607, or immediately after, he first turned his -attention towards the loadstone, on which our countryman Gilbert had -already published his researches, conducted in the true spirit of the -inductive method. Very little that is original is to be found in -Galileo's works on this subject, except some allusions to his method of -arming magnets, in which, as in most of his practical and mechanical -operations, he appears to have been singularly successful. Sir Kenelm -Digby[30] asserts, that the magnets armed by Galileo would support twice -as great a weight as one of Gilbert's of the same size. Galileo was well -acquainted, as appears from his frequent allusions in different parts of -his works, with what Gilbert had done, of whom he says, "I extremely -praise, admire, and envy this author;--I think him, moreover, worthy of -the greatest praise for the many new and true observations that he has -made to the disgrace of so many vain and fabling authors, who write, not -from their own knowledge only, but repeat every thing they hear from the -foolish vulgar, without attempting to satisfy themselves of the same by -experience, perhaps that they may not diminish the size of their books." - -Galileo's reputation being now greatly increased, proposals were made to -him, in 1609, to return to his original situation at Pisa. He had been -in the habit of passing over to Florence during the academic vacation, -for the purpose of giving mathematical instruction to the younger -members of Ferdinand's family; and Cosmo, who had now succeeded his -father as duke of Tuscany, regretted that so masterly a genius had been -allowed to leave the university which he naturally should have graced. A -few extracts from Galileo's answers to these overtures will serve to -show the nature of his situation at Padua, and the manner in which his -time was there occupied. "I will not hesitate to say, having now -laboured during twenty years, and those the best of my life, in dealing -out, as one may say, in detail, at the request of any body, the little -talent which God has granted to my assiduity in my profession, that my -wish certainly would be to have sufficient rest and leisure to enable -me, before my life comes to its close, to conclude three great works -which I have in hand, and to publish them; which might perhaps bring -some credit to me, and to those who had favoured me in this undertaking, -and possibly may be of greater and more frequent service to students -than in the rest of my life I could personally afford them. Greater -leisure than I have here I doubt if I could meet with elsewhere, so long -as I am compelled to support my family from my public and private -lectures, (nor would I willingly lecture in any other city than this, -for several reasons which would be long to mention) nevertheless not -even the liberty I have here is sufficient, where I am obliged to spend -many, and often the best hours of the day at the request of this and -that man.--My public salary here is 520 florins, which I am almost -certain will be advanced to as many crowns upon my re-election, and -these I can greatly increase by receiving pupils, and from private -lectures, to any extent that I please. My public duty does not confine -me during more than 60 half hours in the year, and even that not so -strictly but that I may, on occasion of any business, contrive to get -some vacant days; the rest of my time is absolutely at my own disposal; -but because my private lectures and domestic pupils are a great -hindrance and interruption of my studies, I wish to live entirely exempt -from the former, and in great measure from the latter: for if I am to -return to my native country, I should wish the first object of his -Serene Highness to be, that leisure and opportunity should be given me -to complete my works without employing myself in lecturing.--And, in -short, I should wish to gain my bread from my writings, which I would -always dedicate to my Serene Master.--The works which I have to finish -are principally--two books on the system or structure of the Universe, -an immense work, full of philosophy, astronomy, and geometry; three -books on Local Motion, a science entirely new, no one, either ancient or -modern, having discovered any of the very many admirable accidents which -I demonstrate in natural and violent motions, so that I may with very -great reason call it a new science, and invented by me from its very -first principles; three books of Mechanics, two on the demonstration of -principles and one of problems; and although others have treated this -same matter, yet all that has been hitherto written, neither in -quantity, nor otherwise, is the quarter of what I am writing on it. I -have also different treatises on natural subjects; On sound and speech; -On light and colours; On the tide; On the composition of continuous -quantity; On the motions of animals;--And others besides. I have also -an idea of writing some books relating to the military art, giving not -only a model of a soldier, but teaching with very exact rules every -thing which it is his duty to know that depends upon mathematics; as the -knowledge of castrametation, drawing up battalions, fortifications, -assaults, planning, surveying, the knowledge of artillery, the use of -instruments, &c. I also wish to reprint the 'Use of my Geometrical -Compass,' which is dedicated to his highness, and which is no longer to -be met with; for this instrument has experienced such favour from the -public, that in fact no other instruments of this kind are now made, and -I know that up to this time several thousands of mine have been made.--I -say nothing as to the amount of my salary, feeling convinced that as I -am to live upon it, the graciousness of his highness would not deprive -me of any of those comforts, which, however, I feel the want of less -than many others; and therefore I say nothing more on the subject. -Finally, on the title and profession of my service, I should wish that -to the name of Mathematician, his highness would add that of -Philosopher, as I profess to have studied a greater number of years in -philosophy than months in pure mathematics; and how I have profited by -it, and if I can or ought to deserve this title, I may let their -highnesses see as often as it shall please them to give me an -opportunity of discussing such subjects in their presence with those who -are most esteemed in this knowledge." It may perhaps be seen in the -expressions of this letter, that Galileo was not inclined to undervalue -his own merits, but the peculiar nature of the correspondence should be -taken into account, which might justify his indulging a little more than -usual in self-praise, and it would have been perhaps almost impossible -for him to have remained entirely blind to his vast superiority over his -contemporaries. - -Many of the treatises which Galileo here mentions, as well as another on -dialling, have been irrecoverably lost, through the superstitious -weakness of some of his relations, who after his death suffered the -family confessor to examine his papers, and to destroy whatever seemed -to him objectionable; a portion which, according to the notions then -prevalent, was like to comprise the most valuable part of the papers -submitted to this expurgation. It is also supposed that many were burnt -by his infatuated grandson Cosimo, who conceived he was thus offering a -proper and pious sacrifice before devoting himself to the life of a -missionary. A Treatise on Fortification, by Galileo, was found in 1793, -and is contained among the documents published by Venturi. Galileo does -not profess in it to give much original matter, but to lay before his -readers a compendium of the most approved principles then already known. -It has been supposed that Gustavus Adolphus of Sweden attended Galileo's -lectures on this subject, whilst in Italy; but the fact is not -satisfactorily ascertained. Galileo himself mentions a Prince Gustavus -of Sweden to whom he gave instruction in mathematics, but the dates -cannot well be made to agree. The question deserves notice only from its -having been made the subject of controversy. - -The loss of Galileo's Essay on Continuous Quantity is particularly to be -regretted, as it would be highly interesting to see how far he succeeded -in methodizing his thoughts on this important topic. It is to his pupil -Cavalieri (who refused to publish his book so long as he hoped to see -Galileo's printed) that we owe "The Method of Indivisibles," which is -universally recognized as one of the first germs of the powerful methods -of modern analysis. Throughout Galileo's works we find many indications -of his having thought much on the subject, but his remarks are vague, -and bear little, if at all, on the application of the method. To this -the chief part of Cavalieri's book is devoted, though he was not so -entirely regardless of the principles on which his method of measuring -spaces is founded, as he is sometimes represented. This method consisted -in considering lines as made up of an infinite number of points, -surfaces in like manner as composed of lines, and solids of surfaces; -but there is an observation at the beginning of the 7th book, which -shews clearly that Cavalieri had taken a much more profound view of the -subject than is implied in this superficial exposition, and had -approached very closely to the apparently more exact theories of his -successors. Anticipating the objections to his hypothesis, he argues, -that "there is no necessity to suppose the continuous quantities made up -of these indivisible parts, _but only that they will observe the same -ratios as those parts do_." It ought not to be omitted, that Kepler also -had given an impulse to Cavalieri in his "New method of Gauging," which -is the earliest work with which we are acquainted, where principles of -this sort are employed.[31] - - -FOOTNOTES: - -[26] Vitæ Italorum Illustrium. - -[27] Almagestum Novum, vol. i. - -[28] Math. Coll. vol. ii. - -[29] Constructio Circini Proportionum. Moguntiæ, 1605. - -[30] Treatise of the Nature of Bodies. London, 1665. - -[31] Nova Stereometria Doliorum--Lincii, 1615. - - - - -CHAPTER VI. - - _Invention of the telescope--Fracastoro--Porta--Reflecting - telescope--Roger Bacon--Digges--De - Dominis--Jansen--Lipperhey--Galileo constructs - telescopes--Microscopes--Re-elected Professor at Padua for life._ - - -THE year 1609 was signalized by Galileo's discovery of the telescope, -which, in the minds of many, is the principal, if not the sole invention -associated with his name. It cannot be denied that his fame, as the -founder of the school of experimental philosophy, has been in an -unmerited degree cast into the shade by the splendour of his -astronomical discoveries; yet Lagrange[32] surely errs in the opposite -extreme, when he almost denies that these form any real or solid part of -the glory of this great man; and Montucla[33] omits an important -ingredient in his merit, when he (in other respects very justly) -remarks, that it required far less genius to point a telescope towards -the heavens than to trace the unheeded, because daily recurring, -phenomena of motion up to its simple and primary laws. We are to -remember that in the days of Galileo a telescope could scarcely be -pointed to the heavens with impunity, and that a courageous mind was -required to contradict, and a strong one to bear down, a party, who, -when invited to look on any object in the heavens which Aristotle had -never suspected, immediately refused all credit to those senses, to -which, on other occasions, they so confidently appealed. It surely is a -real and solid part of Galileo's glory that he consumed his life in -laborious and indefatigable observations, and that he persevered in -announcing his discoveries undisgusted by the invectives, and undismayed -by the persecutions, to which they subjected him. Plagiarist! liar! -impostor! heretic! were among the expressions of malignant hatred -lavished upon him, and although he also was not without some violent and -foul-mouthed partisans, yet it must be told to his credit that he -himself seldom condescended to notice these torrents of abuse, otherwise -than by good-humoured retorts, and by prosecuting his observations with -renewed assiduity and zeal. - -The use of single lenses in aid of the sight had been long known. -Spectacles were in common use at the beginning of the fourteenth -century, and there are several hints, more or less obscure, in many -early writers, of the effects which might be expected from a combination -of glasses; but it does not appear with certainty that any of these -authors had attempted to reduce their ideas to practice. After the -discovery of the telescope, almost every country endeavoured to find in -the writings of its early philosophers traces of the knowledge of such -an instrument, but in general with success very inadequate to the zeal -of their national prepossessions. There are two authors especially to -whom the attention of Kepler and others was turned, immediately upon the -promulgation of the discovery, as containing the germ of it in their -works. These are Baptista Porta, and Gerolamo Fracastoro. We have -already had occasion to quote the Homocentrica of Fracastoro, who died -in 1553; the following expressions, though they seem to refer to actual -experiment, yet fall short of the meaning with which it has been -attempted to invest them. After explaining and commenting on some -phenomena of refraction through different media, to which he was led by -the necessity of reconciling his theory with the variable magnitudes of -the planets, he goes on to say--"For which reason, those things which -are seen at the bottom of water, appear greater than those which are at -the top; and if any one look through two eyeglasses, _one placed upon -the other_, he will see every thing much larger and nearer."[34] It -should seem that this passage (as Delambre has already remarked) rather -refers to the close application of one glass upon another, and it may -fairly be doubted whether anything analogous to the composition of the -telescope was in the writer's thoughts. Baptista Porta writes on the -same subject more fully;--"Concave lenses show distant objects most -clearly, convex those which are nearer, whence they may be used to -assist the sight. With a concave glass distant objects will be seen, -small, but distinct; with a convex one those near at hand, larger, but -confused; _if you know rightly how to combine one of each sort, you -will see both far and near objects larger and clearer_."[35] These words -show, if Porta really was then unacquainted with the telescope, how -close it is possible to pass by an invention without lighting on it, for -of precisely such a combination of a convex and concave lens, fitted to -the ends of an organ pipe by way of tube, did the whole of Galileo's -telescope consist. If Porta had stopped here he might more securely have -enjoyed the reputation of the invention, but he then professes to -describe the construction of his instrument, which has no relation -whatever to his previous remarks. "I shall now endeavour to show in what -manner we may contrive to recognize our friends at the distance of -several miles, and how those of weak sight may read the most minute -letters from a distance. It is an invention of great utility, and -grounded on optical principles, nor is it at all difficult of execution; -but it must be so divulged as not to be understood by the vulgar, and -yet be clear to the sharpsighted." The description which follows seems -far enough removed from the apprehended danger of being too clear, and -indeed every writer who has hitherto quoted it has merely given the -passage in its original Latin, apparently despairing of an intelligible -translation. With some alterations in the punctuation, which appear -necessary to bring it into any grammatical construction,[36] it may be -supposed to bear something like the following meaning:--"Let a view be -contrived in the centre of a mirror, where it is most effective. All the -solar rays are exceedingly dispersed, and do not in the least come -together (in the true centre); but there is a concourse of all the rays -in the central part of the said mirror, half way towards the other -centre, where the cross diameters meet. This view is contrived in the -following manner. A concave cylindrical mirror placed directly in front, -but with its axis inclined, must be adapted to that focus: and let -obtuse angled or right angled triangles be cut out with two cross lines -on each side drawn from the centre, and a glass (_specillum_) will be -completed fit for the purposes we mentioned." If it were not for the -word "_specillum_," which, in the passage immediately preceding this, -Porta[37] contrasts with "_speculum_," and which he afterwards explains -to mean a glass lens, it would be very clear that the foregoing passage -(supposing it to have any meaning) must be referred to a reflecting -telescope, and it is a little singular that while this obscure passage -has attracted universal attention, no one, so far as we are aware, has -taken any notice of the following unequivocal description of the -principal part of Newton's construction of the same instrument. It is in -the 5th chapter of the 17th book, where Porta explains by what device -exceedingly minute letters may be read without difficulty. "Place a -concave mirror so that the back of it may lie against your breast; -opposite to it, and within the burning point, place the writing; put a -plane mirror behind it, that may be under your eyes. Then the images of -the letters which are in the concave mirror, and which the concave has -magnified, will be reflected in the plane mirror, so that you may read -without difficulty." - -We have not been able to meet with the Italian translation of Porta's -Natural Magic, which was published in 1611, under his own -superintendence; but the English translator of 1658 would probably have -known if any intelligible interpretation were there given of the -mysterious passage above quoted, and his translation is so devoid of -meaning as strongly to militate against this idea. Porta, indeed, -claimed the invention as his own, and is believed to have hastened his -death, (which happened in 1615, he being then 80 years old,) by the -fatigue of composing a Treatise on the Telescope, in which he had -promised to exhaust the subject. We do not know whether this is the same -work which was published after his death by Stelliola,[38] but which -contains no allusion to Porta's claim, and possibly Stelliola may have -thought it most for his friend's reputation to suppress it. Schott[39] -says, a friend of his had seen Porta's book in manuscript, and that it -did at that time contain the assertion of Porta's title to the -invention. After all it is not improbable that he may have derived his -notions of magnifying distant objects from our celebrated countryman -Roger Bacon, who died about the year 1300. He has been supposed, not -without good grounds, to have been one of the first who recognised the -use of single lenses in producing distinct vision, and he has some -expressions with respect to their combination which promise effects -analogous to those held out by Porta. In "The Admirable Force of Art and -Nature," he says, "Physical figurations are far more strange, for in -such manner may we frame perspects and looking-glasses that one thing -shall appear to be many, as one man shall seeme a whole armie; and -divers sunnes and moones, yea, as many as we please, shall appeare at -one time, &c. And so may the perspects be framed, that things most farre -off may seeme most nigh unto us, and clean contrarie, soe that we may -reade very small letters an incredible distance from us, and behold -things how little soever they be, and make stars to appeare wheresoever -we will, &c. And, besides all these, we may so frame perspects that any -man entering into a house he shall indeed see gold, and silver, and -precious stones, and what else he will, but when he maketh haste to the -place he shall find just nothing." It seems plain, that the author is -here speaking solely of mirrors, and we must not too hastily draw the -conclusion, because in the first and last of these assertions he is, to -a certain extent, borne out by facts, that he therefore was in -possession of a method of accomplishing the middle problem also. In the -previous chapter, he gives a long list of notable things, (much in the -style of the Marquis of Worcester's Century of Inventions) which if we -can really persuade ourselves that he was capable of accomplishing, we -must allow the present age to be still immeasurably inferior to him in -science. - -Thomas Digges, in the preface to his Pantometria, (published in 1591) -declares, "My father, by his continuall painfull practises, assisted -with demonstrations mathematicall, was able, and sundry times hath by -proportionall glasses, duely situate in convenient angles, not only -discouered things farre off, read letters, numbered peeces of money, -with the verye coyne and superscription thereof, cast by some of his -freends of purpose, upon downes in open fields; but also, seuen miles -off, declared what hath beene doone at that instant in priuate places. -He hath also sundrie times, by the sunne beames, fired powder and -dischargde ordnance halfe a mile and more distante; which things I am -the boulder to report, for that there are yet living diverse (of these -his dooings) occulati testes, (eye witnesses) and many other matters -farre more strange and rare, which I omit as impertinent to this place." - -We find another pretender to the honour of the discovery of the -telescope in the celebrated Antonio de Dominis, Archbishop of Spalatro, -famous in the annals of optics for being one of the first to explain the -theory of the rainbow. Montucla, following P. Boscovich, has scarcely -done justice to De Dominis, whom he treats as a mere pretender and -ignorant person. The indisposition of Boscovich towards him is -sufficiently accounted for by the circumstance of his being a Catholic -prelate who had embraced the cause of Protestantism. His nominal -reconciliation with the Church of Rome would probably not have saved him -from the stake, had not a natural death released him when imprisoned on -that account at Rome. Judgment was pronounced upon him notwithstanding, -and his body and books were publicly burnt in the Campo de Fiori, in -1624. His treatise, De Radiis, (which is very rarely to be met with) was -published by Bartolo after the acknowledged invention of the telescope -by Galileo; but Bartolo tells us, in the preface, that the manuscript -was communicated to him from a collection of papers written 20 years -before, on his inquiring the Archbishop's opinion with respect to the -newly discovered instrument, and that he got leave to publish it, "with -the addition of one or two chapters." The treatise contains a complete -description of a telescope, which, however, is professed merely to be an -improvement on spectacles, and if the author's intention had been to -interpolate an afterwritten account, in order to secure to himself the -undeserved honour of the invention, it seems improbable that he would -have suffered an acknowledgment of additions, previous to publication, -to be inserted in the preface. Besides, the whole tone of the work is -that of a candid and truth-seeking philosopher, very far indeed removed -from being, as Montucla calls him, conspicuous for ignorance even among -the ignorant men of his age. He gives a drawing of a convex and concave -lens, and traces the passage of the rays through them; to which he -subjoins, that he has not satisfied himself with any determination of -the precise distance to which the glasses should be separated, according -to their convexity and concavity, but recommends the proper distance to -be found by actual experiment, and tells us, that the effect of the -instrument will be to prevent the confusion arising from the -interference of the direct and refracted rays, and to magnify the object -by increasing the visible angle under which it is viewed. These, among -the many claimants, are certainly the authors who approached the most -nearly to the discovery: and the reader may judge, from the passages -cited, whether the knowledge of the telescope can with probability be -referred to a period earlier than the commencement of the 17th century. -At all events, we can find no earlier trace of its being applied to any -practical use; the knowledge, if it existed, remained speculative and -barren. - -In 1609, Galileo, then being on a visit to a friend at Venice, heard a -rumour of the recent invention, by a Dutch spectacle-maker, of an -instrument which was said to represent distant objects nearer than they -usually appeared. According to his own account, this general rumour, -which was confirmed to him by letters from Paris, was all that he -learned on the subject; and returning to Padua, he immediately applied -himself to consider the means by which such an effect could be produced. -Fuccarius, in an abusive letter which he wrote on the subject, asserts -that one of the Dutch telescopes had been at that time actually brought -to Venice, and that he (Fuccarius) had seen it; which, even if true, is -perfectly consistent with Galileo's statement; and in fact the question, -whether or not Galileo saw the original instrument, becomes important -only from his expressly asserting the contrary, and professing to give -the train of reasoning by which he discovered its principle; so that any -insinuation that he had actually seen the Dutch glass, becomes a direct -impeachment of his veracity. It is certain, from the following extract -of a letter from Lorenzo Pignoria to Paolo Gualdo, that one at least of -the Dutch glasses had been sent to Italy. It is dated Padua, 31st -August, 1609.[40] "We have no news, except the return of His Serene -Highness, and the re-election of the lecturers, among whom Sign. Galileo -has contrived to get 1000 florins for life; and it is said to be on -account of an eyeglass, _like the one which was sent from Flanders to -Cardinal Borghese_. We have seen some here, and truly they succeed -well." - -It is allowed by every one that the Dutchman, or rather Zealander, made -his discovery by mere accident, which greatly derogates from any honour -attached to it; but even this diminished degree of credit has been -fiercely disputed. According to one account, which appears consistent -and probable, it had been made for sometime before its importance was in -the slightest degree understood or appreciated, but was set up in the -optician's shop as a curious philosophical toy, showing a large and -inverted image of a weathercock, towards which it was directed. The -Marquis Spinola, chancing to see it, was struck with the phenomenon, -purchased the instrument, and presented it either to the Archduke Albert -of Austria, or to Prince Maurice of Nassau, whose name appears in every -version of the story, and who first entertained the idea of employing it -in military reconnoissances. - -Zacharias Jansen, and Henry Lipperhey, two spectacle-makers, living -close to each other, near the church of Middleburg, have both had -strenuous supporters of their title to the invention. A third pretender -appeared afterwards in the person of James Metius of Alkmaer, who is -mentioned by Huyghens and Des Cartes, but his claims rest upon no -authority whatever comparable to that which supports the other two. -About half a century afterwards, Borelli was at the pains to collect and -publish a number of letters and depositions which he procured, as well -on one side as on the other.[41] It seems that the truth lies between -them, and that one, probably Jansen, was the inventor of the -_microscope_, which application of the principle was unquestionably of -an earlier date, perhaps as far back as 1590. Jansen gave one of his -microscopes to the Archduke, who gave it to Cornelius Drebbel, a -salaried mathematician at the court of our James the first, where -William Borelli (not the author above mentioned) saw it many years -afterwards, when ambassador from the United Provinces to England, and -got from Drebbel this account of the quarter whence it came. Lipperhey -afterwards, in 1609, accidentally hit upon the _telescope_, and on the -fame of this discovery it would not be difficult for Jansen, already in -possession of an instrument so much resembling it, to perceive the -slight difference between them, and to construct a telescope -independently of Lipperhey, so that each, with some show of reason, -might claim the priority of the invention. A notion of this kind -reconciles the testimony of many conflicting witnesses on the subject, -some of whom do not seem to distinguish very accurately whether the -telescope or microscope is the instrument to which their evidence -refers. Borelli arrives at the conclusion, that Jansen was the inventor; -but not satisfied with this, he endeavours, with a glaring partiality -which makes his former determination suspicious, to secure for him and -his son the more solid reputation of having anticipated Galileo in the -useful employment of the invention. He has however inserted in his -collections a letter from John the son of Zacharias, in which John, -omitting all mention of his father, speaks of his own observation of the -satellites of Jupiter, evidently seeking to insinuate that they were -earlier than Galileo's; and in this sense the letter has since been -quoted,[42] although it appears from John's own deposition, preserved in -the same collection, that at the time of their discovery he could not -have been more than six years old. An oversight of this sort throws -doubt on the whole of the pretended observations, and indeed the letter -has much the air of being the production of a person imperfectly -informed on the subject on which he writes, and probably was compiled to -suit Borelli's purposes, which were to make Galileo's share in the -invention appear as small as possible. - -Galileo himself gives a very intelligible account of the process of -reasoning, by which he detected the secret.--"I argued in the following -manner. The contrivance consists either of one glass or of more--one is -not sufficient, since it must be either convex, concave, or plane; the -last does not produce any sensible alteration in objects, the concave -diminishes them: it is true that the convex magnifies, but it renders -them confused and indistinct; consequently, one glass is insufficient to -produce the desired effect. Proceeding to consider two glasses, and -bearing in mind that the plane glass causes no change, I determined that -the instrument could not consist of the combination of a plane glass -with either of the other two. I therefore applied myself to make -experiments on combinations of the two other kinds, and thus obtained -that of which I was in search." It has been urged against Galileo that, -if he really invented the telescope on theoretical principles, the same -theory ought at once to have conducted him to a more perfect instrument -than that which he at first constructed;[43] but it is plain, from this -statement, that he does not profess to have theorized beyond the -determination of the species of glass which he should employ in his -experiments, and the rest of his operations he avows to have been purely -empirical. Besides, we must take into account the difficulty of grinding -the glasses, particularly when fit tools were yet to be made, and -something must be attributed to Galileo's eagerness to bring his results -to the test of actual experiment, without waiting for that improvement -which a longer delay might and did suggest. Galileo's language bears a -resemblance to the first passage which we quoted from Baptista Porta, -sufficiently close to make it not improbable that he might be assisted -in his inquiries by some recollection of it, and the same passage seems, -in like manner, to have recurred to the mind of Kepler, as soon as he -heard of the invention. Galileo's telescope consisted of a plano-convex -and plano-concave lens, the latter nearest the eye, distant from each -other by the difference of their focal lengths, being, in principle, -exactly the same with the modern opera-glass. He seems to have thought -that the Dutch glass was the same, but this could not be the case, if -the above quoted particular of the _inverted_ weathercock, which belongs -to most traditions of the story, be correct; because it is the -peculiarity of this kind of telescope not to invert objects, and we -should be thus furnished with a demonstrative proof of the falsehood of -Fuccarius's insinuation: in that case the Dutch glass must have been -similar to what was afterwards called the astronomical telescope, -consisting of two convex glasses distant from each other by the sum of -their focal lengths. This supposition is not controverted by the fact, -that this sort of telescope was never employed by astronomers till long -afterwards; for the fame of Galileo's observations, and the superior -excellence of the instruments constructed under his superintendence, -induced every one in the first instance to imitate his constructions as -closely as possible. The astronomical telescope was however eventually -found to possess superior advantages over that which Galileo imagined, -and it is on this latter principle that all modern refracting telescopes -are constructed; the inversion being counteracted in those which are -intended for terrestrial observations, by the introduction of a second -pair of similar glasses, which restore the inverted image to its -original position. For further details on the improvements which have -been subsequently introduced, and on the reflecting telescope, which was -not brought into use till the latter part of the century, the reader is -referred to the Treatise on OPTICAL INSTRUMENTS. - -Galileo, about the same time, constructed microscopes on the same -principle, for we find that, in 1612, he presented one to Sigismund, -King of Poland; but his attention being principally devoted to the -employment and perfection of his telescope, the microscope remained a -long time imperfect in his hands: twelve years later, in 1624, he wrote -to P. Federigo Cesi, that he had delayed to send the microscope, the use -of which he there describes, because he had only just brought it to -perfection, having experienced some difficulty in working the glasses. -Schott tells an amusing story, in his "Magic of Nature," of a Bavarian -philosopher, who, travelling in the Tyrol with one of the newly invented -microscopes about him, was taken ill on the road and died. The -authorities of the village took possession of his baggage, and were -proceeding to perform the last duties to his body, when, on examining -the little glass instrument in his pocket, which chanced to contain a -flea, they were struck with the greatest astonishment and terror, and -the poor Bavarian, condemned by acclamation as a sorcerer who was in the -habit of using a portable familiar, was declared unworthy of Christian -burial. Fortunately for his character, some bold sceptic ventured to -open the instrument, and discovered the true nature of the imprisoned -fiend. - -As soon as Galileo's first telescope was completed, he returned with it -to Venice, and the extraordinary sensation which it excited tends also -strongly to refute Fuccarius's assertion that the Dutch glass was -already known there. During more than a month Galileo's whole time was -employed in exhibiting his instrument to the principal inhabitants of -Venice, who thronged to his house to satisfy themselves of the truth of -the wonderful stories in circulation; and at the end of that time the -Doge, Leonardo Donati, caused it to be intimated to him that such a -present would not be deemed unacceptable by the senate. Galileo took the -hint, and his complaisance was rewarded by a mandate confirming him for -life in his professorship at Padua, at the same time doubling his yearly -salary, which was thus made to amount to 1000 florins. - -It was long before the phrenzy of public curiosity abated. Sirturi -describes a ludicrous violence which was done to himself, when, with the -first telescope which he had succeeded in making, he went up into the -tower of St. Mark, at Venice, in the vain hope of being there entirely -unmolested. Unluckily he was seen by some idlers in the street: a crowd -soon collected round him, who insisted on taking possession of his -instrument, and, handing it one to the other, detained him there for -several hours till their curiosity was satiated, when he was allowed to -return home. Hearing them also inquire eagerly at what inn he lodged, he -thought it better to quit Venice early the next morning, and prosecute -his observations in a less inquisitive neighbourhood.[44] Instruments of -an inferior description were soon manufactured, and vended every where -as philosophical playthings, much in the way in which, in our own time, -the kaleidoscope spread over Europe as fast as travellers could carry -them. But the fabrication of a better sort was long confined, almost -solely, to Galileo and those whom he immediately instructed; and so late -as the year 1637, we find Gaertner, or as he chose to call himself, -Hortensius, assuring Galileo that none could be met with in Holland -sufficiently good to show Jupiter's disc well defined; and in 1634 -Gassendi begs for a telescope from Galileo, informing him that he was -unable to procure a good one either in Venice, Paris, or Amsterdam. - -The instrument, on its first invention, was generally known by the names -of Galileo's tube, the perspective, the double eye-glass: the names of -telescope and microscope were suggested by Demisiano, as we are told by -Lagalla in his treatise on the Moon.[45] - - -FOOTNOTES: - -[32] Mecanique Analytique. - -[33] Histoire des Mathématiques, tom. ii. - -[34] "Per duo specilla ocularia si quis perspiciat, altero alteri -superposito, majora multo et propinquiora videbit omnia."--Fracast. -Homocentrica, § 2, c. 8. - -[35] Si utrumque recte componere noveris, et longinqua et proxima majora -et clara videbis.--Mag. Nat. lib. 17. - -[36] The passage in the original, which is printed alike in the editions -of 1598, 1607, 1619, and 1650, is as follows: Visus constituatur centro -valentissimus speculi, ubi fiet, et valentissimè universales solares -radii disperguntur, et coeunt minimè, sed centro prædicti speculi in -illius medio, ubi diametri transversales, omnium ibi concursus. -Constituitur hoc modo speculum concavum columnare æquidistantibus -lateribus, sed lateri uno obliquo sectionibus illis accomodetur, -trianguli vero obtusianguli, vel orthogonii secentur, hinc inde duobus -transversalibus lineis, ex-centro eductis. Et confectum erit specillum, -ad id, quod diximus utile. - -[37] Diximus de Ptolemæi _speculo_, sive _specillo_ potius, quo per -sexcentena millia pervenientes naves conspiciebat. - -[38] Il Telescopio, 1627. - -[39] Magia Naturæ et Artis Herbipoli, 1657. - -[40] Lettère d'Uomini illustri. Venezia, 1744. - -[41] Borelli. De vero Telescopii inventore, 1655. - -[42] Encyclopædia Britannica. Art. TELESCOPE. - -[43] Ibid. - -[44] Telescopium, Venetiis, 1619. - -[45] De phænomenis in orbe Lunæ. Venetiis, 1612. - - - - -CHAPTER VII. - - _Discovery of Jupiter's - satellites--Kepler--Sizzi--Astrologers--Mæstlin--Horky--Mayer._ - - -AS soon as Galileo had provided himself with a second instrument, he -began a careful examination of the heavenly bodies, and a series of -splendid discoveries soon rewarded his diligence. After considering the -beautiful appearances which the varied surface of the moon presented to -this new instrument, he turned his telescope towards Jupiter, and his -attention was soon arrested by the singular position of three small -stars, near the body of that planet, which appeared almost in a straight -line with it, and in the direction of the ecliptic. The following -evening he was surprised to find that two of the three which had been to -the eastward of the planet, now appeared on the contrary side, which he -could not reconcile with the apparent motion of Jupiter among the fixed -stars, as given by the tables. Observing these night after night, he -could not fail to remark that they changed their relative positions. A -fourth also appeared, and in a short time he could no longer refuse to -believe that these small stars were four moons, revolving round Jupiter -in the same manner in which our earth is accompanied by its single -attendant. In honour of his patron Cosmo, he named them the Medicæan -stars. As they are now hardly known by this appellation, his doubts, -whether he should call them Medicæan, after Cosmo's family, or Cosmical, -from his individual name, are become of less interest. - -An extract from a letter which Galileo received on this occasion from -the court of France, will serve to show how highly the honour of giving -a name to these new planets was at that time appreciated, and also how -much was expected from Galileo's first success in examining the heavens. -"The second request, but the most pressing one which I can make to you, -is, that you should determine, if you discover any other fine star, to -call it by the name of the great star of France, as well as the most -brilliant of all the earth; and, if it seems fit to you, call it rather -by his proper name of Henri, than by the family name of Bourbon: thus -you will have an opportunity of doing a thing just and due and proper in -itself, and at the same time will render yourself and your family rich -and powerful for ever." The writer then proceeds to enumerate the -different claims of Henri IV. to this honour, not forgetting that he -married into the family of the Medici, &c. - -The result of these observations was given to the world, in an Essay -which Galileo entitled _Nuncius Sidereus_, or the Intelligencer of the -Stars; and it is difficult to describe the extraordinary sensation which -its publication produced. Many doubted, many positively refused to -believe, so novel an announcement; all were struck with the greatest -astonishment, according to their respective opinions, either at the new -view of the universe thus offered to them, or at the daring audacity of -Galileo in inventing such fables. We shall proceed to extract a few -passages from contemporary writers relative to this book, and the -discoveries announced in it. - -Kepler deserves precedence, both from his own celebrity, and from the -lively and characteristic account which he gives of his first receiving -the intelligence:--"I was sitting idle at home, thinking of you, most -excellent Galileo, and your letters, when the news was brought me of the -discovery of four planets by the help of the double eye-glass. -Wachenfels stopped his carriage at my door to tell me, when such a fit -of wonder seized me at a report which seemed so very absurd, and I was -thrown into such agitation at seeing an old dispute between us decided -in this way, that between his joy, my colouring, and the laughter of -both, confounded as we were by such a novelty, we were hardly capable, -he of speaking, or I of listening. My amazement was increased by the -assertion of Wachenfels, that those who sent this news from Galileo were -celebrated men, far removed by their learning, weight, and character, -above vulgar folly; that the book was actually in the press, and would -be published immediately. On our separating, the authority of Galileo -had the greatest influence on me, earned by the accuracy of his -judgment, and excellence of his understanding; so I immediately fell to -thinking how there could be any addition to the number of the planets -without overturning my Mysterium Cosmographicum, published thirteen -years ago, according to which Euclid's five regular solids do not allow -more than six planets round the sun." - -This was one of the many wild notions of Kepler's fanciful brain, among -which he was lucky enough at length to hit upon the real and principal -laws of the planetary motions. His theory may be briefly given in his -own words:--"The orbit of the earth is the measure of the rest. About it -circumscribe a dodecahedron. The sphere including this will be that of -Mars. About Mars' orbit describe a tetrahedron: the sphere containing -this will be Jupiter's orbit. Round Jupiter's describe a cube: the -sphere including this will be Saturn's. Within the earth's orbit -inscribe an icosahedron: the sphere inscribed in it will be Venus's -orbit. In Venus inscribe an octahedron: the sphere inscribed in it will -be Mercury's. You have now the reason of the number of the planets:" for -as there are no more than the five regular solids here enumerated, -Kepler conceived this to be a satisfactory reason why there could be -neither more nor less than six planets. His letter continues:--"I am so -far from disbelieving the existence of the four circumjovial planets, -that I long for a telescope to anticipate you, if possible, in -discovering two round Mars, (as the proportion seems to me to require,) -six or eight round Saturn, and perhaps one each round Mercury and -Venus." - -The reader has here an opportunity of verifying Galileo's observation, -that Kepler's method of philosophizing differed widely from his own. The -proper line is certainly difficult to hit between the mere theorist and -the mere observer. It is not difficult at once to condemn the former, -and yet the latter will deprive himself of an important, and often -indispensable assistance, if he neglect from time to time to consolidate -his observations, and thence to conjecture the course of future -observation most likely to reward his assiduity. This cannot be more -forcibly expressed than in the words of Leonardo da Vinci:[46] "Theory -is the general, experiments are the soldiers. The interpreter of the -works of nature is experiment; that is never wrong; it is our judgment -which is sometimes deceived, because we are expecting results which -experiment refuses to give. We must consult experiment, and vary the -circumstances, till we have deduced general rules, for it alone can -furnish us with them. But you will ask, what is the use of these general -rules? I answer, that they direct us in our inquiries into nature and -the operations of art. They keep us from deceiving ourselves and others, -by promising ourselves results which we can never obtain." - -In the instance before us, it is well known that, adopting some of the -opinions of Bruno and Brutti, Galileo, even before he had seen the -satellites of Jupiter, had allowed the possibility of the discovery of -new planets; and we can scarcely suppose that they had weakened his -belief in the probability of further success, or discouraged him from -examining the other heavenly bodies. Kepler on the contrary had taken -the opposite side of the argument; but no sooner was the fallacy of his -first position undeniably demonstrated, than, passing at once from one -extreme to the other, he framed an unsupported theory to account for the -number of satellites which were round Jupiter, and for those which he -expected to meet with elsewhere. Kepler has been styled the legislator -of the skies; his laws were promulgated rather too arbitrarily, and they -often failed, as all laws must do which are not drawn from a careful -observation of the nature of those who are to be governed by them. -Astronomers have reason to be grateful for the theorems which he was the -first to establish; but so far as regards the progress of the science of -inductive reasoning, it is perhaps to be regretted, that the seventeen -years which he wasted in random and unconnected guesses should have been -finally rewarded, by discoveries splendid enough to shed deceitful -lustre upon the method by which he arrived at them. - -Galileo himself clearly perceived the fallacious nature of these -speculations on numbers and proportions, and has expressed his -sentiments concerning them very unequivocally. "How great and common an -error appears to me the mistake of those who persist in making their -knowledge and apprehension the measure of the apprehension and knowledge -of God; as if that alone were perfect, which they understand to be so. -But I, on the contrary, observe that Nature has other scales of -perfection, which we cannot comprehend, and rather seem disposed to -class among imperfections. For instance, among the relations of -different numbers, those appear to us most perfect which exist between -numbers nearly related to each other; as the double, the triple, the -proportion of three to two, &c.; those appear less perfect which exist -between numbers remote from, and prime to each other; as 11 to 7, 17 to -13, 53 to 37, &c.; and most imperfect of all do those appear which exist -between incommensurable quantities, which by us are nameless and -inexplicable. Consequently, if the task had been given to a man, of -establishing and ordering the rapid motions of the heavenly bodies, -according to his notions of perfect proportions, I doubt not that he -would have arranged them according to the former rational proportions; -but, on the contrary, God, with no regard to our imaginary symmetries, -has ordered them in proportions not only incommeasurable and irrational, -but altogether inappreciable by our intellect. A man ignorant of -geometry may perhaps lament, that the circumference of a circle does not -happen to be exactly three times the diameter, or in some other -assignable proportion to it, rather than such that we have not yet been -able to explain what the ratio between them is; but one who has more -understanding will know that if they were other than they are, thousands -of admirable conclusions would have been lost, and that none of the -other properties of the circle would have been true: the surface of the -sphere would not be quadruple of a great circle, nor the cylinder be to -the sphere as three to two: in short, no part of geometry would be true, -and as it now is. If one of our most celebrated architects had had to -distribute this vast multitude of fixed stars through the great vault of -heaven, I believe he would have disposed them with beautiful -arrangements of squares, hexagons, and octagons; he would have dispersed -the larger ones among the middle sized and the less, so as to correspond -exactly with each other; and then he would think he had contrived -admirable proportions: but God, on the contrary, has shaken them out -from His hand as if by chance, and we, forsooth, must think that He has -scattered them up yonder without any regularity, symmetry, and -elegance." - -It is worth remarking that the dangerous ideas of aptitude and -congruence of numbers had taken such deep and general root, that long -afterwards, when the reality of Jupiter's satellites was incontestably -established, and Huyghens had discovered a similar satellite near -Saturn, he was so rash as to declare his belief, (unwarned by the vast -progress which astronomy had made in his own time,) that no more -satellites would be discovered, since the one which he discovered near -Saturn, with Jupiter's four, and our moon, made up the number six, -exactly equal to the number of the principal planets. Every reader knows -that this notion, so unworthy the genius of Huyghens, has been since -exploded by the discovery both of new planets, and new satellites. - -Francesco Sizzi, a Florentine astronomer, took the matter up in a -somewhat different strain from Kepler.[47]--"There are seven windows -given to animals in the domicile of the head, through which the air is -admitted to the rest of the tabernacle of the body, to enlighten, to -warm, and nourish it, which are the principal parts of the [mikrokosmos] -(or little world); two nostrils, two eyes, two ears, and a mouth; so in -the heavens, as in a [makrokosmos] (or great world), there are two -favourable stars, two unpropitious, two luminaries, and Mercury alone -undecided and indifferent. From which and many other similar phenomena -of nature, such as the seven metals, &c., which it were tedious to -enumerate, we gather that the number of planets is necessarily seven. -Moreover, the satellites are invisible to the naked eye, and therefore -can exercise no influence on the earth, and therefore would be useless, -and therefore do not exist. Besides, as well the Jews and other ancient -nations as modern Europeans have adopted the division of the week into -seven days, and have named them from the seven planets: now if we -increase the number of the planets this whole system falls to the -ground." To these remarks Galileo calmly replied, that whatever their -force might be, as a reason for believing beforehand that no more than -seven planets would be discovered, they hardly seemed of sufficient -weight to destroy the new ones when actually seen. - -Others, again, took a more dogged line of opposition, without venturing -into the subtle analogies and arguments of the philosopher just cited. -They contented themselves, and satisfied others, with the simple -assertion, that such things were not, and could not be, and the manner -in which they maintained themselves in their incredulity was -sufficiently ludicrous. "Oh, my dear Kepler,"[48] says Galileo, "how I -wish that we could have one hearty laugh together. Here, at Padua, is -the principal professor of philosophy, whom I have repeatedly and -urgently requested to look at the moon and planets through my glass, -which he pertinaciously refuses to do. Why are you not here? what shouts -of laughter we should have at this glorious folly! and to hear the -professor of philosophy at Pisa labouring before the grand duke with -logical arguments, as if with magical incantations, to charm the new -planets out of the sky." - -Another opponent of Galileo deserves to be named, were it only for the -singular impudence of the charge he ventures to bring against him. "We -are not to think," says Christmann, in the Appendix to his _Nodus -Gordius_, "that Jupiter has four satellites given him by nature, in -order, by revolving round him, to immortalize the name of the Medici, -who first had notice of the observation. These are the dreams of _idle -men_, who love ludicrous ideas better than our laborious and industrious -correction of the heavens.--Nature abhors so horrible a chaos, and to -the truly wise such vanity is detestable." - -Galileo was also urged by the astrologers to attribute some influence, -according to their fantastic notions, to the satellites, and the account -which he gives his friend Dini of his answer to one of this class is -well worth extracting, as a specimen of his method of uniting sarcasm -with serious expostulation; "I must," says he, "tell you what I said a -few days back to one of those nativity-casters, who believe that God, -when he created the heavens and the stars, had no thoughts beyond what -they can themselves conceive, in order to free myself from his tedious -importunity; for he protested, that unless I would declare to him the -effect of the Medicæan planets, he would reject and deny them as -needless and superfluous. I believe this set of men to be of Sizzi's -opinion, that astronomers discovered the other seven planets, not by -seeing them corporally in the skies, but only from their effects on -earth,--much in the manner in which some houses are discovered to be -haunted by evil spirits, not by seeing them, but from the extravagant -pranks which are played there. I replied, that he ought to reconsider -the hundred or thousand opinions which, in the course of his life, he -might have given, and particularly to examine well the events which he -had predicted with the help of Jupiter, and if he should find that all -had succeeded conformably to his predictions, I bid him prophecy merrily -on, according to his old and wonted rules; for I assured him that the -new planets would not in any degree affect the things which are already -past, and that in future he would not be a less fortunate conjuror than -he had been: but if, on the contrary, he should find the events -depending on Jupiter, in some trifling particulars not to have agreed -with his dogmas and prognosticating aphorisms, he ought to set to work -to find new tables for calculating the constitution of the four Jovial -circulators at every bygone moment, and, perhaps, from the diversity of -their aspects, he would be able, with accurate observations and -multiplied conjunctions, to discover the alterations and variety of -influences depending upon them; and I reminded him, that in ages past -they had not acquired knowledge with little labour, at the expense of -others, from written books, but that the first inventors acquired the -most excellent knowledge of things natural and divine with study and -contemplation of the vast book which nature holds ever open before those -who have eyes in their forehead and in their brain; and that it was a -more honourable and praiseworthy enterprize with their own watching, -toil, and study, to discover something admirable and new among the -infinite number which yet remain concealed in the darkest depths of -philosophy, than to pass a listless and lazy existence, labouring only -to darken the toilsome inventions of their neighbours, in order to -excuse their own cowardice and inaptitude for reasoning, while they cry -out that nothing can be added to the discoveries already made." - -The extract given above from Kepler, is taken from an Essay, published -with the later editions of the _Nuncius_, the object and spirit of which -seem to have been greatly misunderstood, even by some of Kepler's -intimate friends.--They considered it as a covert attack upon Galileo, -and, accordingly, Maestlin thus writes to him:--"In your Essay (which I -have just received) you have plucked Galileo's feathers well; I mean, -that you have shown him not to be the inventor of the telescope, not to -have been the first who observed the irregularities of the moon's -surface, not to have been the first discoverer of more worlds than the -ancients were acquainted with, &c. One source of exultation was still -left him, from the apprehension of which Martin Horky has now entirely -delivered me." It is difficult to discover in what part of Kepler's book -Maestlin found all this, for it is one continued encomium upon Galileo; -insomuch that Kepler almost apologizes in the preface for what may seem -his intemperate admiration of his friend. "Some might wish I had spoken -in more moderate terms in praise of Galileo, in consideration of the -distinguished men who are opposed to his opinions, but I have written -nothing fulsome or insincere. I praise him, for myself; I leave other -men's judgments free; and shall be ready to join in condemnation when -some one wiser than myself shall, by sound reasoning, point out his -errors." However, Maestlin was not the only one who misunderstood -Kepler's intentions: the Martin Horky of whom he speaks, a young German, -also signalized himself by a vain attack upon the book which he thought -his patron Kepler condemned. He was then travelling in Italy, whence he -wrote to Kepler his first undetermined thoughts about the new -discoveries. "They are wonderful; they are stupendous; whether they are -true or false I cannot tell."[49] He seems soon to have decided that -most reputation was to be gained on the side of Galileo's opponents, and -his letters accordingly became filled with the most rancorous abuse of -him. At the same time, that the reader may appreciate Horky's own -character, we shall quote a short sentence at the end of one of his -letters, where he writes of a paltry piece of dishonesty with as great -glee as if he had solved an ingenious and scientific problem. After -mentioning his meeting Galileo at Bologna, and being indulged with a -trial of his telescope, which, he says, "does wonders upon the earth, -but represents celestial objects falsely;"[50] he concludes with the -following honourable sentence:--"I must confide to you a theft which I -committed. I contrived to take a mould of the glass in wax, without the -knowledge of any one, and, when I get home, I trust to make a telescope -even better than Galileo's own." - -Horky having declared to Kepler, "I will never concede his four new -planets to that Italian from Padua though I die for it," followed up -this declaration by publishing a book against Galileo, which is the one -alluded to by Maestlin, as having destroyed the little credit which, -according to his view, Kepler's publication had left him. This book -professes to contain the examination of four principal questions -touching the alleged planets; 1st, Whether they exist? 2nd, What they -are? 3rd, What they are like? 4th, Why they are? The first question is -soon disposed of, by Horky's declaring positively that he has examined -the heavens with Galileo's own glass, and that no such thing as a -satellite about Jupiter exists. To the second, he declares solemnly, -that he does not more surely know that he has a soul in his body, than -that reflected rays are the sole cause of Galileo's erroneous -observations. In regard to the third question, he says, that these -planets are like the smallest fly compared to an elephant; and, finally, -concludes on the fourth, that the only use of them is to gratify -Galileo's "thirst of gold," and to afford himself a subject of -discussion.[51] - -Galileo did not condescend to notice this impertinent folly; it was -answered by Roffini, a pupil of Magini, and by a young Scotchman of the -name of Wedderburn, then a student at Padua, and afterwards a physician -at the Court of Vienna. In the latter reply we find it mentioned, that -Galileo was also using his telescope for the examination of insects, -&c.[52] Horky sent his performance triumphantly to Kepler, and, as he -returned home before receiving an answer, he presented himself before -his patron in the same misapprehension under which he had written, but -the philosopher received him with a burst of indignation which rapidly -undeceived him. The conclusion of the story is characteristic enough to -be given in Kepler's own account of the matter to Galileo, in which, -after venting his wrath against this "scum of a fellow," whose -"obscurity had given him audacity," he says, that Horky begged so hard -to be forgiven, that "I have taken him again into favour upon this -preliminary condition, to which he has agreed:--that I am to shew him -Jupiter's satellites, AND HE IS TO SEE THEM, and own that they are -there." - -In the same letter Kepler writes, that although he has himself perfect -confidence in the truth of Galileo's assertions, yet he wishes he could -furnish him with some corroborative testimonies, which Kepler could -quote in arguing the point with others. This request produced the -following reply, from which the reader will also learn the new change -which had now taken place in Galileo's fortunes, the result of the -correspondence with Florence, part of which we have already -extracted.[53] "In the first place, I return you my thanks that you -first, and almost alone, before the question had been sifted (such is -your candour and the loftiness of your mind), put faith in my -assertions. You tell me you have some telescopes, but not sufficiently -good to magnify distant objects with clearness, and that you anxiously -expect a sight of mine, which magnifies images more than a thousand -times. It is mine no longer, for the Grand Duke of Tuscany has asked it -of me, and intends to lay it up in his museum, among his most rare and -precious curiosities, in eternal remembrance of the invention: I have -made no other of equal excellence, for the mechanical labour is very -great: I have, however, devised some instruments for figuring and -polishing them which I am unwilling to construct here, as they could not -conveniently be carried to Florence, where I shall in future reside. You -ask, my dear Kepler, for other testimonies:--I produce, for one, the -Grand Duke, who, after observing the Medicæan planets several times with -me at Pisa during the last months, made me a present, at parting, worth -more than a thousand florins, and has now invited me to attach myself to -him with the annual salary of one thousand florins, and with the title -of Philosopher and Principal Mathematician to His Highness; without the -duties of any office to perform, but with the most complete leisure; so -that I can complete my Treatises on Mechanics, on the Constitution of -the Universe, and on Natural and Violent Local Motion, of which I have -demonstrated geometrically many new and admirable phenomena. I produce, -for another witness, myself, who, although already endowed in this -college with the noble salary of one thousand florins, such as no -professor of mathematics ever before received, and which I might -securely enjoy during my life, even if these planets had deceived me and -should disappear, yet quit this situation, and betake me where want and -disgrace will be my punishment should I prove to have been mistaken." - -It is difficult not to regret that Galileo should be thus called on to -resign his best glasses, but it appears probable that on becoming more -familiar with the Grand Duke, he ventured to suggest that this telescope -would be more advantageously employed in his own hands, than pompously -laid up in a museum; for in 1637 we find him saying, in answer to a -request from his friend Micanzio to send him a telescope--"I am sorry -that I cannot oblige you with the glasses for your friend, but I am no -longer capable of making them, and I have just parted with two tolerably -good ones which I had, reserving only my old discoverer of celestial -novelties which is already promised to the Grand Duke." Cosmo was dead -in 1637, and it is his son Ferdinand who is here meant, who appears to -have inherited his father's love of science. Galileo tells us, in the -same letter, that Ferdinand had been amusing himself for some months -with making object-glasses, and always carried one with him to work at -wherever he went. - -When forwarding this telescope to Cosmo in the first instance, Galileo -adds, with a very natural feeling--"I send it to his highness unadorned -and unpolished, as I made it for my own use, and beg that it may always -be left in the same state; for none of the old parts ought to be -displaced to make room for new ones, which will have had no share in the -watchings and fatigues of these observations." A telescope was in -existence, though with the object glass broken, at the end of the last -century, and probably still is in the Museum at Florence, which was -shewn as the discoverer of Jupiter's satellites. Nelli, on whose -authority this is mentioned, appears to question its genuineness. The -first reflecting telescope, made with Newton's own hands, and scarcely -possessing less interest than the first of Galileo's, is preserved in -the library of the Royal Society. - -By degrees the enemies of Galileo and of the new stars found it -impossible to persevere in their disbelief, whether real or pretended, -and at length seemed resolved to compensate for the sluggishness of -their perception, by its acuteness when brought into action. Simon Mayer -published his "Mundus Jovialis" in 1614, in which he claims to have been -an original observer of the satellites, but, with an affectation of -candour, allows that Galileo observed them probably about the same time. -The earliest observation which he has recorded is dated 29th December, -1609, but, not to mention the total want of probability that Mayer would -not have immediately published so interesting a discovery, it is to be -observed, that, as he used the old style, this date of 29th December -agrees with the 8th January, 1610, of the new style, which was the date -of Galileo's second observation, and Galileo ventured to declare his -opinion, that this pretended observation was in fact a plagiarism. - -Scheiner counted five, Rheita nine, and other observers, with increasing -contempt for Galileo's imperfect announcements, carried the number as -high as twelve.[54] In imitation of Galileo's nomenclature, and to -honour the sovereigns of the respective observers, these supposed -additional satellites were dignified with the names of Vladislavian, -Agrippine, Urbanoctavian, and Ferdinandotertian planets; but a very -short time served to show it was as unsafe to exceed as to fall short of -the number which Galileo had fixed upon, for Jupiter rapidly removed -himself from the neighbourhood of the fixed stars, which gave rise to -these pretended discoveries, carrying with him only his four original -attendants, which continued in every part of his orbit to revolve -regularly about him. - -Perhaps we cannot better wind up this account of the discovery of -Jupiter's satellites, and of the intense interest they have at all times -inspired, than in the words of one who inherits a name worthy to be -ranked with that of Galileo in the list of astronomical discoverers, and -who takes his own place among the most accomplished mathematicians of -the present times. "The discovery of these bodies was one of the first -brilliant results of the invention of the telescope; one of the first -great facts which opened the eyes of mankind to the system of the -universe, which taught them the comparative insignificance of their own -planet, and the superior vastness and nicer mechanism of those other -bodies, which had before been distinguished from the stars only by their -motion, and wherein none but the boldest thinkers had ventured to -suspect a community of nature with our own globe. This discovery gave -the holding turn to the opinions of mankind respecting the Copernican -system; the analogy presented by these little bodies (little however -only in comparison with the great central body about which they revolve) -performing their beautiful revolutions in perfect harmony and order -about it, being too strong to be resisted. This elegant system was -watched with all the curiosity and interest the subject naturally -inspired. The eclipses of the satellites speedily attracted attention, -and the more when it was discerned, as it speedily was, by Galileo -himself, that they afforded a ready method of determining the difference -of longitudes of distant places on the earth's surface, by observations -of the instants of their disappearances and reappearances, -simultaneously made. Thus the first astronomical solution of the great -problem of the longitude, the first mighty step which pointed out a -connection between speculative astronomy and practical utility, and -which, replacing the fast dissipating dreams of astrology by nobler -visions, showed how the stars might really, and without fiction, be -called arbiters of the destinies of empires, we owe to the satellites of -Jupiter, those atoms imperceptible to the naked eye, and floating like -motes in the beam of their primary--itself an atom to our sight, noticed -only by the careless vulgar as a large star, and by the philosophers of -former ages as something moving among the stars, they knew not what, nor -why: perhaps only to perplex the wise with fruitless conjectures, and -harass the weak with fears as idle as their theories."[55] - - -FOOTNOTES: - -[46] Venturi. Essai sur les ouvrages de Leo. da Vinci. - -[47] Dianoia Astronomica, Venetiis, 1610. - -[48] Kepleri Epistolæ. - -[49] Kepleri Epistolæ. - -[50] It may seem extraordinary that any one could support an argument by -this partial disbelief in the instrument, which was allowed on all hands -to represent terrestrial objects correctly. A similar instance of -obstinacy, in an almost identical case though in a more unpretending -station, once came under the writer's own observation. A farmer in -Cambridgeshire, who had acquired some confused notions of the use of the -quadrant, consulted him on a new method of determining the distances and -magnitudes of the sun and moon, which he declared were far different -from the quantities usually assigned to them. After a little -conversation, the root of his error, certainly sufficiently gross, -appeared to be that he had confounded the angular measure of a degree, -with 69½ miles, the linear measure of a degree on the earth's surface. -As a short way of showing his mistake, he was desired to determine, in -the same manner, the height of his barn which stood about 30 yards -distant; he lifted the quadrant to his eye, but perceiving, probably, -the monstrous size to which his principles were forcing him, he said, -"Oh, Sir, the quadrant's only true for the sky." He must have been an -objector of this kind, who said to Galileo,--"Oh, Sir, the telescope's -only true for the earth." - -[51] Venturi. - -[52] Quatuor probl. confut. per J. Wedderbornium, Scotobritannum. -Patavii, 1610. - -[53] See page 18. - -[54] Sherburne's Sphere of Manilius. London, 1675. - -[55] Herschel's Address to the Astronomical Society, 1827. - - - - -CHAPTER VIII. - - _Observations on the Moon--Nebulæ--Saturn--Venus--Mars._ - - -THERE were other discoveries announced in Galileo's book of great and -unprecedented importance, and which scarcely excited less discussion -than the controverted Medicæan planets. His observations on the moon -threw additional light on the constitution of the solar system, and -cleared up the difficulties which encumbered the explanation of the -varied appearance of her surface. The different theories current at that -day, to account for these phenomena, are collected and described by -Benedetti, and also with some liveliness, in a mythological poem, by -Marini.[56] We are told, that, in the opinion of some, the dark shades -on the moon's surface arise from the interposition of opaque bodies -floating between her and the sun, which prevents his light from reaching -those parts: others thought, that on account of her vicinity to the -earth, she was partly tainted with the imperfection of our terrestrial -and elementary nature, and was not of that entirely pure and refined -substance of which the more remote heavens consist: a third party looked -on her as a vast mirror, and maintained that the dark parts of her -surface were the reflected images of our earthly forests and mountains. - -Galileo's glass taught him to believe that the surface of this planet, -far from being smooth and polished, as was generally taken for granted, -really resembled our earth in its structure; he was able distinctly to -trace on it the outlines of mountains and other inequalities, the -summits of which reflected the rays of the sun before these reached the -lower parts, and the sides of which, turned from his beams, lay buried -in deep shadow. He recognised a distribution into something similar to -continents of land, and oceans of water, which reflect the sun's light -to us with greater or less vivacity, according to their constitution. -These conclusions were utterly odious to the Aristotelians; they had -formed a preconceived notion of what the moon ought to be, and they -loathed the doctrines of Galileo, who took delight, as they said, in -distorting and ruining the fairest works of nature. It was in vain he -argued, as to the imaginary perfection of the spherical form, that -although the moon, or the earth, were it absolutely smooth, would indeed -be a more perfect sphere than in its present rough state, yet touching -the perfection of the earth, considered as a natural body calculated for -a particular purpose, every one must see that absolute smoothness and -sphericity would make it not only less perfect, but as far from being -perfect as possible. "What else," he demanded, "would it be but a vast -unblessed desert, void of animals, of plants, of cities and of men; the -abode of silence and inaction; senseless, lifeless, soulless, and stript -of all those ornaments which make it now so various and so beautiful?" - -He reasoned to no purpose with the slaves of the ancient schools: -nothing could console them for the destruction of their smooth -unalterable surface, and to such an absurd length was this hallucination -carried, that one opponent of Galileo, Lodovico delle Colombe, -constrained to allow the evidence of the sensible inequalities of the -moon's surface, attempted to reconcile the old doctrine with the new -observations, by asserting, that every part of the moon, which to the -terrestrial observer appeared hollow and sunken, was in fact entirely -and exactly filled up with a clear crystal substance, perfectly -imperceptible by the senses, but which restored to the moon her -accurately spherical and smooth surface. Galileo met the argument in the -manner most fitting, according to one of Aristotle's own maxims, that -"it is foolish to refute absurd opinions with too much curiosity." -"Truly," says he, "the idea is admirable, its only fault is that it is -neither demonstrated nor demonstrable; but I am perfectly ready to -believe it, provided that, with equal courtesy, I may be allowed to -raise upon your smooth surface, crystal mountains (which nobody can -perceive) ten times higher than those which I have actually seen and -measured." By threatening to proceed to such extremities, he seems to -have scared the opposite party into moderation, for we do not find that -the crystalline theory was persevered in. - -In the same essay, Galileo also explained at some length the cause of -that part of the moon being visible, which is unenlightened directly by -the sun in her first and last quarter. Maestlin, and before him Leonardo -da Vinci, had already declared this to arise from what may be called -_earthshine_, or the reflection of the sun's light from the terrestrial -globe, exactly similar to that which the moon affords us when we are -similarly placed between her and the sun; but the notion had not been -favourably received, because one of the arguments against the earth -being a planet, revolving like the rest round the sun, was, that it did -not shine like them, and was therefore of a different nature; and this -argument, weak as it was in itself, the theory of terrestrial reflection -completely overturned. The more popular opinions ascribed this feeble -light, some to the fixed stars, some to Venus, some to the rays of the -sun, penetrating and shining through the moon. Even the sagacious -Benedetti adopted the notion of this light being caused by Venus, in the -same sentence in which he explains the true reason of the faint light -observed during a total eclipse of the moon, pointing out that it is -occasioned by those rays of the sun, which reach the moon, after being -bent round the sides of the earth by the action of our atmosphere.[57] - -Galileo also announced the detection of innumerable stars, invisible to -the unassisted sight; and those remarkable appearances in the heavens, -generally called nebulæ, the most considerable of which is familiar to -all under the name of the milky way, when examined by his instrument, -were found to resolve themselves into a vast collection of minute stars, -too closely congregated to produce a separate impression upon the -unassisted eye.[58] Benedetti, who divined that the dark shades on the -moon's surface arose from the constitution of those parts which suffered -much of the light to pass into them, and consequently reflected a less -portion of it, had maintained that the milky way was the result of the -converse of the same phenomenon, and declared, in the language of his -astronomy, that it was a part of the eighth orb, which did not, like the -rest, allow the sun's light to traverse it freely, but reflected a small -part feebly to our sight. - -The Anti-Copernicans would probably have been well pleased, if by these -eternally renewed discussions and disputes, they could have occupied -Galileo's time sufficiently to detain his attention from his telescope -and astronomical observations; but he knew too well where his real -strength lay, and they had scarcely time to compound any thing like an -argument against him and his theories, before they found him in -possession of some new facts, which they were unprepared to meet, -otherwise than by the never-failing resource of abuse and affected -contempt. The year had not expired before Galileo had new intelligence -to communicate of the highest importance. Perhaps he had been taught -caution from the numerous piracies which had been committed upon his -discoveries, and he first announced his new discoveries enigmatically, -veiling their real import by transpositions of the letters in the words -which described them, (a practice then common, and not disused even at a -much later date,) and inviting all astronomers to declare, within a -certain time, if they had noted any thing new in the heavens worthy of -observation. The transposed letters which he published were-- - - "_Smaismrmilme poeta leumi bvne nugttaviras._" - -Kepler, in the true spirit of his riddling philosophy, endeavoured to -decypher the meaning, and fancied he had succeeded when he formed a -barbarous Latin verse, - - "_Salve umbistineum geminatum Martia proles_," - -conceiving that the discovery, whatever it might be, related to the -planet Mars, to which Kepler's attention had before been particularly -directed. The reader, however, need not weary himself in seeking a -translation of this solution, for at the request of the Emperor Rodolph, -Galileo speedily sent to him the real reading-- - - _Altissimum planetam tergeminum observavi_; - -that is, "I have observed that the most distant planet is triple," or, -as he further explains the matter, "I have with great admiration -observed that Saturn is not a single star, but three together, which as -it were touch each other; they have no relative motion, and are -constituted in this form [Symbol: oOo] the middle being somewhat larger -than the lateral ones. If we examine them with an eye-glass which -magnifies the surface less than 1000 times, the three stars do not -appear very distinctly, but Saturn has an oblong appearance, like the -appearance of an olive, thus [Symbol: horizontal 0]. Now I have -discovered a court for Jupiter, and two servants for this old man, who -aid his steps and never quit his side." Galileo was, however, no match -in this style of writing for Kepler, who disapproved his friend's -metaphor, and, in his usual fanciful and amusing strain,--"I will not," -said he, "make an old man of Saturn, nor slaves of his attendant globes, -but rather let this tricorporate form be Geryon, so shall Galileo be -Hercules, and the telescope his club; armed with which, he has conquered -that distant planet, and dragged him from the remotest depths of nature, -and exposed him to the view of all." Galileo's glass was not of -sufficient power to shew him the real constitution of this extraordinary -planet; it was reserved for Huyghens, about the year 1656, to declare to -the world that these supposed attendant stars are in fact part of a ring -which surrounds, and yet is completely distinct from the body of -Saturn;[59] and the still more accurate observations of Herschel have -ascertained that it consists of two concentric rings revolving round the -planet, and separated from each other by a space which our most powerful -telescopes scarcely enable us to measure. - -Galileo's second statement concluded with the remark, that "in the other -planets nothing new was to be observed;" but a month had scarcely -elapsed, before he communicated to the world another enigma, - - _Hæc immatura à me jam frustra leguntur oy_, - -which, as he said, contained the announcement of a new phenomenon, in -the highest degree important to the truth of the Copernican system. The -interpretation of this is, - - _Cynthiæ figuras æmulatur mater amorum_, - -that is to say,--Venus rivals the appearances of the moon--for Venus -being now arrived at that part of her orbit in which she is placed -between the earth and the sun, and consequently, with only a part of her -enlightened surface turned towards the earth, the telescope shewed her -in a crescent form, like the moon in a similar position, and tracing her -through the whole of her orbit round the sun, or at least so long as she -was not invisible from his overpowering light, Galileo had the -satisfaction of seeing the enlightened portion in each position assume -the form appropriate to that hypothesis. It was with reason, therefore, -that he laid stress on the importance of this observation, which also -established another doctrine scarcely less obnoxious to the -Anti-Copernicans, namely, that a new point of resemblance was here found -between the earth and one of the principal planets; and as the -reflection from the earth upon the moon had shewn it to be luminous like -the planets when subjected to the rays of the sun, so this change of -apparent figure demonstrated that one of the planets not near the earth, -and therefore probably all, were in their own nature not luminous, and -only reflected the sun's light which fell upon them; an inference, of -which the probability was still farther increased a few years later by -the observation of the transit of Mercury over the sun's disc. - -It is curious that only twenty-five years before this discovery of the -phases (or appearances) of Venus, a commentator of Aristotle, under the -name of Lucillus Philalthæus, had advanced the doctrine that all the -planets except the moon are luminous of themselves, and in proof of his -assertion had urged, "that if the other planets and fixed stars received -their light from the sun, they would, as they approached and receded -from him, or as he approached and receded from them, assume the same -phases as the moon, which, he adds, we have never yet observed."--He -further remarks, "that Mercury and Venus would, in the supposed case of -their being nearer the earth than the sun, eclipse it occasionally, just -as eclipses are occasioned by the moon." Perhaps it is still more -remarkable, that these very passages, in which the reasoning is so -correct, though the facts are too hastily taken for granted, (the common -error of that school,) are quoted by Benedetti, expressly to shew the -ignorance and presumption of the author. Copernicus, whose want of -instruments had prevented him from observing the horned appearance of -Venus when between the earth and sun, had perceived how formidable an -obstacle the non-appearance of this phenomenon presented to his system; -he endeavoured, though unsatisfactorily, to account for it by supposing -that the rays of the sun passed freely through the body of the planet, -and Galileo takes occasion to praise him for not being deterred from -adopting the system, which, on the whole, appeared to agree best with -the phenomena, by meeting with some which it did not enable him to -explain. Milton, whose poem is filled with allusions to Galileo and his -astronomy, has not suffered this beautiful phenomenon to pass unnoticed. -After describing the creation of the Sun, he adds:-- - - Hither, as to their fountain, other stars - Repairing, in their golden urns draw light, - And hence the morning planet gilds her horns.[60] - -Galileo also assured himself, at the same time, that the fixed stars did -not receive their light from the sun. This he ascertained by comparing -the vividness of their light, in all positions, with the feebleness of -that of the distant planets, and by observing the different degrees of -brightness with which all the planets shone at different distances from -the sun. The more remote planets did not, of course, afford equal -facilities with Venus for so decisive an observation; but Galileo -thought he observed, that when Mars was in quadratures, (or in the -quarters, the middle points of his path on either side,) his figure -varied slightly from a perfect circle. Galileo concludes the letter, in -which he announces these last observations to his pupil Castelli, with -the following expressions, shewing how justly he estimated the -opposition they encountered:--"You almost make me laugh by saying that -these clear observations are sufficient to convince the most obstinate: -it seems you have yet to learn that long ago the observations were -enough to convince those who are capable of reasoning, and those who -wish to learn the truth; but that to convince the obstinate, and those -who care for nothing beyond the vain applause of the stupid and -senseless vulgar, not even the testimony of the stars would suffice, -were they to descend on earth to speak for themselves. Let us then -endeavour to procure some knowledge for ourselves, and rest contented -with this sole satisfaction; but of advancing in popular opinion, or -gaining the assent of the book-philosophers, let us abandon both the -hope and the desire." - - -FOOTNOTES: - -[56] Adone di Marini, Venetiis, 1623, Cant. x. - -[57] Speculat. Lib Venetiis, 1585, Epistolæ. - -[58] This opinion, with respect to the milky way, had been held by some -of the ancient astronomers. _See_ Manilius. Lib. i. v. 753. - - "_Anne magis densâ stellarum turba coronâ_ - "_Contexit flammas, et crasso lumine candet,_ - "_Et fulgore nitet collato clarior orbis._" - -[59] Huyghens announced his discovery in this form: _a a a a a a a c c c -c c d e e e e e g h i i i i i i i l l l l m m n n n n n n n n n o o o o -p p q r r s t t t t t u u u u u_, which he afterwards recomposed into -the sentence. _Annulo cingitur, tenui, plano, nusquam cohærente, ad -eclipticam inclinato_. De Saturni Lunâ. Hagæ, 1656. - -[60] B. vii. v. 364. Other passages may be examined in B. i. 286; iii. -565-590, 722-733; iv. 589; v. 261, 414; vii. 577; viii. 1-178. - - - - -CHAPTER IX. - - _Account of the Academia Lincea--Del Cimento--Royal Society._ - - -GALILEO'S resignation of the mathematical professorship at Padua -occasioned much dissatisfaction to all those who were connected with -that university. Perhaps not fully appreciating his desire of returning -to his native country, and the importance to him and to the scientific -world in general, of the complete leisure which Cosmo secured to him at -Florence, (for by the terms of his diploma he was not even required to -reside at Pisa, nor to give any lectures, except on extraordinary -occasions, to sovereign princes and other strangers of distinction,) the -Venetians remembered only that they had offered him an honourable asylum -when almost driven from Pisa; that they had increased his salary to four -times the sum which any previous professor had enjoyed; and, finally, by -an almost unprecedented decree, that they had but just secured him in -his post during the remainder of his life. Many took such offence as to -refuse to have any further communication with him; and Sagredo, a -constant friend of Galileo, wrote him word that he had been threatened -with a similar desertion unless he should concur in the same peremptory -resolution, which threats, however, Sagredo, at the same time, intimates -his intention of braving. - -Early in the year 1611, Galileo made his first appearance in Rome, where -he was received with marks of distinguished consideration, and where all -ranks were eager to share the pleasure of contemplating the new -discoveries. "Whether we consider cardinal, prince, or prelate, he found -an honourable reception from them all, and had their palaces as open and -free to him as the houses of his private friends."[61] Among other -distinctions he was solicited to become a member of the newly-formed -philosophical society, the once celebrated _Academia Lincea_, to which -he readily assented. The founder of this society was Federigo Cesi, the -Marchese di Monticelli, a young Roman nobleman, the devotion of whose -time and fortune to the interests of science has not been by any means -rewarded with a reputation commensurate with his deserts. If the energy -of his mind had been less worthily employed than in fostering the cause -of science and truth, and in extending the advantages of his birth and -fortune to as many as were willing to co-operate with him, the name of -Federigo Cesi might have appeared more prominently on the page of -history. Cesi had scarcely completed his 18th year, when, in 1603, he -formed the plan of a philosophical society, which in the first instance -consisted only of himself and three of his most intimate friends, Hecke, -a Flemish physician, Stelluti, and Anastasio de Filiis. Cesi's father, -the Duca d'Acquasparta, who was of an arbitrary and extravagant temper, -considered such pursuits and associates as derogatory to his son's rank; -he endeavoured to thwart the design by the most violent and -unjustifiable proceedings, in consequence of which, Cesi in the -beginning of 1605 privately quitted Rome, Hecke was obliged to leave -Italy altogether from fear of the Inquisition, which was excited against -him, and the academy was for a time virtually dissolved. The details of -these transactions are foreign to the present narrative: it will be -enough to mention that, in 1609, Cesi, who had never altogether -abandoned his scheme, found the opposition decaying which he at first -experienced, and with better success he renewed the plan which he had -sketched six years before. A few extracts from the Regulations will -serve to shew the spirit in which this distinguished society was -conceived:-- - -"The Lyncean Society desires for its academicians, philosophers eager -for real knowledge, who will give themselves to the study of nature, and -especially to mathematics; at the same time it will not neglect the -ornaments of elegant literature and philology, which like a graceful -garment adorn the whole body of science.--In the pious love of wisdom, -and to the praise of the most good and most high God, let the Lynceans -give their minds, first to observation and reflection, and afterwards to -writing and publishing.--It is not within the Lyncean plan to find -leisure for recitations and declamatory assemblies; the meetings will -neither be frequent nor full, and chiefly for transacting the necessary -business of the society: but those who wish to enjoy such exercises will -in no respect be hindered, provided they attend them as accessory -studies, decently and quietly, and without making promises and -professions of how much they are about to do. For there is ample -philosophical employment for every one by himself, particularly if pains -are taken in travelling and in the observation of natural phenomena, and -in the book of nature which every one has at home, that is to say, the -heavens and the earth; and enough may be learned from the habits of -constant correspondence with each other, and alternate offices of -counsel and assistance.--Let the first fruits of wisdom be love; and so -let the Lynceans love each other as if united by the strictest ties, nor -suffer any interruption of this sincere bond of love and faith, -emanating from the source of virtue and philosophy.--Let them add to -their names the title of Lyncean, which has been advisedly chosen as a -warning and constant stimulus, especially when they write on any -literary subject, also in their private letters to their associates, and -in general when any work comes from them wisely and well performed.--The -Lynceans will pass over in silence all political controversies and -quarrels of every kind, and wordy disputes, especially gratuitous ones, -which give occasion to deceit, unfriendliness, and hatred; like men who -desire peace, and seek to preserve their studies free from molestation, -and to avoid every sort of disturbance. And if any one by command of his -superiors, or from some other necessity, is reduced to handle such -matters, since they are foreign to physical and mathematical science, -and consequently alien to the object of the Academy, let them be printed -without the Lyncean name."[62] - -The society which was eventually organized formed but a very trifling -part of the comprehensive scheme which Cesi originally proposed to -himself; it had been his wish to establish a scientific Order which -should have corresponding lodges in the principal towns of Europe, and -in other parts of the globe, each consisting of not more than five nor -less than three members, besides an unlimited number of Academicians not -restricted to any particular residence or regulations. The -mortifications and difficulties to which he was subjected from his -father's unprincipled behaviour, render it most extraordinary and -admirable that he should have ventured to undertake even so much as he -actually carried into execution. He promised to furnish to the members -of his society such assistance as they might require in the prosecution -of their respective researches, and also to defray the charges of -publishing such of their works as should be thought worthy of appearing -with the common sanction. Such liberal offers were not likely to meet -with an unfavourable reception: they were thankfully accepted by many -well qualified to carry his design into execution, and Cesi was soon -enabled formally to open his academy, the distinctive title of which he -borrowed from the Lynx, with reference to the piercing sight which that -animal has been supposed to possess. This quality seemed to him an -appropriate emblem of those which he desired to find in his -academicians, for the purpose of investigating the secrets of nature; -and although, at the present day, the name may appear to border on the -grotesque, it was conceived in the spirit of the age, and the fantastic -names of the numberless societies which were rapidly formed in various -parts of Italy far exceed whatever degree of quaintness may be thought -to belong to the Lyncean name. The Inflamed--the Transformed--the -Uneasy--the Humorists--the Fantastic--the Intricate--the Indolent--the -Senseless--the Undeceived--the Valiant--the Ætherial Societies are -selected from a vast number of similar institutions, the names of which, -now almost their sole remains, are collected by the industry of Morhof -and Tiraboschi.[63] The Humorists are named by Morhof as the only -Italian philosophical society anterior to the Lynceans; their founder -was Paolo Mancino, and the distinctive symbol which they adopted was -rain dropping from a cloud, with the motto _Redit agmine dulci_;--their -title is derived from the same metaphor. The object of their union -appears to have been similar to that of the Lynceans, but they at no -time attained to the celebrity to which Cesi's society rose from the -moment of its incorporation. Cesi took the presidency for his life, and -the celebrated Baptista Porta was appointed vice president at Naples. -Stelluti acted as the legal representative of the society, with the -title of procuratore. Of the other two original members Anastasio de -Filiis was dead, and although Hecke returned to Italy in 1614, and -rejoined the Academy, yet he was soon afterwards struck off the list in -consequence of his lapsing into insanity. Among the academicians we find -the names of Galileo, Fabio Colonna, Lucas Valerio, Guiducci, Welser, -Giovanni Fabro, Terrentio, Virginio Cesarini, Ciampoli, Molitor, -Cardinal Barberino, (nephew of Pope Urban VIII.) Stelliola, Salviati, -&c. - -The principal monument still remaining of the zeal and industry to which -Cesi incited his academicians is the Phytobasanos, a compendium of the -natural history of Mexico, which must be considered a surprising -performance for the times in which it appeared. It was written by a -Spaniard named Hernandez; and Reccho, who often has the credit of the -whole work, made great additions to it. During fifty years the -manuscript had been neglected, when Cesi discovered it, and employed -Terrentio, Fabro, and Colonna, all Lynceans, to publish it enriched with -their notes and emendations. Cesi himself published several treatises, -two of which are extant; his _Tabulæ Phytosophicæ_, and a Dissertation -on Bees entitled _Apiarium_, the only known copy of which last is in the -library of the Vatican. His great work, _Theatrum Naturæ_, was never -printed; a circumstance which tends to shew that he did not assemble the -society round him for the purpose of ministering to his own vanity, but -postponed the publication of his own productions to the labours of his -coadjutors. This, and many other valuable works belonging to the academy -existed in manuscript till lately in the Albani Library at Rome. Cesi -collected, not a large, but an useful library for the use of the -academy, (which was afterwards augmented on the premature death of -Cesarini by the donation of his books); he filled a botanical garden -with the rarer specimens of plants, and arranged a museum of natural -curiosities; his palace at Rome was constantly open to the academicians; -his purse and his influence were employed with equal liberality in their -service. - -Cesi's death, in 1632, put a sudden stop to the prosperity of the -society, a consequence which may be attributed to the munificence with -which he had from the first sustained it: no one could be found to fill -his place in the princely manner to which the academicians were -accustomed, and the society, after lingering some years under the -nominal patronage of Urban VIII., gradually decayed, till, by the death -of its principal members, and dispersion of the rest, it became entirely -extinct.[64] Bianchi, whose sketch of the academy was almost the only -one till the appearance of Odescalchi's history, made an attempt to -revive it in the succeeding century, but without any permanent effect. A -society under the same name has been formed since 1784, and is still -flourishing in Rome. Before leaving the subject it may be mentioned, -that one of the earliest notices that Bacon's works were known in Italy -is to be found in a letter to Cesi, dated 1625; in which Pozzo, who had -gone to Paris with Cardinal Barberino, mentions having seen them there -with great admiration, and suggests that Bacon would be a fit person to -be proposed as a member of their society. After Galileo's death, three -of his principal followers, Viviani, Torricelli, and Aggiunti formed the -plan of establishing a similar philosophical society, and though -Aggiunti and Torricelli died before the scheme could be realized, -Viviani pressed it forward, and, under the auspices of Ferdinand II., -formed a society, which, in 1657, merged in the famous _Academia del -Cimento_, or Experimental Academy. This latter held its occasional -meetings at the palace of Ferdinand's brother, Leopold de' Medici: it -was composed chiefly, if not entirely, of Galileo's pupils and friends. -During the few years that this society lasted, one of the principal -objects of which was declared to be the repetition and developement of -Galileo's experiments, it kept up a correspondence with the principal -philosophers in every part of Europe, but when Leopold was, in 1666, -created a cardinal, it appears to have been dissolved, scarcely ten -years after its institution.[65] This digression may be excused in -favour of so interesting an establishment as the Academia Lincea, which -preceded by half a century the formation of the Royal Society of London, -and Académie Françoise of Paris. - -These latter two are mentioned together, probably for the first time, by -Salusbury. The passage is curious in an historical point of view, and -worth extracting:--"In imitation of these societies, Paris and London -have erected theirs of _Les Beaux Esprits_, and of the _Virtuosi_: the -one by the countenance of the most eminent Cardinal Richelieu, the other -by the royal encouragement of his sacred Majesty that now is. The _Beaux -Esprits_ have published sundry volumes of their moral and physiological -conferences, with the laws and history of their fellowship; and I hope -the like in due time from our Royal Society; that so such as envie their -fame and felicity, and such as suspect their ability and candor, may be -silenced and disappointed in their detractions and expectations."[66] - - -FOOTNOTES: - -[61] Salusbury, Math. Coll. - -[62] Perhaps it was to deprecate the hostility of the Jesuits that, at -the close of these Regulations, the Lynceans are directed to address -their prayers, among other Saints, especially to Ignatius Loyola, as to -one who greatly favoured the interests of learning. Odescalchi, Memorie -dell'Acad. de' Lincei, Roma. 1806. - -[63] Polyhistor Literarius, &c.--Storia della Letterat. Ital. The still -existing society of Chaff, more generally known by its Italian title, -Della Crusca, belongs to the same period. - -[64] F. Colonnæ Phytobasanus Jano Planco Auctore. Florent, 1744. - -[65] Nelli Saggio di Storia Literaria Fiorentina, Lucca, 1759. - -[66] Salusbury's Math. Coll. vol. ii. London, 1664. - - - - -CHAPTER X. - - _Spots on the Sun--Essay on Floating Bodies--Scheiner--Change in - Saturn._ - - -GALILEO did not indulge the curiosity of his Roman friends by exhibiting -only the wonders already mentioned, which now began to lose the gloss of -novelty, but disclosed a new discovery, which appeared still more -extraordinary, and, to the opposite faction, more hateful than anything -of which he had yet spoken. This was the discovery, which he first made -in the month of March, 1611, of dark spots on the body of the sun. A -curious fact, and one which well serves to illustrate Galileo's -superiority in seeing things simply as they are, is, that these spots -had been observed and recorded centuries before he existed, but, for -want of careful observation, their true nature had been constantly -misapprehended. One of the most celebrated occasions was in the year 807 -of our era, in which a dark spot is mentioned as visible on the face of -the sun during seven or eight days. It was then supposed to be -Mercury.[67] Kepler, whose astronomical knowledge would not suffer him -to overlook that it was impossible that Mercury could remain so long in -conjunction with the sun, preferred to solve the difficulty by supposing -that, in Aimoin's original account, the expression was not _octo dies_ -(eight days), but _octoties_--a barbarous word, which he supposed to -have been written for _octies_ (eight times); and that the other -accounts (in which the number of days mentioned is different) copying -loosely from the first, had both mistaken the word, and misquoted the -time which they thought they found mentioned there. It is impossible to -look on this explanation as satisfactory, but Kepler, who at that time -did not dream of spots on the sun, was perfectly contented with it. In -1609, he himself observed upon the sun a black spot, which he in like -manner mistook for Mercury, and unluckily the day, being cloudy, did -not allow him to contemplate it sufficiently long to discover his -error, which the slowness of its apparent motion would soon have pointed -out.[68] He hastened to publish his supposed observation, but no sooner -was Galileo's discovery of the solar spots announced, than he, with that -candour which as much as his flighty disposition certainly characterized -him at all times, retracted his former opinion, and owned his belief -that he had been mistaken. In fact it is known from the more accurate -theory which we now possess of Mercury's motions, that it did not pass -over the sun's face at the time when Kepler thought he perceived it -there. - -Galileo's observations were in their consequences to him particularly -unfortunate, as in the course of the controversy in which they engaged -him, he first became personally embroiled with the powerful party, whose -prevailing influence was one of the chief causes of his subsequent -misfortunes. Before we enter upon that discussion, it will be proper to -mention another famous treatise which Galileo produced soon after his -return from Rome to Florence, in 1612. This is, his Discourse on -Floating Bodies, which restored Archimedes' theory of hydrostatics, and -has, of course, met with the opposition which few of Galileo's works -failed to encounter. In the commencement, he thought it necessary to -apologize for writing on a subject so different from that which chiefly -occupied the public attention, and declared that he had been too closely -occupied in calculating the periods of the revolutions of Jupiter's -satellites to permit him to publish anything earlier. These periods he -had succeeded in determining during the preceding year, whilst at Rome, -and he now announced them to complete their circuits, the first in about -1 day, 18½ hours; the second in 3 days, 13 hours, 20 minutes; the third -in 7 days, 4 hours; and the outermost in 16 days, 18 hours. All these -numbers he gave merely as approximately true, and promised to continue -his observations, for the purpose of correcting the results. He then -adds an announcement of his recent discovery of the solar spots, "which, -as they change their situation, offer a strong argument, either that the -sun revolves on itself, or that, perhaps, other stars, like Venus and -Mercury, revolve about it, invisible at all other times, on account of -the small distance to which they are removed from him." To this he -afterwards subjoined, that, by continued observation, he had satisfied -himself that these solar spots were in actual contact with the surface -of the sun, where they are continually appearing and disappearing; that -their figures were very irregular, some being very dark, and others not -so black; that one would often divide into three or four, and, at other -times, two, three, or more would unite into one; besides which, that -they had all a common and regular motion, with which they revolved round -with the sun, which turned upon its axis in about the time of a lunar -month. - -Having by these prefatory observations assuaged the public thirst for -astronomical novelties, he ventures to introduce the principal subject -of the treatise above mentioned. The question of floating bridges had -been discussed at one of the scientific parties, assembled at the house -of Galileo's friend Salviati, and the general opinion of the company -appearing to be that the floating or sinking of a body depended -principally upon its shape, Galileo undertook to convince them of their -error. If he had not preferred more direct arguments, he might merely -have told them that in this instance they were opposed to their -favourite Aristotle, whose words are very unequivocal on the point in -dispute. "Form is not the cause why a body moves downwards rather than -upwards, but it does affect the swiftness with which it moves;"[69] -which is exactly the distinction which those who called themselves -Aristotelians were unable to perceive, and to which the opinions of -Aristotle himself were not always true. Galileo states the discussion to -have immediately arisen from the assertion of some one in the company, -that condensation is the effect of cold, and ice was mentioned as an -instance. On this, Galileo observed, that ice is rather water rarefied -than condensed, the proof of which is, that ice always floats upon -water.[70] It was replied, that the reason of this phenomenon was, not -the superior lightness of the ice, but its incapacity, owing to its flat -shape, to penetrate and overcome the resistance of the water. Galileo -denied this, and asserted that ice of any shape would float upon water, -and that, if a flat piece of ice were forcibly taken to the bottom, it -would of itself rise again to the surface. Upon this assertion it -appears that the conversation became so clamorous, that Galileo thought -it pertinent to commence his Essay with the following observation on the -advantage of delivering scientific opinions in writing, "because in -conversational arguments, either one or other party, or perhaps both, -are apt to get overwarm, and to speak overloud, and either do not suffer -each other to be heard, or else, transported with the obstinacy of not -yielding, wander far away from the original proposition, and confound -both themselves and their auditors with the novelty and variety of their -assertions." After this gentle rebuke he proceeds with his argument, in -which he takes occasion to state the famous hydrostatical paradox, of -which the earliest notice is to be found in Stevin's works, a -contemporary Flemish engineer, and refers it to a principle on which we -shall enlarge in another chapter. He then explains the true theory of -buoyancy, and refutes the false reasoning on which the contrary opinions -were founded, with a variety of experiments. - -The whole value and interest of experimental processes generally depends -on a variety of minute circumstances, the detail of which would be -particularly unsuited to a sketch like the present one. For those who -are desirous of becoming more familiar with Galileo's mode of conducting -an argument, it is fortunate that such a series of experiments exists as -that contained in this essay; experiments which, from their simplicity, -admit of being for the most part concisely enumerated, and at the same -time possess so much intrinsic beauty and characteristic power of -forcing conviction. They also present an admirable specimen of the -talent for which Galileo was so deservedly famous, of inventing -ingenious arguments in favour of his adversaries' absurd opinions before -he condescended to crush them, shewing that nothing but his love of -truth stood in the way of his being a more subtle sophist than any -amongst them. In addition to these reasons for giving these experiments -somewhat in detail, is the fact that all explanation of one of the -principal phenomena to which they allude is omitted in many more modern -treatises on Hydrostatics; and in some it is referred precisely to the -false doctrines here confuted. - -The marrow of the dispute is included in Galileo's assertion, that "The -diversity of figure given to any solid cannot be in any way the cause of -its absolutely sinking or floating; so that if a solid, when formed for -example into a spherical figure, sinks or floats in the water, the same -body will sink or float in the same water, when put into any other form. -The breadth of the figure may indeed retard its velocity, as well of -ascent as descent, and more and more according as the said figure is -reduced to a greater breadth and thinness; but that it may be reduced to -such a form as absolutely to put an end to its motion in the same fluid, -I hold to be impossible. In this I have met with great contradictors -who, producing some experiments, and in particular a thin board of -ebony, and a ball of the same wood, and shewing that the ball in water -sinks to the bottom[71], and that the board if put lightly on the -surface floats, have held and confirmed themselves in their opinion with -the authority of Aristotle, that the cause of that rest is the breadth -of the figure, unable by its small weight to pierce and penetrate the -resistance of the water's thickness, which is readily overcome by the -other spherical figure."--For the purpose of these experiments, Galileo -recommends a substance such as wax, which may be easily moulded into any -shape, and with which, by the addition of a few filings of lead, a -substance may be readily made of any required specific gravity. He then -declares that if a ball of wax of the size of an orange, or bigger, be -made in this manner heavy enough to sink to the bottom, but so lightly -that if we take from it only one grain of lead it returns to the top; -and if the same wax be afterwards moulded into a broad and thin cake, or -into any other figure, regular or irregular, the addition of the same -grain of lead will always make it sink, and it will again rise when we -remove the lead from it.--"But methinks I hear some of the adversaries -raise a doubt upon my produced experiment: and, first, they offer to my -consideration that the figure, as a figure simply, and disjunct from the -matter, works no effect, but requires to be conjoined with the matter; -and, moreover, not with every matter, but with those only wherewith it -may be able to execute the desired operation. Just as we see by -experience that an acute and sharp angle is more apt to cut than an -obtuse; yet always provided that both one and the other are joined with -a matter fit to cut, as for instance, steel. Therefore a knife with a -fine and sharp edge cuts bread or wood with much ease, which it will not -do if the edge be blunt and thick; but if, instead of steel, any one -will take wax and mould it into a knife, undoubtedly he will never learn -the effects of sharp and blunt edges, because neither of them will cut; -the wax being unable, by reason of its flexibility, to overcome the -hardness of the wood and bread. And therefore, applying the like -discourse to our argument, they say that the difference of figure will -shew different effects with regard to floating and sinking, but not -conjoined with any kind of matter, but only with those matters which by -their weight are able to overcome the viscosity of the water (like the -ebony which they have selected); and he that will select cork or other -light wood to form solids of different figures, would in vain seek to -find out what operation figure has in sinking or floating, because all -would swim, and that not through any property of this or that figure, -but through the debility of the matter. - -"When I begin to examine one by one all the particulars here produced, I -allow not only that figures, simply as such, do not operate in natural -things, but also that they are never separated from the corporeal -substance, nor have I ever alleged them to be stript of sensible matter: -and also I freely admit, that in our endeavours to examine the diversity -of accidents which depend upon the variety of figures, it is necessary -to apply them to matters which obstruct not the various operations of -those various figures. I admit and grant that I should do very ill if I -were to try the influence of a sharp edge with a knife of wax, applying -it to cut an oak, because no sharpness in wax is able to cut that very -hard wood. But yet, such an experiment of this knife would not be beside -the purpose to cut curded milk, or other very yielding matter; nay, in -such matters, the wax is more convenient than steel for finding the -difference depending on the acuteness of the angles, because milk is cut -indifferently with a razor, or a blunt knife. We must therefore have -regard not only to the hardness, solidity, or weight of the bodies -which, under different figures, are to divide some matters asunder; but -also, on the other hand, to the resistance of the matter to be -penetrated. And, since I have chosen a matter which does penetrate the -resistance of the water, and in all figures descends to the bottom, my -antagonists can charge me with no defect; nor (to revert to their -illustration) have I attempted to test the efficacy of acuteness by -cutting with matters unable to cut. I subjoin withal, that all caution, -distinction, and election of matter would be superfluous and -unnecessary, if the body to be cut should not at all resist the cutting: -if the knife were to be used in cutting a mist, or smoke, one of paper -would serve the purpose as well as one of Damascus steel; and I assert -that this is the case with water, and that there is not any solid of -such lightness or of such a figure, that being put on the water it will -not divide and penetrate its thickness; and if you will examine more -carefully your thin boards of wood, you will see that they have part of -their thickness under water; and, moreover, you will see that the -shavings of ebony, stone, or metal, when they float, have not only thus -broken the continuity of the water, but are with all their thickness -under the surface of it; and that more and more, according as the -floating substance is heavier, so that a thin floating plate of lead -will be lower than the surface of the surrounding water by at least -twelve times the thickness of the plate, and gold will dive below the -level of the water almost twenty times the thickness of the plate, as I -shall shew presently." - -In order to illustrate more clearly the non-resistance of water to -penetration, Galileo then directs a cone to be made of wood or wax, and -asserts that when it floats, either with its base or point in the water, -the solid content of the part immersed will be the same, although the -point is, by its shape, better adapted to overcome the resistance of the -water to division, if that were the cause of the buoyancy. Or the -experiment may be varied by tempering the wax with filings of lead, till -it sinks in the water, when it will be found that in any figure the same -cork must be added to it to raise it to the surface.--"This silences not -my antagonists; but they say that all the discourse hitherto made by me -imports little to them, and that it serves their turn, that they have -demonstrated in one instance, and in such manner and figure as pleases -them best, namely, in a board and a ball of ebony, that one, when put -into the water, sinks to the bottom, and that the other stays to swim at -the top; and the matter being the same, and the two bodies differing in -nothing but in figure, they affirm that with all perspicuity they have -demonstrated and sensibly manifested what they undertook. Nevertheless I -believe, and think I can prove that this very experiment proves nothing -against my theory. And first it is false that the ball sinks, and the -board not; for the board will sink too, if you do to both the figures as -the words of our question require; that is, if you put them both _in_ -the water; for to be in the water implies to be placed in the water, and -by Aristotle's own definition of place, to be placed imports to be -environed by the surface of the ambient body; but when my antagonists -shew the floating board of ebony, they put it not into the water, but -upon the water; where, being detained by a certain impediment (of which -more anon) it is surrounded, partly with water, partly with air, which -is contrary to our agreement, for that was that the bodies should be in -the water, and not part in the water, part in the air. I will not omit -another reason, founded also upon experience, and, if I deceive not -myself, conclusive against the notion that figure, and the resistance of -the water to penetration have anything to do with the buoyancy of -bodies. Choose a piece of wood or other matter, as for instance -walnut-wood, of which a ball rises from the bottom of the water to the -surface more slowly than a ball of ebony of the same size sinks, so that -clearly the ball of ebony divides the water more readily in sinking than -does the walnut in rising. Then take a board of walnut-tree equal to and -like the floating ebony one of my antagonists; and if it be true that -this latter floats by reason of the figure being unable to penetrate the -water, the other of walnut-tree, without all question, if thrust to the -bottom ought to stay there, as having the same impeding figure, and -being less apt to overcome the said resistance of the water. But if we -find by experience that not only the thin board, but every other figure -of the same walnut-tree will return to float, as unquestionably we -shall, then I must desire my opponents to forbear to attribute the -floating of the ebony to the figure of the board, since the resistance -of the water is the same in rising as in sinking, and the force of -ascension of the walnut-tree is less than the ebony's force for going to -the bottom. - -"Now, let us return to the thin plate of gold or silver, or the thin -board of ebony, and let us lay it lightly upon the water, so that it may -stay there without sinking, and carefully observe the effect. It will -appear clearly that the plates are a considerable matter lower than the -surface of the water which rises up, and makes a kind of rampart round -them on every side, in the manner shewn in the annexed figure, in which -BDLF represents the surface of the water, and AEIO the surface of the -plate. But if it have already penetrated and overcome the continuity of -the water, and is of its own nature heavier than the water, why does it -not continue to sink, but stop and suspend itself in that little dimple -that its weight has made in the water? My answer is, because in sinking -till its surface is below the water which rises up in a bank round it, -it draws after and carries along with it the air above it, so that that -which in this case descends and is placed in the water, is not only the -board of ebony or plate of iron, but a compound of ebony and air, from -which composition results a solid no longer specifically heavier than -the water, as was the ebony or gold alone. But, Gentlemen, we want the -same matter; you are to alter nothing but the shape, and therefore have -the goodness to remove this air, which may be done simply by washing the -upper surface of the board, for the water having once got between the -board and air will run together, and the ebony will go to the bottom; -and if it does not, you have won the day. But methinks I hear some of my -antagonists cunningly opposing this, and telling me that they will not -on any account allow their board to be wetted, because the weight of the -water so added, by making it heavier than it was before, draws it to the -bottom, and that the addition of new weight is contrary to our -agreement, which was that the matter should be the same." - -[Illustration] - -"To this I answer first, that nobody can suppose bodies to be put into -the water without their being wet, nor do I wish to do more to the -board than you may do to the ball. Moreover, it is not true that the -board sinks on account of the weight of the water added in the washing; -for I will put ten or twenty drops on the floating board, and so long as -they stand separate it shall not sink; but if the board be taken out, -and all that water wiped off, and the whole surface bathed with one -single drop, and put it again upon the water, there is no question but -it will sink, the other water running to cover it, being no longer -hindered by the air. In the next place it is altogether false that water -can in any way increase the weight of bodies immersed in it, for water -has no weight in water, since it does not sink. Now, just as he who -should say that brass by its own nature sinks, but that when formed into -the shape of a kettle, it acquires from that figure a virtue of lying in -the water without sinking, would say what is false, because that is not -purely brass which then is put into the water, but a compound of brass -and air; so is it neither more nor less false, that a thin plate of -brass or ebony swims by virtue of its dilated and broad figure. Also I -cannot omit to tell my opponents, that this conceit of refusing to bathe -the surface of the board, might beget an opinion in a third person of a -poverty of arguments on their side, especially as the conversation began -about flakes of ice, in which it would be simple to require that the -surfaces should be kept dry; not to mention that such pieces of ice, -whether wet or dry, always float, and as my antagonists say, because of -their shape. - -"Some may wonder that I affirm this power to be in the air of keeping -the plate of brass or silver above water, as if in a certain sense I -would attribute to the air a kind of magnetic virtue for sustaining -heavy bodies with which it is in contact. To satisfy all these doubts, I -have contrived the following experiment to demonstrate how truly the air -does support these solids; for I have found, when one of these bodies -which floats when placed lightly on the water, is thoroughly bathed and -sunk to the bottom, that by carrying down to it a little air without -otherwise touching it in the least, I am able to raise and carry it back -to the top, where it floats as before. To this effect I take a ball of -wax, and with a little lead make it just heavy enough to sink very -slowly to the bottom, taking care that its surface be quite smooth and -even. This, if put gently into the water, submerges almost entirely, -there remaining visible only a little of the very top, which, so long as -it is joined to the air, keeps the ball afloat; but if we take away the -contact of the air by wetting this top, the ball sinks to the bottom, -and remains there. Now to make it return to the surface by virtue of the -air which before sustained it, thrust into the water a glass, with the -mouth downwards, which will carry with it the air it contains; and move -this down towards the ball, until you see by the transparency of the -glass that the air has reached the top of it; then gently draw the glass -upwards, and you will see the ball rise, and afterwards stay on the top -of the water, if you carefully part the glass and water without too much -disturbing it.[72] There is therefore a certain affinity between the air -and other bodies, which holds them united, so that they separate not -without a kind of violence, just as between water and other bodies; for -in drawing them wholly out of the water, we see the water follow them, -and rise sensibly above the level before it quits them." Having -established this principle by this exceedingly ingenious and convincing -experiment, Galileo proceeds to shew from it what must be the dimensions -of a plate of any substance which will float as the wax does, assuming -in each case that we know the greatest height at which the rampart of -water will stand round it. In like manner he shows that a pyramidal or -conical figure may be made of any substance, such that by help of the -air, it shall rest upon the water without wetting more than its base; -and that we may so form a cone of any substance that it shall float if -placed gently on the surface, with its point downwards, whereas no care -or pains will enable it to float with its base downwards, owing to the -different proportions of air which in the two positions remain connected -with it. With this parting blow at his antagonist's theory we close our -extracts from this admirable essay. - -The first elements of the theory of running waters were reserved for -Castelli, an intimate friend and pupil of Galileo. On the present -occasion, Castelli appeared as the ostensible author of a defence -against the attacks made by Vincenzio di Grazia and by Lodovico delle -Columbe (the author of the crystalline composition of the moon) on the -obnoxious theory. After destroying all the objections which they -produced, the writer tauntingly bids them remember, that he was merely -Galileo's pupil, and consider how much more effectually Galileo himself -would have confuted them, had he thought it worth while. It was not -known till several years after his death, that this Essay was in fact -written by Galileo himself.[73] - -These compositions merely occupied the leisure time which he could -withhold from the controversy on the solar spots to which we have -already alluded. A German Jesuit named Christopher Scheiner, who was -professor of mathematics at Ingolstadt, in imitation of Galileo had -commenced a series of observations on them, but adopted the theory -which, as we have seen, Galileo had examined and rejected, that these -spots are planets circulating at some distance from the body of the sun. -The same opinion had been taken up by a French astronomer, who in honour -of the reigning family called them Borbonian stars. Scheiner promulgated -his notions in three letters, addressed to their common friend Welser, -under the quaint signature of "_Apelles latens post tabulam_." Galileo -replied to Scheiner's letters by three others, also addressed to Welser, -and although the dispute was carried on amid mutual professions of -respect and esteem, it laid the foundation of the total estrangement -which afterwards took place between the two authors. Galileo's part of -this controversy was published at Rome by the Lyncean Academy in 1613. -To the last of his letters, written in December, 1612, is annexed a -table of the expected positions of Jupiter's satellites during the -months of March and April of the following year, which, imperfect as it -necessarily was, cannot be looked upon without the greatest interest. - -In the same letter it is mentioned that Saturn presented a novel -appearance, which, for an instant, almost induced Galileo to mistrust -the accuracy of his earlier observations. The lateral appendages of this -planet had disappeared, and the accompanying extract will show the -uneasiness which Galileo could not conceal at the sight of this -phenomenon, although it is admirable to see the contempt with which, -even in that trying moment, he expresses his consciousness that his -adversaries were unworthy of the triumph they appeared on the point of -celebrating.--"Looking on Saturn within these few days, I found it -solitary, without the assistance of its accustomed stars, and in short, -perfectly round and defined like Jupiter, and such it still remains. Now -what can be said of so strange a metamorphosis? are perhaps the two -smaller stars consumed, like the spots on the sun? have they suddenly -vanished and fled? or has Saturn devoured his own children? or was the -appearance indeed fraud and illusion, with which the glasses have for so -long a time mocked me, and so many others who have often observed with -me. Now perhaps the time is come to revive the withering hopes of those, -who, guided by more profound contemplations, have fathomed all the -fallacies of the new observations and recognised their impossibility! I -cannot resolve what to say in a chance so strange, so new, and so -unexpected; the shortness of the time, the unexampled occurrence, the -weakness of my intellect, and the terror of being mistaken, have greatly -confounded me." These first expressions of alarm are not to be wondered -at; however, he soon recovered courage, and ventured to foretel the -periods at which the lateral stars would again show themselves, -protesting at the same time, that he was in no respect to be understood -as classing this prediction among the results which depend on certain -principles and sound conclusions, but merely on some conjectures which -appeared to him probable. From one of the Dialogues on the System, we -learn that this conjecture was, that Saturn might revolve upon his axis, -but the period which he assumed is very different from the true one, as -might be expected from its being intended to account for a phenomenon of -which Galileo had not rightly apprehended the character. - -He closed this letter with renewed professions of courtesy and -friendship towards Apelles, enjoining Welser not to communicate it -without adding his excuses, if he should be thought to dissent too -violently from his antagonist's ideas, declaring that his only object -was the discovery of truth, and that he had freely exposed his own -opinion, which he was still ready to change, so soon as his errors -should be made manifest to him; and that he would consider himself -under special obligation to any one who would be kind enough to discover -and correct them. These letters were written from the villa of his -friend Salviati at Selve near Florence, where he passed great part of -his time, particularly during his frequent indispositions, conceiving -that the air of Florence was prejudicial to him. Cesi was very anxious -for their appearance, since they were (in his own words) so hard a -morsel for the teeth of the Peripatetics, and he exhorted Galileo, in -the name of the society, "to continue to give them, and the nameless -Jesuit, something to gnaw." - - -FOOTNOTES: - -[67] Aimoini Hist. Francorum. Parisiis. 1567. - -[68] Mercurius in sole visus. 1609. - -[69] De Coelo. lib. 4. - -[70] For a discussion of this singular phenomenon, _see_ Treatise on -Heat, p. 12; and it is worth while to remark in passing, what an -admirable instance it affords of Galileo's instantaneous abandonment of -a theory so soon as it became inconsistent with experiment. - -[71] Ebony is one of the few woods heavier than water. _See_ Treatise on -Hydrostatics. - -[72] In making this very beautiful experiment, it is best to keep the -glass a few seconds in the water, to give time for the surface of the -ball to dry. It will also succeed with a light needle, if carefully -conducted. - -[73] Nelli. Saggio di Stor. Liter. Fiorent. - - - - -CHAPTER XI. - - _Letter to Christina, Arch-Duchess of Tuscany--Caccini--Galileo - revisits Rome--Inchoffer--Problem of Longitudes._ - - -THE uncompromising boldness with which Galileo published and supported -his opinions, with little regard to the power and authority of those who -advocated the contrary doctrines, had raised against him a host of -enemies, who each had objections to him peculiar to themselves, but who -now began to perceive the policy of uniting their strength in the common -cause, to crush if possible so dangerous an innovator. All the -professors of the old opinions, who suddenly found the knowledge on -which their reputation was founded struck from under them, and who could -not reconcile themselves to their new situation of learners, were united -against him; and to this powerful cabal was now added the still greater -influence of the jesuits and pseudo-theological party, who fancied they -saw in the spirit of Galileo's writings the same inquisitive temper -which they had already found so inconvenient in Luther and his -adherents. The alarm became greater every day, inasmuch as Galileo had -succeeded in training round him a numerous band of followers who all -appeared imbued with the same dangerous spirit of innovation, and his -favourite scholars were successful candidates for professorships in many -of the most celebrated universities of Italy. - -At the close of 1613, Galileo addressed a letter to his pupil, the Abbé -Castelli, in which he endeavoured to shew that there is as much -difficulty in reconciling the Ptolemaic as the Copernican system of the -world with the astronomical expressions contained in the Scriptures, and -asserted, that the object of the Scriptures not being to teach -astronomy, such expressions are there used as would be intelligible and -conformable to the vulgar belief, without regard to the true structure -of the universe; which argument he afterwards amplified in a letter -addressed to Christina, Grand Duchess of Tuscany, the mother of his -patron Cosmo. He discourses on this subject with the moderation and good -sense which so peculiarly characterized him. "I am," says he, "inclined -to believe, that the intention of the sacred Scriptures is to give to -mankind the information necessary for their salvation, and which, -surpassing all human knowledge, can by no other means be accredited than -by the mouth of the Holy Spirit. But I do not hold it necessary to -believe, that the same God who has endowed us with senses, with speech, -and intellect, intended that we should neglect the use of these, and -seek by other means for knowledge which they are sufficient to procure -us; especially in a science like astronomy, of which so little notice is -taken in the Scriptures, that none of the planets, except the sun and -moon, and, once or twice only, Venus under the name of Lucifer, are so -much as named there. This therefore being granted, methinks that in the -discussion of natural problems we ought not to begin at the authority of -texts of Scripture, but at sensible experiments and necessary -demonstrations: for, from the divine word, the sacred Scripture and -nature did both alike proceed, and I conceive that, concerning natural -effects, that which either sensible experience sets before our eyes, or -necessary demonstrations do prove unto us, ought not upon any account to -be called into question, much less condemned, upon the testimony of -Scriptural texts, which may under their words couch senses seemingly -contrary thereto. - -"Again, to command the very professors of astronomy that they of -themselves see to the confuting of their own observations and -demonstrations, is to enjoin a thing beyond all possibility of doing; -for it is not only to command them not to see that which they do see, -and not to understand that which they do understand, but it is to order -them to seek for and to find the contrary of that which they happen to -meet with. I would entreat these wise and prudent fathers, that they -would with all diligence consider the difference that is between -opinionative and demonstrative doctrines: to the end that well weighing -in their minds with what force necessary inferences urge us, they might -the better assure themselves that it is not in the power of the -professors of demonstrative sciences to change their opinions at -pleasure, and adopt first one side and then another; and that there is a -great difference between commanding a mathematician or a philosopher, -and the disposing of a lawyer or a merchant; and that the demonstrated -conclusions touching the things of nature and of the heavens cannot be -changed with the same facility as the opinions are touching what is -lawful or not in a contract, bargain, or bill of exchange. Therefore, -first let these men apply themselves to examine the arguments of -Copernicus and others, and leave the condemning of them as erroneous and -heretical to whom it belongeth; yet let them not hope to find such rash -and precipitous determinations in the wary and holy fathers, or in the -absolute wisdom of him who cannot err, as those into which they suffer -themselves to be hurried by some particular affection or interest of -their own. In these and such other positions, which are not directly -articles of faith, certainly no man doubts but His Holiness hath always -an absolute power of admitting or condemning them, but it is not in the -power of any creature to make them to be true or false, otherwise than -of their own nature, and in fact they are." We have been more particular -in extracting these passages, because it has been advanced by a writer -of high reputation, that the treatment which Galileo subsequently -experienced was solely in consequence of his persisting in the endeavour -to prove that the Scriptures were reconcileable with the Copernican -theory[74], whereas we see here distinctly that, for the reasons we have -briefly stated, he regarded this as a matter altogether indifferent and -beside the question. - -Galileo had not entered upon this discussion till driven to it by a most -indecent attack, made on him from the pulpit, by a Dominican friar named -Caccini, who thought it not unbecoming his habit or religion to play -upon the words of a Scriptural text for the purpose of attacking Galileo -and his partisans with more personality.[75] Galileo complained formally -of Caccini's conduct to Luigi Maraffi the general of the Dominicans, who -apologised amply to him, adding that he himself was to be pitied for -finding himself implicated in all the brutal conduct of thirty or forty -thousand monks. - -In the mean time, the inquisitors at Rome had taken the alarm, and were -already, in 1615, busily employed in collecting evidence against -Galileo. Lorini, a brother Dominican of Caccini, had given them notice -of the letter to Castelli of which we have spoken, and the utmost -address was employed to get the original into their hands, which attempt -however was frustrated, as Castelli had returned it to the writer. -Caccini was sent for to Rome, settled there with the title of Master of -the Convent of St. Mary of Minerva, and employed to put the depositions -against Galileo into order. Galileo was not at this time fully aware of -the machinations against him, but suspecting something of their nature, -he solicited and obtained permission from Cosmo, towards the end of -1615, to make a journey to Rome, for the purpose of more directly -confronting his enemies in that city. There was a rumour at the time -that this visit was not voluntary, but that Galileo had been cited to -appear at Rome. A contemporary declares that he heard this from Galileo -himself: at any rate, in a letter which Galileo shortly afterwards wrote -to Picchena, the Grand Duke's secretary, he expresses himself well -satisfied with the results of this step, whether forced or not, and -Querenghi thus describes to the Cardinal d'Este the public effect of his -appearance: "Your Eminence would be delighted with Galileo if you heard -him holding forth, as he often does, in the midst of fifteen or twenty, -all violently attacking him, sometimes in one house, sometimes in -another. But he is armed after such fashion that he laughs all of them -to scorn--and even if the novelty of his opinions prevents entire -persuasion, at least he convicts of emptiness most of the arguments with -which his adversaries endeavour to overwhelm him. He was particularly -admirable on Monday last, in the house of Signor Frederico Ghisilieri; -and what especially pleased me was, that before replying to the contrary -arguments, he amplified and enforced them with new grounds of great -plausibility, so as to leave his adversaries in a more ridiculous plight -when he afterwards overturned them all." - -Among the malicious stories which were put into circulation, it had been -said, that the Grand Duke had withdrawn his favour, which emboldened -many, who would not otherwise have ventured on such open opposition, to -declare against Galileo. His appearance at Rome, where he was lodged in -the palace of Cosmo's ambassador, and whence he kept up a close -correspondence with the Grand Duke's family, put an immediate stop to -rumours of this kind. In little more than a month he was apparently -triumphant, so far as regarded himself; but the question now began to be -agitated whether the whole system of Copernicus ought not to be -condemned as impious and heretical. Galileo again writes to Picchena, -"so far as concerns the clearing of my own character, I might return -home immediately; but although this new question regards me no more than -all those who for the last eighty years have supported these opinions -both in public and private, yet, as perhaps I may be of some assistance -in that part of the discussion which depends on the knowledge of truths -ascertained by means of the sciences which I profess, I, as a zealous -and Catholic Christian, neither can nor ought to withhold that -assistance which my knowledge affords; and this business keeps me -sufficiently employed." De Lambre, whose readiness to depreciate -Galileo's merit we have already noticed and lamented, sneeringly and -ungratefully remarks on this part of his life, that "it was scarcely -worth while to compromise his tranquillity and reputation, in order to -become the champion of a truth which could not fail every day to acquire -new partisans by the natural effect of the progress of enlightened -opinions." We need not stop to consider what the natural effects might -have been if none had at any time been found who thought their -tranquillity worthily offered up in such a cause. - -It has been hinted by several, and is indeed probable, that Galileo's -stay at Rome rather injured the cause (so far as provoking the -inquisitorial censures could injure it) which it was his earnest desire -to serve, for we cannot often enough repeat the assertion, that it was -not the doctrine itself, so much as the free, unyielding manner in which -it was supported, which was originally obnoxious. Copernicus had been -allowed to dedicate his great work to Pope Paul III., and from the time -of its first appearance under that sanction in 1543, to the year 1616, -of which we are now writing, this theory was left in the hands of -mathematicians and philosophers, who alternately attacked and defended -it without receiving either support or molestation from ecclesiastical -decrees. But this was henceforward no longer the case, and a higher -degree of importance was given to the controversy from the religious -heresies which were asserted to be involved in the new opinions. We have -already given specimens of the so called philosophical arguments brought -against Copernicus; and the reader may be curious to know the form of -the theological ones. Those which we select are taken from a work, which -indeed did not come forth till the time of Galileo's third visit to -Rome, but it is relative to the matter now before us, as it professed to -be, and its author's party affected to consider it, a complete -refutation of the letters to Castelli and the Archduchess Christina.[76] - -It was the work of a Jesuit, Melchior Inchoffer, and it was greatly -extolled by his companions, "as differing so entirely from the pruriency -of the Pythagorean writings." He quotes with approbation an author who, -first referring to the first verse of Genesis for an argument that the -earth was not created till after the heavens, observes that the whole -question is thus reduced to the examination of this purely geometrical -difficulty--In the formation of a sphere, does the centre or -circumference first come into existence? If the latter (which we presume -Melchior's friend found good reason for deciding upon), the consequence -is inevitable. The earth is in the centre of the universe. - -It may not be unprofitable to contrast the extracts which we have given -from Galileo's letters on the same subject with the following passage, -which appears one of the most subtle and argumentative which is to be -found in Melchior's book. He _professes_ to be enumerating and refuting -the principal arguments which the Copernicans adduced for the motion of -the earth. "Fifth argument. Hell is in the centre of the earth, and in -it is a fire tormenting the damned; therefore it is absolutely necessary -that the earth is moveable. The antecedent is plain." (Inchoffer then -quotes a number of texts of Scripture on which, according to him, the -Copernicans relied in proof of this part of the argument.) "The -consequent is proved: because fire is the cause of motion, for which -reason Pythagoras, who, as Aristotle reports, puts the place of -punishment in the centre, perceived that the earth is animate and -endowed with action. I answer, even allowing that hell is in the centre -of the earth, and a fire in it, I deny the consequence: and for proof I -say, if the argument is worth any thing, it proves also that lime-kilns, -ovens, and fire-grates are animated and spontaneously moveable. I say, -_even allowing_ that hell is in the centre of the earth: for Gregory, -book 4, dial. chap. 42, says, that he dare not decide rashly on this -matter, although he thinks more probable the opinion of those who say -that it is under the earth. St. Thomas, in Opusc. 10, art. 31, says: -Where hell is, whether in the centre of the earth or at the surface, -does not in my opinion, relate to any article of faith; and it is -superfluous to be solicitous about such things, either in asserting or -denying them. And Opusc. 11, art. 24, he says, that it seems to him that -nothing should be rashly asserted on this matter, particularly as -Augustin thinks that nobody knows where it is; but I do not, says he, -think that it is in the centre of the earth. I should be loth, however, -that it should be hence inferred by _some people_ that hell is in the -earth, that we are ignorant where hell is, and therefore that the -situation of the earth is also unknown, and, in conclusion, that it -cannot therefore be the centre of the universe. The argument shall be -retorted in another fashion: for if the place of the earth is unknown, -it cannot be said to be in a great circle, so as to be moved round the -sun. Finally I say that in fact it is known where the earth is." - -It is not impossible that some persons adopted the Copernican theory, -from an affectation of singularity and freethinking, without being able -to give very sound reasons for their change of opinion, of whom we have -an instance in Origanus, the astrological instructor of Wallenstein's -famous attendant Seni, who edited his work. His arguments in favour of -the earth's motion are quite on a level with those advanced on the -opposite side in favour of its immobility; but we have not found any -traces whatever of such absurdities as these having been urged by any of -the leaders of that party, and it is far more probable that they are the -creatures of Melchior's own imagination. At any rate it is worth -remarking how completely he disregards the real physical arguments, -which he ought, in justice to his cause, to have attempted to -controvert. His book was aimed at Galileo and his adherents, and it is -scarcely possible that he could seriously persuade himself that he was -stating and overturning arguments similar to those by which Galileo had -made so many converts to the opinions of Copernicus. Whatever may be our -judgment of his candour, we may at least feel assured that if this had -indeed been a fair specimen of Galileo's philosophy, he might to the end -of his life have taught that the earth moved round the sun, or if his -fancy led him to a different hypothesis, he might like the Abbé Baliani -have sent the earth spinning round the stationary moon, and like him -have remained unmolested by pontifical censures. It is true that Baliani -owned his opinion to be much shaken, on observing it to be opposed to -the decree of those in whose hands was placed the power of judging -articles of faith. But Galileo's uncompromising spirit of analytical -investigation, and the sober but invincible force of reasoning with -which he beat down every sophism opposed to him, the instruments with -which he worked, were more odious than the work itself, and the -condemnation which he had vainly hoped to avert was probably on his very -account accelerated. - -Galileo, according to his own story, had in March 1616 a most gracious -audience of the pope, Paul V., which lasted for nearly an hour, at the -end of which his holiness assured him, that the Congregation were no -longer in a humour to listen lightly to calumnies against him, and that -so long as he occupied the papal chair, Galileo might think himself out -of all danger. But nevertheless he was not allowed to return home, -without receiving formal notice not to teach the opinions of -Copernicus, that the sun is in the centre of the system, and that the -earth moves about it, from that time forward, in any manner. That these -were the literal orders given to Galileo will be presently proved from -the recital of them in the famous decree against him, seventeen years -later. For the present, his letters which we have mentioned, as well as -one of a similar tendency by Foscarini, a Carmelite friar--a commentary -on the book of Joshua by a Spaniard named Diego Zuniga--Kepler's Epitome -of the Copernican Theory--and Copernicus's own work, were inserted in -the list of forbidden books, nor was it till four years afterwards, in -1620, that, on reconsideration, Copernicus was allowed to be read with -certain omissions and alterations then decided upon. - -Galileo quitted Rome scarcely able to conceal his contempt and -indignation. Two years afterwards this spirit had but little subsided, -for in forwarding to the Archduke Leopold his Theory of the Tides, he -accompanied it with the following remarks:--"This theory occurred to me -when in Rome, whilst the theologians were debating on the prohibition of -Copernicus's book, and of the opinion maintained in it of the motion of -the earth, which I at that time believed; until it pleased those -gentlemen to suspend the book, and declare the opinion false and -repugnant to the Holy Scriptures. Now, as I know how well it becomes me -to obey and believe the decisions of my superiors, which proceed out of -more profound knowledge than the weakness of my intellect can attain to, -this theory which I send you, which is founded on the motion of the -earth, I now look upon as a fiction and a dream, and beg your highness -to receive it as such. But, as poets often learn to prize the creations -of their fancy, so, in like manner, do I set some value on this -absurdity of mine. It is true that when I sketched this little work, I -did hope that Copernicus would not, after 80 years, be convicted of -error, and I had intended to develope and amplify it farther, but a -voice from heaven suddenly awakened me, and at once annihilated all my -confused and entangled fancies." - -It might have been predicted, from the tone of this letter alone, that -it would not be long before Galileo would again bring himself under the -censuring notice of the astronomical hierarchy, and indeed he had, so -early as 1610, collected some of the materials for the work which caused -the final explosion, and on which he now employed himself with as little -intermission as the weak state of his health permitted. - -He had been before this time engaged in a correspondence with the court -of Spain, on the method of observing longitudes at sea, for the solution -of which important problem Philip III. had offered a considerable -reward, an example which has since been followed in our own and other -countries. Galileo had no sooner discovered Jupiter's satellites, than -he recognized the use which might be made of them for that purpose, and -devoted himself with peculiar assiduity to acquiring as perfect a -knowledge as possible of their revolutions. The reader will easily -understand how they were to be used, if their motion could be so well -ascertained as to enable Galileo at Florence to predict the exact times -at which any remarkable configurations would occur, as, for instance, -the times at which any one of them would be eclipsed by Jupiter. A -mariner who in the middle of the Atlantic should observe the same -eclipse, and compare the time of night at which he made the observation -(which he might know by setting his watch by the sun on the preceding -day) with the time mentioned in the predictions, would, from the -difference between the two, learn the difference between the hour at -Florence and the hour at the place where the ship at that time happened -to be. As the earth turns uniformly round through 360° of longitude in -24 hours, that is, through 15° in each hour, the hours, minutes, and -seconds of time which express this difference must be multiplied by 15, -and the respective products will give the degrees, minutes, and seconds -of longitude, by which the ship was then distant from Florence. This -statement is merely intended to give those who are unacquainted with -astronomy, a general idea of the manner in which it was proposed to use -these satellites. Our moon had already been occasionally employed in the -same way, but the comparative frequency of the eclipses of Jupiter's -moons, and the suddenness with which they disappear, gives a decided -advantage to the new method. Both methods were embarrassed by the -difficulty of observing the eclipses at sea. In addition to this, it was -requisite, in both methods, that the sailors should be provided with -accurate means of knowing the hour, wherever they might chance to be, -which was far from being the case, for although (in order not to -interrupt the explanation) we have above spoken of their _watches_, yet -the watches and clocks of that day were not such as could be relied on -sufficiently, during the interval which must necessarily occur between -the two observations. This consideration led Galileo to reflect on the -use which might be made of his pendulum for this purpose; and, with -respect to the other difficulty, he contrived a peculiar kind of -telescope, with which he flattered himself, somewhat prematurely, that -it would be as easy to observe on ship-board as on shore. - -During his stay at Rome, in 1615, and the following year, he disclosed -some of these ideas to the Conte di Lemos, the viceroy of Naples, who -had been president of the council of the Spanish Indies, and was fully -aware of the importance of the matter. Galileo was in consequence -invited to communicate directly with the Duke of Lerma, the Spanish -minister, and instructions were accordingly sent by Cosmo, to the Conte -Orso d'Elci, his ambassador at Madrid, to conduct the business there. -Galileo entered warmly into the design, of which he had no other means -of verifying the practicability; for as he says in one of his letters to -Spain--"Your excellency may well believe that if this were an -undertaking which I could conclude by myself, I would never have gone -about begging favours from others; but in my study there are neither -seas, nor Indies, nor islands, nor ports, nor shoals, nor ships, for -which reason I am compelled to share the enterprise with great -personages, and to fatigue myself to procure the acceptance of that, -which ought with eagerness to be asked of me; but I console myself with -the reflection that I am not singular in this, but that it commonly -happens, with the exception of a little reputation, and that too often -obscured and blackened by envy, that the least part of the advantage -falls to the share of the inventors of things, which afterwards bring -great gain, honours, and riches to others; so that I will never cease on -my part to do every thing in my power, and I am ready to leave here all -my comforts, my country, my friends, and family, and to cross over into -Spain, to stay as long as I may be wanted in Seville, or Lisbon, or -wherever it may be convenient, to implant the knowledge of this method, -provided that due assistance and diligence be not wanting on the part of -those who are to receive it, and who should solicit and foster it." But -he could not, with all his enthusiasm, rouse the attention of the -Spanish court. The negotiation languished, and although occasionally -renewed during the next ten or twelve years, was never brought to a -satisfactory issue. Some explanation of this otherwise unaccountable -apathy of the Spanish court, with regard to the solution of a problem -which they had certainly much at heart, is given in Nelli's life of -Galileo; where it is asserted, on the authority of the Florentine -records, that Cosmo required privately from Spain, (in return for the -permission granted for Galileo to leave Florence, in pursuance of this -design,) the privilege of sending every year from Leghorn two -merchantmen, duty free, to the Spanish Indies. - - -FOOTNOTES: - -[74] Ce philosophe (Galilée) ne fut point persecuté comme bon astronome, -mais comme mauvais théologien. C'est son entêtement à vouloir concilier -la Bible avec Copernic qui lui donna des juges. Mais vingt auteurs, -surtout parmi les protestans, ont écrit que Galilée fut persecuté et -imprisonné pour avoir soutenu que la terre tourne autour du soleil, que -ce système a été condanné par l'inquisition comme faux, erroné et -contraire à la Bible, &c.--Bergier, Encyclopédie Méthodique, Paris, -1790, Art. SCIENCES HUMAINES. - -[75] Viri Galilæi, quid statis adspicientes in coelum. _Acts_ I. 11. - -[76] Tractatus Syllepticus. Romæ, 1633. The title-page of this -remarkable production is decorated with an emblematical figure, -representing the earth included in a triangle; and in the three corners, -grasping the globe with their fore feet, are placed three bees, the arms -of Pope Urban VIII. who condemned Galileo and his writings. The motto is -"_His fixa quiescit_," "Fixed by these it is at rest." - - - - -CHAPTER XII. - - _Controversy on Comets--Saggiatore--Galileo's reception by Urban - VIII--His family._ - - -THE year 1618 was remarkable for the appearance of three comets, on -which almost every astronomer in Europe found something to say and -write. Galileo published some of his opinions with respect to them, -through the medium of Mario Guiducci. This astronomer delivered a -lecture before the Florentine academy, the heads of which he was -supposed to have received from Galileo, who, during the whole time of -the appearance of these comets, was confined to his bed by severe -illness. This essay was printed in Florence _at the sign of The Medicean -Stars_.[77] What principally deserves notice in it, is the opinion of -Galileo, that the distance of a comet cannot be safely determined by its -parallax, from which we learn that he inclined to believe that comets -are nothing but meteors occasionally appearing in the atmosphere, like -rainbows, parhelia, and similar phenomena. He points out the difference -in this respect between a fixed object, the distance of which may be -calculated from the difference of direction in which two observers (at a -known distance from each other) are obliged to turn themselves in order -to see it, and meteors like the rainbow, which are simultaneously formed -in different drops of water for each spectator, so that two observers -in different places are in fact contemplating different objects. He then -warns astronomers not to engage with too much warmth in a discussion on -the distance of comets before they assure themselves to which of these -two classes of phenomena they are to be referred. The remark is in -itself perfectly just, although the opinion which occasioned it is now -as certainly known to be erroneous, but it is questionable whether the -observations which, up to that time, had been made upon comets, were -sufficient, either in number or quality, to justify the censure which -has been cast on Galileo for his opinion. The theory, moreover, is -merely introduced as an hypothesis in Guiducci's essay. The same opinion -was for a short time embraced by Cassini, a celebrated Italian -astronomer, invited by Louis XIV. to the Observatory at Paris, when the -science was considerably more advanced, and Newton, in his _Principia_, -did not think it unworthy of him to show on what grounds it is -untenable. - -Galileo was become the object of animosity in so many quarters that none -of his published opinions, whether correct or incorrect, ever wanted a -ready antagonist. The champion on the present occasion was again a -Jesuit; his name was Oratio Grassi, who published _The Astronomical and -Philosophical Balance_, under the disguised signature of Lotario Sarsi. - -Galileo and his friends were anxious that his reply to Grassi should -appear as quickly as possible, but his health had become so precarious -and his frequent illnesses occasioned so many interruptions, that it was -not until the autumn of 1623 that Il Saggiatore (or The Assayer) as he -called his answer, was ready for publication. This was printed by the -Lyncean Academy, and as Cardinal Maffeo Barberino, who had just been -elected Pope, (with the title of Urban VIII.) had been closely connected -with that society, and was also a personal friend of Cesi and of -Galileo, it was thought a prudent precaution to dedicate the pamphlet to -him. This essay enjoys a peculiar reputation among Galileo's works, not -only for the matter contained in it, but also for the style in which it -is written; insomuch that Andrès[78], when eulogizing Galileo as one of -the earliest who adorned philosophical truths with the graces and -ornaments of language, expressly instances the Saggiatore, which is also -quoted by Frisi and Algarotti, as a perfect model of this sort of -composition. In the latter particular, it is unsafe to interfere with -the decisions of an Italian critic; but with respect to its substance, -this famous composition scarcely appears to deserve its preeminent -reputation. It is a prolix and rather tedious examination of Grassi's -Essay; nor do the arguments seem so satisfactory, nor the reasonings so -compact as is generally the case in Galileo's other writings. It does -however, like all his other works, contain many very remarkable -passages, and the celebrity of this production requires that we should -extract one or two of the most characteristic. - -The first, though a very short one, will serve to shew the tone which -Galileo had taken with respect to the Copernican system since its -condemnation at Rome, in 1616. "In conclusion, since the motion -attributed to the earth, which I, as a pious and Catholic person, -consider most false, and not to exist, accommodates itself so well to -explain so many and such different phenomena, I shall not feel sure, -unless Sarsi descends to more distinct considerations than those which -he has yet produced, that, false as it is, it may not just as deludingly -correspond with the phenomena of comets." - -Sarsi had quoted a story from Suidas in support of his argument that -motion always produces heat, how the Babylonians used to cook their eggs -by whirling them in a sling; to which Galileo replies: "I cannot refrain -from marvelling that Sarsi will persist in proving to me, by -authorities, that which at any moment I can bring to the test of -experiment. We examine witnesses in things which are doubtful, past, and -not permanent, but not in those things which are done in our own -presence. If discussing a difficult problem were like carrying a weight, -since several horses will carry more sacks of corn than one alone will, -I would agree that many reasoners avail more than one; but _discoursing_ -is like _coursing_, and not like carrying, and one barb by himself will -run farther than a hundred Friesland horses. When Sarsi brings up such a -multitude of authors, it does not seem to me that he in the least degree -strengthens his own conclusions, but he ennobles the cause of Signor -Mario and myself, by shewing that we reason better than many men of -established reputation. If Sarsi insists that I believe, on Suidas' -credit, that the Babylonians cooked eggs by swiftly whirling them in a -sling, I will believe it; but I must needs say, that the cause of such -an effect is very remote from that to which it is attributed, and to -find the true cause I shall reason thus. If an effect does not follow -with us which followed with others at another time, it is because, in -our experiment, something is wanting which was the cause of the former -success; and if only one thing is wanting to us, that one thing is the -true cause. Now we have eggs, and slings, and strong men to whirl them, -and yet they will not become cooked; nay, if they were hot at first, -they more quickly become cold: and since nothing is wanting to us but to -be Babylonians, it follows that being Babylonians is the true cause why -the eggs became hard, and not the friction of the air, which is what I -wished to prove.--Is it possible that in travelling post, Sarsi has -never noticed what freshness is occasioned on the face by the continual -change of air? and if he has felt it, will he rather trust the relation -by others, of what was done two thousand years ago at Babylon, than what -he can at this moment verify in his own person? I at least will not be -so wilfully wrong, and so ungrateful to nature and to God, that having -been gifted with sense and language, I should voluntarily set less value -on such great endowments than on the fallacies of a fellow man, and -blindly and blunderingly believe whatever I hear, and barter the freedom -of my intellect for slavery to one as liable to error as myself." - -Our final extract shall exhibit a sample of Galileo's metaphysics, in -which may be observed the germ of a theory very closely allied to that -which was afterwards developed by Locke and Berkeley.--"I have now only -to fulfil my promise of declaring my opinions on the proposition that -motion is the cause of heat, and to explain in what manner it appears to -me that it may be true. But I must first make some remarks on that which -we call heat, since I strongly suspect that a notion of it prevails -which is very remote from the truth; for it is believed that there is a -true accident, affection, and quality, really inherent in the substance -by which we feel ourselves heated. This much I have to say, that so soon -as I conceive a material or corporeal substance, I simultaneously feel -the necessity of conceiving that it has its boundaries, and is of some -shape or other; that, relatively to others, it is great or small; that -it is in this or that place, in this or that time; that it is in motion, -or at rest; that it touches, or does not touch another body; that it is -unique, rare, or common; nor can I, by any act of the imagination, -disjoin it from these qualities: but I do not find myself absolutely -compelled to apprehend it as necessarily accompanied by such conditions, -as that it must be white or red, bitter or sweet, sonorous or silent, -smelling sweetly or disagreeably; and if the senses had not pointed out -these qualities, it is probable that language and imagination alone -could never have arrived at them. Because, I am inclined to think that -these tastes, smells, colours, &c., with regard to the subject in which -they appear to reside, are nothing more than mere names, and exist only -in the sensitive body; insomuch that, when the living creature is -removed, all these qualities are carried off and annihilated; although -we have imposed particular names upon them, and different from those of -the other first and real accidents, and would fain persuade ourselves -that they are truly and in fact distinct. But I do not believe that -there exists any thing in external bodies for exciting tastes, smells, -and sounds, but size, shape, quantity, and motion, swift or slow; and if -ears, tongues, and noses were removed, I am of opinion that shape, -number, and motion would remain, but there would be an end of smells, -tastes, and sounds, which, abstractedly from the living creature, I take -to be mere words." - -In the spring following the publication of the "Saggiatore," that is to -say, about the time of Easter, in 1624, Galileo went a third time to -Rome to compliment Urban on his elevation to the pontifical chair. He -was obliged to make this journey in a litter; and it appears from his -letters that for some years he had been seldom able to bear any other -mode of conveyance. In such a state of health it seems unlikely that he -would have quitted home on a mere visit of ceremony, which suspicion is -strengthened by the beginning of a letter from him to Prince Cesi, dated -in October, 1623, in which he says: "I have received the very courteous -and prudent advice of your excellency about the time and manner of my -going to Rome, and shall act upon it; and I will visit you at Acqua -Sparta, that I may be completely informed of the actual state of things -at Rome." However this may be, nothing could be more gratifying than his -public reception there. His stay in Rome did not exceed two months, -(from the beginning of April till June,) and during that time he was -admitted to six long and satisfactory interviews with the Pope, and on -his departure received the promise of a pension for his son Vincenzo, -and was himself presented with "a fine painting, two medals, one of gold -and the other of silver, and a good quantity of agnus dei." He had also -much communication with several of the cardinals, one of whom, Cardinal -Hohenzoller, told him that he had represented to the pope on the subject -of Copernicus, that "all the heretics were of that opinion, and -considered it as undoubted; and that it would be necessary to be very -circumspect in coming to any resolution: to which his holiness replied, -that the church had not condemned it, nor was it to be condemned as -heretical, but only as rash; adding, that there was no fear of any one -undertaking to prove that it must necessarily be true." Urban also -addressed a letter to Ferdinand, who had succeeded his father Cosmo as -Grand Duke of Tuscany, expressly for the purpose of recommending Galileo -to him. "For We find in him not only literary distinction, but also the -love of piety, and he is strong in those qualities by which pontifical -good-will is easily obtained. And now, when he has been brought to this -city to congratulate Us on Our elevation, We have very lovingly embraced -him;--nor can We suffer him to return to the country whither your -liberality recalls him without an ample provision of pontifical love. -And that you may know how dear he is to Us, We have willed to give him -this honourable testimonial of virtue and piety. And We further signify -that every benefit which you shall confer upon him, imitating, or even -surpassing your father's liberality, will conduce to Our gratification." -Honoured with these unequivocal marks of approbation, Galileo returned -to Florence. - -His son Vincenzo is soon afterwards spoken of as being at Rome; and it -is not improbable that Galileo sent him thither on the appointment of -his friend and pupil, the Abbé Castelli, to be mathematician to the -pope. Vincenzo had been legitimated by an edict of Cosmo in 1619, and, -according to Nelli, married, in 1624, Sestilia, the daughter of Carlo -Bocchineri. There are no traces to be found of Vincenzo's mother after -1610, and perhaps she died about that time. Galileo's family by her -consisted of Vincenzo and two daughters, Julia and Polissena, who both -took the veil in the convent of Saint Matthew at Arcetri, under the -names of Sister Arcangiola and Sister Maria Celeste. The latter is said -to have possessed extraordinary talents. The date of Vincenzo's -marriage, as given by Nelli, appears somewhat inconsistent with the -correspondence between Galileo and Castelli, in which, so late as 1629, -Galileo is apparently writing of his son as a student under Castelli's -superintendence, and intimates the amount of pocket-money he can afford -to allow him, which he fixes at three crowns a month; adding, that "he -ought to be contented with as many crowns, as, at his age, I possessed -groats." Castelli had given but an unfavourable account of Vincenzo's -conduct, characterizing him as "dissolute, obstinate, and impudent;" in -consequence of which behaviour, Galileo seems to have thought that the -pension of sixty crowns, which had been granted by the pope, might be -turned to better account than by employing it on his son's education; -and accordingly in his reply he requested Castelli to dispose of it, -observing that the proceeds would be useful in assisting him to -discharge a great load of debt with which he found himself saddled on -account of his brother's family. Besides this pension, another of one -hundred crowns was in a few years granted by Urban to Galileo himself, -but it appears to have been very irregularly paid, if at all. - -About the same time Galileo found himself menaced either with the -deprivation of his stipend as extraordinary professor at Pisa, or with -the loss of that leisure which, on his removal to Florence, he had been -so anxious to secure. In 1629, the question was agitated by the party -opposed to him, whether it were in the power of the grand duke to assign -a pension out of the funds of the University, arising out of -ecclesiastical dues, to one who neither lectured nor resided there. This -scruple had slept during nineteen years which had elapsed since -Galileo's establishment in Florence, but probably those who now raised -it reckoned upon finding in Ferdinand II., then scarcely of age, a less -firm supporter of Galileo than his father Cosmo had been. But the matter -did not proceed so far; for, after full deliberation, the prevalent -opinion of the theologians and jurists who were consulted appeared to be -in favour of this exercise of prerogative, and accordingly Galileo -retained his stipend and privileges. - - -FOOTNOTES: - -[77] In Firenze nella Stamperia di Pietro Cecconcelli alle stelle -Medicee, 1619. - -[78] Dell'Origine d'ogni Literatura: Parma, 1787. - - - - -CHAPTER XIII. - - _Publication of Galileo's 'System of the World'--His Condemnation - and Abjuration._ - - -IN the year 1630, Galileo brought to its conclusion his great work, "The -Dialogue on the Ptolemaic and Copernican Systems," and began to take the -necessary steps for procuring permission to print it. This was to be -obtained in the first instance from an officer at Rome, entitled the -master of the sacred palace; and after a little negotiation Galileo -found it would be necessary for him again to return thither, as his -enemies were still busy in thwarting his views and wishes. Niccolo -Riccardi, who at that time filled the office of master of the palace, -had been a pupil of Galileo, and was well disposed to facilitate his -plans; he pointed out, however, some expressions in the work which he -thought it necessary to erase, and, with the understanding that this -should be done, he returned the manuscript to Galileo with his -subscribed approbation. The unhealthy season was drawing near, and -Galileo, unwilling to face it, returned home, where he intended to -complete the index and dedication, and then to send it back to Rome to -be printed in that city, under the superintendence of Federigo Cesi. -This plan was disconcerted by the premature death of that accomplished -nobleman, in August 1630, in whom Galileo lost one of his steadiest and -most effective friends and protectors. This unfortunate event determined -Galileo to attempt to procure permission to print his book at Florence. -A contagious disorder had broken out in Tuscany with such severity as -almost to interrupt all communication between Florence and Rome, and -this was urged by Galileo as an additional reason for granting his -request. Riccardi at first seemed inclined to insist that the book -should be sent to him a second time, but at last contented himself with -inspecting the commencement and conclusion, and consented that (on its -receiving also a license from the inquisitor-general at Florence, and -from one or two others whose names appear on the title-page) it might be -printed where Galileo wished. - -These protracted negotiations prevented the publication of the work till -late in 1632; it then appeared, with a dedication to Ferdinand, under -the following title:--"A Dialogue, by Galileo Galilei, Extraordinary -Mathematician of the University of Pisa, and Principal Philosopher and -Mathematician of the Most Serene Grand Duke of Tuscany; in which, in a -conversation of four days, are discussed the two principal Systems of -the World, the Ptolemaic and Copernican, indeterminately proposing the -Philosophical Arguments as well on one side as on the other." The -beginning of the introduction, which is addressed "To the discreet -Reader," is much too characteristic to be passed by without -notice.--"Some years ago, a salutary edict was promulgated at Rome, -which, in order to obviate the perilous scandals of the present age, -enjoined an opportune silence on the Pythagorean opinion of the earth's -motion. Some were not wanting, who rashly asserted that this decree -originated, not in a judicious examination, but in ill informed passion; -and complaints were heard that counsellors totally inexperienced in -astronomical observations ought not by hasty prohibitions to clip the -wings of speculative minds. My zeal could not keep silence when I heard -these rash lamentations, and I thought it proper, as being fully -informed with regard to that most prudent determination, to appear -publicly on the theatre of the world as a witness of the actual truth. I -happened at that time to be in Rome: I was admitted to the audiences, -and enjoyed the approbation of the most eminent prelates of that court, -nor did the publication of that decree occur without my receiving some -prior intimation of it.[79] Wherefore it is my intention in this present -work, to show to foreign nations that as much is known of this matter in -Italy, and particularly in Rome, as ultramontane diligence can ever have -formed any notion of, and collecting together all my own speculations on -the Copernican system, to give them to understand that the knowledge of -all these preceded the Roman censures, and that from this country -proceed not only dogmas for the salvation of the soul, but also -ingenious discoveries for the gratification of the understanding. With -this object, I have taken up in the Dialogue the Copernican side of the -question, treating it as a pure mathematical hypothesis; and -endeavouring in every artificial manner to represent it as having the -advantage, not over the opinion of the stability of the earth -absolutely, but according to the manner in which that opinion is -defended by some, who indeed profess to be Peripatetics, but retain only -the name, and are contented without improvement to worship shadows, not -philosophizing with their own reason, but only from the recollection of -four principles imperfectly understood."--This very flimsy veil could -scarcely blind any one as to Galileo's real views in composing this -work, nor does it seem probable that he framed it with any expectation -of appearing neutral in the discussion. It is more likely that he -flattered himself that, under the new government at Rome, he was not -likely to be molested on account of the personal prohibition which he -had received in 1616, "not to believe or teach the motion of the earth -in any manner," provided he kept himself within the letter of the limits -of the more public and general order, that the Copernican system was not -to be brought forward otherwise than as a mere mathematically -convenient, but in fact unreal supposition. So long as this decree -remained in force, a due regard to consistency would compel the Roman -Inquisitors to notice an unequivocal violation of it; and this is -probably what Urban had implied in the remark quoted by Hohenzoller to -Galileo.[80] There were not wanting circumstances which might compensate -for the loss of Cosmo and of Federigo Cesi; Cosmo had been succeeded by -his son, who, though he had not yet attained his father's energy, showed -himself as friendly as possible to Galileo. Cardinal Bellarmine, who had -been mainly instrumental in procuring the decree of 1616, was dead; -Urban on the contrary, who had been among the few Cardinals who then -opposed it as uncalled for and ill-advised, was now possessed of supreme -power, and his recent affability seemed to prove that the increased -difference in their stations had not caused him to forget their early -and long-continued intimacy. It is probable that Galileo would not have -found himself mistaken in this estimate of his position, but for an -unlucky circumstance, of which his enemies immediately saw the -importance, and which they were not slow in making available against -him. The dialogue of Galileo's work is conducted between three -personages;--Salviati and Sagredo, who were two noblemen, friends of -Galileo, and Simplicio, a name borrowed from a noted commentator upon -Aristotle, who wrote in the sixth century. Salviati is the principal -philosopher of the work; it is to him that the others apply for -solutions of their doubts and difficulties, and on him the principal -task falls of explaining the tenets of the Copernican theory. Sagredo is -only a half convert, but an acute and ingenious one; to him are allotted -the objections which seem to have some real difficulty in them, as well -as lively illustrations and digressions, which might have been thought -inconsistent with the gravity of Salviati's character. Simplicio, though -candid and modest, is of course a confirmed Ptolemaist and Aristotelian, -and is made to produce successively all the popular arguments of that -school in support of his master's system. Placed between the wit and the -philosopher, it may be guessed that his success is very indifferent, and -in fact he is alternately ridiculed and confuted at every turn. As -Galileo racked his memory and invention to leave unanswered no argument -which was or could be advanced against Copernicus, it unfortunately -happened, that he introduced some which Urban himself had urged upon him -in their former controversies on this subject; and Galileo's opponents -found means to make His Holiness believe that the character of Simplicio -had been sketched in personal derision of him. We do not think it -necessary to exonerate Galileo from this charge; the obvious folly of -such an useless piece of ingratitude speaks sufficiently for itself. But -self-love is easily irritated; and Urban, who aspired to a reputation -for literature and science, was peculiarly sensitive on this point. His -own expressions almost prove his belief that such had been Galileo's -design, and it seems to explain the otherwise inexplicable change which -took place in his conduct towards his old friend, on account of a book -which he had himself undertaken to examine, and of which he had -authorised the publication. - -One of the earliest notices of what was approaching, is found in the -dispatches, dated August 24, 1632, from Ferdinand's minister, Andrea -Cioli, to Francesco Nicolini, the Tuscan ambassador at the court of -Rome. - -"I have orders to signify to Your Excellency that His Highness remains -greatly astonished that a book, placed by the author himself in the -hands of the supreme authority in Rome, read and read again there most -attentively, and in which every thing, not only with the consent, but at -the request of the author, was amended, altered, added, or removed at -the will of his superiors, which was again subjected here to the same -examination, agreeably to orders from Rome, and which finally was -licensed both there and here, and here printed and published, should now -become an object of suspicion at the end of two years, and the author -and printer be prohibited from publishing any more."--In the sequel is -intimated Ferdinand's desire that the charges, of whatever nature they -might be, either against Galileo or his book, might be reduced to -writing and forwarded to Florence, that he might prepare for his -justification; but this reasonable demand was utterly disregarded. It -appears to have been owing to the mean subserviency of Cioli to the -court of Rome, that Ferdinand refrained from interfering more -strenuously to protect Galileo. Cioli's words are: "The Grand Duke is so -enraged with this business of Galileo, that I do not know what will be -done. I know, at least, that His Holiness shall have no reason to -complain of his ministers, or of their bad advice."[81] - -A letter from Galileo's Venetian friend Micanzio, dated about a month -later, is in rather a bolder and less formal style:--"The efforts of -your enemies to get your book prohibited will occasion no loss either to -your reputation, or to the intelligent part of the world. As to -posterity, this is just one of the surest ways to hand the book down to -them. But what a wretched set this must be to whom every good thing, and -all that is founded in nature, necessarily appears hostile and odious! -The world is not restricted to a single corner; you will see the book -printed in more places and languages than one; and just for this reason, -I wish they would prohibit all good books. My disgust arises from seeing -myself deprived of what I most desire of this sort, I mean your other -dialogues; and if, from this cause, I fail in having the pleasure of -seeing them, I shall devote to a hundred thousand devils these unnatural -and godless hypocrites." - -At the same time, Thomas Campanella, a monk, who had already -distinguished himself by an apology for Galileo (published in 1622), -wrote to him from Rome:--"I learn with the greatest disgust, that a -congregation of angry theologians is forming to condemn your Dialogues, -and that no single member of it has any knowledge of mathematics, or -familiarity with abstruse speculations. I should advise you to procure a -request from the Grand Duke that, among the Dominicans and Jesuits and -Theatins, and secular priests whom they are putting on this congregation -against your book, they should admit also Castelli and myself." It -appears, from subsequent letters both from Campanella and Castelli, that -the required letter was procured and sent to Rome, but it was not -thought prudent to irritate the opposite party by a request which it was -then clearly seen would have been made in vain. Not only were these -friends of Galileo not admitted to the congregation, but, upon some -pretext, Castelli was even sent away from Rome, as if Galileo's enemies -desired to have as few enlightened witnesses as possible of their -proceedings; and on the contrary, Scipio Chiaramonte, who had been long -known for one of the staunchest and most bigoted defenders of the old -system, and who, as Montucla says, seems to have spent a long life in -nothing but retarding, as far as he was able, the progress of discovery, -was summoned from Pisa to complete their number. From this period we -have a tolerably continuous account of the proceedings against Galileo -in the dispatches which Nicolini sent regularly to his court. It appears -from them that Nicolini had several interviews with the Pope, whom he -found highly incensed against Galileo, and in one of the earliest he -received an intimation to advise the Duke "not to engage himself in this -matter as he had done in the other business of Alidosi,[82] because he -would not get through it with honour." Finding Urban in this humour, -Nicolini thought it best to temporize, and to avoid the appearance of -any thing like direct opposition. On the 15th of September, probably as -soon as the first report on Galileo's book had been made, Nicolini -received a private notice from the Pope, "in especial token of the -esteem in which he held the Grand Duke," that he was unable to do less -than consign the work to the consideration of the Inquisition. Nicolini -was permitted to communicate this to the Grand Duke only, and both were -declared liable to "the usual censures" of the Inquisition in case of -divulging the secret. - -The next step was to summon Galileo to Rome, and the only answer -returned to all Nicolini's representations of his advanced age of -seventy years, the very infirm state of his health, and the discomforts -which he must necessarily suffer in such a journey, and in keeping -quarantine, was that he might come at leisure, and that the quarantine -should be relaxed as much as possible in his favour, but that it was -indispensably necessary that he should be personally examined before the -Inquisition at Rome. Accordingly, on the 14th of February, 1633, -Nicolini announces Galileo's arrival, and that he had officially -notified his presence to the Assessor and Commissary of the Holy Office. -Cardinal Barberino, Urban's nephew, who seems on the whole to have acted -a friendly part towards Galileo, intimated to him that his most prudent -course would be to keep himself as much at home and as quiet as -possible, and to refuse to see any but his most intimate friends. With -this advice, which was repeated to him from several quarters, Galileo -thought it best to comply, and kept himself entirely secluded in -Nicolini's palace, where he was as usual maintained at the expense of -the Grand Duke. Nelli quotes two letters, which passed between -Ferdinand's minister Cioli and Nicolini, in which the former intimated -that Galileo's expenses were to be defrayed only during the first month -of his residence at Rome. Nicolini returned a spirited answer, that in -that case, after the time specified, he should continue to treat him as -before at his own private cost. - -The permission to reside at the ambassador's palace whilst his cause was -pending, was granted and received as an extraordinary indulgence on the -part of the Inquisition, and indeed if we estimate the proceedings -throughout against Galileo by the usual practice of that detestable -tribunal, it will appear that he was treated with unusual consideration. -Even when it became necessary in the course of the inquiry to examine -him in person, which was in the beginning of April, although his removal -to the Holy Office was then insisted upon, yet he was not committed to -close or strictly solitary confinement. On the contrary, he was -honourably lodged in the apartments of the Fiscal of the Inquisition, -where he was allowed the attendance of his own servant, who was also -permitted to sleep in an adjoining room, and to come and go at pleasure. -His table was still furnished by Nicolini. But, notwithstanding the -distinction with which he was thus treated, Galileo was annoyed and -uneasy at being (though little more than nominally) within the walls of -the Inquisition. He became exceedingly anxious that the matter should be -brought to a conclusion, and a severe attack of his constitutional -complaints rendered him still more fretful and impatient. On the last -day of April, about ten days after his first examination, he was -unexpectedly permitted to return to Nicolini's house, although the -proceedings were yet far from being brought to a conclusion. Nicolini -attributes this favour to Cardinal Barberino, who, he says, liberated -Galileo on his own responsibility, in consideration of the enfeebled -state of his health. - -In the society of Nicolini and his family, Galileo recovered something -of his courage and ordinary cheerfulness, although his return appears to -have been permitted on express condition of a strict seclusion; for at -the latter end of May, Nicolini was obliged to apply for permission that -Galileo should take that exercise in the open air which was necessary -for his health; on which occasion he was permitted to go into the public -gardens in a half-closed carriage. - -On the evening of the 20th of June, rather more than four months after -Galileo's arrival in Rome, he was again summoned to the Holy Office, -whither he went the following morning; he was detained there during the -whole of that day, and on the next day was conducted in a penitential -dress[83] to the Convent of Minerva, where the Cardinals and Prelates, -his judges, were assembled for the purpose of passing judgment upon him, -by which this venerable old man was solemnly called upon to renounce and -abjure, as impious and heretical, the opinions which his whole existence -had been consecrated to form and strengthen. As we are not aware that -this remarkable record of intolerance and bigoted folly has ever been -printed entire in English, we subjoin a literal translation of the whole -sentence and abjuration. - - -_The Sentence of the Inquisition on Galileo._ - - "We, the undersigned, by the Grace of God, Cardinals of the Holy - Roman Church, Inquisitors General throughout the whole Christian - Republic, Special Deputies of the Holy Apostolical Chair against - heretical depravity, - - "Whereas you, Galileo, son of the late Vincenzo Galilei of Florence, - aged seventy years, were denounced in 1615 to this Holy Office, for - holding as true a false doctrine taught by many, namely, that the - sun is immoveable in the centre of the world, and that the earth - moves, and also with a diurnal motion; also, for having pupils whom - you instructed in the same opinions; also, for maintaining a - correspondence on the same with some German mathematicians; also for - publishing certain letters on the solar spots, in which you - developed the same doctrine as true; also, for answering the - objections which were continually produced from the Holy Scriptures, - by glozing the said Scriptures according to your own meaning; and - whereas thereupon was produced the copy of a writing, in form of a - letter, professedly written by you to a person formerly your pupil, - in which, following the hypotheses of Copernicus, you include - several propositions contrary to the true sense and authority of the - Holy Scripture: therefore this holy tribunal being desirous of - providing against the disorder and mischief which was thence - proceeding and increasing to the detriment of the holy faith, by the - desire of His Holiness, and of the Most Eminent Lords Cardinals of - this supreme and universal Inquisition, the two propositions of the - stability of the sun, and motion of the earth, were _qualified_ by - the _Theological Qualifiers_ as follows: - - "_1st. The proposition that the Sun is in the centre of the world - and immoveable from its place, is absurd, philosophically false, and - formally heretical; because it is expressly contrary to the Holy - Scripture._ - - "_2dly. The proposition that the Earth is not the centre of the - world, nor immoveable, but that it moves, and also with a diurnal - motion, is also absurd, philosophically false, and, theologically - considered, at least erroneous in faith._ - - "But whereas being pleased at that time to deal mildly with you, it - was decreed in the Holy Congregation, held before His Holiness on - the 25th day of February, 1616, that His Eminence the Lord Cardinal - Bellarmine should enjoin you to give up altogether the said false - doctrine; if you should refuse, that you should be ordered by the - Commissary of the Holy Office to relinquish it, not to teach it to - others, nor to defend it, nor ever mention it, and in default of - acquiescence that you should be imprisoned; and in execution of this - decree, on the following day at the palace, in presence of His - Eminence the said Lord Cardinal Bellarmine, after you had been - mildly admonished by the said Lord Cardinal, you were commanded by - the acting Commissary of the Holy Office, before a notary and - witnesses, to relinquish altogether the said false opinion, and in - future neither to defend nor teach it in any manner, neither - verbally nor in writing, and upon your promising obedience you were - dismissed. - - "And in order that so pernicious a doctrine might be altogether - rooted out, nor insinuate itself farther to the heavy detriment of - the Catholic truth, a decree emanated from the Holy Congregation of - the Index[84] prohibiting the books which treat of this doctrine; - and it was declared false, and altogether contrary to the Holy and - Divine Scripture. - - "And whereas a book has since appeared, published at Florence last - year, the title of which shewed that you were the author, which - title is: _The Dialogue of Galileo Galilei, on the two principal - systems of the world, the Ptolemaic and Copernican_; and whereas the - Holy Congregation has heard that, in consequence of the printing of - the said book, the false opinion of the earth's motion and stability - of the sun is daily gaining ground; the said book has been taken - into careful consideration, and in it has been detected a glaring - violation of the said order, which had been intimated to you; - inasmuch as in this book you have defended the said opinion, - already and in your presence condemned; although in the said book - you labour with many circumlocutions to induce the belief that it is - left by you undecided, and in express terms probable: which is - equally a very grave error, since an opinion can in no way be - probable which has been already declared and finally determined - contrary to the divine Scripture. Therefore by Our order you have - been cited to this Holy Office, where, on your examination upon - oath, you have acknowledged the said book as written and printed by - you. You also confessed that you began to write the said book ten or - twelve years ago, after the order aforesaid had been given. Also, - that you demanded license to publish it, but without signifying to - those who granted you this permission that you had been commanded - not to hold, defend, or teach the said doctrine in any manner. You - also confessed that the style of the said book was, in many places, - so composed that the reader might think the arguments adduced on the - false side to be so worded as more effectually to entangle the - understanding than to be easily solved, alleging in excuse, that you - have thus run into an error, foreign (as you say) to your intention, - from writing in the form of a dialogue, and in consequence of the - natural complacency which every one feels with regard to his own - subtilties, and in showing himself more skilful than the generality - of mankind in contriving, even in favour of false propositions, - ingenious and apparently probable arguments. - - "And, upon a convenient time being given to you for making your - defence, you produced a certificate in the hand-writing of His - Eminence the Lord Cardinal Bellarmine, procured, as you said, by - yourself, that you might defend yourself against the calumnies of - your enemies, who reported that you had abjured your opinions, and - had been punished by the Holy Office; in which certificate it is - declared, that you had not abjured, nor had been punished, but - merely that the declaration made by His Holiness, and promulgated by - the Holy Congregation of the Index, had been announced to you, which - declares that the opinion of the motion of the earth, and stability - of the sun, is contrary to the Holy Scriptures, and, therefore, - cannot be held or defended. Wherefore, since no mention is there - made of two articles of the order, to wit, the order 'not to teach,' - and 'in any manner,' you argued that we ought to believe that, in - the lapse of fourteen or sixteen years, they had escaped your - memory, and that this was also the reason why you were silent as to - the order, when you sought permission to publish your book, and that - this is said by you not to excuse your error, but that it may be - attributed to vain-glorious ambition, rather than to malice. But - this very certificate, produced on your behalf, has greatly - aggravated your offence, since it is therein declared that the said - opinion is contrary to the Holy Scripture, and yet you have dared to - treat of it, to defend it, and to argue that it is probable; nor is - there any extenuation in the licence artfully and cunningly extorted - by you, since you did not intimate the command imposed upon you. But - whereas it appeared to Us that you had not disclosed the whole truth - with regard to your intentions, We thought it necessary to proceed - to the rigorous examination of you, in which (without any prejudice - to what you had confessed, and which is above detailed against you, - with regard to your said intention) you answered like a good - Catholic. - - "Therefore, having seen and maturely considered the merits of your - cause, with your said confessions and excuses, and every thing else - which ought to be seen and considered, We have come to the - underwritten final sentence against you. - - "Invoking, therefore, the most holy name of Our Lord Jesus Christ, - and of His Most Glorious Virgin Mother Mary, by this Our final - sentence, which, sitting in council and judgment for the tribunal of - the Reverend Masters of Sacred Theology, and Doctors of both Laws, - Our Assessors, We put forth in this writing touching the matters and - controversies before Us, between The Magnificent Charles Sincerus, - Doctor of both Laws, Fiscal Proctor of this Holy Office of the one - part, and you, Galileo Galilei, an examined and confessed criminal - from this present writing now in progress as above of the other - part, We pronounce, judge, and declare, that you, the said Galileo, - by reason of these things which have been detailed in the course of - this writing, and which, as above, you have confessed, have rendered - yourself vehemently suspected by this Holy Office of heresy: that is - to say, that you believe and hold the false doctrine, and contrary - to the Holy and Divine Scriptures, namely, that the sun is the - centre of the world, and that it does not move from east to west, - and that the earth does move, and is not the centre of the world; - also that an opinion can be held and supported as probable after it - has been declared and finally decreed contrary to the Holy - Scripture, and consequently that you have incurred all the censures - and penalties enjoined and promulgated in the sacred canons, and - other general and particular constitutions against delinquents of - this description. From which it is Our pleasure that you be - absolved, provided that, first, with a sincere heart and unfeigned - faith, in Our presence, you abjure, curse, and detest the said - errors and heresies, and every other error and heresy contrary to - the Catholic and Apostolic Church of Rome, in the form now shown to - you. - - "But, that your grievous and pernicious error and transgression may - not go altogether unpunished, and that you may be made more cautious - in future, and may be a warning to others to abstain from - delinquencies of this sort, We decree that the book of the dialogues - of Galileo Galilei be prohibited by a public edict, and We condemn - you to the formal prison of this Holy Office for a period - determinable at Our pleasure; and, by way of salutary penance, We - order you, during the next three years, to recite once a week the - seven penitential psalms, reserving to Ourselves the power of - moderating, commuting, or taking off the whole or part of the said - punishment and penance. - - "And so We say, pronounce, and by Our sentence declare, decree, and - reserve, in this and in every other better form and manner, which - lawfully We may and can use. - - "So We, the subscribing Cardinals, pronounce. - - Felix, Cardinal di Ascoli, - Guido, Cardinal Bentivoglio, - Desiderio, Cardinal di Cremona, - Antonio, Cardinal S. Onofrio, - Berlingero, Cardinal Gessi, - Fabricio, Cardinal Verospi, - Martino, Cardinal Ginetti." - -We cannot suppose that Galileo, even broken down as he was with age and -infirmities, and overawed by the merciless tribunal to whose power he -was subjected, could without extreme reluctance thus formally give the -lie to his whole life, and call upon God to witness his renunciation of -the opinions which even his bigoted judges must have felt that he still -clung to in his heart. - -We know indeed that his friends were unanimous in recommending an -unqualified acquiescence in whatever might be required, but some persons -have not been able to find an adequate explanation of his submission, -either in their exhortations, or in the mere dread of the alternative -which might await him in case of non-compliance. It has in short been -supposed, although the suspicion scarcely rests upon grounds -sufficiently strong to warrant the assertion, that Galileo did not -submit to this abjuration until forced to it, not merely by the -apprehension, but by the actual experience of personal violence. The -arguments on which this horrible idea appears to be mainly founded are -the two following: First, the Inquisitors declare in their sentence -that, not satisfied with Galileo's first confession, they judged it -necessary to proceed "to the rigorous examination of him, in which he -answered like a good Catholic."[85] It is pretended by those who are -more familiar with inquisitorial language than we can profess to be, -that the words _il rigoroso esame_, form the official phrase for the -application of the torture, and accordingly they interpret this passage -to mean, that the desired answers and submission had thus been extorted -from Galileo, which his judges had otherwise failed to get from him. -And, secondly, the partisans of this opinion bring forward in -corroboration of it, that Galileo immediately on his departure from -Rome, in addition to his old complaints, was found to be afflicted with -hernia, and this was a common consequence of the torture of the cord, -which they suppose to have been inflicted. It is right to mention that -no other trace can be found of this supposed torturing in all the -documents relative to the proceedings against Galileo, at least Venturi -was so assured by one who had inspected the originals at Paris.[86] - -Although the arguments we have mentioned appear to us slight, yet -neither can we attach much importance to the contrast which the -favourers of the opposite opinion profess to consider so incredible -between the honourable manner in which Galileo was treated throughout -the rest of the inquiry, and the suspected harsh proceeding against him. -Whether Galileo should be lodged in a prison or a palace, was a matter -of far other importance to the Inquisitors and to their hold upon public -opinion, than the question whether or not he should be suffered to -exhibit a persevering resistance to the censures which they were -prepared to cast upon him. Nor need we shrink from the idea, as we might -from suspecting of some gross crime, on trivial grounds, one of hitherto -unblemished innocence and character. The question may be disencumbered -of all such scruples, since one atrocity more or less can do little -towards affecting our judgment of the unholy Office of the Inquisition. - -Delambre, who could find so much to reprehend in Galileo's former -uncompromising boldness, is deeply penetrated with the insincerity of -his behaviour on the present occasion. He seems to have forgotten that a -tribunal which finds it convenient to carry on its inquiries in secret, -is always liable to the suspicion of putting words into the mouth of its -victims; and if it were worth while, there is sufficient internal -evidence that the language which Galileo is made to hold in his defence -and confession, is rather to be read as the composition of his judges -than his own. For instance, in one of the letters which we have -extracted[87], it may be seen that this obnoxious work was already in -forward preparation as early as 1610, and yet he is made to confess, and -the circumstance appears to be brought forward in aggravation of his -guilt, that he began to write it after the prohibition which he had -received in 1616. - -The abjuration was drawn up in the following terms:-- - - _The Abjuration of Galileo._ - - "I Galileo Galilei, son of the late Vincenzo Galilei, of Florence, - aged 70 years, being brought personally to judgment, and kneeling - before you, Most Eminent and Most Reverend Lords Cardinals, General - Inquisitors of the universal Christian republic against heretical - depravity, having before my eyes the Holy Gospels, which I touch - with my own hands, swear, that I have always believed, and now - believe, and with the help of God will in future believe, every - article which the Holy Catholic and Apostolic Church of Rome holds, - teaches, and preaches. But because I had been enjoined by this Holy - Office altogether to abandon the false opinion which maintains that - the sun is the centre and immoveable, and forbidden to hold, defend, - or teach, the said false doctrine in any manner, and after it had - been signified to me that the said doctrine is repugnant with the - Holy Scripture, I have written and printed a book, in which I treat - of the same doctrine now condemned, and adduce reasons with great - force in support of the same, without giving any solution, and - therefore have been judged grievously suspected of heresy; that is - to say, that I held and believed that the sun is the centre of the - world and immoveable, and that the earth is not the centre and - moveable. Willing, therefore, to remove from the minds of Your - Eminences, and of every Catholic Christian, this vehement suspicion - rightfully entertained towards me, with a sincere heart and - unfeigned faith, I abjure, curse, and detest, the said errors and - heresies, and generally every other error and sect contrary to the - said Holy Church; and I swear, that I will never more in future say - or assert anything verbally, or in writing, which may give rise to a - similar suspicion of me: but if I shall know any heretic, or any one - suspected of heresy, that I will denounce him to this Holy Office, - or to the Inquisitor and Ordinary of the place in which I may be. I - swear, moreover, and promise, that I will fulfil, and observe fully, - all the penances which have been, or shall be laid on me by this - Holy Office. But if it shall happen that I violate any of my said - promises, oaths, and protestations, (which God avert!) I subject - myself to all the pains and punishments, which have been decreed and - promulgated by the sacred canons, and other general and particular - constitutions, against delinquents of this description. So may God - help me, and his Holy Gospels, which I touch with my own hands. I, - the above-named Galileo Galilei, have abjured, sworn, promised, and - bound myself, as above, and in witness thereof with my own hand have - subscribed this present writing of my abjuration, which I have - recited word for word. At Rome in the Convent of Minerva, 22d June, - 1633. I, Galileo Galilei, have abjured as above with my own hand." - -It is said that Galileo, as he rose from his knees, stamped on the -ground, and whispered to one of his friends, _E pur si muove_--(It does -move though). - -Copies of Galileo's sentence and abjuration were immediately promulgated -in every direction, and the professors at several universities received -directions to read them publicly. At Florence this ceremony took place -in the church of Sta. Croce, whither Guiducci, Aggiunti, and all others -who were known in that city as firm adherents to Galileo's opinions, -were specially summoned. The triumph of the "Paper Philosophers" was so -far complete, and the alarm occasioned by this proof of their dying -power extended even beyond Italy. "I have been told," writes Descartes -from Holland to Mersenne at Paris, "that Galileo's system was printed in -Italy last year, but that every copy has been burnt at Rome, and himself -condemned to some sort of penance, which has astonished me so much that -I have almost determined to burn all my papers, or at least never to let -them be seen by any one. I cannot collect that he, who is an Italian and -even a friend of the Pope, as I understand, has been criminated on any -other account than for having attempted to establish the motion of the -earth. I know that this opinion was formerly censured by some Cardinals, -but I thought I had since heard, that no objection was now made to its -being publicly taught, even at Rome." - -The sentiments of all who felt themselves secured against the -apprehension of personal danger could take but one direction, for, as -Pascal well expressed it in one of his celebrated letters to the -Jesuits--"It is in vain that you have procured against Galileo a decree -from Rome condemning his opinion of the earth's motion. Assuredly, that -will never prove it to be at rest; and if we have unerring observations -proving that it turns round, not all mankind together can keep it from -turning, nor themselves from turning with it." - -The assembly of doctors of the Sorbonne at Paris narrowly escaped from -passing a similar sentence upon the system of Copernicus. The question -was laid before them by Richelieu, and it appears that their opinion was -for a moment in favour of confirming the Roman decree. It is to be -wished that the name had been preserved of one of its members, who, by -his strong and philosophical representations, saved that celebrated body -from this disgrace. - -Those who saw nothing in the punishment of Galileo but passion and -blinded superstition, took occasion to revert to the history of a -similar blunder of the Court of Rome in the middle of the eighth -century. A Bavarian bishop, named Virgil, eminent both as a man of -letters and politician, had asserted the existence of Antipodes, which -excited in the ignorant bigots of his time no less alarm than did the -motion of the earth in the seventeenth century. Pope Zachary, who was -scandalized at the idea of another earth, inhabited by another race of -men, and enlightened by another sun and moon (for this was the shape -which Virgil's system assumed in his eyes), sent out positive orders to -his legate in Bavaria. "With regard to Virgil, the philosopher, (I know -not whether to call him priest,) if he own these perverse opinions, -strip him of his priesthood, and drive him from the church and altars of -God." But Virgil had himself occasionally acted as legate, and was -moreover too necessary to his sovereign to be easily displaced. He -utterly disregarded these denunciations, and during twenty-five years -which elapsed before his death, retained his opinions, his bishopric of -Salzburg, and his political power. He was afterwards canonized.[88] - -Even the most zealous advocates of the authority of Rome were -embarrassed in endeavouring to justify the treatment which Galileo -experienced. Tiraboschi has attempted to draw a somewhat subtle -distinction between the bulls of the Pope and the inquisitorial decrees -which were sanctioned and approved by him; he dwells on the reflection -that no one, even among the most zealous Catholics, has ever claimed -infallibility as an attribute of the Inquisition, and looks upon it as a -special mark of grace accorded to the Roman Catholic Church, that during -the whole period in which most theologians rejected the opinions of -Copernicus, as contrary to the Scriptures, the head of that Church was -never permitted to compromise his infallible character by formally -condemning it.[89] - -Whatever may be the value of this consolation, it can hardly be -conceded, unless it be at the same time admitted that many scrupulous -members of the Church of Rome have been suffered to remain in singular -misapprehension of the nature and sanction of the authority to which -Galileo had yielded. The words of the bull of Sixtus V., by which the -Congregation of the Index was remodelled in 1588, are quoted by a -professor of the University of Louvain, a zealous antagonist of Galileo, -as follows: "They are to examine and expose the books which are -repugnant to the Catholic doctrines and Christian discipline, and after -reporting on them to us, they are to condemn them by our authority."[90] -Nor does it appear that the learned editors of what is commonly called -the Jesuit's edition of Newton's "Principia" were of opinion, that in -adopting the Copernican system they should transgress a mandate -emanating from any thing short of infallible wisdom. The remarkable -words which they were compelled to prefix to their book, show how -sensitive the court of Rome remained, even so late as 1742, with regard -to this rashly condemned theory. In their preface they say: "Newton in -this third book supposes the motion of the earth. We could not explain -the author's propositions otherwise than by making the same supposition. -We are therefore forced to sustain a character which is not our own; but -we profess to pay the obsequious reverence which is due to the decrees -pronounced by the supreme Pontiffs against the motion of the earth."[91] - -This coy reluctance to admit what nobody any longer doubts has survived -to the present time; for Bailli informs us,[92] that the utmost -endeavours of Lalande, when at Rome, to obtain that Galileo's work -should be erased from the Index, were entirely ineffectual, in -consequence of the decree which had been fulminated against him; and in -fact both it, and the book of Copernicus, "Nisi Corrigatur," are still -to be seen on the forbidden list of 1828. - -The condemnation of Galileo and his book was not thought sufficient. -Urban's indignation also vented itself upon those who had been -instrumental in obtaining the licence for him. The Inquisitor at -Florence was reprimanded; Riccardi, the master of the sacred palace, and -Ciampoli, Urban's secretary, were both dismissed from their situations. -Their punishment appears rather anomalous and inconsistent with the -proceedings against Galileo, in which it was assumed that his book was -not properly licensed; yet the others suffered on account of granting -that very licence, which he was accused of having surreptitiously -obtained from them, by concealing circumstances with which they were not -bound to be otherwise acquainted. Riccardi, in exculpation of his -conduct, produced a letter in the hand-writing of Ciampoli, in which was -contained that His Holiness, in whose presence the letter professed to -be written, ordered the licence to be given. Urban only replied that -this was a Ciampolism; that his secretary and Galileo had circumvented -him; that he had already dismissed Ciampoli, and that Riccardi must -prepare to follow him. - -As soon as the ceremony of abjuration was concluded, Galileo was -consigned, pursuant to his sentence, to the prison of the Inquisition. -Probably it was never intended that he should long remain there, for at -the end of four days, he was reconducted on a very slight representation -of Nicolini to the ambassador's palace, there to await his further -destination. Florence was still suffering under the before-mentioned -contagion; and Sienna was at last fixed on as the place of his -relegation. He would have been shut up in some convent in that city, if -Nicolini had not recommended as a more suitable residence, the palace of -the Archbishop Piccolomini, whom he knew to be among Galileo's warmest -friends. Urban consented to the change, and Galileo finally left Rome -for Sienna in the early part of July. - -Piccolomini received him with the utmost kindness, controlled of course -by the strict injunctions which were dispatched from Rome, not to suffer -him on any account to quit the confines of the palace. Galileo continued -at Sienna in this state of seclusion till December of the same year, -when the contagion having ceased in Tuscany, he applied for permission -to return to his villa at Arcetri. This was allowed, subject to the same -restrictions under which he had been residing with the archbishop. - - -FOOTNOTES: - -[79] Delambre quotes this sentence from a passage which is so obviously -ironical throughout, as an instance of Galileo's mis-statement of -facts!--_Hist. de l'Astr. Mod._, vol, i. p. 666. - -[80] Page 54. - -[81] Galuzzi. Storia di Toscana. Firenze, 1822. - -[82] Alidosi was a Florentine nobleman, whose estate Urban wished to -confiscate on a charge of heresy.--_Galuzzi._ - -[83] S'irrito il Papa, e lo fece abjurare, comparendo il pover uomo con -uno straccio di camicia indosso, che faceva compassione, MS. nella Bibl. -Magliab. Venturi. - -[84] The Index is a list of books, the reading of which is prohibited to -Roman Catholics. This list, in the early periods of the Reformation, was -often consulted by the curious, who were enlarging their libraries; and -a story is current in England, that, to prevent this mischief, the Index -itself was inserted in its own forbidden catalogue. The origin of this -story is, that an Index was published in Spain, particularizing the -objectionable passages in such books as were only partially condemned; -and although compiled with the best intentions, this was found to be so -racy, that it became necessary to forbid the circulation of this edition -in subsequent lists. - -[85] Giudicassimo esser necessario venir contro di te al rigoroso esame -nel quale rispondesti cattolicamente. - -[86] The fate of these documents is curious; after being long preserved -at Rome, they were carried away in 1809, by order of Buonaparte, to -Paris, where they remained till his first abdication. Just before the -hundred days, the late king of France, wishing to inspect them, ordered -that they should be brought to his own apartments for that purpose. In -the hasty flight which soon afterwards followed, the manuscripts were -forgotten, and it is not known what became of them. A French -translation, begun by Napoleon's desire, was completed only down to the -30th of April, 1633, the date of Galileo's first return to Nicolini's -palace. - -[87] Page 18. - -[88] Annalium Bolorum, libri vii. Ingolstadii, 1554. - -[89] La Chiesa non ha mai dichiarati eretici i sostenitori del Sistema -Copernicano, e questa troppo rigorosa censura non usci che dal tribunale -della Romana Inquisizione a cui niuno tra Cattolici ancor piu zelanti ha -mai attribuito it diritto dell'infallibilità. Anzi in cio ancora è d' -ammirarsi la providenza di Dio à favor della Chiesa, percioche in un -tempo in cui la maggior parte dei teologi fermamente credavano che il -Sistema Copernicano fosse all' autorità delle sacre Carte contrario, pur -non permise che dalla Chiesa si proferisse su cio un solenne -giudizio.--Stor. della Lett. Ital. - -[90] Lib. Fromondi Antaristarchus, Antwerpiæ, 1631. - -[91] Newtoni Principia, Coloniæ, 1760. - -[92] Histoire de l'Astronomie Moderne. - - - - -CHAPTER XIV. - - _Extracts from the Dialogues on the System._ - - -AFTER narrating the treatment to which Galileo was subject on account of -his admirable Dialogues, it will not be irrelevant to endeavour, by a -few extracts, to convey some idea of the style in which they are -written. It has been mentioned, that he is considered to surpass all -other Italian writers (unless we except Machiavelli) in the purity and -beauty of his language, and indeed his principal followers, who avowedly -imitated his style, make a distinguished group among the classical -authors of modern Italy. He professed to have formed himself from the -study of Ariosto, whose poems he passionately admired, insomuch that he -could repeat the greater part of them, as well as those of Berni and -Petrarca, all which he was in the frequent habit of quoting in -conversation. The fashion and almost universal practice of that day was -to write on philosophical subjects in Latin; and although Galileo wrote -very passably in that language, yet he generally preferred the use of -Italian, for which he gave his reasons in the following characteristic -manner:-- - -"I wrote in Italian because I wished every one to be able to read what I -wrote; and for the same cause I have written my last treatise in the -same language: the reason which has induced me is, that I see young men -brought together indiscriminately to study to become physicians, -philosophers, &c., and whilst many apply to such professions who are -most unfit for them, others who would be competent remain occupied -either with domestic business, or with other employments alien to -literature; who, although furnished, as Ruzzante might say, with a -_decent set of brains_, yet, not being able to understand things written -in _gibberish_, take it into their heads, that in these crabbed folios -there must be some grand _hocus pocus_ of logic and philosophy much too -high up for them to think of jumping at. I want them to know, that as -Nature has given eyes to them just as well as to philosophers for the -purpose of seeing her works, she has also given them brains for -examining and understanding them." - -The general structure of the dialogues has been already described;[93] -we shall therefore premise no more than the judgment pronounced on them -by a highly gifted writer, to supply the deficiencies of our necessarily -imperfect analysis. - -"One forms a very imperfect idea of Galileo, from considering the -discoveries and inventions, numerous and splendid as they are, of which -he was the undisputed author. It is by following his reasonings, and by -pursuing the train of his thoughts, in his own elegant, though somewhat -diffuse exposition of them, that we become acquainted with the fertility -of his genius--with the sagacity, penetration, and comprehensiveness of -his mind. The service which he rendered to real knowledge is to be -estimated, not only from the truths which he discovered, but from the -errors which he detected--not merely from the sound principles which he -established, but from the pernicious idols which he overthrew. The -dialogues on the system are written with such singular felicity, that -one reads them at the present day, when the truths contained in them are -known and admitted, with all the delight of novelty, and feels one's -self carried back to the period when the telescope was first directed to -the heavens, and when the earth's motion, with all its train of -consequences, was proved for the first time."[94] - -The first Dialogue is opened by an attack upon the arguments by which -Aristotle pretended to determine _à priori_ the necessary motions -belonging to different parts of the world, and on his favourite -principle that particular motions belong naturally to particular -substances. Salviati (representing Galileo) then objects to the -Aristotelian distinctions between the corruptible elements and -incorruptible skies, instancing among other things the solar spots and -newly appearing stars, as arguments that the other heavenly bodies may -probably be subjected to changes similar to those which are continually -occurring on the earth, and that it is the great distance alone which -prevents their being observed. After a long discussion on this point, -Sagredo exclaims, "I see into the heart of Simplicio, and perceive that -he is much moved by the force of these too conclusive arguments; but -methinks I hear him say--'Oh, to whom must we betake ourselves to settle -our disputes if Aristotle be removed from the chair? What other author -have we to follow in our schools, our studies, and academies? What -philosopher has written on all the parts of Natural Philosophy, and so -methodically as not to have overlooked a single conclusion? Must we then -desolate this fabric, by which so many travellers have been sheltered? -Must we destroy this asylum, this Prytaneum wherein so many students -have found a convenient resting-place, where without being exposed to -the injuries of the weather, one may acquire an intimate knowledge of -nature, merely by turning over a few leaves? Shall we level this -bulwark, behind which we are safe from every hostile attack?' I pity him -no less than I do one who at great expense of time and treasure, and -with the labour of hundreds, has built up a very noble palace; and then, -because of insecure foundations, sees it ready to fall--unable to bear -that those walls be stripped that are adorned with so many beautiful -pictures, or to suffer those columns to fall that uphold the stately -galleries, or to see ruined the gilded roofs, the chimney-pieces, the -friezes, and marble cornices erected at so much cost, he goes about it -with girders and props, with shores and buttresses, to hinder its -destruction." - -Salviati proceeds to point out the many points of similarity between the -earth and moon, and among others which we have already mentioned, the -following remark deserves especial notice:-- - -"Just as from the mutual and universal tendency of the parts of the -earth to form a whole, it follows that they all meet together with equal -inclination, and that they may unite as closely as possible, assume the -spherical form; why ought we not to believe that the moon, the sun, and -other mundane bodies are also of a round figure, from no other reason -than from a common instinct and natural concourse of all their component -parts; of which if by accident any one should be violently separated -from its whole, is it not reasonable to believe that spontaneously, and -of its natural instinct, it would return? It may be added that if any -centre of the universe may be assigned, to which the whole terrene globe -if thence removed would seek to return, we shall find most probable that -the sun is placed in it, as by the sequel you shall understand." - -Many who are but superficially acquainted with the History of Astronomy, -are apt to suppose that Newton's great merit was in his being the first -to suppose an attractive force existing in and between the different -bodies composing the solar system. This idea is very erroneous; Newton's -discovery consisted in conceiving and proving the identity of the force -with which a stone falls, and that by which the moon falls, towards the -earth (on an assumption that this force becomes weaker in a certain -proportion as the distance increases at which it operates), and in -generalizing this idea, in applying it to all the visible creation, and -tracing the principle of universal gravitation with the assistance of a -most refined and beautiful geometry into many of its most remote -consequences. But the general notion of an attractive force between the -sun, moon, and planets, was very commonly entertained before Newton was -born, and may be traced back to Kepler, who was probably the first -modern philosopher who suggested it. The following extraordinary -passages from his "Astronomy" will shew the nature of his conceptions on -this subject:-- - -"The true doctrine of gravity is founded on these axioms: every -corporeal substance, so far forth as it is corporeal, has a natural -fitness for resting in every place where it may be situated by itself -beyond the sphere of influence of its cognate body. Gravity is a mutual -affection between cognate bodies towards union or conjunction (similar -in kind to the magnetic virtue), so that the earth attracts a stone much -rather than the stone seeks the earth. Heavy bodies (if in the first -place we put the earth in the centre of the world) are not carried to -the centre of the world in its quality of centre of the world, but as to -the centre of a cognate round body, namely the earth. So that -wheresoever the earth may be placed or whithersoever it may be carried -by its animal faculty, heavy bodies will always be carried towards it. -If the earth were not round heavy bodies would not tend from every side -in a straight line towards the centre of the earth, but to different -points from different sides. If two stones were placed in any part of -the world near each other and beyond the sphere of influence of a third -cognate body, these stones, like two magnetic needles, would come -together in the intermediate point, each approaching the other by a -space proportional to the comparative mass of the other. If the moon -and earth were not retained in their orbits by their animal force or -some other equivalent, the earth would mount to the moon by a -fifty-fourth part of their distance, and the moon fall towards the earth -through the other fifty-three parts, and would there meet, assuming -however that the substance of both is of the same density. If the earth -should cease to attract its waters to itself, all the waters of the sea -would be raised, and would flow to the body of the moon."[95] - -He also conjectured that the irregularities in the moon's motion were -caused by the joint action of the sun and earth, and recognized the -mutual action of the sun and planets, when he declared the mass and -density of the sun to be so great that the united attraction of the -other planets cannot remove it from its place. Among these bold and -brilliant ideas, his temperament led him to introduce others which show -how unsafe it was to follow his guidance, and which account for, if they -do not altogether justify, the sarcastic remark of Ross, that "Kepler's -opinion that the planets are moved round by the sunne, and that this is -done by sending forth a magnetic virtue, and that the sun-beames are -like the teethe of a wheele taking hold of the planets, are senslesse -crotchets fitter for a wheeler or a miller than a philosopher."[96] -Roberval took up Kepler's notions, especially in the tract which he -falsely attributed to Aristarchus, and it is much to be regretted that -Roberval should deserve credit for anything connected with that impudent -fraud. The principle of universal gravitation, though not the varying -proportion, is distinctly assumed in it, as the following passages will -sufficiently prove: "In every single particle of the earth, and the -terrestrial elements, is a certain property or accident which we suppose -common to the whole system of the world, by virtue of which all its -parts are forced together, and reciprocally attract each other; and this -property is found in a greater or less degree in the different -particles, according to their density. If the earth be considered by -itself, its centres of magnitude and virtue, or gravity, as we usually -call it, will coincide, to which all its parts tend in a straight line, -as well by their own exertion or gravity, as by the reciprocal -attraction of all the rest." In a subsequent chapter, Roberval repeats -these passages nearly in the same words, applying them to the whole -solar system, adding, that "the force of this attraction is not to be -considered as residing in the centre itself, as some ignorant people -think, but in the whole system whose parts are equally disposed round -the centre."[97] This very curious work was reprinted in the third -volume of the _Reflexiones Physico-Mathematicæ_ of Mersenne, from whom -Roberval pretended to have received the Arabic manuscript, and who is -thus irretrievably implicated in the forgery.[98] The last remark, -denying the attractive force to be due to any property of the central -point, seems aimed at Aristotle, who, in a no less curious passage, -maintaining exactly the opposite opinion, says, "Hence, we may better -understand what the ancients have related, that like things are wont to -have a tendency to each other. For this is not absolutely true; for if -the earth were to be removed to the place now occupied by the moon, no -part of the earth would then have a tendency towards that place, but -would still fall towards the point which the earth's centre now -occupies."[99] Mersenne considered the consequences of the attractive -force of each particle of matter so far as to remark, that if a body -were supposed to fall towards the centre of the earth, it would be -retarded by the attraction of the part through which it had already -fallen.[100] Galileo had not altogether neglected to speculate on such a -supposition, as is plain from the following extract. It is taken from a -letter to Carcaville, dated from Arcetri, in 1637. "I will say farther, -that I have not absolutely and clearly satisfied myself that a heavy -body would arrive sooner at the centre of the earth, if it began to fall -from the distance only of a single yard, than another which should start -from the distance of a thousand miles. I do not affirm this, but I offer -it as a paradox."[101] - -It is very difficult to offer any satisfactory comment upon this -passage; it may be sufficient to observe that this paradoxical result -was afterwards deduced by Newton, as one of the consequences of the -general law with which all nature is pervaded, but with which there is -no reason to believe that Galileo had any acquaintance; indeed the idea -is fully negatived by other passages in this same letter. This is one of -the many instances from which we may learn to be cautious how we invest -detached passages of the earlier mathematicians with a meaning which in -many cases their authors did not contemplate. The progressive -development of these ideas in the hands of Wallis, Huyghens, Hook, Wren, -and Newton, would lead us too far from our principal subject. There is -another passage in the third dialogue connected with this subject, which -it may be as well to notice in this place. "The parts of the earth have -such a propensity to its centre, that when it changes its place, -although they may be very distant from the globe at the time of the -change, yet must they follow. An example similar to this is the -perpetual sequence of the Medicean stars, although always separated from -Jupiter. The same may be said of the moon, obliged to follow the earth. -And this may serve for those simple ones who have difficulty in -comprehending how these two globes, not being chained together, nor -strung upon a pole, mutually follow each other, so that on the -acceleration or retardation of the one, the other also moves quicker or -slower." - -The second Dialogue is appropriated chiefly to the discussion of the -diurnal motion of the earth; and the principal arguments urged by -Aristotle, Ptolemy, and others, are successively brought forward and -confuted. The opposers of the earth's diurnal motion maintained, that if -it were turning round, a stone dropped from the top of a tower would not -fall at its foot; but, by the rotation of the earth to the eastward -carrying away the tower with it, would be left at a great distance to -the westward; it was common to compare this effect to a stone dropped -from the mast-head of a ship, and without any regard to truth it was -boldly asserted that this would fall considerably nearer the stern than -the foot of the mast, if the ship were in rapid motion. The same -argument was presented in a variety of forms,--such as that a -cannon-ball shot perpendicularly upwards would not fall at the same -spot; that if fired to the eastward it would fly farther than to the -westward; that a mark to the east or west would never be hit, because of -the rising or sinking of the horizon during the flight of the ball; that -ladies' ringlets would all stand out to the westward,[102] with other -conceits of the like nature: to which the general reply is given, that -in all these cases the stone, or ball, or other body, participates -equally in the motion of the earth, which, therefore, so far as regards -the relative motion of its parts, may be disregarded. The manner in -which this is illustrated, appears in the following extract from the -dialogue:--"_Sagredo._ If the nib of a writing pen which was in the ship -during my voyage direct from Venice to Alexandria, had had the power of -leaving a visible mark of all its path, what trace, what mark, what line -would it have left?--_Simplicio._ It would have left a line stretched -out thither from Venice not perfectly straight, or to speak more -correctly, not perfectly extended in an exact circular arc, but here and -there more and less curved accordingly as the vessel had pitched more or -less; but this variation in some places of one or two yards to the right -or left, or up or down in a length of many hundred miles, would have -occasioned but slight alteration in the whole course of the line, so -that it would have been hardly sensible, and without any great error we -may speak of it as a perfectly circular arc.--_Sagred._ So that the true -and most exact motion of the point of the pen would also have been a -perfect arc of a circle if the motion of the vessel, abstracting from -the fluctuations of the waves, had been steady and gentle; and if I had -held this pen constantly in my hand, and had merely moved it an inch or -two one way or the other, what alteration would that have made in the -true and principal motion?--_Simpl._ Less than that which would be -occasioned in a line a thousand yards long, by varying here and there -from perfect straightness by the quantity of a flea's eye.--_Sagred._ If -then a painter on our quitting the port had begun to draw with this pen -on paper, and had continued his drawing till we got to Alexandria, he -would have been able by its motion, to produce an accurate -representation of many objects perfectly shadowed, and filled up on all -sides with landscapes, buildings, and animals, although all the true, -real, and essential motion of the point of his pen would have been no -other but a very long and very simple line; and as to the peculiar work -of the painter, he would have drawn it exactly the same if the ship had -stood still. Therefore, of the very protracted motion of the pen, there -remain no other traces than those marks drawn upon the paper, the reason -of this being that the great motion from Venice to Alexandria was common -to the paper, the pen, and everything that was in the ship; but the -trifling motion forwards and backwards, to the right and left, -communicated by the painter's fingers to the pen, and not to the paper, -from being peculiar to the pen, left its mark upon the paper, which as -to this motion was immoveable. Thus it is likewise true that in the -supposition of the earth's rotation, the motion of a falling stone is -really a long track of many hundreds and thousands of yards; and if it -could have delineated its course in the calm air, or on any other -surface, it would have left behind it a very long transversal line; but -that part of all this motion which is common to the stone, the tower, -and ourselves, is imperceptible by us and the same as if not existing, -and only that part remains to be observed of which neither we nor the -tower partake, which in short is the fall of the stone along the tower." - -The mechanical doctrines introduced into this second dialogue will be -noticed on another occasion; we shall pass on to other extracts, -illustrative of the general character of Galileo's reasoning:-- -"_Salviati._ I did not say that the earth has no principle, either -internal or external, of its motion of rotation, but I do say that I -know not which of the two it has, and that my ignorance has no power to -take its motion away; but if this author knows by what principle other -mundane bodies, of the motion of which we are certain, are turned round, -I say that what moves the Earth is something like that by which Mars and -Jupiter, and, as he believes, the starry sphere, are moved round; and if -he will satisfy me as to the cause of their motion, I bind myself to be -able to tell him what moves the earth. Nay more; I undertake to do the -same if he can teach me what it is which moves the parts of the earth -downwards.--_Simpl._ The cause of this effect is notorious, and every -one knows that it is Gravity.--_Salv._ You are out, Master Simplicio; -you should say that every one knows that it is called Gravity; but I do -not ask you the name but the nature of the thing, of which nature you do -not know one tittle more than you know of the nature of the moving cause -of the rotation of the stars, except it be the name which has been given -to the one, and made familiar and domestic, by the frequent experience -we have of it many thousand times in a day; but of the principle or -virtue by which a stone falls to the ground, we really know no more than -we know of the principle which carries it upwards when thrown into the -air, or which carries the moon round its orbit, except, as I have said, -the name of gravity which we have peculiarly and exclusively assigned to -it; whereas we speak of the other with a more generic term, and talk of -the virtue impressed, and call it either an assisting or an informing -intelligence, and are content to say that Nature is the cause of an -infinite number of other motions." - -Simplicio is made to quote a passage from Scheiner's book of Conclusions -against Copernicus, to the following effect:--"'If the whole earth and -water were annihilated, no hail or rain would fall from the clouds, but -would only be naturally carried round in a circle, nor would any fire or -fiery thing ascend, since, according to the not improbable opinion of -these others, there is no fire in the upper regions.'--_Salv._ The -foresight of this philosopher is most admirable and praiseworthy, for he -is not content with providing for things that might happen during the -common course of nature, but persists in shewing his care for the -consequences of what he very well knows will never come to pass. -Nevertheless, for the sake of hearing some of his notable conceits, I -will grant that if the earth and water were annihilated there would be -no more hail or rain, nor would fiery matter ascend any more, but would -continue a motion of revolution. What is to follow? What conclusion is -the philosopher going to draw?--_Simpl._ This objection is in the very -next words--'Which nevertheless (says he) is contrary to experience and -reason.'--_Salv._ Now I must yield: since he has so great an advantage -over me as experience, with which I am quite unprovided. For hitherto I -have never happened to see the terrestrial earth and water annihilated, -so as to be able to observe what the hail and fire did in the confusion. -But does he tell us for our information at least what they did?--_Simp._ -No, he does not say any thing more.--_Salv._ I would give something to -have a word or two with this person, to ask him whether, when this globe -vanished, it also carried away the common centre of gravity, as I fancy -it did, in which case I take it that the hail and water would remain -stupid and confounded amongst the clouds, without knowing what to do -with themselves.... And lastly, that I may give this philosopher a less -equivocal answer, I tell him that I know as much of what would follow -after the annihilation of the terrestrial globe, as he could have known -what was about to happen in and about it, before it was created." - -Great part of the third Dialogue is taken up with discussions on the -parallax of the new stars of 1572 and 1604, in which Delambre notices -that Galileo does not employ logarithms in his calculations, although -their use had been known since Napier discovered them in 1616: the -dialogue then turns to the annual motion "first taken from the Sun and -conferred upon the Earth by Aristarchus Samius, and afterwards by -Copernicus." Salviati speaks of his contemporary philosophers with great -contempt--"If you had ever been worn out as I have been many and many a -time with hearing what sort of stuff is sufficient to make the obstinate -vulgar unpersuadable, I do not say to agree with, but even to listen to -these novelties, I believe your wonder at finding so few followers of -these opinions would greatly fall off. But little regard in my judgment -is to be had of those understandings who are convinced and immoveably -persuaded of the fixedness of the earth, by seeing that they are not -able to breakfast this morning at Constantinople, and sup in the evening -in Japan, and who feel satisfied that the earth, so heavy as it is, -cannot climb up above the sun, and then come tumbling in a breakneck -fashion down again!"[103] This remark serves to introduce several -specious arguments against the annual motion of the earth, which are -successively confuted, and it is shewn how readily the apparent stations -and retrogradations of the planets are accounted for on this -supposition. - -The following is one of the frequently recurring passages in which -Galileo, whilst arguing in favour of the enormous distances at which the -theory of Copernicus necessarily placed the fixed stars, inveighs -against the arrogance with which men pretend to judge of matters removed -above their comprehension. "_Simpl._ All this is very well, and it is -not to be denied that the heavens may surpass in bigness the capacity of -our imaginations, as also that God might have created it yet a thousand -times larger than it really is, but we ought not to admit anything to be -created in vain, and useless in the universe. Now whilst we see this -beautiful arrangement of the planets, disposed round the earth at -distances proportioned to the effects they are to produce on us for our -benefit, to what purpose should a vast vacancy be afterwards interposed -between the orbit of Saturn and the starry spheres, containing not a -single star, and altogether useless and unprofitable? to what end? for -whose use and advantage?--_Salv._ Methinks we arrogate too much to -ourselves, Simplicio, when we will have it that the care of us alone is -the adequate and sufficient work and bound, beyond which the divine -wisdom and power does and disposes of nothing. I feel confident that -nothing is omitted by the Divine Providence of what concerns the -government of human affairs; but that there may not be other things in -the universe dependant upon His supreme wisdom, I cannot for myself, by -what my reason holds out to me, bring myself to believe. So that when I -am told of the uselessness of an immense space interposed between the -orbits of the planets and the fixed stars, empty and valueless, I reply -that there is temerity in attempting by feeble reason to judge the works -of God, and in calling vain and superfluous every part of the universe -which is of no use to us.--_Sagr._ Say rather, and I believe you would -say better, that we have no means of knowing what is of use to us; and I -hold it to be one of the greatest pieces of arrogance and folly that can -be in this world to say, because I know not of what use Jupiter or -Saturn are to me, that therefore these planets are superfluous; nay -more, that there are no such things in nature. To understand what effect -is worked upon us by this or that heavenly body (since you will have it -that all their use must have a reference to us), it would be necessary -to remove it for a while, and then the effect which I find no longer -produced in me, I may say that it depended upon that star. Besides, who -will dare say that the space which they call too vast and useless -between Saturn and the fixed stars is void of other bodies belonging to -the universe. Must it be so because we do not see them: then I suppose -the four Medicean planets, and the companions of Saturn, came into the -heavens when we first began to see them, and not before! and, by the -same rule, the other innumerable fixed stars did not exist before men -saw them. The nebulæ were till lately only white flakes, till with the -telescope we have made of them constellations of bright and beautiful -stars. Oh presumptuous! rather, Oh rash ignorance of man!" - -After a discussion on Gilbert's Theory of Terrestrial Magnetism, -introduced by the parallelism of the earth's axis, and of which Galileo -praises very highly both the method and results, the dialogue proceeds -as follows:--"_Simpl._ It appears to me that Sig. Salviati, with a fine -circumlocution, has so clearly explained the cause of these effects, -that any common understanding, even though unacquainted with science, -may comprehend it: but we, confining ourselves to the terms of art, -reduce the cause of these and other similar natural phenomena to -sympathy, which is a certain agreement and mutual appetency arising -between things which have the same qualities, just as, on the other -hand, that disagreement and aversion, with which other things naturally -repel and abhor each other, we style antipathy.--_Sagr._ And thus with -these two words they are able to give a reason for the great number of -effects and accidents which we see, not without admiration, to be -produced in Nature. But it strikes me that this mode of philosophising -has a great sympathy with the style in which one of my friends used to -paint: on one part of the canvas he would write with chalk--there I will -have a fountain, with Diana and her nymphs; here some harriers; in this -corner I will have a huntsman, with a stag's head; the rest may be a -landscape of wood and mountain; and what remains to be done may be put -in by the colourman: and thus he flattered himself that he had painted -the story of Actæon, having contributed nothing to it beyond the names." - -The fourth Dialogue is devoted entirely to an examination of the tides, -and is a development and extension of the treatise already mentioned to -have been sent to the Archduke Leopold, in 1618.[104] Galileo was -uncommonly partial to his theory of the tides, from which he thought to -derive a direct proof of the earth's motion in her orbit; and although -his theory was erroneous, it required a farther advance in the science -of motion than had been attained even at a much later period to point -out the insufficiency of it. It is well known that the problem of -explaining the cause of this alternate motion of the waters had been -considered from the earliest ages one of the most difficult that could -be proposed, and the solutions with which different inquirers were -obliged to rest contented, shew that it long deserved the name given to -it, of "the grave of human curiosity."[105] Riccioli has enumerated -several of the opinions which in turn had their favourers and -supporters. One party supposed the rise of the waters to be occasioned -by the influx of rivers into the sea; others compared the earth to a -large animal, of which the tides indicated the respiration; a third -theory supposed the existence of subterraneous fires, by which the sea -was periodically made to boil; others attributed the cause of a similar -change of temperature to the sun and moon. - -There is an unfounded legend, that Aristotle drowned himself in despair -of being able to invent a plausible explanation of the extraordinary -tides in the Euripus. His curiosity on the subject does not appear to -have been so acute (judging from his writings) as this story would -imply. In one of his books he merely mentions a rumour, that there are -great elevations or swellings of the seas, which recur periodically, -according to the course of the moon. Lalande, in the fourth volume of -his Astronomy, has given an interesting account of the opinion of the -connection of the tides with the moon's motion. Pytheas of Marseilles, a -contemporary of Aristotle, was the first who has been recorded as -observing, that the full tides occur at full moon, and the ebbs at new -moon.[106] This is not quite correctly stated; for the tide of new moon -is known to be still higher than the rise at the full, but it is likely -enough, that the seeming inaccuracy should be attributed, not to -Pytheas, but to his biographer Plutarch, who, in many instances, -appears to have viewed the opinions of the old philosophers through the -mist of his own prejudices and imperfect information. The fact is, that, -on the same day when the tide rises highest, it also ebbs lowest; and -Pytheas, who, according to Pliny, had recorded a tide in Britain of -eighty cubits, could not have been ignorant of this. Posidonius, as -quoted by Strabo, maintained the existence of three periods of the tide, -daily, monthly, and annual, "in sympathy with the moon."[107] Pliny, in -his vast collection of natural observations, not unaptly styled the -Encyclopædia of the Antients, has the following curious passages:--"The -flow and ebb of the tide is very wonderful; it happens in a variety of -ways, but the cause is in the sun and moon."[108] He then very -accurately describes the course of the tide during a revolution of the -moon, and adds: "The flow takes place every day at a different hour; -being waited on by the star, which rises every day in a different place -from that of the day before, and with greedy draught drags the seas with -it."[109] "When the moon is in the north, and further removed from the -earth, the tides are more gentle than when digressing to the south, she -exerts her force with a closer effort."[110] - -The College of Jesuits at Coimbra appears to deserve the credit of first -clearly pointing out the true relation between the tides and the moon, -which was also maintained a few years later by Antonio de Dominis and -Kepler. In the Society's commentary on Aristotle's book on Meteors, -after refuting the notion that the tides are caused by the light of the -sun and moon, they say, "It appears more probable to us, without any -rarefaction, of which there appears no need or indication, that the moon -raises the waters by some inherent power of impulsion, in the same -manner as a magnet moves iron; and according to its different aspects -and approaches to the sea, and the obtuse or acute angles of its -bearing, at one time to attract and raise the waters along the shore, -and then again to leave them to sink down by their own weight, and to -gather into a lower level."[111] The theory of Universal Gravitation -seems here within the grasp of these philosophers, but unfortunately it -did not occur to them that possibly the same attraction might be exerted -on the earth as well as the water, and that the tide was merely an -effect of the diminution of force, owing to the increase of distance, -with which the centre of the earth is attracted, as compared with that -exerted on its surface. This idea, so happily seized afterwards by -Newton, might at once have furnished them with a satisfactory -explanation of the tide, which is observed on the opposite side of the -earth as well as immediately under the moon. They might have seen that -in the latter case the centre of the earth is pulled away from the -water, just as in the former the water is pulled away from the centre of -the earth, the sensible effect to us being in both cases precisely the -same. For want of this generalization, the inferior tide as it is called -presented a formidable obstacle to this theory, and the most plausible -explanation that was given was, that this magnetic virtue radiated out -from the moon was reflected by the solid heavens, and concentrated again -as in a focus on the opposite side of the earth. The majority of modern -astronomers who did not admit the existence of any solid matter fit for -producing the effect assigned to it, found a reasonable difficulty in -acquiescing in this explanation. Galileo, who mentions the Archbishop of -Spalatro's book, treated the theory of attraction by the moon as absurd. -"This motion of the seas is local and sensible, made in an immense mass -of water, and cannot be brought to obey light, and warmth, and -predominancy of occult qualities, and such like vain fancies; all which -are so far from being the cause of the tide, that on the contrary the -tide is the cause of them, inasmuch as it gives rise to these ideas in -brains which are more apt for talkativeness and ostentation, than for -speculation and inquiry into the secrets of Nature; who, rather than see -themselves driven to pronounce these wise, ingenuous, and modest -words--_I do not know_,--will blurt out from their tongues and pens all -sorts of extravagancies." - -Galileo's own theory is introduced by the following illustration, which -indeed probably suggested it, as he was in the habit of suffering no -natural phenomena, however trivial in appearance, to escape him. He felt -the advantage of this custom in being furnished on all occasions with a -stock of homely illustrations, to which the daily experience of his -hearers readily assented, and which he could shew to be identical in -principle with the phenomena under discussion. That he was mistaken in -applying his observations in the present instance cannot be urged -against the incalculable value of such a habit. - -"We may explain and render sensible these effects by the example of one -of those barks which come continually from Lizza Fusina, with fresh -water for the use of the city of Venice. Let us suppose one of these -barks to come thence with moderate velocity along the canal, carrying -gently the water with which it is filled, and then, either by touching -the bottom, or from some other hindrance which is opposed to it, let it -be notably retarded; the water will not on that account lose like the -bark the impetus it has already acquired, but will forthwith run on -towards the prow where it will sensibly rise, and be depressed at the -stern. If on the contrary the said vessel in the middle of its steady -course shall receive a new and sensible increase of velocity, the -contained water before giving into it will persevere for some time in -its slowness, and will be left behind that is to say towards the stern -where consequently it will rise, and sink at the head.--Now, my masters, -that which the vessel does in respect of the water contained in it, and -that which the water does in respect of the vessel containing it, is the -same to a hair as what the Mediterranean vase does in respect of the -water which it contains, and that the waters do in respect of the -Mediterranean vase which contains them. We have now only to demonstrate -how, and in what manner it is true that the Mediterranean, and all other -gulfs, and in short all the parts of the earth move with a motion -sensibly not uniform, although no motion results thence to the whole -globe which is not perfectly uniform and regular." - -This unequable motion is derived from a combination of the earth's -motion on her axis, and in her orbit, the consequence of which is that a -point turned from the sun is carried in the same direction by the annual -and diurnal velocities, whereas a point on the opposite side of the -globe is carried in opposite directions by the annual and diurnal -motions, so that in every twenty-four hours the absolute motion through -space of every point in the earth completes a cycle of varying -swiftness. Those readers who are unacquainted with the mathematical -theory of motion must be satisfied with the assurance that this specious -representation is fallacious, and that the oscillation of the water does -not in the least result from the causes here assigned to it: the -reasoning necessary to prove this is not elementary enough to be -introduced here with propriety. - -Besides the principal daily oscillation of the water, there is a monthly -inequality in the rise and fall, of which the extremes are called the -spring and neap tides: the manner in which Galileo attempted to bring -his theory to bear upon these phenomena is exceedingly curious. - -"It is a natural and necessary truth, that if a body be made to revolve, -the time of revolution will be greater in a greater circle than in a -less: this is universally allowed, and fully confirmed by experiments, -such for instance as these:--In wheel clocks, especially in large ones, -to regulate the going, the workmen fit up a bar capable of revolving -horizontally, and fasten two leaden weights to the ends of it; and if -the clock goes too slow, by merely approaching these weights somewhat -towards the centre of the bar, they make its vibrations more frequent, -at which time they are moving in smaller circles than before.[112]--Or, -if you fasten a weight to a cord which you pass round a pulley in the -ceiling, and whilst the weight is vibrating draw in the cord towards -you, the vibrations will become sensibly accelerated as the length of -the string diminishes. We may observe the same rule to hold among the -celestial motions of the planets, of which we have a ready instance in -the Medicean planets, which revolve in such short periods round Jupiter. -We may therefore safely conclude, that if the moon for instance shall -continue to be forced round by the same moving power, and were to move -in a smaller circle, it would shorten the time of its revolution. Now -this very thing happens in fact to the moon, which I have just advanced -on a supposition. Let us call to mind that we have already concluded -with Copernicus, that it is impossible to separate the moon from the -earth, round which without doubt it moves in a month: we must also -remember that the globe of the earth, accompanied always by the moon, -revolves in the great circle round the sun in a year, in which time the -moon revolves round the earth about thirteen times, whence it follows -that the moon is sometimes near the sun, that is to say between the -earth and sun, sometimes far from it, when she is on the outside of the -earth. Now if it be true that the power which moves the earth and the -moon round the sun remains of the same efficacy, and if it be true that -the same moveable, acted on by the same force, passes over similar arcs -of circles in a time which is least when the circle is smallest, we are -forced to the conclusion that at new moon, when in conjunction with the -sun, the moon passes over greater arcs of the orbit round the sun, than -when in opposition at full moon; and this inequality of the moon will be -shared by the earth also. So that exactly the same thing happens as in -the balance of the clocks; for the moon here represents the leaden -weight, which at one time is fixed at a greater distance from the centre -to make the vibrations slower, and at another time nearer to accelerate -them." - -Wallis adopted and improved this theory in a paper which he inserted in -the Philosophical Transactions for 1666, in which he declares, that the -circular motion round the sun should be considered as taking place at a -point which is the centre of gravity of the earth and moon. "To the -first objection, that it appears not how two bodies that have no tie can -have one common centre of gravity, I shall only answer, that it is -harder to show how they have it, than that they have it."[113] As Wallis -was perfectly competent from the time at which he lived, and his -knowledge of the farthest advances of science in his time, to appreciate -the value of Galileo's writings, we shall conclude this chapter with the -judgment that he has passed upon them in the same paper. "Since Galileo, -and after him Torricelli and others have applied mechanical principles -to the solving of philosophical difficulties, natural philosophy is well -known to have been rendered more intelligible, and to have made a much -greater progress in less than a hundred years than before for many -ages." - - -FOOTNOTES: - -[93] See page 56. - -[94] Playfair's Dissertation, Supp. Encyc. Brit. - -[95] Astronomia Nova. Pragæ. 1609. - -[96] The new Planet no Planet, or the Earth no wandering Star, except in -the wandering heads of Galileans. London, 1646. - -[97] Aristarchi Samii de Mundi Systemate. Parisiis 1644. - -[98] See page 12. - -[99] De Coelo, lib. iv. cap. 3. - -[100] Reflexiones Physico-Mathematicæ, Parisiis, 1647. - -[101] Venturi. - -[102] Riccioli. - -[103] The notions commonly entertained of 'up' and 'down,' as connected -with the observer's own situation, had long been a stumbling-block in -the way of the new doctrines. When Columbus held out the certainty of -arriving in India by sailing to the westward on account of the earth's -roundness, it was gravely objected, that it might be well enough to sail -down to India, but that the chief difficulty would consist in climbing -up back again. - -[104] See page 50. - -[105] Riccioli Almag. Nov. - -[106] Plutarch, De placit. Philos. lib. iii. c. 17. - -[107] [sympatheôs tê selênê]. Geographiæ, lib. iii. - -[108] Historia Naturalis, lib. ii. c, 97. - -[109] Ut ancillante sidere, trahenteque secum avido haustu maria. - -[110] Eâdem Aquiloniâ, et à terris longius recedente, mitiores quam cum, -in Austros digressâ, propiore nisu vim suam exercet. - -[111] Commentarii Collegii Conimbricensis. Coloniæ, 1603. - -[112] See fig. 1. p. 96. - -[113] Phil. Trans., No. 16, August 1666. - - - - -CHAPTER XV. - - _Galileo at Arcetri--Becomes Blind--Moon's Libration--Publication of - the Dialogues on Motion._ - - -WE have already alluded to the imperfect state of the knowledge -possessed with regard to Galileo's domestic life and personal habits; -there is reason however to think that unpublished materials exist from -which these outlines might be in part filled up. Venturi informs us that -he had seen in the collection from which he derived a great part of the -substance of his Memoirs of Galileo, about one hundred and twenty -manuscript letters, dated between the years 1623 and 1633, addressed to -him by his daughter Maria, who with her sister had attached herself to -the convent of St. Matthew, close to Galileo's usual place of residence. -It is difficult not to think that much interesting information might be -obtained from these, with respect to Galileo's domestic character. The -very few published extracts confirm our favourable impressions of it, -and convey a pleasing idea of this his favourite daughter. Even when, in -her affectionate eagerness to soothe her father's wounded feelings at -the close of his imprisonment in Rome, she dwells with delight upon her -hopes of being allowed to relieve him, by taking on herself the -penitential recitations which formed a part of his sentence, the -prevalent feeling excited in every one by the perusal must surely be -sympathy with the filial tenderness which it is impossible to -misunderstand. - -The joy she had anticipated in again meeting her parent, and in -compensating to him by her attentive affection the insults of his -malignant enemies, was destined to be but of short duration. Almost in -the same month in which Galileo returned to Arcetri she was seized with -a fatal illness; and already in the beginning of April, 1634, we learn -her death from the fruitless condolence of his friends. He was deeply -and bitterly affected by this additional blow, which came upon him when -he was himself in a weak and declining state of health, and his answers -breathe a spirit of the most hopeless and gloomy despondency. - -In a letter written in April to Bocchineri, his son's father-in-law, he -says: "The hernia has returned worse than at first: my pulse is -intermitting, accompanied with a palpitation of the heart; an -immeasurable sadness and melancholy; an entire loss of appetite; I am -hateful to myself; and in short I feel that I am called incessantly by -my dear daughter. In this state, I do not think it advisable that -Vincenzo should set out on his journey, and leave me, when every hour -something may occur, which would make it expedient that he should be -here." In this extremity of ill health, Galileo requested leave to go to -Florence for the advantage of medical assistance; but far from obtaining -permission, it was intimated that any additional importunities would be -noticed by depriving him of the partial liberty he was then allowed to -enjoy. After several years confinement at Arcetri, during the whole of -which time he suffered from continual indisposition, the inquisitor -Fariano wrote to him in 1638, that the Pope permitted his removal to -Florence, for the purpose of recovering his health; requiring him at the -same time to present himself at the Office of the Inquisition, where he -would learn the conditions on which this favour had been granted. These -were that he should neither quit his house nor receive his friends -there; and so closely was the letter of these instructions adhered to, -that he was obliged to obtain a special permission to go out to attend -mass during Passion week. The strictness with which all personal -intercourse with his friends was interrupted, is manifest from the -result of the following letter from the Duke of Tuscany's secretary of -state to Nicolini, his ambassador at Rome. "Signor Galileo Galilei, from -his great age and the illnesses which afflict him, is in a condition -soon to go to another world; and although in this the eternal memory of -his fame and value is already secured, yet his Highness is greatly -desirous that the world should sustain as little loss as possible by his -death; that his labours may not perish, but for the public good may be -brought to that perfection which he will not be able to give them. He -has in his thoughts many things worthy of him, which he cannot be -prevailed on to communicate to any but Father Benedetto Castelli, in -whom he has entire confidence. His Highness wishes therefore that you -should see Castelli, and induce him to procure leave to come to Florence -for a few months for this purpose, which his Highness has very much at -heart; and if he obtains permission, as his Highness hopes, you will -furnish him with money and every thing else he may require for his -journey." Castelli, it will be remembered, was at this time salaried by -the court of Rome. Nicolini answered that Castelli had been himself to -the Pope to ask leave to go to Florence. Urban immediately intimated his -suspicions that his design was to see Galileo, and upon Castelli's -stating that certainly it would be impossible for him to refrain from -attempting to see him, he received permission to visit him in the -company of an officer of the Inquisition. At the end of some months -Galileo was remanded to Arcetri, which he never again quitted. - -In addition to his other infirmities, a disorder which some years before -had affected the sight of his right eye returned in 1636; in the course -of the ensuing year the other eye began to fail also, and in a few -months he became totally blind. It would be difficult to find any even -among those who are the most careless to make a proper use of the -invaluable blessing of sight, who could bear unmoved to be deprived of -it, but on Galileo the loss fell with peculiar and terrible severity; on -him who had boasted that he would never cease from using the senses -which God had given him, in declaring the glory of his works, and the -business of whose life had been the splendid fulfilment of that -undertaking. "The noblest eye is darkened," said Castelli, "which nature -ever made: an eye so privileged, and gifted with such rare qualities, -that it may with truth be said to have seen more than all of those who -are gone, and to have opened the eyes of all who are to come." His own -patience and resignation under this fatal calamity are truly wonderful; -and if occasionally a word of complaint escaped him, it was in the -chastened tone of the following expressions--"Alas! your dear friend and -servant Galileo has become totally and irreparably blind; so that this -heaven, this earth, this universe, which with wonderful observations I -had enlarged a hundred and thousand times beyond the belief of by-gone -ages, henceforward for me is shrunk into the narrow space which I myself -fill in it.--So it pleases God: it shall therefore please me also." -Hopes were at first entertained by Galileo's friends, that the -blindness was occasioned by cataracts, and that he might look forward to -relief from the operation of couching; but it very soon appeared that -the disorder was not in the humours of the eye, but in a cloudiness of -the cornea, the symptoms of which all external remedies failed to -alleviate. - -As long as the power was left him, he had indefatigably continued his -astronomical observations. Just before his sight began to decay, he had -observed a new phenomenon in the moon, which is now known by the name of -the moon's libration, the nature of which we will shortly explain. A -remarkable circumstance connected with the moon's motion is, that the -same side is always visible from the earth, showing that the moon turns -once on her own axis in exactly the time of her monthly revolution.[114] -But Galileo, who was by this time familiar with the whole of the moon's -visible surface, observed that the above-mentioned effect does not -accurately take place, but that a small part on either side comes -alternately forward into sight, and then again recedes, according to the -moon's various positions in the heavens. He was not long in detecting -one of the causes of this apparent libratory or rocking motion. It is -partly occasioned by our distance as spectators from the centre of the -earth, which is also the centre of the moon's motion. In consequence of -this, as the moon rises in the sky we get an additional view of the -lower half, and lose sight of a small part of the upper half which was -visible to us while we were looking down upon her when low in the -horizon. The other cause is not quite so simple, nor is it so certain -that Galileo adverted to it: it is however readily intelligible even to -those who are unacquainted with astronomy, if they will receive as a -fact that the monthly motion of the moon is not uniform, but that she -moves quicker at one time than another, whilst the motion of rotation on -her own axis, like that of the earth, is perfectly uniform. A very -little reflection will show that the observed phenomenon will -necessarily follow. If the moon did not turn on her axis, every side of -her would be successively presented, in the course of a month, towards -the earth; it is the motion of rotation which tends to carry the newly -discovered parts out of sight. - -Let us suppose the moon to be in that part of her orbit where she moves -with her average motion, and that she is moving towards the part where -she moves most quickly. If the motion in the orbit were to remain the -same all the way round, the motion of rotation would be just sufficient -at every point to bring round the same part of the moon directly in -front of the earth. But since, from the supposed point, the moon is -moving for some time round the earth with a motion continually growing -quicker, the motion of rotation is not sufficiently quick to carry out -of sight the entire part discovered by the motion of translation. We -therefore get a glimpse of a narrow strip on the side _from_ which the -moon is moving, which strip grows broader and broader, till she passes -the point where she moves most swiftly, and reaches the point of average -swiftness on the opposite side of her orbit. Her motion is now -continually growing slower, and therefore from this point the motion of -rotation is too swift, and carries too much out of sight, or in other -words, brings into sight a strip on the side _towards_ which the moon is -moving. This increases till she passes the point of least swiftness, and -arrives at the point from which we began to trace her course, and the -phenomena are repeated in the same order. - -This interesting observation closes the long list of Galileo's -discoveries in the heavens. After his abjuration, he ostensibly withdrew -himself in a great measure from his astronomical pursuits, and employed -himself till 1636 principally with his Dialogues on Motion, the last -work of consequence that he published. In that year he entered into -correspondence with the Elzevirs, through his friend Micanzio, on the -project of printing a complete edition of his writings. Among the -letters which Micanzio wrote on the subject is one intimating that he -had enjoyed the gratification, in his quality of Theologian to the -Republic of Venice, of refusing his sanction to a work written against -Galileo and Copernicus. The temper however in which this refusal was -announced, contrasts singularly with that of the Roman Inquisitors. "A -book was brought to me which a Veronese Capuchin has been writing, and -wished to print, denying the motion of the earth. I was inclined to let -it go, to make the world laugh, for the ignorant beast entitles every -one of the twelve arguments which compose his book, 'An irrefragable and -undeniable demonstration,' and then adduces nothing but such childish -trash as every man of sense has long discarded. For instance, this poor -animal understands so much geometry and mathematics, that he brings -forward as a demonstration, that if the earth could move, having nothing -to support it, it must necessarily fall. He ought to have added that -then we should catch all the quails. But when I saw that he speaks -indecently of you, and has had the impudence to put down an account of -what passed lately, saying that he is in possession of the whole of your -process and sentence, I desired the man who brought it to me to go and -be hanged. But you know the ingenuity of impertinence; I suspect he will -succeed elsewhere, because he is so enamoured of his absurdities, that -he believes them more firmly than his Bible." - -After Galileo's condemnation at Rome, he had been placed by the -Inquisition in the list of authors the whole of whose writings, '_edita -et edenda_,' were strictly forbidden. Micanzio could not even obtain -permission to reprint the Essay on Floating Bodies, in spite of his -protestations that it did not in any way relate to the Copernican -theory. This was the greatest stigma with which the Inquisition were in -the habit of branding obnoxious authors; and, in consequence of it, when -Galileo had completed his Dialogues on Motion, he found great difficulty -in contriving their publication, the nature of which may be learned from -the account which Pieroni sent to Galileo of his endeavours to print -them in Germany. He first took the manuscript to Vienna, but found that -every book printed there must receive the approbation of the Jesuits; -and Galileo's old antagonist, Scheiner, happening to be in that city, -Pieroni feared lest he should interfere to prevent the publication -altogether, if the knowledge of it should reach him. Through the -intervention of Cardinal Dietrichstein, he therefore got permission to -have it printed at Olmutz, and that it should be approved by a -Dominican, so as to keep the whole business a secret from Scheiner and -his party; but during this negociation the Cardinal suddenly died, and -Pieroni being besides dissatisfied with the Olmutz type, carried back -the manuscript to Vienna, from which he heard that Scheiner had gone -into Silesia. A new approbation was there procured, and the work was -just on the point of being sent to press, when the dreaded Scheiner -re-appeared in Vienna, on which Pieroni again thought it advisable to -suspend the impression till his departure. In the mean time his own duty -as a military architect in the Emperor's service carried him to Prague, -where Cardinal Harrach, on a former occasion, had offered him the use of -the newly-erected University press. But Harrach happened not to be at -Prague, and this plan like the rest became abortive. In the meantime -Galileo, wearied with these delays, had engaged with Louis Elzevir, who -undertook to print the Dialogues at Amsterdam. - -It is abundantly evident from Galileo's correspondence that this edition -was printed with his full concurrence, although, in order to obviate -further annoyance, he pretended that it was pirated from a manuscript -copy which he sent into France to the Comte de Noailles, to whom the -work is dedicated. The same dissimulation had been previously thought -necessary, on occasion of the Latin translation of "The Dialogues on the -System," by Bernegger, which Galileo expressly requested through his -friend Deodati, and of which he more than once privately signified his -approbation, presenting the translator with a valuable telescope, -although he publicly protested against its appearance. The story which -Bernegger introduced in his preface, tending to exculpate Galileo from -any share in the publication, is by his own confession a mere fiction. -Noailles had been ambassador at Rome, and, by his conduct there, well -deserved the compliment which Galileo paid him on the present occasion. - -As an introduction to the account of this work, which Galileo considered -the best he had ever produced, it will become necessary to premise a -slight sketch of the nature of the mechanical philosophy which he found -prevailing, nearly as it had been delivered by Aristotle, with the same -view with which we introduced specimens of the astronomical opinions -current when Galileo began to write on that subject: they serve to show -the nature and objects of the reasoning which he had to oppose; and, -without some exposition of them, the aim and value of many of his -arguments would be imperfectly understood and appreciated. - - -FOOTNOTES: - -[114] Frisi says that Galileo did not perceive this conclusion (Elogio -del Galileo); but see The Dial. on the System, Dial. 1. pp. 61, 62, 85. -Edit. 1744. Plutarch says, (De Placitis Philos. lib. ii. c. 28,) that -the Pythagoreans believed the moon to have inhabitants fifteen times as -large as men, and that their day is fifteen times as long as ours. It -seems probable, that the former of these opinions was engrafted on the -latter, which is true, and implies a perception of the fact in the text. - - - - -CHAPTER XVI. - - _State of the Science of Motion before Galileo._ - - -IT is generally difficult to trace any branch of human knowledge up to -its origin, and more especially when, as in the case of mechanics, it is -very closely connected with the immediate wants of mankind. Little has -been told to us when we are informed that so soon as a man might wish to -remove a heavy stone, "he would be led, by natural instinct, to slide -under it the end of some long instrument, and that the same instinct -would teach him either to raise the further end, or to press it -downwards, so as to turn round upon some support placed as near to the -stone as possible."[115] - -Montucla's history would have lost nothing in value, if, omitting "this -philosophical view of the birth of the art," he had contented himself -with his previous remark, that there can be little doubt that men were -familiar with the use of mechanical contrivances long before the idea -occurred of enumerating or describing them, or even of examining very -closely the nature and limits of the aid they are capable of affording. -The most careless observer indeed could scarcely overlook that the -weights heaved up with a lever, or rolled along a slope into their -intended places, reached them more slowly than those which the workmen -could lift directly in their hands; but it probably needed a much longer -time to enable them to see the exact relation which, in these and all -other machines, exists between the increase of the power to move, and -the decreasing swiftness of the thing moved. - -In the preface to Galileo's Treatise on Mechanical Science, published in -1592, he is at some pains to set in a clear light the real advantages -belonging to the use of machines, "which (says he) I have thought it -necessary to do, because, if I mistake not, I see almost all mechanics -deceiving themselves in the belief that, by the help of a machine, they -can raise a greater weight than they are able to lift by the exertion of -the same force without it.--Now if we take any determinate weight, and -any force, and any distance whatever, it is beyond doubt that we can -move the weight to that distance by means of that force; because even -although the force may be exceedingly small, if we divide the weight -into a number of fragments, each of which is not too much for our force, -and carry these pieces one by one, at length we shall have removed the -whole weight; nor can we reasonably say at the end of our work, that -this great weight has been moved and carried away by a force less than -itself, unless we add that the force has passed several times over the -space through which the whole weight has gone but once. From which it -appears that the velocity of the force (understanding by velocity the -space gone through in a given time) has been as many times greater than -that of the weight, as the weight is greater than the force: nor can we -on that account say that a great force is overcome by a small one, -contrary to nature: then only might we say that nature is overcome when -a small force moves a great weight as swiftly as itself, which we assert -to be absolutely impossible with any machine either already or hereafter -to be contrived. But since it may occasionally happen that we have but a -small force, and want to move a great weight without dividing it into -pieces, then we must have recourse to a machine by means of which we -shall remove the given weight, with the given force, through the -required space. But nevertheless the force as before will have to travel -over that very same space as many times repeated as the weight surpasses -its power, so that, at the end of our work, we shall find that we have -derived no other benefit from our machine than that we have carried away -the same weight altogether, which if divided into pieces we could have -carried without the machine, by the same force, through the same space, -in the same time. This is one of the advantages of a machine, because it -often happens that we have a lack of force but abundance of time, and -that we wish to move great weights all at once." - -This compensation of force and time has been fancifully personified by -saying that Nature cannot be cheated, and in scientific treatises on -mechanics, is called the "principle of virtual velocities," consisting -in the theorem that two weights will balance each other on any machine, -no matter how complicated or intricate the connecting contrivances may -be, when one weight bears to the other the same proportion that the -space through which the latter would be raised bears to that through -which the former would sink, in the first instant of their motion, if -the machine were stirred by a third force. The whole theory of machines -consists merely in generalizing and following out this principle into -its consequences; combined, when the machines are in a state of motion, -with another principle equally elementary, but to which our present -subject does not lead us to allude more particularly. - -The credit of making known the principle of virtual velocities is -universally given to Galileo; and so far deservedly, that he undoubtedly -perceived the importance of it, and by introducing it everywhere into -his writings succeeded in recommending it to others; so that five and -twenty years after his death, Borelli, who had been one of Galileo's -pupils, calls it "that mechanical principle with which everybody is so -familiar[116]," and from that time to the present it has continued to be -taught as an elementary truth in most systems of mechanics. But although -Galileo had the merit in this, as in so many other cases, of -familiarizing and reconciling the world to the reception of truth, there -are remarkable traces before his time of the employment of this same -principle, some of which have been strangely disregarded. Lagrange -asserts[117] that the ancients were entirely ignorant of the principle -of virtual velocities, although Galileo, to whom he refers it, -distinctly mentions that he himself found it in the writings of -Aristotle. Montucla quotes a passage from Aristotle's Physics, in which -the law is stated generally, but adds that he did not perceive its -immediate application to the lever, and other machines. The passage to -which Galileo alludes is in Aristotle's Mechanics, where, in discussing -the properties of the lever, he says expressly, "the same force will -raise a greater weight, in proportion as the force is applied at a -greater distance from the fulcrum, and the reason, as I have already -said, is because it describes a greater circle; and a weight which is -farther removed from the centre is made to move through a greater -space."[118] - -It is true, that in the last mentioned treatise, Aristotle has given -other reasons which belong to a very different kind of philosophy, and -which may lead us to doubt whether he fully saw the force of the one we -have just quoted. It appeared to him not wonderful that so many -mechanical paradoxes (as he called them) should be connected with -circular motion, since the circle itself seemed of so paradoxical a -nature. "For, in the first place, it is made up of an immoveable centre, -and a moveable radius, qualities which are contrary to each other. 2dly. -Its circumference is both convex and concave. 3dly. The motion by which -it is described is both forward and backward, for the describing radius -comes back to the place from which it started. 4thly. The radius is -_one_; but every point of it moves in describing the circle with a -different degree of swiftness." - -Perhaps Aristotle may have borrowed the idea of virtual velocities, -contrasting so strongly with his other physical notions, from some older -writer; possibly from Archytas, who, we are told, was the first to -reduce the science of mechanics to methodical order;[119] and who by the -testimony of his countrymen was gifted with extraordinary talents, -although none of his works have come down to us. The other principles -and maxims of Aristotle's mechanical philosophy, which we shall have -occasion to cite, are scattered through his books on Mechanics, on the -Heavens, and in his Physical Lectures, and will therefore follow rather -unconnectedly, though we have endeavoured to arrange them with as much -regularity as possible. - -After defining a body to be that which is divisible in every direction, -Aristotle proceeds to inquire how it happens that a body has only the -three dimensions of length, breadth, and thickness; and seems to think -he has given a reason in saying that, when we speak of two things, we do -not say "all," but "both," and three is the first number of which we say -"all."[120] When he comes to speak of motion, he says, "If motion is not -understood, we cannot but remain ignorant of Nature. Motion appears to -be of the nature of continuous quantities, and in continuous quantity -infinity first makes its appearance; so as to furnish some with a -definition who say that continuous quantity is that which is infinitely -divisible.--Moreover, unless there be time, space, and a vacuum, it is -impossible that there should be motion."[121]--Few propositions of -Aristotle's physical philosophy are more notorious than his assertion -that nature abhors a vacuum, on which account this last passage is the -more remarkable, as he certainly did not go so far as to deny the -existence of motion, and therefore asserts here the necessity of that of -which he afterwards attempts to show the absurdity.--"Motion is the -energy of what exists in power so far forth as so existing. It is that -act of a moveable which belongs to its power of moving."[122] After -struggling through such passages as the preceding we come at last to a -resting-place.--"It is difficult to understand what motion is."--When -the same question was once proposed to another Greek philosopher, he -walked away, saying, "I cannot tell you, but I will show you;" an answer -intrinsically worth more than all the subtleties of Aristotle, who was -not humble-minded enough to discover that he was tasking his genius -beyond the limits marked out for human comprehension. - -He labours in the same manner and with the same success to vary the idea -of space. He begins the next book with declaring, that "those who say -there is a vacuum assert the existence of space; for a vacuum is space, -in which there is no substance;" and after a long and tedious reasoning -concludes that, "not only what space is, but also whether there be such -a thing, cannot but be doubted."[123] Of time he is content to say -merely, that "it is clear that time is not motion, but that without -motion there would be no time;"[124] and there is perhaps little fault -to be found with this remark, understanding motion in the general sense -in which Aristotle here applies it, of every description of change. - -Proceeding after these remarks on the nature of motion in general to the -motion of bodies, we are told that "all local motion is either straight, -circular, or compounded of these two; for these two are the only simple -sorts of motion. Bodies are divided into simple and concrete; simple -bodies are those which have naturally a principle of motion, as fire and -earth, and their kinds. By simple motion is meant the motion of a simple -body."[125] By these expressions Aristotle did not mean that a simple -body cannot have what he calls a compound motion, but in that case he -called the motion violent or unnatural; this division of motion into -natural and violent runs through the whole of the mechanical philosophy -founded upon his principles. "Circular motion is the only one which can -be endless;"[126] the reason of which is given in another place: for -"that cannot be doing, which cannot be done; and therefore it cannot be -that a body should be moving towards a point (_i.e._ the end of an -infinite straight line) whither no motion is sufficient to bring -it."[127] Bacon seems to have had these passages in view when he -indulged in the reflections which we have quoted in page 14. "There are -four kinds of motion of one thing by another: Drawing, Pushing, -Carrying, Rolling. Of these, Carrying and Rolling may be referred to -Drawing and Pushing.[128]--The prime mover and the thing moved are -always in contact." - -The principle of the composition of motions is stated very plainly: -"when a moveable is urged in two directions with motions bearing an -indefinitely small ratio to each other, it moves necessarily in a -straight line, which is the diameter of the figure formed by drawing the -two lines of direction in that ratio;"[129] and adds, in a singularly -curious passage, "but when it is urged for any time with two motions -which have an indefinitely small ratio one to another, the motion cannot -be straight, so that a body describes a curve, when it is urged by two -motions bearing an indefinitely small ratio one to another, and lasting -an indefinitely small time."[130] - -He seemed on the point of discovering some of the real laws of motion, -when he was led to ask--"Why are bodies in motion more easily moved than -those which are at rest?--And why does the motion cease of things cast -into the air? Is it that the force has ceased which sent them forth, or -is there a struggle against the motion, or is it through the disposition -to fall, does it become stronger than the projectile force, or is it -foolish to entertain doubts on this question, when the body has quitted -the principle of its motion?" A commentator at the close of the -sixteenth century says on this passage: "They fall because every thing -recurs to its nature; for if you throw a stone a thousand times into the -air, it will never accustom itself to move upwards." Perhaps we shall -now find it difficult not to smile at the idea we may form of this -luckless experimentalist, teaching stones to fly; yet it may be useful -to remember that it is only because we have already collected an opinion -from the results of a vast number of observations in the daily -experience of life, that our ridicule would not be altogether misplaced, -and that we are totally unable to determine by any kind of reasoning, -unaccompanied by experiment, whether a stone thrown into the air would -fall again to the earth, or move for ever upwards, or in any other -conceivable manner and direction. - -The opinion which Aristotle held, that motion must be caused by -something in contact with the body moved, led him to his famous theory -that falling bodies are accelerated by the air through which they pass. -We will show how it was attempted to explain this process when we come -to speak of more modern authors. He classed natural bodies into heavy -and light, remarking at the same time that it is clear that there are -some bodies possessing neither gravity nor levity."[131] By light bodies -he understood those which have a natural tendency to move from the -earth, observing that "that which is lighter is not always light."[132] -He maintained that the heavenly bodies were altogether devoid of -gravity; and we have already had occasion to mention his assertion, that -a large body falls faster than a small one in proportion to its -weight.[133] With this opinion may be classed another great mistake, in -maintaining that the same bodies fall through different mediums, as air -or water, with velocities reciprocally proportional to their densities. -By a singular inversion of experimental science, Cardan, relying on this -assertion, proposed in the sixteenth century to determine the densities -of air and water by observing the different times taken by a stone in -falling through them.[134] Galileo inquired afterwards why the -experiment should not be made with a cork, which pertinent question put -an end to the theory. - -There are curious traces still preserved in the poem of Lucretius of a -mechanical philosophy, of which the credit is in general given to -Democritus, where many principles are inculcated strongly at variance -with Aristotle's notions. We find absolute levity denied, and not only -the assertion that in a vacuum all things would fall, but that they -would fall with the same velocity; and the inequalities which we observe -are attributed to the right cause, the impediment of the air, although -the error remains of believing the velocity of bodies falling through -the air to be proportional to their weight.[135] Such specimens of this -earlier philosophy may well indispose us towards Aristotle, who was as -successful in the science of motion as he was in astronomy in -suppressing the knowledge of a theory so much sounder than that which he -imposed so long upon the credulity of his blinded admirers. - -An agreeable contrast to Aristotle's mystical sayings and fruitless -syllogisms is presented in Archimedes' book on Equilibrium, in which he -demonstrates very satisfactorily, though with greater cumbrousness of -apparatus than is now thought necessary, the principal properties of the -lever. This and the Treatise on the Equilibrium of Floating Bodies are -the only mechanical works which have reached us of this writer, who was -by common consent one of the most accomplished mathematicians of -antiquity. Ptolemy the astronomer wrote also a Treatise on Mechanics, -now lost, which probably contained much that would be interesting in the -history of mechanics; for Pappus says, in the Preface to the Eighth Book -of his Mathematical Collections: "There is no occasion for me to explain -what is meant by a heavy, and what by a light body, and why bodies are -carried up and down, and in what sense these very words 'up' and 'down' -are to be taken, and by what limits they are bounded; for all this is -declared in Ptolemy's Mechanics."[136] This book of Ptolemy's appears to -have been also known by Eutocius, a commentator of Archimedes, who lived -about the end of the fifth century of our era; he intimates that the -doctrines contained in it are grounded upon Aristotle's; if so, its loss -is less to be lamented. Pappus's own book deserves attention for the -enumeration which he makes of the mechanical powers, namely, the wheel -and axle, the lever, pullies, the wedge and the screw. He gives the -credit to Hero and Philo of having shown, in works which have not -reached us, that the theory of all these machines is the same. In Pappus -we also find the first attempt to discover the force necessary to -support a given weight on an inclined plane. This in fact is involved in -the theory of the screw; and the same vicious reasoning which Pappus -employs on this occasion was probably found in those treatises which he -quotes with so much approbation. Numerous as are the faults of his -pretended demonstration, it was received undoubtingly for a long period. - -[Illustration: Chain.] - -The credit of first giving the true theory of equilibrium on the -inclined plane is usually ascribed to Stevin, although, as we shall -presently show, with very little reason. Stevin supposed a chain to be -placed over two inclined planes, and to hang down in the manner -represented in the figure. He then urged that the chain would be in -equilibrium; for otherwise, it would incessantly continue in motion, if -there were any cause why it should begin to move. This being conceded, -he remarks further, that the parts AD and BD are also in equilibrium, -being exactly similar to each other; and therefore if they are taken -away, the remaining parts AC and BC will also be in equilibrium. The -weights of these parts are proportional to the lengths AC and BC; and -hence Stevin concluded that two weights would balance on two inclined -planes, which are to each other as the lengths of the planes included -between the same parallels to the horizon.[137] This conclusion is the -correct one, and there is certainly great ingenuity in this contrivance -to facilitate the demonstration; it must not however be mistaken for an -_à priori_ proof, as it sometimes seems to have been: we should remember -that the experiments which led to the principle of virtual velocities -are also necessary to show the absurdity of supposing a perpetual -motion, which is made the foundation of this theorem. That principle had -been applied directly to determine the same proportion in a work written -long before, where it has remained singularly concealed from the notice -of most who have written on this subject. The book bears the name of -Jordanus, who lived at Namur in the thirteenth century; but Commandine, -who refers to it in his Commentary on Pappus, considers it as the work -of an earlier period. The author takes the principle of virtual -velocities for the groundwork of his explanations, both of the lever and -inclined plane; the latter will not occupy much space, and in an -historical point of view is too curious to be omitted. - -"_Quæst. 10._--If two weights descend by paths of different -obliquities, and the proportion be the same of the weights and the -inclinations taken in the same order, they will have the same descending -force. By the inclinations, I do not mean the angles, but the paths up -to the point in which both meet the same perpendicular.[138] Let, -therefore, _e_ be the weight upon _dc_, and _h_ upon _da_, and let _e_ -be to _h_ as _dc_ to _da_. I say these weights, in this situation, are -equally effective. Take _dk_ equally inclined with _dc_, and upon it a -weight equal to _e_, which call 6. If possible let _e_ descend to _l_, -so as to raise _h_ to _m_, and take 6_n_ equal to _hm_ or _el_, and draw -the horizontal and perpendicular lines as in the figure. - -[Illustration] - - Then _nz_:_n_6 :: _db_:_dk_ - and _mh_:_mx_ :: _da_:_db_ - -therefore _nz_:_mx_ :: _da_:_dk_ :: _h_:6, _and therefore since er is -not able to raise_ 6 _to n, neither will it be able to raise h to m_; -therefore they will remain as they are."[139] The passage in Italics -tacitly assumes the principle in question. Tartalea, who edited -Jordanus's book in 1565, has copied this theorem _verbatim_ into one of -his own treatises, and from that time it appears to have attracted no -further attention. The rest of the book is of an inferior description. -We find Aristotle's doctrine repeated, that the velocity of a falling -body is proportional to its weight; that the weight of a heavy body -changes with its form; and other similar opinions. The manner in which -falling bodies are accelerated by the air is given in detail. "By its -first motion the heavy body will drag after it what is behind, and move -what is just below it; and these when put in motion move what is next to -them, so that by being set in motion they less impede the falling body. -In this manner it has the effect of being heavier, and impels still more -those which give way before it, until at last they are no longer -impelled, but begin to drag. And thus it happens that its gravity is -increased by their attraction, and their motion by its gravity, whence -we see that its velocity is continually multiplied." - -In this short review of the state of mechanical science before Galileo, -the name of Guido Ubaldi ought not to be omitted, although his works -contain little or nothing original. We have already mentioned Benedetti -as having successfully attacked some of Aristotle's statical doctrines, -but it is to be noticed that the laws of motion were little if at all -examined by any of these writers. There are a few theorems connected -with this latter subject in Cardan's extraordinary book "On -Proportions," but for the most part false and contradictory. In the -seventy-first proposition of his fifth book, he examines the force of -the screw in supporting a given weight, and determines it accurately on -the principle of virtual velocities; namely, that the power applied at -the end of the horizontal lever must make a complete circuit at that -distance from the centre, whilst the weight rises through the -perpendicular height of the thread. The very next proposition in the -same page is to find the same relation between the power and weight on -an inclined plane; and although the identity of principle in these two -mechanical aids was well known, yet Cardan declares the necessary -sustaining force to vary as the angle of inclination of the plane, for -no better reason than that such an expression will properly represent it -at the two limiting angles of inclination, since the force is nothing -when the plane is horizontal, and equal to the weight when -perpendicular. This again shows how cautious we should be in attributing -the full knowledge of general principles to these early writers, on -account of occasional indications of their having employed them. - - -FOOTNOTES: - -[115] Histoire des Mathématiques, vol. i. p. 97. - -[116] De vi Percussionis, Bononiæ, 1667. - -[117] Mec. Analyt. - -[118] Mechanica. - -[119] Diog. Laert. In vit. Archyt. - -[120] De Coelo, lib. i. c. 1. - -[121] Phys. lib. i. c. 3. - -[122] Lib. iii. c. 2. The Aristotelians distinguished between things as -existing in act or energy ([energeia]) and things in capacity or power -([dynamis]). For the advantage of those who may think the distinction -worth attending to, we give an illustration of Aristotle's meaning, from -a very acute and learned commentator:--"It (motion) is something more -than dead capacity; something less than perfect actuality; capacity -roused, and striving to quit its latent character; not the capable -brass, nor yet the actual statue, but the capacity in energy; that is to -say, the brass in fusion while it is becoming the statue and is not yet -become."--"The bow moves not because it may be bent, nor because it is -bent; but the motion lies between; lies in an imperfect and obscure -union of the two together; is the actuality (if I may so say) even of -capacity itself: imperfect and obscure, because such is capacity to -which it belongs."--Harris, Philosophical Arrangements. - -[123] Lib. iv. c. 1. - -[124] Lib. iv. c. 11. - -[125] De Coelo, lib. i. c. 2. - -[126] Phys. lib. vii. c. 8. - -[127] De Coelo, lib. i. c. 6. - -[128] Phys. lib. vii. c. 2. - -[129] Mechanica. - -[130] [Ean de en mêdeni logô pherêtai duo phoras kata mêdena chronon, -adynaton eutheian einai tên phoran. Ean gar tina logon enechthê en -chronô tini touton anagkê ton chronon eutheian einai phoran dia ta -proeirêmena, hôste peripheres ginetai duo pheromenon phoras en mêdeni -logô mêdena chronon.]--_i.e._ v = ds/dt - -[131] De Coelo, lib. i. c. 3. - -[132] Lib. iv. c. 2. - -[133] Phys., lib. iv. c. 8. - -[134] De Proport. Basileæ, 1570. - -[135] - - "Nunc locus est, ut opinor, in his illud quoque rebus - Confirmare tibi, nullam rem posse suâ vi - Corpoream sursum ferri, sursumque meare.-- - Nec quom subsiliunt ignes ad tecta domorum, - Et celeri flammâ degustant tigna trabeisque - Sponte suâ facere id sine vi subicente putandum est. - --Nonne vides etiam quantâ vi tigna trabeisque - Respuat humor aquæ? Nam quod magi' mersimus altum - Directâ et magnâ vi multi pressimus ægre:-- - Tam cupide sursum revomit magis atque remittit - Plus ut parte foras emergant, exsiliantque: - --Nec tamen hæc, quantu'st in sedubitamus, opinor, - Quinvacuum per inane deorsum cuncta ferantur, - Sic igitur debent flammæ quoque posse per auras - Aeris expressæ sursum subsidere, quamquam - Pondera quantum in se est deorsum deducere pugnent. - --Quod si forte aliquis credit Graviora potesse - Corpora, quo citius rectum per Inane feruntur, - --Avius a verâ longe ratione recedit. - Nam per Aquas quæcunque cadunt atque Aera deorsum - Hæc pro ponderibus casus celerare necesse 'st - Propterea quia corpus Aquæ, naturaque tenuis - Aeris haud possunt æque rem quamque morari: - Sed citius cedunt Gravioribus exsuperata. - At contra nulli de nullâ parte, neque ullo - Tempore Inane potest Vacuum subsistere reii - Quin, sua quod natura petit, considere pergat: - Omnia quâ propter debent per Inane quietum - Æque ponderibus non æquis concita ferri." - - De Rerum Natura, lib. ii, v. 184-239. - -[136] Math. Coll. Pisani, 1662. - -[137] Oeuvres Mathématiques. Leyde, 1634. - -[138] This is not a literal translation, but by what follows, is -evidently the Author's meaning. His words are, "Proportionem igitur -declinationum dico non angulorum, sed linearum usque ad æquidistantem -resecationem in quâ æqualiter sumunt de directo." - -[139] Opusculum De Ponderositate. Venetiis, 1565. - - - - -CHAPTER XVII. - - _Galileo's theory of Motion--Extracts from the Dialogues._ - - -DURING Galileo's residence at Sienna, when his recent persecution had -rendered astronomy an ungrateful, and indeed an unsafe occupation for -his ever active mind, he returned with increased pleasure to the -favourite employment of his earlier years, an inquiry into the laws and -phenomena of motion. His manuscript treatises on motion, written about -1590, which are mentioned by Venturi to be in the Ducal library at -Florence, seem, from the published titles of the chapters, to consist -principally of objections to the theory of Aristotle; a few only appear -to enter on a new field of speculation. The 11th, 13th, and 17th -chapters relate to the motion of bodies on variously inclined planes, -and of projectiles. The title of the 14th implies a new theory of -accelerated motion, and the assertion in that of the 16th, that a body -falling naturally for however great a time would never acquire more than -an assignable degree of velocity, shows that at this early period -Galileo had formed just and accurate notions of the action of a -resisting medium. It is hazardous to conjecture how much he might have -then acquired of what we should now call more elementary knowledge; a -safer course will be to trace his progress through existing documents in -their chronological order. In 1602 we find Galileo apologizing in a -letter addressed to his early patron the Marchese Guido Ubaldi, for -pressing again upon his attention the isochronism of the pendulum, which -Ubaldi had rejected as false and impossible. It may not be superfluous -to observe that Galileo's results are not quite accurate, for there is a -perceptible increase in the time occupied by the oscillations in larger -arcs; it is therefore probable that he was induced to speak so -confidently of their perfect equality, from attributing the increase of -time which he could not avoid remarking to the increased resistance of -the air during the larger vibrations. The analytical methods then known -would not permit him to discover the curious fact, that the time of a -total vibration is not sensibly altered by this cause, except so far as -it diminishes the extent of the swing, and thus in fact, (paradoxical as -it may sound) renders each oscillation successively more rapid, though -in a very small degree. He does indeed make the same remark, that the -resistance of the air will not affect the time of the oscillation, but -that assertion was a consequence of his erroneous belief that the time -of vibration in all arcs is the same. Had he been aware of the -variation, there is no reason to think that he could have perceived that -this result is not affected by it. In this letter is the first mention -of the theorem, that the times of fall down all the chords drawn from -the lowest point of a circle are equal; and another, from which Galileo -afterwards deduced the curious result, that it takes less time to fall -down the curve than down the chord, notwithstanding the latter is the -direct and shortest course. In conclusion he says, "Up to this point I -can go without exceeding the limits of mechanics, but I have not yet -been able to demonstrate that all arcs are passed in the same time, -which is what I am seeking." In 1604 he addressed the following letter -to Sarpi, suggesting the false theory sometimes called Baliani's, who -took it from Galileo. - -[Illustration: - - A-+ - | - | - B-+ - | - | - C-+ - | - | - D-+ ] - -"Returning to the subject of motion, in which I was entirely without a -fixed principle, from which to deduce the phenomena I have observed, I -have hit upon a proposition, which seems natural and likely enough; and -if I take it for granted, I can show that the spaces passed in natural -motion are in the double proportion of the times, and consequently that -the spaces passed in equal times are as the odd numbers beginning from -unity, and the rest. The principle is this, that the swiftness of the -moveable increases in the proportion of its distance from the point -whence it began to move; as for instance,--if a heavy body drop from A -towards D, by the line ABCD, I suppose the degree of velocity which it -has at B to bear to the velocity at C the ratio of AB to AC. I shall be -very glad if your Reverence will consider this, and tell me your opinion -of it. If we admit this principle, not only, as I have said, shall we -demonstrate the other conclusions, but we have it in our power to show -that a body falling naturally, and another projected upwards, pass -through the same degrees of velocity. For if the projectile be cast up -from D to A, it is clear that at D it has force enough to reach A, and -no farther; and when it has reached C and B, it is equally clear that it -is still joined to a degree of force capable of carrying it to A: thus -it is manifest that the forces at D, C and B decrease in the proportion -of AB, AC, and AD; so that if, in falling, the degrees of velocity -observe the same proportion, that is true which I have hitherto -maintained and believed." - -We have no means of knowing how early Galileo discovered the fallacy of -this reasoning. In his Dialogues on Motion, which contain the correct -theory, he has put this erroneous supposition in the mouth of Sagredo, -on which Salviati remarks, "Your discourse has so much likelihood in it, -that our author himself did not deny to me when I proposed it to him, -that he also had been for some time in the same mistake. But that which -I afterwards extremely wondered at, was to see discovered in four plain -words, not only the falsity, but the impossibility of a supposition -carrying with it so much of seeming truth, that although I proposed it -to many, I never met with any one but did freely admit it to be so; and -yet it is as false and impossible as that motion is made in an instant: -for if the velocities are as the spaces passed, those spaces will be -passed in equal times, and consequently all motion must be -instantaneous." The following manner of putting this reasoning will -perhaps make the conclusion clearer. The velocity at any point is the -space that would be passed in the next moment of time, if the motion be -supposed to continue the same as at that point. At the beginning of the -time, when the body is at rest, the motion is none; and therefore, on -this theory, the space passed in the next moment is none, and thus it -will be seen that the body cannot begin to move according to the -supposed law. - -A curious fact, noticed by Guido Grandi in his commentary on Galileo's -Dialogues on Motion, is that this false law of acceleration is precisely -that which would make a circular arc the shortest line of descent -between two given points; and although in general Galileo only declared -that the fall down the arc is made in less time than down the chord (in -which he is quite correct), yet in some places he seems to assert that -the circular arc is absolutely the shortest line of descent, which is -not true. It has been thought possible that the law, which on reflection -he perceived to be impossible, might have originally recommended itself -to him from his perception that it satisfied his prejudice in this -respect. - -John Bernouilli, one of the first mathematicians in Europe at the -beginning of the last century, has given us a proof that such a reason -might impose even on a strong understanding, in the following argument -urged by him in favour of Galileo's second and correct theory, that the -spaces vary as the squares of the times. He had been investigating the -curve of swiftest descent, and found it to be a cycloid, the same curve -in which Huyghens had already proved that all oscillations are made in -accurately equal times. "I think it," says he, "worthy of remark that -this identity only occurs on Galileo's supposition, so that this alone -might lead us to presume it to be the real law of nature. For nature, -which always does everything in the very simplest manner, thus makes one -line do double work, whereas on any other supposition, we must have had -two lines, one for equal oscillations, the other for the shortest -descent."[140] - -Venturi mentions a letter addressed to Galileo in May 1609 by Luca -Valerio, thanking him for his experiments on the descent of bodies on -inclined planes. His method of making these experiments is detailed in -the Dialogues on Motion:--"In a rule, or rather plank of wood, about -twelve yards long, half a yard broad one way, and three inches the -other, we made upon the narrow side or edge a groove of little more than -an inch wide: we cut it very straight, and, to make it very smooth and -sleek, we glued upon it a piece of vellum, polished and smoothed as -exactly as possible, and in that we let fall a very hard, round, and -smooth brass ball, raising one of the ends of the plank a yard or two at -pleasure above the horizontal plane. We observed, in the manner that I -shall tell you presently, the time which it spent in running down, and -repeated the same observation again and again to assure ourselves of the -time, in which we never found any difference, no, not so much as the -tenth part of one beat of the pulse. Having made and settled this -experiment, we let the same ball descend through a fourth part only of -the length of the groove, and found the measured time to be exactly half -the former. Continuing our experiments with other portions of the -length, comparing the fall through the whole with the fall through half, -two-thirds, three-fourths, in short, with the fall through any part, we -found by many hundred experiments that the spaces passed over were as -the squares of the times, and that this was the case in all inclinations -of the plank; during which, we also remarked that the times of descent, -on different inclinations, observe accurately the proportion assigned to -them farther on, and demonstrated by our author. As to the estimation of -the time, we hung up a great bucket full of water, which by a very small -hole pierced in the bottom squirted out a fine thread of water, which we -caught in a small glass during the whole time of the different descents: -then weighing from time to time, in an exact pair of scales, the -quantity of water caught in this way, the differences and proportions of -their weights gave the differences and proportions of the times; and -this with such exactness that, as I said before, although the -experiments were repeated again and again, they never differed in any -degree worth noticing." In order to get rid of the friction, Galileo -afterwards substituted experiments with the pendulum; but with all his -care he erred very widely in his determination of the space through -which a body would fall in 1´´, if the resistance of the air and all -other impediments were removed. He fixed it at 4 _braccia_: Mersenne has -engraved the length of the '_braccia_' used by Galileo, in his "Harmonie -Universelle," from which it appears to be about 23½ English inches, so -that Galileo's result is rather less than eight feet. Mersenne's own -result from direct observation was thirteen feet: he also made -experiments in St. Peter's at Rome, with a pendulum 325 feet long, the -vibrations of which were made in 10´´; from this the fall in 1´´ might -have been deduced rather more than sixteen feet, which is very close to -the truth. - -From another letter also written in the early part of 1609, we learn -that Galileo was then busied with examining the strength and resistance -"of beams of different sizes and forms, and how much weaker they are in -the middle than at the ends, and how much greater weight they can -support laid along their whole length, than if sustained on a single -point, and of what form they should be so as to be equally strong -throughout." He was also speculating on the motion of projectiles, and -had satisfied himself that their motion in a vertical direction is -unaffected by their horizontal velocity; a conclusion which, combined -with his other experiments, led him afterwards to determine the path of -a projectile in a non-resisting medium to be parabolical. - -Tartalea is supposed to have been the first to remark that no bullet -moves in a horizontal line; but his theory beyond this point was very -erroneous, for he supposed the bullet's path through the air to be made -up of an ascending and descending straight line, connected in the middle -by a circular arc. - -Thomas Digges, in his treatise on the Newe Science of Great Artillerie, -came much nearer the truth; for he remarked[141], that "The bullet -violentlye throwne out of the peece by the furie of the poulder hath two -motions: the one violent, which endeuoreth to carry the bullet right out -in his line diagonall, according to the direction of the peece's axis, -from whence the violent motion proceedeth; the other naturall in the -bullet itselfe, which endeuoreth still to carrye the same directlye -downeward by a right line perpendiculare to the horizon, and which dooth -though insensiblye euen from the beginning by little and little drawe it -from that direct and diagonall course." And a little farther he observes -that "These middle curve arkes of the bullet's circuite, compounded of -the violent and naturall motions of the bullet, albeit they be indeed -mere helicall, yet have they a very great resemblance of the Arkes -Conical. And in randons above 45° they doe much resemble the Hyperbole, -and in all vnder the Ellepsis. But exactlye they neuer accorde, being -indeed Spirall mixte and Helicall." - -Perhaps Digges deserves no greater credit from this latter passage than -the praise of a sharp and accurate eye, for he does not appear to have -founded this determination of the form of the curve on any theory of the -direct fall of bodies; but Galileo's arrival at the same result was -preceded, as we have seen, by a careful examination of the simplest -phenomena into which this compound motion may be resolved. But it is -time to proceed to the analysis of his "Dialogues on Motion," these -preliminary remarks on their subject matter having been merely intended -to show how long before their publication Galileo was in possession of -the principal theories contained in them. - -Descartes, in one of his letters to Mersenne, insinuates that Galileo -had taken many things in these Dialogues from him: the two which he -especially instances are the isochronism of the pendulum, and the law of -the spaces varying as the squares of the times.[142] Descartes was born -in 1596: we have shown that Galileo observed the isochronism of the -pendulum in 1583, and knew the law of the spaces in 1604, although he -was then attempting to deduce it from an erroneous principle. As -Descartes on more than one occasion has been made to usurp the credit -due to Galileo, (in no instance more glaringly so than when he has been -absurdly styled the forerunner of Newton,) it will not be misplaced to -mention a few of his opinions on these subjects, recorded in his letters -to Mersenne in the collection of his letters just cited:--"I am -astonished at what you tell me of having found by experiment that bodies -thrown up in the air take neither more nor less time to rise than to -fall again; and you will excuse me if I say that I look upon the -experiment as a very difficult one to make accurately. This proportion -of increase according to the odd numbers 1, 3, 5, 7, &c., which is in -Galileo, and which I think I wrote to you some time back, cannot be -true, as I believe I intimated at the same time, unless we make two or -three suppositions which are entirely false. One is Galileo's opinion, -that motion increases gradually from the slowest degree; and the other -is, that the air makes no resistance." In a later letter to the same -person he says, apparently with some uneasiness, "I have been revising -my notes on Galileo, in which I have not said expressly, that falling -bodies do not pass through every degree of slowness, but I said that -this cannot be determined without knowing what weight is; _which comes -to the same thing_. As to your example, I grant that it proves that -every degree of velocity is infinitely divisible, but not that a falling -body actually passes through all these divisions.--It is certain that a -stone is not equally disposed to receive a new motion or increase of -velocity, when it is already moving very quickly, and when it is moving -slowly. But I believe that I am now able to determine in what proportion -the velocity of a stone increases, not when falling in a vacuum, but in -this substantial atmosphere.--However I have now got my mind full of -other things, and I cannot amuse myself with hunting this out, _nor is -it a matter of much utility_." He afterwards returns once more to the -same subject:--"As to what Galileo says, that falling bodies pass -through every degree of velocity, I do not believe that it generally -happens, but I allow it is not impossible that it may happen -occasionally." After this the reader will know what value to attach to -the following assertion by the same Descartes:--"I see nothing in -Galileo's books to envy him, and hardly any thing which I would own as -mine;" and then may judge how far Salusbury's blunt declaration is borne -out, "Where or when did any one appear that durst enter the lists with -our Galileus? save only one bold and unfortunate Frenchman, who yet no -sooner came within the ring but he was hissed out again."[143] - -The principal merit of Descartes must undoubtedly be derived from the -great advances he made in what are generally termed Abstract or Pure -Mathematics; nor was he slow to point out to Mersenne and his other -friends the acknowledged inferiority of Galileo to himself in this -respect. We have not sufficient proof that this difference would have -existed if Galileo's attention had been equally directed to that object; -the singular elegance of some of his geometrical constructions indicates -great talent for this as well as for his own more favourite -speculations. But he was far more profitably employed: geometry and pure -mathematics already far outstripped any useful application of their -results to physical science, and it was the business of Galileo's life -to bring up the latter to the same level. He found abstract theorems -already demonstrated in sufficient number for his purpose, nor was there -occasion to task his genius in search of new methods of inquiry, till -all was exhausted which could be learned from those already in use. The -result of his labours was that in the age immediately succeeding -Galileo, the study of nature was no longer in arrear of the abstract -theories of number and measure; and when the genius of Newton pressed it -forward to a still higher degree of perfection, it became necessary to -discover at the same time more powerful instruments of investigation. -This alternating process has been successfully continued to the present -time; the analyst acts as the pioneer of the naturalist, so that the -abstract researches, which at first have no value but in the eyes of -those to whom an elegant formula, in its own beauty, is a source of -pleasure as real and as refined as a painting or a statue, are often -found to furnish the only means for penetrating into the most intricate -and concealed phenomena of natural philosophy. - -Descartes and Delambre agree in suspecting that Galileo preferred the -dialogistic form for his treatises, because it afforded a ready -opportunity for him to praise his own inventions: the reason which he -himself gave is, the greater facility for introducing new matter and -collateral inquiries, such as he seldom failed to add each time that he -reperused his work. We shall select in the first place enough to show -the extent of his knowledge on the principal subject, motion, and shall -then allude as well as our limits will allow to the various other points -incidentally brought forward. - -The dialogues are between the same speakers as in the "System of the -World;" and in the first Simplicio gives Aristotle's proof,[144] that -motion in a vacuum is impossible, because according to him bodies move -with velocities in the compound proportion of their weights and the -rarities of the mediums through which they move. And since the density -of a vacuum bears no assignable ratio to that of any medium in which -motion has been observed, any body which should employ time in moving -through the latter, would pass through the same distance in a vacuum -instantaneously, which is impossible. Salviati replies by denying the -axioms, and asserts that if a cannon ball weighing 200 lbs., and a -musket ball weighing half a pound, be dropped together from a tower 200 -yards high, the former will not anticipate the latter by so much as a -foot; "and I would not have you do as some are wont, who fasten upon -some saying of mine that may want a hair's breadth of the truth, and -under this hair they seek to hide another man's blunder as big as a -cable. Aristotle says that an iron ball weighing 100 lbs. will fall from -the height of 100 yards while a weight of one pound falls but one yard: -I say they will reach the ground together. They find the bigger to -anticipate the less by two inches, and under these two inches they seek -to hide Aristotle's 99 yards." In the course of his reply to this -argument Salviati formally announces the principle which is the -foundation of the whole of Galileo's theory of motion, and which must -therefore be quoted in his own words:--"A heavy body has by nature an -intrinsic principle of moving towards the common centre of heavy things; -that is to say, to the centre of our terrestrial globe, with a motion -continually accelerated in such manner that in equal times there are -always equal additions of velocity. This is to be understood as holding -true only when all accidental and external impediments are removed, -amongst which is one that we cannot obviate, namely, the resistance of -the medium. This opposes itself, less or more, accordingly as it is to -open more slowly or hastily to make way for the moveable, which being by -its own nature, as I have said, continually accelerated, consequently -encounters a continually increasing resistance in the medium, until at -last the velocity reaches that degree, and the resistance that power, -that they balance each other; all further acceleration is prevented, and -the moveable continues ever after with an uniform and equable motion." -That such a limiting velocity is not greater than some which may be -exhibited may be proved as Galileo suggested by firing a bullet upwards, -which will in its descent strike the ground with less force than it -would have done if immediately from the mouth of the gun; for he argued -that the degree of velocity which the air's resistance is capable of -diminishing must be greater than that which could ever be reached by a -body falling naturally from rest. "I do not think the present occasion a -fit one for examining the cause of this acceleration of natural motion, -on which the opinions of philosophers are much divided; some referring -it to the approach towards the centre, some to the continual diminution -of that part of the medium remaining to be divided, some to a certain -extrusion of the ambient medium, which uniting again behind the moveable -presses and hurries it forwards. All these fancies, with others of the -like sort, we might spend our time in examining, and with little to gain -by resolving them. It is enough for our author at present that we -understand his object to be the investigation and examination of some -phenomena of a motion so accelerated, (no matter what may be the cause,) -that the momenta of velocity, from the beginning to move from rest, -increase in the simple proportion in which the time increases, which is -as much as to say, that in equal times are equal additions of velocity. -And if it shall turn out that the phenomena demonstrated on this -supposition are verified in the motion of falling and naturally -accelerated weights, we may thence conclude that the assumed definition -does describe the motion of heavy bodies, and that it is true that their -acceleration varies in the ratio of the time of motion." - -When Galileo first published these Dialogues on Motion, he was obliged -to rest his demonstrations upon another principle besides, namely, that -the velocity acquired in falling down all inclined planes of the same -perpendicular height is the same. As this result was derived directly -from experiment, and from that only, his theory was so far imperfect -till he could show its consistency with the above supposed law of -acceleration. When Viviani was studying with Galileo, he expressed his -dissatisfaction at this chasm in the reasoning; the consequence of which -was, that Galileo, as he lay the same night, sleepless through -indisposition, discovered the proof which he had long sought in vain, -and introduced it into the subsequent editions. The third dialogue is -principally taken up with theorems on the direct fall of bodies, their -times of descent down differently inclined planes, which in planes of -the same height he determined to be as the lengths, and with other -inquiries connected with the same subject, such as the straight lines of -shortest descent under different data, &c. - -[Illustration] - -The fourth dialogue is appropriated to projectile motion, determined -upon the principle that the horizontal motion will continue the same as -if there were no vertical motion, and the vertical motion as if there -were no horizontal motion. "Let AB represent a horizontal line or plane -placed on high, on which let a body be carried with an equable motion -from A towards B, and the support of the plane being taken away at B, -let the natural motion downwards due to the body's weight come upon it -in the direction of the perpendicular BN. Moreover let the straight line -BE drawn in the direction AB be taken to represent the flow, or measure, -of the time, on which let any number of equal parts BC, CD, DE, &c. be -marked at pleasure, and from the points C, D, E, let lines be drawn -parallel to BN; in the first of these let any part CI be taken, and let -DF be taken four times as great as CI, EH nine times as great, and so -on, proportionally to the squares of the lines BC, BD, BE, &c., or, as -we say, in the double proportion of these lines. Now if we suppose that -whilst by its equable horizontal motion the body moves from B to C, it -also descends by its weight through CI, at the end of the time denoted -by BC it will be at I. Moreover in the time BD, double of BC, it will -have fallen four times as far, for in the first part of the Treatise it -has been shewn that the spaces fallen through by a heavy body vary as -the squares of the times. Similarly at the end of the time BE, or three -times BC, it will have fallen through EH, and will be at H. And it is -plain that the points I, F, H, are in the same parabolical line BIFH. -The same demonstration will apply if we take any number of equal -particles of time of whatever duration." - -The curve called here a Parabola by Galileo, is one of those which -results from cutting straight through a Cone, and therefore is called -also one of the Conic Sections, the curious properties of which curves -had drawn the attention of geometricians long before Galileo thus began -to point out their intimate connexion with the phenomena of motion. -After the proposition we have just extracted, he proceeds to anticipate -some objections to the theory, and explains that the course of a -projectile will not be accurately a parabola for two reasons; partly on -account of the resistance of the air, and partly because a horizontal -line, or one equidistant from the earth's centre, is not straight, but -circular. The latter cause of difference will, however, as he says, be -insensible in all such experiments as we are able to make. The rest of -the Dialogue is taken up with different constructions for determining -the circumstances of the motion of projectiles, as their range, greatest -height, &c.; and it is proved that, with a given force of projection, -the range will be greatest when a ball is projected at an elevation of -45°, ranges of all angles equally inclined above and below 45° -corresponding exactly to each other. - -[Illustration] - -One of the most interesting subjects discussed in these dialogues is the -famous notion of Nature's horror of a vacuum or empty space, which the -old school of philosophy considered as impossible to be obtained. -Galileo's notions of it were very different; for although he still -unadvisedly adhered to the old phrase to denote the resistance -experienced in endeavouring to separate two smooth surfaces, he was so -far from looking upon a vacuum as an impossibility, that he has -described an apparatus by which he endeavoured to measure the force -necessary to produce one. This consisted of a cylinder, into which is -tightly fitted a piston; through the centre of the piston passes a rod -with a conical valve, which, when drawn down, shuts the aperture -closely, supporting a basket. The space between the piston and cylinder -being filled full of water poured in through the aperture, the valve is -closed, the vessel reversed, and weights are added till the piston is -drawn forcibly downwards. Galileo concluded that the weight of the -piston, rod, and added weights, would be the measure of the force of -resistance to the vacuum which he supposed would take place between the -piston and lower surface of the water. The defects in this apparatus for -the purpose intended are of no consequence, so far as regards the -present argument, and it is perhaps needless to observe that he was -mistaken in supposing the water would not descend with the piston. This -experiment occasions a remark from Sagredo, that he had observed that a -lifting-pump would not work when the water in the cistern had sunk to -the depth of thirty-five feet below the valve; that he thought the pump -was injured, and sent for the maker of it, who assured him that no pump -upon that construction would lift water from so great a depth. This -story is sometimes told of Galileo, as if he had said sneeringly on this -occasion that Nature's horror of a vacuum does not extend beyond -thirty-five feet; but it is very plain that if he had made such an -observation, it would have been seriously; and in fact by such a -limitation he deprived the notion of the principal part of its -absurdity. He evidently had adopted the common notion of suction, for he -compares the column of water to a rod of metal suspended from its upper -end, which may be lengthened till it breaks with its own weight. It is -certainly very extraordinary that he failed to observe how simply these -phenomena may be explained by a reference to the weight of the elastic -atmosphere, which he was perfectly well acquainted with, and endeavoured -by the following ingenious experiment to determine:--"Take a large glass -flask with a bent neck, and round its mouth tie a leathern pipe with a -valve in it, through which water may be forced into the flask with a -syringe without suffering any air to escape, so that it will be -compressed within the bottle. It will be found difficult to force in -more than about three-fourths of what the flask will hold, which must be -carefully weighed. The valve must then be opened, and just so much air -will rush out as would in its natural density occupy the space now -filled by the water. Weigh the vessel again; the difference will show -the weight of that quantity of air."[145] By these means, which the -modern experimentalist will see were scarcely capable of much accuracy, -Galileo found that air was four hundred times lighter than water, -instead of ten times, which was the proportion fixed on by Aristotle. -The real proportion is about 830 times. - -The true theory of the rise of water in a lifting-pump is commonly dated -from Torricelli's famous experiment with a column of mercury, in 1644, -when he found that the greatest height at which it would stand is -fourteen times less than the height at which water will stand, which is -exactly the proportion of weight between water and mercury. The -following curious letter from Baliani, in 1630, shows that the original -merit of suggesting the real cause belongs to him, and renders it still -more unaccountable that Galileo, to whom it was addressed, should not at -once have adopted the same view of the subject:--"I have believed that a -vacuum may exist naturally ever since I knew that the air has sensible -weight, and that you taught me in one of your letters how to find its -weight exactly, though I have not yet succeeded with that experiment. -From that moment I took up the notion that it is not repugnant to the -nature of things that there should be a vacuum, but merely that it is -difficult to produce. To explain myself more clearly: if we allow that -the air has weight, there is no difference between air and water except -in degree. At the bottom of the sea the weight of the water above me -compresses everything round my body, and it strikes me that the same -thing must happen in the air, we being placed at the bottom of its -immensity; we do not feel its weight, nor the compression round us, -because our bodies are made capable of supporting it. But if we were in -a vacuum, then the weight of the air above our heads would be felt. It -would be felt very great, but not infinite, and therefore determinable, -and it might be overcome by a force proportioned to it. In fact I -estimate it to be such that, to make a vacuum, I believe we require a -force greater than that of a column of water thirty feet high."[146] - -[Illustration] - -This subject is introduced by some observations on the force of -cohesion, Galileo seeming to be of opinion that, although it cannot be -adequately accounted for by "the great and principal resistance to a -vacuum, yet that perhaps a sufficient cause may be found by considering -every body as composed of very minute particles, between every two of -which is exerted a similar resistance." This remark serves to lead to a -discussion on indivisibles and infinite quantities, of which we shall -merely extract what Galileo gives as a curious paradox suggested in the -course of it. He supposes a basin to be formed by scooping a hemisphere -out of a cylinder, and a cone to be taken of the same depth and base as -the hemisphere. It is easy to show, if the cone and scooped cylinder be -both supposed to be cut by the same plane, parallel to the one on which -both stand, that the area of the ring CDEF thus discovered in the -cylinder is equal to the area of the corresponding circular section AB -of the cone, wherever the cutting plane is supposed to be.[147] He then -proceeds with these remarkable words:--"If we raise the plane higher and -higher, one of these areas terminates in the circumference of a circle, -and the other in a point, for such are the upper rim of the basin and -the top of the cone. Now since in the diminution of the two areas they -to the very last maintain their equality to one another, it is in my -thoughts proper to say that the highest and ultimate terms[148] of such -diminutions are equal, and not one infinitely bigger than the other. It -seems therefore that the circumference of a large circle may be said to -be equal to one single point. And why may not these be called equal if -they be the last remainders and vestiges left by equal magnitudes[149]?" - -We think no one can refuse to admit the probability, that Newton may -have found in such passages as these the first germ of the idea of his -prime and ultimate ratios, which afterwards became in his hands an -instrument of such power. As to the paradoxical result, Descartes -undoubtedly has given the true answer to it in saying that it only -proves that the line is not a greater area than the point is. Whilst on -this subject, it may not be uninteresting to remark that something -similar to the doctrine of fluxions seems to have been lying dormant in -the minds of the mathematicians of Galileo's era, for Inchoffer -illustrates his argument in the treatise we have already mentioned, that -the Copernicans may deduce some true results from what he terms their -absurd hypothesis, by observing, that mathematicians may deduce the -truth that a line is length without breadth, from the false and -physically impossible supposition that a point flows, and that a line is -the fluxion of a point.[150] - -A suggestion that perhaps fire dissolves bodies by insinuating itself -between their minute particles, brings on the subject of the violent -effects of heat and light; on which Sagredo inquires, whether we are to -take for granted that the effect of light does or does not require time. -Simplicio is ready with an answer, that the discharge of artillery -proves the transmission of light to be instantaneous, to which Sagredo -cautiously replies, that nothing can be gathered from that experiment -except that light travels more swiftly than sound; nor can we draw any -decisive conclusion from the rising of the sun. "Who can assure us that -he is not in the horizon before his rays reach our sight?" Salviati then -mentions an experiment by which he endeavoured to examine this question. -Two observers are each to be furnished with a lantern: as soon as the -first shades his light, the second is to discover his, and this is to be -repeated at a short distance till the observers are perfect in the -practice. The same thing is to be tried at the distance of several -miles, and if the first observer perceive any delay between shading his -own light and the appearance of his companion's, it is to be attributed -to the time taken by the light in traversing twice the distance between -them. He allows that he could discover no perceptible interval at the -distance of a mile, at which he had tried the experiment, but recommends -that with the help of a telescope it should be tried at much greater -distances. Sir Kenelm Digby remarks on this passage: "It may be objected -(if there be some observable tardity in the motion of light) that the -sunne would never be truly in that place in which unto our eyes he -appeareth to be; because that it being seene by means of the light which -issueth from it, if that light required time to move in, the sunne -(whose motion is so swifte) would be removed from the place where the -light left it, before it could be with us to give tidings of him. To -this I answer, allowing peradventure that it may be so, who knoweth the -contrary? Or what inconvenience would follow if it be admitted[151]?" - -The principal thing remaining to be noticed is the application of the -theory of the pendulum to musical concords and dissonances, which are -explained, in the same manner as by Kepler in his "Harmonices Mundi," to -result from the concurrence or opposition of vibrations in the air -striking upon the drum of the ear. It is suggested that these vibrations -may be made manifest by rubbing the finger round a glass set in a large -vessel of water; "and if by pressure the note is suddenly made to rise -to the octave above, every one of the undulations which will be seen -regularly spreading round the glass, will suddenly split into two, -proving that the vibrations that occasion the octave are double those -belonging to the simple note." Galileo then describes a method he -discovered by accident of measuring the length of these waves more -accurately than can be done in the agitated water. He was scraping a -brass plate with an iron chisel, to take out some spots, and moving the -tool rapidly upon the plate, he occasionally heard a hissing and -whistling sound, very shrill and audible, and whenever this occurred, -and then only, he observed the light dust on the plate to arrange itself -in a long row of small parallel streaks equidistant from each other. In -repeated experiments he produced different tones by scraping with -greater or less velocity, and remarked that the streaks produced by the -acute sounds stood closer together than those from the low notes. Among -the sounds produced were two, which by comparison with a viol he -ascertained to differ by an exact fifth; and measuring the spaces -occupied by the streaks in both experiments, he found thirty of the one -equal to forty-five of the other, which is exactly the known proportion -of the lengths of strings of the same material which sound a fifth to -each other.[152] - -Salviati also remarks, that if the material be not the same, as for -instance if it be required to sound an octave to a note on catgut, on a -wire of the same length, the weight of the wire must be made four times -as great, and so for other intervals. "The immediate cause of the forms -of musical intervals is neither the length, the tension, nor the -thickness, but the proportion of the numbers of the undulations of the -air which strike upon the drum of the ear, and make it vibrate in the -same intervals. Hence we may gather a plausible reason of the different -sensations occasioned to us by different couples of sounds, of which we -hear some with great pleasure, some with less, and call them accordingly -concords, more or less perfect, whilst some excite in us great -dissatisfaction, and are called discords. The disagreeable sensation -belonging to the latter probably arises from the disorderly manner in -which the vibrations strike the drum of the ear; so that for instance a -most cruel discord would be produced by sounding together two strings, -of which the lengths are to each other as the side and diagonal of a -square, which is the discord of the false fifth. On the contrary, -agreeable consonances will result from those strings of which the -numbers of vibrations made in the same time are commensurable, "to the -end that the cartilage of the drum may not undergo the incessant torture -of a double inflexion from the disagreeing percussions." Something -similar may be exhibited to the eye by hanging up pendulums of different -lengths: "if these be proportioned so that the times of their vibrations -correspond with those of the musical concords, the eye will observe with -pleasure their crossings and interweavings still recurring at -appreciable intervals; but if the times of vibration be incommensurate, -the eye will be wearied and worn out with following them." - -The second dialogue is occupied entirely with an investigation of the -strength of beams, a subject which does not appear to have been examined -by any one before Galileo beyond Aristotle's remark, that long beams are -weaker, because they are at once the weight, the lever, and the fulcrum; -and it is in the development of this observation that the whole theory -consists. The principle assumed by Galileo as the basis of his inquiries -is, that the force of cohesion with which a beam resists a cross -fracture in any section may all be considered as acting at the centre of -gravity of the section, and that it breaks always at the lowest point: -from this he deduced that the effect of the weight of a prismatic beam -in overcoming the resistance of one end by which it is fastened to a -wall, varies directly as the square of the length, and inversely as the -side of the base. From this it immediately follows, that if for instance -the bone of a large animal be three times as long as the corresponding -one in a smaller beast, it must be nine times as thick to have the same -strength, provided we suppose in both cases that the materials are of -the same consistence. An elegant result which Galileo also deduced from -this theory, is that the form of such a beam, to be equally strong in -every part, should be that of a parabolical prism, the vertex of the -parabola being the farthest removed from the wall. As an easy mode of -describing the parabolic curve for this purpose, he recommends tracing -the line in which a heavy flexible string hangs. This curve is not an -accurate parabola: it is now called a catenary; but it is plain from the -description of it in the fourth dialogue, that Galileo was perfectly -aware that this construction is only approximately true. In the same -place he makes the remark, which to many is so paradoxical, that no -force, however great, exerted in a horizontal direction, can stretch a -heavy thread, however slender, into an accurately straight line. - -The fifth and sixth dialogues were left unfinished, and annexed to the -former ones by Viviani after Galileo's death: the fragment of the fifth, -which is on the subject of Euclid's Definition of Ratio, was at first -intended to have formed a part of the third, and followed the first -proposition on equable motion: the sixth was intended to have embodied -Galileo's researches on the nature and laws of Percussion, on which he -was employed at the time of his death. Considering these solely as -fragments, we shall not here make any extracts from them. - - -FOOTNOTES: - -[140] Joh. Bernouilli, Opera Omnia, Lausannæ, 1744. tom. i. p. 192. - -[141] Pantometria, 1591. - -[142] Lettres de Descartes. Paris, 1657. - -[143] Math. Coll. vol. ii. - -[144] Phys. Lib. iv. c. 8. - -[145] It has been recently proposed to determine the density of -high-pressure steam by a process analogous to this. - -[146] Venturi, vol. ii. - -[147] Galileo also reasons in the same way on the equality of the solids -standing on the cutting plane, but one is sufficient for our present -purpose. - -[148] Gli altissimi e ultimi termini. - -[149] Le ultime reliquie e vestigie lasciate da grandezze eguali. - -[150] Punctum fluere, et lineam esse fluxum puncti. Tract. Syllept. -Romæ, 1633. - -[151] "Treatise of the Nature of Bodies. London, 1665." - -[152] This beautiful experiment is more easily tried by drawing the bow -of a violin across the edge of glass strewed with fine dry sand. Those -who wish to see more on the subject may consult Chladni's 'Acoustique.' - - - - -CHAPTER XVIII. - - _Correspondence on Longitudes.--Pendulum Clock._ - - -IN the spring of 1636, having finished his Dialogues on Motion, Galileo -resumed the plan of determining the longitude by means of Jupiter's -satellites. Perhaps he suspected something of the private intrigue which -thwarted his former expectations from the Spanish government, and this -may have induced him on the present occasion to negotiate the matter -without applying for Ferdinand's assistance and recommendation. -Accordingly he addressed himself to Lorenz Real, who had been Governor -General of the Dutch possessions in India, freely and unconditionally -offering the use of his theory to the States General of Holland. Not -long before, his opinion had been requested by the commissioners -appointed at Paris to examine and report on the practicability of -another method proposed by Morin,[153] which consisted in observing the -distance of the moon from a known star. Morin was a French philosopher, -principally known as an astrologer and zealous Anti-Copernican; but his -name deserves to be recorded as undoubtedly one of the first to -recommend a method, which, under the name of a Lunar distance, is now in -universal practice. - -The monthly motion of the moon is so rapid, that her distance from a -given star sensibly varies in a few minutes even to the unassisted eye; -and with the aid of the telescope, we can of course appreciate the -change more accurately. Morin proposed that the distances of the moon -from a number of fixed stars lying near her path in the heavens should -be beforehand calculated and registered for every day in the year, at a -certain hour, in the place from which the longitudes were to be -reckoned, as for instance at Paris. Just as in the case of the eclipses -of Jupiter's satellites, the observer, when he saw that the moon had -arrived at the registered distance, would know the hour at Paris: he -might also make allowance for intermediate distances. Observing at the -same instant the hour on board his ship, the difference between the two -would show his position in regard of longitude. In using this method as -it is now practised, several modifications are to be attended to, -without which it would be wholly useless, in consequence of the -refraction of the atmosphere, and the proximity of the moon to the -earth. Owing to the latter cause, if two spectators should at the same -instant of time, but in different places, measure the distance of the -moon in the East, from a star still more to the eastward, it would -appear greater to the more easterly spectator than to the other -observer, who as seen from the star would be standing more directly -behind the moon. The mode of allowing for these alterations is taught by -trigonometry and astronomy. - -The success of this method depends altogether upon the exact knowledge -which we now have of the moon's course, and till that knowledge was -perfected it would have been found altogether illusory. Such in fact was -the judgment which Galileo pronounced upon it. "As to Morin's book on -the method of finding the longitude by means of the moon's motion, I say -freely that I conceive this idea to be as accurate in theory, as -fallacious and impossible in practice. I am sure that neither you nor -any one of the other four gentlemen can doubt the possibility of finding -the difference of longitude between two meridians by means of the moon's -motion, provided we are sure of the following requisites: First, an -Ephemeris of the moon's motion exactly calculated for the first meridian -from which the others are to be reckoned; secondly, exact instruments, -and convenient to handle, in taking the distance between the moon and a -fixed star; thirdly, great practical skill in the observer; fourthly, -not less accuracy in the scientific calculations, and astronomical -computations; fifthly, very perfect clocks to number the hours, or other -means of knowing them exactly, &c. Supposing, I say, all these elements -free from error, the longitude will be accurately found; but I reckon it -more easy and likely to err in all of these together, than to be -practically right in one alone. Morin ought to require his judges to -assign, at their pleasure, eight or ten moments of different nights -during four or six months to come, and pledge himself to predict and -assign by his calculations the distances of the moon at those determined -instants from some star which would then be near her. If it is found -that the distances assigned by him agree with those which the quadrant -or sextant[154] will actually show, the judges would be satisfied of his -success, or rather of the truth of the matter, and nothing would remain -but to show that his operations were such as could be performed by men -of moderate skill, and also practicable at sea as well as on land. I -incline much to think that an experiment of this kind would do much -towards abating the opinion and conceit which Morin has of himself, -which appears to me so lofty, that I should consider myself the eighth -sage, if I knew the half of what Morin presumes to know." - -It is probable that Galileo was biassed by a predilection for his own -method, on which he had expended so much time and labour; but the -objections which he raises against Morin's proposal in the foregoing -letter are no other than those to which at that period it was -undoubtedly open. With regard to his own, he had already, in 1612, given -a rough prediction of the course of Jupiter's satellites, which had been -found to agree tolerably well with subsequent observations; and since -that time, amid all his other employments, he had almost -unintermittingly during twenty-four years continued his observations, -for the sake of bringing the tables of their motions to as high a state -of perfection as possible. This was the point to which the inquiries of -the States in their answer to Galileo's frank proposal were principally -directed. They immediately appointed commissioners to communicate with -him, and report the various points on which they required information. -They also sent him a golden chain, and assured him that in the case of -the design proving successful, he should have no cause to complain of -their want of gratitude and generosity. The commissioners immediately -commenced an active correspondence with him, in the course of which he -entered into more minute details with regard to the methods by which he -proposed to obviate the practical difficulties of the necessary -observations. - -It is worth noticing that the secretary to the Prince of Orange, who was -mainly instrumental in forming this commission, was Constantine -Huyghens, father of the celebrated mathematician of that name, of whom -it has been said that he seemed destined to complete the discoveries of -Galileo; and it is not a little remarkable, that Huyghens nowhere in his -published works makes any allusion to this connexion between his father -and Galileo, not even during the discussion that arose some years later -on the subject of the pendulum clock, which must necessarily have forced -it upon his recollection. - -The Dutch commissioners had chosen one of their number to go into Italy -for the purpose of communicating personally with Galileo, but he -discouraged this scheme, from a fear of its giving umbrage at Rome. The -correspondence being carried on at so great a distance necessarily -experienced many tedious delays, till in the very midst of Galileo's -labours to complete his tables, he was seized with the blindness which -we have already mentioned. He then resolved to place all the papers -containing his observations and calculations for this purpose in the -hands of Renieri, a former pupil of his, and then professor of -mathematics at Pisa, who undertook to finish and to forward them into -Holland. Before this was done, a new delay was occasioned by the deaths -which speedily followed each other of every one of the four -commissioners; and for two or three years the correspondence with -Holland was entirely interrupted. Constantine Huyghens, who was capable -of appreciating the value of the scheme, succeeded after some trouble in -renewing it, but only just before the death of Galileo himself, by which -of course it was a second time broken off; and to complete the singular -series of obstacles by which the trial of this method was impeded, just -as Renieri, by order of the Duke of Tuscany, was about to publish the -ephemeris and tables which Galileo had entrusted to him, and which the -Duke told Viviani he had seen in his possession, he also was attacked -with a mortal malady; and upon his death the manuscripts were nowhere to -be found, nor has it since been discovered what became of them. Montucla -has intimated his suspicions that Renieri himself destroyed them, from a -consciousness that they were insufficient for the purpose to which it -was intended to apply them; a bold conjecture, and one which ought to -rest upon something more than mere surmise: for although it may be -considered certain, that the practical value of these tables would be -very inconsiderable in the present advanced state of knowledge, yet it -is nearly as sure that they were unique at that time, and Renieri was -aware of the value which Galileo himself had set upon them, and should -not be lightly accused of betraying his trust in so gross a manner. In -1665, Borelli calculated the places of the satellites for every day in -the ensuing year, which he professed to have deduced (by desire of the -Grand Duke) from Galileo's tables;[155] but he does not say whether or -not these tables were the same that had been in Renieri's possession. - -We have delayed till this opportunity to examine how far the invention -of the pendulum clock belongs to Galileo. It has been asserted that the -isochronism of the pendulum had been noticed by Leonardo da Vinci, but -the passage on which this assertion is founded (as translated from his -manuscripts by Venturi) scarcely warrants this conclusion. "A rod which -engages itself in the opposite teeth of a spur-wheel can act like the -arm of the balance in clocks, that is to say, it will act alternately, -first on one side of the wheel, then on the opposite one, without -interruption." If Da Vinci had constructed a clock on this principle, -and recognized the superiority of the pendulum over the old balance, he -would surely have done more than merely mention it as affording an -unintermitted motion "like the arm of the balance." The use of the -balance is supposed to have been introduced at least as early as the -fourteenth century. Venturi mentions the drawing and description of a -clock in one of the manuscripts of the King's Library at Paris, dated -about the middle of the fifteenth century, which as he says nearly -resembles a modern watch. The balance is there called "The circle -fastened to the stem of the pallets, and moved by the force with -it."[156] In that singularly wild and extravagant book, entitled "A -History of both Worlds," by Robert Flud, are given two drawings of the -wheel-work of the clocks and watches in use before the application of -the pendulum. An inspection of them will show how little remained to be -done when the isochronism of the pendulum was discovered. _Fig. 1._ -represents "the large clocks moved by a weight, such as are put up in -churches and turrets; _fig. 2._ the small ones moved by a spring, such -as are worn round the neck, or placed on a shelf or table. The use of -the chain is to equalize the spring, which is strongest at the beginning -of its motion."[157] This contrivance of the chain is mentioned by -Cardan, in 1570, and is probably still older. In both figures the name -given to the cross bar, with the weight attached to it, is "the time or -balance (_tempus seu libratio_) by which the motion is equalized." The -manner in which Huyghens first applied the pendulum is shown in _fig. -3._[158] The action in the old clocks of the balance, or _rake_, as it -was also called, was by checking the motion of the descending weight -till its inertia was overcome; it was then forced round till the -opposite pallet engaged in the toothed wheel. The balance was thus -suddenly and forcibly reduced to a state of rest, and again set in -motion in the opposite direction. It will be observed that these -balances wanted the spiral spring introduced in all modern watches, -which has a property of isochronism similar to that of the pendulum. -Hooke is generally named as the discoverer of this property of springs, -and as the author of its application to the improvement of watches, but -the invention is disputed with him by Huyghens. Lahire asserts[159] that -the isochronism of springs was communicated to Huyghens at Paris by -Hautefeuille, and that this was the reason why Huyghens failed to obtain -the patent he solicited for the construction of spring watches. A great -number of curious contrivances at this early period in the history of -Horology, may be seen in Schott's Magia Naturæ, published at Nuremberg -in 1664. - -[Illustration: _Fig. 2. Fig. 1. Fig. 3._] - -Galileo was early convinced of the importance of his pendulum to the -accuracy of astronomical observations; but the progress of invention is -such that the steps which on looking back seem the easiest to make, are -often those which are the longest delayed. Galileo recognized the -principle of the isochronism of the pendulum, and recommended it as a -measurer of time in 1583; yet fifty years later, although constantly -using it, he had not devised a more convenient method of doing so, than -is contained in the following description taken from his "Astronomical -Operations." - -"A very exact time-measurer for minute intervals of time, is a heavy -pendulum of any size hanged by a fine thread, which, if removed from the -perpendicular and allowed to swing freely, always completes its -vibrations, be they great or small, in exactly the same time."[160] - -The mode of finding exactly by means of this the quantity of any time -reduced to hours, minutes, seconds, &c., which are the divisions -commonly used among astronomers, is this:--"Fit up a pendulum of any -length, as for instance about a foot long, and count patiently (only for -once) the number of vibrations during a natural day. Our object will be -attained if we know the exact revolution of the natural day. The -observer must then fix a telescope in the direction of any star, and -continue to watch it till it disappears from the field of view. At that -instant he must begin to count the vibrations of the pendulum, -continuing all night and the following day till the return of the same -star within the field of view of the telescope, and its second -disappearance, as on the first night. Bearing in recollection the total -number of vibrations thus made in twenty-four hours, the time -corresponding to any other number of vibrations will be immediately -given by the Golden Rule." - -A second extract out of Galileo's Dutch correspondence, in 1637, will -show the extent of his improvements at that time:--"I come now to the -second contrivance for increasing immensely the exactness of -astronomical observations. I allude to my time-measurer, the precision -of which is so great, and such, that it will give the exact quantity of -hours, minutes, seconds, and even thirds, if their recurrence could be -counted; and its constancy is such that two, four, or six such -instruments will go on together so equably that one will not differ from -another so much as the beat of a pulse, not only in an hour, but even in -a day or a month."--"I do not make use of a weight hanging by a thread, -but a heavy and solid pendulum, made for instance of brass or copper, in -the shape of a circular sector of twelve or fifteen degrees, the radius -of which may be two or three palms, and the greater it is the less -trouble will there be in attending it. This sector, such as I have -described, I make thickest in the middle radius, tapering gradually -towards the edges, where I terminate it in a tolerably sharp line, to -obviate as much as possible the resistance of the air, which is the sole -cause of its retardation."--[These last words deserve notice, because, -in a previous discussion, Galileo had observed that the parts of the -pendulum nearest the point of suspension have a tendency to vibrate -quicker than those at the other end, and seems to have thought -erroneously that the stoppage of the pendulum is partly to be attributed -to this cause.]--"This is pierced in the centre, through which is passed -an iron bar shaped like those on which steelyards hang, terminated below -in an angle, and placed on two bronze supports, that they may wear away -less during a long motion of the sector. If the sector (when accurately -balanced) be removed several degrees from its perpendicular position, it -will continue a reciprocal motion through a very great number of -vibrations before it will stop; and in order that it may continue its -motion as long as is wanted, the attendant must occasionally give it a -smart push, to carry it back to large vibrations." Galileo then -describes as before the method of counting the vibrations in the course -of a day, and gives the rule that the lengths of two similar pendulums -will have the same proportion as the squares of their times of -vibration. He then continues: "Now to save the fatigue of the assistant -in continually counting the vibrations, this is a convenient -contrivance: A very small and delicate needle extends out from the -middle of the circumference of the sector, which in passing strikes a -rod fixed at one end; this rod rests upon the teeth of a wheel as light -as paper, placed in a horizontal plane near the pendulum, having round -it teeth cut like those of a saw, that is to say, with one side of each -tooth perpendicular to the rim of the wheel and the other inclined -obliquely. The rod striking against the perpendicular side of the tooth -moves it, but as the same rod returns against the oblique side, it does -not move it the contrary way, but slips over it and falls at the foot of -the following tooth, so that the motion of the wheel will be always in -the same direction. And by counting the teeth you may see at will the -number of teeth passed, and consequently the number of vibrations and of -particles of time elapsed. You may also fit to the axis of this first -wheel a second, with a small number of teeth, touching another greater -toothed wheel, &c. But it is superfluous to point out this to you, who -have by you men very ingenious and well skilled in making clocks and -other admirable machines; and on this new principle, that the pendulum -makes its great and small vibrations in the same time exactly, they will -invent contrivances more subtle than any I can suggest; and as the error -of clocks consists principally in the disability of workmen hitherto to -adjust what we call the balance of the clock, so that it may vibrate -regularly, my very simple pendulum, which is not liable to any -alteration, affords a mean of maintaining the measures of time always -equal." The contrivance thus described would be somewhat similar to the -annexed representation, but it is almost certain that no such instrument -was actually constructed. - -[Illustration] - -It must be owned that Galileo greatly overrated the accuracy of his -timekeeper; and in asserting so positively that which he had certainly -not experienced, he seems to depart from his own principles of -philosophizing. It will be remarked that in this passage he still is of -the erroneous opinion, that all the vibrations great or small of the -same pendulum take exactly the same time; and we have not been able to -find any trace of his having ever held a different opinion, unless -perhaps in the Dialogues, where he says, "If the vibrations are not -exactly equal, they are at least insensibly different." This is very -much at variance with the statement in the Memoirs of the Academia del -Cimento, edited by their secretary Magalotti, on the credit of which -Galileo's claim to the pendulum-clock chiefly rests. It is there said -that experience shows that the smallest vibrations are rather the -quickest, "as Galileo announced after the observation, which in 1583 he -was the first to make of their approximate equality." It is not possible -immediately in connexion with so glaring a misstatement, to give -implicit credence to the assertion in the next sentence, that "_to -obviate this inconvenience_" Galileo was the first to contrive a clock, -constructed in 1649, by his son Vincenzo, in which, by the action of a -weight or spring, the pendulum was constrained to move always from the -same height. Indeed it appears as if Magalotti did not always tell this -story in the same manner, for he is referred to as the author of the -account given by Becher, "that Galileo himself made a pendulum-clock one -of which was sent to Holland," plainly insinuating that Huyghens was a -mere copyist.[161] These two accounts therefore serve to invalidate each -other's credibility. Tiraboschi[162] asserts that, at the time he wrote, -the mathematical professor at Pisa was in possession of the identical -clock constructed by Treffler under Vincenzo's directions; and quotes a -letter from Campani, to whom it was shown by Ferdinand, "old, rusty, and -unfinished as Galileo's son made it before 1649." Viviani on the other -hand says that Treffler constructed this same clock some time after -Vincenzo's death (which happened in 1649), on a different principle from -Vincenzo's ideas, although he says distinctly that he heard Galileo -describe an application of the pendulum to a clock similar to Huyghens' -contrivance. Campani did not actually see this clock till 1659, which -was three years after Huyghens' invention, so that perhaps Huyghens was -too easily satisfied when, on occasion of the answer which Ferdinand -sent to his complaints of the Memorie del Cimento he wrote to Bouillaud, -"I must however believe, since such a prince assures me, that Galileo -had this idea before me." - -There is another circumstance almost amounting to a proof that it was an -afterthought to attribute the merit of constructing the pendulum-clock -to Galileo, for on the reverse of a medal struck by Viviani, and -inscribed "to the memory of his excellent instructor,"[163] is a rude -exhibition of the principal objects to which Galileo's attention was -directed. The pendulum is represented simply by a weight attached to a -string hanging on the face of a rock. It is probable that, in a design -expressly intended to commemorate Galileo's inventions, Viviani would -have introduced the timekeeper in the most perfect form to which it had -been brought by him. Riccioli,[164] whose industry was unwearied in -collecting every fact and argument which related in any way to the -astronomical and mechanical knowledge and opinions of his time, -expressly recommends swinging a pendulum, or perpendicular as it was -often called (only a few years before Huyghens' publication), as much -more accurate _than any clock_.[165] Join to all these arguments -Huyghens' positive assertion, that if Galileo had conceived any such -idea, he at least was entirely ignorant of it,[166] and no doubt can -remain that the merit of the original invention (such as it was) rests -entirely with Huyghens. The step indeed seems simple enough for a less -genius than his: for the property of the pendulum was known, and the -conversion of a rotatory into a reciprocating motion was known; but the -connexion of the one with the other having been so long delayed, we must -suppose that difficulties existed where we are not now able to perceive -them, for Huyghens' improvement was received with universal admiration. - -There may be many who will consider the pendulum as undeserving so long -a discussion; who do not know or remember that the telescope itself has -hardly done more for the precision of astronomical observations than -this simple instrument, not to mention the invaluable convenience of an -uniform and accurate timekeeper in the daily intercourse of life. The -patience and industry of modern observers are often the theme of -well-merited praise, but we must look with a still higher degree of -wonder on such men as Tycho Brahe and his contemporaries, who were -driven by the want of any timekeeper on which they could depend to the -most laborious expedients, and who nevertheless persevered to the best -of their ability, undisgusted either by the tedium of such processes, or -by the discouraging consciousness of the necessary imperfection of their -most approved methods and instruments. - -The invariable regularity of the pendulum's motion was soon made -subservient to ulterior purposes beyond that of merely registering time. -We have seen the important assistance it afforded in establishing the -laws of motion; and when the theory founded on those laws was extended -and improved, the pendulum was again instrumental, by a species of -approximate reasoning familiar to all who are acquainted with physical -inquiries, in pointing out by its minute irregularities in different -parts of the earth, a corresponding change in the weight of all bodies -in those different situations, supposed to be the consequence of a -greater distance from the axis of the earth's rotation; since that would -occasion the force of attraction to be counterbalanced by an increased -centrifugal force. The theory which kept pace with the constantly -increasing accuracy of such observations, proving consistent in all -trials of it, has left little room for future doubts; and in this manner -the pendulum in intelligent hands became the simplest instrument for -ascertaining the form of the globe which we inhabit. An English -astronomer, who corresponded with Kepler under the signature of Brutius -(whose real name perhaps might be Bruce), had already declared his -belief in 1603, that "the earth on which we tread is neither round nor -globular, but more nearly of an oval figure."[167] There is nothing to -guide us to the grounds on which he formed this opinion, which was -perhaps only a lucky guess. Kepler's note upon it is: "This is not -altogether to be contemned." - -A farther use of the pendulum is in furnishing a general and unperishing -standard of measure. This application is suggested in the third volume -of the 'Reflections' of Mersenne, published in 1647, where he observes -that it may be best for the future not to divide time into hours, -minutes, and seconds, but to express its parts by the number of -vibrations of a pendulum of given length, swinging through a given arc. -It was soon seen that it would be more convenient to invert this -process, and to choose as an unit of length the pendulum which should -make a certain number of vibrations in the unit of time, naturally -determined by the revolution of the earth on its axis. Our Royal -Society took an active part in these experiments, which seem, -notwithstanding their utility, to have met from the first with much of -the same ridicule which was lavished upon them by the ignorant, when -recently repeated for the same purpose. "I contend," says Graunt[168] in -a dedication to the Royal Society, dated 1662, "against the envious -schismatics of your society (who think you do nothing unless you -presently transmute metals, make butter and cheese without milk, and, as -their own ballad hath it, make leather without hides), by asserting the -usefulness of even all your preparatory and luciferous experiments, -being not the ceremonies, but the substance and principles of useful -arts. For I find in trade the want of an universal measure, and have -heard musicians wrangle about the just and uniform keeping of time in -their consorts, and therefore cannot with patience hear that your -labours about vibrations, eminently conducing to both, should be -slighted, nor your pendula called swing-swangs with scorn."[169] - - -FOOTNOTES: - -[153] One of the Commissioners was the father of Blaise Pascal. - -[154] These instruments were very inferior to those now in use under the -same name. See "Treatise on Opt. Instrum." - -[155] Theoricæ Mediceorum Planetarum, Florentiæ, 1666. - -[156] Circulus affixus virgæ paletorum qui cum eâ de vi movetur. - -[157] Utriusque Cosmi Historia. Oppenhemii, 1617. - -[158] Huygenii Opera. Lugduni, 1724. - -[159] Mémoires de l'Academie, 1717. - -[160] See page 84. - -[161] De nova Temporis dimetiendi ratione. Londini, 1680. - -[162] Storia della Lett. Ital. - -[163] Museum Mazuchellianum, vol. ii. Tab. cvii. p. 29. - -[164] Almagestum Novum, vol. i. - -[165] Quovis horologio accuratius. - -[166] Clarorum Belgarum ad Ant. Magliabech. Epistolæ. Florence, 1745, -tom. i. p. 235. - -[167] Kepleri Epistolæ. - -[168] Natural and Political Observations. London, 1665. - -[169] See also Hudibras, Part II. Cant. III. - - They're guilty by their own confessions - Of felony, and at the Sessions - Upon the bench I will so handle 'em, - That the vibration of this pendulum - Shall make all taylors' yards of one - Unanimous opinion; - A thing he long has vaunted of, - But now shall make it out of proof. - -Hudibras was certainly written before 1663: ten years later Huyghens -speaks of the idea of so employing the pendulum as a common one. - - - - -CHAPTER XIX. - - _Character of Galileo--Miscellaneous details--his - Death--Conclusion._ - - -THE remaining years of Galileo's life were spent at Arcetri, where -indeed, even if the Inquisition had granted his liberty, his increasing -age and infirmities would probably have detained him. The rigid caution -with which he had been watched in Florence was in great measure relaxed, -and he was permitted to see the friends who crowded round him to express -their respect and sympathy. The Grand Duke visited him frequently, and -many distinguished strangers, such as Gassendi and Deodati, came into -Italy solely for the purpose of testifying their admiration of his -character. Among other visitors the name of Milton will be read with -interest: we may probably refer to the effects of this interview the -allusions to Galileo's discoveries, so frequently introduced into his -poem. Milton mentions in his 'Areopagitica,' that he saw Galileo whilst -in Italy, but enters into no details of his visit. - -Galileo was fond of society, and his cheerful and popular manners -rendered him an universal favourite among those who were admitted to his -intimacy. Among these, Viviani, who formed one of his family during the -three last years of his life, deserves particular notice, on account of -the strong attachment and almost filial veneration with which he ever -regarded his master and benefactor. His long life, which was prolonged -to the completion of his 81st year in 1703, enabled him to see the -triumphant establishment of the truths on account of which Galileo had -endured so many insults; and even in his old age, when in his turn he -had acquired a claim to the reverence of a younger generation, our Royal -Society, who invited him among them in 1696, felt that the complimentary -language in which they addressed him as the first mathematician of the -age would have been incomplete and unsatisfactory without an allusion to -the friendship that gained him the cherished title of "The last pupil of -Galileo."[170] - -Torricelli, another of Galileo's most celebrated followers, became a -member of his family in October, 1641: he first learned mathematics from -Castelli, and occasionally lectured for him at Rome, in which manner he -was employed when Galileo, who had seen his book 'On Motion,' and -augured the greatest success from such a beginning, invited him to his -house--an offer which Torricelli eagerly embraced, although he enjoyed -the advantages of it but for a short time. He afterwards succeeded -Galileo in his situation at the court of Florence,[171] but survived him -only a few years. - -It is from the accounts of Viviani and Gherardini that we principally -draw the following particulars of Galileo's person and character:--Signor -Galileo was of a cheerful and pleasant countenance, especially in his -old age, square built, and well proportioned in stature, and rather -above the middle size. His complexion was fair and sanguine, his eyes -brilliant, and his hair of a reddish cast. His constitution was -naturally strong, but worn out by fatigue of mind and body, so as -frequently to be reduced to a state of the utmost weakness. He was -subject to attacks of hypochondria, and often molested by severe and -dangerous illnesses, occasioned in great measure by his sleepless -nights, the whole of which he frequently spent in astronomical -observations. During upwards of forty-eight years of his life, he was -tormented with acute rheumatic pains, suffering particularly on any -change of weather. He found himself most free from these pains whilst -residing in the country, of which consequently he became very fond: -besides, he used to say that in the country he had greater freedom to -read the book of Nature, which lay there open before him. His library -was very small, but well chosen, and open to the use of the friends whom -he loved to see assembled round him, and whom he was accustomed to -receive in the most hospitable manner. He ate sparingly himself; but was -particularly choice in the selection of his wines, which in the latter -part of his life were regularly supplied out of the Grand Duke's -cellars. This taste gave an additional stimulus to his agricultural -pursuits, and many of his leisure hours were spent in the cultivation -and superintendence of his vineyards. It should seem that he was -considered a good judge of wine; for Viviani has preserved one of his -receipts in a collection of miscellaneous experiments. In it he strongly -recommends that for wine of the first quality, that juice only should be -employed, which is pressed out by the mere weight of the heaped grapes, -which would probably be that of the ripest fruit. The following letter, -written in his 74th year, is dated, "From my prison at Arcetri.--I am -forced to avail myself of your assistance and favour, agreeably to your -obliging offers, in consequence of the excessive chill of the weather, -and of old age, and from having drained out my grand stock of a hundred -bottles, which I laid in two years ago; not to mention some minor -particulars during the last two months, which I received from my Serene -Master, the Most Eminent Lord Cardinal, their Highnesses the Princes, -and the Most Excellent Duke of Guise, besides cleaning out two barrels -of the wine of this country. Now, I beg that with all due diligence and -industry, and with consideration, and taking counsel with the most -refined palates, you will provide me with two cases, that is to say, -with forty flasks of different wines, the most exquisite that you can -find: take no thought of the expense, because I stint myself so much in -all other pleasures that I can afford to lay out something at the -request of Bacchus, without giving offence to his two companions Ceres -and Venus. You must be careful to leave out neither Scillo nor Carino (I -believe they meant to call them Scylla and Charybdis), nor the country -of my master, Archimedes of Syracuse, nor Greek wines, nor clarets, &c. -&c. The expense I shall easily be able to satisfy, but not the infinite -obligation." - -In his expenditure Galileo observed a just mean between avarice and -profusion: he spared no cost necessary for the success of his many and -various experiments, and spent large sums in charity and hospitality, -and in assisting those in whom he discovered excellence in any art or -profession, many of whom he maintained in his own house. His temper was -easily ruffled, but still more easily pacified. He seldom conversed on -mathematical or philosophical topics except among his intimate friends; -and when such subjects were abruptly brought before him, as was often -the case by the numberless visitors he was in the habit of receiving, he -showed great readiness in turning the conversation into more popular -channels, in such manner however that he often contrived to introduce -something to satisfy the curiosity of the inquirers. His memory was -uncommonly tenacious, and stored with a vast variety of old songs and -stories, which he was in the constant habit of quoting and alluding to. -His favourite Italian authors were Ariosto, Petrarca, and Berni, great -part of whose poems he was able to repeat. His excessive admiration of -Ariosto determined the side which he took against Tasso in the virulent -and unnecessary controversy which has divided Italy so long on the -respective merits of these two great poets; and he was accustomed to say -that reading Tasso after Ariosto was like tasting cucumbers after -melons. When quite a youth, he wrote a great number of critical remarks -on Tasso's Gerusalemme Liberata, which one of his friends borrowed, and -forgot to return. For a long time it was thought that the manuscript had -perished, till the Abbé Serassi discovered it, whilst collecting -materials for his Life of Tasso, published at Rome in 1785. Serassi -being a violent partizan of Tasso, but also unwilling to lose the credit -of the discovery, copied the manuscript, but without any intention of -publishing it, "till he could find leisure for replying properly to the -sophistical and unfounded attacks of a critic so celebrated on other -accounts." He announced his discovery as having been made "in one of the -famous libraries at Rome," which vague indication he with some reason -considered insufficient to lead to a second discovery. On Serassi's -death his copy was found, containing a reference to the situation of the -original; the criticisms were published, and form the greatest part of -the last volume of the Milan edition of Galileo's works. The manuscript -was imperfect at the time of this second discovery, several leaves -having been torn out, it is not known by whom. - -The opinion of the most judicious Italian critics appears to be, that it -would have been more for Galileo's credit if these remarks had never -been made public: they are written in a spirit of flippant violence, -such as might not be extraordinary in a common juvenile critic, but -which it is painful to notice from the pen of Galileo. Two or three -sonnets are extant written by Galileo himself, and in two instances he -has not scrupled to appropriate the conceits of the poet he affected to -undervalue.[172] It should be mentioned that Galileo's matured taste -rather receded from the violence of his early prejudices, for at a later -period of his life he used to shun comparing the two; and when forced to -give an opinion he said, "that Tasso's appeared the finer poem, but that -Ariosto gave him the greater pleasure." Besides these sonnets, there is -extant a short burlesque poem written by him, "In abuse of Gowns," when, -on his first becoming Professor at Pisa, he found himself obliged by -custom to wear his professional habit in every company. It is written -not without humour, but does not bear comparison with Berni, whom he -imitated. - -There are several detached subjects treated of by Galileo, which may be -noticed in this place. A letter by him containing the solution of a -problem in Chances is probably the earliest notice extant of the -application of mathematics to that interesting subject: the -correspondence between Pascal and Fermat, with which its history is -generally made to begin, not having taken place till at least twelve -years later. There can be little doubt after the clear account of Carlo -Dati, that Galileo was the first to examine the curve called the -Cycloid, described by a point in the rim of a wheel rolling on a -straight line, which he recommended as a graceful form for the arch of a -bridge at Pisa. He even divined that the area contained between it and -its base is exactly three times that of the generating circle. He seems -to have been unable to verify this guess by strict geometrical -reasoning, for Viviani tells an odd story, that in order to satisfy his -doubts he cut out several large cycloids of pasteboard, but finding the -weight in every trial to be rather less than three times that of the -circle, he suspected the proportion to be irrational, and that there was -some error in his estimation; the inquiry he abandoned was afterwards -resumed with success by his pupil Torricelli.[173] - -The account which Lagalla gives of an experiment shown in his presence -by Galileo, carries the observation of the phosphorescence of the -Bologna stone at least as far back as 1612.[174] Other writers mention -the name of an alchymist, who according to them discovered it -accidentally in 1603. Cesi, Lagalla, and one or two others, had passed -the night at Galileo's house, with the intention of observing Venus and -Saturn; but, the night being cloudy, the conversation turned on other -matters, and especially on the nature of light, "on which Galileo took a -small wooden box at daybreak before sunrise, and showed us some small -stones in it, desiring us to observe that they were not in the least -degree luminous. Having then exposed them for some time to the twilight, -he shut the window again; and in the midst of the dark room showed us -the stones, shining and glistening with a faint light, which we saw -presently decay and become extinguished." In 1640, Liceti attempted to -refer the effect of the earthshine upon the moon to a similar -phosphorescent quality of that luminary, to which Galileo, then aged 76, -replied by a long and able letter, enforcing the true explanation he had -formerly given. - -Although quite blind, and nearly deaf, the intellectual powers of -Galileo remained to the end of his life; but he occasionally felt that -he was overworking himself, and used to complain to his friend Micanzio -that he found his head too busy for his body. "I cannot keep my restless -brain from grinding on, although with great loss of time; for whatever -idea comes into my head with respect to any novelty, drives out of it -whatever I had been thinking of just before." He was busily engaged in -considering the nature of the force of percussion, and Torricelli was -employed in arranging his investigations for a continuation of the -'Dialogues on Motion,' when he was seized with an attack of fever and -palpitation of the heart, which, after an illness of two months, put an -end to his long, laborious, and useful life, on the 8th of January, -1642, just one year before his great successor Newton was born. - -The malice of his enemies was scarcely allayed by his death. His right -of making a will was disputed, as having died a prisoner to the -Inquisition, as well as his right to burial in consecrated ground. These -were at last conceded, but Urban anxiously interfered to prevent the -design of erecting a monument to him in the church of Santa Croce, in -Florence, for which a large sum had been subscribed. His body was -accordingly buried in an obscure corner of the church, which for upwards -of thirty years after his death was unmarked even by an inscription to -his memory. It was not till a century later that the splendid monument -was erected which now covers his and Viviani's remains. When their -bodies were disinterred in 1737 for the purpose of being removed to -their new resting-place, Capponi, the president of the Florentine -Academy, in a spirit of spurious admiration, mutilated Galileo's body, -by removing the thumb and forefinger of the right-hand, and one of the -vertebræ of the back, which are still preserved in some of the Italian -museums. The monument was put up at the expense of his biographer, -Nelli, to whom Viviani's property descended, charged with the condition -of erecting it. Nor was this the only public testimony which Viviani -gave of his attachment. The medal which he struck in honour of Galileo -has already been mentioned; he also, as soon as it was safe to do so, -covered every side of the house in which he lived with laudatory -inscriptions to the same effect. A bust of Galileo was placed over the -door, and two bas-reliefs on each side representing some of his -principal discoveries. Not less than five other medals were struck in -honour of him during his residence at Padua and Florence, which are all -engraved in Venturi's Memoirs. - -There are several good portraits of Galileo extant, two of which, by -Titi and Subtermanns, are engraved in Nelli's Life of Galileo. Another -by Subtermanns is in the Florentine Gallery, and an engraving from a -copy of this is given by Venturi. There is also a very fine engraving -from the original picture. An engraving from another original picture is -in the frontispiece of the Padua edition of his works. Salusbury seems -in the following passage to describe a portrait of Galileo painted by -himself: "He did not contemn the other inferior arts, for he had a good -hand in sculpture and carving; but his particular care was to paint -well. By the pencil he described what his telescope discovered; in one -he exceeded art, in the other, nature. Osorius, the eloquent bishop of -Sylva, esteems one piece of Mendoza the wise Spanish minister's -felicity, to have been this, that he was contemporary to Titian, and -that by his hand he was drawn in a fair tablet. And Galilæus, lest he -should want the same good fortune, made so great a progress in this -curious art, that he became his own _Buonarota_; and because there was -no other copy worthy of his pencil, drew himself." No other author makes -the slightest allusion to such a painting; and it appears more likely -that Salusbury should be mistaken than that so interesting a portrait -should have been entirely lost sight of. - -Galileo's house at Arcetri was standing in 1821, when Venturi visited -it, and found it in the same state in which Galileo might be supposed to -have left it. It is situated nearly a mile from Florence, on the -south-eastern side, and about a gun-shot to the north-west of the -convent of St. Matthew. Nelli placed a suitable inscription over the -door of the house, which belonged in 1821 to a Signor Alimari.[175] - -Although Nelli's Life of Galileo disappointed the expectations that had -been formed of it, it is impossible for any admirer of Galileo not to -feel the greatest degree of gratitude towards him, for the successful -activity with which he rescued so many records of the illustrious -philosopher from destruction. After Galileo's death, the principal part -of his books, manuscripts, and instruments, were put into the charge of -Viviani, who was himself at that time an object of great suspicion; most -of them he thought it prudent to conceal, till the superstitious -outcries against Galileo should be silenced. At Viviani's death, he left -his library, containing a very complete collection of the works of all -the mathematicians who had preceded him (and amongst them those of -Galileo, Torricelli, and Castelli, all which were enriched with notes -and additions by himself), to the hospital of St. Mary at Florence, -where an extensive library already existed. The directors of the -hospital sold this unique collection in 1781, when it became entirely -dispersed. The manuscripts in Viviani's possession passed to his nephew, -the Abbé Panzanini, together with the portraits of the chief personages -of the Galilean school, Galileo's instruments, and, among other -curiosities, the emerald ring which he wore as a member of the Lyncean -Academy. A great number of these books and manuscripts were purchased at -different times by Nelli, after the death of Panzanini, from his -relations, who were ignorant or regardless of their value. One of his -chief acquisitions was made by an extraordinary accident, related by -Tozzetti with the following details, which we repeat, as they seem to -authenticate the story:--"In the spring of 1739, the famous Doctor Lami -went out according to his custom to breakfast with some of his friends -at the inn of the Bridge, by the starting-place; and as he and Sig. -Nelli were passing through the market, it occurred to them to buy some -Bologna sausages from the pork-butcher, Cioci, who was supposed to excel -in making them. They went into the shop, had their sausages cut off and -rolled in paper, which Nelli put into his hat. On reaching the inn, and -calling for a plate to put them in, Nelli observed that the paper in -which they had been rolled was one of Galileo's letters. He cleaned it -as well as he could with his napkin, and put it into his pocket without -saying a word to Lami; and as soon as he returned into the city, and -could get clear of him, he flew to the shop of Cioci, who told him that -a servant whom he did not know brought him from time to time similar -letters, which he bought by weight as waste paper. Nelli bought all that -remained, and on the servant's next reappearance in a few days, he -learned the quarter whence they came, and after some time succeeded at a -small expense in getting into his own possession an old corn-chest, -containing all that still remained of the precious treasures which -Viviani had concealed in it ninety years before."[176] - -The earliest biographical notice of Galileo is that in the Obituary of -the Mercurio Italico, published at Venice in 1647, by Vittorio Siri. It -is very short, but contains an exact enumeration of his principal works -and discoveries. Rossi, who wrote under the name of Janus Nicius -Erythræus, introduced an account of Galileo in his Pinacotheca Imaginum -Illustrium, in which the story of his illegitimacy first made its -appearance. In 1664, Salusbury published a life of Galileo in the second -volume of his Mathematical Collections, the greater part of which is a -translation of Galileo's principal works. Almost the whole edition of -the second volume of Salusbury's book was burnt in the great fire of -London. Chauffepié says that only one copy is known to be extant in -England: this is now in the well-known library of the Earl of -Macclesfield, to whose kindness the author is much indebted for the use -he has been allowed to make of this unique volume. A fragment of this -second volume is in the Bodleian Library at Oxford. The translations in -the preceding pages are mostly founded upon Salusbury's version. -Salusbury's account, although that of an enthusiastic admirer of -Galileo, is too prolix to be interesting: the general style of the -performance may be guessed from the title of the first chapter--'Of Man -in general, and how he excelleth all the other Animals.' After informing -his readers that Galileo was born at Pisa, he proceeds:--"Italy is -affirmed to have been the first that peopled the world after the -universal deluge, being governed by Janus, Cameses, and Saturn, &c." His -description of Galileo's childhood is somewhat quaint. "Before others -had left making of dirt pyes, he was framing of diagrams; and whilst -others were whipping of toppes, he was considering the cause of their -motion." It is on the whole tolerably correct, especially if we take -into account that Salusbury had not yet seen Viviani's Life, though -composed some years earlier. - -The Life of Galileo by Viviani was first written as an outline of an -intended larger work, but this latter was never completed. This sketch -was published in the Memoirs of the Florentine Academy, of which Galileo -had been one of the annual presidents, and afterwards prefixed to the -complete editions of Galileo's works; it is written in a very agreeable -and flowing style, and has been the groundwork of most subsequent -accounts. Another original memoir by Niccolò Gherardini, was published -by Tozzetti. A great number of references to authors who have treated of -Galileo is given by Sach in his Onomasticon. An approved Latin memoir by -Brenna is in the first volume of Fabroni's Vitæ Italorum Illustrium; he -has however fallen into several errors: this same work contains the -lives of several of his principal followers. - -The article in Chauffepié's Continuation of Bayle's Dictionary does not -contain anything which is not in the earlier accounts. - -Andrès wrote an essay entitled 'Saggio sulla Filosofia del Galileo,' -published at Mantua 1776; and Jagemann published his 'Geschichte des -Leben des Galileo' at Leipzig, in 1787;[177] neither of these the author -has been able to meet with. An analysis of the latter may be seen in -Kästner's 'Geschichte der Mathematik, Göttingen, 1800,' from which it -does not appear to contain any additional details. The 'Elogio del -Galileo' by Paolo Frisi, first published at Leghorn in 1775, is, as its -title expresses, rather in the nature of a panegyric than of a -continuous biographical account. It is written with very great elegance -and intimate knowledge of the subjects of which it treats. Nelli gave -several curious particulars with respect to Galileo in his 'Saggio di -Storia Letteraria Fiorentina, Lucca, 1759;' and in 1793 published his -large work entitled 'Vita e Commercio Letterario di Galileo Galilei.' So -uninteresting a book was probably never written from such excellent -materials. Two thick quarto volumes are filled with repetitions of the -accounts that were already in print, the bulky preparation of which -compelled the author to forego the publication of the vast collection of -original documents which his unwearied zeal and industry had collected. -This defect has been in great measure supplied by Venturi in 1818 and -1821, who has not only incorporated in his work many of Nelli's -manuscripts, but has brought together a number of scattered notices of -Galileo and his writings from a variety of outlying sources--a service -which the writer is able to appreciate from having gone through the -greatest part of the same labour before he was fortunate enough to meet -with Venturi's book. Still there are many letters cited by Nelli, which -do not appear either in his book or Venturi's. Carlo Dati, in 1663, -quotes "the registers of Galileo's correspondence arranged in -alphabetical order, in ten large volumes."[178] The writer has no means -of ascertaining what collection this may have been; it is difficult to -suppose that one so arranged should have been lost sight of. It is -understood that a life of Galileo is preparing at this moment in -Florence, by desire of the present Grand Duke, which will probably throw -much additional light on the character and merits of this great and -useful philosopher. - -The first editions of his various treatises, as mentioned by Nelli, are -given below. Clement, in his 'Bibliothèque Curieuse,' has pointed out -such among them, and the many others which have been printed, as have -become rare. - -The Florentine edition is the one used by the Academia della Crusca for -their references; for which reason its paging is marked in the margin of -the edition of Padua, which is much more complete, and is the one which -has been on the present occasion principally consulted. - -The latter contains the Dialogue on the System, which was not suffered -to be printed in the former editions. The twelve first volumes of the -last edition of Milan are a mere transcript of that of Padua: the -thirteenth contains in addition the Letter to the Grand Duchess, the -Commentary on Tasso, with some minor pieces. A complete edition is still -wanted, embodying all the recently discovered documents, and omitting -the verbose commentaries, which, however useful when they were written, -now convey little information that cannot be more agreeably and more -profitably learned in treatises of a later date. - -Such was the life, and such were the pursuits, of this extraordinary -man. The numberless inventions of his acute industry; the use of the -telescope, and the brilliant discoveries to which it led; the patient -investigation of the laws of weight and motion; must all be looked upon -as forming but a part of his real merits, as merely particular -demonstrations of the spirit in which he everywhere withstood the -despotism of ignorance, and appealed boldly from traditional opinions to -the judgments of reason and common sense. He claimed and bequeathed to -us the right of exercising our faculties in examining the beautiful -creation which surrounds us. Idolized by his friends, he deserved their -affection by numberless acts of kindness; by his good humour, his -affability, and by the benevolent generosity with which he devoted -himself and a great part of his limited income to advance their talents -and fortunes. If an intense desire of being useful is everywhere worthy -of honour; if its value is immeasurably increased, when united to genius -of the highest order; if we feel for one who, notwithstanding such -titles to regard, is harassed by cruel persecution,--then none deserve -our sympathy, our admiration, and our gratitude, more than Galileo. - - -_List of Galileo's Works._ - - Le Operazioni del Compasso Geom. e Milit. - Padova, 1606. - Fol. Difesa di Gal. Galilei contr. all. cal. et impost. di Bald. Capra - Venezza, 1607. 4to. - Sydereus Nuncius Venetiis, 1610. 4to. - Discorso int. alle cose che stanno in su l'Acqua - Firenze, 1612. 4to. - Novantiqua SS. PP. Doctrina de S. Scripturæ Testimoniis - Argent, 1612. 4to. - Istoria e Demostr. int. alle Macchie Solari - Roma, 1613. 4to. - Risp. alle oppos. del S. Lod. delle Colombe e del S. Vinc. di Grazia - Firenze, 1615. 4to. - Discorso delle Comete di Mario Guiducci - Firenze, 1619. 4to. - Dialogo sopra i due Massimi Sistemi del Mondo - Firenze, 1632. 4to. - Discorso e Demostr. intorno alle due nuove Scienze - Leida, 1638. 4to. - Della Scienza Meccanica Ravenna, 1649. 4to. - Trattato della Sfera Roma, 1655. 4to. - Discorso sopra il Flusso e Reflusso. (Scienze Fisiche di Tozzetti.) - Firenze, 1780. 4to. - Considerazioni sul Tasso Roma, 1793. - Trattato della Fortificazione. (Memorie di Venturi.) - Modena, 1818. 4to. - -The editions of his collected works (in which is contained much that was -never published separately) are-- - - Opere di Gal. Galilei, Linc. Nob. Fior. &c. - Bologna, 1656. 2 vols. 4to. - Opere di Gal. Galilei, Nob. Fior. Accad. Linc. &c. - Firenze, 1718. 3 vols. 4to. - Opere di Gal. Galilei Padova, 1744. 4 vols. 4to. - Opere di Gal. Galilei Milano, 1811. 13 vols. 8vo. - - -CORRECTIONS. - - _Page Co. Line._ - - 5 1 2, - _Add_: His instructor was the celebrated botanist, Andreas - Cæsalpinus, who was professor of medicine at Pisa from 1567 to 1592. - Hist. Acad. Pisan.; Pisis, 1791. - - 8 2 18, - _Add_: According to Kästner, his German name was Wursteisen. - - 8 2 21, _for_ 1588 _read_ 1586. - 15 1 57, _for_ 1632 _read_ 1630. - 17 1 29, - Salusbury alludes to the instrument described and figured in "The - Use of the Sector, Crosse Staffe, and other Instruments. London, - 1624." It is exactly Galileo's Compass. - - 17 1 52, _for_ Burg, a German, _read_ Burgi, a Swiss. - 27 2 17, - The author here called Brutti was an Englishman: his real name, - perhaps, was Bruce. See p. 99. - - 50 1 14, - Kepler's Epitome was not published till 1619: it was then inserted - in the Index. - - 73 1 60, _for_ under _read_ turned from. - 80 2 44, _for_ any _read_ an indefinitely small. - - -FOOTNOTES: - -[170] The words of his diploma are: Galilæi in mathematicis disciplinis -discipulus, in ærumnis socius, Italicum ingenium ita perpolivit optimis -artibus ut inter mathematicos sæculi nostri facile princeps per orbem -litterarium numeretur.--Tiraboschi. - -[171] On this occasion the taste of the time showed itself in the -following anagram:-- - - Evangelista Torricellieus, - En virescit Galilæus alter. - -[172] Compare Son. ii. v. 8 & 9; and Son. iii. v. 2 & 3, with Ger. Lib. -c. iv. st. 76, and c. vii. st. 19.--The author gladly owns his -obligation for these remarks to the kindness of Sig. Panizzi, Professor -of Italian in the University of London. - -[173] Lettera di Timauro Antiate. Firenze, 1663. - -[174] De phænomenis in orbe Lunæ. Venetiis, 1612. - -[175] Venturi. - -[176] Notizie sul Ingrandimento delle Scienze Fisiche. Firenze, 1780. - -[177] Venturi. - -[178] Lettera di Timauro Antiate. - - - - -LIFE OF KEPLER. - - - - -CHAPTER I. - - _Introduction--Birth and Education of Kepler--He is appointed - Astronomical Professor at Gratz--Publishes the 'Mysterium - Cosmographicum.'_ - - -IN the account of the life and discoveries of Galileo, we have -endeavoured to inculcate the safety and fruitfulness of the method -followed by that great reformer in his search after physical truth. As -his success furnishes the best instance of the value of the inductive -process, so the failures and blunders of his adversaries supply equally -good examples of the dangers and the barrenness of the opposite course. -The history of JOHN KEPLER might, at the first view, suggest conclusions -somewhat inconsistent with this remark. Every one who is but moderately -acquainted with astronomy is familiar with the discoveries which that -science owes to him; the manner in which he made them is, perhaps, not -so generally known. This extraordinary man pursued, almost invariably, -the hypothetical method. His life was passed in speculating on the -results of a few principles assumed by him, from very precarious -analogies, as the causes of the phenomena actually observed in Nature. -We nevertheless find that he did, in spite of this unphilosophical -method, arrive at discoveries which have served as guides to some of the -most valuable truths of modern science. - -The difficulty will disappear if we attend more closely to the details -of Kepler's investigations. We shall perceive that to an unusual degree -of rashness in the formation of his systems, he added a quality very -rarely possessed by philosophers of the hypothetical school. One of the -greatest intellectual vices of the latter was a wilful blindness to the -discrepancy of facts from their creed, a perverse and obstinate -resistance to physical evidence, leading not unfrequently to an attempt -at disguising the truth. From this besetting sin of the school, which -from an intellectual fault often degenerated into a moral one, Kepler -was absolutely free. Scheme after scheme, resting originally upon little -beyond his own glowing imagination, but examined and endeared by the -ceaseless labour of years, was unhesitatingly sacrificed, as soon as its -insufficiency became indisputable, to make room for others as little -deserving support. The history of philosophy affords no more remarkable -instance of sincere uncompromising love of truth. To this virtue he owed -his great discoveries: it must be attributed to his unhappy method that -he made no more. - -In considering this opinion upon the real nature of Kepler's title to -fame, it ought not to be forgotten that he has exposed himself at a -disadvantage on which certainly very few philosophers would venture. His -singular candour allowed him to comment upon his own errors with the -same freedom as if scrutinizing the work of a stranger; careless whether -the impression on his readers were favourable or otherwise to himself, -provided it was instructive. Few writers have spoken so much, and so -freely of themselves, as Kepler. He records, on almost every occasion, -the train of thought by which he was led to each of the discoveries that -eventually repaid his perseverance; and he has thus given us a most -curious and interesting view of the workings of a mind of great, though -eccentric power. "In what follows," says he (when introducing a long -string of suppositions, of which he had already discovered the fallacy), -"let the reader pardon my credulity, whilst working out all these -matters by my own ingenuity. For it is my opinion that the occasions by -which men have acquired a knowledge of celestial phenomena are not less -admirable than the discoveries themselves." Agreeing altogether with -this opinion in its widest application, we have not scrupled, in the -following sketch, to introduce at some length an account even of -Kepler's erroneous speculations; they are in themselves very amusing, -and will have the additional utility of proving the dangerous tendency -of his method; they will show by how many absurd theories, and how many -years of wasted labour, his real discoveries and services to science lie -surrounded. - -JOHN KEPLER was born (as we are assured by his earliest biographer -Hantsch) in long. 29° 7´, lat. 48° 54´, on the 21st day of December, -1571. On this spot stands the imperial city of Weil, in the duchy of -Wirtemberg. His parents were Henry Kepler and Catherine Guldenmann, both -of noble, though decayed families. Henry Kepler, at the time of his -marriage, was a petty officer in the Duke of Wirtemberg's service; and a -few years after the birth of his eldest son John, he joined the army -then serving in the Netherlands. His wife followed him, leaving their -son, then in his fifth year, at Leonberg, under the care of his -grandfather. He was a seven months child, very weak and sickly; and -after recovering with difficulty from a severe attack of small-pox, he -was sent to school in 1577. Henry Kepler's limited income was still -farther reduced on his return into Germany, the following year, in -consequence of the absconding of one of his acquaintance, for whom he -had incautiously become surety. His circumstances were so much narrowed -by this misfortune, that he was obliged to sell his house, and nearly -all that he possessed, and for several years he supported his family by -keeping a tavern at Elmendingen. This occasioned great interruption to -young Kepler's education; he was taken from school, and employed in -menial services till his twelfth year, when he was again placed in the -school at Elmendingen. In the following year he was again seized with a -violent illness, so that his life was almost despaired of. In 1586, he -was admitted into the monastic school of Maulbronn, where the cost of -his education was defrayed by the Duke of Wirtemberg. This school was -one of those established on the suppression of the monasteries at the -Reformation, and the usual course of education followed there required -that the students, after remaining a year in the superior classes, -should offer themselves for examination at the college of Tubingen for -the degree of bachelor: they then returned to their school with the -title of veterans; and after completing the studies taught there, they -were admitted as resident students at Tubingen, proceeded in about a -year to the degree of master, and were then allowed to commence their -course of theology. The three years of Kepler's life following his -admission to Maulbronn, were marked by periodical returns of several of -the disorders which had well nigh proved fatal to him in his childhood. -During the same time disagreements arose between his parents, in -consequence of which his father quitted his home, and soon after died -abroad. After his father's departure, his mother also quarrelled with -her relations, having been treated, says Hantsch, "with a degree of -barbarity by her husband and brother-in-law that was hardly exceeded -even by her own perverseness:" one of his brothers died, and the -family-affairs were in the greatest confusion. Notwithstanding these -disadvantages, Kepler took his degree of master in August 1591, -attaining the second place in the annual examination. The first name on -the list was John Hippolytus Brentius. - -Whilst he was thus engaged at Tubingen, the astronomical lectureship at -Gratz, the chief town of Styria, became vacant by the death of George -Stadt, and the situation was offered to Kepler. Of this first occasion -of turning his thoughts towards astronomy, he has himself given the -following account: "As soon as I was of an age to feel the charms of -philosophy, I embraced every part of it with intense desire, but paid no -especial regard to astronomy. I had indeed capacity enough for it, and -learned without difficulty the geometrical and astronomical theorems -occurring in the usual course of the school, being well grounded in -figures, numbers, and proportions. But those were compulsory -studies--there was nothing to show a particular turn for astronomy. I -was educated at the expense of the Duke of Wirtemberg, and when I saw -such of my companions as the duke selected to send abroad shrink in -various ways from their employments, out of fondness for home, I, who -was more callous, had early made up my mind to go with the utmost -readiness whithersoever I might be sent. The first offering itself was -an astronomical post, which I was in fact forced to accept by the -authority of my tutors; not that I was alarmed, in the manner I had -condemned in others, by the remoteness of the situation, but by the -unexpected and contemptible nature of the office, and by the slightness -of my information in this branch of philosophy. I entered on it, -therefore, better furnished with talent than knowledge: with many -protestations that I was not abandoning my claim to be provided for in -some other more brilliant profession. What progress I made in the first -two years of my studies, may be seen in my 'Mysterium Cosmographicum;' -and the encouragement given me by my tutor, Mästlin, to take up the -science of astronomy, may be read in the same book, and in his letter -which is prefixed to the 'Narrative of Rheticus.' I looked on that -discovery as of the highest importance, and still more so, because I saw -how greatly it was approved by Mästlin." - -The nature of the singular work to which Kepler thus refers with so much -complacency, will be best shown by quoting some of the most remarkable -parts of it, and especially the preface, in which he briefly details -some of the theories he successively examined and rejected, before -detecting (as he imagined he had here done) the true cause of the number -and order of the heavenly bodies. The other branches of philosophy with -which he occupied himself in his younger years, were those treated by -Scaliger in his 'Exoteric Exercises,' to the study of which book Kepler -attributed the formation of many of his opinions; and he tells us that -he devoted much time "to the examination of the nature of heaven, of -souls, of genii, of the elements, of the essence of fire, of the cause -of fountains, the ebb and flow of the tide, the shape of the continents, -and inland seas, and things of this sort." He also says, that by his -first success with the heavens, his hopes were greatly inflamed of -discovering similar analogies in the rest of the visible world, and for -this reason, named his book merely a Prodromus, or Forerunner, meaning, -at some future period, to subjoin the Aftercomer, or Sequel. But this -intention was never fulfilled; either his imagination failed him, or, -what is more likely, the laborious calculations in which his -astronomical theories engaged him, left him little time for turning his -attention to objects unconnected with his first pursuit. - -It is seldom that we are admitted to trace the progress of thought in -those who have distinguished themselves by talent and originality; and -although the whole of the following speculations begin and end in error, -yet they are so characteristic, and exhibit such an extraordinary -picture of the extravagances into which Kepler's lively imagination was -continually hurrying him, that we cannot refrain from citing nearly the -whole preface. From it, better than from any enumeration of -peculiarities, the reader will at once apprehend the nature of his -disposition. - -"When I was attending the celebrated Mästlin, six years ago, at -Tubingen, I was disturbed by the manifold inconveniences of the common -theory of the universe, and so delighted with Copernicus, whom Mästlin -was frequently in the habit of quoting with great respect, that I not -only often defended his propositions in the physical disputations of the -candidates, but also wrote a correct essay on the primary motion, -maintaining, that it is caused by the rotation of the earth. And I was -then at that point that I attributed to the earth the motion of the sun -on physical (or, if you will, on metaphysical) grounds, as Copernicus -had done for mathematical reasons. And, by this practice, I came by -degrees, partly from Mästlin's instructions, and partly from my own -efforts, to understand the superior mathematical convenience of the -system of Copernicus beyond Ptolemy's. This labour might have been -spared me, by Joachim Rheticus, who has shortly and clearly explained -everything in his first Narrative. While incidentally engaged in these -labours, in the intermission of my theology, it happened conveniently -that I succeeded George Stadt in his situation at Gratz, where the -nature of my office connected me more closely with these studies. -Everything I had learned from Mästlin, or had acquired of myself, was -there of great service to me in explaining the first elements of -astronomy. And, as in Virgil, '_Fama mobilitate viget, viresque acquirit -eundo_,' so it was with me, that the diligent thought on these things -was the occasion of still further thinking: until, at last, in the year -1595, when I had some intermission of my lectures allowed me, I brooded -with the whole energy of my mind on this subject. There were three -things in particular, of which I pertinaciously sought the causes why -they are not other than they are: the number, the size, and the motion -of the orbits. I attempted the thing at first with numbers, and -considered whether one of the orbits might be double, triple, quadruple, -or any other multiple of the others, and how much, according to -Copernicus, each differed from the rest. I spent a great deal of time in -that labour, as if it were mere sport, but could find no equality either -in the proportions or the differences, and I gained nothing from this -beyond imprinting deeply in my memory the distances as assigned by -Copernicus; unless, perhaps, reader, this record of my various attempts -may force your assent, backwards and forwards, as the waves of the sea; -until tired at length, you will willingly repose yourself, as in a safe -haven, on the reasons explained in this book. However, I was comforted -in some degree, and my hopes of success were supported as well by other -reasons which will follow presently, as by observing that the motions in -every case seemed to be connected with the distances, and that where -there was a great gap between the orbits, there was the same between the -motions. And I reasoned, that if God had adapted motions to the orbits -in some relation to the distances, it was probable that he had also -arrayed the distances themselves in relation to something else. - -"Finding no success by this method, I tried another, of singular -audacity. I inserted a new planet between Mars and Jupiter, and another -between Venus and Mercury, both of which I supposed invisible, perhaps -on account of their smallness, and I attributed to each a certain period -of revolution.[179] I thought that I could thus contrive some equality -of proportions, increasing between every two, from the sun to the fixed -stars. For instance, the Earth is nearer Venus in parts of the -terrestrial orbit, than Mars is to the Earth in parts of the orbit of -Mars. But not even the interposition of a new planet sufficed for the -enormous gap between Mars and Jupiter; for the proportion of Jupiter to -the new planet was still greater than that of Saturn to Jupiter. And -although, by this supposition, I got some sort of a proportion, yet -there was no reasonable conclusion, no certain determination of the -number of the planets either towards the fixed stars, till we should get -as far as them, nor ever towards the Sun, because the division in this -proportion of the residuary space within Mercury might be continued -without end. Nor could I form any conjecture, from the mobility of -particular numbers, why, among an infinite number, so few should be -moveable. The opinion advanced by Rheticus in his Narrative is -improbable, where he reasons from the sanctity of the number six to the -number of the six moveable heavens; for he who is inquiring of the frame -of the world itself, must not derive reasons from these numbers, which -have gained importance from things of later date. - -"I sought again, in another way, whether the distance of every planet is -not as the residuum of a sine; and its motion as the residuum of the -sine of the complement in the same quadrant. - -[Illustration] - -"Conceive the square AB to be constructed, whose side AC is equal to the -semidiameter of the universe. From the angle B opposite to A the place -of the sun, or centre of the world, describe the quadrant DC with the -radius BC. Then in AC, the true radius of the world, let the sun, fixed -stars, and planets be marked at their respective distances, and from -these points draw lines parallel to BC, meeting the quadrant. I imagined -the moving force acting on each of the planets to be in the proportion -of these parallels. In the line of the sun is infinity, because AD is -touched, and not cut, by the quadrant: therefore the moving force is -infinite in the sun, as deriving no motion except from its own act. In -Mercury the infinite line is cut off at K, and therefore at this point -the motion is comparable with the others. In the fixed stars the line is -altogether lost, and compressed into a mere point C; therefore at that -point there is no moving force. This was the theorem, which was to be -tried by calculation; but if any one will reflect that two things were -wanting to me, first, that I did not know the size of the _Sinus Totus_, -that is, the radius of the proposed quadrant; secondly, that the -energies of the motions were not thus expressed otherwise than in -relation one to another; whoever, I say, well considers this, will -doubt, not without reason, as to the progress I was likely to make in -this difficult course. And yet, with unremitting labour, and an infinite -reciprocation of sines and arcs, I did get so far as to be convinced -that this theory could not hold. - -"Almost the whole summer was lost in these annoying labours; at last, by -a trifling accident, I lighted more nearly on the truth. I looked on it -as an interposition of Providence, that I should obtain by chance, what -I had failed to discover with my utmost exertions; and I believed this -the more, because I prayed constantly that I might succeed, if -Copernicus had really spoken the truth. It happened on the 9th or -19th[180] day of July, in the year 1595, that, having occasion to show, -in my lecture-room, the passages of the great conjunctions through eight -signs, and how they pass gradually from one trine aspect to another, I -inscribed in a circle a great number of triangles, or quasi-triangles, -so that the end of one was made the beginning of another. In this manner -a smaller circle was shadowed out by the points in which the lines -crossed each other. - -[Illustration: A Scheme of the great Conjunctions of SATURN & JUPITER, -their leaps through eight Signs, and their passages through all the four -Triplicities of the Zodiac.] - -"The radius of a circle inscribed in a triangle is half the radius of -that described about it; therefore the proportion between these two -circles struck the eye as almost identical with that between Saturn and -Jupiter, and the triangle is the first figure, just as Saturn and -Jupiter are the first planets. On the spot I tried the second distance -between Jupiter and Mars with a square, the third with a pentagon, the -fourth with a hexagon. And as the eye again cried out against the second -distance between Jupiter and Mars, I combined the square with a triangle -and a pentagon. There would be no end of mentioning every trial. The -failure of this fruitless attempt was the beginning of the last -fortunate one; for I reflected, that in this way I should never reach -the sun, if I wished to observe the same rule throughout; nor should I -have any reason why there were six, rather than twenty or a hundred -moveable orbits. And yet figures pleased me, as being quantities, and as -having existed before the heavens; for quantity was created with matter, -and the heavens afterwards. But if (this was the current of my -thoughts), in relation to the quantity and proportion of the six orbits, -as Copernicus has determined them among the infinite other figures, five -only could be found having peculiar properties above the rest, my -business would be done. And then again it struck me, what have plane -figures to do among solid orbits? Solid bodies ought rather to be -introduced. This, reader, is the invention and the whole substance of -this little work; for if any one, though but moderately skilled in -geometry, should hear these words hinted, the five regular solids will -directly occur to him with the proportions of their circumscribed and -inscribed spheres: he has immediately before his eyes that scholium of -Euclid to the 18th proposition of his 13th Book, in which it is proved -to be impossible that there should be, or be imagined, more than five -regular bodies. - -"What is worthy of admiration (since I had then no proof of any -prerogatives of the bodies with regard to their order) is, that -employing a conjecture which was far from being subtle, derived from the -distances of the planets, I should at once attain my end so happily in -arranging them, that I was not able to change anything afterwards with -the utmost exercise of my reasoning powers. In memory of the event, I -write down here for you the sentence, just as it fell from me, and in -the words in which it was that moment conceived:--The Earth is the -circle, the measurer of all; round it describe a dodecahedron, the -circle including this will be Mars. Round Mars describe a tetrahedron, -the circle including this will be Jupiter. Describe a cube round -Jupiter, the circle including this will be Saturn. Now, inscribe in the -Earth an icosahedron, the circle inscribed in it will be Venus. Inscribe -an octahedron in Venus, the circle inscribed in it will be Mercury. This -is the reason of the number of the planets. - -[Illustration] - -"This was the cause, and such the success, of my labour: now read my -propositions in this book. The intense pleasure I have received from -this discovery never can be told in words. I regretted no more the time -wasted; I tired of no labour; I shunned no toll of reckoning; days and -nights I spent in calculations; until I could see whether this opinion -would agree with the orbits of Copernicus, or whether my joy was to -vanish into air. I willingly subjoin that sentiment of Archytas, as -given by Cicero: 'If I could mount up into heaven, and thoroughly -perceive the nature of the world, and beauty of the stars, that -admiration would be without a charm for me, unless I had some one like -you, reader, candid, attentive, and eager for knowledge, to whom to -describe it.' If you acknowledge this feeling, and are candid, you will -refrain from blame, such as not without cause I anticipate; but if, -leaving that to itself, you fear lest these things be not ascertained, -and that I have shouted triumph before victory, at least approach these -pages, and learn the matter in consideration: you will not find, as just -now, new and unknown planets interposed; that boldness of mine is not -approved, but those old ones very little loosened, and so furnished by -the interposition (however absurd you may think it) of rectilinear -figures, that in future you may give a reason to the rustics when they -ask for the hooks which keep the skies from falling.--Farewell." - -In the third chapter Kepler mentions, that a thickness must be allowed -to each orb sufficient to include the greatest and least distance of -the planet from the sun. The form and result of his comparison with the -real distances are as follows:-- - - Book V. - If the {Saturn } be taken {Jupiter = 577} {635 Ch. 9 - inner {Jupiter} at 1000 {Mars = 333} According to {333--14 - Surface {Mars } then the {Earth = 795} Copernicus {757--19 - of the {Earth } outer {Venus = 795} they are {794--21, 22 - orbit of {Venus } one of {Mercury = 577} {723--27 - -It will be observed, that Kepler's results were far from being entirely -satisfactory; but he seems to have flattered himself, that the -differences might be attributed to erroneous measurements. Indeed, the -science of observation was then so much in its infancy, that such an -assertion might be made without incurring much risk of decisive -refutation. - -Kepler next endeavoured to determine why the regular solids followed in -this rather than any other order; and his imagination soon created a -variety of essential distinctions between the cube, pyramid, and -dodecahedron, belonging to the superior planets, and the other two. - -The next question examined in the book, is the reason why the zodiac is -divided into 360 degrees; and on this subject, he soon becomes enveloped -in a variety of subtle considerations, (not very intelligible in the -original, and still more difficult to explain shortly to others -unacquainted with it,) in relation to the divisions of the musical -scale; the origin of which he identifies with his five favourite solids. -The twentieth chapter is appropriated to a more interesting inquiry, -containing the first traces of his finally successful researches into -the proportion between the distances of the planets, and the times of -their motions round the sun. He begins with the generally admitted fact, -that the more distant planets move more slowly; but in order to show -that the proportion, whatever it may be, is not the simple one of the -distances, he exhibits the following little Table:-- - - [Saturn] - +---------+--------+ - | |D. Scr. |[Jupiter] - +---------+--------+---------+ - |[Saturn] |10759.12| D. Scr. |[Mars] - +---------+--------+---------+--------+ - |[Jupiter]| 6159 | 4332.37 |D. Scr. |[Earth] - +---------+--------+---------+--------+-------+ - |[Mars] | 1785 | 1282 | 686.59 |D. Scr.|[Venus] - +---------+--------+---------+--------+-------+-------+ - |[Earth] | 1174 | 843 | 452 |365.15 |D. Scr.| [Mercury] - +---------+--------+---------+--------+-------+-------+----------+ - |[Venus] | 844 | 606 | 325 |262.30 |224.42 | D. Scr. | - +---------+--------+---------+--------+-------+-------+----------+ - |[Mercury]| 434 | 312 | 167 |135 |115 | 87.58 | - -At the head of each vertical column is placed the real time (in days and -sexagesimal parts) of the revolution of the planet placed above it, and -underneath the days due to the other inferior planets, if they observed -the proportion of distance. Hence it appears that this proportion in -every case gives a time greater than the truth; as for instance, if the -earth's rate of revolution were to Jupiter's in the proportion of their -distances, the second column shows that the time of her period would be -843 instead of 365¼ days; so of the rest. His next attempt was to -compare them by two by two, in which he found that he arrived at a -proportion something like the proportion of the distances, although as -yet far from obtaining it exactly. This process amounts to taking the -quotients obtained by dividing the period of each planet by the period -of the one next beyond. - - { [Saturn] 10759.27} be successively { [Jupiter] 403 - For if { [Jupiter] 4332.37} taken to consist of { [Mars] 159 - each { } 1000 equal parts, { - of the { [Mars] 686.59} the periods of { [Earth] 532 - periods { [Earth] 365.15} the planet next { [Venus] 615 - of { } below will contain { - { [Venus] 244.42} of those parts in { [Mercury] 392 - - But if the distance of each planet in {[Jupiter] 572 - succession be taken to consist of {[Mars] 290 - 1000 equal parts, the distance of {[Earth] 658 - the next below will contain, according {[Venus] 719 - to Copernicus, in {[Mercury] 500 - -From this table he argued that to make the proportions agree, we must -assume one of two things, "either that the moving intelligences of the -planets are weakest in those which are farthest from the Sun, or that -there is one moving intelligence in the Sun, the common centre forcing -them all round, but those most violently which are nearest, and that it -languishes in some sort, and grows weaker at the most distant, because -of the remoteness and the attenuation of the virtue." - -We stop here to insert a note added by Kepler to the later editions, and -shall take advantage of the same interruption to warn the reader not to -confound this notion of Kepler with the theory of a gravitating force -towards the Sun, in the sense in which we now use those words. According -to our theory, the effect of the presence of the Sun upon the planet is -to pull it towards the centre in a straight line, and the effect of the -motion thus produced combined with the motion of the planet, which if -undisturbed would be in a straight line inclined to the direction of the -radius, is, that it describes a curve round the Sun. Kepler considered -his planets as perfectly quiet and unwilling to move when left alone; -and that this virtue supposed by him to proceed in every direction out -of the Sun, swept them round, just as the sails of a windmill would -carry round anything which became entangled in them. In other parts of -his works Kepler mentions having speculated on a real attractive force -in the centre; but as he knew that the planets are not always at the -same distance from the Sun, and conceived erroneously, that to remove -them from their least to their greatest distance a repulsive force must -be supposed alternating with an attractive one, he laid aside this -notion as improbable. In a note he acknowledges that when he wrote the -passage just quoted, imbued as he then was with Scaliger's notions on -moving intelligences, he literally believed "that each planet was moved -by a living spirit, but afterwards came to look on the moving cause as a -corporeal though immaterial substance, something in the nature of light -which is observed to diminish similarly at increased distances." He then -proceeds as follows in the original text. - -"Let us then assume, as is very probable, that motion is dispensed by -the sun in the same manner as light. The proportion in which light -emanating from a centre is diminished, is taught by optical writers: for -there is the same quantity of light, or of the solar rays, in the small -circles as in the large; and therefore, as it is more condensed in the -former, more attenuated in the latter, a measure of the attenuation may -be derived from the proportion of the circles themselves, both in the -case of light and of the moving virtue. Therefore, by how much the orbit -of Venus is greater than that of Mercury, in the same proportion will -the motion of the latter be stronger, or more hurried, or more swift, or -more powerful, or by whatever other word you like to express the fact, -than that of the former. But a larger orbit would require a -proportionably longer time of revolution, even though the moving force -were the same. Hence it follows that the one cause of a greater distance -of the planet from the Sun, produces a double effect in increasing the -period, and conversely the increase of the periods will be double the -difference of the distances. Therefore, half the increment added to the -shorter period ought to give the true proportion of the distances, so -that the sum should represent the distance of the superior planet, on -the same scale on which the shorter period represents the distance of -the interior one. For instance, the period of Mercury is nearly 88 days; -that of Venus is 224-2/3, the difference is 136-2/3: half of this is -68-1/3, which, added to 88, gives 156-1/3. The mean distance of Venus -ought, therefore, to be, in proportion to that of Mercury, as 156-1/3 to -88. If this be done with all the planets, we get the following results, -taking successively, as before, the distance of each planet at 1000. - - The distance in } [Jupiter] 574 But according { 572 - parts of which } [Mars] 274 to Copernicus { 290 - the distance of } [Earth] 694 they are { 658 - the next superior } [Venus] 762 respectively { 719 - planet contains } { - 1000, is at } [Mercury] 563 { 500 - -As you see, we have now got nearer the truth." - -Finding that this theory of the rate of diminution would not bring him -quite close to the result he desired to find, Kepler immediately -imagined another. This latter occasioned him a great deal of perplexity, -and affords another of the frequently recurring instances of the waste -of time and ingenuity occasioned by his impetuous and precipitate -temperament. Assuming the distance of any planet, as for instance of -Mars, to be the unit of space, and the virtue at that distance to be the -unit of force, he supposed that as many particles as the virtue at the -Earth gained upon that of Mars, so many particles of distance did the -Earth lose. He endeavoured to determine the respective positions of the -planets upon this theory, by the rules of false position, but was much -astonished at finding the same exactly as on his former hypothesis. The -fact was, as he himself discovered, although not until after several -years, that he had become confused in his calculation; and when half -through the process, had retraced his steps so as of course to arrive -again at the numbers from which he started, and which he had taken from -his former results. This was the real secret of the identity of the two -methods; and if, when he had taken the distance of Mars at 1000, instead -of assuming the distance of the earth at 694, as he did, he had taken -any other number, and operated upon it in the same manner, he would -have had the same reason for relying on the accuracy of his supposition. -As it was, the result utterly confounded him; and he was obliged to -leave it with the remark, that "the two theories are thus proved to be -the same in fact, and only different in form; although how that can -possibly be, I have never to this day been able to understand."--His -perplexity was very reasonable; they are by no means the same; it was -only his method of juggling with the figures which seemed to connect -them. - -Notwithstanding all its faults, the genius and unwearied perseverance -displayed by Kepler in this book, immediately ranked him among -astronomers of the first class; and he received the most flattering -encomiums from many of the most celebrated; among others, from Galileo -and Tycho Brahe, whose opinion he invited upon his performance. Galileo -contented himself with praising in general terms the ingenuity and good -faith which appeared so conspicuously in it. Tycho Brahe entered into a -more detailed criticism of the work, and, as Kepler shrewdly remarked, -showed how highly he thought of it by advising him to try to adapt -something of the same kind to the Tychonic system. Kepler also sent a -copy of his book to the imperial astronomer, Raimar, with a -complimentary letter, in which he exalted him above all other -astronomers of the age. Raimar had surreptitiously acquired a notion of -Tycho Brahe's theory, and published it as his own; and Tycho, in his -letter, complained of Kepler's extravagant flattery. This drew a long -apologetical reply from Kepler, in which he attributed the admiration he -had expressed of Raimar to his own want of information at that time, -having since met with many things in Euclid and Regiomontanus, which he -then believed original in Raimar. With this explanation, Tycho professed -himself perfectly satisfied. - - -FOOTNOTES: - -[179] The following scrupulous note added by Kepler in 1621 to a -subsequent edition of this work, deserves to be quoted. It shows how -entirely superior he was to the paltriness of attempting to appropriate -the discoveries of others, of which many of his contemporaries had -exhibited instances even on slighter pretences than this passage might -have afforded him. The note is as follows: "Not circulating round -Jupiter like the Medicæan stars. Be not deceived. I never had them in my -thoughts, but, like the other primary planets, including the sun in the -centre of the system within their orbits." - -[180] This inconvenient mode of dating was necessary before the new or -Gregorian style was universally adopted. - - - - -CHAPTER II. - - _Kepler's Marriage--He joins Tycho Brahe at Prague--Is appointed - Imperial Mathematician--Treatise on the New Star._ - - -THE publication of this extraordinary book, early as it occurs in the -history of Kepler's life, was yet preceded by his marriage. He had -contemplated this step so early as 1592; but that suit having been -broken off, he paid his addresses, in 1596, to Barbara Muller von -Muhleckh. This lady was already a widow for the second time, although -two years younger than Kepler himself. On occasion of this alliance he -was required to prove the nobility of his family, and the delay -consequent upon the inquiry postponed the marriage till the following -year. He soon became involved in difficulties in consequence of this -inconsiderate engagement: his wife's fortune was less than he had been -led to expect, and he became embroiled on that account with her -relations. Still more serious inconvenience resulted to him from the -troubled state in which the province of Styria was at that time, arising -out of the disputes in Bohemia and the two great religious parties into -which the empire was now divided, the one headed by Rodolph, the feeble -minded emperor,--the other by Matthias, his ambitious and enterprising -brother. - -In the year following his marriage, he thought it prudent, on account of -some opinions he had unadvisedly promulgated, (of what nature does not -very distinctly appear,) to withdraw himself from Gratz into Hungary. -Thence he transmitted several short treatises to his friend Zehentmaier, -at Tubingen--"On the Magnet," "On the Cause of the Obliquity of the -Ecliptic," and "On the Divine Wisdom, as shown in the Creation." Little -is known of these works beyond the notice taken of them in Zehentmaier's -answers. Kepler has himself told us, that his magnetic philosophy was -built upon the investigations of Gilbert, of whom he always justly spoke -with the greatest respect. - -About the same time a more violent persecution had driven Tycho Brahe -from his observatory of Uraniburg, in the little island of Hueen, at the -entrance of the Baltic. This had been bestowed on him by the munificence -of Frederick I. of Denmark, who liberally furnished him with every means -of prosecuting his astronomical observations. After Frederick's death, -Tycho found himself unable to withstand the party which had constantly -opposed him, and was forced, at a great loss and much inconvenience, to -quit his favourite island. On the invitation of the emperor, Rudolph -II., he then betook himself, after a short stay at Hamburg, to the -castle of Benach, near Prague, which was assigned to him with an annual -pension of three thousand florins, a truly munificent provision in those -times and that country. - -Kepler had been eager to see Tycho Brahe since the latter had intimated -that his observations had led him to a more accurate determination of -the excentricities of the orbits of the planets. By help of this, Kepler -hoped that his theory might be made to accord more nearly with the -truth; and on learning that Tycho was in Bohemia, he immediately set out -to visit him, and arrived at Prague in January, 1600. From thence he -wrote a second letter to Tycho, not having received the answer to his -former apology, again excusing himself for the part he had appeared to -take with Raimar against him. Tycho replied immediately in the kindest -manner, and begged he would repair to him directly:--"Come not as a -stranger, but as a very welcome friend; come and share in my -observations with such instruments as I have with me, and as a dearly -beloved associate." During his stay of three or four months at Benach, -it was settled that Tycho should apply to the emperor, to procure him -the situation of assistant in the observatory. Kepler then returned to -Gratz, having previously received an intimation, that he might do so in -safety. The plan, as it had been arranged between them was, that a -letter should be procured from the emperor to the states of Styria, -requesting that Kepler might join Tycho Brahe for two years, and retain -his salary during that time: a hundred florins were to be added annually -by the emperor, on account of the greater dearness of living at Prague. -But before everything was concluded, Kepler finally threw up his -situation at Gratz, in consequence of new dissensions. Fearing that this -would utterly put an end to his hopes of connecting himself with Tycho, -he determined to revive his claims on the patronage of the Duke of -Wirtemberg. With this view he entered into correspondence with Mästlin -and some of his other friends at Tubingen, intending to prosecute his -medical studies, and offer himself for the professorship of medicine in -that university. He was dissuaded from this scheme by the pressing -instances of Tycho, who undertook to exert himself in procuring a -permanent settlement for him from the emperor, and assured him, even if -that attempt should fail, that the language he had used when formerly -inviting him to visit him at Hamburg, should not be forgotten. In -consequence of this encouragement, Kepler abandoned his former scheme, -and travelled again with his wife to Prague. He was detained a long time -on the road by violent illness, and his money became entirely exhausted. -On this he wrote complainingly to Tycho, that he was unable without -assistance to travel even the short distance which still separated them, -far less to await much longer the fulfilment of the promises held out to -him. - -By his subsequent admissions, it appears that for a considerable time he -lived entirely on Tycho's bounty, and by way of return, he wrote an -essay against Raimar, and against a Scotchman named Liddell, professor -at Rostoch and Helmstadt, who, like Raimar, had appropriated to himself -the credit of the Tychonic system. Kepler never adopted this theory, and -indeed, as the question merely regarded priority of invention, there -could be no occasion, in the discussion, for an examination of its -principles. - -This was followed by a transaction, not much to Kepler's credit, who in -the course of the following year, and during a second absence from -Prague, fancied that he had some reason to complain of Tycho's -behaviour, and wrote him a violent letter, filled with reproaches and -insults. Tycho appears to have behaved in this affair with great -moderation: professing to be himself occupied with the marriage of his -daughter, he gave the care of replying to Kepler's charges, to Ericksen, -one of his assistants, who, in a very kind and temperate letter, pointed -out to him the ingratitude of his behaviour, and the groundlessness of -his dissatisfaction. His principal complaint seems to have been, that -Tycho had not sufficiently supplied his wife with money during his -absence. Ericksen's letter produced an immediate and entire change in -Kepler's temper, and it is only from the humble recantation which he -instantaneously offered that we learn the extent of his previous -violence. "Most noble Tycho," these are the words of his letter, "how -shall I enumerate or rightly estimate your benefits conferred on me! For -two months you have liberally and gratuitously maintained me, and my -whole family; you have provided for all my wishes; you have done me -every possible kindness; you have communicated to me everything you hold -most dear; no one, by word or deed, has intentionally injured me in -anything: in short, not to your children, your wife, or yourself have -you shown more indulgence than to me. This being so, as I am anxious to -put upon record, I cannot reflect without consternation that I should -have been so given up by God to my own intemperance, as to shut my eyes -on all these benefits; that, instead of modest and respectful gratitude, -I should indulge for three weeks in continual moroseness towards all -your family, in headlong passion, and the utmost insolence towards -yourself, who possess so many claims on my veneration from your noble -family, your extraordinary learning, and distinguished reputation. -Whatever I have said or written against the person, the fame, the -honour, and the learning of your excellency; or whatever, in any other -way, I have injuriously spoken or written, (if they admit no other more -favourable interpretation,) as to my grief I have spoken and written -many things, and more than I can remember; all and everything I recant, -and freely and honestly declare and profess to be groundless, false, and -incapable of proof." Hoffmann, the president of the states of Styria, -who had taken Kepler to Prague on his first visit, exerted himself to -perfect the reconciliation, and this hasty quarrel was entirely passed -over. - -On Kepler's return to Prague, in September, 1601, he was presented to -the Emperor by Tycho, and honoured with the title of Imperial -Mathematician, on condition of assisting Tycho in his calculations. -Kepler desired nothing more than this condition, since Tycho was at that -time probably the only person in the world who possessed observations -sufficient for the reform which he now began to meditate in the theory -of astronomy. Rudolph appears to have valued both Tycho Brahe and Kepler -as astrologers rather than astronomers; but although unable to -appreciate rightly the importance of the task they undertook, of -compiling a new set of astronomical tables founded upon Tycho's -observations, yet his vanity was flattered with the prospect of his name -being connected with such a work, and he made liberal promises to defray -the expense of the new Rudolphine Tables. Tycho's principal assistant at -this time was Longomontanus, who altered his name to this form, -according to the prevalent fashion of giving to every name a Latin -termination. Lomborg or Longbierg was the name, not of his family, but -of the village in Denmark, where he was born, just as Müller was seldom -called by any other name than Regiomontanus, from his native town -Königsberg, as George Joachim Rheticus was so surnamed from Rhetia, the -country of the Grisons, and as Kepler himself was sometimes called -Leonmontanus, from Leonberg, where he passed his infancy. It was agreed -between Longomontanus and Kepler, that in discussing Tycho's -observations, the former should apply himself especially to the Moon, -and the latter to Mars, on which planet, owing to its favourable -position, Tycho was then particularly engaged. The nature of these -labours will be explained when we come to speak of the celebrated book -"On the Motions of Mars." - -This arrangement was disturbed by the return of Longomontanus into -Denmark, where he had been offered an astronomical professorship, and -still more by the sudden death of Tycho Brahe himself in the following -October. Kepler attended him during his illness, and after his death -undertook to arrange some of his writings. But, in consequence of a -misunderstanding between him and Tycho's family, the manuscripts were -taken out of his hands; and when, soon afterwards, the book appeared, -Kepler complained heavily that they had published, without his consent -or knowledge, the notes and interlineations added by him for his own -private guidance whilst preparing it for publication. - -On Tycho's death, Kepler succeeded him as principal mathematician to the -emperor; but although he was thus nominally provided with a liberal -salary, it was almost always in arrear. The pecuniary embarrassments in -which he constantly found himself involved, drove him to the resource of -gaining a livelihood by casting nativities. His peculiar temperament -rendered him not averse from such speculations, and he enjoyed -considerable reputation in this line, and received ample remuneration -for his predictions. But although he did not scruple, when consulted, to -avail himself in this manner of the credulity of his contemporaries, he -passed over few occasions in his works of protesting against the -futility of this particular genethliac astrology. His own astrological -creed was in a different strain, more singular, but not less -extravagant. We shall defer entering into any details concerning it, -till we come to treat of his book on Harmonics, in which he has -collected and recapitulated the substance of his scattered opinions on -this strange subject. - -His next works deserving notice are those published on occasion of the -new star which shone out with great splendour in 1604, in the -constellation Cassiopeia.[181] Immediately on its appearance, Kepler -wrote a short account of it in German, marked with all the oddity which -characterises most of his productions. We shall see enough of his -astronomical calculations when we come to his book on Mars; the -following passage will probably be found more amusing. - -After comparing this star with that of 1572, and mentioning that many -persons who had seen it maintained this to be the brighter of the two, -since it was nearly twice the size of its nearest neighbour, Jupiter, he -proceeds as follows:--"Yonder one chose for its appearance a time no way -remarkable, and came into the world quite unexpectedly, like an enemy -storming a town, and breaking into the market-place before the citizens -are aware of his approach; but ours has come exactly in the year of -which astrologers have written so much about the fiery trigon that -happens in it;[182] just in the month in which (according to Cyprian) -Mars comes up to a very perfect conjunction with the other two superior -planets; just in the day when Mars has joined Jupiter, and just in the -place where this conjunction has taken place. Therefore the apparition -of this star is not like a secret hostile irruption, as was that one of -1572, but the spectacle of a public triumph, or the entry of a mighty -potentate; when the couriers ride in some time before, to prepare his -lodgings, and the crowd of young urchins begin to think the time -over-long to wait: then roll in, one after another, the ammunition, and -money, and baggage waggons, and presently the trampling of horse, and -the rush of people from every side to the streets and windows; and when -the crowd have gazed with their jaws all agape at the troops of knights; -then at last, the trumpeters, and archers, and lackeys, so distinguish -the person of the monarch, that there is no occasion to point him out, -but every one cries out of his own accord--'Here we have him!'--What it -may portend is hard to determine, and thus much only is certain, that it -comes to tell mankind either nothing at all, or high and weighty news, -quite beyond human sense and understanding. It will have an important -influence on political and social relations; not indeed by its own -nature, but, as it were, accidentally through the disposition of -mankind. First, it portends to the booksellers great disturbances, and -tolerable gains; for almost every _Theologus_, _Philosophicus_, -_Medicus_, and _Mathematicus_, or whoever else, having no laborious -occupation intrusted to him, seeks his pleasure _in studiis_, will make -particular remarks upon it, and will wish to bring these remarks to the -light. Just so will others, learned and unlearned, wish to know its -meaning, and they will buy the authors who profess to tell them. I -mention these things merely by way of example, because, although thus -much can be easily predicted without great skill, yet may it happen just -as easily, and in the same manner, that the vulgar, or whoever else is -of easy faith, or it may be, crazy, may wish to exalt himself into a -great prophet; or it may even happen that some powerful lord, who has -good foundation and beginning of great dignities, will be cheered on by -this phenomenon to venture on some new scheme, just as if God had set up -this star in the darkness merely to enlighten them." - -It would hardly be supposed, from the tenor of this last passage, that -the writer of it was not a determined enemy to astrological predictions -of every description. In 1602 he had published a disputation, not now -easily met with, "On the Principles of Astrology," in which it seems -that he treated the professed astrologers with great severity. The -essence of this book is probably contained in the second treatise on the -new star, which he published in 1606.[183] In this volume he inveighs -repeatedly against the vanity and worthlessness of ordinary astrology, -declaring at the same time, that the professors of that art know that -this judgment is pronounced by one well acquainted with its principles. -"For if the vulgar are to pronounce who is the best astrologer, my -reputation is known to be of the highest order; if they prefer the -judgment of the learned, they are already condemned. Whether they stand -with me in the eyes of the populace, or I fall with them before the -learned, in both cases I am in their ranks; I am on a level with them; I -cannot be renounced." - -The theory which Kepler proposed to substitute is intimated shortly in -the following passage: "I maintain that the colours and aspects, and -conjunctions of the planets, are impressed on the natures or faculties -of sublunary things, and when they occur, that these are excited as well -in forming as in moving the body over whose motion they preside. Now let -no one conceive a prejudice that I am anxiously seeking to mend the -deplorable and hopeless cause of astrology by far-fetched subtilties and -miserable quibbling. I do not value it sufficiently, nor have I ever -shunned having astrologers for my enemies. But a most unfailing -experience (as far as can be hoped in natural phenomena) of the -excitement of sublunary natures by the conjunctions and aspects of the -planets, has instructed and compelled my unwilling belief." - -After exhausting other topics suggested by this new star, he examines -the different opinions on the cause of its appearance. Among others he -mentions the Epicurean notion, that it was a fortuitous concourse of -atoms, whose appearance in this form was merely one of the infinite -number of ways in which, since the beginning of time, they have been -combined. Having descanted for some time on this opinion, and declared -himself altogether hostile to it, Kepler proceeds as follows:--"When I -was a youth, with plenty of idle time on my hands, I was much taken with -the vanity, of which some grown men are not ashamed, of making anagrams, -by transposing the letters of my name, written in Greek, so as to make -another sentence: out of [Iôannês Keplêros] I made [Seirênôn -kapêlos];[184] in Latin, out of _Joannes Keplerus_ came _Serpens in -akuleo_.[185] But not being satisfied with the meaning of these words, -and being unable to make another, I trusted the thing to chance, and -taking out of a pack of playing cards as many as there were letters in -the name, I wrote one upon each, and then began to shuffle them, and at -each shuffle to read them in the order they came, to see if any meaning -came of it. Now, may all the Epicurean gods and goddesses confound this -same chance, which, although I spent a good deal of time over it, never -showed me anything like sense even from a distance.[186] So I gave up my -cards to the Epicurean eternity, to be carried away into infinity, and, -it is said, they are still flying about there, in the utmost confusion -among the atoms, and have never yet come to any meaning. I will tell -these disputants, my opponents, not my own opinion, but my wife's. -Yesterday, when weary with writing, and my mind quite dusty with -considering these atoms, I was called to supper, and a salad I had asked -for was set before me. It seems then, said I aloud, that if pewter -dishes, leaves of lettuce, grains of salt, drops of water, vinegar, and -oil, and slices of egg, had been flying about in the air from all -eternity, it might at last happen by chance that there would come a -salad. Yes, says my wife, but not so nice and well dressed as this of -mine is." - - -FOOTNOTES: - -[181] See Life of Galileo, p. 16. - -[182] The fiery trigon occurs about once in every 800 years, when -Saturn, Jupiter, and Mars are in the three fiery signs, Aries, Leo, and -Sagittarius. - -[183] The copy of this work in the British Museum is Kepler's -presentation copy to our James I. On the blank leaf, opposite the -title-page, is the following inscription, apparently in the author's -hand-writing:--"Regi philosophanti, philosophus serviens, Platoni -Diogenes, Britannias tenenti, Pragæ stipem mendicans ab Alexandro, e -dolio conductitio, hoc suum philosophema misit et commendavit." - -[184] The tapster of the Sirens. - -[185] A serpent in his sting. - -[186] In one of his anonymous writings Kepler has anagrammatized his -name, _Joannes Keplerus_, in a variety of other forms, probably selected -from the luckiest of his shuffles:--"_Kleopas Herennius, Helenor -Kapuensis, Raspinus Enkeleo, Kanones Pueriles._" - - - - -CHAPTER III. - - _Kepler publishes his Supplement to Vitellion--Theory of - Refraction._ - - -DURING several years Kepler remained, as he himself forcibly expressed -it, begging his bread from the emperor at Prague, and the splendour of -his nominal income served only to increase his irritation, at the real -neglect under which he nevertheless persevered in his labours. His -family was increasing, and he had little wherewith to support them -beyond the uncertain proceeds of his writings and nativities. His salary -was charged partly on the states of Silesia, partly on the imperial -treasury; but it was in vain that repeated orders were procured for the -payment of the arrears due to him. The resources of the empire were -drained by the constant demands of an engrossing war, and Kepler had not -sufficient influence to enforce his claims against those who thought -even the smallest sum bestowed upon him ill spent, in fostering -profitless speculations. In consequence of this niggardliness, Kepler -was forced to postpone the publication of the Rudolphine Tables, which -he was engaged in constructing from his own and Tycho Brahe's -observations, and applied himself to other works of a less costly -description. Among these may be mentioned a "Treatise on Comets," -written on occasion of one which appeared in 1607: in this he suggests -that they are planets moving in straight lines. The book published in -1604, which he entitles "A Supplement to Vitellion," may be considered -as containing the first reasonable and consistent theory of optics, -especially in that branch of it usually termed dioptrics, which relates -to the theory of vision through transparent substances. In it was first -explained the true use of the different parts of the eye, to the -knowledge of which Baptista Porta had already approached very nearly, -though he stopped short of the accurate truth. Kepler remarked the -identity of the mechanism in the eye with that beautiful invention of -Porta's, the camera obscura; showing, that the light which falls from -external objects on the eye is refracted through a transparent -substance, called, from its form and composition, the crystalline lens, -and makes a picture on the fine net-work of nerves, called the retina, -which lies at the back of the eye. The manner in which the existence of -this coloured picture on the retina causes to the individual the -sensation of sight, belongs to a theory not purely physical; and beyond -this point Kepler did not attempt to go. - -The direction into which rays of light (as they are usually called) are -bent or refracted in passing through the air and other transparent -substances or mediums, is discussed in this treatise at great length. -Tycho Brahe had been the first astronomer who recognized the necessity -of making some allowance on this account in the observed heights of the -stars. A long controversy arose on this subject between Tycho Brahe and -Rothman, the astronomer at Hesse Cassel, a man of unquestionable talent, -but of odd and eccentric habits. Neither was altogether in the right, -although Tycho had the advantage in the argument. He failed however to -establish the true law of refraction, and Kepler has devoted a chapter -to an examination of the same question. It is marked by precisely the -same qualities as those appearing so conspicuously in his astronomical -writings:--great ingenuity; wonderful perseverance; bad philosophy. That -this may not be taken solely upon assertion, some samples of it are -subjoined. The writings of the authors of this period are little read or -known at the present day; and it is only by copious extracts that any -accurate notion can be formed of the nature and value of their labours. -The following tedious specimen of Kepler's mode of examining physical -phenomena is advisedly selected to contrast with his astronomical -researches: though the luck and consequently the fame that attended his -divination were widely different on the two occasions, the method -pursued was the same. After commenting on the points of difference -between Rothman and Tycho Brahe, Kepler proceeds to enumerate his own -endeavours to discover the law of refraction. - -"I did not leave untried whether, by assuming a horizontal refraction -according to the density of the medium, the rest would correspond with -the sines of the distances from the vertical direction, but calculation -proved that it was not so: and indeed there was no occasion to have -tried it, for thus the refractions would increase according to the same -law in all mediums, which is contradicted by experiment. - -"The same kind of objection may be brought against the cause of -refraction alleged by Alhazen and Vitellion. They say that the light -seeks to be compensated for the loss sustained at the oblique impact; so -that in proportion as it is enfeebled by striking against the denser -medium, in the same degree does it restore its energy by approaching the -perpendicular, that it may strike the bottom of the denser medium with -greater force; for those impacts are most forcible which are direct. And -they add some subtle notions, I know not what, how the motion of -obliquely incident light is compounded of a motion perpendicular and a -motion parallel to the dense surface, and that this compound motion is -not destroyed, but only retarded by meeting the denser medium. - -[Illustration] - -"I tried another way of measuring the refraction, which should include -the density of the medium and the incidence: for, since a denser medium -is the cause of refraction, it seems to be the same thing as if we were -to prolong the depth of the medium in which the rays are refracted into -as much space as would be filled by the denser medium under the force of -the rarer one. - -"Let A be the place of the light, BC the surface of the denser medium, -DE its bottom. Let AB, AG, AF be rays falling obliquely, which would -arrive at D, I, H, if the medium were uniform. But because it is denser, -suppose the bottom to be depressed to KL, determined by this that there -is as much of the denser matter contained in the space DC as of the -rarer in LC: and thus, on the sinking of the whole bottom DE, the points -D, I, H, E will descend vertically to L, M, N, K. Join the points BL, -GM, FN, cutting DE in O, P, Q; the refracted rays will be ABO, AGP, -AFQ."--"This method is refuted by experiment; it gives the refractions -near the perpendicular AC too great in respect of those near the -horizon. Whoever has leisure may verify this, either by calculation or -compasses. It may be added that the reasoning itself is not very -sure-footed, and, whilst seeking to measure other things, scarcely takes -in and comprehends itself." This reflection must not be mistaken for the -dawn of suspicion that his examination of philosophical questions began -not altogether at the right end: it is merely an acknowledgment that he -had not yet contrived a theory with which he was quite satisfied before -it was disproved by experiment. - -After some experience of Kepler's miraculous good fortune in seizing -truths across the wildest and most absurd theories, it is not easy to -keep clear of the opposite feeling of surprise whenever any of his -extravagancies fail to discover to him some beautiful law of nature. But -we must follow him as he plunges deeper in this unsuccessful inquiry; -and the reader must remember, in order fully to appreciate this method -of philosophizing, that it is almost certain that Kepler laboured upon -every one of the gratuitous suppositions that he makes, until positive -experiment satisfied him of their incorrectness. - -"I go on to other methods. Since density is clearly connected with the -cause of the refractions, and refraction itself seems a kind of -compression of light, as it were, towards the perpendicular, it occurred -to me to examine whether there was the same proportion between the -mediums in respect of density and the parts of the bottom illuminated by -the light, when let into a vessel, first empty, and afterwards filled -with water. This mode branches out into many: for the proportion may be -imagined, either in the straight lines, as if one should say that the -line EQ, illuminated by refraction, is to EH illuminated directly, as -the density of the one medium is to that of the other--Or another may -suppose the proportion to be between FC and FH--Or it may be conceived -to exist among surfaces, or so that some power of EQ should be to some -power of EH in this proportion, or the circles or similar figures -described on them. In this manner the proportion of EQ to EP would be -double that of EH to EI--Or the proportion may be conceived existing -among the solidities of the pyramidal frustums FHEC, FQEC--Or, since the -proportion of the mediums involves a threefold consideration, since they -have density in length, breadth, and thickness, I proceeded also to -examine the cubic proportions among the lines EQ, EH. - -"I also considered other lines. From any of the points of refraction as -G, let a perpendicular GY be dropped upon the bottom. It may become a -question whether possibly the triangle IGY, that is, the base IY, is -divided by the refracted ray GP, in the proportion of the densities of -the mediums. - -"I have put all these methods here together, because the same remark -disproves them all. For, in whatever manner, whether as line, plane, or -pyramid, EI observes a given proportion to EP, or the abbreviated line -YI to YP, namely, the proportion of the mediums, it is sure that EI, the -tangent of the distance of the point A from the vertex, will become -infinite, and will, therefore make EP or YP, also infinite. Therefore, -IGP, the angle of refraction, will be entirely lost; and, as it -approaches the horizon, will gradually become less and less, which is -contrary to experiment. - -"I tried again whether the images are equally removed from their points -of refraction, and whether the ratio of the densities measures the least -distance. For instance, supposing E to be the image, C the surface of -the water, K the bottom, and CE to CK in the proportion of the densities -of the mediums. Now, let F, G, B, be three other points of refraction -and images at S, T, V, and let CE be equal to FS, GT, and BV. But -according to this rule an image E would still be somewhat raised in the -perpendicular AK, which is contrary to experiment, not to mention other -contradictions. Thirdly, whether the proportion of the mediums holds -between FH and FX, supposing H to be the place of the image? Not at all. -For so, CE would be in the same proportion to CK, so that the height of -the image would always be the same, which we have just refuted. -Fourthly, whether the raising of the image at E is to the raising at H, -as CE to FH? Not in the least; for so the images either would never -begin to be raised, or, having once begun, would at last be infinitely -raised, because FH at last becomes infinite. Fifthly, whether the images -rise in proportion to the sines of the inclinations? Not at all; for so -the proportion of ascent would be the same in all mediums. Sixthly, are -then the images raised at first, and in perpendicular radiation, -according to the proportion of the mediums, and do they subsequently -rise more and more according to the sines of the inclinations? For so -the proportion would be compound, and would become different in -different mediums. There is nothing in it: for the calculation disagreed -with experiment. And generally it is in vain to have regard to the image -or the place of the image, for that very reason, that it is imaginary. -For there is no connexion between the density of the medium or any real -quality or refraction of the light, and an accident of vision, by an -error of which the image happens. - -"Up to this point, therefore, I had followed a nearly blind mode of -inquiry, and had trusted to good fortune; but now I opened the other -eye, and hit upon a sure method, for I pondered the fact, that the image -of a thing seen under water approaches closely to the true ratio of the -refraction, and almost measures it; that it is low if the thing is -viewed directly from above; that by degrees it rises as the eye passes -towards the horizon of the water. Yet, on the other hand, the reason -alleged above, proves that the measure is not to be sought in the image, -because the image is not a thing actually existing, but arises from a -deception of vision which is purely accidental. By a comparison of these -conflicting arguments, it occurred to me at length, to seek the causes -themselves of the existence of the image under water, and in these -causes the measure of the refractions. This opinion was strengthened in -me by seeing that opticians had not rightly pointed out the cause of the -image which appears both in mirrors and in water. And this was the -origin of that labour which I undertook in the third chapter. Nor, -indeed, was that labour trifling, whilst hunting down false opinions of -all sorts among the principles, in a matter rendered so intricate by the -false traditions of optical writers; whilst striking out half a dozen -different paths, and beginning anew the whole business. How often did it -happen that a rash confidence made me look upon that which I sought with -such ardour, as at length discovered! - -"At length I cut this worse than Gordian knot of catoptrics by analogy -alone, by considering what happens in mirrors, and what must happen -analogically in water. In mirrors, the image appears at a distance from -the real place of the object, not being itself material, but produced -solely by reflection at the polished surface. Whence it followed in -water also, that the images rise and approach the surface, not according -to the law of the greater or less density in the water, as the view is -less or more oblique, but solely because of the refraction of the ray of -light passing from the object to the eye. On which assumption, it is -plain that every attempt I had hitherto made to measure refractions by -the image, and its elevation, must fall to the ground. And this became -more evident when I discovered the true reason why the image is in the -same perpendicular line with the object both in mirrors and in dense -mediums. When I had succeeded thus far by analogy in this most difficult -investigation, as to the place of the image, I began to follow out the -analogy further, led on by the strong desire of measuring refraction. -For I wished to get hold of some measure of some sort, no matter how -blindly, having no fear but that so soon as the measure should be -accurately known, the cause would plainly appear. I went to work as -follows. In convex mirrors the image is diminished, and just so in rarer -mediums; in denser mediums it is magnified, as in concave mirrors. In -convex mirrors the central parts of the image approach, and recede in -concave farther than towards the circumference; the same thing happens -in different mediums, so that in water the bottom appears depressed, and -the surrounding parts elevated. Hence it appears that a denser medium -corresponds with a concave reflecting surface, and a rarer one with a -convex one: it was clear, at the same time, that the plane surface of -the water affects a property of curvature. I was, therefore, to -excogitate causes consistent with its having this effect of curvature, -and to see if a reason could be given, why the parts of the water -surrounding the incident perpendicular should represent a greater -density than the parts just under the perpendicular. And so the thing -came round again to my former attempts, which being refuted by reason -and experiment, I was forced to abandon the search after a cause. I then -proceeded to measurements." - -Kepler then endeavoured to connect his measurements of different -quantities of refraction with the conic sections, and was tolerably well -pleased with some of his results. They were however not entirely -satisfactory, on which he breaks off with the following sentence: "Now, -reader, you and I have been detained sufficiently long whilst I have -been attempting to collect into one faggot the measure of different -refractions: I acknowledge that the cause cannot be connected with this -mode of measurement: for what is there in common between refractions -made at the plane surfaces of transparent mediums, and mixtilinear conic -sections? Wherefore, _quod Deus bene vortat_, we will now have had -enough of the causes of this measure; and although, even now, we are -perhaps erring something from the truth, yet it is better, by working -on, to show our industry, than our laziness by neglect." - -Notwithstanding the great length of this extract, we must add the -concluding paragraph of the Chapter, directed, as we are told in the -margin, against the "Tychonomasticks:"-- - -"I know how many blind men at this day dispute about colours, and how -they long for some one to give some assistance by argument to their rash -insults of Tycho, and attacks upon this whole matter of refractions; -who, if they had kept to themselves their puerile errors and naked -ignorance, might have escaped censure; for that may happen to many great -men. But since they venture forth publicly, and with thick books and -sounding titles, lay baits for the applause of the unwary, (for -now-a-days there is more danger from the abundance of bad books, than -heretofore from the lack of good ones,) therefore let them know that a -time is set for them publicly to amend their own errors. If they longer -delay doing this, it shall be open, either to me or any other, to do to -these unhappy meddlers in geometry as they have taken upon themselves to -do with respect to men of the highest reputation. And although this -labour will be despicable, from the vile nature of the follies against -which it will be directed, yet so much more necessary than that which -they have undertaken against others, as he is a greater public nuisance, -who endeavours to slander good and necessary inventions, than he who -fancies he has found what is impossible to discover. Meanwhile, let them -cease to plume themselves on the silence which is another word for their -own obscurity." - -Although Kepler failed, as we have seen, to detect the true law of -refraction, (which was discovered some years later by Willibrord Snell, -a Flemish mathematician,) there are many things well deserving notice in -his investigations. He remarked, that the quantity of refraction would -alter, if the height of the atmosphere should vary; and also, that it -would be different at different temperatures. Both these sources of -variation are now constantly taken into account, the barometer and -thermometer giving exact indications of these changes. There is also a -very curious passage in one of his letters to Bregger, written in 1605, -on the subject of the colours in the rainbow. It is in these -words:--"Since every one sees a different rainbow, it is possible that -some one may see a rainbow in the very place of my sight. In this case, -the medium is coloured at the place of my vision, to which the solar ray -comes to me through water, rain, or aqueous vapours. For the rainbow is -seen when the sun is shining between rain, that is to say, when the sun -also is visible. Why then do I not see the sun green, yellow, red, and -blue, if vision takes place according to the mode of illumination? I -will say something for you to attack or examine. The sun's rays are not -coloured, except with a definite quantity of refraction. Whether you are -in the optical chamber, or standing opposite glass globes, or walking in -the morning dew, everywhere it is obvious that a certain and definite -angle is observed, under which, when seen in dew, in glass, in water, -the sun's splendour appears coloured, and under no other angle. There is -no colouring by mere reflexion, without the refraction of a denser -medium." How closely does Kepler appear, in this passage, to approach -the discovery which forms not the least part of Newton's fame! - -We also find in this work a defence of the opinion that the planets are -luminous of themselves; on the ground that the inferior planets would, -on the contrary supposition, display phases like those of the moon when -passing between us and the sun. The use of the telescope was not then -known; and, when some years later the form of the disk of the planets -was more clearly defined with their assistance, Kepler had the -satisfaction of finding his assertions verified by the discoveries of -Galileo, that these changes do actually take place. In another of his -speculations, connected with the same subject, he was less fortunate. In -1607 a black spot appeared on the face of sun, such as may almost always -be seen with the assistance of the telescope, although they are seldom -large enough to be visible to the unassisted eye. Kepler saw it for a -short time, and mistook it for the planet Mercury, and with his usual -precipitancy hastened to publish an account of his observation of this -rare phenomenon. A few years later, Galileo discovered with his glasses, -a great number of similar spots; and Kepler immediately retracted the -opinion announced in his treatise, and acknowledged his belief that -previous accounts of the same occurrence which he had seen in old -authors, and which he had found great difficulty in reconciling with his -more accurate knowledge of the motions of Mercury, were to be referred -to a like mistake. On this occasion of the invention of the telescope, -Kepler's candour and real love of truth appeared in a most favourable -light. Disregarding entirely the disagreeable necessity, in consequence -of the discoveries of this new instrument, of retracting several -opinions which he had maintained with considerable warmth, he ranged -himself at once on the side of Galileo, in opposition to the bitter and -determined hostility evinced by most of those whose theories were -endangered by the new views thus offered of the heavens. Kepler's -quarrel with his pupil, Horky, on this account, has been mentioned in -the "Life of Galileo;" and this is only a selected instance from the -numerous occasions on which he espoused the same unpopular side of the -argument. He published a dissertation to accompany Galileo's -"Intelligencer of the Stars," in which he warmly expressed his -admiration of that illustrious inquirer into nature. His conduct in this -respect was the more remarkable, as some of his most intimate friends -had taken a very opposite view of Galileo's merit, and seem to have -laboured much to disturb their mutual regard; Mästlin especially, -Kepler's early instructor, seldom mentioned to him the name of Galileo, -without some contemptuous expression of dislike. These statements have -rather disturbed the chronological order of the account of Kepler's -works. We now return to the year 1609, in which he published his great -and extraordinary book, "On the Motions of Mars;" a work which holds the -intermediate place, and is in truth the connecting link, between the -discoveries of Copernicus and Newton. - - - - -CHAPTER IV. - - _Sketch of the Astronomical Theories before Kepler._ - - -KEPLER had begun to labour upon these commentaries from the moment when -he first made Tycho's acquaintance; and it is on this work that his -reputation should be made mainly to rest. It is marked in many places -with his characteristic precipitancy, and indeed one of the most -important discoveries announced in it (famous among astronomers by the -name of the Equable Description of Areas) was blundered upon by a lucky -compensation of errors, of the nature of which Kepler remained ignorant -to the very last. Yet there is more of the inductive method in this than -in any of his other publications; and the unwearied perseverance with -which he exhausted years in hunting down his often renewed theories, -till at length he seemed to arrive at the true one, almost by having -previously disproved every other, excites a feeling of astonishment -nearly approaching to awe. It is wonderful how he contrived to retain -his vivacity and creative fancy amongst the clouds of figures which he -conjured up round him; for the slightest hint or shade of probability -was sufficient to plunge him into the midst of the most laborious -computations. He was by no means an accurate calculator, according to -the following character which he has given of himself:--"Something of -these delays must be attributed to my own temper, for _non omnia -possumus omnes_, and I am totally unable to observe any order; what I do -suddenly, I do confusedly, and if I produce any thing well arranged, it -has been done ten times over. Sometimes an error of calculation -committed by hurry, delays me a great length of time. I could indeed -publish an infinity of things, for though my reading is confined, my -imagination is abundant, but I grow dissatisfied with such confusion: I -get disgusted and out of humour, and either throw them away, or put them -aside to be looked at again; or, in other words, to be written again, -for that is generally the end of it. I entreat you, my friends, not to -condemn me for ever to grind in the mill of mathematical calculations: -allow me some time for philosophical speculations, my only delight." - -He was very seldom able to afford the expense of maintaining an -assistant, and was forced to go through most of the drudgery of his -calculations by himself; and the most confirmed and merest arithmetician -could not have toiled more doggedly than Kepler did in the work of which -we are about to speak. - -In order that the language of his astronomy may be understood, it is -necessary to mention briefly some of the older theories. When it had -been discovered that the planets did not move regularly round the earth, -which was supposed to be fixed in the centre of the world, a mechanism -was contrived by which it was thought that the apparent irregularity -could be represented, and yet the principle of uniform motion, which was -adhered to with superstitious reverence, might be preserved. This, in -its simplest form, consisted in supposing the planet to move uniformly -in a small circle, called an _epicycle_, the centre of which moved with -an equal angular motion in the opposite direction round the earth.[187] -The circle D_d_, described by D, the centre of the epicycle, was called -the _deferent_. For instance, if the planet was supposed to be at A when -the centre of the epicycle was at D, its position, when the centre of -the epicycle had removed to _d_, would be at _p_, found by drawing _dp_ -parallel to DA. Thus, the angle _adp_, measuring the motion of the -planet in its epicycle, would be equal to DE_d_, the angle described by -the centre of the epicycle in the deferent. The angle _p_E_d_ between -E_p_, the direction in which a planet so moving would be seen from the -earth, supposed to be at E, and E_d_ the direction in which it would -have been seen had it been moving in the centre of the deferent, was -called the equation of the orbit, the word equation, in the language of -astronomy, signifying what must be added or taken from an irregularly -varying quantity to make it vary uniformly. - -[Illustration] - -As the accuracy of observations increased, minor irregularities were -discovered, which were attempted to be accounted for by making a second -deferent of the epicycle, and making the centre of a second epicycle -revolve in the circumference of the first, and so on, or else by -supposing the revolution in the epicycle not to be completed in exactly -the time in which its centre is carried round the deferent. Hipparchus -was the first to make a remark by which the geometrical representation -of these inequalities was considerably simplified. In fact, if EC be -taken equal to _pd_, C_d_ will be a parallelogram, and consequently -C_p_ equal to E_d_, so that the machinery of the first deferent and -epicycle amounts to supposing that the planet revolves uniformly in a -circle round the point C, not coincident with the place of the earth. -This was consequently called the excentric theory, in opposition to the -former or concentric one, and was received as a great improvement. As -the point _d_ is not represented by this construction, the equation to -the orbit was measured by the angle C_p_E, which is equal to _p_E_d_. It -is not necessary to give any account of the manner in which the old -astronomers determined the magnitudes and positions of these orbits, -either in the concentric or excentric theory, the present object being -little more than to explain the meaning of the terms it will be -necessary to use in describing Kepler's investigations. - -To explain the irregularities observed in the other planets, it became -necessary to introduce another hypothesis, in adopting which the -severity of the principle of uniform motion was somewhat relaxed. The -machinery consisted partly of an excentric deferent round E, the earth, -and on it an epicycle, in which the planet revolved uniformly; but the -centre of the epicycle, instead of revolving uniformly round C, the -centre of the deferent, as it had hitherto been made to do, was -supposed to move in its circumference with an uniform angular motion -round a third point, Q; the necessary effect of which supposition was, -that the linear motion of the centre of the epicycle ceased to be -uniform. There were thus three points to be considered within the -deferent; E, the place of the earth; C, the centre of the deferent, and -sometimes called the centre of the orbit; and Q, called the centre of -the equant, because, if any circle were described round Q, the planet -would appear to a spectator at Q, to be moving equably in it. It was -long uncertain what situation should be assigned to the centre of the -equant, so as best to represent the irregularities to a spectator on the -earth, until Ptolemy decided on placing it (in every case but that of -Mercury, the observations on which were very doubtful) so that C, the -centre of the orbit, lay just half way in the straight line, joining Q, -the centre of equable motion, and E, the place of the earth. This is the -famous principle, known by the name of the bisection of the -excentricity. - -[Illustration] - -The first equation required for the planet's motion was thus supposed to -be due to the displacement of E, the earth, from Q, the centre of -uniform motion, which was called the excentricity of the equant: it -might be represented by the angle _d_EM, drawing EM parallel to Q_d_; -for clearly M would have been the place of the centre of the epicycle at -the end of a time proportional to D_d_, had it moved with an equable -angular motion round E instead of Q. This angle _d_EM, or its equal -E_d_Q, was called the equation of the centre (_i.e._ of the centre of -the epicycle); and is clearly greater than if EQ, the excentricity of -the equant, had been no greater than EC, called the excentricity of the -orbit. The second equation was measured by the angle subtended at E by -_d_, the centre of the epicycle, and _p_ the planet's place in its -circumference: it was called indifferently the equation of the orbit, or -of the argument. In order to account for the apparent stations and -retrogradations of the planets, it became necessary to suppose that many -revolutions in the latter were completed during one of the former. The -variations of latitude of the planets were exhibited by supposing not -only that the planes of their deferents were oblique to the plane of the -ecliptic, and that the plane of the epicycle was also oblique to that of -the deferent, but that the inclination of the two latter was continually -changing, although Kepler doubts whether this latter complication was -admitted by Ptolemy. In the inferior planets, it was even thought -necessary to give to the plane of the epicycle two oscillatory motions -on axes at right angles to each other. - -The astronomers at this period were much struck with a remarkable -connexion between the revolutions of the superior planets in their -epicycles, and the apparent motion of the sun; for when in conjunction -with the sun, as seen from the earth, they were always found to be in -the apogee, or point of greatest distance from the earth, of their -epicycle; and when in opposition to the Sun, they were as regularly in -the perigee, or point of nearest approach of the epicycle. This -correspondence between two phenomena, which, according to the old -astronomy, were entirely unconnected, was very perplexing, and it seems -to have been one of the facts which led Copernicus to substitute the -theory of the earth's motion round the sun. - -As time wore on, the superstructure of excentrics and epicycles, which -had been strained into representing the appearances of the heavens at a -particular moment, grew out of shape, and the natural consequence of -such an artificial system was, that it became next to impossible to -foresee what ruin might be produced in a remote part of it by any -attempt to repair the derangements and refit the parts to the changes, -as they began to be remarked in any particular point. In the ninth -century of our era, Ptolemy's tables were already useless, and all those -that were contrived with unceasing toil to supply their place, rapidly -became as unserviceable as they. Still the triumph of genius was seen in -the veneration that continued to be paid to the assumptions of Ptolemy -and Hipparchus; and even when the great reformer, Copernicus, appeared, -he did not for a long time intend to do more than slightly modify their -principles. That which he found difficult in the Ptolemaic system, was -none of the inconveniences by which, since the establishment of the new -system, it has become common to demonstrate the inferiority of the old -one; it was the displacement of the centre of the equant from the centre -of the orbit that principally indisposed him against it, and led him to -endeavour to represent the appearances by some other combinations of -really uniform circular motions. - -There was an old system, called the Egyptian, according to which Saturn, -Jupiter, Mars, and the Sun circulated round the earth, the sun carrying -with it, as two moons or satellites, the other two planets, Venus and -Mercury. This system had never entirely lost credit: it had been -maintained in the fifth century by Martianus Capella[188], and indeed it -was almost sanctioned, though not formally taught, by Ptolemy himself, -when he made the mean motion of the sun the same as that of the centres -of the epicycles of both these planets. The remark which had also been -made by the old astronomers, of the connexion between the motion of the -sun and the revolutions of the superior planets in their epicycles, led -him straight to the expectation that he might, perhaps, produce the -uniformity he sought by extending the Egyptian system to these also, and -this appears to have been the shape in which his reform was originally -projected. It was already allowed that the centre of the orbits of all -the planets was not coincident with the earth, but removed from it by -the space EC. This first change merely made EC the same for all the -planets, and equal to the mean distance of the earth from the sun. This -system afterwards acquired great celebrity through its adoption by Tycho -Brahe, who believed it originated with himself. It might perhaps have -been at this period of his researches, that Copernicus was struck with -the passages in the Latin and Greek authors, to which he refers as -testifying the existence of an old belief in the motion of the earth -round the sun. He immediately recognised how much this alteration would -further his principles of uniformity, by referring all the planetary -motions to one centre, and did not hesitate to embrace it. The idea of -explaining the daily and principal apparent motions of the heavenly -bodies by the revolution of the earth on its axis, would be the -concluding change, and became almost a necessary consequence of his -previous improvements, as it was manifestly at variance with his -principles to give to all the planets and starry worlds a rapid daily -motion round the centre of the earth, now that the latter was removed -from its former supposed post in the centre of the universe, and was -itself carried with an annual motion round another fixed point. - -[Illustration] - -The reader would, however, form an inaccurate notion of the system of -Copernicus, if he supposed that it comprised no more than the theory -that each planet, including the earth among them, revolved in a simple -circular orbit round the sun. Copernicus was too well acquainted with -the motions of the heavenly bodies, not to be aware that such orbits -would not accurately represent them; the motion he attributed to the -earth round the sun, was at first merely intended to account for those -which were called the second inequalities of the planets, according to -which they appear one while to move forwards, then backwards, and at -intermediate periods, stationary, and which thenceforward were also -called the optical equations, as being merely an optical illusion. With -regard to what were called the first inequalities, or physical -equations, arising from a real inequality of motion, he still retained -the machinery of the deferent and epicycle; and all the alteration he -attempted in the orbits of the superior planets was an extension of the -concentric theory to supply the place of the equant, which he considered -the blot of the system. His theory for this purpose is shown in the -accompanying diagram, where S represents the sun, D_d_, the deferent or -mean orbit of the planet, on which revolves the centre of the great -epicycle, whose radius, DF, was taken at ¾ of Ptolemy's excentricity of -the equant; and round the circumference of this revolved, in the -opposite direction, the centre of the little epicycle, whose radius, FP, -was made equal to the remaining ¼ of the excentricity of the equant. - -The planet P revolved in the circumference of the little epicycle, in -the same direction with the centre of the great epicycle in the -circumference of the deferent, but with a double angular velocity. The -planet was supposed to be in the perigee of the little epicycle, when -its centre was in the apogee of the greater; and whilst, for instance, D -moved equably though the angle DS_d_, F moved through _hdf_ = DS_d_, -and P through _rfp_ = 2 DS_d_. - -It is easy to show that this construction gives nearly the same result -as Ptolemy's; for the deferent and great epicycle have been already -shown exactly equivalent to an excentric circle round S, and indeed -Copernicus latterly so represented it: the effect of his construction, -as given above, may therefore be reproduced in the following simpler -form, in which only the smaller epicycle is retained: - -[Illustration] - -In this construction, the place of the planet is found at the end of any -time proportional to F _f_ by drawing _fr_ parallel to SF, and taking -_rfp_ = 2F _of_. Hence it is plain, if we take OQ, equal to FP, (already -assumed equal to ¼ of Ptolemy's excentricity of the equant,) since SO is -equal to ¾ of the same, that SQ is the whole of Ptolemy's excentricity -of the equant; and therefore, that Q is the position of the centre of -his equant. It is also plain if we join Q_p_, since _rfp_ = 2F _of_, and -_o_Q = _fp_, that _p_Q is parallel to _fo_, and, therefore, _p_QP is -proportional to the time; so that the planet moves uniformly about the -same point Q, as in Ptolemy's theory; and if we bisect SQ in C, which is -the position of the centre of Ptolemy's deferent, the planet will, -according to Copernicus, move very nearly, though not exactly, in the -same circle, whose radius is CP, as that given by the simple excentric -theory. - -The explanation offered by Copernicus, of the motions of the inferior -planets, differed again in form from that of the others. He here -introduced what was called a _hypocycle_, which, in fact, was nothing -but a deferent not including the sun, round which the centre of the -orbit revolved. An epicycle in addition to the hypocycle was introduced -into Mercury's orbit. In this epicycle he was not supposed to revolve, -but to librate, or move up and down in its diameter. Copernicus had -recourse to this complication to satisfy an erroneous assertion of -Ptolemy with regard to some of Mercury's inequalities. He also retained -the oscillatory motions ascribed by Ptolemy to the planes of the -epicycles, in order to explain the unequal latitudes observed at the -same distance from the nodes, or intersections of the orbit of the -planet with the ecliptic. Into this intricacy, also, he was led by -placing too much confidence in Ptolemy's observations, which he was -unable to satisfy by an unvarying obliquity. Other very important -errors, such as his belief that the line of nodes always coincided with -the line of apsides, or places of greatest and least distance from the -central body, (whereas, at that time, in the case of Mars, for instance, -they were nearly 90° asunder,) prevented him from accurately -representing many of the celestial phenomena. - -These brief details may serve to show that the adoption or rejection of -the theory of Copernicus was not altogether so simple a question as -sometimes it may have been considered. It is, however, not a little -remarkable, while it is strongly illustrative of the spirit of the -times, that these very intricacies, with which Kepler's theories have -enabled us to dispense, were the only parts of the system of Copernicus -that were at first received with approbation. His theory of Mercury, -especially, was considered a masterpiece of subtle invention. Owing to -his dread of the unfavourable judgment he anticipated on the main -principles of his system, his work remained unpublished during forty -years, and was at last given to the world only just in time to allow -Copernicus to receive the first copy of it a few hours before his -death. - - -FOOTNOTES: - -[187] By "the opposite direction" is meant, that while the motion in the -circumference of one circle appeared, as viewed from its centre, to be -from left to right, the other, viewed from its centre, appeared from -right to left. This must be understood whenever these or similar -expressions are repeated. - -[188] Venus Mercuriusque, licet ortus occasusque quotidianos ostendunt, -tamen eorum circuli terras omnino non ambiunt, sed circa solem laxiore -ambitu circulantur. Denique circulorum suorum centron in sole -constituunt.--De Nuptiis Philologiæ et Mercurii. Vicentiæ. 1499. - - - - -CHAPTER V. - - _Account of the Commentaries on the motions of Mars--Discovery of - the Law of the equable description of Areas, and of Elliptic - Orbits._ - - -WE may now proceed to examine Kepler's innovations, but it would be -doing injustice to one of the brightest points of his character, not to -preface them by his own animated exhortation to his readers. "If any one -be too dull to comprehend the science of astronomy, or too feeble-minded -to believe in Copernicus without prejudice to his piety, my advice to -such a one is, that he should quit the astronomical schools, and -condemning, if he has a mind, any or all of the theories of -philosophers, let him look to his own affairs, and leaving this worldly -travail, let him go home and plough his fields: and as often as he lifts -up to this goodly heaven those eyes with which alone he is able to see, -let him pour out his heart in praises and thanksgiving to God the -Creator; and let him not fear but he is offering a worship not less -acceptable than his to whom God has granted to see yet more clearly with -the eyes of his mind, and who both can and will praise his God for what -he has so discovered." - -Kepler did not by any means underrate the importance of his labours, as -is sufficiently shewn by the sort of colloquial motto which he prefixed -to his work. It consists in the first instance of an extract from the -writings of the celebrated and unfortunate Peter Ramus. This -distinguished philosopher was professor of mathematics in Paris, and in -the passage in question, after calling on his contemporaries to turn -their thoughts towards the establishment of a system of Astronomy -unassisted by any hypothesis, he promised as an additional inducement to -vacate his own chair in favour of any one who should succeed in this -object. Ramus perished in the massacre of St. Bartholomew, and Kepler -apostrophizes him as follows:--"It is well, Ramus, that you have -forfeited your pledge, by quitting your life and professorship together: -for if you still held it, I would certainly claim it as of right -belonging to me on account of this work, as I could convince you even -with your own logic." It was rather bold in Kepler to assert his claim -to a reward held out for a theory resting on no hypothesis, by right of -a work filled with hypotheses of the most startling description; but of -the vast importance of this book there can be no doubt; and throughout -the many wild and eccentric ideas to which we are introduced in the -course of it, it is fit always to bear in mind that they form part of a -work which is almost the basis of modern Astronomy. - -The introduction contains a curious criticism of the commonly-received -theory of gravity, accompanied with a declaration of Kepler's own -opinions on the same subject. Some of the most remarkable passages in it -have been already quoted in the life of Galileo; but, nevertheless, they -are too important to Kepler's reputation to be omitted here, containing -as they do a distinct and positive enunciation of the law of universal -gravitation. It does not appear, however, that Kepler estimated rightly -the importance of the theory here traced out by him, since on every -other occasion he advocated principles with which it is scarcely -reconcileable. The discussion is introduced in the following terms:-- - -"The motion of heavy bodies hinders many from believing that the earth -is moved by an animal motion, or rather a magnetic one. Let such -consider the following propositions. A mathematical point, whether the -centre of the universe or not, has no power, either effectively or -objectively, to move heavy bodies to approach it. Let physicians prove -if they can, that such power can be possessed by a point, which, neither -is a body, nor is conceived unless by relation alone. It is impossible -that the form[189] of a stone should, by moving its own body, seek a -mathematical point, or in other words, the centre of the universe, -without regard of the body in which that point exists. Let physicians -prove if they can, that natural things have any sympathy with that which -is nothing. Neither do heavy bodies tend to the centre of the universe -by reason that they are avoiding the extremities of the round universe; -for their distance from the centre is insensible, in proportion to their -distance from the extremities of the universe. And what reason could -there be for this hatred? How strong, how wise must those heavy bodies -be, to be able to escape so carefully from an enemy lying on all sides -of them: what activity in the extremities of the world to press their -enemy so closely! Neither are heavy bodies driven into the centre by the -whirling of the first moveable, as happens in revolving water. For if we -assume such a motion, either it would not be continued down to us, or -otherwise we should feel it, and be carried away with it, and the earth -also with us; nay, rather, we should be hurried away first, and the -earth would follow; all which conclusions are allowed by our opponents -to be absurd. It is therefore plain that the vulgar theory of gravity is -erroneous. - -"The true theory of gravity is founded on the following axioms:--Every -corporeal substance, so far forth as it is corporeal, has a natural -fitness for resting in every place where it may be situated by itself -beyond the sphere of influence of a body cognate with it. Gravity is a -mutual affection between cognate bodies towards union or conjunction -(similar in kind to the magnetic virtue), so that the earth attracts a -stone much rather than the stone seeks the earth. Heavy bodies (if we -begin by assuming the earth to be in the centre of the world) are not -carried to the centre of the world in its quality of centre of the -world, but as to the centre of a cognate round body, namely, the earth; -so that wheresoever the earth may be placed, or whithersoever it may be -carried by its animal faculty, heavy bodies will always be carried -towards it. If the earth were not round, heavy bodies would not tend -from every side in a straight line towards the centre of the earth, but -to different points from different sides. If two stones were placed in -any part of the world near each other, and beyond the sphere of -influence of a third cognate body, these stones, like two magnetic -needles, would come together in the intermediate point, each approaching -the other by a space proportional to the comparative mass of the other. -If the moon and earth were not retained in their orbits by their animal -force or some other equivalent, the earth would mount to the moon by a -fifty-fourth part of their distance, and the moon fall towards the earth -through the other fifty-three parts and they would there meet; assuming -however that the substance of both is of the same density. If the earth -should cease to attract its waters to itself, all the waters of the sea -would be raised and would flow to the body of the moon. The sphere of -the attractive virtue which is in the moon extends as far as the earth, -and entices up the waters; but as the moon flies rapidly across the -zenith, and the waters cannot follow so quickly, a flow of the ocean is -occasioned in the torrid zone towards the westward. If the attractive -virtue of the moon extends as far as the earth, it follows with greater -reason that the attractive virtue of the earth extends as far as the -moon, and much farther; and in short, nothing which consists of earthly -substance any how constituted, although thrown up to any height, can -ever escape the powerful operation of this attractive virtue. Nothing -which consists of corporeal matter is absolutely light, but that is -comparatively lighter which is rarer, either by its own nature, or by -accidental heat. And it is not to be thought that light bodies are -escaping to the surface of the universe while they are carried upwards, -or that they are not attracted by the earth. They are attracted, but in -a less degree, and so are driven outwards by the heavy bodies; which -being done, they stop, and are kept by the earth in their own place. But -although the attractive virtue of the earth extends upwards, as has been -said, so very far, yet if any stone should be at a distance great enough -to become sensible, compared with the earth's diameter, it is true that -on the motion of the earth such a stone would not follow altogether; its -own force of resistance would be combined with the attractive force of -the earth, and thus it would extricate itself in some degree from the -motion of the earth." - -Who, after perusing such passages in the works of an author, whose -writings were in the hands of every student of astronomy, can believe -that Newton waited for the fall of an apple to set him thinking for the -first time on the theory which has immortalized his name? An apple may -have fallen, and Newton may have seen it; but such speculations as those -which it is asserted to have been the cause of originating in him had -been long familiar to the thoughts of every one in Europe pretending to -the name of natural philosopher. - -As Kepler always professed to have derived his notion of a magnetic -attraction among the planetary bodies from the writings of Gilbert, it -may be worth while to insert here an extract from the "New Philosophy" -of that author, to show in what form he presented a similar theory of -the tides, which affords the most striking illustration of that -attraction. This work was not published till the middle of the -seventeenth century, but a knowledge of its contents may, in several -instances, be traced back to the period in which it was written:-- - -"There are two primary causes of the motion of the seas--the moon, and -the diurnal revolution. The moon does not act on the seas by its rays or -its light. How then? Certainly by the common effort of the bodies, and -(to explain it by something similar) by their magnetic attraction. It -should be known, in the first place, that the whole quantity of water is -not contained in the sea and rivers, but that the mass of earth (I mean -this globe) contains moisture and spirit much deeper even than the sea. -The moon draws this out by sympathy, so that they burst forth on the -arrival of the moon, in consequence of the attraction of that star; and -for the same reason, the quicksands which are in the sea open themselves -more, and perspire their moisture and spirits during the flow of the -tide, and the whirlpools in the sea disgorge copious waters; and as the -star retires, they devour the same again, and attract the spirits and -moisture of the terrestrial globe. Hence the moon attracts, not so much -the sea as the subterranean spirits and humours; and the interposed -earth has no more power of resistance than a table or any other dense -body has to resist the force of a magnet. The sea rises from the -greatest depths, in consequence of the ascending humours and spirits; -and when it is raised up, it necessarily flows on to the shores, and -from the shores it enters the rivers."[190] - -This passage sets in the strongest light one of the most notorious -errors of the older philosophy, to which Kepler himself was remarkably -addicted. If Gilbert had asserted, in direct terms, that the moon -attracted the water, it is certain that the notion would have been -stigmatized (as it was for a long time in Newton's hands) as arbitrary, -occult, and unphilosophical: the idea of these subterranean humours was -likely to be treated with much more indulgence. A simple statement, that -when the moon was over the water the latter had a tendency to rise -towards it, was thought to convey no instruction; but the assertion that -the moon draws out subterranean spirits by sympathy, carried with it a -more imposing appearance of theory. The farther removed these humours -were from common experience, the easier it became to discuss them in -vague and general language; and those who called themselves philosophers -could endure to hear attributes bestowed on these fictitious elements -which revolted their imaginations when applied to things of whose -reality at least some evidence existed. - -It is not necessary to dwell upon the system of Tycho Brahe, which was -identical, as we have said, with one rejected by Copernicus, and -consisted in making the sun revolve about the earth, carrying with it -all the other planets revolving about him. Tycho went so far as to deny -the rotation of the earth to explain the vicissitudes of day and night, -but even his favourite assistant Longomontanus differed from him in this -part of his theory. The great merit of Tycho Brahe, and the service he -rendered to astronomy, was entirely independent of any theory; -consisting in the vast accumulation of observations made by him during a -residence of fifteen years at Uraniburg, with the assistance of -instruments, and with a degree of care, very far superior to anything -known before his time in practical astronomy. Kepler is careful -repeatedly to remind us, that without Tycho's observations he could have -done nothing. The degree of reliance that might be placed on the results -obtained by observers who acknowledged their inferiority to Tycho Brahe, -maybe gathered from an incidental remark of Kepler to Longomontanus. He -had been examining Tycho's registers, and had occasionally found a -difference amounting sometimes to 4´ in the right ascensions of the same -planet, deduced from different stars on the same night. Longomontanus -could not deny the fact, but declared that it was impossible to be -always correct within such limits. The reader should never lose sight of -this uncertainty in the observations, when endeavouring to estimate the -difficulty of finding a theory that would properly represent them. - -When Kepler first joined Tycho Brahe at Prague, he found him and -Longomontanus very busily engaged in correcting the theory of Mars, and -accordingly it was this planet to which he also first directed his -attention. They had formed a catalogue of the mean oppositions of Mars -during twenty years, and had discovered a position of the equant, which -(as they said) represented them with tolerable exactness. On the other -hand, they were much embarrassed by the unexpected difficulties they met -in applying a system which seemed on the one hand so accurate, to the -determination of the latitudes, with which it could in no way be made to -agree. Kepler had already suspected the cause of this imperfection, and -was confirmed in the view he took of their theory, when, on a more -careful examination, he found that they overrated the accuracy even of -their longitudes. The errors in these, instead of amounting as they -said, nearly to 2´, rose sometimes above 21´. In fact they had reasoned -ill on their own principles, and even if the foundations of their theory -had been correctly laid, could not have arrived at true results. But -Kepler had satisfied himself of the contrary, and the following diagram -shews the nature of the first alteration he introduced, not perhaps so -celebrated as some of his later discoveries, but at least of equal -consequence to astronomy, which could never have been extricated from -the confusion into which it had fallen, till this important change had -been effected. - -[Illustration] - -The practice of Tycho Brahe, indeed of all astronomers till the time of -Kepler, had been to fix the position of the planet's orbit and equant -from observations on its mean oppositions, that is to say, on the times -when it was precisely six signs or half a circle distant from the mean -place of the sun. In the annexed figure, let S represent the sun, C the -centre of the earth's orbit, T_t_. Tycho Brahe's practice amounted to -this, that if Q were supposed the place of the centre of the planet's -equant, the centre of P_p_ its orbit was taken in QC, and not in QS, as -Kepler suggested that it ought to be taken. The consequence of this -erroneous practice was, that the observations were deprived of the -character for which oppositions were selected, of being entirely free -from the second inequalities. It followed therefore that as part of the -second inequalities were made conducive towards fixing the relative -position of the orbit and equant, to which they did not naturally -belong, there was an additional perplexity in accounting for the -remainder of them by the size and motion of the epicycle. As the line of -nodes of every planet was also made to pass through C instead of S, -there could not fail to be corresponding errors in the latitudes. It -would only be in the rare case of an opposition of the planet in the -line CS, that the time of its taking place would be the same, whether O, -the centre of the orbit, was placed in CQ or SQ. Every other opposition -would involve an error, so much the greater as it was observed at a -greater distance from the line CS. - -It was long however before Tycho Brahe could be made to acquiesce in the -propriety of the proposed alteration; and, in order to remove his doubts -as to the possibility that a method could be erroneous which, as he -still thought, had given him such accurate longitudes, Kepler undertook -the ungrateful labour of the first part of his "Commentaries." He there -shewed, in the three systems of Copernicus, Tycho Brahe, and Ptolemy, -and in both the concentric and excentric theories, that though a false -position were given to the orbit, the longitudes of a planet might be so -represented, by a proper position of the centre of the equant, as never -to err in oppositions above 5´ from those given by observation; though -the second inequalities and the latitudes would thereby be very greatly -deranged. - -The change Kepler introduced, of observing apparent instead of mean -oppositions, made it necessary to be very accurate in his reductions of -the planet's place to the ecliptic; and in order to be able to do this, -a previous knowledge of the parallax of Mars became indispensable. His -next labour was therefore directed to this point; and finding that the -assistants to whom Tycho Brahe had previously committed this labour had -performed it in a negligent and imperfect manner, he began afresh with -Tycho's original observations. Having satisfied himself as to the -probable limits of his errors in the parallax on which he finally fixed, -he proceeded to determine the inclination of the orbit and the position -of the line of nodes. In all these operations his talent for -astronomical inquiries appeared pre-eminent in a variety of new methods -by which he combined and availed himself of the observations; but it -must be sufficient merely to mention this fact, without entering into -any detail. One important result may be mentioned, at which he arrived -in the course of them, the constancy of the inclination of the planet's -orbit, which naturally strengthened him in his new theory. - -Having gone through these preliminary inquiries, he came at last to fix -the proportions of the orbit; and, in doing so, he determined, in the -first instance, not to assume, as Ptolemy appeared to have done -arbitrarily, the bisection of the excentricity, but to investigate its -proportion along with the other elements of the orbit, which resolution -involved him in much more laborious calculations. After he had gone over -all the steps of his theory no less than seventy times--an appalling -labour, especially if we remember that logarithms were not then -invented--his final result was, that in 1587, on the 6th of March, at -7^{h} 23´, the longitude of the aphelion of Mars was 4^{s} 28° 48´ 55´´; -that the planet's mean longitude was 6^{s} 0° 51´ 35´´; that if the -semidiameter of the orbit was taken at 100000, the excentricity was -11332; and the excentricity of the equant 18564. He fixed the radius of -the greater epicycle at 14988, and that of the smaller at 3628. - -When he came to compare the longitudes as given by this, which he -afterwards called the _vicarious_ theory, with the observations at -opposition, the result seemed to promise him the most brilliant success. -His greatest error did not exceed 2´; but, notwithstanding these -flattering anticipations, he soon found by a comparison of longitudes -out of opposition and of latitudes, that it was yet far from being so -complete as he had imagined, and to his infinite vexation he soon found -that the labour of four years, which he had expended on this theory, -must be considered almost entirely fruitless. Even his favourite -principle of dividing the excentricity in a different ratio from -Ptolemy, was found to lead him into greater error than if he had -retained the old bisection. By restoring that, he made his latitudes -more accurate, but produced a corresponding change for the worse in his -longitudes; and although the errors of 8´, to which they now amounted, -would probably have been disregarded by former theorists, Kepler could -not remain satisfied till they were accounted for. Accordingly he found -himself forced to the conclusion that one of the two principles on which -this theory rested must be erroneous; either the orbit of the planet is -not a perfect circle, or there is no fixed point within it round which -it moves with an uniform angular motion. He had once before admitted the -possibility of the former of these facts, conceiving it possible that -the motion of the planets is not at all curvilinear, but that they move -in polygons round the sun, a notion to which he probably inclined in -consequence of his favourite harmonics and geometrical figures. - -In consequence of the failure of a theory conducted with such care in -all its practical details, Kepler determined that his next trial should -be of an entirely different complexion. Instead of first satisfying the -first inequalities of the planet, and then endeavouring to account for -the second inequalities, he resolved to reverse the process, or, in -other words, to ascertain as accurately as possible what part of the -planet's apparent motion should be referred solely to the optical -illusion produced by the motion of the earth, before proceeding to any -inquiry of the real inequality of the planet's proper motion. It had -been hitherto taken for granted, that the earth moved equably round the -centre of its orbit; but Kepler, on resuming the consideration of it, -recurred to an opinion he had entertained very early in his astronomical -career (rather from his conviction of the existence of general laws, -than that he had then felt the want of such a supposition), that it -required an equant distinct from its orbit no less than the other -planets. He now saw, that if this were admitted, the changes it would -everywhere introduce in the optical part of the planet's irregularities -might perhaps relieve him from the perplexity in which the vicarious -theory had involved him. Accordingly he applied himself with renewed -assiduity to the examination of this important question, and the result -of his calculations (founded principally on observations of Mars' -parallax) soon satisfied him not only that the earth's orbit does -require such an equant, but that its centre is placed according to the -general law of the bisection of the excentricity which he had previously -found indispensable in the other planets. This was an innovation of the -first magnitude, and accordingly Kepler did not venture to proceed -farther in his theory, till by evidence of the most varied and -satisfactory nature, he had established it beyond the possibility of -cavil. - -It may be here remarked, that this principle of the bisection of the -eccentricity, so familiar to the Ptolemaic astronomers, is identical -with the theory afterwards known by the name of the simple elliptic -hypothesis, advocated by, Seth Ward and others. That hypothesis -consisted in supposing the sun to be placed in one focus of the elliptic -orbit of the planet, whose angular motion was uniform round the other -focus. In Ptolemaic phraseology, that other focus was the centre of the -equant, and it is well known that the centre of the ellipse lies in the -middle point between the two foci. - -It was at this period also, that Kepler first ventured upon the new -method of representing inequalities which terminated in one of his most -celebrated discoveries. We have already seen, in the account of the -"Mysterium Cosmographicum," that he was speculating, even at that time, -on the effects of a whirling force exerted by the sun on the planets -with diminished energy at increased distances, and on the proportion -observed between the distances of the planets from the sun, and their -periods of revolution. He seems even then to have believed in the -possibility of discovering a relation between the times and distances in -different planets. Another analogous consequence of his theory of the -radiation of the whirling force would be, that if the same planet should -recede to a greater distance from the central body, it would be acted on -by a diminished energy of revolution, and consequently, a relation might -be found between the velocity at any point of its orbit, and its -distance at that point from the sun. Hence he expected to derive a more -direct and natural method of calculating the inequalities, than from the -imaginary equant. But these ingenious ideas had been checked in the -outset by the erroneous belief which Kepler, in common with other -astronomers, then entertained of the coincidence of the earth's equant -with its orbit; in other words, by the belief that the earth's linear -motion was uniform, though it was known not to remain constantly at the -same distance from the sun. As soon as this prejudice was removed, his -former ideas recurred to him with increased force, and he set himself -diligently to consider what relation could be found between the velocity -and distance of a planet from the sun. The method he adopted in the -beginning of this inquiry was to assume as approximately correct -Ptolemy's doctrine of the bisection of the excentricity, and to -investigate some simple relation nearly representing the same effect. - -In the annexed figure, S is the place of the sun, C the centre of the -planet's orbit AB_ab_, Q the centre of the equant represented by the -equal circle DE_de_, AB, _ab_, two equal small arcs described by the -planet at the apsides of its orbit: then, according to Ptolemy's -principles, the arc DE of the equant would be proportional to the time -of passing along AB, on the same scale on which _de_ would represent the -time of passing through the equal arc _ab_. - -[Illustration] - -QD:QA :: DE:AB, nearly; and because QS is bisected in C, QA, CA or QD, -and SA, are in arithmetical proportion: and, therefore, since an -arithmetical mean, when the difference is small, does not differ much -from a geometrical mean, QD:QA :: SA:QD, nearly. Therefore, DE:AB :: S -A:QD, nearly, and in the same manner _de_:_ab_ :: S_a_:Q_d_ nearly; and -therefore DE:_de_ :: SA:S_a_ nearly. Therefore at the apsides, the -times of passing over equal spaces, on Ptolemy's theory, are nearly as -the distances from the sun, and Kepler, with his usual hastiness, -immediately concluded that this was the accurate and general law, and -that the errors of the old theory arose solely from having departed from -it. - -It followed immediately from this assumption, that after leaving the -point A, the time in which the planet would arrive at any point P of -its orbit would be proportional to, and might be represented by, the -sums of all the lines that could be drawn from S to the arc AP, on the -same scale that the whole period of revolution would be denoted by the -sum of all the lines drawn to every point of the orbit. Kepler's first -attempt to verify this supposition approximately, was made by dividing -the whole circumference of the orbit into 360 equal parts, and -calculating the distances at every one of the points of division. Then -supposing the planet to move uniformly, and to remain at the same -distance from the sun during the time of passing each one of these -divisions, (a supposition which manifestly would not differ much from -the former one, and would coincide with it more nearly, the greater was -the number of divisions taken) he proceeded to add together these -calculated distances, and hoped to find that the time of arriving at any -one of the divisions bore the same ratio to the whole period, as the sum -of the corresponding set of distances did to the sum of the whole 360. - -This theory was erroneous; but by almost miraculous good fortune, he was -led by it in the following manner to the true measure. The discovery was -a consequence of the tediousness of his first method, which required, in -order to know the time of arriving at any point, that the circle should -be subdivided, until one of the points of division fell exactly upon the -given place. Kepler therefore endeavoured to discover some shorter -method of representing these sums of the distances. The idea then -occurred to him of employing for that purpose the area inclosed between -the two distances, SA, SP, and the arc AP, in imitation of the manner in -which he remembered that Archimedes had found the area of the circle, by -dividing it into an infinite number of small triangles by lines drawn -from the centre. He hoped therefore to find, that the time of passing -from A to P bore nearly the same ratio to the whole period of revolution -that the area ASP bore to the whole circle. - -This last proportion is in fact accurately observed in the revolution of -one body round another, in consequence of an attractive force in the -central body. Newton afterwards proved this, grounding his demonstration -upon laws of motion altogether irreconcileable with Kepler's opinions; -and it is impossible not to admire Kepler's singular good fortune in -arriving at this correct result in spite, or rather through the means, -of his erroneous principles. It is true that the labour which he -bestowed unsparingly upon every one of his successive guesses, joined -with his admirable candour, generally preserved him from long retaining -a theory altogether at variance with observations; and if any relation -subsisted between the times and distances which could any way be -expressed by any of the geometrical quantities under consideration, he -could scarcely have failed--it might be twenty years earlier or twenty -years later,--to light upon it at last, having once put his -indefatigable fancy upon this scent. But in order to prevent an -over-estimate of his merit in detecting this beautiful law of nature, -let us for a moment reflect what might have been his fate had he -endeavoured in the same manner, and with the same perseverance, to -discover a relation, where, in reality, none existed. Let us take for -example the inclinations or the excentricities of the planetary orbits, -among which no relation has yet been discovered; and if any exists, it -is probably of too complicated a nature to be hit at a venture. If -Kepler had exerted his ingenuity in this direction, he might have wasted -his life in fruitless labour, and whatever reputation he might have left -behind him as an industrious calculator, it would have been very far -inferior to that which has procured for him the proud title of the -"Legislator of the Heavens." - -However this may be, the immediate consequence of thus lighting upon the -real law observed by the earth in its passage round the sun was, that he -found himself in possession of a much more accurate method of -representing its inequalities than had been reached by any of his -predecessors; and with renewed hopes he again attacked the planet Mars, -whose path he was now able to consider undistorted by the illusions -arising out of the motion of the earth. Had the path of Mars been -accurately circular, or even as nearly approaching a circle as that of -the earth, the method he chose of determining its position and size by -means of three distances carefully calculated from his observed -parallaxes, would have given a satisfactory result; but finding, as he -soon did, that almost every set of three distances led him to a -different result, he began to suspect another error in the long-received -opinion, that the orbits of the planets must consist of a combination -of circles; he therefore, determined, in the first instance, to fix the -distances of the planet at the apsides without any reference to the form -of the intermediate orbit. Half the difference between these would, of -course, be the excentricity of the orbit; and as this quantity came out -very nearly the same as had been determined on the vicarious theory, it -seemed clear that the error of that theory, whatever it might be, did -not lie in these elements. - -Kepler also found that in the case of this planet likewise, the times of -describing equal arcs at the apsides were proportional to its distances -from the sun, and he naturally expected that the method of areas would -measure the planet's motion with as much accuracy as he had found in the -case of the earth. This hope was disappointed: when he calculated the -motion of the planet by this method, he obtained places too much -advanced when near the apsides, and too little advanced at the mean -distances. He did not, on that account, immediately reject the opinion -of circular orbits, but was rather inclined to suspect the principle of -measurement, at which he felt that he had arrived in rather a precarious -manner. He was fully sensible that his areas did not accurately -represent the sums of any distances except those measured from the -centre of the circle; and for some time he abandoned the hope of being -able to use this substitution, which he always considered merely as an -approximate representation of the true measure, the sum of the -distances. But on examination he found that the errors of this -substitution were nearly insensible, and those it did in fact produce, -were in the contrary direction of the errors he was at this time -combating. As soon as he had satisfied himself of this, he ventured once -more on the supposition, which by this time had, in his eyes, almost -acquired the force of demonstration, that the orbits of the planets are -not circular, but of an oval form, retiring within the circle at the -mean distances, and coinciding with it at the apsides. - -This notion was not altogether new; it had been suggested in the case of -Mercury, by Purbach, in his "Theories of the Planets." In the edition of -this work published by Reinhold, the pupil of Copernicus, we read the -following passage. "Sixthly, it appears from what has been said, that -the centre of Mercury's epicycle, by reason of the motions -above-mentioned, does not, as is the case with the other planets, -describe the circumference of a circular deferent, but rather the -periphery of a figure resembling a plane oval." To this is added the -following note by Reinhold. "The centre of the Moon's epicycle describes -a path of a lenticular shape; Mercury's on the contrary is egg-shaped, -the big end lying towards his apogee, and the little end towards his -perigee."[191] The excentricity of Mercury's orbit is, in fact, much -greater than that of any of the other planets, and the merit of making -this first step cannot reasonably be withheld from Purbach and his -commentator, although they did not pursue the inquiry so far as Kepler -found himself in a condition to do. - -Before proceeding to the consideration of the particular oval which -Kepler fixed upon in the first instance, it will be necessary, in order -to render intelligible the source of many of his doubts and -difficulties, to make known something more of his theory of the moving -force by which he supposed the planets to be carried round in their -orbits. In conformity with the plan hitherto pursued, this shall be done -as much as possible in his own words. - -"It is one of the commonest axioms in natural philosophy, that if two -things always happen together and in the same manner, and admit the same -measure, either the one is the cause of the other, or both are the -effect of a common cause. In the present case, the increase or languor -of motion invariably corresponds with an approach to or departure from -the centre of the universe. Therefore, either the languor is the cause -of the departure of the star, or the departure of the languor, or both -have a common cause. But no one can be of opinion that there is a -concurrence of any third thing to be a common cause of these two -effects, and in the following chapters it will be made clear that there -is no occasion to imagine any such third thing, since the two are of -themselves sufficient. Now, it is not agreeable to the nature of things -that activity or languor in linear motion should be the cause of -distance from the centre. For, distance from the centre is conceived -anteriorly to linear motion. In fact linear motion cannot exist without -distance from the centre, since it requires space for its -accomplishment, but distance from the centre can be conceived without -motion. Therefore distance is the cause of the activity of motion, and a -greater or less distance of a greater or less delay. And since distance -is of the kind of relative quantities, whose essence consists in -boundaries, (for there is no efficacy in relation _per se_ without -regard to bounds,) it follows that the cause of the varying activity of -motion rests in one of the boundaries. But the body of the planet -neither becomes heavier by receding, nor lighter by approaching. -Besides, it would perhaps be absurd on the very mention of it, that an -animal force residing in the moveable body of the planet for the purpose -of moving it, should exert and relax itself so often without weariness -or decay. It remains, therefore, that the cause of this activity and -languor resides at the other boundary, that is, in the very centre of -the world, from which the distances are computed.--Let us continue our -investigation of this moving virtue which resides in the sun, and we -shall presently recognize its very close analogy to light. And although -this moving virtue cannot be identical with the light of the sun, let -others look to it whether the light is employed as a sort of instrument, -or vehicle, to convey the moving virtue. There are these seeming -contradictions:--first, light is obstructed by opaque bodies, for which -reason if the moving virtue travelled on the light, darkness would be -followed by a stoppage of the moveable bodies. Again, light flows out in -right lines spherically, the moving virtue in right lines also, but -cylindrically; that is, it turns in one direction only, from west to -east; not in the opposite direction, not towards the poles, &c. But -perhaps we shall be able presently to reply to these objections. In -conclusion, since there is as much virtue in a large and remote circle -as in a narrow and close one, nothing of the virtue perishes in the -passage from its source, nothing is scattered between the source and the -moveable. Therefore the efflux, like that of light, is not material, and -is unlike that of odours, which are accompanied by a loss of substance, -unlike heat from a raging furnace, unlike every other emanation by which -mediums are filled. It remains, therefore, that as light which -illuminates all earthly things, is the immaterial species of that fire -which is in the body of the sun, so this virtue, embracing and moving -all the planetary bodies, is the immaterial species of that virtue which -resides in the sun itself, of incalculable energy, and so the primary -act of all mundane motion.--I should like to know who ever said that -there was anything material in light!--Guided by our notion of the -efflux of this species (or archetype), let us contemplate the more -intimate nature of the source itself. For it seems as if something -divine were latent in the body of the sun, and comparable to our own -soul, whence that species emanates which drives round the planets; just -as from the mind of a slinger the species of motion sticks to the -stones, and carries them forward, even after he who cast them has drawn -back his hand. But to those who wish to proceed soberly, reflections -differing a little from these will be offered." - -Our readers will, perhaps, be satisfied with the assurance, that these -sober considerations will not enable them to form a much more accurate -notion of Kepler's meaning than the passages already cited. We shall -therefore proceed to the various opinions he entertained on the motion -of the planets. - -He considered it as established by his theory, that the centre E of the -planet's epicycle (see fig. p. 33.) moved round the circumference of the -deferent D_d_, according to the law of the planet's distances; the point -remaining to be settled was the motion of the planet in the epicycle. If -it were made to move according to the same law, so that when the centre -of the epicycle reached E, the planet should be at F, taking the angle -BEF equal to BSA, it has been shewn (p. 19) that the path of F would -still be a circle, excentric from D_d_ by DA the radius of the epicycle. - -But Kepler fancied that he saw many sound reasons why this could not be -the true law of motion in the epicycle, on which reasons he relied much -more firmly than on the indisputable fact, which he mentions as a -collateral proof, that it was contradicted by the observations. Some of -these reasons are subjoined: "In the beginning of the work it has been -declared to be most absurd, that a planet (even though we suppose it -endowed with mind) should form any notion of a centre, and a distance -from it, if there be no body in that centre to serve for a -distinguishing mark. And although you should say, that the planet has -respect to the sun, and knows beforehand, and remembers the order in -which the distances from the sun are comprised, so as to make a perfect -excentric; in the first place, this is rather far-fetched, and requires, -in any mind, means for connecting the effect of an accurately circular -path with the sign of an increasing and diminishing diameter of the sun. -But there are no such means, except the position of the centre of the -excentric at a given distance from the sun; and I have already said, -that this is beyond the power of a mere mind. I do not deny that a -centre may be imagined, and a circle round it; but this I do say, if the -circle exists only in imagination, with no external sign or division, -that it is not possible that the path of a moveable body should be -really ordered round it in an exact circle. Besides, if the planet -chooses from memory its just distances from the sun, so as exactly to -form a circle, it must also take from the same source, as if out of the -Prussian or Alphonsine tables, equal excentric arcs, to be described in -unequal times, and to be described by a force extraneous from the sun; -and thus would have, from its memory, a foreknowledge of what effects a -virtue, senseless and extraneous from the sun, was about to produce: all -these consequences are absurd. - -"It is therefore more agreeable to reason that the planet takes no -thought, either of the excentric or epicycle; but that the work which it -accomplishes, or joins in effecting, is a libratory path in the diameter -B_b_ of the epicycle, in the direction towards the sun. The law is now -to be discovered, according to which the planet arrives at the proper -distances in any time. And indeed in this inquiry, it is easier to say -what the law is not than what it is."--Here, according to his custom, -Kepler enumerates several laws of motion by which the planet might -choose to regulate its energies, each of which is successively -condemned. Only one of them is here mentioned, as a specimen of the -rest. "What then if we were to say this? Although the motions of the -planet are not epicyclical, perhaps the libration is so arranged that -the distances from the sun are equal to what they would have been in a -real epicyclical motion.--This leads to more incredible consequences -than the former suppositions, and yet in the dearth of better opinions, -let us for the present content ourselves with this. The greater number -of absurd conclusions it will be found to involve, the more ready will a -physician be, when we come to the fifty-second chapter, to admit what -the observations testify, that the path of the planet is not circular." - -The first oval path on which Kepler was induced to fix, by these and -many other similar considerations, was in the first instance very -different from the true elliptical form. Most authors would have thought -it unnecessary to detain their readers with a theory which they had once -entertained and rejected; but Kepler's work was written on a different -plan. He thus introduces an explanation of his first oval. "As soon as I -was thus taught by Brahe's very accurate observations that the orbit of -a planet is not circular, but more compressed at the sides, on the -instant I thought that I understood the natural cause of this -deflection. But the old proverb was verified in my case;--the more haste -the less speed.--For having violently laboured in the 39th chapter, in -consequence of my inability to find a sufficiently probable cause why -the orbit of the planet should be a perfect circle, (some absurdities -always remaining with respect to that virtue which resides in the body -of the planet,) and having now discovered from the observations, that -the orbit is not a perfect circle, I felt furiously inclined to believe -that if the theory which had been recognized as absurd, when employed in -the 39th chapter for the purpose of fabricating a circle, were modulated -into a more probable form, it would produce an accurate orbit agreeing -with the observations. If I had entered on this course a little more -warily, I might have detected the truth immediately. But, being blinded -by my eagerness, and not sufficiently regardful of every part of the -39th chapter, and clinging to my first opinion, which offered itself to -me with a wonderful show of probability, on account of the equable -motion in the epicycle, I got entangled in new perplexities, with which -we shall now have to struggle in this 45th chapter and the following -ones as far as the 50th chapter." - -In this theory, Kepler supposed that whilst the centre of the epicycle -was moving round a circular deferent according to the law of the -planets' distances (or areas) the planet itself moved equably in the -epicycle, with the mean angular velocity of its centre in the deferent. -In consequence of this supposition, since at D, when the planet is at A -the aphelion, the motion in the deferent is less than the mean motion, -the planet will have advanced through an angle BEP greater than BEF or -BSA, through which the centre of the epicycle has moved; and -consequently, the path will lie everywhere within the circle A_a_, -except at the apsides. Here was a new train of laborious calculations to -undergo for the purpose of drawing the curve AP_a_ according to this -law, and of measuring the area of any part of it. After a variety of -fruitless attempts, for this curve is one of singular complexity, he was -reduced, as a last resource, to suppose it insensibly different from an -ellipse on the same principal axes, as an approximate means of -estimating its area. Not content even with the results so obtained, and -not being able to see very clearly what might be the effect of his -alteration in substituting the ellipse for the oval, and in other -simplifications introduced by him, he had courage enough to obtain the -sums of the 360 distances by direct calculation, as he had done in the -old circular theory. - -[Illustration] - -In the preface to his book he had spoken of his labours under the -allegory of a war carried on by him against the planet; and when -exulting in the early prospects of success this calculation seemed to -offer, he did not omit once more to warn his readers, in his peculiar -strain, that this exultation was premature. - -"Allow me, gentle reader, to enjoy so splendid a triumph for one little -day (I mean through the five next chapters), meantime be all rumours -suppressed of new rebellion, that our preparations may not perish, -yielding us no delight. Hereafter if anything shall come to pass, we -will go through it in its own time and season; now let us be merry, as -then we will be bold and vigorous." At the time foretold, that is to -say, at the end of the five merry chapters, the bad news could no longer -be kept a secret. It is announced in the following bulletin:--"While -thus triumphing over Mars, and preparing for him, as for one altogether -vanquished, tabular prisons, and equated eccentric fetters, it is buzzed -here and there that the victory is vain, and that the war is raging anew -as violently as before. For the enemy, left at home a despised captive, -has burst all the chains of the equations, and broken forth of the -prisons of the tables. For no method of geometrically administering the -theory of the 45th chapter was able to come near the accuracy of -approximation of the vicarious theory of the 16th chapter, which gave me -true equations derived from false principles. Skirmishers, disposed all -round the circuit of the excentric, (I mean the true distances,) routed -my forces of physical causes levied out of the 45th chapter, and shaking -off the yoke, regained their liberty. And now there was little to -prevent the fugitive enemy from effecting a junction with his rebellious -supporters, and reducing me to despair, had I not suddenly sent into the -field a reserve of new physical reasonings on the rout and dispersion of -the veterans, and diligently followed, without allowing him the -slightest respite, in the direction in which he had broken out." - -In plainer terms, Kepler found, after this labour was completed, that -the errors in longitude he was still subject to were precisely of an -opposite nature to those he had found with the circle; instead of being -too quick at the apsides, the planet was now too slow there, and too -much accelerated in the mean distances; and the distances obtained from -direct observation were everywhere greater, except at the apsides, than -those furnished by this oval theory. It was in the course of these -tedious investigations that he established, still more satisfactorily -than he had before done, that the inclinations of the planets' orbits -are invariable, and that the lines of their nodes pass through the -centre of the Sun, and not, as before his time had been supposed, -through the centre of the ecliptic. - -When Kepler found with certainty that this oval from which he expected -so much would not satisfy the observations, his vexation was extreme, -not merely from the mortification of finding a theory confuted on which -he had spent such excessive labour, for he was accustomed to -disappointments of that kind, but principally from many anxious and -fruitless speculations as to the real physical causes why the planet did -not move in the supposed epicycle, that being the point of view, as has -been already shewn, from which he always preferred to begin his -inquiries. One part of the reasoning by which he reconciled himself to -the failure exhibits much too curious a view of the state of his mind to -be passed over in silence. The argument is founded on the difficulty -which he met with, as above mentioned, in calculating the proportions of -the oval path he had imagined. "In order that you may see the cause of -the impracticability of this method which we have just gone through, -consider on what foundations it rests. The planet is supposed to move -equably in the epicycle, and to be carried by the Sun unequably in the -proportion of the distances. But by this method it is impossible to be -known how much of the oval path corresponds to any given time, although -the distance at that part is known, unless we first know the length of -the whole oval. But the length of the oval cannot be known, except from -the law of the entry of the planet within the sides of the circle. But -neither can the law of this entry be known before we know how much of -the oval path corresponds to any given time. Here you see that there is -a _petitio principii_; and in my operations I was assuming that of which -I was in search, namely, the length of the oval. This is at least not -the fault of my understanding, but it is also most alien to the primary -Ordainer of the planetary courses: I have never yet found so -ungeometrical a contrivance in his other works. Therefore we must either -hit upon some other method of reducing the theory of the 45th chapter to -calculation; or if that cannot be done, the theory itself, suspected on -account of this _petitio principii_, will totter." Whilst his mind was -thus occupied, one of those extraordinary accidents which it has been -said never occur but to those capable of deriving advantage from them -(but which, in fact, are never noticed when they occur to any one else), -fortunately put him once more upon the right path. Half the extreme -breadth between the oval and the circle nearly represented the errors of -his distances at the mean point, and he found that this half was 429 -parts of a radius, consisting of 100000 parts; and happening to advert -to the greatest optical inequality of Mars, which amounts to about 5° -18´, it struck him that 429 was precisely the excess of the secant of 5° -18´ above the radius taken at 100000. This was a ray of light, and, to -use his own words, it roused him as out of sleep. In short, this single -observation was enough to produce conviction in his singularly -constituted mind, that instead of the distances SF, he should everywhere -substitute FV, determined by drawing SV perpendicular on the line FC, -since the excess of SF above FV is manifestly that of the secant above -the radius in the optical equation SFC at that point. It is still more -extraordinary that a substitution made for such a reason should have the -luck, as is again the case, to be the right one. This substitution in -fact amounted to supposing that the planet, instead of being at the -distance SP or SF, was at S_n_; or, in other words, that instead of -revolving in the circumference, it librated in the diameter of the -epicycle, which was to him an additional recommendation. Upon this new -supposition a fresh set of distances was rapidly calculated, and to -Kepler's inexpressible joy, they were found to agree with the -observations within the limits of the errors to which the latter were -necessarily subject. Notwithstanding this success, he had to undergo, -before arriving at the successful termination of his labours, one more -disappointment. Although the distance corresponding to a time from the -aphelion represented approximately by the area ASF, was thus found to be -accurately represented by the line S_n_, there was still an error with -regard to the direction in which that distance was to be measured. -Kepler's first idea was to set it off in the direction SF, but this he -found to lead to inaccurate longitudes; and it was not until after much -perplexity, driving him, as he tells us, "almost to insanity," that he -satisfied himself that the distance SQ equal to FV ought to be taken -terminating in F_m_, the line from F perpendicular to A_a_, the line of -apsides, and that the curve so traced out by Q would be an accurate -ellipse. - -[Illustration] - -He then found to his equal gratification and amazement, a small part of -which he endeavoured to express by a triumphant figure on the side of -his diagram, that the error he had committed in taking the area ASF to -represent the sums of the distances SF, was exactly counterbalanced; for -this area does accurately represent the sums of the distances FV or SQ. -This compensation, which seemed to Kepler the greatest confirmation of -his theory, is altogether accidental and immaterial, resulting from the -relation between the ellipse and circle. If the laws of planetary -attraction had chanced to have been any other than those which cause -them to describe ellipses, this last singular confirmation of an -erroneous theory could not have taken place, and Kepler would have been -forced either to abandon the theory of the areas, which even then would -have continued to measure and define their motions, or to renounce the -physical opinions from which he professed to have deduced it as an -approximative truth. - -These are two of the three celebrated theorems called Kepler's laws: the -first is, that the planets move in ellipses round the sun, placed in the -focus; the second, that the time of describing any arc is proportional -in the same orbit to the area included between the arc and the two -bounding distances from the sun. The third will be mentioned on another -occasion, as it was not discovered till twelve years later. On the -establishment of these two theorems, it became important to discover a -method of measuring such elliptic areas, but this is a problem which -cannot be accurately solved. Kepler, in offering it to the attention of -geometricians, stated his belief that its solution was unattainable by -direct processes, on account of the incommensurability of the arc and -sine, on which the measurement of the two parts AQ_m_, SQ_m_ depends. -"This," says he in conclusion, "this is my belief, and whoever shall -shew my mistake, and point out the true solution, - - _Is erit mihi magnus Apollonius._" - - -FOOTNOTES: - -[189] It is not very easy to carry the understanding aright among these -Aristotelian ideas. Many at the present day might think they understood -better what is meant, if for "form" had been written "nature." - -[190] De mundo nostro sublunari, Philosóphia Nova. Amstelodami, 1651. - -[191] Theoricæ novæ planetarum. G. Purbachii, Parisiis, 1553. - - - - -CHAPTER VI. - - _Kepler appointed Professor at Linz--His second marriage--Publishes - his new Method of Gauging--Refuses a Professorship at Bologna._ - - -WHEN presenting this celebrated book to the emperor, Kepler gave notice -that he contemplated a farther attack upon Mars's relations, father -Jupiter, brother Mercury, and the rest; and promised that he would be -successful, provided the emperor would not forget the sinews of war, and -order him to be furnished anew with means for recruiting his army. The -death of his unhappy patron, the Emperor Rodolph, which happened in -1612, barely in time to save him from the last disgrace of deposition -from the Imperial throne, seemed to put additional difficulties in the -way of Kepler's receiving the arrears so unjustly denied to him; but on -the accession of Rodolph's brother, Matthias, he was again named to his -post of Imperial Mathematician, and had also a permanent professorship -assigned to him in the University of Linz. He quitted Prague without -much regret, where he had struggled against poverty during eleven years. -Whatever disinclination he might feel to depart, arose from his -unwillingness to loosen still more the hold he yet retained upon the -wreck of Tycho Brahe's instruments and observations. Tengnagel, -son-in-law of Tycho, had abandoned astronomy for a political career, and -the other members of his family, who were principally females, suffered -the costly instruments to lie neglected and forgotten, although they had -obstructed with the utmost jealousy Kepler's attempts to continue their -utility. The only two instruments Kepler possessed of his own property, -were "An iron sextant of 2½ feet diameter, and a brass azimuthal -quadrant, of 3½ feet diameter, both divided into minutes of a degree." -These were the gift of his friend and patron, Hoffman, the President of -Styria, and with these he made all the observations which he added to -those of Tycho Brahe. His constitution was not favourable to these -studies, his health being always delicate, and suffering much from -exposure to the night air; his eyes also were very weak, as he mentions -himself in several places. In the summary of his character which he drew -up when proposing to become Tycho Brahe's assistant, he describes -himself as follows:--"For observations my sight is dull; for mechanical -operations my hand is awkward; in politics and domestic matters my -nature is troublesome and choleric; my constitution will not allow me, -even when in good health, to remain a long time sedentary (particularly -for an extraordinary time after dinner); I must rise often and walk -about, and in different seasons am forced to make corresponding changes -in my diet." - -The year preceding his departure to Linz was denounced by him as -pregnant with misfortune and misery. "In the first place I could get no -money from the court, and my wife, who had for a long time been -suffering under low spirits and despondency, was taken violently ill -towards the end of 1610, with the Hungarian fever, epilepsy, and -phrenitis. She was scarcely convalescent when all my three children were -at once attacked with small-pox. Leopold with his army occupied the town -beyond the river, just as I lost the dearest of my sons, him whose -nativity you will find in my book on the new star. The town on this side -of the river where I lived was harassed by the Bohemian troops, whose -new levies were insubordinate and insolent: to complete the whole, the -Austrian army brought the plague with them into the city. I went into -Austria, and endeavoured to procure the situation which I now hold. -Returning in June, I found my wife in a decline from her grief at the -death of her son, and on the eve of an infectious fever; and I lost her -also, within eleven days after my return. Then came fresh annoyance, of -course, and her fortune was to be divided with my step-sisters. The -Emperor Rodolph would not agree to my departure; vain hopes were given -me of being paid from Saxony; my time and money were wasted together, -till on the death of the emperor, in 1612, I was named again by his -successor, and suffered to depart to Linz. These, methinks, were reasons -enough why I should have overlooked not only your letters, but even -astronomy itself." - -Kepler's first marriage had not been a happy one; but the necessity in -which he felt himself of providing some one to take charge of his two -surviving children, of whom the eldest, Susanna, was born in 1602, and -Louis in 1607, determined him on entering a second time into the married -state. The account he has left us of the various negotiations which -preceded his final choice, does not, in any point, belie the oddity of -his character. His friends seem to have received a general commission to -look out for a suitable match, and in a long and most amusing letter to -the Baron Strahlendorf, we are made acquainted with the pretensions and -qualifications of no less than eleven ladies among whom his inclinations -wavered. - -The first on the list was a widow, an intimate friend of his first -wife's, and who, on many accounts, appeared a most eligible match. "At -first she seemed favourably inclined to the proposal; it is certain that -she took time to consider it, but at last she very quietly excused -herself." It must have been from a recollection of this lady's good -qualities that Kepler was induced to make his offer; for we learn rather -unexpectedly, after being informed of her decision, that when he soon -afterwards paid his respects to her, it was for the first time that he -had seen her during the last six years; and he found, to his great -relief, that "there was no single pleasing point about her." The truth -seems to be that he was nettled by her answer, and he is at greater -pains than appear necessary, considering this last discovery, to -determine why she would not accept his offered hand. Among other reasons -he suggested her children, among whom were two marriageable daughters; -and it is diverting afterwards to find them also in the catalogue which -Kepler appeared to be making of all his female acquaintance. He seems to -have been much perplexed in attempting to reconcile his astrological -theory with the fact of his having taken so much trouble about a -negotiation not destined to succeed. "Have the stars exercised any -influence here? For just about this time the direction of the Mid-Heaven -is in hot opposition to Mars, and the passage of Saturn, through the -ascending point of the zodiac, in the scheme of my nativity, will happen -again next November and December. But if these are the causes, how do -they act? Is that explanation the true one which I have elsewhere given? -For I can never think of handing over to the stars the office of deities -to produce effects. Let us therefore suppose it accounted for by the -stars, that at this season I am violent in my temper and affections, in -rashness of belief, in a shew of pitiful tender-heartedness; in catching -at reputation by new and paradoxical notions, and the singularity of my -actions; in busily inquiring into, and weighing and discussing, various -reasons; in the uneasiness of my mind with respect to my choice. I thank -God that that did not happen which might have happened; that this -marriage did not take place: now for the others." Of these others, one -was too old, another in bad health, another too proud of her birth and -quarterings; a fourth had learned nothing but shewy accomplishments, -"not at all suitable to the sort of life she would have to lead with -me." Another grew impatient, and married a more decided admirer, whilst -he was hesitating. "The mischief (says he) in all these attachments was, -that whilst I was delaying, comparing, and balancing conflicting -reasons, every day saw me inflamed with a new passion." By the time he -reached the eighth, he found his match in this respect. "Fortune at -length has avenged herself on my doubtful inclinations. At first she was -quite complying, and her friends also: presently, whether she did or did -not consent, not only I, but she herself did not know. After the lapse -of a few days, came a renewed promise, which however had to be confirmed -a third time; and four days after that, she again repented her -confirmation, and begged to be excused from it. Upon this I gave her up, -and this time all my counsellors were of one opinion." This was the -longest courtship in the list, having lasted three whole months; and -quite disheartened by its bad success, Kepler's next attempt was of a -more timid complexion. His advances to No. 9, were made by confiding to -her the whole story of his recent disappointment, prudently determining -to be guided in his behaviour, by observing whether the treatment he had -experienced met with a proper degree of sympathy. Apparently the -experiment did not succeed; and almost reduced to despair, Kepler betook -himself to the advice of a friend, who had for some time past complained -that she was not consulted in this difficult negotiation. When she -produced No. 10, and the first visit was paid, the report upon her was -as follows:--"She has, undoubtedly, a good fortune, is of good family, -and of economical habits: but her physiognomy is most horribly ugly; she -would be stared at in the streets, not to mention the striking -disproportion in our figures. I am lank, lean, and spare; she is short -and thick: in a family notorious for fatness she is considered -superfluously fat." The only objection to No. 11 seems to have been her -excessive youth; and when this treaty was broken of on that account, -Kepler turned his back upon all his advisers, and chose for himself one -who had figured as No. 5 in the list, to whom he professes to have felt -attached throughout, but from whom the representations of his friends -had hitherto detained him, probably on account of her humble station. - -The following is Kepler's summary of her character. "Her name is -Susanna, the daughter of John Reuthinger and Barbara, citizens of the -town of Eferdingen; the father was by trade a cabinet-maker, but both -her parents are dead. She has received an education well worth the -largest dowry, by favour of the Lady of Stahrenberg, the strictness of -whose household is famous throughout the province. Her person and -manners are suitable to mine; no pride, no extravagance; she can bear to -work; she has a tolerable knowledge how to manage a family; middle-aged, -and of a disposition and capability to acquire what she still wants. Her -I shall marry by favour of the noble baron of Stahrenberg at twelve -o'clock on the 30th of next October, with all Eferdingen assembled to -meet us, and we shall eat the marriage-dinner at Maurice's at the Golden -Lion." - -Hantsch has made an absurd mistake with regard to this marriage, in -stating that the bride was only twelve years old. Kästner and other -biographers have been content to repeat the same assertion without any -comment, notwithstanding its evident improbability. The origin of the -blunder is to be found in Kepler's correspondence with Bernegger, to -whom, speaking of his wife, he says "She has been educated for twelve -years by the Lady of Stahrenberg." This is by no means a single instance -of carelessness in Hantsch; Kästner has pointed out others of greater -consequence. It was owing to this marriage, that Kepler took occasion to -write his new method of gauging, for as he tells us in his own peculiar -style "last November I brought home a new wife, and as the whole course -of Danube was then covered with the produce of the Austrian vineyards, -to be sold at a reasonable rate, I purchased a few casks, thinking it my -duty as a good husband and a father of a family, to see that my -household was well provided with drink." When the seller came to -ascertain the quantity, Kepler objected to his method of gauging, for -he allowed no difference, whatever might be the proportion of the -bulging parts. The reflections to which this incident gave rise, -terminated in the publication of the above-mentioned treatise, which -claims a place among the earliest specimens of what is now called the -modern analysis. In it he extended several properties of plane figures -to segments of cones and cylinders, from the consideration that "these -solids are incorporated circles," and, therefore, that those properties -are true of the whole which belong to each component part. That the book -might end as oddly as it began, Kepler concluded it with a parody of -Catullus: - - "Et cum pocula mille mensi erîmus - Conturbabimus illa, ne sciamus." - -His new residence at Linz was not long undisturbed. He quarrelled there, -as he had done in the early part of his life at Gratz, with the Roman -Catholic party, and was excommunicated. "Judge," says he to Peter -Hoffman, "how far I can assist you, in a place where the priest and -school-inspector have combined to brand me with the public stigma of -heresy, because in every question I take that side which seems to me to -be consonant with the word of God." The particular dogma which -occasioned his excommunication, was connected with the doctrine of -transubstantiation. He published his creed in a copy of Latin verses, -preserved by his biographer Hantsch. - -Before this occurrence, Kepler had been called to the diet at Ratisbon -to give his opinion on the propriety of adopting the Gregorian -reformation of the calendar, and he published a short essay, pointing -out the respective convenience of doing so, or of altering the old -Julian Calendar in some other manner. Notwithstanding the readiness of -the diet to avail themselves of his talents for the settlement of a -difficult question, the arrears of his salary were not paid much more -regularly than they had been in Rodolph's time, and he was driven to -provide himself with money by the publication of his almanac, of which -necessity he heavily and justly complained. "In order to pay the expense -of the Ephemeris for these two years, I have also written a vile -prophesying almanac, which is scarcely more respectable than begging; -unless it be because it saves the emperor's credit, who abandons me -entirely; and with all his frequent and recent orders in council, would -suffer me to perish with hunger." Kepler published this Ephemeris -annually till 1620; ten years later he added those belonging to the -years from 1620 to 1628. - -In 1617 Kepler was invited into Italy, to succeed Magini as Professor of -Mathematics at Bologna. The offer tempted him; but, after mature -consideration, he rejected it, on grounds which he thus explained to -Roffini:--"By birth and spirit I am a German, imbued with German -principles, and bound by such family ties, that even if the emperor -should consent, I could not, without the greatest difficulty, remove my -dwelling-place from Germany into Italy. And although the glory of -holding so distinguished a situation among the venerable professors of -Bologna stimulates me, and there appears great likelihood of notably -increasing my fortune, as well from the great concourse to the public -lectures, as from private tuition; yet, on the other hand, that period -of my life is past which was once excited by novelty, or which might -promise itself a long enjoyment of these advantages. Besides, from a boy -up to my present years, living a German among Germans, I am accustomed -to a degree of freedom in my speech and manners, which, if persevered in -on my removal to Bologna, seems likely to draw upon me, if not danger, -at least notoriety, and might expose me to suspicion and party malice. -Notwithstanding this answer, I have yet hopes that your most honourable -invitation will be of service to me, and may make the imperial treasurer -more ready than he has hitherto been to fulfil his master's intentions -towards me. In that case I shall the sooner be able to publish the -Rudolphine Tables and the Ephemerides, of which you had the scheme so -many years back; and in this manner you and your advisers may have no -reason to regret this invitation, though for the present it seems -fruitless." - -In 1619, the Emperor Matthias died, and was succeeded by Ferdinand III., -who retained Kepler in the post he had filled under his two predecessors -on the imperial throne. Kästner, in his "History of Mathematics," has -corrected a gross error of Hantsch, in asserting that Kepler -prognosticated Matthias's death. The letter to which Hantsch refers, in -support of his statement, does indeed mention the emperor's death, but -merely as a notorious event, for the purpose of recalling a date to the -memory of his correspondent. - - - - -CHAPTER VII. - - _Kepler publishes his Harmonics--Account of his Astrological - Opinions and Discovery of the Law of the Periods of the Planetary - Revolutions--Sketch of Newton's proof of Kepler's Laws._ - - -THE "Cosmographical Mystery" was written, as has been already mentioned, -when Kepler was only twenty-six, and the wildness of its theories might -be considered as due merely to the vivacity of a young man; but as if -purposely to shew that his maturer age did not renounce the creations of -his youthful fancy, he reprinted the "Mystery" in 1619, nearly at the -same time when he published his celebrated work on Harmonics; and the -extravagance of the latter publication does not at all lose in -comparison with its predecessor. It is dedicated to James I. of England, -and divided into five books: "The first, Geometrical, on the origin and -demonstration of the laws of the figures which produce harmonious -proportions;--the second, Architectonical, on figurate geometry, and the -congruence of plane and solid regular figures;--the third, properly -Harmonic, on the derivation of musical proportions from figures, and on -the nature and distinction of things relating to song, in opposition to -the old theories;--the fourth, Metaphysical, Psychological, and -Astrological, on the mental essence of harmonies, and of their kinds in -the world, especially on the harmony of rays emanating on the earth from -the heavenly bodies, and on their effect in nature, and on the sublunary -and human soul;--the fifth, Astronomical and Metaphysical, on the very -exquisite harmonies of the celestial motions, and the origin of the -excentricities in harmonious proportions." - -The two first books are almost strictly, as Kepler styles them, -geometrical, relating in great measure to the inscription of regular -polygons in a circle. The following passage is curious, presenting an -analogous idea to that contained in one of the extracts already given -from the Commentaries on Mars. "The heptagon, and all other polygons and -stars beyond it, which have a prime number of sides, and all other -figures derived from them, cannot be inscribed geometrically in a -circle; although their sides have a necessary magnitude, it is equally a -matter of necessity that we remain ignorant of it. This is a question of -great importance, for on this account is it that the heptagon, and other -figures of this kind, have not been employed by God in the adornment of -the world, as the other intelligible figures are employed which have -been already explained." Kepler then introduces the algebraical -equation, on the solution of which this problem depends, and makes a -remark which is curious at this period of the history of algebra--that -the root of an equation which cannot be accurately found, may yet be -found within any degree of approximation by an expert calculator. In -conclusion he again remarks that "the side of the heptagon has no place -among scientific existences, since its formal description is impossible, -and therefore it cannot be known by the human mind, since the -possibility of description precedes the possibility of knowledge; nor is -it known even by the simple eternal act of an omniscient mind, because -its nature belongs to things which cannot be known. And yet this -scientific nonentity has some scientific properties, for if a heptagon -were described in a circle, the proportion of its sides would have -analogous proportions." - -The third book is a treatise on music, in the confined and ordinary -sense in which we now use that word, and apparently a sober and rational -one, at least as nearly so as Kepler could be trusted to write on a -subject so dangerous to his discretion. All the extravagance of the work -seems reserved for the fourth book, the title of which already conveys -some notion of the nature of its contents. In this book he has collected -the substance of the astrological opinions scattered through his other -works. We shall content ourselves with merely citing his own words, -without any attempt to explain the difference between the astrology -which he believed, and that which he contemptuously rejected. The -distinctive line seems very finely drawn, and as both one and the other -are now discarded by all who enjoy the full use of their reasoning -powers, it is not of much consequence that it should be accurately -traced. - -It is to be observed, that he does not in this treatise modify or recant -anything of his earlier opinions, but refers to the favourable judgment -of his contemporary philosophers as a reason for embodying them in a -regular form. "Since many very celebrated professors of philosophy and -medicine are of opinion that I have created a new and most true -philosophy, this tender plant, like all novelties, ought to be carefully -nursed and cherished, so that it may strike root in the minds of -philosophers, and not be choked by the excessive humours of vain -sophistications, or washed away by the torrents of vulgar prejudices, or -frozen by the chill of public neglect; and if I succeed in guarding it -from these dangers, I have no fear that it will be crushed by the storms -of calumny, or parched by the sun of sterling criticism." - -One thing is very remarkable in Kepler's creed, that he whose candour is -so indisputable in every other part of his conduct, professed to have -been forced to adopt his astrological opinions from direct and positive -observation.--"It is now more than twenty years since I began to -maintain opinions like these on the predominant nature of the elements, -which, adopting the common name, I call sublunary. I have been driven to -this not by studying or admiring Plato, but singly and solely by -observing seasons, and noting the aspects by which they are produced. I -have seen the state of the atmosphere almost uniformly disturbed as -often as the planets are in conjunction, or in the other configurations -so celebrated among astrologers. I have noticed its tranquil state, -either when there are none or few such aspects, or when they are -transitory and of short duration. I have not formed an opinion on this -matter without good grounds, like the common herd of prophesiers, who -describe the operations of the stars as if they were a sort of deities, -the lords of heaven and earth, and producing everything at their -pleasure. They never trouble themselves to consider what means the stars -have of working any effects among us on the earth, whilst they remain in -the sky, and send down nothing to us which is obvious to the senses -except rays of light. This is the principal source of the filthy -astrological superstitions of that vulgar and childish race of dreamers, -the prognosticators." - -The real manner in which the configurations of the stars operate, -according to Kepler, is as follows:--"Like one who listens to a sweet -melodious song, and by the gladness of his countenance, by his voice, -and by the beating of his hand or foot attuned to the music, gives token -that he perceives and approves the harmony: just so does sublunary -nature, with the notable and evident emotion of the bowels of the earth, -bear like witness to the same feelings, especially at those times when -the rays of the planets form harmonious configurations on the -earth."--"I have been confirmed in this theory by that which might have -deterred others; I mean, by observing that the emotions do not agree -nicely with the instants of the configurations; but the earth sometimes -appears lazy and obstinate, and at another time (after important and -long-continued configurations) she becomes exasperated, and gives way to -her passion, even without the continuation of aspects. For in fact the -earth is not an animal like a dog, ready at every nod; but more like a -bull, or an elephant, slow to become angry, and so much the more furious -when incensed." - -This singular doctrine must not be mistaken for one of Kepler's -favourite allegories; he actually and literally professed to believe -that the earth was an enormous living animal; and he has enumerated, -with a particularity of details into which we forbear to follow him, the -analogies he recognized between its habits and those of men and other -animals. A few samples of these may speak for the rest. "If any one who -has climbed the peaks of the highest mountains throw a stone down their -very deep clefts, a sound is heard from them; or if he throw it into one -of the mountain lakes, which beyond doubt are bottomless, a storm will -immediately arise, just as when you thrust a straw into the ear or nose -of a ticklish animal, it shakes its head, or runs shuddering away. What -so like breathing, especially of those fish who draw water into their -mouths and spout it out again through their gills, as that wonderful -tide! For although it is so regulated according to the course of the -moon, that, in the preface to my 'Commentaries on Mars,' I have -mentioned it as probable that the waters are attracted by the moon as -iron is by the loadstone; yet, if any one uphold that the earth -regulates its breathing according to the motion of the sun and moon, as -animals have daily and nightly alternations of sleep and waking, I shall -not think his philosophy unworthy of being listened to; especially if -any flexible parts should be discovered in the depths of the earth to -supply the functions of lungs or gills." - -From the next extract, we must leave the reader to learn as well as he -may, how much Kepler did, and how much he did not believe on the -subject of genethliac astrology.--"Hence it is that human spirits, at -the time of celestial aspects, are particularly urged to complete the -matters which they have in hand. What the goad is to the ox, what the -spur or the rowel is to the horse, to the soldier the bell and trumpet, -an animated speech to an audience, to a crowd of rustics a performance -on the fife and bagpipes, that to all, and especially in the aggregate, -is a heavenly configuration of suitable planets; so that every single -one is excited in his thoughts and actions, and all become more ready to -unite and associate their efforts. For instance, in war you may see that -tumults, battles, fights, invasions, assaults, attacks, and panic fears, -generally happen at the time of the aspects of Mars and Mercury, Mars -and Jupiter, Mars and the Sun, Mars and Saturn, &c. In epidemic -diseases, a greater number of persons are attacked at the times of the -powerful aspects, they suffer more severely, or even die, owing to the -failure of nature in her strife with the disease, which strife (and not -the death) is occasioned by the aspect. It is not the sky which does all -these things immediately, but the faculty of the vital soul, associating -its operation with the celestial harmonies, is the principal agent in -this so-called influence of the heavens. Indeed this word influence has -so fascinated some philosophers that they prefer raving with the -senseless vulgar, to learning the truth with me. This essential property -is the principal foundation of that admirable genethliac art. For when -anything begins to have its being when that is working harmonies, the -sensible harmony of the rays of the planets has peculiar influence on -it. This then is the cause why those who are born under a season of many -aspects among the planets, generally turn out busy and industrious, -whether they accustom themselves from childhood to amass wealth, or are -born or chosen to direct public affairs, or finally, have given their -attention to study. If any one think that I might be taken as an -instance of this last class, I do not grudge him the knowledge of my -nativity. I am not checked by the reproach of boastfulness, -notwithstanding those who, by speech or conduct, condemn as folly all -kinds of writing on this subject; the idiots, the half-learned, the -inventors of titles and trappings, to throw dust in the eyes of the -people, and those whom Picus calls the plebeian theologians: among the -true lovers of wisdom, I easily clear myself of this imputation, by the -advantage of my reader; for there is no one whose nativity or whose -internal disposition and temper I can learn so well as I know my own. -Well then, Jupiter nearest the nonagesimal had passed by four degrees -the trine of Saturn; the Sun and Venus, in conjunction, were moving from -the latter towards the former, nearly in sextiles with both: they were -also removing from quadratures with Mars, to which Mercury was closely -approaching: the moon drew near the trine of the same planet, close to -the Bull's Eye, even in latitude. The 25th degree of Gemini was rising, -and the 22d of Aquarius culminating. That there was this triple -configuration on that day--namely, the sextile of Saturn and the Sun, -the sextile of Mars and Jupiter, the quadrature of Mercury and Mars, is -proved by the change of weather; for, after a frost of some days, that -very day became warmer, there was a thaw and a fall of rain.[192] - -"I do not wish this single instance to be taken as a defence and proof -of all the aphorisms of astrologers, nor do I attribute to the heavens -the government of human affairs: what a vast interval still separates -these philosophical observations from that folly or madness as it should -rather be called. For, following up this example, I knew a lady[193], -born under nearly the same aspects, whose disposition, indeed, was -exceedingly restless, but who not only makes no progress in literature -(that is not strange in a woman), but troubles her whole family, and is -the cause to herself of deplorable misery. What, in my case, assisted -the aspects was--firstly, the fancy of my mother when pregnant with me, -a great admirer of her mother-in-law, my grandmother, who had some -knowledge of medicine, my grandfather's profession; a second cause is, -that I was born a male, and not a female, for astrologers have sought -in vain to distinguish sexes in the sky; thirdly, I derive from my -mother a habit of body, more fit for study than other kinds of life; -fourthly, my parents' fortune was not large, and there was no landed -property to which I might succeed and become attached; fifthly, there -were the schools, and the liberality of the magistracy towards such boys -as were apt for learning. But now if I am to speak of the result of my -studies, what I pray can I find in the sky, even remotely alluding to -it. The learned confess that several not despicable branches of -philosophy have been newly extricated or amended or brought to -perfection by me: but here my constellations were, not Mercury from the -east, in the angle of the seventh, and in quadratures with Mars, but -Copernicus, but Tycho Brahe, without whose books of observations -everything now set by me in the clearest light must have remained buried -in darkness; not Saturn predominating Mercury, but my Lords the Emperors -Rodolph and Matthias; not Capricorn, the house of Saturn, but Upper -Austria, the home of the Emperor, and the ready and unexampled bounty of -his nobles to my petition. Here is that corner, not the western one of -the horoscope, but on the Earth, whither, by permission of my imperial -master, I have betaken myself from a too uneasy court; and whence, -during these years of my life, which now tends towards its setting, -emanate these Harmonies, and the other matters on which I am engaged. - -"However, it may be owing to Jupiter's ascendancy that I take greater -delight in the application of geometry to physics, than in that abstract -pursuit which partakes of the dryness of Saturn; and it is perhaps the -gibbous moon, in the bright constellation of the Bull's forehead, which -fills my mind with fantastic images." - -The most remarkable thing contained in the 5th Book, is the announcement -of the celebrated law connecting the mean distances of the planets with -the periods of their revolution about the Sun. This law is expressed in -mathematical language, by saying that the squares of the times vary as -the cubes of the distances.[194] Kepler's rapture on detecting it was -unbounded, as may be seen from the exulting rhapsody with which he -announced it. "What I prophecied two-and-twenty years ago, as soon as I -discovered the five solids among the heavenly orbits--what I firmly -believed long before I had seen Ptolemy's 'Harmonics'--what I had -promised my friends in the title of this book, which I named before I -was sure of my discovery--what, sixteen years ago, I urged as a thing to -be sought--that for which I joined Tycho Brahe, for which I settled in -Prague, for which I have devoted the best part of my life to -astronomical contemplations, at length I have brought to light, and have -recognized its truth beyond my most sanguine expectations. Great as is -the absolute nature of Harmonics with all its details, as set forth in -my third book, it is all found among the celestial motions, not indeed -in the manner which I imagined, (that is not the least part of my -delight,) but in another very different, and yet most perfect and -excellent. It is now eighteen months since I got the first glimpse of -light, three months since the dawn, very few days since the unveiled -sun, most admirable to gaze on, burst out upon me. Nothing holds me; I -will indulge in my sacred fury; I will triumph over mankind by the -honest confession, that I have stolen the golden vases of the -Egyptians[195], to build up a tabernacle for my God far away from the -confines of Egypt. If you forgive me, I rejoice; if you are angry, I can -bear it: the die is cast, the book is written; to be read either now or -by posterity, I care not which: it may well wait a century for a reader, -as God has waited six thousand years for an observer." - -He has told, with his usual particularity, the manner and precise moment -of the discovery. "Another part of my 'Cosmographical Mystery,' -suspended twenty-two years ago, because it was then undetermined, is -completed and introduced here, after I had discovered the true intervals -of the orbits, by means of Brahe's observations, and had spent the -continuous toil of a long time in investigating the true proportion of -the periodic times to the orbits, - - Sera quidem respexit inertem, - Respexit tamen, et longo post tempore venit. - -If you would know the precise moment, the first idea came across me on -the 8th March of this year, 1618; but chancing to make a mistake in the -calculation, I rejected it as false. I returned again to it with new -force on the 15th May, and it has dissipated the darkness of my mind by -such an agreement between this idea and my seventeen years' labour on -Brahe's observations, that at first I thought I must be dreaming, and -had taken my result for granted in my first assumptions. But the fact is -perfect, the fact is certain, that the proportion existing between the -periodic times of any two planets is exactly the sesquiplicate -proportion of the mean distances of the orbits." - -There is high authority for not attempting over anxiously to understand -the rest of the work. Delambre sums it up as follows:--"In the music of -the celestial bodies it appears that Saturn and Jupiter take the bass, -Mars the tenor, the Earth and Venus the counter-tenor, and Mercury the -treble." If the patience of this indefatigable historian gave way, as he -confesses, in the perusal, any further notice of it here may be well -excused. Kepler became engaged, in consequence of this publication, in -an angry controversy with the eccentric Robert Fludd, who was at least -Kepler's match in wild extravagance and mysticism, if far inferior to -him in genius. It is diverting to hear each reproaching the other with -obscurity. - -In the "Epitome of the Copernican Astronomy," which Kepler published -about the same time, we find the manner in which he endeavoured to -deduce the beautiful law of periodic times, from his principles of -motion and radiation of whirling forces. This work is in fact a summary -of all his astronomical opinions, drawn up in a popular style in the -form of question and answer. We find there a singular argument against -believing, as some did, that each planet is carried round by an angel, -for in that case, says Kepler, "the orbits would be perfectly circular; -but the elliptic form, which we find in them, rather smacks of the -nature of the lever and material necessity." - -The investigation of the relation between the periodic times and -distances of the planets is introduced by a query whether or not they -are to be considered heavy. The answer is given in the following -terms:--"Although none of the celestial globes are heavy, in the sense -in which we say on earth that a stone is heavy, nor light as fire is -light with us, yet have they, by reason of their materiality, a natural -inability to move from place to place: they have a natural inertness or -quietude, in consequence of which they remain still in every situation -where they are placed alone. - -"_P._ Is it then the sun, which by its turning carries round the -planets? How can the sun do this, having no hands to seize the planet at -so great a distance, and force it round along with itself?--Its bodily -virtue, sent forth in straight lines into the whole space of the world, -serves instead of hands; and this virtue, being a corporeal species, -turns with the body of the sun like a very rapid vortex, and travels -over the whole of that space which it fills as quickly as the sun -revolves in its very confined space round the centre. - -"_P._ Explain what this virtue is, and belonging to what class of -things?--As there are two bodies, the mover and the moved, so are there -two powers by which the motion is obtained. The one is passive, and -rather belonging to matter, namely, the resemblance of the body of the -planet to the body of the sun in its corporeal form, and so that part of -the planetary body is friendly, the opposite part hostile to the sun. -The other power is active, and bearing more relation to form, namely, -the body of the sun has a power of attracting the planet by its friendly -part, of repelling it by the hostile part, and finally, of retaining it -if it be placed so that neither the one nor the other be turned directly -towards the sun. - -"_P._ How can it be that the whole body of the planet should be like or -cognate to the body of the sun, and yet part of the planet friendly, -part hostile to the sun?--Just as when one magnet attracts another, the -bodies are cognate; but attraction takes place only on one side, -repulsion on the other. - -"_P._ Whence, then, arises that difference of opposite parts in the same -body?--In magnets the diversity arises from the situation of the parts -with respect to the whole. In the heavens the matter is a little -differently arranged, for the sun does not, like the magnet, possess -only on one side, but in all the parts of its substance, this active and -energetic faculty of attracting, repelling, or retaining the planet. So -that it is probable that the centre of the solar body corresponds to one -extremity or pole of the magnet, and its whole surface to the other -pole. - -"_P._ If this were so, all the planets would be restored[196] in the -same time with the sun?--True, if this were all: but it has been said -already that, besides this carrying power of the sun, there is also in -the planets a natural inertness to motion, which causes that, by reason -of their material substance, they are inclined to remain each in its -place. The carrying power of the sun, and the impotence or material -inertness of the planet, are thus in opposition. Each shares the -victory; the sun moves the planet from its place, although in some -degree it escapes from the chains with which it was held by the sun, and -so is taken hold of successively by every part of this circular virtue, -or, as it may be called, solar circumference, namely, by the parts which -follow those from which it has just extricated itself. - -"_P._ But how does one planet extricate itself more than another from -this violence--First, because the virtue emanating from the sun has the -same degree of weakness at different distances, as the distances or the -width of the circles described on these distances.[197] This is the -principal reason. Secondly, the cause is partly in the greater or less -inertness or resistance of the planetary globes, which reduces the -proportions to one-half; but of this more hereafter. - -"_P._ How can it be that the virtue emanating from the sun becomes -weaker at a greater distance? What is there to hurt or weaken -it?--Because that virtue is corporeal, and partaking of quantity, which -can be spread out and rarefied. Then, since there is as much virtue -diffused in the vast orb of Saturn as is collected in the very narrow -one of Mercury, it is very rare and therefore weak in Saturn's orbit, -very dense and therefore powerful at Mercury. - -"_P._ You said, in the beginning of this inquiry into motion, that the -periodic times of the planets are exactly in the sesquiplicate -proportion of their orbits or circles: pray what is the cause of -this?--Four causes concur for lengthening the periodic time. First, the -length of the path; secondly, the weight or quantity of matter to be -carried; thirdly, the degree of strength of the moving virtue; fourthly, -the bulk or space into which is spread out the matter to be moved. The -circular paths of the planets are in the simple ratio of the distances; -the weights or quantities of matter in different planets are in the -subduplicate ratio of the same distances, as has been already proved; so -that with every increase of distance, a planet has more matter, and -therefore is moved more slowly, and accumulates more time in its -revolution, requiring already as it did more time by reason of the -length of the way. The third and fourth causes compensate each other in -a comparison of different planets: the simple and subduplicate -proportion compound the sesquiplicate proportion, which therefore is the -ratio of the periodic times." - -Three of the four suppositions here made by Kepler to explain the -beautiful law he had detected, are now indisputably known to be false. -Neither the weights nor the sizes of the different planets observe the -proportions assigned by him, nor is the force by which they are retained -in their orbits in any respect similar in its effects to those -attributed by him to it. The wonder which might naturally be felt that -he should nevertheless reach the desired conclusion, will be -considerably abated on examining the mode in which he arrived at and -satisfied himself of the truth of these three suppositions. It has been -already mentioned that his notions on the existence of a whirling force -emanating from the sun, and decreasing in energy at increased distances, -are altogether inconsistent with all the experiments and observations we -are able to collect. His reason for asserting that the sizes of the -different planets are proportional to their distances from the sun, was -simply because he chose to take for granted that either their -solidities, surfaces, or diameters, must necessarily be in that -proportion, and of the three, the solidities appeared to him least -liable to objection. The last element of his precarious reasoning rested -upon equally groundless assumptions. Taking as a principle, that where -there is a number of different things they must be different in every -respect, he declared that it was quite unreasonable to suppose all the -planets of the same density. He thought it indisputable that they must -be rarer as they were farther from the sun, "and yet not in the -proportion of their distances, for thus we should sin against the law of -variety in another way, and make the quantity of matter (according to -what he had just said of their bulk) the same in all. But if we assume -the ratio of the quantities of matter to be half that of the distances, -we shall observe the best mean of all; for thus Saturn will be half as -heavy again as Jupiter, and Jupiter half again as dense as Saturn. And -the strongest argument of all is, that unless we assume this proportion -of the densities, the law of the periodic times will not answer." This -is the _proof_ alluded to, and it is clear that by such reasoning any -required result might be deduced from any given principles. - -It may not be uninstructive to subjoin a sketch of the manner in which -Newton established the same celebrated results, starting from principles -of motion diametrically opposed to Kepler's, and it need scarcely be -added, reasoning upon them in a manner not less different. For this -purpose, a very few prefatory remarks will be found sufficient. - -The different motions seen in nature are best analysed and classified by -supposing that every body in motion, if left to itself, will continue to -move forward at the same rate in a straight line, and by considering all -the observed deviations from this manner of moving, as exceptions and -disturbances occasioned by some external cause. To this supposed cause -is generally given the name of Force, and it is said to be the first law -of motion, that, unless acted on by some force, every body at rest -remains at rest, and every body in motion proceeds uniformly in a -straight line. Many employ this language, without perceiving that it -involves a definition of force, on the admission of which, it is reduced -to a truism. We see common instances of force in a blow, or a pull from -the end of a string fastened to the body: we shall also have occasion -presently to mention some forces where no visible connexion exists -between the moving body and that towards which the motion takes place, -and from which the force is said to proceed. - -[Illustration: - - _c_ C - +-------------+ - \ / \ - \ / \ - \ / \ - \ / \ - \ / \ - \ / \ - +-------------+ - B C' ] - -A second law of motion, founded upon experiment, is this: if a body have -motion communicated to it in two directions, by one of which motions -alone it would have passed through a given space in a given time, as for -instance, through BC´ in one second, and by the other alone through any -other space B_c_ in the same time, it will, when both are given to it at -the same instant, pass in the same time (in the present instance in one -second) through BC the diagonal of the parallelogram of which BC´ and -B_c_ are sides. - -[Illustration: - - / S \ - / /|\ \ - / / | \ \ - / / | \ \ - / / | \ \ - / / | \ \ - / / | \ \ - --------+-+------+------+-+ - A B C D E ] - -Let a body, acted upon by no force, be moving along the line AE; that -means, according to what has been said, let it pass over the equal -straight lines AB, BC, CD, DE, &c., in equal times. If we take any point -S not in the line AE, and join AS, BS, &c., the triangles ASB, BSC, &c. -are also equal, having a common altitude and standing on equal bases, so -that if a string were conceived reaching from S to the moving body -(being lengthened or shortened in each position to suit its distance -from S), this string, as the body moved along AE, would sweep over equal -triangular areas in equal times. - -[Illustration] - -Let us now examine how far these conclusions will be altered if the body -from time to time is forced towards S. We will suppose it moving -uniformly from A to B as before, no matter for the present how it got to -A, or into the direction AB. If left to itself it would, in an equal -time (say 1´´) go through BC´ in the same straight line with and equal -to AB. But just as it reaches B, and is beginning to move along BC´, let -it be suddenly pulled towards S with a motion which, had it been at -rest, would have carried it in the same time, 1´´ through any other -space B_c_. According to the second law of motion, its direction during -this 1´´, in consequence of the two motions combined, will be along BC, -the diagonal of the parallelogram of which BC´, B_c_, are sides. In -this case, as this figure is drawn, BC, though passed in the same time, -is longer than AB; that is to say, the body is moving quicker than at -first. How is it with the triangular areas, supposed as before to be -swept by a string constantly stretched between S and the body? It will -soon be seen that these still remain equal, notwithstanding the change -of direction, and increased swiftness. For since CC´ is parallel to -B_c_, the triangles SCB, SC´B are equal, being on the same base SB, and -between the same parallels SB, CC´, and SC´B is equal to SBA as before, -therefore SCB, SBA are equal. The body is now moving uniformly (though -quicker than along AB) along BC. As before, it would in a time equal to -the time of passing along BC, go through an equal space CD´ in the same -straight line. But if at C it has a second pull towards S, strong enough -to carry it to _d_ in the same time, its direction will change a second -time to CD, the diagonal of the parallelogram, whose sides are CD´, -C_d_; and the circumstances being exactly similar to those at the first -pull, it is shewn in the same manner that the triangular area SDC = SCB -= SBA. - -Thus it appears, that in consequence of these intermitting pulls towards -S, the body may be moving round, sometimes faster, sometimes slower, but -that the triangles formed by any of the straight portions of its path -(which are all described in equal times), and the lines joining S to the -ends of that portion, are all equal. The path it will take depends of -course, in other respects, upon the frequency and strength of the -different pulls, and it might happen, if they were duly proportionate, -that when at H, and moving off in the direction HA´, the pull H_a_ -might be such as just to carry the body back to A, the point from which -it started, and with such a motion, that after one pull more, A_b_, at -A, it might move along AB as it did at first. If this were so, the body -would continue to move round in the same polygonal path, alternately -approaching and receding from S, as long as the same pulls were repeated -in the same order, and at the same intervals. - -It seems almost unnecessary to remark, that the same equality which -subsists between any two of these triangular areas subsists also between -an equal number of them, from whatever part of the path taken; so that, -for instance, the four paths AB, BC, CD, DE, corresponding to the four -areas ASB, BSC, CSD, DSE, that is, to the area ABCDES, are passed in the -same time as the four EF, FG, GH, HA, corresponding to the equal area -EFGHAS. Hence it may be seen, if the whole time of revolution from A -round to A again be called a year, that in half a year the body will -have got to E, which in the present figure is more than half way round, -and so of any other periods. - -The more frequently the pulls are supposed to recur, the more frequently -will the body change its direction; and if the pull were supposed -constantly exerted in the direction towards S, the body would move in a -curve round S, for no three successive positions of it could be in a -straight line. Those who are not familiar with the methods of measuring -curvilinear spaces must here be contented to observe, that the law -holds, however close the pulls are brought together, and however closely -the polygon is consequently made to resemble a curve: they may, if they -please, consider the minute portions into which the curve is so divided, -as differing insensibly from little rectilinear triangles, any equal -number of which, according to what has been said above, wherever taken -in the curve, would be swept in equal times. The theorem admits, in this -case also, a rigorous proof; but it is not easy to make it entirely -satisfactory, without entering into explanations which would detain us -too long from our principal subject. - -The proportion in which the pull is strong or weak at different -distances from the central spot, is called "_the law of the central or -centripetal force_," and it may be observed, that after assuming the -laws of motion, our investigations cease to have anything hypothetical -or experimental in them; and that if we wish, according to these -principles of motion, to determine the law of force necessary to make a -body move in a curve of any required form, or conversely to discover the -form of the curve described, in consequence of any assumed law of force, -the inquiry is purely geometrical, depending upon the nature and -properties of geometrical quantities only. This distinction between what -is hypothetical, and what necessary truth, ought never to be lost sight -of. - -As the object of the present treatise is not to teach geometry, we shall -describe, in very general terms, the manner in which Newton, who was -the first who systematically extended the laws of motion to the heavenly -bodies, identified their results with the two remaining laws of Kepler. -His "Principles of Natural Philosophy" contain general propositions with -regard to any law of centripetal force, but that which he supposed to be -the true one in our system, is expressed in mathematical language, by -saying that the centripetal force varies inversely as the square of the -distance, which means, that if the force at any distance be taken for -the unit of force, at half that distance, it is two times twice, or four -times as strong; at one-third the distance, three times thrice, or nine -times as strong, and so for other distances. He shewed the probability -of this law in the first instance by comparing the motion of the moon -with that of heavy bodies at the surface of the earth. Taking LP to -represent part of the moon's orbit described in one minute, the line PM -between the orbit and the tangent at L would shew the space through -which the central force at the earth (assuming the above principles of -motion to be correct) would draw the moon. From the known distance and -motion of the moon, this line PM is found to be about sixteen feet. The -distance of the moon is about sixty times the radius of the earth, and -therefore if the law of the central force in this instance were such as -has been supposed, the force at the earth's surface would be 60 times -60, or 3600 times stronger, and at the earth's surface, the central -force would make a body fall through 3600 times 16 feet in one minute. -Galileo had already taught that the spaces through which a body would be -made to fall, by the constant action of the same unvarying force, would -be proportional to the squares of the times during which the force was -exerted, and therefore according to these laws, a body at the earth's -surface ought (since there are sixty seconds in a minute) to fall -through 16 feet in one second, which was precisely the space previously -established by numerous experiments. - -[Illustration] - -With this confirmation of the supposition, Newton proceeded to the -purely geometrical calculation of the law of centripetal[198] force -necessary to make a moving body describe an ellipse round its focus, -which Kepler's observations had established to be the form of the orbits -of the planets round the sun. The result of the inquiry shewed that this -curve required the same law of the force, varying inversely as the -square of the distance, which therefore of course received additional -confirmation. His method of doing this may, perhaps, be understood by -referring to the last figure but one, in which C_d_, for instance, -representing the space fallen from any point C towards S, in a given -time, and the area CSD being proportional to the corresponding time, the -space through which the body would have fallen at C in any other time -(which would be greater, by Galileo's law, in proportion to the squares -of the times), might be represented by a quantity varying directly as -C_d_, and inversely in the duplicate proportion of the triangular area -CSD, that is to say, proportional to C_d_/(SC × D_k_)², if D_k_ be drawn -from D perpendicular on SC. If this polygon represent an ellipse, so -that CD represents a small arc of the curve, of which S is the focus, it -is found by the nature of that curve, that C_d_/(D_k_)² is the same at -all points of the curve, so that the law of variation of the force in -the same ellipse is represented solely by 1/(SC)². If C_d_, &c. are -drawn so that C_d_/(D_k_)² is not the same at every point, the curve -ceases to be an ellipse whose focus is at S, as Newton has shewn in the -same work. The line to which (Dk)²/Cd is found to be equal, is one drawn -through the focus at right angles to the longest axis of the ellipse -till it meets the curve;--this line is called the _latus rectum_, and is -a third proportional to the two principal axes. - -Kepler's third law follows as an immediate consequence of this -determination; for, according to what has been already shown, the time -of revolution round the whole ellipse, or, as it is commonly called, -the periodic time, bears the same ratio to the unit of time as the whole -area of the ellipse does to the area described in that unit. The area of -the whole ellipse is proportional in different ellipses to the rectangle -contained by the two principal axes, and the area described in an unit -of time is proportional to SC × D_k_, that is to say, is in the -subduplicate ratio of SC² × D_k_², or D_k_²/C_d_, when the force varies -inversely as the square of the distance SC; and in the ellipse, as we -have said already, this is equal to a third proportional to the -principal axes; consequently the periodic times in different ellipses, -which are proportional to the whole areas of the ellipses directly, and -the areas described in the unit of time inversely, are in the compound -ratio of the rectangle of the axes directly, and subduplicately as a -third proportional to the axes inversely; that is to say, the squares of -these times are proportional to the cubes of the longest axes, which is -Kepler's law. - - -FOOTNOTES: - -[192] This mode of verifying configurations, though something of the -boldest, was by no means unusual. On a former occasion Kepler, wishing -to cast the nativity of his friend Zehentmaier, and being unable to -procure more accurate information than that he was born about three -o'clock in the afternoon of the 21st of October, 1751, supplied the -deficiency by a record of fevers and accidents at known periods of his -life, from which he deduced a more exact horoscope. - -[193] Kepler probably meant his own mother, whose horoscope he in many -places declared to be nearly the same as his own. - -[194] See Preliminary Treatise, p. 13. - -[195] In allusion to the Harmonics of Ptolemy. - -[196] This is a word borrowed from the Ptolemaic astronomy, according to -which the sun and planets are hurried from their places by the daily -motion of the _primum mobile_, and by their own peculiar motion seek to -regain or be restored to their former places. - -[197] In other parts of his works, Kepler assumes the diminution to be -proportional to the circles themselves, not to the diameters. - -[198] In many curves, as in the circle and ellipse, there is a point to -which the name of centre is given, on account of peculiar properties -belonging to it: but the term "centripetal force" always refers to the -place towards which the force is directed, whether or not situated in -the centre of the curve. - - - - -CHAPTER VIII. - - _The Epitome prohibited at Rome--Logarithmic Tables--Trial of - Catharine Kepler--Kepler invited to England--Rudolphine - Tables--Death--Conclusion._ - - -KEPLER'S "Epitome," almost immediately on its appearance, enjoyed the -honour of being placed by the side of the work of Copernicus, on the -list of books prohibited by the congregation of the Index at Rome. He -was considerably alarmed on receiving this intelligence, anticipating -that it might occasion difficulties in publishing his future writings. -His words to Remus, who had communicated the news to him, are as -follows:--"I learn from your letter, for the first time, that my book is -prohibited at Rome and Florence. I particularly beg of you, to send me -the exact words of the censure, and that you will inform me whether that -censure would be a snare for the author, if he were caught in Italy, or -whether, if taken, he would be enjoined a recantation. It is also of -consequence for me to know whether there is any chance of the same -censure being extended into Austria. For if this be so, not only shall I -never again find a printer there, but also the copies which the -bookseller has left in Austria at my desire will be endangered, and the -ultimate loss will fall upon me. It will amount to giving me to -understand, that I must cease to profess Astronomy, after I have grown -old in the belief of these opinions, having been hitherto gainsayed by -no one,--and, in short, I must give up Austria itself, if room is no -longer to be left in it for philosophical liberty." He was, however, -tranquillized, in a great degree, by the reply of his friend, who told -him that "the book is only prohibited as contrary to the decree -pronounced by the holy office two years ago. This has been partly -occasioned by a Neapolitan monk (Foscarini), who was spreading these -notions by publishing them in Italian, whence were arising dangerous -consequences and opinions: and besides, Galileo was at the same time -pleading his cause at Rome with too much violence. Copernicus has been -corrected in the same manner for some lines, at least in the beginning -of his first book. But by obtaining a permission, they may be read (and, -as I suppose, this "Epitome" also) by the learned and skilful in this -science, both at Rome and throughout all Italy. There is therefore no -ground for your alarm, either in Italy or Austria; only keep yourself -within bounds, and put a guard upon your own passions." - -We shall not dwell upon Kepler's different works on comets, beyond -mentioning that they were divided, on the plan of many of his other -publications, into three parts, Astronomical, Physical, and -Astrological. He maintained that comets move in straight lines, with a -varying degree of velocity. Later theories have shewn that they obey the -same laws of motion as the planets, differing from them only in the -extreme excentricity of their orbits. In the second book, which contains -the Physiology of Comets, there is a passing remark that comets come out -from the remotest parts of ether, as whales and monsters from the depth -of the sea; and the suggestion is thrown out that perhaps comets are -something of the nature of silkworms, and are wasted and consumed in -spinning their own tails. - -Among his other laborious employments, Kepler yet found time to -calculate tables of logarithms, he having been one of the first in -Germany to appreciate the full importance of the facilities they afford -to the numerical calculator. In 1618 he wrote to his friend Schickhard: -"There is a Scottish Baron (whose name has escaped my memory), who has -made a famous contrivance, by which all need of multiplication and -division is supplied by mere addition and subtraction; and he does it -without sines. But even he wants a table of tangents[199], and the -variety, frequency, and difficulty of the additions and subtractions, in -some cases, is greater than the labour of multiplying and dividing." - -Kepler dedicated his "Ephemeris" for 1620 to the author of this -celebrated invention, Baron Napier, of Merchistoun; and in 1624, -published what he called "Chilias Logarithmorum," containing the -Napierian logarithms of the quotients of 100,000 divided by the first -ten numbers, then proceeding by the quotients of every ten to 100, and -by hundreds to 100,000. In the supplement published the following year, -is a curious notice of the manner in which this subtle contrivance was -at first received: "In the year 1621, when I had gone into Upper -Austria, and had conferred everywhere with those skilled in mathematics, -on the subject of Napier's logarithms, I found that those whose prudence -had increased, and whose readiness had diminished, through age, were -hesitating whether to adopt this new sort of numbers, instead of a table -of sines; because they said it was disgraceful to a professor of -mathematics to exult like a child at some compendious method of working, -and meanwhile to admit a form of calculation, resting on no legitimate -proof, and which at some time might entangle us in error, when we least -feared it. They complained that Napier's demonstration rested on a -fiction of geometrical motion, too loose and slippery for a sound method -of reasonable demonstration to be founded on it.[200] "This led me -forthwith to conceive the germ of a legitimate demonstration, which -during that same winter I attempted, without reference to lines or -motion, or flow, or any other which I may call sensible quality. - -"Now to answer the question; what is the use of logarithms? Exactly what -ten years ago was announced by their author, Napier, and which may be -told in these words.--Wheresoever in common arithmetic, and in the Rule -of Three, come two numbers to be multiplied together, there the sum of -the logarithms is to be taken; where one number is to be divided by -another, the difference; and the number corresponding to this sum or -difference, as the case may be, will be the required product or -quotient. This, I say, is the use of logarithms. But in the same work in -which I gave the demonstration of the principles, I could not satisfy -the unfledged arithmetical chickens, greedy of facilities, and gaping -with their beaks wide open, at the mention of this use, as if to bolt -down every particular gobbet, till they are crammed with my -precepticles." - -The year 1622 was marked by the catastrophe of a singular adventure -which befell Kepler's mother, Catharine, then nearly seventy years old, -and by which he had been greatly harassed and annoyed during several -years. From her youth she had been noted for a rude and passionate -temper, which on the present occasion involved her in serious -difficulties. One of her female acquaintance, whose manner of life had -been by no means unblemished, was attacked after a miscarriage by -violent headaches, and Catharine, who had often taken occasion to sneer -at her notorious reputation, was accused with having produced these -consequences, by the administration of poisonous potions. She repelled -the charge with violence, and instituted an action of scandal against -this person, but was unlucky (according to Kepler's statement) in the -choice of a young doctor, whom she employed as her advocate. Considering -the suit to be very instructive, he delayed its termination during five -years, until the judge before whom it was tried was displaced. He was -succeeded by another, already indisposed against Catharine Kepler, who -on some occasion had taunted him with his sudden accession to wealth -from a very inferior situation. Her opponent, aware of this advantage, -turned the tables on her, and in her turn became the accuser. The end -of the matter was, that in July, 1620, Catharine was imprisoned, and -condemned to the torture. Kepler was then at Linz, but as soon as he -learned his mother's danger, hurried to the scene of trial. He found the -charges against her supported only by evidence which never could have -been listened to, if her own intemperate conduct had not given advantage -to her adversaries. He arrived in time to save her from the question, -but she was not finally acquitted and released from prison till November -in the following year. Kepler then returned to Linz, leaving behind him -his mother, whose spirit seemed in no degree broken by the unexpected -turn in the course of her litigation. She immediately commenced a new -action for costs and damages against the same antagonist, but this was -stopped by her death, in April 1622, in her seventy-fifth year. - -In 1620 Kepler was visited by Sir Henry Wotton, the English ambassador -at Venice, who finding him, as indeed he might have been found at every -period of his life, oppressed by pecuniary difficulties, urged him to go -over to England, where he assured him of a welcome and honourable -reception; but Kepler could not resolve upon the proposed journey, -although in his letters he often returned to the consideration of it. In -one of them, dated a year later, he says, "The fires of civil war are -raging in Germany--they who are opposed to the honour of the empire are -getting the upper hand--everything in my neighbourhood seems abandoned -to flame and destruction. Shall I then cross the sea, whither Wotton -invites me? I, a German? a lover of firm land? who dread the confinement -of an island? who presage its dangers, and must drag along with me my -little wife and flock of children? Besides my son Louis, now thirteen -years old, I have a marriageable daughter, a two-year old son by my -second marriage, an infant daughter, and its mother but just recovering -from her confinement." Six years later, he says again,--"As soon as the -Rudolphine Tables are published, my desire will be to find a place where -I can lecture on them to a considerable assembly; if possible, in -Germany; if not, why then in Italy, France, the Netherlands, or England, -provided the salary is adequate for a traveller." - -In the same year in which he received this invitation an affront was put -upon Kepler by his early patrons, the States of Styria, who ordered all -the copies of his "Calendar," for 1624, to be publicly burnt. Kepler -declares that the reason of this was, that he had given precedence in -the title-page to the States of Upper Ens, in whose service he then was, -above Styria. As this happened during his absence in Wirtemberg, it was -immediately coupled by rumour with his hasty departure from Linz: it was -said that he had incurred the Emperor's displeasure, and that a large -sum was set upon his head. At this period Matthias had been succeeded by -Ferdinand III., who still continued to Kepler his barren title of -imperial mathematician. - -In 1624 Kepler went to Vienna, in the hopes of getting money to complete -the Rudolphine Tables, but was obliged to be satisfied with the sum of -6000 florins and with recommendatory letters to the States of Suabia, -from whom he also collected some money due to the emperor. On his return -he revisited the University of Tubingen, where he found his old -preceptor, Mästlin, still alive, but almost worn out with old age. -Mästlin had well deserved the regard Kepler always appears to have -entertained for him; he had treated him with great liberality whilst at -the University, where he refused to receive any remuneration for his -instruction. Kepler took every opportunity of shewing his gratitude; -even whilst he was struggling with poverty he contrived to send his old -master a handsome silver cup, in acknowledging the receipt of which -Mästlin says,--"Your mother had taken it into her head that you owed me -two hundred florins, and had brought fifteen florins and a chandelier -towards reducing the debt, which I advised her to send to you. I asked -her to stay to dinner, which she refused: however, we handselled your -cup, as you know she is of a thirsty temperament." - -The publication of the Rudolphine Tables, which Kepler always had so -much at heart, was again delayed, notwithstanding the recent grant, by -the disturbances arising out of the two parties into which the -Reformation had divided the whole of Germany. Kepler's library was -sealed up by desire of the Jesuits, and nothing but his connexion with -the Imperial Court secured to him his own personal indemnity. Then -followed a popular insurrection, and the peasantry blockaded Linz, so -that it was not until 1627 that these celebrated tables finally made -their appearance, the earliest calculated on the supposition that the -planets move in elliptic orbits. Ptolemy's tables had been succeeded by -the "Alphonsine," so called from Alphonso, King of Castile, who, in the -thirteenth century, was an enlightened patron of astronomy. After the -discoveries of Copernicus, these again made way for the Prussian, or -Prutenic tables, calculated by his pupils Reinhold and Rheticus. These -remained in use till the observations of Tycho Brahe showed their -insufficiency, and Kepler's new theories enabled him to improve upon -them. The necessary types for these tables were cast at Kepler's own -expense. They are divided into four parts, the first and third -containing a variety of logarithmic and other tables, for the purpose of -facilitating astronomical calculations. In the second are tables of the -elements of the sun, moon, and planets. The fourth gives the places of -1000 stars as determined by Tycho, and also at the end his table of -refractions, which appears to have been different for the sun, moon, and -stars. Tycho Brahe assumed the horizontal refraction of the sun to be 7´ -30´´, of the moon 8´, and of the other stars 3´. He considered all -refraction of the atmosphere to be insensible above 45° of altitude, and -even at half that altitude in the case of the fixed stars. A more -detailed account of these tables is here obviously unsuitable: it will -be sufficient to say merely, that if Kepler had done nothing in the -course of his whole life but construct these, he would have well earned -the title of a most useful and indefatigable calculator. - -Some copies of these tables have prefixed to them a very remarkable map, -divided by hour lines, the object of which is thus explained:-- - -"The use of this nautical map is, that if at a given hour the place of -the moon is known by its edge being observed to touch any known star, or -the edges of the sun, or the shadow of the earth; and if that place -shall (if necessary) be reduced from apparent to real by clearing it of -parallax; and if the hour at Uraniburg be computed by the Rudolphine -tables, when the moon occupied that true place, the difference will show -the observer's meridian, whether the picture of the shores be accurate -or not, for by this means it may come to be corrected." - -This is probably one of the earliest announcements of the method of -determining longitudes by occultations; the imperfect theory of the moon -long remained a principal obstacle to its introduction in practice. -Another interesting passage connected with the same object may be -introduced here. In a letter to his friend Cruger, dated in 1616, Kepler -says: "You propose a method of observing the distances of places by -sundials and automata. It is good, but needs a very accurate practice, -and confidence in those who have the care of the clocks. Let there be -only one clock, and let it be transported; and in both places let -meridian lines be drawn with which the clock may be compared when -brought. The only doubt remaining is, whether a greater error is likely -from the unequal tension in the automaton, and from its motion, which -varies with the state of the air, or from actually measuring the -distances. For if we trust the latter, we can easily determine the -longitudes by observing the differences of the height of the pole." - -In an Appendix to the Rudolphine Tables, or, as Kepler calls it, "an -alms doled out to the nativity casters," he has shown how they may use -his tables for their astrological predictions. Everything in his hands -became an allegory; and on this occasion he says,--"Astronomy is the -daughter of Astrology, and this modern Astrology, again, is the daughter -of Astronomy, bearing something of the lineaments of her grandmother; -and, as I have already said, this foolish daughter, Astrology, supports -her wise but needy mother, Astronomy, from the profits of a profession -not generally considered creditable." - -Soon after the publication of these tables, the Grand Duke of Tuscany -sent him a golden chain; and if we remember the high credit in which -Galileo stood at this time in Florence, it does not seem too much to -attribute this honourable mark of approbation to his representation of -the value of Kepler's services to astronomy. This was soon followed by a -new and final change in his fortunes. He received permission from the -emperor to attach himself to the celebrated Duke of Friedland, Albert -Wallenstein, one of the most remarkable men in the history of that -time. Wallenstein was a firm believer in astrology, and the reception -Kepler experienced by him was probably due, in great measure, to his -reputation in that art. However that may be, Kepler found in him a more -munificent patron than any one of his three emperors; but he was not -destined long to enjoy the appearance of better fortune. Almost the last -work which he published was a commentary on the letter addressed, by the -missionary Terrentio, from China, to the Jesuits at Ingolstadt. The -object of this communication was to obtain from Europe means for -carrying into effect a projected scheme for improving the Chinese -calendar. In this essay Kepler maintains the opinion, which has been -discussed with so much warmth in more modern times, that the pretended -ancient observations of the Chinese were obtained by computing them -backwards from a much more recent date. Wallenstein furnished him with -an assistant for his calculations, and with a printing press; and -through his influence nominated him to the professorship in the -University of Rostoch, in the Duchy of Mecklenburg. His claims on the -imperial treasury, which amounted at this time to 8000 crowns, and which -Ferdinand would gladly have transferred to the charge of Wallenstein, -still remained unsatisfied. Kepler made a last attempt to obtain them at -Ratisbon, where the imperial meeting was held, but without success. The -fatigue and vexation occasioned by his fruitless journey brought on a -fever, which unexpectedly put an end to his life, in the early part of -November, 1630, in his fifty-ninth year. His old master, Mästlin, -survived him for about a year, dying at the age of eighty-one. - -Kepler left behind him two children by his first wife, Susanna and -Louis; and three sons and two daughters, Sebald, Cordelia, Friedman, -Hildebert, and Anna Maria, by his widow. Susanna married, a few months -before her father's death, a physician named Jacob Bartsch, the same who -latterly assisted Kepler in preparing his "Ephemeris." He died very -shortly after Kepler himself. Louis studied medicine, and died in 1663, -whilst practising as a physician at Konigsberg. The other children died -young. - -Upon Kepler's death the Duke of Friedland caused an inventory to be -taken of his effects, when it appeared that near 24,000 florins were due -to him, chiefly on account of his salary from the emperor. His daughter -Susanna, Bartsch's widow, managed to obtain a part of these arrears by -refusing to give up Tycho Brahe's observations till her claims were -satisfied. The widow and younger children were left in very straightened -circumstances, which induced Louis, Kepler's eldest son, to print, for -their relief, one of his father's works, which had been left by him -unpublished. It was not without much reluctance, in consequence of a -superstitious feeling which he did not attempt to conceal or deny. -Kepler himself, and his son-in-law, Bartsch, had been employed in -preparing it for publication at the time of their respective deaths; and -Louis confessed that he did not approach the task without apprehension -that he was incurring some risk of a similar fate. This little rhapsody -is entitled a "Dream on Lunar Astronomy;" and was intended to illustrate -the appearances which would present themselves to an astronomer living -upon the moon. - -The narrative in the dream is put into the mouth of a personage, named -Duracoto, the son of an Icelandic enchantress, of the name of -Fiolxhildis. Kepler tells us that he chose the last name from an old map -of Europe in his house, in which Iceland was called Fiolx: Duracoto -seemed to him analogous to the names he found in the history of -Scotland, the neighbouring country. Fiolxhildis was in the habit of -selling winds to mariners, and used to collect herbs to use in her -incantations on the sides of Mount Hecla, on the Eve of St. John. -Duracoto cut open one of his mother's bags, in punishment of which she -sold him to some traders, who brought him to Denmark, where he became -acquainted with Tycho Brahe. On his return to Iceland, Fiolxhildis -received him kindly, and was delighted with the progress he had made in -astronomy. She then informed him of the existence of certain spirits, or -demons, from whom, although no traveller herself, she acquired a -knowledge of other countries, and especially of a very remarkable -country, called Livania. Duracoto requesting further information, the -necessary ceremonies were performed for invoking the demon; Duracoto and -his mother enveloped their heads in their clothing, and presently "the -screaking of a harsh dissonant voice began to speak in the Icelandic -tongue." The island of Livania is situated in the depths of ether, at -the distance of about 250000 miles; the road thence or thither is very -seldom open, and even when it is passable, mankind find the journey a -most difficult and dangerous one. The demon describes the method -employed by his fellow spirits to convey such travellers as are thought -fit for the undertaking: "We bring no sedentary people into our company, -no corpulent or delicate persons; but we pick out those who waste their -life in the continual use of post-horses, or who sail frequently to the -Indies; who are accustomed to live upon biscuit, garlic, dried fish, and -such abominable feeding. Those withered old hags are exactly fit for us, -of whom the story is familiar that they travel immense distances by -night on goats, and forks, and old petticoats. The Germans do not suit -us at all; but we do not reject the dry Spaniards." This extract will -probably be sufficient to show the style of the work. The inhabitants of -Livania are represented to be divided into two classes, the Privolvans -and Subvolvans, by whom are meant those supposed to live in the -hemisphere facing the earth, which is called the Volva, and those on the -opposite half of the moon: but there is nothing very striking in the -account given of the various phenomena as respects these two classes. In -some notes which were added some time after the book was first written, -are some odd insights into Kepler's method of composing. Fiolxhildis had -been made to invoke the dæmon with twenty-one characters; Kepler -declares, in a note, that he cannot remember why he fixed on this -number, "except because that is the number of letters in _Astronomia -Copernicana_, or because there are twenty-one combinations of the -planets, two together, or because there are twenty-one different throws -upon two dice." The dream is abruptly terminated by a storm, in which, -says Kepler, "I suddenly waked; the Demon, Duracoto, and Fiolxhildis -were gone, and instead of their covered heads, I found myself rolled up -among the blankets." - -Besides this trifle, Kepler left behind him a vast mass of unpublished -writings, which came at last into the hands of his biographer, Hantsch. -In 1714, Hantsch issued a prospectus for publishing them by -subscription, in twenty-two folio volumes. The plan met no -encouragement, and nothing was published but a single folio volume of -letters to and from Kepler, which seem to have furnished the principal -materials for the memoir prefixed to them. After various unavailing -attempts to interest different learned bodies in their appearance, the -manuscripts were purchased for the library at St. Petersburg, where -Euler, Lexell, and Kraft, undertook to examine them, and select the most -interesting parts for publication. The result of this examination does -not appear. - -Kepler's body was buried in St. Peter's churchyard at Ratisbon, and a -simple inscription was placed on his tombstone. This appears to have -been destroyed not long after, in the course of the wars which still -desolated the country. In 1786, a proposal was made to erect a marble -monument to his memory, but nothing was done. Kästner, on whose -authority it is mentioned, says upon this, rather bitterly, that it -matters little whether or not Germany, having almost refused him bread -during his life, should, a century and a half after his death, offer him -a stone. - -Delambre mentions, in his History of Astronomy, that this design was -resumed in 1803 by the Prince Bishop of Constance, and that a monument -has been erected in the Botanical Garden at Ratisbon, near the place of -his interment. It is built in the form of a temple, surmounted by a -sphere; in the centre is placed a bust of Kepler, in Carrara marble. -Delambre does not mention the original of the bust; but says it is not -unlike the figure engraved in the frontispiece of the Rudolphine Tables. -That frontispiece consists of a portico of ten pillars, supporting a -cupola covered with astronomical emblems. Copernicus, Tycho Brahe, -Ptolemy, Hipparchus, and other astronomers, are seen among them. In one -of the compartments of the common pedestal is a plan of the observatory -at Uraniburg; in another, a printing press; in a third is the figure of -a man, meant for Kepler, seated at a table. He is identified by the -titles of his works, which are round him; but the whole is so small as -to convey very little idea of his figure or countenance. The only -portrait known of Kepler was given by him to his assistant Gringallet, -who presented it to Bernegger; and it was placed by the latter in the -library at Strasburg. Hantsch had a copy taken for the purpose of -engraving it, but died before it was completed. A portrait of Kepler is -engraved in the seventh part of Boissard's Bibliotheca Chalcographica. -It is not known whence this was taken, but it may, perhaps, be a copy of -that which was engraved by desire of Bernegger in 1620. The likeness is -said not to have been well preserved. "His heart and genius," says -Kästner, "are faithfully depicted in his writings; and that may console -us, if we cannot entirely trust his portrait." In the preceding pages, -it has been endeavoured to select such passages from his writings as -might throw the greatest light on his character, with a subordinate -reference only to the importance of the subjects treated. In conclusion, -it may be well to support the opinion which has been ventured on the -real nature of his triumphs, and on the danger of attempting to follow -his method in the pursuit of truth, by the judgment pronounced by -Delambre, as well on his failures as on his success. "Considering these -matters in another point of view, it is not impossible to convince -ourselves that Kepler may have been always the same. Ardent, restless, -burning to distinguish himself by his discoveries, he attempted -everything; and having once obtained a glimpse of one, no labour was too -hard for him in following or verifying it. All his attempts had not the -same success, and, in fact, that was impossible. Those which have failed -seem to us only fanciful; those which have been more fortunate appear -sublime. When in search of that which really existed, he has sometimes -found it; when he devoted himself to the pursuit of a chimera, he could -not but fail; but even there he unfolded the same qualities, and that -obstinate perseverance that must triumph over all difficulties but those -which are insurmountable."[201] - - -_List of Kepler's published Works._ - - Ein Calender _Gratz_, 1594 - Prodromus Dissertat. Cosmograph. _Tubingæ_, 1596, 4to. - De fundamentis Astrologiæ _Pragæ_, 1602, 4to. - Paralipomena ad Vitellionem _Francofurti_, 1604, 4to. - Epistola de Solis deliquio 1605 - De stellâ novâ _Pragæ_, 1606, 4to. - Vom Kometen _Halle_, 1608, 4to. - Antwort an Röslin _Pragæ_, 1609, 4to. - Astronomia Nova _Pragæ_, 1609, fol. - Tertius interveniens _Frankfurt_, 1610, 4to. - Dissertatio cum Nuncio Sidereo _Francofurti_, 1610, 4to. - Strena, seu De dive sexangulâ _Frankfurt_, 1611, 4to. - Dioptrica _Francofurti_, 1611, 4to. - Vom Geburts Jahre des Heylandes _Strasburg_, 1613, 4to. - Respons. ad epist S. Calvisiii _Francofurti_, 1614, 4to. - Eclogæ Chronicæ _Frankfurt_, 1615, 4to. - Nova Stereometria _Lincii_, 1615, 4to. - Ephemerides 1617-1620 _Lincii_, 1616, 4to. - Epitomes Astron. Copern. Libri i. ii. iii. _Lentiis_, 1618, 8vo. - De Cometis _Aug. Vindelic._ 1619, 4to. - Harmonice Mundi _Lincii_, 1619, fol. - Kanones Pueriles _Ulmæ_, 1620 - Epitomes Astron. Copern. Liber iv. _Lentiis_, 1622, 8vo. - Epitomes Astron. Copern. Libri v. vi. vii. _Francofurti_, 1622, 8vo. - Discurs von der grossen Conjunction _Linz._ 1623, 4to. - Chilias Logarithmorum _Marpurgi_, 1624, fol. - Supplementum _Lentiis_, 1625, 4to. - Hyperaspistes _Francofurti_, 1625, 8vo. - Tabulæ Rudolphinæ _Ulmæ_, 1627, fol. - Resp. ad epist. J. Bartschii _Sagani_, 1629, 4to. - De anni 1631 phænomenis _Lipsæ_, 1629, 4to. - Terrentii epistolium cum commentatiunculâ _Sagani_, 1630, 4to. - Ephemerides. _Sagani_, 1630, 4to. - - Somnium _Francofurti_, 1634, 4to. - Tabulæ mannales _Argentorati_, 1700, 12mo. - - -FOOTNOTES: - -[199] The meaning of this passage is not very clear: Kepler evidently -had seen and used logarithms at the time of writing this letter; yet -there is nothing in the method to justify this expression,--"_At tamen -opus est ipsi Tangentium canone._" - -[200] This was the objection originally made to Newton's "Fluxions," and -in fact, Napier's idea of logarithms is identical with that method of -conceiving quantities. This may be seen at once from a few of his -definitions, - - 1 Def. A line is said to increase uniformly, when the point by which - it is described passes through equal intervals, in equal times. - - 2 Def. A line is said to diminish to a shorter one proportionally, - when the point passing along it cuts off in equal times segments - proportional to the remainder. - - 6 Def. The logarithm of any sine is the number most nearly denoting - the line, which has increased uniformly, whilst the radius has - diminished to that sine proportionally, the initial velocity being - the same in both motions. (Mirifici logarithmorum canonis - descriptio, Edinburgi 1614.) - -This last definition contains what we should now call the differential -equation between a number and the logarithm of its reciprocal. - -[201] Histoire del'Astronomie Moderne, Paris, 1821. - - - - -Transcriber's Notes. - -Corrections. - -The first line indicates the original, the second the correction. - - -Life of Galileo Galilei - -p. 20: - - success very inadeqnate to the zeal - success very inadequate to the zeal - -p. 20: - - "New method of Guaging, - "New method of Gauging, - -p. 23: - - the knowlege, if it existed - the knowledge, if it existed - -p. 30, note: - - to represent terrestial objects correctly. - to represent terrestrial objects correctly. - -p. 64: - - the palace of the Archishop Piccolomini - the palace of the Archbishop Piccolomini - -p. 68: - - that ladies ringlets - that ladies' ringlets - -p. 69: - - For hitherto I have never happened to see the terrestial earth - For hitherto I have never happened to see the terrestrial earth - -p. 106: - - 80 1 50, _for_ any _read_ an indefinitely small. - 80 2 44, _for_ any _read_ an indefinitely small. - - -Life of Kepler - -p. 6: - - Now, inscribe in the Earth an icosaedron, the circle inscribed in it - will be Venus. - - Now, inscribe in the Earth an icosahedron, the circle inscribed in - it will be Venus. - - Inscribe an octaedron in Venus, the circle inscribed in it will be - Mercury. - - Inscribe an octahedron in Venus, the circle inscribed in it will be - Mercury. - -p. 32: - - Butthere are no such means - But there are no such means - -p. 48: - - the compound ratio of the rectangle of the axes directly, and - subduplicatly - - the compound ratio of the rectangle of the axes directly, and - subduplicately - -p. 52: - - and was in-intended to illustrate the appearances - and was intended to illustrate the appearances - - - - - - -End of the Project Gutenberg EBook of The Life of Galileo Galilei, with -Illustrations of the Advancement of Experimental Philosophy, by John Elliot Drinkwater Bethune - -*** END OF THIS PROJECT GUTENBERG EBOOK THE LIFE OF GALILEO GALILEI *** - -***** This file should be named 43877-8.txt or 43877-8.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/3/8/7/43877/ - -Produced by David Garcia, Bryan Ness, Eleni Christofaki -and the Online Distributed Proofreading Team at -http://www.pgdp.net - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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Thus, we do not necessarily -keep eBooks in compliance with any particular paper edition. - -Most people start at our Web site which has the main PG search facility: - - www.gutenberg.org - -This Web site includes information about Project Gutenberg-tm, -including how to make donations to the Project Gutenberg Literary -Archive Foundation, how to help produce our new eBooks, and how to -subscribe to our email newsletter to hear about new eBooks. - - - -</pre> - +<div>*** END OF THE PROJECT GUTENBERG EBOOK 43877 ***</div> </body> </html> diff --git a/43877.txt b/43877.txt deleted file mode 100644 index 84ab643..0000000 --- a/43877.txt +++ /dev/null @@ -1,12663 +0,0 @@ -The Project Gutenberg EBook of The Life of Galileo Galilei, with -Illustrations of the Advancement of Experimental Philosophy, by John Elliot Drinkwater Bethune - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org - - -Title: The Life of Galileo Galilei, with Illustrations of the Advancement of Experimental Philosophy - Life of Kepler - -Author: John Elliot Drinkwater Bethune - -Release Date: October 3, 2013 [EBook #43877] - -Language: English - -Character set encoding: ASCII - -*** START OF THIS PROJECT GUTENBERG EBOOK THE LIFE OF GALILEO GALILEI *** - - - - -Produced by David Garcia, Bryan Ness, Eleni Christofaki -and the Online Distributed Proofreading Team at -http://www.pgdp.net - - - - - - - - - -Transcriber's Note. - -Variable spelling and hyphenation have been retained. Minor punctuation -inconsistencies have been silently repaired. The author's corrections, -additions and comments have been applied in the text. Changes made by -the transcriber can be found at the end of the book. The original text -is printed in a two-column layout. Formatting and special characters are -indicated as follows: - - Letters in superscript are presented ^{like this}. - _italic_ - [Greek] - - - - -[Illustration: Galileo Galilei] - - - - - THE - LIFE - OF - GALILEO GALILEI, - WITH - ILLUSTRATIONS OF THE ADVANCEMENT - OF - EXPERIMENTAL PHILOSOPHY. - - MDCCCXXX. - - LONDON. - - - - -LIFE OF GALILEO: - -WITH ILLUSTRATIONS OF THE ADVANCEMENT OF EXPERIMENTAL PHILOSOPHY. - - - - -CHAPTER I. - - _Introduction._ - - -THE knowledge which we at present possess of the phenomena of nature and -of their connection has not by any means been regularly progressive, as -we might have expected, from the time when they first drew the attention -of mankind. Without entering into the question touching the scientific -acquirements of eastern nations at a remote period, it is certain that -some among the early Greeks were in possession of several truths, -however acquired, connected with the economy of the universe, which were -afterwards suffered to fall into neglect and oblivion. But the -philosophers of the old school appear in general to have confined -themselves at the best to observations; very few traces remain of their -having instituted _experiments_, properly so called. This putting of -nature to the torture, as Bacon calls it, has occasioned the principal -part of modern philosophical discoveries. The experimentalist may so -order his examination of nature as to vary at pleasure the circumstances -in which it is made, often to discard accidents which complicate the -general appearances, and at once to bring any theory which he may form -to a decisive test. The province of the mere observer is necessarily -limited: the power of selection among the phenomena to be presented is -in great measure denied to him, and he may consider himself fortunate if -they are such as to lead him readily to a knowledge of the laws which -they follow. - -Perhaps to this imperfection of method it may be attributed that natural -philosophy continued to be stationary, or even to decline, during a long -series of ages, until little more than two centuries ago. Within this -comparatively short period it has rapidly reached a degree of perfection -so different from its former degraded state, that we can hardly -institute any comparison between the two. Before that epoch, a few -insulated facts, such as might first happen to be noticed, often -inaccurately observed and always too hastily generalized, were found -sufficient to excite the naturalist's lively imagination; and having -once pleased his fancy with the supposed fitness of his artificial -scheme, his perverted ingenuity was thenceforward employed in forcing -the observed phenomena into an imaginary agreement with the result of -his theory; instead of taking the more rational, and it should seem, the -more obvious, method of correcting the theory by the result of his -observations, and considering the one merely as the general and -abbreviated expression of the other. But natural phenomena were not then -valued on their own account, and for the proofs which they afford of a -vast and beneficent design in the structure of the universe, so much as -for the fertile topics which the favourite mode of viewing the subject -supplied to the spirit of scholastic disputation: and it is a -humiliating reflection that mankind never reasoned so ill as when they -most professed to cultivate the art of reasoning. However specious the -objects, and alluring the announcements of this art, the then prevailing -manner of studying it curbed and corrupted all that is free and noble in -the human mind. Innumerable fallacies lurked every where among the most -generally received opinions, and crowds of dogmatic and self-sufficient -pedants fully justified the lively definition, that "logic is the art of -talking unintelligibly on things of which we are ignorant."[1] - -The error which lay at the root of the philosophy of the middle ages was -this:--from the belief that general laws and universal principles might -be discovered, of which the natural phenomena were _effects_, it was -thought that the proper order of study was, first to detect the general -_cause_, and then to pursue it into its consequences; it was considered -absurd to begin with the effect instead of the cause; whereas the real -choice lay between proceeding from particular facts to general facts, -or from general facts to particular facts; and it was under this -misrepresentation of the real question that all the sophistry lurked. As -soon as it is well understood that the general _cause_ is no other than -a single fact, common to a great number of phenomena, it is necessarily -perceived that an accurate scrutiny of these latter must precede any -safe reasoning with respect to the former. But at the time of which we -are speaking, those who adopted this order of reasoning, and who began -their inquiries by a minute and sedulous investigation of facts, were -treated with disdain, as men who degraded the lofty name of philosophy -by bestowing it upon mere mechanical operations. Among the earliest and -noblest of these was Galileo. - -It is common, especially in this country, to name Bacon as the founder -of the present school of experimental philosophy; we speak of the -Baconian or inductive method of reasoning as synonimous and convertible -terms, and we are apt to overlook what Galileo had already done before -Bacon's writings appeared. Certainly the Italian did not range over the -circle of the sciences with the supreme and searching glance of the -English philosopher, but we find in every part of his writings -philosophical maxims which do not lose by comparison with those of -Bacon; and Galileo deserves the additional praise, that he himself gave -to the world a splendid practical illustration of the value of the -principles which he constantly recommended. In support of this view of -the comparative deserts of these two celebrated men, we are able to -adduce the authority of Hume, who will be readily admitted as a -competent judge of philosophical merit, where his prejudices cannot bias -his decision. Discussing the character of Bacon, he says, "If we -consider the variety of talents displayed by this man, as a public -speaker, a man of business, a wit, a courtier, a companion, an author, a -philosopher, he is justly the object of great admiration. If we consider -him merely as an author and philosopher, the light in which we view him -at present, though very estimable, he was yet inferior to his -contemporary Galileo, perhaps even to Kepler. Bacon pointed out at a -distance the road to true philosophy: Galileo both pointed it out to -others, and made himself considerable advances in it. The Englishman was -ignorant of geometry: the Florentine revived that science, excelled in -it, and was the first that applied it, together with experiment, to -natural philosophy. The former rejected with the most positive disdain -the system of Copernicus: the latter fortified it with new proofs -derived both from reason and the senses."[2] - -If we compare them from another point of view, not so much in respect of -their intrinsic merit, as of the influence which each exercised on the -philosophy of his age, Galileo's superior talent or better fortune, in -arresting the attention of his contemporaries, seems indisputable. The -fate of the two writers is directly opposed the one to the other; -Bacon's works seem to be most studied and appreciated when his readers -have come to their perusal, imbued with knowledge and a philosophical -spirit, which, however, they have attained independently of his -assistance. The proud appeal to posterity which he uttered in his will, -"For my name and memory, I leave it to men's charitable speeches, and to -foreign nations, and the next ages," of itself indicates a consciousness -of the fact that his contemporary countrymen were but slightly affected -by his philosophical precepts. But Galileo's personal exertions changed -the general character of philosophy in Italy: at the time of his death, -his immediate pupils had obtained possession of the most celebrated -universities, and were busily engaged in practising and enforcing the -lessons which he had taught them; nor was it then easy to find there a -single student of natural philosophy who did not readily ascribe the -formation of his principles to the direct or remote influence of -Galileo's example. Unlike Bacon's, his reputation, and the value of his -writings, were higher among his contemporaries than they have since -become. This judgment perhaps awards the highest intellectual prize to -him whose disregarded services rise in estimation with the advance of -knowledge; but the praise due to superior usefulness belongs to him who -succeeded in training round him a school of imitators, and thereby -enabled his imitators to surpass himself. - -The biography of men who have devoted themselves to philosophical -pursuits seldom affords so various and striking a succession of -incidents as that of a soldier or statesman. The life of a man who is -shut up during the greater part of his time in his study or laboratory -supplies but scanty materials for personal details; and the lapse of -time rapidly removes from us the opportunities of preserving such -peculiarities as might have been worth recording. An account of it will -therefore consist chiefly in a review of his works and opinions, and of -the influence which he and they have exercised over his own and -succeeding ages. Viewed in this light, few lives can be considered more -interesting than that of Galileo; and if we compare the state in which -he found, with that in which he left, the study of nature, we shall feel -how justly an enthusiastic panegyric pronounced upon the age immediately -following him may be transferred to this earlier period. "This is the -age wherein all men's minds are in a kind of fermentation, and the -spirit of wisdom and learning begins to mount and free itself from those -drossie and terrene impediments wherewith it has been so long clogged, -and from the insipid phlegm and _caput mortuum_ of useless notions in -which it hath endured so violent and long a fixation. This is the age -wherein, methinks, philosophy comes in with a spring tide, and the -peripatetics may as well hope to stop the current of the tide, or, with -Xerxes, to fetter the ocean, as hinder the overflowing of free -philosophy. Methinks I see how all the old rubbish must be thrown away, -and the rotten buildings be overthrown and carried away, with so -powerful an inundation. These are the days that must lay a new -foundation of a more magnificent philosophy, never to be overthrown, -that will empirically and sensibly canvass the phenomena of nature, -deducing the causes of things from such originals in nature as we -observe are producible by art, and the infallible demonstration of -mechanics: and certainly this is the way, and no other, to build a true -and permanent philosophy."[3] - - -FOOTNOTES: - -[1] Menage. - -[2] Hume's England, James I. - -[3] Power's Experimental Philosophy, 1663. - - - - -CHAPTER II. - - _Galileo's Birth--Family--Education--Observation of the - Pendulum--Pulsilogies--Hydrostatical Balance--Lecturer at Pisa._ - - -GALILEO GALILEI was born at Pisa, on the 15th day of February, 1564, of -a noble and ancient Florentine family, which, in the middle of the -fourteenth century, adopted this surname instead of Bonajuti, under -which several of their ancestors filled distinguished offices in the -Florentine state. Some misapprehension has occasionally existed, in -consequence of the identity of his proper name with that of his family; -his most correct appellation would perhaps be Galileo de' Galilei, but -the surname usually occurs as we have written it. He is most commonly -spoken of by his Christian name, agreeably to the Italian custom; just -as Sanzio, Buonarotti, Sarpi, Reni, Vecelli, are universally known by -their Christian names of Raphael, Michel Angelo, Fra Paolo, Guido, and -Titian. - -Several authors have followed Rossi in styling Galileo illegitimate, but -without having any probable grounds even when they wrote, and the -assertion has since been completely disproved by an inspection of the -registers at Pisa and Florence, in which are preserved the dates of his -birth, and of his mother's marriage, eighteen months previous to it.[4] - -His father, Vincenzo Galilei, was a man of considerable talent and -learning, with a competent knowledge of mathematics, and particularly -devoted to the theory and practice of music, on which he published -several esteemed treatises. The only one which it is at present easy to -procure--his Dialogue on ancient and modern music--exhibits proofs, not -only of a thorough acquaintance with his subject, but of a sound and -vigorous understanding applied to other topics incidentally discussed. -There is a passage in the introductory part, which becomes interesting -when considered as affording some traces of the precepts by which -Galileo was in all probability trained to reach his preeminent station -in the intellectual world. "It appears to me," says one of the speakers -in the dialogue, "that they who in proof of any assertion rely simply on -the weight of authority, without adducing any argument in support of it, -act very absurdly: I, on the contrary, wish to be allowed freely to -question and freely to answer you without any sort of adulation, as well -becomes those who are truly in search of truth." Sentiments like these -were of rare occurrence at the close of the sixteenth century, and it is -to be regretted that Vincenzo hardly lived long enough to witness his -idea of a true philosopher splendidly realized in the person of his son. -Vincenzo died at an advanced age, in 1591. His family consisted of three -sons, Galileo, Michel Angelo, and Benedetto, and the same number of -daughters, Giulia, Virginia, and Livia. After Vincenzo's death the chief -support of the family devolved upon Galileo, who seems to have assisted -them to his utmost power. In a letter to his mother, dated 1600, -relative to the intended marriage of his sister Livia with a certain -Pompeo Baldi, he agrees to the match, but recommends its temporary -postponement, as he was at that time exerting himself to furnish money -to his brother Michel Angelo, who had received the offer of an -advantageous settlement in Poland. As the sum advanced to his brother, -which prevented him from promoting his sister's marriage, did not exceed -200 crowns, it may be inferred that the family were in a somewhat -straitened condition. However he promises, as soon as his brother should -repay him, "to take measures for the young lady, since she too is bent -upon _coming out_ to prove the miseries of this world."--As Livia was at -the date of this letter in a convent, the last expression seems to -denote that she had been destined to take the veil. This proposed -marriage never took place, but Livia was afterwards married to Taddeo -Galletti: her sister Virginia married Benedetto Landucci. Galileo -mentions one of his sisters, (without naming her) as living with him in -1619 at Bellosguardo. Michel Angelo is probably the same brother of -Galileo who is mentioned by Liceti as having communicated from Germany -some observations on natural history.[5] He finally settled in the -service of the Elector of Bavaria; in what situation is not known, but -upon his death the Elector granted a pension to his family, who then -took up their abode at Munich. On the taking of that city in 1636, in -the course of the bloody thirty years' war, which was then raging -between the Austrians and Swedes, his widow and four of his children -were killed, and every thing which they possessed was either burnt or -carried away. Galileo sent for his two nephews, Alberto and a younger -brother, to Arcetri near Florence, where he was then living. These two -were then the only survivors of Michel Angelo's family; and many of -Galileo's letters about that date contain allusions to the assistance he -had been affording them. The last trace of Alberto is on his return into -Germany to the Elector, in whose service his father had died. These -details include almost every thing which is known of the rest of -Vincenzo's family. - -Galileo exhibited early symptoms of an active and intelligent mind, and -distinguished himself in his childhood by his skill in the construction -of ingenious toys and models of machinery, supplying the deficiencies of -his information from the resources of his own invention; and he -conciliated the universal good-will of his companions by the ready good -nature with which he employed himself in their service and for their -amusement. It is worthy of observation, that the boyhood of his great -follower Newton, whose genius in many respects so closely resembled his -own, was marked by a similar talent. Galileo's father was not opulent, -as has been already stated: he was burdened with a large family, and was -unable to provide expensive instructors for his son; but Galileo's own -energetic industry rapidly supplied the want of better opportunities; -and he acquired, under considerable disadvantages, the ordinary -rudiments of a classical education, and a competent knowledge of the -other branches of literature which were then usually studied. His -leisure hours were applied to music and drawing; for the former -accomplishment he inherited his father's talent, being an excellent -performer on several instruments, especially on the lute; this continued -to be a favourite recreation during the whole of his life. He was also -passionately fond of painting, and at one time he wished to make it his -profession: and his skill and judgment of pictures were highly esteemed -by the most eminent contemporary artists, who did not scruple to own -publicly their deference to young Galileo's criticism. - -When he had reached his nineteenth year, his father, becoming daily more -sensible of his superior genius, determined, although at a great -personal sacrifice, to give him the advantages of an university -education. Accordingly, in 1581, he commenced his academical studies in -the university of his native town, Pisa, his father at this time -intending that he should adopt the profession of medicine. In the -matriculation lists at Pisa, he is styled Galileo, the son of Vincenzo -Galilei, a Florentine, Scholar in Arts. His instructor was the -celebrated botanist, Andreas Caesalpinus, who was professor of medicine -at Pisa from 1567 to 1592. Hist. Acad. Pisan.; Pisis, 1791. It is dated -5th November, 1581. Viviani, his pupil, friend, and panegyrist, declares -that, almost from the first day of his being enrolled on the lists of -the academy, he was noticed for the reluctance with which he listened to -the dogmas of the Aristotelian philosophy, then universally taught; and -he soon became obnoxious to the professors from the boldness with which -he promulgated what they styled his philosophical paradoxes. His early -habits of free inquiry were irreconcileable with the mental quietude of -his instructors, whose philosophic doubts, when they ventured to -entertain any, were speedily lulled by a quotation from Aristotle. -Galileo thought himself capable of giving the world an example of a -sounder and more original mode of thinking; he felt himself destined to -be the founder of a new school of rational and experimental philosophy. -Of this we are now securely enjoying the benefits; and it is difficult -at this time fully to appreciate the obstacles which then presented -themselves to free inquiry: but we shall see, in the course of this -narrative, how arduous their struggle was who happily effected this -important revolution. The vindictive rancour with which the partisans of -the old philosophy never ceased to assail Galileo is of itself a -sufficient proof of the prominent station which he occupied in the -contest. - -Galileo's earliest mechanical discovery, to the superficial observer -apparently an unimportant one, occurred during the period of his studies -at Pisa. His attention was one day arrested by the vibrations of a lamp -swinging from the roof of the cathedral, which, whether great or small, -seemed to recur at equal intervals. The instruments then employed for -measuring time were very imperfect: Galileo attempted to bring his -observation to the test before quitting the church, by comparing the -vibrations with the beatings of his own pulse, and his mind being then -principally employed upon his intended profession, it occurred to him, -when he had further satisfied himself of their regularity by repeated -and varied experiments, that the process he at first adopted might be -reversed, and that an instrument on this principle might be usefully -employed in ascertaining the rate of the pulse, and its variation from -day to day. He immediately carried the idea into execution, and it was -for this sole and limited purpose that the first pendulum was -constructed. Viviani tells us, that the value of the invention was -rapidly appreciated by the physicians of the day, and was in common use -in 1654, when he wrote. - -[Illustration: Instrument No. 1, No. 2, No. 3] - -Santorio, who was professor of medicine at Padua, has given -representations of four different forms of these instruments, which he -calls pulsilogies, (_pulsilogias_,) and strongly recommends to medical -practitioners.[6] These instruments seem to have been used in the -following manner: No. 1 consists merely of a weight fastened to a string -and a graduated scale. The string being gathered up into the hand till -the vibrations of the weight coincided with the beatings of the -patient's pulse, the length was ascertained from the scale, which, of -course, if great, indicated a languid, if shorter, a more lively action. -In No. 2 the improvement is introduced of connecting the scale and -string, the length of the latter is regulated by the turns of a peg at -_a_, and a bead upon the string at _b_ showed the measure. No. 3 is -still more compact, the string being shortened by winding upon an axle -at the back of the dial-plate. The construction of No. 4, which Santorio -claims as his own improvement, is not given, but it is probable that the -principal index, by its motion, shifted a weight to different distances -from the point of suspension, and that the period of vibration was -still more accurately adjusted by a smaller weight connected with the -second index. Venturi seems to have mistaken the third figure for that -of a pendulum clock, as he mentions this as one of the earliest -adaptations of Galileo's principle to that purpose;[7] but it is -obvious, from Santorio's description, that it is nothing more than a -circular scale, the index showing, by the figure to which it points, the -length of string remaining unwound upon the axis. We shall, for the -present, postpone the consideration of the invention of pendulum clocks, -and the examination of the different claims to the honour of their first -construction. - -At the time of which we are speaking, Galileo was entirely ignorant of -mathematics, the study of which was then at a low ebb, not only in -Italy, but in every part of Europe. Commandine had recently revived a -taste for the writings of Euclid and Archimedes, and Vieta Tartalea and -others had made considerable progress in algebra, Guido Ubaldi and -Benedetti had done something towards establishing the principles of -statics, which was the only part of mechanics as yet cultivated; but -with these inconsiderable exceptions the application of mathematics to -the phenomena of nature was scarcely thought of. Galileo's first -inducement to acquire a knowledge of geometry arose from his partiality -for drawing and music, and from the wish to understand their principles -and theory. His father, fearful lest he should relax his medical -studies, refused openly to encourage him in this new pursuit; but he -connived at the instruction which his son now began to receive in the -writings of Euclid, from the tuition of an intimate friend, named -Ostilio Ricci, who was one of the professors in the university. -Galileo's whole attention was soon directed to the enjoyment of the new -sensations thus communicated to him, insomuch that Vincenzo, finding his -prognostics verified, began to repent his indirect sanction, and -privately requested Ricci to invent some excuse for discontinuing his -lessons. But it was fortunately too late; the impression was made and -could not be effaced; from that time Hippocrates and Galen lay unheeded -before the young physician, and served only to conceal from his father's -sight the mathematical volumes on which the whole of his time was really -employed. His progress soon revealed the true nature of his pursuits: -Vincenzo yielded to the irresistible predilection of his son's mind, and -no longer attempted to turn him from the speculations to which his whole -existence was thenceforward abandoned. - -After mastering the elementary writers, Galileo proceeded to the study -of Archimedes, and, whilst perusing the Hydrostatics of that author, -composed his earliest work,--an Essay on the Hydrostatical Balance. In -this he explains the method probably adopted by Archimedes for the -solution of Hiero's celebrated question[8], and shows himself already -well acquainted with the true principles of specific gravities. This -essay had an immediate and important influence on young Galileo's -fortunes, for it introduced him to the approving notice of Guido Ubaldi, -then one of the most distinguished mathematicians of Italy. At his -suggestion Galileo applied himself to consider the position of the -centre of gravity in solid bodies, a choice of subject that sufficiently -showed the estimate Ubaldi had formed of his talents; for it was a -question on which Commandine had recently written, and which engaged at -that time the attention of geometricians of the highest order. Galileo -tells us himself that he discontinued these researches on meeting with -Lucas Valerio's treatise on the same subject. Ubaldi was so much struck -with the genius displayed in the essay with which Galileo furnished him, -that he introduced him to his brother, the Cardinal Del Monte: by this -latter he was mentioned to Ferdinand de' Medici, the reigning Duke of -Tuscany, as a young man of whom the highest expectations might be -entertained. By the Duke's patronage he was nominated, in 1589, to the -lectureship of mathematics at Pisa, being then in his twenty-sixth year. -His public salary was fixed at the insignificant sum of sixty crowns -annually, but he had an opportunity of greatly adding to his income by -private tuition. - - -FOOTNOTES: - -[4] Erythraeus, Pinacotheca, vol. i.; Salusbury's Life of Galileo. Nelli, -Vita di Gal. Galilei. - -[5] De his quae diu vivunt. Patavii, 1612. - -[6] Comment, in Avicennam. Venetiis, 1625. - - - - -CHAPTER III. - - _Galileo at Pisa--Aristotle--Leonardo da Vinci--Galileo becomes a - Copernican--Urstisius--Bruno--Experiments on falling - bodies--Galileo at Padua--Thermometer._ - - -NO sooner was Galileo settled in his new office than he renewed his -inquiries into the phenomena of nature with increased diligence. He -instituted a course of experiments for the purpose of putting to the -test the mechanical doctrines of Aristotle, most of which he found -unsupported even by the pretence of experience. It is to be regretted -that we do not more frequently find detailed his method of -experimenting, than occasionally in the course of his dialogues, and it -is chiefly upon the references which he makes to the results with which -the experiments furnished him, and upon the avowed and notorious -character of his philosophy, that the truth of these accounts must be -made to depend. Venturi has found several unpublished papers by Galileo -on the subject of motion, in the Grand Duke's private library at -Florence, bearing the date of 1590, in which are many of the theorems -which he afterwards developed in his Dialogues on Motion. These were not -published till fifty years afterwards, and we shall reserve an account -of their contents till we reach that period of his life. - -Galileo was by no means the first who had ventured to call in question -the authority of Aristotle in matters of science, although he was -undoubtedly the first whose opinions and writings produced a very marked -and general effect. Nizzoli, a celebrated scholar who lived in the early -part of the 16th century, had condemned Aristotle's philosophy, -especially his Physics, in very unequivocal and forcible terms, -declaring that, although there were many excellent truths in his -writings, the number was scarcely less of false, useless, and ridiculous -propositions.[9] About the time of Galileo's birth, Benedetti had -written expressly in confutation of several propositions contained in -Aristotle's mechanics, and had expounded in a clear manner some of the -doctrines of statical equilibrium.[10] Within the last forty years it -has been established that the celebrated painter Leonardo da Vinci, who -died in 1519, amused his leisure hours in scientific pursuits; and many -ideas appear to have occurred to him which are to be found in the -writings of Galileo at a later date. It is not impossible (though there -are probably no means of directly ascertaining the fact) that Galileo -may have been acquainted with Leonardo's investigations, although they -remained, till very lately, almost unknown to the mathematical world. -This supposition is rendered more probable from the fact, that Mazenta, -the preserver of Leonardo's manuscripts, was, at the very time of their -discovery, a contemporary student with Galileo at Pisa. Kopernik, or, as -he is usually called, Copernicus, a native of Thorn in Prussia, had -published his great work, De Revolutionibus, in 1543, restoring the -knowledge of the true theory of the solar system, and his opinions were -gradually and silently gaining ground. - -It is not satisfactorily ascertained at what period Galileo embraced -the new astronomical theory. Gerard Voss attributes his conversion -to a public lecture of Maestlin, the instructor of Kepler; and later -writers (among whom is Laplace) repeat the same story, but without -referring to any additional sources of information, and in most -instances merely transcribing Voss's words, so as to shew indisputably -whence they derived their account. Voss himself gives no authority, -and his general inaccuracy makes his mere word not of much weight. The -assertion appears, on many accounts, destitute of much probability. -If the story were correct, it seems likely that some degree of -acquaintance, if not of friendly intercourse, would have subsisted -between Maestlin, and his supposed pupil, such as in fact we find -subsisting between Maestlin and his acknowledged pupil Kepler, the -devoted friend of Galileo; but, on the contrary, we find Maestlin -writing to Kepler himself of Galileo as an entire stranger, and in -the most disparaging terms. If Maestlin could lay claim to the honour -of so celebrated a disciple, it is not likely that he could fail so -entirely to comprehend the distinction it must confer upon himself as -to attempt diminishing it by underrating his pupil's reputation. There -is a passage in Galileo's works which more directly controverts the -claim advanced for Maestlin, although Salusbury, in his life of Galileo, -having apparently an imperfect recollection of its tenor, refers to -this very passage in confirmation of Voss's statement. In the second -part of the dialogue on the Copernican system, Galileo makes Sagredo, -one of the speakers in it, give the following account:--"Being very -young, and having scarcely finished my course of philosophy, which I -left off as being set upon other employments, there chanced to come -into these parts a certain foreigner of Rostoch, _whose name, as I -remember, was Christianus Urstisius_, a follower of Copernicus, who, -in an academy, gave two or three lectures upon this point, to whom -many flocked as auditors; but I, thinking they went more for the -novelty of the subject than otherwise, did not go to hear him; for I -had concluded with myself that that opinion could be no other than a -solemn madness; and questioning some of those who had been there, I -perceived they all made a jest thereof, except one, who told me that -the business was not altogether to be laughed at: and because the man -was reputed by me to be very intelligent and wary, I repented that I -was not there, and began from that time forward, as oft as I met with -any one of the Copernican persuasion, to demand of them if they had -been always of the same judgment. Of as many as I examined I found not -so much as one who told me not that he had been a long time of the -contrary opinion, but to have changed it for this, as convinced by the -strength of the reasons proving the same; and afterwards questioning -them one by one, to see whether they were well possessed of the reasons -of the other side, I found them all to be very ready and perfect in -them, so that I could not truly say that they took this opinion out -of ignorance, vanity, or to show the acuteness of their wits. On the -contrary, of as many of the Peripatetics and Ptolemeans as I have -asked, (and out of curiosity I have talked with many,) what pains they -had taken in the book of Copernicus, I found very few that had so much -as superficially perused it, but of those who I thought had understood -the same, not one: and, moreover, I have inquired amongst the followers -of the Peripatetic doctrine, if ever any of them had held the contrary -opinion, and likewise found none that had. Whereupon, considering that -there was no man who followed the opinion of Copernicus that had not -been first on the contrary side, and that was not very well acquainted -with the reasons of Aristotle and Ptolemy, and, on the contrary, that -there was not one of the followers of Ptolemy that had ever been of -the judgment of Copernicus, and had left that to embrace this of -Aristotle;--considering, I say, these things, I began to think that -one who leaveth an opinion imbued with his milk and followed by very -many, to take up another, owned by very few, and denied by all the -schools, and that really seems a great paradox, must needs have been -moved, not to say forced, by more powerful reasons. For this cause I -am become very curious to dive, as they say, into the bottom of this -business." It seems improbable that Galileo should think it worth while -to give so detailed an account of the birth and growth of opinion in -any one besides himself; and although Sagredo is not the personage who -generally in the dialogue represents Galileo, yet as the real Sagredo -was a young nobleman, a pupil of Galileo himself, the account cannot -refer to him. The circumstance mentioned of the intermission of his -philosophical studies, though in itself trivial, agrees very well with -Galileo's original medical destination. Urstisius is not a fictitious -name, as possibly Salusbury may have thought, when alluding to this -passage; he was mathematical professor at Bale, about 1567, and several -treatises by him are still extant. According to Kaestner, his German name -was Wursteisen. In 1568 Voss informs us that he published some new -questions on Purbach's Theory of the Planets. He died at Bale in 1586, -when Galileo was about twenty-two years old. - -It is not unlikely that Galileo also, in part, owed his emancipation -from popular prejudices to the writings of Giordano Bruno, an -unfortunate man, whose unsparing boldness in exposing fallacies and -absurdities was rewarded by a judicial murder, and by the character of -heretic and infidel, with which his executioners endeavoured to -stigmatize him for the purpose of covering over their own atrocious -crime. Bruno was burnt at Rome in 1600, but not, as Montucla supposes, -on account of his "Spaccio della Bestia trionfante." The title of this -book has led him to suppose that it was directed against the church of -Rome, to which it does not in the slightest degree relate. Bruno -attacked the fashionable philosophy alternately with reason and -ridicule, and numerous passages in his writings, tedious and obscure as -they generally are, show that he had completely outstripped the age in -which he lived. Among his astronomical opinions, he believed that the -universe consisted of innumerable systems of suns with assemblages of -planets revolving round each of them, like our own earth, the smallness -of which, alone, prevented their being observed by us. He remarked -further, "that it is by no means improbable that there are yet other -planets revolving round our own sun, which we have not yet noticed, -either on account of their minute size or too remote distance from us." -He declined asserting that all the apparently fixed stars are really so, -considering this as not sufficiently proved, "because at such enormous -distances the motions become difficult to estimate, and it is only by -long observation that we can determine if any of these move round each -other, or what other motions they may have." He ridiculed the -Aristotelians in no very measured terms--"They harden themselves, and -heat themselves, and embroil themselves for Aristotle; they call -themselves his champions, they hate all but Aristotle's friends, they -are ready to live and die for Aristotle, and yet they do not understand -so much as the titles of Aristotle's chapters." And in another place he -introduces an Aristotelian inquiring, "Do you take Plato for an -ignoramus--Aristotle for an ass?" to whom he answers, "My son, I neither -call them asses, nor you mules,--them baboons, nor you apes,--as you -would have me: I told you that I esteem them the heroes of the world, -but I will not credit them without sufficient reason; and if you were -not both blind and deaf, you would understand that I must disbelieve -their absurd and contradictory assertions."[11] Bruno's works, though in -general considered those of a visionary and madman, were in very -extensive circulation, probably not the less eagerly sought after from -being included among the books prohibited by the Romish church; and -although it has been reserved for later observations to furnish complete -verification of his most daring speculations, yet there was enough, -abstractedly taken, in the wild freedom of his remarks, to attract a -mind like Galileo's; and it is with more satisfaction that we refer the -formation of his opinions to a man of undoubted though eccentric genius, -like Bruno, than to such as Maestlin, who, though a diligent and careful -observer, seems seldom to have taken any very enlarged views of the -science on which he was engaged. - -With a few exceptions similar to those above mentioned, the rest of -Galileo's contemporaries well deserved the contemptuous epithet which he -fixed on them of Paper Philosophers, for, to use his own words, in a -letter to Kepler on this subject, "this sort of men fancied philosophy -was to be studied like the AEneid or Odyssey, and that the true reading -of nature was to be detected by the collation of texts." Galileo's own -method of philosophizing was widely different; seldom omitting to bring -with every new assertion the test of experiment, either directly in -confirmation of it, or tending to show its probability and consistency. -We have already seen that he engaged in a series of experiments to -investigate the truth of some of Aristotle's positions. As fast as he -succeeded in demonstrating the falsehood of any of them, he denounced -them from his professorial chair with an energy and success which -irritated more and more against him the other members of the academic -body. - -There seems something in the stubborn opposition which he encountered in -establishing the truth of his mechanical theorems, still more stupidly -absurd than in the ill will to which, at a later period of his life, his -astronomical opinions exposed him: it is intelligible that the vulgar -should withhold their assent from one who pretended to discoveries in -the remote heavens, which few possessed instruments to verify, or -talents to appreciate; but it is difficult to find terms for -stigmatizing the obdurate folly of those who preferred the evidence of -their books to that of their senses, in judging of phenomena so obvious -as those, for instance, presented by the fall of bodies to the ground. -Aristotle had asserted, that if two different weights of the same -material were let fall from the same height, the heavier one would reach -the ground sooner than the other, in the proportion of their weights. -The experiment is certainly not a very difficult one, but nobody thought -of that method of argument, and consequently this assertion had been -long received, upon his word, among the axioms of the science of motion. -Galileo ventured to appeal from the authority of Aristotle to that of -his own senses, and maintained that, with the exception of an -inconsiderable difference, which he attributed to the disproportionate -resistance of the air, they would fall in the same time. The -Aristotelians ridiculed and refused to listen to such an idea. Galileo -repeated his experiments in their presence from the famous leaning tower -at Pisa: and with the sound of the simultaneously falling weights still -ringing in their ears, they could persist in gravely maintaining that a -weight of ten pounds would reach the ground in a tenth part of the time -taken by one of a single pound, because they were able to quote chapter -and verse in which Aristotle assures them that such is the fact. A -temper of mind like this could not fail to produce ill will towards him -who felt no scruples in exposing their wilful folly; and the watchful -malice of these men soon found the means of making Galileo desirous of -quitting his situation at Pisa. Don Giovanni de' Medici, a natural son -of Cosmo, who possessed a slight knowledge of mechanics on which he -prided himself, had proposed a contrivance for cleansing the port of -Leghorn, on the efficiency of which Galileo was consulted. His opinion -was unfavourable, and the violence of the inventor's disappointment, -(for Galileo's judgment was verified by the result,) took the somewhat -unreasonable direction of hatred towards the man whose penetration had -foreseen the failure. Galileo's situation was rendered so unpleasant by -the machinations of this person, that he decided on accepting overtures -elsewhere, which had already been made to him; accordingly, under the -negotiation of his staunch friend Guido Ubaldi, and with the consent of -Ferdinand, he procured from the republic of Venice a nomination for six -years to the professorship of mathematics in the university of Padua, -whither he removed in September 1592. - -Galileo's predecessor in the mathematical chair at Padua was Moleti, who -died in 1588, and the situation had remained unfilled during the -intervening four years. This seems to show that the directors attributed -but little importance to the knowledge which it was the professor's duty -to impart. This inference is strengthened by the fact, that the amount -of the annual salary attached to it did not exceed 180 florins, whilst -the professors of philosophy and civil law, in the same university, were -rated at the annual stipends of 1400 and 1680 florins.[12] Galileo -joined the university about a year after its triumph over the Jesuits, -who had established a school in Padua about the year 1542, and, -increasing yearly in influence, had shown symptoms of a design to get -the whole management of the public education into the hands of their own -body.[13] After several violent disputes it was at length decreed by the -Venetian senate, in 1591, that no Jesuit should be allowed to give -instruction at Padua in any of the sciences professed in the university. -It does not appear that after this decree they were again troublesome to -the university, but this first decree against them was followed, in -1606, by a second more peremptory, which banished them entirely from the -Venetian territory. Galileo would of course find his fellow-professors -much embittered against that society, and would naturally feel inclined -to make common cause with them, so that it is not unlikely that the -hatred which the Jesuits afterwards bore to Galileo on personal -considerations, might be enforced by their recollection of the -university to which he had belonged. - -Galileo's writings now began to follow each other with great rapidity, -but he was at this time apparently so careless of his reputation, that -many of his works and inventions, after a long circulation in manuscript -among his pupils and friends, found their way into the hands of those -who were not ashamed to publish them as their own, and to denounce -Galileo's claim to the authorship as the pretence of an impudent -plagiarist. He was, however, so much beloved and esteemed by his -friends, that they vied with each other in resenting affronts of this -nature offered to him, and in more than one instance he was relieved, by -their full and triumphant answers, from the trouble of vindicating his -own character. - -To this epoch of Galileo's life may be referred his re-invention of the -thermometer. The original idea of this useful instrument belongs to the -Greek mathematician Hero; and Santorio himself, who has been named as -the inventor by Italian writers, and at one time claimed it himself, -refers it to him. In 1638, Castelli wrote to Cesarini that "he -remembered an experiment shown to him more than thirty-five years back -by Galileo, who took a small glass bottle, about the size of a hen's -egg, the neck of which was twenty-two inches long, and as narrow as a -straw. Having well heated the bulb in his hands, and then introducing -its mouth into a vessel in which was a little water, and withdrawing the -heat of his hand from the bulb, the water rose in the neck of the bottle -more than eleven inches above the level in the vessel, and Galileo -employed this principle in the construction of an instrument for -measuring heat and cold."[14] In 1613, a Venetian nobleman named -Sagredo, who has been already mentioned as Galileo's friend and pupil, -writes to him in the following words: "I have brought the instrument -which you invented for measuring heat into several convenient and -perfect forms, so that the difference of temperature between two rooms -is seen as far as 100 degrees."[15] This date is anterior to the claims -both of Santorio and Drebbel, a Dutch physician, who was the first to -introduce it into Holland. - -Galileo's thermometer, as we have just seen, consisted merely of a glass -tube ending in a bulb, the air in which, being partly expelled by heat, -was replaced by water from a glass into which the open end of the tube -was plunged, and the different degrees of temperature were indicated by -the expansion of the air which yet remained in the bulb, so that the -scale would be the reverse of that of the thermometer now in use, for -the water would stand at the highest level in the coldest weather. It -was, in truth, a barometer also, in consequence of the communication -between the tube and external air, although Galileo did not intend it -for this purpose, and when he attempted to determine the relative weight -of the air, employed a contrivance still more imperfect than this rude -barometer would have been. A passage among his posthumous fragments -intimates that he subsequently used spirit of wine instead of water. - -Viviani attributes an improvement of this imperfect instrument, but -without specifying its nature, to Ferdinand II., a pupil and subsequent -patron of Galileo, and, after the death of his father Cosmo, reigning -duke of Florence. It was still further improved by Ferdinand's younger -brother, Leopold de' Medici, who invented the modern process of -expelling all the air from the tube by boiling the spirit of wine in it, -and of hermetically sealing the end of the tube, whilst the contained -liquid is in this expanded state, which deprived it of its barometrical -character, and first made it an accurate thermometer. The final -improvement was the employment of mercury instead of spirit of wine, -which is recommended by Lana so early as 1670, on account of its equable -expansion.[16] For further details on the history and use of this -instrument, the reader may consult the Treatises on the THERMOMETER and -PYROMETER. - - -FOOTNOTES: - -[7] Essai sur les Ouvrages de Leonard da Vinci. Paris, 1797. - -[8] See Treatise on HYDROSTATICS. - -[9] Antibarbarus Philosophicus. Francofurti, 1674. - -[10] Speculationum liber. Venetiis, 1585. - -[11] De l'Infinito Universo. Dial. 3. La Cena de le Cenere, 1584. - -[12] Riccoboni, Commentarii de Gymnasio Patavino, 1598. - -[13] Nelli. - -[14] Nelli. - -[15] Venturi. Memorie e Lettere di Gal. Galilei. Modena, 1821. - -[16] Prodromo all' Arte Maestra. Brescia, 1670. - - - - -CHAPTER IV. - - _Astronomy before Copernicus--Fracastoro--Bacon--Kepler--Galileo's - Treatise on the Sphere._ - - -THIS period of Galileo's lectureship at Padua derives interest from its -including the first notice which we find of his having embraced the -doctrines of the Copernican astronomy. Most of our readers are aware of -the principles of the theory of the celestial motions which Copernicus -restored; but the number of those who possess much knowledge of the -cumbrous and unwieldy system which it superseded is perhaps more -limited. The present is not a fit opportunity to enter into many details -respecting it; these will find their proper place in the History of -Astronomy: but a brief sketch of its leading principles is necessary to -render what follows intelligible. - -The earth was supposed to be immoveably fixed in the centre of the -universe, and immediately surrounding it the atmospheres of air and -fire, beyond which the sun, moon, and planets, were thought to be -carried round the earth, fixed each to a separate orb or heaven of solid -but transparent matter. The order of distance in which they were -supposed to be placed with regard to the central earth was as follows: -The Moon, Mercury, Venus, The Sun, Mars, Jupiter, and Saturn. It became -a question in the ages immediately preceding Copernicus, whether the Sun -was not nearer the Earth than Mercury, or at least than Venus; and this -question was one on which the astronomical theorists were then chiefly -divided. - -We possess at this time a curious record of a former belief in this -arrangement of the Sun and planets, in the order in which the days of -the week have been named from them. According to the dreams of -Astrology, each planet was supposed to exert its influence in -succession, reckoning from the most distant down to the nearest, over -each hour of the twenty-four. The planet which was supposed to -predominate over the first hour, gave its name to that day.[17] The -general reader will trace this curious fact more easily with the French -or Latin names than with the English, which have been translated into -the titles of the corresponding Saxon deities. Placing the Sun and -planets in the following order, and beginning, for instance, with -Monday, or the Moon's day; Saturn ruled the second hour of that day, -Jupiter the third, and so round till we come again and again to the Moon -on the 8th, 15th, and 22d hours; Saturn ruled the 23d, Jupiter the -24th, so that the next day would be the day of Mars, or, as the Saxons -translated it, Tuisco's day, or Tuesday. In the same manner the -following days would belong respectively to Mercury or Woden, Jupiter or -Thor, Venus or Frea, Saturn or Seater, the Sun, and again the Moon. In -this manner the whole week will be found to complete the cycle of the -seven planets. - -[Illustration: Cycle of the seven planets.] - -The other stars were supposed to be fixed in an outer orb, beyond which -were two crystalline spheres, (as they were called,) and on the outside -of all, the _primum mobile_ or _first moveable_, which sphere was -supposed to revolve round the earth in twenty-four hours, and by its -friction, or rather, as most of the philosophers of that day chose to -term it, by the sort of heavenly influence which it exercised on the -interior orbs, to carry them round with a similar motion. Hence the -diversity of day and night. But beside this principal and general -motion, each orb was supposed to have one of its own, which was intended -to account for the apparent changes of position of the planets with -respect to the fixed stars and to each other. This supposition, however, -proving insufficient to account for all the irregularities of motion -observed, two hypotheses were introduced.--First, that to each planet -belonged several concentric spheres or heavens, casing each other like -the coats of an onion, and, secondly, that the centres of these solid -spheres, with which the planet revolved, were placed in the -circumference of a secondary revolving sphere, the centre of which -secondary sphere was situated at the earth. They thus acquired the names -of Eccentrics or Epicycles, the latter word signifying a circle upon a -circle. The whole art of astronomers was then directed towards inventing -and combining different eccentric and epicyclical motions, so as to -represent with tolerable fidelity the ever varying phenomena of the -heavens. Aristotle had lent his powerful assistance in this, as in other -branches of natural philosophy, in enabling the false system to prevail -against and obliterate the knowledge of the true, which, as we gather -from his own writings, was maintained by some philosophers before his -time. Of these ancient opinions, only a few traces now remain, -principally preserved in the works of those who were adverse to them. -Archimedes says expressly that Aristarchus of Samos, who lived about 300 -B. C., taught the immobility of the sun and stars, and that the earth is -carried round the central sun.[18] Aristotle's words are: "Most of those -who assert that the whole concave is finite, say that the earth is -situated in the middle point of the universe: those who are called -Pythagoreans, who live in Italy, are of a contrary opinion. For they say -that fire is in the centre, and that the earth, which, according to -them, is one of the stars, occasions the change of day and night by its -own motion, with which it is carried about the centre." It might be -doubtful, upon this passage alone, whether the Pythagorean theory -embraced more than the diurnal motion of the earth, but a little -farther, we find the following passage: "Some, as we have said, make the -earth to be one of the stars: others say that it is placed in the centre -of the Universe, and revolves on a central axis."[19] From which, in -conjunction with the former extract, it very plainly appears that the -Pythagoreans maintained both the diurnal and annual motions of the -earth. - -Some idea of the supererogatory labour entailed upon astronomers by the -adoption of the system which places the earth in the centre, may be -formed in a popular manner by observing, in passing through a thickly -planted wood, in how complicated a manner the relative positions of the -trees appear at each step to be continually changing, and by considering -the difficulty with which the laws of their apparent motions could be -traced, if we were to attempt to refer these changes to a real motion of -the trees instead of the traveller. The apparent complexity in the -heavens is still greater than in the case suggested; because, in -addition to the earth's motions, with which all the stars appear to be -impressed, each of the planets has also a real motion of its own, which -of course greatly contributes to perplex and complicate the general -appearances. Accordingly the heavens rapidly became, under this system, - - "With centric and eccentric scribbled o'er, - Cycle and epicycle, orb in orb;"[20] - -crossing and penetrating each other in every direction. Maestlin has -given a concise enumeration of the principal orbs which belonged to this -theory. After warning the readers that "they are not mere fictions which -have nothing to correspond with them out of the imagination, but that -they exist really, and bodily in the heavens,"[21] he describes seven -principal spheres belonging to each planet, which he classes as -Eccentrics, Epicycles, and Concentrepicycles, and explains their use in -accounting for the planet's revolutions, motions of the apogee, and -nodes, &c. &c. In what manner this multitude of solid and crystalline -orbs were secured from injuring or interfering with each other was not -very closely inquired into. - -The reader will cease to expect any very intelligible explanation of -this and numberless other difficulties which belong to this unwieldy -machinery when he is introduced to the reasoning by which it was upheld. -Gerolamo Fracastoro, who lived in the sixteenth century, writes in the -following terms, in his work entitled Homocentrica, (certainly one of -the best productions of the day,) in which he endeavours to simplify the -necessary apparatus, and to explain all the phenomena (as the title of -his book implies) by concentric spheres round the earth. "There are -some, not only of the ancients but also among the moderns, who believe -that the stars move freely without any such agency; but it is difficult -to conceive in what manner they have imbued themselves with this notion, -_since not only reason, but the very senses, inform us that all the -stars are carried round fastened to solid spheres_." What ideas -Fracastoro entertained of the evidence of the "senses" it is not now -easy to guess, but he goes on to give a specimen of the "reasoning" -which appeared to him so incontrovertible. "The planets are observed to -move one while forwards, then backwards, now to the right, now to the -left, quicker and slower by turns; which variety is consistent with a -compound structure like that of an animal, which possesses in itself -various springs and principles of action, but is totally at variance -with our notion of a simple and undecaying substance like the heavens -and heavenly bodies. For that which is simple, is altogether single, and -singleness is of one only nature, and one nature can be the cause of -only one effect; and therefore it is altogether impossible that the -stars of themselves should move with such variety of motion. And -besides, if the stars move by themselves, they either move in an empty -space, or in a fluid medium like the air. But there cannot be such a -thing as empty space, and if there were such a medium, the motion of the -star would occasion condensation and rarefaction in different parts of -it, which is the property of corruptible bodies and where they exist -some violent motion is going on; but the heavens are incorruptible and -are not susceptible of violent motion, and hence, and from many other -similar reasons, any one who is not obstinate may satisfy himself that -the stars cannot have any independent motion." - -Some persons may perhaps think that arguments of this force are -unnecessarily dragged from the obscurity to which they are now for the -most part happily consigned; but it is essential, in order to set -Galileo's character and merits in their true light, to show how low at -this time philosophy had fallen. For we shall form a very inadequate -notion of his powers and deserts if we do not contemplate him in the -midst of men who, though of undoubted talent and ingenuity, could so far -bewilder themselves as to mistake such a string of unmeaning phrases for -argument: we must reflect on the difficulty every one experiences in -delivering himself from the erroneous impressions of infancy, which will -remain stamped upon the imagination in spite of all the efforts of -matured reason to erase them, and consider every step of Galileo's -course as a triumph over difficulties of a like nature. We ought to be -fully penetrated with this feeling before we sit down to the perusal of -his works, every line of which will then increase our admiration of the -penetrating acuteness of his invention and unswerving accuracy of his -judgment. In almost every page we discover an allusion to some new -experiment, or the germ of some new theory; and amid all this wonderful -fertility it is rarely indeed that we find the exuberance of his -imagination seducing him from the rigid path of philosophical induction. -This is the more remarkable as he was surrounded by friends and -contemporaries of a different temperament and much less cautious -disposition. A disadvantageous contrast is occasionally furnished even -by the sagacious Bacon, who could so far deviate from the sound -principles of inductive philosophy, as to write, for instance, in the -following strain, bordering upon the worst manner of the -Aristotelians:--"Motion in a circle has no limit, and seems to emanate -from the appetite of the body, which moves only for the sake of moving, -and that it may follow itself and seek its own embraces, and put in -action and enjoy its own nature, and exercise its peculiar operation: on -the contrary, motion in a straight line seems transitory, and to move -towards a limit of cessation or rest, and that it may reach some point, -and then put off its motion."[22] Bacon rejected all the machinery of -the _primum mobile_ and the solid spheres, the eccentrics and the -epicycles, and carried his dislike of these doctrines so far as to -assert that nothing short of their gross absurdity could have driven -theorists to the extravagant supposition of the motion of the earth, -which, said he, "we know to be most false."[23] Instances of extravagant -suppositions and premature generalizations are to be found in almost -every page of his other great contemporary, Kepler. - -It is with pain that we observe Delambre taking every opportunity, in -his admirable History of Astronomy, to undervalue and sneer at Galileo, -seemingly for the sake of elevating the character of Kepler, who appears -his principal favourite, but whose merit as a philosopher cannot safely -be brought into competition with that of his illustrious contemporary. -Delambre is especially dissatisfied with Galileo, for taking no notice, -in his "System of the World," of the celebrated laws of the planetary -motions which Kepler discovered, and which are now inseparably connected -with his name. The analysis of Newton and his successors has now -identified those apparently mysterious laws with the general phenomena -of motion, and has thus entitled them to an attention of which, before -that time, they were scarcely worthy; at any rate not more than is at -present the empirical law which includes the distances of all the -planets from the sun (roughly taken) in one algebraical formula. The -observations of Kepler's day were scarcely accurate enough to prove that -the relations which he discovered between the distances of the planets -from the sun and the periods of their revolutions around him were -necessarily to be received as demonstrated truths; and Galileo surely -acted most prudently and philosophically in holding himself altogether -aloof from Kepler's fanciful devices and numeral concinnities, although, -with all the extravagance, they possessed much of the genius of the -Platonic reveries, and although it did happen that Galileo, by -systematically avoiding them, failed to recognise some important truths. -Galileo probably was thinking of those very laws, when he said of -Kepler, "He possesses a bold and free genius, perhaps too much so; but -his mode of philosophizing is widely different from mine." We shall have -further occasion in the sequel to recognise the justice of this remark. - -In the treatise on the Sphere which bears Galileo's name, and which, if -he be indeed the author of it, was composed during the early part of his -residence at Padua, he also adopts the Ptolemaic system, placing the -earth immoveable in the centre, and adducing against its motion the -usual arguments, which in his subsequent writings he ridicules and -refutes. Some doubts have been expressed of its authenticity; but, -however this may be, we have it under Galileo's own hand that he taught -the Ptolemaic system, in compliance with popular prejudices, for some -time after he had privately become a convert to the contrary opinions. -In a letter, apparently the first which he wrote to Kepler, dated from -Padua, 1597, he says, acknowledging the receipt of Kepler's Mysterium -Cosmographicum, "I have as yet read nothing beyond the preface of your -book, from which however I catch a glimpse of your meaning, and feel -great joy on meeting with so powerful an associate in the pursuit of -truth, and consequently such a friend to truth itself, for it is -deplorable that there should be so few who care about truth, and who do -not persist in their perverse mode of philosophizing; but as this is not -the fit time for lamenting the melancholy condition of our times, but -for congratulating you on your elegant discoveries in confirmation of -the truth, I shall only add a promise to peruse your book -dispassionately, and with a conviction that I shall find in it much to -admire. _This I shall do the more willingly because many years ago I -became a convert to the opinions of Copernicus_,[24] and by that theory -have succeeded in fully explaining many phenomena, which on the contrary -hypothesis are altogether inexplicable. I have arranged many arguments -and confutations of the opposite opinions, _which however I have not yet -dared to publish_, fearing the fate of our master Copernicus, who, -although he has earned immortal fame among a few, yet by an infinite -number (for so only can the number of fools be measured) is exploded and -derided. If there were many such as you, I would venture to publish my -speculations; but, since that is not so, I shall take time to consider -of it." This interesting letter was the beginning of the friendship of -these two great men, which lasted uninterruptedly till 1630, the date of -Kepler's death. That extraordinary genius never omitted an opportunity -of testifying his admiration of Galileo, although there were not wanting -persons envious of their good understanding, who exerted themselves to -provoke coolness and quarrel between them. Thus Brutius writes to Kepler -in 1602[25]: "Galileo tells me he has written to you, and has got your -book, which however he denied to Magini, and I abused him for praising -you with too many qualifications. I know it to be a fact that, both in -his lectures, and elsewhere, he is publishing your inventions as his -own; but I have taken care, and shall continue to do so, that all this -shall redound not to his credit but to yours." The only notice which -Kepler took of these repeated insinuations, which appear to have been -utterly groundless, was, by renewed expressions of respect and -admiration, to testify the value he set upon his friend and -fellow-labourer in philosophy. - - -FOOTNOTES: - -[17] Dion Cassius, lib. 37. - -[18] The pretended translation by Roberval of an Arabic version of -Aristarchus, "De Systemate Mundi," in which the Copernican system is -fully developed, is spurious. Menage asserts this in his observations on -Diogen. Laert. lib. 8, sec. 85, tom. ii., p. 389. (Ed. Amst. 1692.) The -commentary contains many authorities well worth consulting. Delambre, -Histoire de l'Astronomie, infers it from its not containing some -opinions which Archimedes tells us were held by Aristarchus. A more -direct proof may be gathered from the following blunder of the supposed -translator. Astronomers had been long aware that the earth in different -parts of her orbit is at different distances from the sun. Roberval -wished to claim for Aristarchus the credit of having known this, and -introduced into his book, not only the mention of the fact, but an -explanation of its cause. Accordingly he makes Aristarchus give a reason -"why the sun's apogee (or place of greatest distance from the earth) -must always be at the north summer solstice." In fact, it was there, or -nearly so, in Roberval's time, and he knew not but that it had always -been there. It is however moveable, and, when Aristarchus lived, was -nearly half way between the solstices and equinoxes. He therefore would -hardly have given a reason for the necessity of a phenomenon of which, -if he observed anything on the subject, he must have observed the -contrary. The change in the obliquity of the earth's axis to the -ecliptic was known in the time of Roberval, and he accordingly has -introduced the proper value which it had in Aristarchus's time. - -[19] De Coelo. lib. 2. - -[20] Paradise Lost, b. viii. v. 83. - -[21] Itaque tam circulos primi motus quam orbes secundorum mobilium -revera in coelesti corpore esse concludimus, &c. Non ergo sunt mera -figmenta, quibus extra mentem nihil correspondeat. M. Maestlini, De -Astronomiae Hypothesibus disputatio. Heidelbergae, 1582. - -[22] Opuscula Philosophica, Thema Coeli. - -[23] "Nobis constat falsissimum esse." De Aug. Scient. lib. iii. c. 3, -1623. - -[24] Id autum eo libentius faciam, quod in Copernici sententiam multis -abhinc annis venerim.--Kepl. Epistolae. - -[25] Kepleri Epistolae. - - - - -CHAPTER V. - - _Galileo re-elected Professor at Padua--New star--Compass of - proportion--Capra--Gilbert--Proposals to return to Pisa--Lost - writings--Cavalieri._ - - -GALILEO'S reputation was now rapidly increasing: his lectures were -attended by many persons of the highest rank; among whom were the -Archduke Ferdinand, afterwards Emperor of Germany, the Landgrave of -Hesse, and the Princes of Alsace and Mantua. On the expiration of the -first period for which he had been elected professor, he was rechosen -for a similar period, with a salary increased to 320 florins. The -immediate occasion of this augmentation is said by Fabroni[26], to have -arisen out of the malice of an ill wisher of Galileo, who, hoping to do -him disservice, apprized the senate that he was not married to Marina -Gamba, then living with him, and the mother of his son Vincenzo. Whether -or not the senate might consider themselves entitled to inquire into the -morality of his private life, it was probably from a wish to mark their -sense of the informer's impertinence, that they returned the brief -answer, that "if he had a family to provide for, he stood the more in -need of an increased stipend." - -During Galileo's residence at Padua, and, according to Viviani's -intimation, towards the thirtieth year of his age, that is to say in -1594, he experienced the first attack of a disease which pressed -heavily on him for the rest of his life. He enjoyed, when a young man, a -healthy and vigorous constitution, but chancing to sleep one afternoon -near an open window, through which was blowing a current of air cooled -artificially by the fall of water, the consequences were most disastrous -to him. He contracted a sort of chronic complaint, which showed itself -in acute pains in his limbs, chest, and back, accompanied with frequent -haemorrhages and loss of sleep and appetite; and this painful disorder -thenceforward never left him entirely, but recurred intermittingly, with -greater or less violence, as long as he lived. Others of the party did -not even escape so well, but died shortly after committing this -imprudence. - -In 1604, the attention of astronomers was called to the contemplation of -a new star, which appeared suddenly with great splendour in the -constellation Serpentarius, or Ophiuchus, as it is now more commonly -called. Maestlin, who was one of the earliest to notice it, relates his -observations in the following words: "How wonderful is this new star! I -am certain that I did not see it before the 29th of September, nor -indeed, on account of several cloudy nights, had I a good view till the -6th of October. Now that it is on the other side of the sun, instead of -surpassing Jupiter as it did, and almost rivalling Venus, it scarcely -matches the Cor Leonis, and hardly surpasses Saturn. It continues -however to shine with the same bright and strongly sparkling light, and -changes its colours almost with every moment; first tawny, then yellow, -presently purple and red, and, when it has risen above the vapours, most -frequently white." This was by no means an unprecedented phenomenon; and -the curious reader may find in Riccioli[27] a catalogue of the principal -new stars which have at different times appeared. There is a tradition -of a similar occurrence as early as the times of the Greek astronomer -Hipparchus, who is said to have been stimulated by it to the formation -of his catalogue of the stars; and only thirty-two years before, in -1572, the same remarkable phenomenon in the constellation Cassiopeia was -mainly instrumental in detaching the celebrated Tycho Brahe from the -chemical studies, which till then divided his attention with astronomy. -Tycho's star disappeared at the end of two years; and at that time -Galileo was a child. On the present occasion, he set himself earnestly -to consider the new phenomenon, and embodied the results of his -observations in three lectures, which have been unfortunately lost. Only -the exordium of the first has been preserved: in this he reproaches his -auditors with their general insensibility to the magnificent wonders of -creation daily exposed to their view, in no respect less admirable than -the new prodigy, to hear an explanation of which they had hurried in -crowds to his lecture room. He showed, from the absence of parallax, -that the new star could not be, as the vulgar hypothesis represented, a -mere meteor engendered in our atmosphere and nearer the earth than the -moon, but must be situated among the most remote heavenly bodies. This -was inconceivable to the Aristotelians, whose notions of a perfect, -simple, and unchangeable sky were quite at variance with the -introduction of any such new body; and we may perhaps consider these -lectures as the first public declaration of Galileo's hostility to the -old Ptolemaic and Aristotelian astronomy. - -In 1606 he was reappointed to the lectureship, and his salary a second -time increased, being raised to 520 florins. His public lectures were at -this period so much thronged that the ordinary place of meeting was -found insufficient to contain his auditors, and he was on several -occasions obliged to adjourn to the open air,--even from the school of -medicine, which was calculated to contain one thousand persons. - -About this time he was considerably annoyed by a young Milanese, of the -name of Balthasar Capra, who pirated an instrument which Galileo had -invented some years before, and had called the geometrical and military -compass. The original offender was a German named Simon Mayer, whom we -shall meet with afterwards arrogating to himself the merit of one of -Galileo's astronomical discoveries; but on this occasion, as soon as he -found Galileo disposed to resent the injury done to him, he hastily -quitted Italy, leaving his friend Capra to bear alone the shame of the -exposure which followed. The instrument is of simple construction, -consisting merely of two straight rulers, connected by a joint; so that -they can be set to any required angle. This simple and useful -instrument, now called the Sector, is to be found in almost every case -of mathematical instruments. Instead of the trigonometrical and -logarithmic lines which are now generally engraved upon it, Galileo's -compass merely contained, on one side, three pairs of lines, divided in -simple, duplicate, and triplicate proportion, with a fourth pair on -which were registered the specific gravities of several of the most -common metals. These were used for multiplications, divisions, and the -extraction of roots; for finding the dimensions of equally heavy balls -of different materials, &c. On the other side were lines contrived for -assisting to describe any required polygon on a given line; for finding -polygons of one kind equal in area to those of another; and a multitude -of other similar operations useful to the practical engineer. - -Unless the instrument, which is now called Gunter's scale, be much -altered from what it originally was, it is difficult to understand on -what grounds Salusbury charges Gunter with plagiarism from Galileo's -Compass. He declares that he has closely compared the two, and can find -no difference between them.[28] There has also been some confusion, by -several writers, between this instrument and what is now commonly called -the Proportional Compass. The latter consists of two slips of metal -pointed at each end, and connected by a pin which, sliding in a groove -through both, can be shifted to different positions. Its use is to find -proportional lines; for it is obvious that the openings measured by each -pair of legs will be in the same proportion in which the slips are -divided by the centre. The divisions usually marked on it are calculated -for finding the submultiples of straight lines, and the chords of -submultiple arcs. Montucla has mentioned this mistake of one instrument -for the other, and charges Voltaire with the more inexcusable error of -confounding Galileo's with the Mariner's Compass. He refers to a -treatise by Hulsius for his authority in attributing the Proportional -Compass to Burgi, a Swiss astronomer of some celebrity. Horcher also has -been styled the inventor; but he did no more than describe its form and -application. In the frontispiece of his book is an engraving of this -compass exactly similar to those which are now used.[29] To the -description which Galileo published of his compass, he added a short -treatise on the method of measuring heights and distances with the -quadrant and plumb line. The treatise, which is printed by itself at the -end of the first volume of the Padua edition of Galileo's works, -contains nothing more than the demonstrations belonging to the same -operations. They are quite elementary, and contain little or nothing -that was new even at that time. - -Such an instrument as Galileo's Compass was of much more importance -before the grand discovery of logarithms than it can now be considered: -however it acquires an additional interest from the value which he -himself set on it. In 1607, Capra, at the instigation of Mayer, -published as his own invention what he calls the proportional hoop, -which is a mere copy of Galileo's instrument. This produced from Galileo -a long essay, entitled "A Defence of Galileo against the Calumnies and -Impostures of Balthasar Capra." His principal complaint seems to have -been of the misrepresentations which Capra had published of his lectures -on the new star already mentioned, but he takes occasion, after pointing -out the blunders and falsehoods which Capra had committed on that -occasion, to add a complete proof of his piracy of the geometrical -compass. He showed, from the authenticated depositions of workmen, and -of those for whom the instruments had been fabricated, that he had -devised them as early as the year 1597, and had explained their -construction and use both to Balthasar himself and to his father Aurelio -Capra, who was then residing in Padua. He gives, in the same essay, the -minutes of a public meeting between himself and Capra, in which he -proved, to the satisfaction of the university, that wherever Capra had -endeavoured to introduce into his book propositions which were not to be -met with in Galileo's, he had fallen into the greatest absurdities, and -betrayed the most complete ignorance of his subject. The consequence of -this public exposure, and of the report of the famous Fra Paolo Sarpi, -to whom the matter had been referred, was a formal prohibition by the -university of Capra's publication, and all copies of the book then on -hand were seized, and probably destroyed, though Galileo has preserved -it from oblivion by incorporating it in his own publication. - -Nearly at the same time, 1607, or immediately after, he first turned his -attention towards the loadstone, on which our countryman Gilbert had -already published his researches, conducted in the true spirit of the -inductive method. Very little that is original is to be found in -Galileo's works on this subject, except some allusions to his method of -arming magnets, in which, as in most of his practical and mechanical -operations, he appears to have been singularly successful. Sir Kenelm -Digby[30] asserts, that the magnets armed by Galileo would support twice -as great a weight as one of Gilbert's of the same size. Galileo was well -acquainted, as appears from his frequent allusions in different parts of -his works, with what Gilbert had done, of whom he says, "I extremely -praise, admire, and envy this author;--I think him, moreover, worthy of -the greatest praise for the many new and true observations that he has -made to the disgrace of so many vain and fabling authors, who write, not -from their own knowledge only, but repeat every thing they hear from the -foolish vulgar, without attempting to satisfy themselves of the same by -experience, perhaps that they may not diminish the size of their books." - -Galileo's reputation being now greatly increased, proposals were made to -him, in 1609, to return to his original situation at Pisa. He had been -in the habit of passing over to Florence during the academic vacation, -for the purpose of giving mathematical instruction to the younger -members of Ferdinand's family; and Cosmo, who had now succeeded his -father as duke of Tuscany, regretted that so masterly a genius had been -allowed to leave the university which he naturally should have graced. A -few extracts from Galileo's answers to these overtures will serve to -show the nature of his situation at Padua, and the manner in which his -time was there occupied. "I will not hesitate to say, having now -laboured during twenty years, and those the best of my life, in dealing -out, as one may say, in detail, at the request of any body, the little -talent which God has granted to my assiduity in my profession, that my -wish certainly would be to have sufficient rest and leisure to enable -me, before my life comes to its close, to conclude three great works -which I have in hand, and to publish them; which might perhaps bring -some credit to me, and to those who had favoured me in this undertaking, -and possibly may be of greater and more frequent service to students -than in the rest of my life I could personally afford them. Greater -leisure than I have here I doubt if I could meet with elsewhere, so long -as I am compelled to support my family from my public and private -lectures, (nor would I willingly lecture in any other city than this, -for several reasons which would be long to mention) nevertheless not -even the liberty I have here is sufficient, where I am obliged to spend -many, and often the best hours of the day at the request of this and -that man.--My public salary here is 520 florins, which I am almost -certain will be advanced to as many crowns upon my re-election, and -these I can greatly increase by receiving pupils, and from private -lectures, to any extent that I please. My public duty does not confine -me during more than 60 half hours in the year, and even that not so -strictly but that I may, on occasion of any business, contrive to get -some vacant days; the rest of my time is absolutely at my own disposal; -but because my private lectures and domestic pupils are a great -hindrance and interruption of my studies, I wish to live entirely exempt -from the former, and in great measure from the latter: for if I am to -return to my native country, I should wish the first object of his -Serene Highness to be, that leisure and opportunity should be given me -to complete my works without employing myself in lecturing.--And, in -short, I should wish to gain my bread from my writings, which I would -always dedicate to my Serene Master.--The works which I have to finish -are principally--two books on the system or structure of the Universe, -an immense work, full of philosophy, astronomy, and geometry; three -books on Local Motion, a science entirely new, no one, either ancient or -modern, having discovered any of the very many admirable accidents which -I demonstrate in natural and violent motions, so that I may with very -great reason call it a new science, and invented by me from its very -first principles; three books of Mechanics, two on the demonstration of -principles and one of problems; and although others have treated this -same matter, yet all that has been hitherto written, neither in -quantity, nor otherwise, is the quarter of what I am writing on it. I -have also different treatises on natural subjects; On sound and speech; -On light and colours; On the tide; On the composition of continuous -quantity; On the motions of animals;--And others besides. I have also -an idea of writing some books relating to the military art, giving not -only a model of a soldier, but teaching with very exact rules every -thing which it is his duty to know that depends upon mathematics; as the -knowledge of castrametation, drawing up battalions, fortifications, -assaults, planning, surveying, the knowledge of artillery, the use of -instruments, &c. I also wish to reprint the 'Use of my Geometrical -Compass,' which is dedicated to his highness, and which is no longer to -be met with; for this instrument has experienced such favour from the -public, that in fact no other instruments of this kind are now made, and -I know that up to this time several thousands of mine have been made.--I -say nothing as to the amount of my salary, feeling convinced that as I -am to live upon it, the graciousness of his highness would not deprive -me of any of those comforts, which, however, I feel the want of less -than many others; and therefore I say nothing more on the subject. -Finally, on the title and profession of my service, I should wish that -to the name of Mathematician, his highness would add that of -Philosopher, as I profess to have studied a greater number of years in -philosophy than months in pure mathematics; and how I have profited by -it, and if I can or ought to deserve this title, I may let their -highnesses see as often as it shall please them to give me an -opportunity of discussing such subjects in their presence with those who -are most esteemed in this knowledge." It may perhaps be seen in the -expressions of this letter, that Galileo was not inclined to undervalue -his own merits, but the peculiar nature of the correspondence should be -taken into account, which might justify his indulging a little more than -usual in self-praise, and it would have been perhaps almost impossible -for him to have remained entirely blind to his vast superiority over his -contemporaries. - -Many of the treatises which Galileo here mentions, as well as another on -dialling, have been irrecoverably lost, through the superstitious -weakness of some of his relations, who after his death suffered the -family confessor to examine his papers, and to destroy whatever seemed -to him objectionable; a portion which, according to the notions then -prevalent, was like to comprise the most valuable part of the papers -submitted to this expurgation. It is also supposed that many were burnt -by his infatuated grandson Cosimo, who conceived he was thus offering a -proper and pious sacrifice before devoting himself to the life of a -missionary. A Treatise on Fortification, by Galileo, was found in 1793, -and is contained among the documents published by Venturi. Galileo does -not profess in it to give much original matter, but to lay before his -readers a compendium of the most approved principles then already known. -It has been supposed that Gustavus Adolphus of Sweden attended Galileo's -lectures on this subject, whilst in Italy; but the fact is not -satisfactorily ascertained. Galileo himself mentions a Prince Gustavus -of Sweden to whom he gave instruction in mathematics, but the dates -cannot well be made to agree. The question deserves notice only from its -having been made the subject of controversy. - -The loss of Galileo's Essay on Continuous Quantity is particularly to be -regretted, as it would be highly interesting to see how far he succeeded -in methodizing his thoughts on this important topic. It is to his pupil -Cavalieri (who refused to publish his book so long as he hoped to see -Galileo's printed) that we owe "The Method of Indivisibles," which is -universally recognized as one of the first germs of the powerful methods -of modern analysis. Throughout Galileo's works we find many indications -of his having thought much on the subject, but his remarks are vague, -and bear little, if at all, on the application of the method. To this -the chief part of Cavalieri's book is devoted, though he was not so -entirely regardless of the principles on which his method of measuring -spaces is founded, as he is sometimes represented. This method consisted -in considering lines as made up of an infinite number of points, -surfaces in like manner as composed of lines, and solids of surfaces; -but there is an observation at the beginning of the 7th book, which -shews clearly that Cavalieri had taken a much more profound view of the -subject than is implied in this superficial exposition, and had -approached very closely to the apparently more exact theories of his -successors. Anticipating the objections to his hypothesis, he argues, -that "there is no necessity to suppose the continuous quantities made up -of these indivisible parts, _but only that they will observe the same -ratios as those parts do_." It ought not to be omitted, that Kepler also -had given an impulse to Cavalieri in his "New method of Gauging," which -is the earliest work with which we are acquainted, where principles of -this sort are employed.[31] - - -FOOTNOTES: - -[26] Vitae Italorum Illustrium. - -[27] Almagestum Novum, vol. i. - -[28] Math. Coll. vol. ii. - -[29] Constructio Circini Proportionum. Moguntiae, 1605. - -[30] Treatise of the Nature of Bodies. London, 1665. - -[31] Nova Stereometria Doliorum--Lincii, 1615. - - - - -CHAPTER VI. - - _Invention of the telescope--Fracastoro--Porta--Reflecting - telescope--Roger Bacon--Digges--De - Dominis--Jansen--Lipperhey--Galileo constructs - telescopes--Microscopes--Re-elected Professor at Padua for life._ - - -THE year 1609 was signalized by Galileo's discovery of the telescope, -which, in the minds of many, is the principal, if not the sole invention -associated with his name. It cannot be denied that his fame, as the -founder of the school of experimental philosophy, has been in an -unmerited degree cast into the shade by the splendour of his -astronomical discoveries; yet Lagrange[32] surely errs in the opposite -extreme, when he almost denies that these form any real or solid part of -the glory of this great man; and Montucla[33] omits an important -ingredient in his merit, when he (in other respects very justly) -remarks, that it required far less genius to point a telescope towards -the heavens than to trace the unheeded, because daily recurring, -phenomena of motion up to its simple and primary laws. We are to -remember that in the days of Galileo a telescope could scarcely be -pointed to the heavens with impunity, and that a courageous mind was -required to contradict, and a strong one to bear down, a party, who, -when invited to look on any object in the heavens which Aristotle had -never suspected, immediately refused all credit to those senses, to -which, on other occasions, they so confidently appealed. It surely is a -real and solid part of Galileo's glory that he consumed his life in -laborious and indefatigable observations, and that he persevered in -announcing his discoveries undisgusted by the invectives, and undismayed -by the persecutions, to which they subjected him. Plagiarist! liar! -impostor! heretic! were among the expressions of malignant hatred -lavished upon him, and although he also was not without some violent and -foul-mouthed partisans, yet it must be told to his credit that he -himself seldom condescended to notice these torrents of abuse, otherwise -than by good-humoured retorts, and by prosecuting his observations with -renewed assiduity and zeal. - -The use of single lenses in aid of the sight had been long known. -Spectacles were in common use at the beginning of the fourteenth -century, and there are several hints, more or less obscure, in many -early writers, of the effects which might be expected from a combination -of glasses; but it does not appear with certainty that any of these -authors had attempted to reduce their ideas to practice. After the -discovery of the telescope, almost every country endeavoured to find in -the writings of its early philosophers traces of the knowledge of such -an instrument, but in general with success very inadequate to the zeal -of their national prepossessions. There are two authors especially to -whom the attention of Kepler and others was turned, immediately upon the -promulgation of the discovery, as containing the germ of it in their -works. These are Baptista Porta, and Gerolamo Fracastoro. We have -already had occasion to quote the Homocentrica of Fracastoro, who died -in 1553; the following expressions, though they seem to refer to actual -experiment, yet fall short of the meaning with which it has been -attempted to invest them. After explaining and commenting on some -phenomena of refraction through different media, to which he was led by -the necessity of reconciling his theory with the variable magnitudes of -the planets, he goes on to say--"For which reason, those things which -are seen at the bottom of water, appear greater than those which are at -the top; and if any one look through two eyeglasses, _one placed upon -the other_, he will see every thing much larger and nearer."[34] It -should seem that this passage (as Delambre has already remarked) rather -refers to the close application of one glass upon another, and it may -fairly be doubted whether anything analogous to the composition of the -telescope was in the writer's thoughts. Baptista Porta writes on the -same subject more fully;--"Concave lenses show distant objects most -clearly, convex those which are nearer, whence they may be used to -assist the sight. With a concave glass distant objects will be seen, -small, but distinct; with a convex one those near at hand, larger, but -confused; _if you know rightly how to combine one of each sort, you -will see both far and near objects larger and clearer_."[35] These words -show, if Porta really was then unacquainted with the telescope, how -close it is possible to pass by an invention without lighting on it, for -of precisely such a combination of a convex and concave lens, fitted to -the ends of an organ pipe by way of tube, did the whole of Galileo's -telescope consist. If Porta had stopped here he might more securely have -enjoyed the reputation of the invention, but he then professes to -describe the construction of his instrument, which has no relation -whatever to his previous remarks. "I shall now endeavour to show in what -manner we may contrive to recognize our friends at the distance of -several miles, and how those of weak sight may read the most minute -letters from a distance. It is an invention of great utility, and -grounded on optical principles, nor is it at all difficult of execution; -but it must be so divulged as not to be understood by the vulgar, and -yet be clear to the sharpsighted." The description which follows seems -far enough removed from the apprehended danger of being too clear, and -indeed every writer who has hitherto quoted it has merely given the -passage in its original Latin, apparently despairing of an intelligible -translation. With some alterations in the punctuation, which appear -necessary to bring it into any grammatical construction,[36] it may be -supposed to bear something like the following meaning:--"Let a view be -contrived in the centre of a mirror, where it is most effective. All the -solar rays are exceedingly dispersed, and do not in the least come -together (in the true centre); but there is a concourse of all the rays -in the central part of the said mirror, half way towards the other -centre, where the cross diameters meet. This view is contrived in the -following manner. A concave cylindrical mirror placed directly in front, -but with its axis inclined, must be adapted to that focus: and let -obtuse angled or right angled triangles be cut out with two cross lines -on each side drawn from the centre, and a glass (_specillum_) will be -completed fit for the purposes we mentioned." If it were not for the -word "_specillum_," which, in the passage immediately preceding this, -Porta[37] contrasts with "_speculum_," and which he afterwards explains -to mean a glass lens, it would be very clear that the foregoing passage -(supposing it to have any meaning) must be referred to a reflecting -telescope, and it is a little singular that while this obscure passage -has attracted universal attention, no one, so far as we are aware, has -taken any notice of the following unequivocal description of the -principal part of Newton's construction of the same instrument. It is in -the 5th chapter of the 17th book, where Porta explains by what device -exceedingly minute letters may be read without difficulty. "Place a -concave mirror so that the back of it may lie against your breast; -opposite to it, and within the burning point, place the writing; put a -plane mirror behind it, that may be under your eyes. Then the images of -the letters which are in the concave mirror, and which the concave has -magnified, will be reflected in the plane mirror, so that you may read -without difficulty." - -We have not been able to meet with the Italian translation of Porta's -Natural Magic, which was published in 1611, under his own -superintendence; but the English translator of 1658 would probably have -known if any intelligible interpretation were there given of the -mysterious passage above quoted, and his translation is so devoid of -meaning as strongly to militate against this idea. Porta, indeed, -claimed the invention as his own, and is believed to have hastened his -death, (which happened in 1615, he being then 80 years old,) by the -fatigue of composing a Treatise on the Telescope, in which he had -promised to exhaust the subject. We do not know whether this is the same -work which was published after his death by Stelliola,[38] but which -contains no allusion to Porta's claim, and possibly Stelliola may have -thought it most for his friend's reputation to suppress it. Schott[39] -says, a friend of his had seen Porta's book in manuscript, and that it -did at that time contain the assertion of Porta's title to the -invention. After all it is not improbable that he may have derived his -notions of magnifying distant objects from our celebrated countryman -Roger Bacon, who died about the year 1300. He has been supposed, not -without good grounds, to have been one of the first who recognised the -use of single lenses in producing distinct vision, and he has some -expressions with respect to their combination which promise effects -analogous to those held out by Porta. In "The Admirable Force of Art and -Nature," he says, "Physical figurations are far more strange, for in -such manner may we frame perspects and looking-glasses that one thing -shall appear to be many, as one man shall seeme a whole armie; and -divers sunnes and moones, yea, as many as we please, shall appeare at -one time, &c. And so may the perspects be framed, that things most farre -off may seeme most nigh unto us, and clean contrarie, soe that we may -reade very small letters an incredible distance from us, and behold -things how little soever they be, and make stars to appeare wheresoever -we will, &c. And, besides all these, we may so frame perspects that any -man entering into a house he shall indeed see gold, and silver, and -precious stones, and what else he will, but when he maketh haste to the -place he shall find just nothing." It seems plain, that the author is -here speaking solely of mirrors, and we must not too hastily draw the -conclusion, because in the first and last of these assertions he is, to -a certain extent, borne out by facts, that he therefore was in -possession of a method of accomplishing the middle problem also. In the -previous chapter, he gives a long list of notable things, (much in the -style of the Marquis of Worcester's Century of Inventions) which if we -can really persuade ourselves that he was capable of accomplishing, we -must allow the present age to be still immeasurably inferior to him in -science. - -Thomas Digges, in the preface to his Pantometria, (published in 1591) -declares, "My father, by his continuall painfull practises, assisted -with demonstrations mathematicall, was able, and sundry times hath by -proportionall glasses, duely situate in convenient angles, not only -discouered things farre off, read letters, numbered peeces of money, -with the verye coyne and superscription thereof, cast by some of his -freends of purpose, upon downes in open fields; but also, seuen miles -off, declared what hath beene doone at that instant in priuate places. -He hath also sundrie times, by the sunne beames, fired powder and -dischargde ordnance halfe a mile and more distante; which things I am -the boulder to report, for that there are yet living diverse (of these -his dooings) occulati testes, (eye witnesses) and many other matters -farre more strange and rare, which I omit as impertinent to this place." - -We find another pretender to the honour of the discovery of the -telescope in the celebrated Antonio de Dominis, Archbishop of Spalatro, -famous in the annals of optics for being one of the first to explain the -theory of the rainbow. Montucla, following P. Boscovich, has scarcely -done justice to De Dominis, whom he treats as a mere pretender and -ignorant person. The indisposition of Boscovich towards him is -sufficiently accounted for by the circumstance of his being a Catholic -prelate who had embraced the cause of Protestantism. His nominal -reconciliation with the Church of Rome would probably not have saved him -from the stake, had not a natural death released him when imprisoned on -that account at Rome. Judgment was pronounced upon him notwithstanding, -and his body and books were publicly burnt in the Campo de Fiori, in -1624. His treatise, De Radiis, (which is very rarely to be met with) was -published by Bartolo after the acknowledged invention of the telescope -by Galileo; but Bartolo tells us, in the preface, that the manuscript -was communicated to him from a collection of papers written 20 years -before, on his inquiring the Archbishop's opinion with respect to the -newly discovered instrument, and that he got leave to publish it, "with -the addition of one or two chapters." The treatise contains a complete -description of a telescope, which, however, is professed merely to be an -improvement on spectacles, and if the author's intention had been to -interpolate an afterwritten account, in order to secure to himself the -undeserved honour of the invention, it seems improbable that he would -have suffered an acknowledgment of additions, previous to publication, -to be inserted in the preface. Besides, the whole tone of the work is -that of a candid and truth-seeking philosopher, very far indeed removed -from being, as Montucla calls him, conspicuous for ignorance even among -the ignorant men of his age. He gives a drawing of a convex and concave -lens, and traces the passage of the rays through them; to which he -subjoins, that he has not satisfied himself with any determination of -the precise distance to which the glasses should be separated, according -to their convexity and concavity, but recommends the proper distance to -be found by actual experiment, and tells us, that the effect of the -instrument will be to prevent the confusion arising from the -interference of the direct and refracted rays, and to magnify the object -by increasing the visible angle under which it is viewed. These, among -the many claimants, are certainly the authors who approached the most -nearly to the discovery: and the reader may judge, from the passages -cited, whether the knowledge of the telescope can with probability be -referred to a period earlier than the commencement of the 17th century. -At all events, we can find no earlier trace of its being applied to any -practical use; the knowledge, if it existed, remained speculative and -barren. - -In 1609, Galileo, then being on a visit to a friend at Venice, heard a -rumour of the recent invention, by a Dutch spectacle-maker, of an -instrument which was said to represent distant objects nearer than they -usually appeared. According to his own account, this general rumour, -which was confirmed to him by letters from Paris, was all that he -learned on the subject; and returning to Padua, he immediately applied -himself to consider the means by which such an effect could be produced. -Fuccarius, in an abusive letter which he wrote on the subject, asserts -that one of the Dutch telescopes had been at that time actually brought -to Venice, and that he (Fuccarius) had seen it; which, even if true, is -perfectly consistent with Galileo's statement; and in fact the question, -whether or not Galileo saw the original instrument, becomes important -only from his expressly asserting the contrary, and professing to give -the train of reasoning by which he discovered its principle; so that any -insinuation that he had actually seen the Dutch glass, becomes a direct -impeachment of his veracity. It is certain, from the following extract -of a letter from Lorenzo Pignoria to Paolo Gualdo, that one at least of -the Dutch glasses had been sent to Italy. It is dated Padua, 31st -August, 1609.[40] "We have no news, except the return of His Serene -Highness, and the re-election of the lecturers, among whom Sign. Galileo -has contrived to get 1000 florins for life; and it is said to be on -account of an eyeglass, _like the one which was sent from Flanders to -Cardinal Borghese_. We have seen some here, and truly they succeed -well." - -It is allowed by every one that the Dutchman, or rather Zealander, made -his discovery by mere accident, which greatly derogates from any honour -attached to it; but even this diminished degree of credit has been -fiercely disputed. According to one account, which appears consistent -and probable, it had been made for sometime before its importance was in -the slightest degree understood or appreciated, but was set up in the -optician's shop as a curious philosophical toy, showing a large and -inverted image of a weathercock, towards which it was directed. The -Marquis Spinola, chancing to see it, was struck with the phenomenon, -purchased the instrument, and presented it either to the Archduke Albert -of Austria, or to Prince Maurice of Nassau, whose name appears in every -version of the story, and who first entertained the idea of employing it -in military reconnoissances. - -Zacharias Jansen, and Henry Lipperhey, two spectacle-makers, living -close to each other, near the church of Middleburg, have both had -strenuous supporters of their title to the invention. A third pretender -appeared afterwards in the person of James Metius of Alkmaer, who is -mentioned by Huyghens and Des Cartes, but his claims rest upon no -authority whatever comparable to that which supports the other two. -About half a century afterwards, Borelli was at the pains to collect and -publish a number of letters and depositions which he procured, as well -on one side as on the other.[41] It seems that the truth lies between -them, and that one, probably Jansen, was the inventor of the -_microscope_, which application of the principle was unquestionably of -an earlier date, perhaps as far back as 1590. Jansen gave one of his -microscopes to the Archduke, who gave it to Cornelius Drebbel, a -salaried mathematician at the court of our James the first, where -William Borelli (not the author above mentioned) saw it many years -afterwards, when ambassador from the United Provinces to England, and -got from Drebbel this account of the quarter whence it came. Lipperhey -afterwards, in 1609, accidentally hit upon the _telescope_, and on the -fame of this discovery it would not be difficult for Jansen, already in -possession of an instrument so much resembling it, to perceive the -slight difference between them, and to construct a telescope -independently of Lipperhey, so that each, with some show of reason, -might claim the priority of the invention. A notion of this kind -reconciles the testimony of many conflicting witnesses on the subject, -some of whom do not seem to distinguish very accurately whether the -telescope or microscope is the instrument to which their evidence -refers. Borelli arrives at the conclusion, that Jansen was the inventor; -but not satisfied with this, he endeavours, with a glaring partiality -which makes his former determination suspicious, to secure for him and -his son the more solid reputation of having anticipated Galileo in the -useful employment of the invention. He has however inserted in his -collections a letter from John the son of Zacharias, in which John, -omitting all mention of his father, speaks of his own observation of the -satellites of Jupiter, evidently seeking to insinuate that they were -earlier than Galileo's; and in this sense the letter has since been -quoted,[42] although it appears from John's own deposition, preserved in -the same collection, that at the time of their discovery he could not -have been more than six years old. An oversight of this sort throws -doubt on the whole of the pretended observations, and indeed the letter -has much the air of being the production of a person imperfectly -informed on the subject on which he writes, and probably was compiled to -suit Borelli's purposes, which were to make Galileo's share in the -invention appear as small as possible. - -Galileo himself gives a very intelligible account of the process of -reasoning, by which he detected the secret.--"I argued in the following -manner. The contrivance consists either of one glass or of more--one is -not sufficient, since it must be either convex, concave, or plane; the -last does not produce any sensible alteration in objects, the concave -diminishes them: it is true that the convex magnifies, but it renders -them confused and indistinct; consequently, one glass is insufficient to -produce the desired effect. Proceeding to consider two glasses, and -bearing in mind that the plane glass causes no change, I determined that -the instrument could not consist of the combination of a plane glass -with either of the other two. I therefore applied myself to make -experiments on combinations of the two other kinds, and thus obtained -that of which I was in search." It has been urged against Galileo that, -if he really invented the telescope on theoretical principles, the same -theory ought at once to have conducted him to a more perfect instrument -than that which he at first constructed;[43] but it is plain, from this -statement, that he does not profess to have theorized beyond the -determination of the species of glass which he should employ in his -experiments, and the rest of his operations he avows to have been purely -empirical. Besides, we must take into account the difficulty of grinding -the glasses, particularly when fit tools were yet to be made, and -something must be attributed to Galileo's eagerness to bring his results -to the test of actual experiment, without waiting for that improvement -which a longer delay might and did suggest. Galileo's language bears a -resemblance to the first passage which we quoted from Baptista Porta, -sufficiently close to make it not improbable that he might be assisted -in his inquiries by some recollection of it, and the same passage seems, -in like manner, to have recurred to the mind of Kepler, as soon as he -heard of the invention. Galileo's telescope consisted of a plano-convex -and plano-concave lens, the latter nearest the eye, distant from each -other by the difference of their focal lengths, being, in principle, -exactly the same with the modern opera-glass. He seems to have thought -that the Dutch glass was the same, but this could not be the case, if -the above quoted particular of the _inverted_ weathercock, which belongs -to most traditions of the story, be correct; because it is the -peculiarity of this kind of telescope not to invert objects, and we -should be thus furnished with a demonstrative proof of the falsehood of -Fuccarius's insinuation: in that case the Dutch glass must have been -similar to what was afterwards called the astronomical telescope, -consisting of two convex glasses distant from each other by the sum of -their focal lengths. This supposition is not controverted by the fact, -that this sort of telescope was never employed by astronomers till long -afterwards; for the fame of Galileo's observations, and the superior -excellence of the instruments constructed under his superintendence, -induced every one in the first instance to imitate his constructions as -closely as possible. The astronomical telescope was however eventually -found to possess superior advantages over that which Galileo imagined, -and it is on this latter principle that all modern refracting telescopes -are constructed; the inversion being counteracted in those which are -intended for terrestrial observations, by the introduction of a second -pair of similar glasses, which restore the inverted image to its -original position. For further details on the improvements which have -been subsequently introduced, and on the reflecting telescope, which was -not brought into use till the latter part of the century, the reader is -referred to the Treatise on OPTICAL INSTRUMENTS. - -Galileo, about the same time, constructed microscopes on the same -principle, for we find that, in 1612, he presented one to Sigismund, -King of Poland; but his attention being principally devoted to the -employment and perfection of his telescope, the microscope remained a -long time imperfect in his hands: twelve years later, in 1624, he wrote -to P. Federigo Cesi, that he had delayed to send the microscope, the use -of which he there describes, because he had only just brought it to -perfection, having experienced some difficulty in working the glasses. -Schott tells an amusing story, in his "Magic of Nature," of a Bavarian -philosopher, who, travelling in the Tyrol with one of the newly invented -microscopes about him, was taken ill on the road and died. The -authorities of the village took possession of his baggage, and were -proceeding to perform the last duties to his body, when, on examining -the little glass instrument in his pocket, which chanced to contain a -flea, they were struck with the greatest astonishment and terror, and -the poor Bavarian, condemned by acclamation as a sorcerer who was in the -habit of using a portable familiar, was declared unworthy of Christian -burial. Fortunately for his character, some bold sceptic ventured to -open the instrument, and discovered the true nature of the imprisoned -fiend. - -As soon as Galileo's first telescope was completed, he returned with it -to Venice, and the extraordinary sensation which it excited tends also -strongly to refute Fuccarius's assertion that the Dutch glass was -already known there. During more than a month Galileo's whole time was -employed in exhibiting his instrument to the principal inhabitants of -Venice, who thronged to his house to satisfy themselves of the truth of -the wonderful stories in circulation; and at the end of that time the -Doge, Leonardo Donati, caused it to be intimated to him that such a -present would not be deemed unacceptable by the senate. Galileo took the -hint, and his complaisance was rewarded by a mandate confirming him for -life in his professorship at Padua, at the same time doubling his yearly -salary, which was thus made to amount to 1000 florins. - -It was long before the phrenzy of public curiosity abated. Sirturi -describes a ludicrous violence which was done to himself, when, with the -first telescope which he had succeeded in making, he went up into the -tower of St. Mark, at Venice, in the vain hope of being there entirely -unmolested. Unluckily he was seen by some idlers in the street: a crowd -soon collected round him, who insisted on taking possession of his -instrument, and, handing it one to the other, detained him there for -several hours till their curiosity was satiated, when he was allowed to -return home. Hearing them also inquire eagerly at what inn he lodged, he -thought it better to quit Venice early the next morning, and prosecute -his observations in a less inquisitive neighbourhood.[44] Instruments of -an inferior description were soon manufactured, and vended every where -as philosophical playthings, much in the way in which, in our own time, -the kaleidoscope spread over Europe as fast as travellers could carry -them. But the fabrication of a better sort was long confined, almost -solely, to Galileo and those whom he immediately instructed; and so late -as the year 1637, we find Gaertner, or as he chose to call himself, -Hortensius, assuring Galileo that none could be met with in Holland -sufficiently good to show Jupiter's disc well defined; and in 1634 -Gassendi begs for a telescope from Galileo, informing him that he was -unable to procure a good one either in Venice, Paris, or Amsterdam. - -The instrument, on its first invention, was generally known by the names -of Galileo's tube, the perspective, the double eye-glass: the names of -telescope and microscope were suggested by Demisiano, as we are told by -Lagalla in his treatise on the Moon.[45] - - -FOOTNOTES: - -[32] Mecanique Analytique. - -[33] Histoire des Mathematiques, tom. ii. - -[34] "Per duo specilla ocularia si quis perspiciat, altero alteri -superposito, majora multo et propinquiora videbit omnia."--Fracast. -Homocentrica, Sec. 2, c. 8. - -[35] Si utrumque recte componere noveris, et longinqua et proxima majora -et clara videbis.--Mag. Nat. lib. 17. - -[36] The passage in the original, which is printed alike in the editions -of 1598, 1607, 1619, and 1650, is as follows: Visus constituatur centro -valentissimus speculi, ubi fiet, et valentissime universales solares -radii disperguntur, et coeunt minime, sed centro praedicti speculi in -illius medio, ubi diametri transversales, omnium ibi concursus. -Constituitur hoc modo speculum concavum columnare aequidistantibus -lateribus, sed lateri uno obliquo sectionibus illis accomodetur, -trianguli vero obtusianguli, vel orthogonii secentur, hinc inde duobus -transversalibus lineis, ex-centro eductis. Et confectum erit specillum, -ad id, quod diximus utile. - -[37] Diximus de Ptolemaei _speculo_, sive _specillo_ potius, quo per -sexcentena millia pervenientes naves conspiciebat. - -[38] Il Telescopio, 1627. - -[39] Magia Naturae et Artis Herbipoli, 1657. - -[40] Lettere d'Uomini illustri. Venezia, 1744. - -[41] Borelli. De vero Telescopii inventore, 1655. - -[42] Encyclopaedia Britannica. Art. TELESCOPE. - -[43] Ibid. - -[44] Telescopium, Venetiis, 1619. - -[45] De phaenomenis in orbe Lunae. Venetiis, 1612. - - - - -CHAPTER VII. - - _Discovery of Jupiter's - satellites--Kepler--Sizzi--Astrologers--Maestlin--Horky--Mayer._ - - -AS soon as Galileo had provided himself with a second instrument, he -began a careful examination of the heavenly bodies, and a series of -splendid discoveries soon rewarded his diligence. After considering the -beautiful appearances which the varied surface of the moon presented to -this new instrument, he turned his telescope towards Jupiter, and his -attention was soon arrested by the singular position of three small -stars, near the body of that planet, which appeared almost in a straight -line with it, and in the direction of the ecliptic. The following -evening he was surprised to find that two of the three which had been to -the eastward of the planet, now appeared on the contrary side, which he -could not reconcile with the apparent motion of Jupiter among the fixed -stars, as given by the tables. Observing these night after night, he -could not fail to remark that they changed their relative positions. A -fourth also appeared, and in a short time he could no longer refuse to -believe that these small stars were four moons, revolving round Jupiter -in the same manner in which our earth is accompanied by its single -attendant. In honour of his patron Cosmo, he named them the Medicaean -stars. As they are now hardly known by this appellation, his doubts, -whether he should call them Medicaean, after Cosmo's family, or Cosmical, -from his individual name, are become of less interest. - -An extract from a letter which Galileo received on this occasion from -the court of France, will serve to show how highly the honour of giving -a name to these new planets was at that time appreciated, and also how -much was expected from Galileo's first success in examining the heavens. -"The second request, but the most pressing one which I can make to you, -is, that you should determine, if you discover any other fine star, to -call it by the name of the great star of France, as well as the most -brilliant of all the earth; and, if it seems fit to you, call it rather -by his proper name of Henri, than by the family name of Bourbon: thus -you will have an opportunity of doing a thing just and due and proper in -itself, and at the same time will render yourself and your family rich -and powerful for ever." The writer then proceeds to enumerate the -different claims of Henri IV. to this honour, not forgetting that he -married into the family of the Medici, &c. - -The result of these observations was given to the world, in an Essay -which Galileo entitled _Nuncius Sidereus_, or the Intelligencer of the -Stars; and it is difficult to describe the extraordinary sensation which -its publication produced. Many doubted, many positively refused to -believe, so novel an announcement; all were struck with the greatest -astonishment, according to their respective opinions, either at the new -view of the universe thus offered to them, or at the daring audacity of -Galileo in inventing such fables. We shall proceed to extract a few -passages from contemporary writers relative to this book, and the -discoveries announced in it. - -Kepler deserves precedence, both from his own celebrity, and from the -lively and characteristic account which he gives of his first receiving -the intelligence:--"I was sitting idle at home, thinking of you, most -excellent Galileo, and your letters, when the news was brought me of the -discovery of four planets by the help of the double eye-glass. -Wachenfels stopped his carriage at my door to tell me, when such a fit -of wonder seized me at a report which seemed so very absurd, and I was -thrown into such agitation at seeing an old dispute between us decided -in this way, that between his joy, my colouring, and the laughter of -both, confounded as we were by such a novelty, we were hardly capable, -he of speaking, or I of listening. My amazement was increased by the -assertion of Wachenfels, that those who sent this news from Galileo were -celebrated men, far removed by their learning, weight, and character, -above vulgar folly; that the book was actually in the press, and would -be published immediately. On our separating, the authority of Galileo -had the greatest influence on me, earned by the accuracy of his -judgment, and excellence of his understanding; so I immediately fell to -thinking how there could be any addition to the number of the planets -without overturning my Mysterium Cosmographicum, published thirteen -years ago, according to which Euclid's five regular solids do not allow -more than six planets round the sun." - -This was one of the many wild notions of Kepler's fanciful brain, among -which he was lucky enough at length to hit upon the real and principal -laws of the planetary motions. His theory may be briefly given in his -own words:--"The orbit of the earth is the measure of the rest. About it -circumscribe a dodecahedron. The sphere including this will be that of -Mars. About Mars' orbit describe a tetrahedron: the sphere containing -this will be Jupiter's orbit. Round Jupiter's describe a cube: the -sphere including this will be Saturn's. Within the earth's orbit -inscribe an icosahedron: the sphere inscribed in it will be Venus's -orbit. In Venus inscribe an octahedron: the sphere inscribed in it will -be Mercury's. You have now the reason of the number of the planets:" for -as there are no more than the five regular solids here enumerated, -Kepler conceived this to be a satisfactory reason why there could be -neither more nor less than six planets. His letter continues:--"I am so -far from disbelieving the existence of the four circumjovial planets, -that I long for a telescope to anticipate you, if possible, in -discovering two round Mars, (as the proportion seems to me to require,) -six or eight round Saturn, and perhaps one each round Mercury and -Venus." - -The reader has here an opportunity of verifying Galileo's observation, -that Kepler's method of philosophizing differed widely from his own. The -proper line is certainly difficult to hit between the mere theorist and -the mere observer. It is not difficult at once to condemn the former, -and yet the latter will deprive himself of an important, and often -indispensable assistance, if he neglect from time to time to consolidate -his observations, and thence to conjecture the course of future -observation most likely to reward his assiduity. This cannot be more -forcibly expressed than in the words of Leonardo da Vinci:[46] "Theory -is the general, experiments are the soldiers. The interpreter of the -works of nature is experiment; that is never wrong; it is our judgment -which is sometimes deceived, because we are expecting results which -experiment refuses to give. We must consult experiment, and vary the -circumstances, till we have deduced general rules, for it alone can -furnish us with them. But you will ask, what is the use of these general -rules? I answer, that they direct us in our inquiries into nature and -the operations of art. They keep us from deceiving ourselves and others, -by promising ourselves results which we can never obtain." - -In the instance before us, it is well known that, adopting some of the -opinions of Bruno and Brutti, Galileo, even before he had seen the -satellites of Jupiter, had allowed the possibility of the discovery of -new planets; and we can scarcely suppose that they had weakened his -belief in the probability of further success, or discouraged him from -examining the other heavenly bodies. Kepler on the contrary had taken -the opposite side of the argument; but no sooner was the fallacy of his -first position undeniably demonstrated, than, passing at once from one -extreme to the other, he framed an unsupported theory to account for the -number of satellites which were round Jupiter, and for those which he -expected to meet with elsewhere. Kepler has been styled the legislator -of the skies; his laws were promulgated rather too arbitrarily, and they -often failed, as all laws must do which are not drawn from a careful -observation of the nature of those who are to be governed by them. -Astronomers have reason to be grateful for the theorems which he was the -first to establish; but so far as regards the progress of the science of -inductive reasoning, it is perhaps to be regretted, that the seventeen -years which he wasted in random and unconnected guesses should have been -finally rewarded, by discoveries splendid enough to shed deceitful -lustre upon the method by which he arrived at them. - -Galileo himself clearly perceived the fallacious nature of these -speculations on numbers and proportions, and has expressed his -sentiments concerning them very unequivocally. "How great and common an -error appears to me the mistake of those who persist in making their -knowledge and apprehension the measure of the apprehension and knowledge -of God; as if that alone were perfect, which they understand to be so. -But I, on the contrary, observe that Nature has other scales of -perfection, which we cannot comprehend, and rather seem disposed to -class among imperfections. For instance, among the relations of -different numbers, those appear to us most perfect which exist between -numbers nearly related to each other; as the double, the triple, the -proportion of three to two, &c.; those appear less perfect which exist -between numbers remote from, and prime to each other; as 11 to 7, 17 to -13, 53 to 37, &c.; and most imperfect of all do those appear which exist -between incommensurable quantities, which by us are nameless and -inexplicable. Consequently, if the task had been given to a man, of -establishing and ordering the rapid motions of the heavenly bodies, -according to his notions of perfect proportions, I doubt not that he -would have arranged them according to the former rational proportions; -but, on the contrary, God, with no regard to our imaginary symmetries, -has ordered them in proportions not only incommeasurable and irrational, -but altogether inappreciable by our intellect. A man ignorant of -geometry may perhaps lament, that the circumference of a circle does not -happen to be exactly three times the diameter, or in some other -assignable proportion to it, rather than such that we have not yet been -able to explain what the ratio between them is; but one who has more -understanding will know that if they were other than they are, thousands -of admirable conclusions would have been lost, and that none of the -other properties of the circle would have been true: the surface of the -sphere would not be quadruple of a great circle, nor the cylinder be to -the sphere as three to two: in short, no part of geometry would be true, -and as it now is. If one of our most celebrated architects had had to -distribute this vast multitude of fixed stars through the great vault of -heaven, I believe he would have disposed them with beautiful -arrangements of squares, hexagons, and octagons; he would have dispersed -the larger ones among the middle sized and the less, so as to correspond -exactly with each other; and then he would think he had contrived -admirable proportions: but God, on the contrary, has shaken them out -from His hand as if by chance, and we, forsooth, must think that He has -scattered them up yonder without any regularity, symmetry, and -elegance." - -It is worth remarking that the dangerous ideas of aptitude and -congruence of numbers had taken such deep and general root, that long -afterwards, when the reality of Jupiter's satellites was incontestably -established, and Huyghens had discovered a similar satellite near -Saturn, he was so rash as to declare his belief, (unwarned by the vast -progress which astronomy had made in his own time,) that no more -satellites would be discovered, since the one which he discovered near -Saturn, with Jupiter's four, and our moon, made up the number six, -exactly equal to the number of the principal planets. Every reader knows -that this notion, so unworthy the genius of Huyghens, has been since -exploded by the discovery both of new planets, and new satellites. - -Francesco Sizzi, a Florentine astronomer, took the matter up in a -somewhat different strain from Kepler.[47]--"There are seven windows -given to animals in the domicile of the head, through which the air is -admitted to the rest of the tabernacle of the body, to enlighten, to -warm, and nourish it, which are the principal parts of the [mikrokosmos] -(or little world); two nostrils, two eyes, two ears, and a mouth; so in -the heavens, as in a [makrokosmos] (or great world), there are two -favourable stars, two unpropitious, two luminaries, and Mercury alone -undecided and indifferent. From which and many other similar phenomena -of nature, such as the seven metals, &c., which it were tedious to -enumerate, we gather that the number of planets is necessarily seven. -Moreover, the satellites are invisible to the naked eye, and therefore -can exercise no influence on the earth, and therefore would be useless, -and therefore do not exist. Besides, as well the Jews and other ancient -nations as modern Europeans have adopted the division of the week into -seven days, and have named them from the seven planets: now if we -increase the number of the planets this whole system falls to the -ground." To these remarks Galileo calmly replied, that whatever their -force might be, as a reason for believing beforehand that no more than -seven planets would be discovered, they hardly seemed of sufficient -weight to destroy the new ones when actually seen. - -Others, again, took a more dogged line of opposition, without venturing -into the subtle analogies and arguments of the philosopher just cited. -They contented themselves, and satisfied others, with the simple -assertion, that such things were not, and could not be, and the manner -in which they maintained themselves in their incredulity was -sufficiently ludicrous. "Oh, my dear Kepler,"[48] says Galileo, "how I -wish that we could have one hearty laugh together. Here, at Padua, is -the principal professor of philosophy, whom I have repeatedly and -urgently requested to look at the moon and planets through my glass, -which he pertinaciously refuses to do. Why are you not here? what shouts -of laughter we should have at this glorious folly! and to hear the -professor of philosophy at Pisa labouring before the grand duke with -logical arguments, as if with magical incantations, to charm the new -planets out of the sky." - -Another opponent of Galileo deserves to be named, were it only for the -singular impudence of the charge he ventures to bring against him. "We -are not to think," says Christmann, in the Appendix to his _Nodus -Gordius_, "that Jupiter has four satellites given him by nature, in -order, by revolving round him, to immortalize the name of the Medici, -who first had notice of the observation. These are the dreams of _idle -men_, who love ludicrous ideas better than our laborious and industrious -correction of the heavens.--Nature abhors so horrible a chaos, and to -the truly wise such vanity is detestable." - -Galileo was also urged by the astrologers to attribute some influence, -according to their fantastic notions, to the satellites, and the account -which he gives his friend Dini of his answer to one of this class is -well worth extracting, as a specimen of his method of uniting sarcasm -with serious expostulation; "I must," says he, "tell you what I said a -few days back to one of those nativity-casters, who believe that God, -when he created the heavens and the stars, had no thoughts beyond what -they can themselves conceive, in order to free myself from his tedious -importunity; for he protested, that unless I would declare to him the -effect of the Medicaean planets, he would reject and deny them as -needless and superfluous. I believe this set of men to be of Sizzi's -opinion, that astronomers discovered the other seven planets, not by -seeing them corporally in the skies, but only from their effects on -earth,--much in the manner in which some houses are discovered to be -haunted by evil spirits, not by seeing them, but from the extravagant -pranks which are played there. I replied, that he ought to reconsider -the hundred or thousand opinions which, in the course of his life, he -might have given, and particularly to examine well the events which he -had predicted with the help of Jupiter, and if he should find that all -had succeeded conformably to his predictions, I bid him prophecy merrily -on, according to his old and wonted rules; for I assured him that the -new planets would not in any degree affect the things which are already -past, and that in future he would not be a less fortunate conjuror than -he had been: but if, on the contrary, he should find the events -depending on Jupiter, in some trifling particulars not to have agreed -with his dogmas and prognosticating aphorisms, he ought to set to work -to find new tables for calculating the constitution of the four Jovial -circulators at every bygone moment, and, perhaps, from the diversity of -their aspects, he would be able, with accurate observations and -multiplied conjunctions, to discover the alterations and variety of -influences depending upon them; and I reminded him, that in ages past -they had not acquired knowledge with little labour, at the expense of -others, from written books, but that the first inventors acquired the -most excellent knowledge of things natural and divine with study and -contemplation of the vast book which nature holds ever open before those -who have eyes in their forehead and in their brain; and that it was a -more honourable and praiseworthy enterprize with their own watching, -toil, and study, to discover something admirable and new among the -infinite number which yet remain concealed in the darkest depths of -philosophy, than to pass a listless and lazy existence, labouring only -to darken the toilsome inventions of their neighbours, in order to -excuse their own cowardice and inaptitude for reasoning, while they cry -out that nothing can be added to the discoveries already made." - -The extract given above from Kepler, is taken from an Essay, published -with the later editions of the _Nuncius_, the object and spirit of which -seem to have been greatly misunderstood, even by some of Kepler's -intimate friends.--They considered it as a covert attack upon Galileo, -and, accordingly, Maestlin thus writes to him:--"In your Essay (which I -have just received) you have plucked Galileo's feathers well; I mean, -that you have shown him not to be the inventor of the telescope, not to -have been the first who observed the irregularities of the moon's -surface, not to have been the first discoverer of more worlds than the -ancients were acquainted with, &c. One source of exultation was still -left him, from the apprehension of which Martin Horky has now entirely -delivered me." It is difficult to discover in what part of Kepler's book -Maestlin found all this, for it is one continued encomium upon Galileo; -insomuch that Kepler almost apologizes in the preface for what may seem -his intemperate admiration of his friend. "Some might wish I had spoken -in more moderate terms in praise of Galileo, in consideration of the -distinguished men who are opposed to his opinions, but I have written -nothing fulsome or insincere. I praise him, for myself; I leave other -men's judgments free; and shall be ready to join in condemnation when -some one wiser than myself shall, by sound reasoning, point out his -errors." However, Maestlin was not the only one who misunderstood -Kepler's intentions: the Martin Horky of whom he speaks, a young German, -also signalized himself by a vain attack upon the book which he thought -his patron Kepler condemned. He was then travelling in Italy, whence he -wrote to Kepler his first undetermined thoughts about the new -discoveries. "They are wonderful; they are stupendous; whether they are -true or false I cannot tell."[49] He seems soon to have decided that -most reputation was to be gained on the side of Galileo's opponents, and -his letters accordingly became filled with the most rancorous abuse of -him. At the same time, that the reader may appreciate Horky's own -character, we shall quote a short sentence at the end of one of his -letters, where he writes of a paltry piece of dishonesty with as great -glee as if he had solved an ingenious and scientific problem. After -mentioning his meeting Galileo at Bologna, and being indulged with a -trial of his telescope, which, he says, "does wonders upon the earth, -but represents celestial objects falsely;"[50] he concludes with the -following honourable sentence:--"I must confide to you a theft which I -committed. I contrived to take a mould of the glass in wax, without the -knowledge of any one, and, when I get home, I trust to make a telescope -even better than Galileo's own." - -Horky having declared to Kepler, "I will never concede his four new -planets to that Italian from Padua though I die for it," followed up -this declaration by publishing a book against Galileo, which is the one -alluded to by Maestlin, as having destroyed the little credit which, -according to his view, Kepler's publication had left him. This book -professes to contain the examination of four principal questions -touching the alleged planets; 1st, Whether they exist? 2nd, What they -are? 3rd, What they are like? 4th, Why they are? The first question is -soon disposed of, by Horky's declaring positively that he has examined -the heavens with Galileo's own glass, and that no such thing as a -satellite about Jupiter exists. To the second, he declares solemnly, -that he does not more surely know that he has a soul in his body, than -that reflected rays are the sole cause of Galileo's erroneous -observations. In regard to the third question, he says, that these -planets are like the smallest fly compared to an elephant; and, finally, -concludes on the fourth, that the only use of them is to gratify -Galileo's "thirst of gold," and to afford himself a subject of -discussion.[51] - -Galileo did not condescend to notice this impertinent folly; it was -answered by Roffini, a pupil of Magini, and by a young Scotchman of the -name of Wedderburn, then a student at Padua, and afterwards a physician -at the Court of Vienna. In the latter reply we find it mentioned, that -Galileo was also using his telescope for the examination of insects, -&c.[52] Horky sent his performance triumphantly to Kepler, and, as he -returned home before receiving an answer, he presented himself before -his patron in the same misapprehension under which he had written, but -the philosopher received him with a burst of indignation which rapidly -undeceived him. The conclusion of the story is characteristic enough to -be given in Kepler's own account of the matter to Galileo, in which, -after venting his wrath against this "scum of a fellow," whose -"obscurity had given him audacity," he says, that Horky begged so hard -to be forgiven, that "I have taken him again into favour upon this -preliminary condition, to which he has agreed:--that I am to shew him -Jupiter's satellites, AND HE IS TO SEE THEM, and own that they are -there." - -In the same letter Kepler writes, that although he has himself perfect -confidence in the truth of Galileo's assertions, yet he wishes he could -furnish him with some corroborative testimonies, which Kepler could -quote in arguing the point with others. This request produced the -following reply, from which the reader will also learn the new change -which had now taken place in Galileo's fortunes, the result of the -correspondence with Florence, part of which we have already -extracted.[53] "In the first place, I return you my thanks that you -first, and almost alone, before the question had been sifted (such is -your candour and the loftiness of your mind), put faith in my -assertions. You tell me you have some telescopes, but not sufficiently -good to magnify distant objects with clearness, and that you anxiously -expect a sight of mine, which magnifies images more than a thousand -times. It is mine no longer, for the Grand Duke of Tuscany has asked it -of me, and intends to lay it up in his museum, among his most rare and -precious curiosities, in eternal remembrance of the invention: I have -made no other of equal excellence, for the mechanical labour is very -great: I have, however, devised some instruments for figuring and -polishing them which I am unwilling to construct here, as they could not -conveniently be carried to Florence, where I shall in future reside. You -ask, my dear Kepler, for other testimonies:--I produce, for one, the -Grand Duke, who, after observing the Medicaean planets several times with -me at Pisa during the last months, made me a present, at parting, worth -more than a thousand florins, and has now invited me to attach myself to -him with the annual salary of one thousand florins, and with the title -of Philosopher and Principal Mathematician to His Highness; without the -duties of any office to perform, but with the most complete leisure; so -that I can complete my Treatises on Mechanics, on the Constitution of -the Universe, and on Natural and Violent Local Motion, of which I have -demonstrated geometrically many new and admirable phenomena. I produce, -for another witness, myself, who, although already endowed in this -college with the noble salary of one thousand florins, such as no -professor of mathematics ever before received, and which I might -securely enjoy during my life, even if these planets had deceived me and -should disappear, yet quit this situation, and betake me where want and -disgrace will be my punishment should I prove to have been mistaken." - -It is difficult not to regret that Galileo should be thus called on to -resign his best glasses, but it appears probable that on becoming more -familiar with the Grand Duke, he ventured to suggest that this telescope -would be more advantageously employed in his own hands, than pompously -laid up in a museum; for in 1637 we find him saying, in answer to a -request from his friend Micanzio to send him a telescope--"I am sorry -that I cannot oblige you with the glasses for your friend, but I am no -longer capable of making them, and I have just parted with two tolerably -good ones which I had, reserving only my old discoverer of celestial -novelties which is already promised to the Grand Duke." Cosmo was dead -in 1637, and it is his son Ferdinand who is here meant, who appears to -have inherited his father's love of science. Galileo tells us, in the -same letter, that Ferdinand had been amusing himself for some months -with making object-glasses, and always carried one with him to work at -wherever he went. - -When forwarding this telescope to Cosmo in the first instance, Galileo -adds, with a very natural feeling--"I send it to his highness unadorned -and unpolished, as I made it for my own use, and beg that it may always -be left in the same state; for none of the old parts ought to be -displaced to make room for new ones, which will have had no share in the -watchings and fatigues of these observations." A telescope was in -existence, though with the object glass broken, at the end of the last -century, and probably still is in the Museum at Florence, which was -shewn as the discoverer of Jupiter's satellites. Nelli, on whose -authority this is mentioned, appears to question its genuineness. The -first reflecting telescope, made with Newton's own hands, and scarcely -possessing less interest than the first of Galileo's, is preserved in -the library of the Royal Society. - -By degrees the enemies of Galileo and of the new stars found it -impossible to persevere in their disbelief, whether real or pretended, -and at length seemed resolved to compensate for the sluggishness of -their perception, by its acuteness when brought into action. Simon Mayer -published his "Mundus Jovialis" in 1614, in which he claims to have been -an original observer of the satellites, but, with an affectation of -candour, allows that Galileo observed them probably about the same time. -The earliest observation which he has recorded is dated 29th December, -1609, but, not to mention the total want of probability that Mayer would -not have immediately published so interesting a discovery, it is to be -observed, that, as he used the old style, this date of 29th December -agrees with the 8th January, 1610, of the new style, which was the date -of Galileo's second observation, and Galileo ventured to declare his -opinion, that this pretended observation was in fact a plagiarism. - -Scheiner counted five, Rheita nine, and other observers, with increasing -contempt for Galileo's imperfect announcements, carried the number as -high as twelve.[54] In imitation of Galileo's nomenclature, and to -honour the sovereigns of the respective observers, these supposed -additional satellites were dignified with the names of Vladislavian, -Agrippine, Urbanoctavian, and Ferdinandotertian planets; but a very -short time served to show it was as unsafe to exceed as to fall short of -the number which Galileo had fixed upon, for Jupiter rapidly removed -himself from the neighbourhood of the fixed stars, which gave rise to -these pretended discoveries, carrying with him only his four original -attendants, which continued in every part of his orbit to revolve -regularly about him. - -Perhaps we cannot better wind up this account of the discovery of -Jupiter's satellites, and of the intense interest they have at all times -inspired, than in the words of one who inherits a name worthy to be -ranked with that of Galileo in the list of astronomical discoverers, and -who takes his own place among the most accomplished mathematicians of -the present times. "The discovery of these bodies was one of the first -brilliant results of the invention of the telescope; one of the first -great facts which opened the eyes of mankind to the system of the -universe, which taught them the comparative insignificance of their own -planet, and the superior vastness and nicer mechanism of those other -bodies, which had before been distinguished from the stars only by their -motion, and wherein none but the boldest thinkers had ventured to -suspect a community of nature with our own globe. This discovery gave -the holding turn to the opinions of mankind respecting the Copernican -system; the analogy presented by these little bodies (little however -only in comparison with the great central body about which they revolve) -performing their beautiful revolutions in perfect harmony and order -about it, being too strong to be resisted. This elegant system was -watched with all the curiosity and interest the subject naturally -inspired. The eclipses of the satellites speedily attracted attention, -and the more when it was discerned, as it speedily was, by Galileo -himself, that they afforded a ready method of determining the difference -of longitudes of distant places on the earth's surface, by observations -of the instants of their disappearances and reappearances, -simultaneously made. Thus the first astronomical solution of the great -problem of the longitude, the first mighty step which pointed out a -connection between speculative astronomy and practical utility, and -which, replacing the fast dissipating dreams of astrology by nobler -visions, showed how the stars might really, and without fiction, be -called arbiters of the destinies of empires, we owe to the satellites of -Jupiter, those atoms imperceptible to the naked eye, and floating like -motes in the beam of their primary--itself an atom to our sight, noticed -only by the careless vulgar as a large star, and by the philosophers of -former ages as something moving among the stars, they knew not what, nor -why: perhaps only to perplex the wise with fruitless conjectures, and -harass the weak with fears as idle as their theories."[55] - - -FOOTNOTES: - -[46] Venturi. Essai sur les ouvrages de Leo. da Vinci. - -[47] Dianoia Astronomica, Venetiis, 1610. - -[48] Kepleri Epistolae. - -[49] Kepleri Epistolae. - -[50] It may seem extraordinary that any one could support an argument by -this partial disbelief in the instrument, which was allowed on all hands -to represent terrestrial objects correctly. A similar instance of -obstinacy, in an almost identical case though in a more unpretending -station, once came under the writer's own observation. A farmer in -Cambridgeshire, who had acquired some confused notions of the use of the -quadrant, consulted him on a new method of determining the distances and -magnitudes of the sun and moon, which he declared were far different -from the quantities usually assigned to them. After a little -conversation, the root of his error, certainly sufficiently gross, -appeared to be that he had confounded the angular measure of a degree, -with 691/2 miles, the linear measure of a degree on the earth's surface. -As a short way of showing his mistake, he was desired to determine, in -the same manner, the height of his barn which stood about 30 yards -distant; he lifted the quadrant to his eye, but perceiving, probably, -the monstrous size to which his principles were forcing him, he said, -"Oh, Sir, the quadrant's only true for the sky." He must have been an -objector of this kind, who said to Galileo,--"Oh, Sir, the telescope's -only true for the earth." - -[51] Venturi. - -[52] Quatuor probl. confut. per J. Wedderbornium, Scotobritannum. -Patavii, 1610. - -[53] See page 18. - -[54] Sherburne's Sphere of Manilius. London, 1675. - -[55] Herschel's Address to the Astronomical Society, 1827. - - - - -CHAPTER VIII. - - _Observations on the Moon--Nebulae--Saturn--Venus--Mars._ - - -THERE were other discoveries announced in Galileo's book of great and -unprecedented importance, and which scarcely excited less discussion -than the controverted Medicaean planets. His observations on the moon -threw additional light on the constitution of the solar system, and -cleared up the difficulties which encumbered the explanation of the -varied appearance of her surface. The different theories current at that -day, to account for these phenomena, are collected and described by -Benedetti, and also with some liveliness, in a mythological poem, by -Marini.[56] We are told, that, in the opinion of some, the dark shades -on the moon's surface arise from the interposition of opaque bodies -floating between her and the sun, which prevents his light from reaching -those parts: others thought, that on account of her vicinity to the -earth, she was partly tainted with the imperfection of our terrestrial -and elementary nature, and was not of that entirely pure and refined -substance of which the more remote heavens consist: a third party looked -on her as a vast mirror, and maintained that the dark parts of her -surface were the reflected images of our earthly forests and mountains. - -Galileo's glass taught him to believe that the surface of this planet, -far from being smooth and polished, as was generally taken for granted, -really resembled our earth in its structure; he was able distinctly to -trace on it the outlines of mountains and other inequalities, the -summits of which reflected the rays of the sun before these reached the -lower parts, and the sides of which, turned from his beams, lay buried -in deep shadow. He recognised a distribution into something similar to -continents of land, and oceans of water, which reflect the sun's light -to us with greater or less vivacity, according to their constitution. -These conclusions were utterly odious to the Aristotelians; they had -formed a preconceived notion of what the moon ought to be, and they -loathed the doctrines of Galileo, who took delight, as they said, in -distorting and ruining the fairest works of nature. It was in vain he -argued, as to the imaginary perfection of the spherical form, that -although the moon, or the earth, were it absolutely smooth, would indeed -be a more perfect sphere than in its present rough state, yet touching -the perfection of the earth, considered as a natural body calculated for -a particular purpose, every one must see that absolute smoothness and -sphericity would make it not only less perfect, but as far from being -perfect as possible. "What else," he demanded, "would it be but a vast -unblessed desert, void of animals, of plants, of cities and of men; the -abode of silence and inaction; senseless, lifeless, soulless, and stript -of all those ornaments which make it now so various and so beautiful?" - -He reasoned to no purpose with the slaves of the ancient schools: -nothing could console them for the destruction of their smooth -unalterable surface, and to such an absurd length was this hallucination -carried, that one opponent of Galileo, Lodovico delle Colombe, -constrained to allow the evidence of the sensible inequalities of the -moon's surface, attempted to reconcile the old doctrine with the new -observations, by asserting, that every part of the moon, which to the -terrestrial observer appeared hollow and sunken, was in fact entirely -and exactly filled up with a clear crystal substance, perfectly -imperceptible by the senses, but which restored to the moon her -accurately spherical and smooth surface. Galileo met the argument in the -manner most fitting, according to one of Aristotle's own maxims, that -"it is foolish to refute absurd opinions with too much curiosity." -"Truly," says he, "the idea is admirable, its only fault is that it is -neither demonstrated nor demonstrable; but I am perfectly ready to -believe it, provided that, with equal courtesy, I may be allowed to -raise upon your smooth surface, crystal mountains (which nobody can -perceive) ten times higher than those which I have actually seen and -measured." By threatening to proceed to such extremities, he seems to -have scared the opposite party into moderation, for we do not find that -the crystalline theory was persevered in. - -In the same essay, Galileo also explained at some length the cause of -that part of the moon being visible, which is unenlightened directly by -the sun in her first and last quarter. Maestlin, and before him Leonardo -da Vinci, had already declared this to arise from what may be called -_earthshine_, or the reflection of the sun's light from the terrestrial -globe, exactly similar to that which the moon affords us when we are -similarly placed between her and the sun; but the notion had not been -favourably received, because one of the arguments against the earth -being a planet, revolving like the rest round the sun, was, that it did -not shine like them, and was therefore of a different nature; and this -argument, weak as it was in itself, the theory of terrestrial reflection -completely overturned. The more popular opinions ascribed this feeble -light, some to the fixed stars, some to Venus, some to the rays of the -sun, penetrating and shining through the moon. Even the sagacious -Benedetti adopted the notion of this light being caused by Venus, in the -same sentence in which he explains the true reason of the faint light -observed during a total eclipse of the moon, pointing out that it is -occasioned by those rays of the sun, which reach the moon, after being -bent round the sides of the earth by the action of our atmosphere.[57] - -Galileo also announced the detection of innumerable stars, invisible to -the unassisted sight; and those remarkable appearances in the heavens, -generally called nebulae, the most considerable of which is familiar to -all under the name of the milky way, when examined by his instrument, -were found to resolve themselves into a vast collection of minute stars, -too closely congregated to produce a separate impression upon the -unassisted eye.[58] Benedetti, who divined that the dark shades on the -moon's surface arose from the constitution of those parts which suffered -much of the light to pass into them, and consequently reflected a less -portion of it, had maintained that the milky way was the result of the -converse of the same phenomenon, and declared, in the language of his -astronomy, that it was a part of the eighth orb, which did not, like the -rest, allow the sun's light to traverse it freely, but reflected a small -part feebly to our sight. - -The Anti-Copernicans would probably have been well pleased, if by these -eternally renewed discussions and disputes, they could have occupied -Galileo's time sufficiently to detain his attention from his telescope -and astronomical observations; but he knew too well where his real -strength lay, and they had scarcely time to compound any thing like an -argument against him and his theories, before they found him in -possession of some new facts, which they were unprepared to meet, -otherwise than by the never-failing resource of abuse and affected -contempt. The year had not expired before Galileo had new intelligence -to communicate of the highest importance. Perhaps he had been taught -caution from the numerous piracies which had been committed upon his -discoveries, and he first announced his new discoveries enigmatically, -veiling their real import by transpositions of the letters in the words -which described them, (a practice then common, and not disused even at a -much later date,) and inviting all astronomers to declare, within a -certain time, if they had noted any thing new in the heavens worthy of -observation. The transposed letters which he published were-- - - "_Smaismrmilme poeta leumi bvne nugttaviras._" - -Kepler, in the true spirit of his riddling philosophy, endeavoured to -decypher the meaning, and fancied he had succeeded when he formed a -barbarous Latin verse, - - "_Salve umbistineum geminatum Martia proles_," - -conceiving that the discovery, whatever it might be, related to the -planet Mars, to which Kepler's attention had before been particularly -directed. The reader, however, need not weary himself in seeking a -translation of this solution, for at the request of the Emperor Rodolph, -Galileo speedily sent to him the real reading-- - - _Altissimum planetam tergeminum observavi_; - -that is, "I have observed that the most distant planet is triple," or, -as he further explains the matter, "I have with great admiration -observed that Saturn is not a single star, but three together, which as -it were touch each other; they have no relative motion, and are -constituted in this form [Symbol: oOo] the middle being somewhat larger -than the lateral ones. If we examine them with an eye-glass which -magnifies the surface less than 1000 times, the three stars do not -appear very distinctly, but Saturn has an oblong appearance, like the -appearance of an olive, thus [Symbol: horizontal 0]. Now I have -discovered a court for Jupiter, and two servants for this old man, who -aid his steps and never quit his side." Galileo was, however, no match -in this style of writing for Kepler, who disapproved his friend's -metaphor, and, in his usual fanciful and amusing strain,--"I will not," -said he, "make an old man of Saturn, nor slaves of his attendant globes, -but rather let this tricorporate form be Geryon, so shall Galileo be -Hercules, and the telescope his club; armed with which, he has conquered -that distant planet, and dragged him from the remotest depths of nature, -and exposed him to the view of all." Galileo's glass was not of -sufficient power to shew him the real constitution of this extraordinary -planet; it was reserved for Huyghens, about the year 1656, to declare to -the world that these supposed attendant stars are in fact part of a ring -which surrounds, and yet is completely distinct from the body of -Saturn;[59] and the still more accurate observations of Herschel have -ascertained that it consists of two concentric rings revolving round the -planet, and separated from each other by a space which our most powerful -telescopes scarcely enable us to measure. - -Galileo's second statement concluded with the remark, that "in the other -planets nothing new was to be observed;" but a month had scarcely -elapsed, before he communicated to the world another enigma, - - _Haec immatura a me jam frustra leguntur oy_, - -which, as he said, contained the announcement of a new phenomenon, in -the highest degree important to the truth of the Copernican system. The -interpretation of this is, - - _Cynthiae figuras aemulatur mater amorum_, - -that is to say,--Venus rivals the appearances of the moon--for Venus -being now arrived at that part of her orbit in which she is placed -between the earth and the sun, and consequently, with only a part of her -enlightened surface turned towards the earth, the telescope shewed her -in a crescent form, like the moon in a similar position, and tracing her -through the whole of her orbit round the sun, or at least so long as she -was not invisible from his overpowering light, Galileo had the -satisfaction of seeing the enlightened portion in each position assume -the form appropriate to that hypothesis. It was with reason, therefore, -that he laid stress on the importance of this observation, which also -established another doctrine scarcely less obnoxious to the -Anti-Copernicans, namely, that a new point of resemblance was here found -between the earth and one of the principal planets; and as the -reflection from the earth upon the moon had shewn it to be luminous like -the planets when subjected to the rays of the sun, so this change of -apparent figure demonstrated that one of the planets not near the earth, -and therefore probably all, were in their own nature not luminous, and -only reflected the sun's light which fell upon them; an inference, of -which the probability was still farther increased a few years later by -the observation of the transit of Mercury over the sun's disc. - -It is curious that only twenty-five years before this discovery of the -phases (or appearances) of Venus, a commentator of Aristotle, under the -name of Lucillus Philalthaeus, had advanced the doctrine that all the -planets except the moon are luminous of themselves, and in proof of his -assertion had urged, "that if the other planets and fixed stars received -their light from the sun, they would, as they approached and receded -from him, or as he approached and receded from them, assume the same -phases as the moon, which, he adds, we have never yet observed."--He -further remarks, "that Mercury and Venus would, in the supposed case of -their being nearer the earth than the sun, eclipse it occasionally, just -as eclipses are occasioned by the moon." Perhaps it is still more -remarkable, that these very passages, in which the reasoning is so -correct, though the facts are too hastily taken for granted, (the common -error of that school,) are quoted by Benedetti, expressly to shew the -ignorance and presumption of the author. Copernicus, whose want of -instruments had prevented him from observing the horned appearance of -Venus when between the earth and sun, had perceived how formidable an -obstacle the non-appearance of this phenomenon presented to his system; -he endeavoured, though unsatisfactorily, to account for it by supposing -that the rays of the sun passed freely through the body of the planet, -and Galileo takes occasion to praise him for not being deterred from -adopting the system, which, on the whole, appeared to agree best with -the phenomena, by meeting with some which it did not enable him to -explain. Milton, whose poem is filled with allusions to Galileo and his -astronomy, has not suffered this beautiful phenomenon to pass unnoticed. -After describing the creation of the Sun, he adds:-- - - Hither, as to their fountain, other stars - Repairing, in their golden urns draw light, - And hence the morning planet gilds her horns.[60] - -Galileo also assured himself, at the same time, that the fixed stars did -not receive their light from the sun. This he ascertained by comparing -the vividness of their light, in all positions, with the feebleness of -that of the distant planets, and by observing the different degrees of -brightness with which all the planets shone at different distances from -the sun. The more remote planets did not, of course, afford equal -facilities with Venus for so decisive an observation; but Galileo -thought he observed, that when Mars was in quadratures, (or in the -quarters, the middle points of his path on either side,) his figure -varied slightly from a perfect circle. Galileo concludes the letter, in -which he announces these last observations to his pupil Castelli, with -the following expressions, shewing how justly he estimated the -opposition they encountered:--"You almost make me laugh by saying that -these clear observations are sufficient to convince the most obstinate: -it seems you have yet to learn that long ago the observations were -enough to convince those who are capable of reasoning, and those who -wish to learn the truth; but that to convince the obstinate, and those -who care for nothing beyond the vain applause of the stupid and -senseless vulgar, not even the testimony of the stars would suffice, -were they to descend on earth to speak for themselves. Let us then -endeavour to procure some knowledge for ourselves, and rest contented -with this sole satisfaction; but of advancing in popular opinion, or -gaining the assent of the book-philosophers, let us abandon both the -hope and the desire." - - -FOOTNOTES: - -[56] Adone di Marini, Venetiis, 1623, Cant. x. - -[57] Speculat. Lib Venetiis, 1585, Epistolae. - -[58] This opinion, with respect to the milky way, had been held by some -of the ancient astronomers. _See_ Manilius. Lib. i. v. 753. - - "_Anne magis densa stellarum turba corona_ - "_Contexit flammas, et crasso lumine candet,_ - "_Et fulgore nitet collato clarior orbis._" - -[59] Huyghens announced his discovery in this form: _a a a a a a a c c c -c c d e e e e e g h i i i i i i i l l l l m m n n n n n n n n n o o o o -p p q r r s t t t t t u u u u u_, which he afterwards recomposed into -the sentence. _Annulo cingitur, tenui, plano, nusquam cohaerente, ad -eclipticam inclinato_. De Saturni Luna. Hagae, 1656. - -[60] B. vii. v. 364. Other passages may be examined in B. i. 286; iii. -565-590, 722-733; iv. 589; v. 261, 414; vii. 577; viii. 1-178. - - - - -CHAPTER IX. - - _Account of the Academia Lincea--Del Cimento--Royal Society._ - - -GALILEO'S resignation of the mathematical professorship at Padua -occasioned much dissatisfaction to all those who were connected with -that university. Perhaps not fully appreciating his desire of returning -to his native country, and the importance to him and to the scientific -world in general, of the complete leisure which Cosmo secured to him at -Florence, (for by the terms of his diploma he was not even required to -reside at Pisa, nor to give any lectures, except on extraordinary -occasions, to sovereign princes and other strangers of distinction,) the -Venetians remembered only that they had offered him an honourable asylum -when almost driven from Pisa; that they had increased his salary to four -times the sum which any previous professor had enjoyed; and, finally, by -an almost unprecedented decree, that they had but just secured him in -his post during the remainder of his life. Many took such offence as to -refuse to have any further communication with him; and Sagredo, a -constant friend of Galileo, wrote him word that he had been threatened -with a similar desertion unless he should concur in the same peremptory -resolution, which threats, however, Sagredo, at the same time, intimates -his intention of braving. - -Early in the year 1611, Galileo made his first appearance in Rome, where -he was received with marks of distinguished consideration, and where all -ranks were eager to share the pleasure of contemplating the new -discoveries. "Whether we consider cardinal, prince, or prelate, he found -an honourable reception from them all, and had their palaces as open and -free to him as the houses of his private friends."[61] Among other -distinctions he was solicited to become a member of the newly-formed -philosophical society, the once celebrated _Academia Lincea_, to which -he readily assented. The founder of this society was Federigo Cesi, the -Marchese di Monticelli, a young Roman nobleman, the devotion of whose -time and fortune to the interests of science has not been by any means -rewarded with a reputation commensurate with his deserts. If the energy -of his mind had been less worthily employed than in fostering the cause -of science and truth, and in extending the advantages of his birth and -fortune to as many as were willing to co-operate with him, the name of -Federigo Cesi might have appeared more prominently on the page of -history. Cesi had scarcely completed his 18th year, when, in 1603, he -formed the plan of a philosophical society, which in the first instance -consisted only of himself and three of his most intimate friends, Hecke, -a Flemish physician, Stelluti, and Anastasio de Filiis. Cesi's father, -the Duca d'Acquasparta, who was of an arbitrary and extravagant temper, -considered such pursuits and associates as derogatory to his son's rank; -he endeavoured to thwart the design by the most violent and -unjustifiable proceedings, in consequence of which, Cesi in the -beginning of 1605 privately quitted Rome, Hecke was obliged to leave -Italy altogether from fear of the Inquisition, which was excited against -him, and the academy was for a time virtually dissolved. The details of -these transactions are foreign to the present narrative: it will be -enough to mention that, in 1609, Cesi, who had never altogether -abandoned his scheme, found the opposition decaying which he at first -experienced, and with better success he renewed the plan which he had -sketched six years before. A few extracts from the Regulations will -serve to shew the spirit in which this distinguished society was -conceived:-- - -"The Lyncean Society desires for its academicians, philosophers eager -for real knowledge, who will give themselves to the study of nature, and -especially to mathematics; at the same time it will not neglect the -ornaments of elegant literature and philology, which like a graceful -garment adorn the whole body of science.--In the pious love of wisdom, -and to the praise of the most good and most high God, let the Lynceans -give their minds, first to observation and reflection, and afterwards to -writing and publishing.--It is not within the Lyncean plan to find -leisure for recitations and declamatory assemblies; the meetings will -neither be frequent nor full, and chiefly for transacting the necessary -business of the society: but those who wish to enjoy such exercises will -in no respect be hindered, provided they attend them as accessory -studies, decently and quietly, and without making promises and -professions of how much they are about to do. For there is ample -philosophical employment for every one by himself, particularly if pains -are taken in travelling and in the observation of natural phenomena, and -in the book of nature which every one has at home, that is to say, the -heavens and the earth; and enough may be learned from the habits of -constant correspondence with each other, and alternate offices of -counsel and assistance.--Let the first fruits of wisdom be love; and so -let the Lynceans love each other as if united by the strictest ties, nor -suffer any interruption of this sincere bond of love and faith, -emanating from the source of virtue and philosophy.--Let them add to -their names the title of Lyncean, which has been advisedly chosen as a -warning and constant stimulus, especially when they write on any -literary subject, also in their private letters to their associates, and -in general when any work comes from them wisely and well performed.--The -Lynceans will pass over in silence all political controversies and -quarrels of every kind, and wordy disputes, especially gratuitous ones, -which give occasion to deceit, unfriendliness, and hatred; like men who -desire peace, and seek to preserve their studies free from molestation, -and to avoid every sort of disturbance. And if any one by command of his -superiors, or from some other necessity, is reduced to handle such -matters, since they are foreign to physical and mathematical science, -and consequently alien to the object of the Academy, let them be printed -without the Lyncean name."[62] - -The society which was eventually organized formed but a very trifling -part of the comprehensive scheme which Cesi originally proposed to -himself; it had been his wish to establish a scientific Order which -should have corresponding lodges in the principal towns of Europe, and -in other parts of the globe, each consisting of not more than five nor -less than three members, besides an unlimited number of Academicians not -restricted to any particular residence or regulations. The -mortifications and difficulties to which he was subjected from his -father's unprincipled behaviour, render it most extraordinary and -admirable that he should have ventured to undertake even so much as he -actually carried into execution. He promised to furnish to the members -of his society such assistance as they might require in the prosecution -of their respective researches, and also to defray the charges of -publishing such of their works as should be thought worthy of appearing -with the common sanction. Such liberal offers were not likely to meet -with an unfavourable reception: they were thankfully accepted by many -well qualified to carry his design into execution, and Cesi was soon -enabled formally to open his academy, the distinctive title of which he -borrowed from the Lynx, with reference to the piercing sight which that -animal has been supposed to possess. This quality seemed to him an -appropriate emblem of those which he desired to find in his -academicians, for the purpose of investigating the secrets of nature; -and although, at the present day, the name may appear to border on the -grotesque, it was conceived in the spirit of the age, and the fantastic -names of the numberless societies which were rapidly formed in various -parts of Italy far exceed whatever degree of quaintness may be thought -to belong to the Lyncean name. The Inflamed--the Transformed--the -Uneasy--the Humorists--the Fantastic--the Intricate--the Indolent--the -Senseless--the Undeceived--the Valiant--the AEtherial Societies are -selected from a vast number of similar institutions, the names of which, -now almost their sole remains, are collected by the industry of Morhof -and Tiraboschi.[63] The Humorists are named by Morhof as the only -Italian philosophical society anterior to the Lynceans; their founder -was Paolo Mancino, and the distinctive symbol which they adopted was -rain dropping from a cloud, with the motto _Redit agmine dulci_;--their -title is derived from the same metaphor. The object of their union -appears to have been similar to that of the Lynceans, but they at no -time attained to the celebrity to which Cesi's society rose from the -moment of its incorporation. Cesi took the presidency for his life, and -the celebrated Baptista Porta was appointed vice president at Naples. -Stelluti acted as the legal representative of the society, with the -title of procuratore. Of the other two original members Anastasio de -Filiis was dead, and although Hecke returned to Italy in 1614, and -rejoined the Academy, yet he was soon afterwards struck off the list in -consequence of his lapsing into insanity. Among the academicians we find -the names of Galileo, Fabio Colonna, Lucas Valerio, Guiducci, Welser, -Giovanni Fabro, Terrentio, Virginio Cesarini, Ciampoli, Molitor, -Cardinal Barberino, (nephew of Pope Urban VIII.) Stelliola, Salviati, -&c. - -The principal monument still remaining of the zeal and industry to which -Cesi incited his academicians is the Phytobasanos, a compendium of the -natural history of Mexico, which must be considered a surprising -performance for the times in which it appeared. It was written by a -Spaniard named Hernandez; and Reccho, who often has the credit of the -whole work, made great additions to it. During fifty years the -manuscript had been neglected, when Cesi discovered it, and employed -Terrentio, Fabro, and Colonna, all Lynceans, to publish it enriched with -their notes and emendations. Cesi himself published several treatises, -two of which are extant; his _Tabulae Phytosophicae_, and a Dissertation -on Bees entitled _Apiarium_, the only known copy of which last is in the -library of the Vatican. His great work, _Theatrum Naturae_, was never -printed; a circumstance which tends to shew that he did not assemble the -society round him for the purpose of ministering to his own vanity, but -postponed the publication of his own productions to the labours of his -coadjutors. This, and many other valuable works belonging to the academy -existed in manuscript till lately in the Albani Library at Rome. Cesi -collected, not a large, but an useful library for the use of the -academy, (which was afterwards augmented on the premature death of -Cesarini by the donation of his books); he filled a botanical garden -with the rarer specimens of plants, and arranged a museum of natural -curiosities; his palace at Rome was constantly open to the academicians; -his purse and his influence were employed with equal liberality in their -service. - -Cesi's death, in 1632, put a sudden stop to the prosperity of the -society, a consequence which may be attributed to the munificence with -which he had from the first sustained it: no one could be found to fill -his place in the princely manner to which the academicians were -accustomed, and the society, after lingering some years under the -nominal patronage of Urban VIII., gradually decayed, till, by the death -of its principal members, and dispersion of the rest, it became entirely -extinct.[64] Bianchi, whose sketch of the academy was almost the only -one till the appearance of Odescalchi's history, made an attempt to -revive it in the succeeding century, but without any permanent effect. A -society under the same name has been formed since 1784, and is still -flourishing in Rome. Before leaving the subject it may be mentioned, -that one of the earliest notices that Bacon's works were known in Italy -is to be found in a letter to Cesi, dated 1625; in which Pozzo, who had -gone to Paris with Cardinal Barberino, mentions having seen them there -with great admiration, and suggests that Bacon would be a fit person to -be proposed as a member of their society. After Galileo's death, three -of his principal followers, Viviani, Torricelli, and Aggiunti formed the -plan of establishing a similar philosophical society, and though -Aggiunti and Torricelli died before the scheme could be realized, -Viviani pressed it forward, and, under the auspices of Ferdinand II., -formed a society, which, in 1657, merged in the famous _Academia del -Cimento_, or Experimental Academy. This latter held its occasional -meetings at the palace of Ferdinand's brother, Leopold de' Medici: it -was composed chiefly, if not entirely, of Galileo's pupils and friends. -During the few years that this society lasted, one of the principal -objects of which was declared to be the repetition and developement of -Galileo's experiments, it kept up a correspondence with the principal -philosophers in every part of Europe, but when Leopold was, in 1666, -created a cardinal, it appears to have been dissolved, scarcely ten -years after its institution.[65] This digression may be excused in -favour of so interesting an establishment as the Academia Lincea, which -preceded by half a century the formation of the Royal Society of London, -and Academie Francoise of Paris. - -These latter two are mentioned together, probably for the first time, by -Salusbury. The passage is curious in an historical point of view, and -worth extracting:--"In imitation of these societies, Paris and London -have erected theirs of _Les Beaux Esprits_, and of the _Virtuosi_: the -one by the countenance of the most eminent Cardinal Richelieu, the other -by the royal encouragement of his sacred Majesty that now is. The _Beaux -Esprits_ have published sundry volumes of their moral and physiological -conferences, with the laws and history of their fellowship; and I hope -the like in due time from our Royal Society; that so such as envie their -fame and felicity, and such as suspect their ability and candor, may be -silenced and disappointed in their detractions and expectations."[66] - - -FOOTNOTES: - -[61] Salusbury, Math. Coll. - -[62] Perhaps it was to deprecate the hostility of the Jesuits that, at -the close of these Regulations, the Lynceans are directed to address -their prayers, among other Saints, especially to Ignatius Loyola, as to -one who greatly favoured the interests of learning. Odescalchi, Memorie -dell'Acad. de' Lincei, Roma. 1806. - -[63] Polyhistor Literarius, &c.--Storia della Letterat. Ital. The still -existing society of Chaff, more generally known by its Italian title, -Della Crusca, belongs to the same period. - -[64] F. Colonnae Phytobasanus Jano Planco Auctore. Florent, 1744. - -[65] Nelli Saggio di Storia Literaria Fiorentina, Lucca, 1759. - -[66] Salusbury's Math. Coll. vol. ii. London, 1664. - - - - -CHAPTER X. - - _Spots on the Sun--Essay on Floating Bodies--Scheiner--Change in - Saturn._ - - -GALILEO did not indulge the curiosity of his Roman friends by exhibiting -only the wonders already mentioned, which now began to lose the gloss of -novelty, but disclosed a new discovery, which appeared still more -extraordinary, and, to the opposite faction, more hateful than anything -of which he had yet spoken. This was the discovery, which he first made -in the month of March, 1611, of dark spots on the body of the sun. A -curious fact, and one which well serves to illustrate Galileo's -superiority in seeing things simply as they are, is, that these spots -had been observed and recorded centuries before he existed, but, for -want of careful observation, their true nature had been constantly -misapprehended. One of the most celebrated occasions was in the year 807 -of our era, in which a dark spot is mentioned as visible on the face of -the sun during seven or eight days. It was then supposed to be -Mercury.[67] Kepler, whose astronomical knowledge would not suffer him -to overlook that it was impossible that Mercury could remain so long in -conjunction with the sun, preferred to solve the difficulty by supposing -that, in Aimoin's original account, the expression was not _octo dies_ -(eight days), but _octoties_--a barbarous word, which he supposed to -have been written for _octies_ (eight times); and that the other -accounts (in which the number of days mentioned is different) copying -loosely from the first, had both mistaken the word, and misquoted the -time which they thought they found mentioned there. It is impossible to -look on this explanation as satisfactory, but Kepler, who at that time -did not dream of spots on the sun, was perfectly contented with it. In -1609, he himself observed upon the sun a black spot, which he in like -manner mistook for Mercury, and unluckily the day, being cloudy, did -not allow him to contemplate it sufficiently long to discover his -error, which the slowness of its apparent motion would soon have pointed -out.[68] He hastened to publish his supposed observation, but no sooner -was Galileo's discovery of the solar spots announced, than he, with that -candour which as much as his flighty disposition certainly characterized -him at all times, retracted his former opinion, and owned his belief -that he had been mistaken. In fact it is known from the more accurate -theory which we now possess of Mercury's motions, that it did not pass -over the sun's face at the time when Kepler thought he perceived it -there. - -Galileo's observations were in their consequences to him particularly -unfortunate, as in the course of the controversy in which they engaged -him, he first became personally embroiled with the powerful party, whose -prevailing influence was one of the chief causes of his subsequent -misfortunes. Before we enter upon that discussion, it will be proper to -mention another famous treatise which Galileo produced soon after his -return from Rome to Florence, in 1612. This is, his Discourse on -Floating Bodies, which restored Archimedes' theory of hydrostatics, and -has, of course, met with the opposition which few of Galileo's works -failed to encounter. In the commencement, he thought it necessary to -apologize for writing on a subject so different from that which chiefly -occupied the public attention, and declared that he had been too closely -occupied in calculating the periods of the revolutions of Jupiter's -satellites to permit him to publish anything earlier. These periods he -had succeeded in determining during the preceding year, whilst at Rome, -and he now announced them to complete their circuits, the first in about -1 day, 181/2 hours; the second in 3 days, 13 hours, 20 minutes; the third -in 7 days, 4 hours; and the outermost in 16 days, 18 hours. All these -numbers he gave merely as approximately true, and promised to continue -his observations, for the purpose of correcting the results. He then -adds an announcement of his recent discovery of the solar spots, "which, -as they change their situation, offer a strong argument, either that the -sun revolves on itself, or that, perhaps, other stars, like Venus and -Mercury, revolve about it, invisible at all other times, on account of -the small distance to which they are removed from him." To this he -afterwards subjoined, that, by continued observation, he had satisfied -himself that these solar spots were in actual contact with the surface -of the sun, where they are continually appearing and disappearing; that -their figures were very irregular, some being very dark, and others not -so black; that one would often divide into three or four, and, at other -times, two, three, or more would unite into one; besides which, that -they had all a common and regular motion, with which they revolved round -with the sun, which turned upon its axis in about the time of a lunar -month. - -Having by these prefatory observations assuaged the public thirst for -astronomical novelties, he ventures to introduce the principal subject -of the treatise above mentioned. The question of floating bridges had -been discussed at one of the scientific parties, assembled at the house -of Galileo's friend Salviati, and the general opinion of the company -appearing to be that the floating or sinking of a body depended -principally upon its shape, Galileo undertook to convince them of their -error. If he had not preferred more direct arguments, he might merely -have told them that in this instance they were opposed to their -favourite Aristotle, whose words are very unequivocal on the point in -dispute. "Form is not the cause why a body moves downwards rather than -upwards, but it does affect the swiftness with which it moves;"[69] -which is exactly the distinction which those who called themselves -Aristotelians were unable to perceive, and to which the opinions of -Aristotle himself were not always true. Galileo states the discussion to -have immediately arisen from the assertion of some one in the company, -that condensation is the effect of cold, and ice was mentioned as an -instance. On this, Galileo observed, that ice is rather water rarefied -than condensed, the proof of which is, that ice always floats upon -water.[70] It was replied, that the reason of this phenomenon was, not -the superior lightness of the ice, but its incapacity, owing to its flat -shape, to penetrate and overcome the resistance of the water. Galileo -denied this, and asserted that ice of any shape would float upon water, -and that, if a flat piece of ice were forcibly taken to the bottom, it -would of itself rise again to the surface. Upon this assertion it -appears that the conversation became so clamorous, that Galileo thought -it pertinent to commence his Essay with the following observation on the -advantage of delivering scientific opinions in writing, "because in -conversational arguments, either one or other party, or perhaps both, -are apt to get overwarm, and to speak overloud, and either do not suffer -each other to be heard, or else, transported with the obstinacy of not -yielding, wander far away from the original proposition, and confound -both themselves and their auditors with the novelty and variety of their -assertions." After this gentle rebuke he proceeds with his argument, in -which he takes occasion to state the famous hydrostatical paradox, of -which the earliest notice is to be found in Stevin's works, a -contemporary Flemish engineer, and refers it to a principle on which we -shall enlarge in another chapter. He then explains the true theory of -buoyancy, and refutes the false reasoning on which the contrary opinions -were founded, with a variety of experiments. - -The whole value and interest of experimental processes generally depends -on a variety of minute circumstances, the detail of which would be -particularly unsuited to a sketch like the present one. For those who -are desirous of becoming more familiar with Galileo's mode of conducting -an argument, it is fortunate that such a series of experiments exists as -that contained in this essay; experiments which, from their simplicity, -admit of being for the most part concisely enumerated, and at the same -time possess so much intrinsic beauty and characteristic power of -forcing conviction. They also present an admirable specimen of the -talent for which Galileo was so deservedly famous, of inventing -ingenious arguments in favour of his adversaries' absurd opinions before -he condescended to crush them, shewing that nothing but his love of -truth stood in the way of his being a more subtle sophist than any -amongst them. In addition to these reasons for giving these experiments -somewhat in detail, is the fact that all explanation of one of the -principal phenomena to which they allude is omitted in many more modern -treatises on Hydrostatics; and in some it is referred precisely to the -false doctrines here confuted. - -The marrow of the dispute is included in Galileo's assertion, that "The -diversity of figure given to any solid cannot be in any way the cause of -its absolutely sinking or floating; so that if a solid, when formed for -example into a spherical figure, sinks or floats in the water, the same -body will sink or float in the same water, when put into any other form. -The breadth of the figure may indeed retard its velocity, as well of -ascent as descent, and more and more according as the said figure is -reduced to a greater breadth and thinness; but that it may be reduced to -such a form as absolutely to put an end to its motion in the same fluid, -I hold to be impossible. In this I have met with great contradictors -who, producing some experiments, and in particular a thin board of -ebony, and a ball of the same wood, and shewing that the ball in water -sinks to the bottom[71], and that the board if put lightly on the -surface floats, have held and confirmed themselves in their opinion with -the authority of Aristotle, that the cause of that rest is the breadth -of the figure, unable by its small weight to pierce and penetrate the -resistance of the water's thickness, which is readily overcome by the -other spherical figure."--For the purpose of these experiments, Galileo -recommends a substance such as wax, which may be easily moulded into any -shape, and with which, by the addition of a few filings of lead, a -substance may be readily made of any required specific gravity. He then -declares that if a ball of wax of the size of an orange, or bigger, be -made in this manner heavy enough to sink to the bottom, but so lightly -that if we take from it only one grain of lead it returns to the top; -and if the same wax be afterwards moulded into a broad and thin cake, or -into any other figure, regular or irregular, the addition of the same -grain of lead will always make it sink, and it will again rise when we -remove the lead from it.--"But methinks I hear some of the adversaries -raise a doubt upon my produced experiment: and, first, they offer to my -consideration that the figure, as a figure simply, and disjunct from the -matter, works no effect, but requires to be conjoined with the matter; -and, moreover, not with every matter, but with those only wherewith it -may be able to execute the desired operation. Just as we see by -experience that an acute and sharp angle is more apt to cut than an -obtuse; yet always provided that both one and the other are joined with -a matter fit to cut, as for instance, steel. Therefore a knife with a -fine and sharp edge cuts bread or wood with much ease, which it will not -do if the edge be blunt and thick; but if, instead of steel, any one -will take wax and mould it into a knife, undoubtedly he will never learn -the effects of sharp and blunt edges, because neither of them will cut; -the wax being unable, by reason of its flexibility, to overcome the -hardness of the wood and bread. And therefore, applying the like -discourse to our argument, they say that the difference of figure will -shew different effects with regard to floating and sinking, but not -conjoined with any kind of matter, but only with those matters which by -their weight are able to overcome the viscosity of the water (like the -ebony which they have selected); and he that will select cork or other -light wood to form solids of different figures, would in vain seek to -find out what operation figure has in sinking or floating, because all -would swim, and that not through any property of this or that figure, -but through the debility of the matter. - -"When I begin to examine one by one all the particulars here produced, I -allow not only that figures, simply as such, do not operate in natural -things, but also that they are never separated from the corporeal -substance, nor have I ever alleged them to be stript of sensible matter: -and also I freely admit, that in our endeavours to examine the diversity -of accidents which depend upon the variety of figures, it is necessary -to apply them to matters which obstruct not the various operations of -those various figures. I admit and grant that I should do very ill if I -were to try the influence of a sharp edge with a knife of wax, applying -it to cut an oak, because no sharpness in wax is able to cut that very -hard wood. But yet, such an experiment of this knife would not be beside -the purpose to cut curded milk, or other very yielding matter; nay, in -such matters, the wax is more convenient than steel for finding the -difference depending on the acuteness of the angles, because milk is cut -indifferently with a razor, or a blunt knife. We must therefore have -regard not only to the hardness, solidity, or weight of the bodies -which, under different figures, are to divide some matters asunder; but -also, on the other hand, to the resistance of the matter to be -penetrated. And, since I have chosen a matter which does penetrate the -resistance of the water, and in all figures descends to the bottom, my -antagonists can charge me with no defect; nor (to revert to their -illustration) have I attempted to test the efficacy of acuteness by -cutting with matters unable to cut. I subjoin withal, that all caution, -distinction, and election of matter would be superfluous and -unnecessary, if the body to be cut should not at all resist the cutting: -if the knife were to be used in cutting a mist, or smoke, one of paper -would serve the purpose as well as one of Damascus steel; and I assert -that this is the case with water, and that there is not any solid of -such lightness or of such a figure, that being put on the water it will -not divide and penetrate its thickness; and if you will examine more -carefully your thin boards of wood, you will see that they have part of -their thickness under water; and, moreover, you will see that the -shavings of ebony, stone, or metal, when they float, have not only thus -broken the continuity of the water, but are with all their thickness -under the surface of it; and that more and more, according as the -floating substance is heavier, so that a thin floating plate of lead -will be lower than the surface of the surrounding water by at least -twelve times the thickness of the plate, and gold will dive below the -level of the water almost twenty times the thickness of the plate, as I -shall shew presently." - -In order to illustrate more clearly the non-resistance of water to -penetration, Galileo then directs a cone to be made of wood or wax, and -asserts that when it floats, either with its base or point in the water, -the solid content of the part immersed will be the same, although the -point is, by its shape, better adapted to overcome the resistance of the -water to division, if that were the cause of the buoyancy. Or the -experiment may be varied by tempering the wax with filings of lead, till -it sinks in the water, when it will be found that in any figure the same -cork must be added to it to raise it to the surface.--"This silences not -my antagonists; but they say that all the discourse hitherto made by me -imports little to them, and that it serves their turn, that they have -demonstrated in one instance, and in such manner and figure as pleases -them best, namely, in a board and a ball of ebony, that one, when put -into the water, sinks to the bottom, and that the other stays to swim at -the top; and the matter being the same, and the two bodies differing in -nothing but in figure, they affirm that with all perspicuity they have -demonstrated and sensibly manifested what they undertook. Nevertheless I -believe, and think I can prove that this very experiment proves nothing -against my theory. And first it is false that the ball sinks, and the -board not; for the board will sink too, if you do to both the figures as -the words of our question require; that is, if you put them both _in_ -the water; for to be in the water implies to be placed in the water, and -by Aristotle's own definition of place, to be placed imports to be -environed by the surface of the ambient body; but when my antagonists -shew the floating board of ebony, they put it not into the water, but -upon the water; where, being detained by a certain impediment (of which -more anon) it is surrounded, partly with water, partly with air, which -is contrary to our agreement, for that was that the bodies should be in -the water, and not part in the water, part in the air. I will not omit -another reason, founded also upon experience, and, if I deceive not -myself, conclusive against the notion that figure, and the resistance of -the water to penetration have anything to do with the buoyancy of -bodies. Choose a piece of wood or other matter, as for instance -walnut-wood, of which a ball rises from the bottom of the water to the -surface more slowly than a ball of ebony of the same size sinks, so that -clearly the ball of ebony divides the water more readily in sinking than -does the walnut in rising. Then take a board of walnut-tree equal to and -like the floating ebony one of my antagonists; and if it be true that -this latter floats by reason of the figure being unable to penetrate the -water, the other of walnut-tree, without all question, if thrust to the -bottom ought to stay there, as having the same impeding figure, and -being less apt to overcome the said resistance of the water. But if we -find by experience that not only the thin board, but every other figure -of the same walnut-tree will return to float, as unquestionably we -shall, then I must desire my opponents to forbear to attribute the -floating of the ebony to the figure of the board, since the resistance -of the water is the same in rising as in sinking, and the force of -ascension of the walnut-tree is less than the ebony's force for going to -the bottom. - -"Now, let us return to the thin plate of gold or silver, or the thin -board of ebony, and let us lay it lightly upon the water, so that it may -stay there without sinking, and carefully observe the effect. It will -appear clearly that the plates are a considerable matter lower than the -surface of the water which rises up, and makes a kind of rampart round -them on every side, in the manner shewn in the annexed figure, in which -BDLF represents the surface of the water, and AEIO the surface of the -plate. But if it have already penetrated and overcome the continuity of -the water, and is of its own nature heavier than the water, why does it -not continue to sink, but stop and suspend itself in that little dimple -that its weight has made in the water? My answer is, because in sinking -till its surface is below the water which rises up in a bank round it, -it draws after and carries along with it the air above it, so that that -which in this case descends and is placed in the water, is not only the -board of ebony or plate of iron, but a compound of ebony and air, from -which composition results a solid no longer specifically heavier than -the water, as was the ebony or gold alone. But, Gentlemen, we want the -same matter; you are to alter nothing but the shape, and therefore have -the goodness to remove this air, which may be done simply by washing the -upper surface of the board, for the water having once got between the -board and air will run together, and the ebony will go to the bottom; -and if it does not, you have won the day. But methinks I hear some of my -antagonists cunningly opposing this, and telling me that they will not -on any account allow their board to be wetted, because the weight of the -water so added, by making it heavier than it was before, draws it to the -bottom, and that the addition of new weight is contrary to our -agreement, which was that the matter should be the same." - -[Illustration] - -"To this I answer first, that nobody can suppose bodies to be put into -the water without their being wet, nor do I wish to do more to the -board than you may do to the ball. Moreover, it is not true that the -board sinks on account of the weight of the water added in the washing; -for I will put ten or twenty drops on the floating board, and so long as -they stand separate it shall not sink; but if the board be taken out, -and all that water wiped off, and the whole surface bathed with one -single drop, and put it again upon the water, there is no question but -it will sink, the other water running to cover it, being no longer -hindered by the air. In the next place it is altogether false that water -can in any way increase the weight of bodies immersed in it, for water -has no weight in water, since it does not sink. Now, just as he who -should say that brass by its own nature sinks, but that when formed into -the shape of a kettle, it acquires from that figure a virtue of lying in -the water without sinking, would say what is false, because that is not -purely brass which then is put into the water, but a compound of brass -and air; so is it neither more nor less false, that a thin plate of -brass or ebony swims by virtue of its dilated and broad figure. Also I -cannot omit to tell my opponents, that this conceit of refusing to bathe -the surface of the board, might beget an opinion in a third person of a -poverty of arguments on their side, especially as the conversation began -about flakes of ice, in which it would be simple to require that the -surfaces should be kept dry; not to mention that such pieces of ice, -whether wet or dry, always float, and as my antagonists say, because of -their shape. - -"Some may wonder that I affirm this power to be in the air of keeping -the plate of brass or silver above water, as if in a certain sense I -would attribute to the air a kind of magnetic virtue for sustaining -heavy bodies with which it is in contact. To satisfy all these doubts, I -have contrived the following experiment to demonstrate how truly the air -does support these solids; for I have found, when one of these bodies -which floats when placed lightly on the water, is thoroughly bathed and -sunk to the bottom, that by carrying down to it a little air without -otherwise touching it in the least, I am able to raise and carry it back -to the top, where it floats as before. To this effect I take a ball of -wax, and with a little lead make it just heavy enough to sink very -slowly to the bottom, taking care that its surface be quite smooth and -even. This, if put gently into the water, submerges almost entirely, -there remaining visible only a little of the very top, which, so long as -it is joined to the air, keeps the ball afloat; but if we take away the -contact of the air by wetting this top, the ball sinks to the bottom, -and remains there. Now to make it return to the surface by virtue of the -air which before sustained it, thrust into the water a glass, with the -mouth downwards, which will carry with it the air it contains; and move -this down towards the ball, until you see by the transparency of the -glass that the air has reached the top of it; then gently draw the glass -upwards, and you will see the ball rise, and afterwards stay on the top -of the water, if you carefully part the glass and water without too much -disturbing it.[72] There is therefore a certain affinity between the air -and other bodies, which holds them united, so that they separate not -without a kind of violence, just as between water and other bodies; for -in drawing them wholly out of the water, we see the water follow them, -and rise sensibly above the level before it quits them." Having -established this principle by this exceedingly ingenious and convincing -experiment, Galileo proceeds to shew from it what must be the dimensions -of a plate of any substance which will float as the wax does, assuming -in each case that we know the greatest height at which the rampart of -water will stand round it. In like manner he shows that a pyramidal or -conical figure may be made of any substance, such that by help of the -air, it shall rest upon the water without wetting more than its base; -and that we may so form a cone of any substance that it shall float if -placed gently on the surface, with its point downwards, whereas no care -or pains will enable it to float with its base downwards, owing to the -different proportions of air which in the two positions remain connected -with it. With this parting blow at his antagonist's theory we close our -extracts from this admirable essay. - -The first elements of the theory of running waters were reserved for -Castelli, an intimate friend and pupil of Galileo. On the present -occasion, Castelli appeared as the ostensible author of a defence -against the attacks made by Vincenzio di Grazia and by Lodovico delle -Columbe (the author of the crystalline composition of the moon) on the -obnoxious theory. After destroying all the objections which they -produced, the writer tauntingly bids them remember, that he was merely -Galileo's pupil, and consider how much more effectually Galileo himself -would have confuted them, had he thought it worth while. It was not -known till several years after his death, that this Essay was in fact -written by Galileo himself.[73] - -These compositions merely occupied the leisure time which he could -withhold from the controversy on the solar spots to which we have -already alluded. A German Jesuit named Christopher Scheiner, who was -professor of mathematics at Ingolstadt, in imitation of Galileo had -commenced a series of observations on them, but adopted the theory -which, as we have seen, Galileo had examined and rejected, that these -spots are planets circulating at some distance from the body of the sun. -The same opinion had been taken up by a French astronomer, who in honour -of the reigning family called them Borbonian stars. Scheiner promulgated -his notions in three letters, addressed to their common friend Welser, -under the quaint signature of "_Apelles latens post tabulam_." Galileo -replied to Scheiner's letters by three others, also addressed to Welser, -and although the dispute was carried on amid mutual professions of -respect and esteem, it laid the foundation of the total estrangement -which afterwards took place between the two authors. Galileo's part of -this controversy was published at Rome by the Lyncean Academy in 1613. -To the last of his letters, written in December, 1612, is annexed a -table of the expected positions of Jupiter's satellites during the -months of March and April of the following year, which, imperfect as it -necessarily was, cannot be looked upon without the greatest interest. - -In the same letter it is mentioned that Saturn presented a novel -appearance, which, for an instant, almost induced Galileo to mistrust -the accuracy of his earlier observations. The lateral appendages of this -planet had disappeared, and the accompanying extract will show the -uneasiness which Galileo could not conceal at the sight of this -phenomenon, although it is admirable to see the contempt with which, -even in that trying moment, he expresses his consciousness that his -adversaries were unworthy of the triumph they appeared on the point of -celebrating.--"Looking on Saturn within these few days, I found it -solitary, without the assistance of its accustomed stars, and in short, -perfectly round and defined like Jupiter, and such it still remains. Now -what can be said of so strange a metamorphosis? are perhaps the two -smaller stars consumed, like the spots on the sun? have they suddenly -vanished and fled? or has Saturn devoured his own children? or was the -appearance indeed fraud and illusion, with which the glasses have for so -long a time mocked me, and so many others who have often observed with -me. Now perhaps the time is come to revive the withering hopes of those, -who, guided by more profound contemplations, have fathomed all the -fallacies of the new observations and recognised their impossibility! I -cannot resolve what to say in a chance so strange, so new, and so -unexpected; the shortness of the time, the unexampled occurrence, the -weakness of my intellect, and the terror of being mistaken, have greatly -confounded me." These first expressions of alarm are not to be wondered -at; however, he soon recovered courage, and ventured to foretel the -periods at which the lateral stars would again show themselves, -protesting at the same time, that he was in no respect to be understood -as classing this prediction among the results which depend on certain -principles and sound conclusions, but merely on some conjectures which -appeared to him probable. From one of the Dialogues on the System, we -learn that this conjecture was, that Saturn might revolve upon his axis, -but the period which he assumed is very different from the true one, as -might be expected from its being intended to account for a phenomenon of -which Galileo had not rightly apprehended the character. - -He closed this letter with renewed professions of courtesy and -friendship towards Apelles, enjoining Welser not to communicate it -without adding his excuses, if he should be thought to dissent too -violently from his antagonist's ideas, declaring that his only object -was the discovery of truth, and that he had freely exposed his own -opinion, which he was still ready to change, so soon as his errors -should be made manifest to him; and that he would consider himself -under special obligation to any one who would be kind enough to discover -and correct them. These letters were written from the villa of his -friend Salviati at Selve near Florence, where he passed great part of -his time, particularly during his frequent indispositions, conceiving -that the air of Florence was prejudicial to him. Cesi was very anxious -for their appearance, since they were (in his own words) so hard a -morsel for the teeth of the Peripatetics, and he exhorted Galileo, in -the name of the society, "to continue to give them, and the nameless -Jesuit, something to gnaw." - - -FOOTNOTES: - -[67] Aimoini Hist. Francorum. Parisiis. 1567. - -[68] Mercurius in sole visus. 1609. - -[69] De Coelo. lib. 4. - -[70] For a discussion of this singular phenomenon, _see_ Treatise on -Heat, p. 12; and it is worth while to remark in passing, what an -admirable instance it affords of Galileo's instantaneous abandonment of -a theory so soon as it became inconsistent with experiment. - -[71] Ebony is one of the few woods heavier than water. _See_ Treatise on -Hydrostatics. - -[72] In making this very beautiful experiment, it is best to keep the -glass a few seconds in the water, to give time for the surface of the -ball to dry. It will also succeed with a light needle, if carefully -conducted. - -[73] Nelli. Saggio di Stor. Liter. Fiorent. - - - - -CHAPTER XI. - - _Letter to Christina, Arch-Duchess of Tuscany--Caccini--Galileo - revisits Rome--Inchoffer--Problem of Longitudes._ - - -THE uncompromising boldness with which Galileo published and supported -his opinions, with little regard to the power and authority of those who -advocated the contrary doctrines, had raised against him a host of -enemies, who each had objections to him peculiar to themselves, but who -now began to perceive the policy of uniting their strength in the common -cause, to crush if possible so dangerous an innovator. All the -professors of the old opinions, who suddenly found the knowledge on -which their reputation was founded struck from under them, and who could -not reconcile themselves to their new situation of learners, were united -against him; and to this powerful cabal was now added the still greater -influence of the jesuits and pseudo-theological party, who fancied they -saw in the spirit of Galileo's writings the same inquisitive temper -which they had already found so inconvenient in Luther and his -adherents. The alarm became greater every day, inasmuch as Galileo had -succeeded in training round him a numerous band of followers who all -appeared imbued with the same dangerous spirit of innovation, and his -favourite scholars were successful candidates for professorships in many -of the most celebrated universities of Italy. - -At the close of 1613, Galileo addressed a letter to his pupil, the Abbe -Castelli, in which he endeavoured to shew that there is as much -difficulty in reconciling the Ptolemaic as the Copernican system of the -world with the astronomical expressions contained in the Scriptures, and -asserted, that the object of the Scriptures not being to teach -astronomy, such expressions are there used as would be intelligible and -conformable to the vulgar belief, without regard to the true structure -of the universe; which argument he afterwards amplified in a letter -addressed to Christina, Grand Duchess of Tuscany, the mother of his -patron Cosmo. He discourses on this subject with the moderation and good -sense which so peculiarly characterized him. "I am," says he, "inclined -to believe, that the intention of the sacred Scriptures is to give to -mankind the information necessary for their salvation, and which, -surpassing all human knowledge, can by no other means be accredited than -by the mouth of the Holy Spirit. But I do not hold it necessary to -believe, that the same God who has endowed us with senses, with speech, -and intellect, intended that we should neglect the use of these, and -seek by other means for knowledge which they are sufficient to procure -us; especially in a science like astronomy, of which so little notice is -taken in the Scriptures, that none of the planets, except the sun and -moon, and, once or twice only, Venus under the name of Lucifer, are so -much as named there. This therefore being granted, methinks that in the -discussion of natural problems we ought not to begin at the authority of -texts of Scripture, but at sensible experiments and necessary -demonstrations: for, from the divine word, the sacred Scripture and -nature did both alike proceed, and I conceive that, concerning natural -effects, that which either sensible experience sets before our eyes, or -necessary demonstrations do prove unto us, ought not upon any account to -be called into question, much less condemned, upon the testimony of -Scriptural texts, which may under their words couch senses seemingly -contrary thereto. - -"Again, to command the very professors of astronomy that they of -themselves see to the confuting of their own observations and -demonstrations, is to enjoin a thing beyond all possibility of doing; -for it is not only to command them not to see that which they do see, -and not to understand that which they do understand, but it is to order -them to seek for and to find the contrary of that which they happen to -meet with. I would entreat these wise and prudent fathers, that they -would with all diligence consider the difference that is between -opinionative and demonstrative doctrines: to the end that well weighing -in their minds with what force necessary inferences urge us, they might -the better assure themselves that it is not in the power of the -professors of demonstrative sciences to change their opinions at -pleasure, and adopt first one side and then another; and that there is a -great difference between commanding a mathematician or a philosopher, -and the disposing of a lawyer or a merchant; and that the demonstrated -conclusions touching the things of nature and of the heavens cannot be -changed with the same facility as the opinions are touching what is -lawful or not in a contract, bargain, or bill of exchange. Therefore, -first let these men apply themselves to examine the arguments of -Copernicus and others, and leave the condemning of them as erroneous and -heretical to whom it belongeth; yet let them not hope to find such rash -and precipitous determinations in the wary and holy fathers, or in the -absolute wisdom of him who cannot err, as those into which they suffer -themselves to be hurried by some particular affection or interest of -their own. In these and such other positions, which are not directly -articles of faith, certainly no man doubts but His Holiness hath always -an absolute power of admitting or condemning them, but it is not in the -power of any creature to make them to be true or false, otherwise than -of their own nature, and in fact they are." We have been more particular -in extracting these passages, because it has been advanced by a writer -of high reputation, that the treatment which Galileo subsequently -experienced was solely in consequence of his persisting in the endeavour -to prove that the Scriptures were reconcileable with the Copernican -theory[74], whereas we see here distinctly that, for the reasons we have -briefly stated, he regarded this as a matter altogether indifferent and -beside the question. - -Galileo had not entered upon this discussion till driven to it by a most -indecent attack, made on him from the pulpit, by a Dominican friar named -Caccini, who thought it not unbecoming his habit or religion to play -upon the words of a Scriptural text for the purpose of attacking Galileo -and his partisans with more personality.[75] Galileo complained formally -of Caccini's conduct to Luigi Maraffi the general of the Dominicans, who -apologised amply to him, adding that he himself was to be pitied for -finding himself implicated in all the brutal conduct of thirty or forty -thousand monks. - -In the mean time, the inquisitors at Rome had taken the alarm, and were -already, in 1615, busily employed in collecting evidence against -Galileo. Lorini, a brother Dominican of Caccini, had given them notice -of the letter to Castelli of which we have spoken, and the utmost -address was employed to get the original into their hands, which attempt -however was frustrated, as Castelli had returned it to the writer. -Caccini was sent for to Rome, settled there with the title of Master of -the Convent of St. Mary of Minerva, and employed to put the depositions -against Galileo into order. Galileo was not at this time fully aware of -the machinations against him, but suspecting something of their nature, -he solicited and obtained permission from Cosmo, towards the end of -1615, to make a journey to Rome, for the purpose of more directly -confronting his enemies in that city. There was a rumour at the time -that this visit was not voluntary, but that Galileo had been cited to -appear at Rome. A contemporary declares that he heard this from Galileo -himself: at any rate, in a letter which Galileo shortly afterwards wrote -to Picchena, the Grand Duke's secretary, he expresses himself well -satisfied with the results of this step, whether forced or not, and -Querenghi thus describes to the Cardinal d'Este the public effect of his -appearance: "Your Eminence would be delighted with Galileo if you heard -him holding forth, as he often does, in the midst of fifteen or twenty, -all violently attacking him, sometimes in one house, sometimes in -another. But he is armed after such fashion that he laughs all of them -to scorn--and even if the novelty of his opinions prevents entire -persuasion, at least he convicts of emptiness most of the arguments with -which his adversaries endeavour to overwhelm him. He was particularly -admirable on Monday last, in the house of Signor Frederico Ghisilieri; -and what especially pleased me was, that before replying to the contrary -arguments, he amplified and enforced them with new grounds of great -plausibility, so as to leave his adversaries in a more ridiculous plight -when he afterwards overturned them all." - -Among the malicious stories which were put into circulation, it had been -said, that the Grand Duke had withdrawn his favour, which emboldened -many, who would not otherwise have ventured on such open opposition, to -declare against Galileo. His appearance at Rome, where he was lodged in -the palace of Cosmo's ambassador, and whence he kept up a close -correspondence with the Grand Duke's family, put an immediate stop to -rumours of this kind. In little more than a month he was apparently -triumphant, so far as regarded himself; but the question now began to be -agitated whether the whole system of Copernicus ought not to be -condemned as impious and heretical. Galileo again writes to Picchena, -"so far as concerns the clearing of my own character, I might return -home immediately; but although this new question regards me no more than -all those who for the last eighty years have supported these opinions -both in public and private, yet, as perhaps I may be of some assistance -in that part of the discussion which depends on the knowledge of truths -ascertained by means of the sciences which I profess, I, as a zealous -and Catholic Christian, neither can nor ought to withhold that -assistance which my knowledge affords; and this business keeps me -sufficiently employed." De Lambre, whose readiness to depreciate -Galileo's merit we have already noticed and lamented, sneeringly and -ungratefully remarks on this part of his life, that "it was scarcely -worth while to compromise his tranquillity and reputation, in order to -become the champion of a truth which could not fail every day to acquire -new partisans by the natural effect of the progress of enlightened -opinions." We need not stop to consider what the natural effects might -have been if none had at any time been found who thought their -tranquillity worthily offered up in such a cause. - -It has been hinted by several, and is indeed probable, that Galileo's -stay at Rome rather injured the cause (so far as provoking the -inquisitorial censures could injure it) which it was his earnest desire -to serve, for we cannot often enough repeat the assertion, that it was -not the doctrine itself, so much as the free, unyielding manner in which -it was supported, which was originally obnoxious. Copernicus had been -allowed to dedicate his great work to Pope Paul III., and from the time -of its first appearance under that sanction in 1543, to the year 1616, -of which we are now writing, this theory was left in the hands of -mathematicians and philosophers, who alternately attacked and defended -it without receiving either support or molestation from ecclesiastical -decrees. But this was henceforward no longer the case, and a higher -degree of importance was given to the controversy from the religious -heresies which were asserted to be involved in the new opinions. We have -already given specimens of the so called philosophical arguments brought -against Copernicus; and the reader may be curious to know the form of -the theological ones. Those which we select are taken from a work, which -indeed did not come forth till the time of Galileo's third visit to -Rome, but it is relative to the matter now before us, as it professed to -be, and its author's party affected to consider it, a complete -refutation of the letters to Castelli and the Archduchess Christina.[76] - -It was the work of a Jesuit, Melchior Inchoffer, and it was greatly -extolled by his companions, "as differing so entirely from the pruriency -of the Pythagorean writings." He quotes with approbation an author who, -first referring to the first verse of Genesis for an argument that the -earth was not created till after the heavens, observes that the whole -question is thus reduced to the examination of this purely geometrical -difficulty--In the formation of a sphere, does the centre or -circumference first come into existence? If the latter (which we presume -Melchior's friend found good reason for deciding upon), the consequence -is inevitable. The earth is in the centre of the universe. - -It may not be unprofitable to contrast the extracts which we have given -from Galileo's letters on the same subject with the following passage, -which appears one of the most subtle and argumentative which is to be -found in Melchior's book. He _professes_ to be enumerating and refuting -the principal arguments which the Copernicans adduced for the motion of -the earth. "Fifth argument. Hell is in the centre of the earth, and in -it is a fire tormenting the damned; therefore it is absolutely necessary -that the earth is moveable. The antecedent is plain." (Inchoffer then -quotes a number of texts of Scripture on which, according to him, the -Copernicans relied in proof of this part of the argument.) "The -consequent is proved: because fire is the cause of motion, for which -reason Pythagoras, who, as Aristotle reports, puts the place of -punishment in the centre, perceived that the earth is animate and -endowed with action. I answer, even allowing that hell is in the centre -of the earth, and a fire in it, I deny the consequence: and for proof I -say, if the argument is worth any thing, it proves also that lime-kilns, -ovens, and fire-grates are animated and spontaneously moveable. I say, -_even allowing_ that hell is in the centre of the earth: for Gregory, -book 4, dial. chap. 42, says, that he dare not decide rashly on this -matter, although he thinks more probable the opinion of those who say -that it is under the earth. St. Thomas, in Opusc. 10, art. 31, says: -Where hell is, whether in the centre of the earth or at the surface, -does not in my opinion, relate to any article of faith; and it is -superfluous to be solicitous about such things, either in asserting or -denying them. And Opusc. 11, art. 24, he says, that it seems to him that -nothing should be rashly asserted on this matter, particularly as -Augustin thinks that nobody knows where it is; but I do not, says he, -think that it is in the centre of the earth. I should be loth, however, -that it should be hence inferred by _some people_ that hell is in the -earth, that we are ignorant where hell is, and therefore that the -situation of the earth is also unknown, and, in conclusion, that it -cannot therefore be the centre of the universe. The argument shall be -retorted in another fashion: for if the place of the earth is unknown, -it cannot be said to be in a great circle, so as to be moved round the -sun. Finally I say that in fact it is known where the earth is." - -It is not impossible that some persons adopted the Copernican theory, -from an affectation of singularity and freethinking, without being able -to give very sound reasons for their change of opinion, of whom we have -an instance in Origanus, the astrological instructor of Wallenstein's -famous attendant Seni, who edited his work. His arguments in favour of -the earth's motion are quite on a level with those advanced on the -opposite side in favour of its immobility; but we have not found any -traces whatever of such absurdities as these having been urged by any of -the leaders of that party, and it is far more probable that they are the -creatures of Melchior's own imagination. At any rate it is worth -remarking how completely he disregards the real physical arguments, -which he ought, in justice to his cause, to have attempted to -controvert. His book was aimed at Galileo and his adherents, and it is -scarcely possible that he could seriously persuade himself that he was -stating and overturning arguments similar to those by which Galileo had -made so many converts to the opinions of Copernicus. Whatever may be our -judgment of his candour, we may at least feel assured that if this had -indeed been a fair specimen of Galileo's philosophy, he might to the end -of his life have taught that the earth moved round the sun, or if his -fancy led him to a different hypothesis, he might like the Abbe Baliani -have sent the earth spinning round the stationary moon, and like him -have remained unmolested by pontifical censures. It is true that Baliani -owned his opinion to be much shaken, on observing it to be opposed to -the decree of those in whose hands was placed the power of judging -articles of faith. But Galileo's uncompromising spirit of analytical -investigation, and the sober but invincible force of reasoning with -which he beat down every sophism opposed to him, the instruments with -which he worked, were more odious than the work itself, and the -condemnation which he had vainly hoped to avert was probably on his very -account accelerated. - -Galileo, according to his own story, had in March 1616 a most gracious -audience of the pope, Paul V., which lasted for nearly an hour, at the -end of which his holiness assured him, that the Congregation were no -longer in a humour to listen lightly to calumnies against him, and that -so long as he occupied the papal chair, Galileo might think himself out -of all danger. But nevertheless he was not allowed to return home, -without receiving formal notice not to teach the opinions of -Copernicus, that the sun is in the centre of the system, and that the -earth moves about it, from that time forward, in any manner. That these -were the literal orders given to Galileo will be presently proved from -the recital of them in the famous decree against him, seventeen years -later. For the present, his letters which we have mentioned, as well as -one of a similar tendency by Foscarini, a Carmelite friar--a commentary -on the book of Joshua by a Spaniard named Diego Zuniga--Kepler's Epitome -of the Copernican Theory--and Copernicus's own work, were inserted in -the list of forbidden books, nor was it till four years afterwards, in -1620, that, on reconsideration, Copernicus was allowed to be read with -certain omissions and alterations then decided upon. - -Galileo quitted Rome scarcely able to conceal his contempt and -indignation. Two years afterwards this spirit had but little subsided, -for in forwarding to the Archduke Leopold his Theory of the Tides, he -accompanied it with the following remarks:--"This theory occurred to me -when in Rome, whilst the theologians were debating on the prohibition of -Copernicus's book, and of the opinion maintained in it of the motion of -the earth, which I at that time believed; until it pleased those -gentlemen to suspend the book, and declare the opinion false and -repugnant to the Holy Scriptures. Now, as I know how well it becomes me -to obey and believe the decisions of my superiors, which proceed out of -more profound knowledge than the weakness of my intellect can attain to, -this theory which I send you, which is founded on the motion of the -earth, I now look upon as a fiction and a dream, and beg your highness -to receive it as such. But, as poets often learn to prize the creations -of their fancy, so, in like manner, do I set some value on this -absurdity of mine. It is true that when I sketched this little work, I -did hope that Copernicus would not, after 80 years, be convicted of -error, and I had intended to develope and amplify it farther, but a -voice from heaven suddenly awakened me, and at once annihilated all my -confused and entangled fancies." - -It might have been predicted, from the tone of this letter alone, that -it would not be long before Galileo would again bring himself under the -censuring notice of the astronomical hierarchy, and indeed he had, so -early as 1610, collected some of the materials for the work which caused -the final explosion, and on which he now employed himself with as little -intermission as the weak state of his health permitted. - -He had been before this time engaged in a correspondence with the court -of Spain, on the method of observing longitudes at sea, for the solution -of which important problem Philip III. had offered a considerable -reward, an example which has since been followed in our own and other -countries. Galileo had no sooner discovered Jupiter's satellites, than -he recognized the use which might be made of them for that purpose, and -devoted himself with peculiar assiduity to acquiring as perfect a -knowledge as possible of their revolutions. The reader will easily -understand how they were to be used, if their motion could be so well -ascertained as to enable Galileo at Florence to predict the exact times -at which any remarkable configurations would occur, as, for instance, -the times at which any one of them would be eclipsed by Jupiter. A -mariner who in the middle of the Atlantic should observe the same -eclipse, and compare the time of night at which he made the observation -(which he might know by setting his watch by the sun on the preceding -day) with the time mentioned in the predictions, would, from the -difference between the two, learn the difference between the hour at -Florence and the hour at the place where the ship at that time happened -to be. As the earth turns uniformly round through 360 deg. of longitude in -24 hours, that is, through 15 deg. in each hour, the hours, minutes, and -seconds of time which express this difference must be multiplied by 15, -and the respective products will give the degrees, minutes, and seconds -of longitude, by which the ship was then distant from Florence. This -statement is merely intended to give those who are unacquainted with -astronomy, a general idea of the manner in which it was proposed to use -these satellites. Our moon had already been occasionally employed in the -same way, but the comparative frequency of the eclipses of Jupiter's -moons, and the suddenness with which they disappear, gives a decided -advantage to the new method. Both methods were embarrassed by the -difficulty of observing the eclipses at sea. In addition to this, it was -requisite, in both methods, that the sailors should be provided with -accurate means of knowing the hour, wherever they might chance to be, -which was far from being the case, for although (in order not to -interrupt the explanation) we have above spoken of their _watches_, yet -the watches and clocks of that day were not such as could be relied on -sufficiently, during the interval which must necessarily occur between -the two observations. This consideration led Galileo to reflect on the -use which might be made of his pendulum for this purpose; and, with -respect to the other difficulty, he contrived a peculiar kind of -telescope, with which he flattered himself, somewhat prematurely, that -it would be as easy to observe on ship-board as on shore. - -During his stay at Rome, in 1615, and the following year, he disclosed -some of these ideas to the Conte di Lemos, the viceroy of Naples, who -had been president of the council of the Spanish Indies, and was fully -aware of the importance of the matter. Galileo was in consequence -invited to communicate directly with the Duke of Lerma, the Spanish -minister, and instructions were accordingly sent by Cosmo, to the Conte -Orso d'Elci, his ambassador at Madrid, to conduct the business there. -Galileo entered warmly into the design, of which he had no other means -of verifying the practicability; for as he says in one of his letters to -Spain--"Your excellency may well believe that if this were an -undertaking which I could conclude by myself, I would never have gone -about begging favours from others; but in my study there are neither -seas, nor Indies, nor islands, nor ports, nor shoals, nor ships, for -which reason I am compelled to share the enterprise with great -personages, and to fatigue myself to procure the acceptance of that, -which ought with eagerness to be asked of me; but I console myself with -the reflection that I am not singular in this, but that it commonly -happens, with the exception of a little reputation, and that too often -obscured and blackened by envy, that the least part of the advantage -falls to the share of the inventors of things, which afterwards bring -great gain, honours, and riches to others; so that I will never cease on -my part to do every thing in my power, and I am ready to leave here all -my comforts, my country, my friends, and family, and to cross over into -Spain, to stay as long as I may be wanted in Seville, or Lisbon, or -wherever it may be convenient, to implant the knowledge of this method, -provided that due assistance and diligence be not wanting on the part of -those who are to receive it, and who should solicit and foster it." But -he could not, with all his enthusiasm, rouse the attention of the -Spanish court. The negotiation languished, and although occasionally -renewed during the next ten or twelve years, was never brought to a -satisfactory issue. Some explanation of this otherwise unaccountable -apathy of the Spanish court, with regard to the solution of a problem -which they had certainly much at heart, is given in Nelli's life of -Galileo; where it is asserted, on the authority of the Florentine -records, that Cosmo required privately from Spain, (in return for the -permission granted for Galileo to leave Florence, in pursuance of this -design,) the privilege of sending every year from Leghorn two -merchantmen, duty free, to the Spanish Indies. - - -FOOTNOTES: - -[74] Ce philosophe (Galilee) ne fut point persecute comme bon astronome, -mais comme mauvais theologien. C'est son entetement a vouloir concilier -la Bible avec Copernic qui lui donna des juges. Mais vingt auteurs, -surtout parmi les protestans, ont ecrit que Galilee fut persecute et -imprisonne pour avoir soutenu que la terre tourne autour du soleil, que -ce systeme a ete condanne par l'inquisition comme faux, errone et -contraire a la Bible, &c.--Bergier, Encyclopedie Methodique, Paris, -1790, Art. SCIENCES HUMAINES. - -[75] Viri Galilaei, quid statis adspicientes in coelum. _Acts_ I. 11. - -[76] Tractatus Syllepticus. Romae, 1633. The title-page of this -remarkable production is decorated with an emblematical figure, -representing the earth included in a triangle; and in the three corners, -grasping the globe with their fore feet, are placed three bees, the arms -of Pope Urban VIII. who condemned Galileo and his writings. The motto is -"_His fixa quiescit_," "Fixed by these it is at rest." - - - - -CHAPTER XII. - - _Controversy on Comets--Saggiatore--Galileo's reception by Urban - VIII--His family._ - - -THE year 1618 was remarkable for the appearance of three comets, on -which almost every astronomer in Europe found something to say and -write. Galileo published some of his opinions with respect to them, -through the medium of Mario Guiducci. This astronomer delivered a -lecture before the Florentine academy, the heads of which he was -supposed to have received from Galileo, who, during the whole time of -the appearance of these comets, was confined to his bed by severe -illness. This essay was printed in Florence _at the sign of The Medicean -Stars_.[77] What principally deserves notice in it, is the opinion of -Galileo, that the distance of a comet cannot be safely determined by its -parallax, from which we learn that he inclined to believe that comets -are nothing but meteors occasionally appearing in the atmosphere, like -rainbows, parhelia, and similar phenomena. He points out the difference -in this respect between a fixed object, the distance of which may be -calculated from the difference of direction in which two observers (at a -known distance from each other) are obliged to turn themselves in order -to see it, and meteors like the rainbow, which are simultaneously formed -in different drops of water for each spectator, so that two observers -in different places are in fact contemplating different objects. He then -warns astronomers not to engage with too much warmth in a discussion on -the distance of comets before they assure themselves to which of these -two classes of phenomena they are to be referred. The remark is in -itself perfectly just, although the opinion which occasioned it is now -as certainly known to be erroneous, but it is questionable whether the -observations which, up to that time, had been made upon comets, were -sufficient, either in number or quality, to justify the censure which -has been cast on Galileo for his opinion. The theory, moreover, is -merely introduced as an hypothesis in Guiducci's essay. The same opinion -was for a short time embraced by Cassini, a celebrated Italian -astronomer, invited by Louis XIV. to the Observatory at Paris, when the -science was considerably more advanced, and Newton, in his _Principia_, -did not think it unworthy of him to show on what grounds it is -untenable. - -Galileo was become the object of animosity in so many quarters that none -of his published opinions, whether correct or incorrect, ever wanted a -ready antagonist. The champion on the present occasion was again a -Jesuit; his name was Oratio Grassi, who published _The Astronomical and -Philosophical Balance_, under the disguised signature of Lotario Sarsi. - -Galileo and his friends were anxious that his reply to Grassi should -appear as quickly as possible, but his health had become so precarious -and his frequent illnesses occasioned so many interruptions, that it was -not until the autumn of 1623 that Il Saggiatore (or The Assayer) as he -called his answer, was ready for publication. This was printed by the -Lyncean Academy, and as Cardinal Maffeo Barberino, who had just been -elected Pope, (with the title of Urban VIII.) had been closely connected -with that society, and was also a personal friend of Cesi and of -Galileo, it was thought a prudent precaution to dedicate the pamphlet to -him. This essay enjoys a peculiar reputation among Galileo's works, not -only for the matter contained in it, but also for the style in which it -is written; insomuch that Andres[78], when eulogizing Galileo as one of -the earliest who adorned philosophical truths with the graces and -ornaments of language, expressly instances the Saggiatore, which is also -quoted by Frisi and Algarotti, as a perfect model of this sort of -composition. In the latter particular, it is unsafe to interfere with -the decisions of an Italian critic; but with respect to its substance, -this famous composition scarcely appears to deserve its preeminent -reputation. It is a prolix and rather tedious examination of Grassi's -Essay; nor do the arguments seem so satisfactory, nor the reasonings so -compact as is generally the case in Galileo's other writings. It does -however, like all his other works, contain many very remarkable -passages, and the celebrity of this production requires that we should -extract one or two of the most characteristic. - -The first, though a very short one, will serve to shew the tone which -Galileo had taken with respect to the Copernican system since its -condemnation at Rome, in 1616. "In conclusion, since the motion -attributed to the earth, which I, as a pious and Catholic person, -consider most false, and not to exist, accommodates itself so well to -explain so many and such different phenomena, I shall not feel sure, -unless Sarsi descends to more distinct considerations than those which -he has yet produced, that, false as it is, it may not just as deludingly -correspond with the phenomena of comets." - -Sarsi had quoted a story from Suidas in support of his argument that -motion always produces heat, how the Babylonians used to cook their eggs -by whirling them in a sling; to which Galileo replies: "I cannot refrain -from marvelling that Sarsi will persist in proving to me, by -authorities, that which at any moment I can bring to the test of -experiment. We examine witnesses in things which are doubtful, past, and -not permanent, but not in those things which are done in our own -presence. If discussing a difficult problem were like carrying a weight, -since several horses will carry more sacks of corn than one alone will, -I would agree that many reasoners avail more than one; but _discoursing_ -is like _coursing_, and not like carrying, and one barb by himself will -run farther than a hundred Friesland horses. When Sarsi brings up such a -multitude of authors, it does not seem to me that he in the least degree -strengthens his own conclusions, but he ennobles the cause of Signor -Mario and myself, by shewing that we reason better than many men of -established reputation. If Sarsi insists that I believe, on Suidas' -credit, that the Babylonians cooked eggs by swiftly whirling them in a -sling, I will believe it; but I must needs say, that the cause of such -an effect is very remote from that to which it is attributed, and to -find the true cause I shall reason thus. If an effect does not follow -with us which followed with others at another time, it is because, in -our experiment, something is wanting which was the cause of the former -success; and if only one thing is wanting to us, that one thing is the -true cause. Now we have eggs, and slings, and strong men to whirl them, -and yet they will not become cooked; nay, if they were hot at first, -they more quickly become cold: and since nothing is wanting to us but to -be Babylonians, it follows that being Babylonians is the true cause why -the eggs became hard, and not the friction of the air, which is what I -wished to prove.--Is it possible that in travelling post, Sarsi has -never noticed what freshness is occasioned on the face by the continual -change of air? and if he has felt it, will he rather trust the relation -by others, of what was done two thousand years ago at Babylon, than what -he can at this moment verify in his own person? I at least will not be -so wilfully wrong, and so ungrateful to nature and to God, that having -been gifted with sense and language, I should voluntarily set less value -on such great endowments than on the fallacies of a fellow man, and -blindly and blunderingly believe whatever I hear, and barter the freedom -of my intellect for slavery to one as liable to error as myself." - -Our final extract shall exhibit a sample of Galileo's metaphysics, in -which may be observed the germ of a theory very closely allied to that -which was afterwards developed by Locke and Berkeley.--"I have now only -to fulfil my promise of declaring my opinions on the proposition that -motion is the cause of heat, and to explain in what manner it appears to -me that it may be true. But I must first make some remarks on that which -we call heat, since I strongly suspect that a notion of it prevails -which is very remote from the truth; for it is believed that there is a -true accident, affection, and quality, really inherent in the substance -by which we feel ourselves heated. This much I have to say, that so soon -as I conceive a material or corporeal substance, I simultaneously feel -the necessity of conceiving that it has its boundaries, and is of some -shape or other; that, relatively to others, it is great or small; that -it is in this or that place, in this or that time; that it is in motion, -or at rest; that it touches, or does not touch another body; that it is -unique, rare, or common; nor can I, by any act of the imagination, -disjoin it from these qualities: but I do not find myself absolutely -compelled to apprehend it as necessarily accompanied by such conditions, -as that it must be white or red, bitter or sweet, sonorous or silent, -smelling sweetly or disagreeably; and if the senses had not pointed out -these qualities, it is probable that language and imagination alone -could never have arrived at them. Because, I am inclined to think that -these tastes, smells, colours, &c., with regard to the subject in which -they appear to reside, are nothing more than mere names, and exist only -in the sensitive body; insomuch that, when the living creature is -removed, all these qualities are carried off and annihilated; although -we have imposed particular names upon them, and different from those of -the other first and real accidents, and would fain persuade ourselves -that they are truly and in fact distinct. But I do not believe that -there exists any thing in external bodies for exciting tastes, smells, -and sounds, but size, shape, quantity, and motion, swift or slow; and if -ears, tongues, and noses were removed, I am of opinion that shape, -number, and motion would remain, but there would be an end of smells, -tastes, and sounds, which, abstractedly from the living creature, I take -to be mere words." - -In the spring following the publication of the "Saggiatore," that is to -say, about the time of Easter, in 1624, Galileo went a third time to -Rome to compliment Urban on his elevation to the pontifical chair. He -was obliged to make this journey in a litter; and it appears from his -letters that for some years he had been seldom able to bear any other -mode of conveyance. In such a state of health it seems unlikely that he -would have quitted home on a mere visit of ceremony, which suspicion is -strengthened by the beginning of a letter from him to Prince Cesi, dated -in October, 1623, in which he says: "I have received the very courteous -and prudent advice of your excellency about the time and manner of my -going to Rome, and shall act upon it; and I will visit you at Acqua -Sparta, that I may be completely informed of the actual state of things -at Rome." However this may be, nothing could be more gratifying than his -public reception there. His stay in Rome did not exceed two months, -(from the beginning of April till June,) and during that time he was -admitted to six long and satisfactory interviews with the Pope, and on -his departure received the promise of a pension for his son Vincenzo, -and was himself presented with "a fine painting, two medals, one of gold -and the other of silver, and a good quantity of agnus dei." He had also -much communication with several of the cardinals, one of whom, Cardinal -Hohenzoller, told him that he had represented to the pope on the subject -of Copernicus, that "all the heretics were of that opinion, and -considered it as undoubted; and that it would be necessary to be very -circumspect in coming to any resolution: to which his holiness replied, -that the church had not condemned it, nor was it to be condemned as -heretical, but only as rash; adding, that there was no fear of any one -undertaking to prove that it must necessarily be true." Urban also -addressed a letter to Ferdinand, who had succeeded his father Cosmo as -Grand Duke of Tuscany, expressly for the purpose of recommending Galileo -to him. "For We find in him not only literary distinction, but also the -love of piety, and he is strong in those qualities by which pontifical -good-will is easily obtained. And now, when he has been brought to this -city to congratulate Us on Our elevation, We have very lovingly embraced -him;--nor can We suffer him to return to the country whither your -liberality recalls him without an ample provision of pontifical love. -And that you may know how dear he is to Us, We have willed to give him -this honourable testimonial of virtue and piety. And We further signify -that every benefit which you shall confer upon him, imitating, or even -surpassing your father's liberality, will conduce to Our gratification." -Honoured with these unequivocal marks of approbation, Galileo returned -to Florence. - -His son Vincenzo is soon afterwards spoken of as being at Rome; and it -is not improbable that Galileo sent him thither on the appointment of -his friend and pupil, the Abbe Castelli, to be mathematician to the -pope. Vincenzo had been legitimated by an edict of Cosmo in 1619, and, -according to Nelli, married, in 1624, Sestilia, the daughter of Carlo -Bocchineri. There are no traces to be found of Vincenzo's mother after -1610, and perhaps she died about that time. Galileo's family by her -consisted of Vincenzo and two daughters, Julia and Polissena, who both -took the veil in the convent of Saint Matthew at Arcetri, under the -names of Sister Arcangiola and Sister Maria Celeste. The latter is said -to have possessed extraordinary talents. The date of Vincenzo's -marriage, as given by Nelli, appears somewhat inconsistent with the -correspondence between Galileo and Castelli, in which, so late as 1629, -Galileo is apparently writing of his son as a student under Castelli's -superintendence, and intimates the amount of pocket-money he can afford -to allow him, which he fixes at three crowns a month; adding, that "he -ought to be contented with as many crowns, as, at his age, I possessed -groats." Castelli had given but an unfavourable account of Vincenzo's -conduct, characterizing him as "dissolute, obstinate, and impudent;" in -consequence of which behaviour, Galileo seems to have thought that the -pension of sixty crowns, which had been granted by the pope, might be -turned to better account than by employing it on his son's education; -and accordingly in his reply he requested Castelli to dispose of it, -observing that the proceeds would be useful in assisting him to -discharge a great load of debt with which he found himself saddled on -account of his brother's family. Besides this pension, another of one -hundred crowns was in a few years granted by Urban to Galileo himself, -but it appears to have been very irregularly paid, if at all. - -About the same time Galileo found himself menaced either with the -deprivation of his stipend as extraordinary professor at Pisa, or with -the loss of that leisure which, on his removal to Florence, he had been -so anxious to secure. In 1629, the question was agitated by the party -opposed to him, whether it were in the power of the grand duke to assign -a pension out of the funds of the University, arising out of -ecclesiastical dues, to one who neither lectured nor resided there. This -scruple had slept during nineteen years which had elapsed since -Galileo's establishment in Florence, but probably those who now raised -it reckoned upon finding in Ferdinand II., then scarcely of age, a less -firm supporter of Galileo than his father Cosmo had been. But the matter -did not proceed so far; for, after full deliberation, the prevalent -opinion of the theologians and jurists who were consulted appeared to be -in favour of this exercise of prerogative, and accordingly Galileo -retained his stipend and privileges. - - -FOOTNOTES: - -[77] In Firenze nella Stamperia di Pietro Cecconcelli alle stelle -Medicee, 1619. - -[78] Dell'Origine d'ogni Literatura: Parma, 1787. - - - - -CHAPTER XIII. - - _Publication of Galileo's 'System of the World'--His Condemnation - and Abjuration._ - - -IN the year 1630, Galileo brought to its conclusion his great work, "The -Dialogue on the Ptolemaic and Copernican Systems," and began to take the -necessary steps for procuring permission to print it. This was to be -obtained in the first instance from an officer at Rome, entitled the -master of the sacred palace; and after a little negotiation Galileo -found it would be necessary for him again to return thither, as his -enemies were still busy in thwarting his views and wishes. Niccolo -Riccardi, who at that time filled the office of master of the palace, -had been a pupil of Galileo, and was well disposed to facilitate his -plans; he pointed out, however, some expressions in the work which he -thought it necessary to erase, and, with the understanding that this -should be done, he returned the manuscript to Galileo with his -subscribed approbation. The unhealthy season was drawing near, and -Galileo, unwilling to face it, returned home, where he intended to -complete the index and dedication, and then to send it back to Rome to -be printed in that city, under the superintendence of Federigo Cesi. -This plan was disconcerted by the premature death of that accomplished -nobleman, in August 1630, in whom Galileo lost one of his steadiest and -most effective friends and protectors. This unfortunate event determined -Galileo to attempt to procure permission to print his book at Florence. -A contagious disorder had broken out in Tuscany with such severity as -almost to interrupt all communication between Florence and Rome, and -this was urged by Galileo as an additional reason for granting his -request. Riccardi at first seemed inclined to insist that the book -should be sent to him a second time, but at last contented himself with -inspecting the commencement and conclusion, and consented that (on its -receiving also a license from the inquisitor-general at Florence, and -from one or two others whose names appear on the title-page) it might be -printed where Galileo wished. - -These protracted negotiations prevented the publication of the work till -late in 1632; it then appeared, with a dedication to Ferdinand, under -the following title:--"A Dialogue, by Galileo Galilei, Extraordinary -Mathematician of the University of Pisa, and Principal Philosopher and -Mathematician of the Most Serene Grand Duke of Tuscany; in which, in a -conversation of four days, are discussed the two principal Systems of -the World, the Ptolemaic and Copernican, indeterminately proposing the -Philosophical Arguments as well on one side as on the other." The -beginning of the introduction, which is addressed "To the discreet -Reader," is much too characteristic to be passed by without -notice.--"Some years ago, a salutary edict was promulgated at Rome, -which, in order to obviate the perilous scandals of the present age, -enjoined an opportune silence on the Pythagorean opinion of the earth's -motion. Some were not wanting, who rashly asserted that this decree -originated, not in a judicious examination, but in ill informed passion; -and complaints were heard that counsellors totally inexperienced in -astronomical observations ought not by hasty prohibitions to clip the -wings of speculative minds. My zeal could not keep silence when I heard -these rash lamentations, and I thought it proper, as being fully -informed with regard to that most prudent determination, to appear -publicly on the theatre of the world as a witness of the actual truth. I -happened at that time to be in Rome: I was admitted to the audiences, -and enjoyed the approbation of the most eminent prelates of that court, -nor did the publication of that decree occur without my receiving some -prior intimation of it.[79] Wherefore it is my intention in this present -work, to show to foreign nations that as much is known of this matter in -Italy, and particularly in Rome, as ultramontane diligence can ever have -formed any notion of, and collecting together all my own speculations on -the Copernican system, to give them to understand that the knowledge of -all these preceded the Roman censures, and that from this country -proceed not only dogmas for the salvation of the soul, but also -ingenious discoveries for the gratification of the understanding. With -this object, I have taken up in the Dialogue the Copernican side of the -question, treating it as a pure mathematical hypothesis; and -endeavouring in every artificial manner to represent it as having the -advantage, not over the opinion of the stability of the earth -absolutely, but according to the manner in which that opinion is -defended by some, who indeed profess to be Peripatetics, but retain only -the name, and are contented without improvement to worship shadows, not -philosophizing with their own reason, but only from the recollection of -four principles imperfectly understood."--This very flimsy veil could -scarcely blind any one as to Galileo's real views in composing this -work, nor does it seem probable that he framed it with any expectation -of appearing neutral in the discussion. It is more likely that he -flattered himself that, under the new government at Rome, he was not -likely to be molested on account of the personal prohibition which he -had received in 1616, "not to believe or teach the motion of the earth -in any manner," provided he kept himself within the letter of the limits -of the more public and general order, that the Copernican system was not -to be brought forward otherwise than as a mere mathematically -convenient, but in fact unreal supposition. So long as this decree -remained in force, a due regard to consistency would compel the Roman -Inquisitors to notice an unequivocal violation of it; and this is -probably what Urban had implied in the remark quoted by Hohenzoller to -Galileo.[80] There were not wanting circumstances which might compensate -for the loss of Cosmo and of Federigo Cesi; Cosmo had been succeeded by -his son, who, though he had not yet attained his father's energy, showed -himself as friendly as possible to Galileo. Cardinal Bellarmine, who had -been mainly instrumental in procuring the decree of 1616, was dead; -Urban on the contrary, who had been among the few Cardinals who then -opposed it as uncalled for and ill-advised, was now possessed of supreme -power, and his recent affability seemed to prove that the increased -difference in their stations had not caused him to forget their early -and long-continued intimacy. It is probable that Galileo would not have -found himself mistaken in this estimate of his position, but for an -unlucky circumstance, of which his enemies immediately saw the -importance, and which they were not slow in making available against -him. The dialogue of Galileo's work is conducted between three -personages;--Salviati and Sagredo, who were two noblemen, friends of -Galileo, and Simplicio, a name borrowed from a noted commentator upon -Aristotle, who wrote in the sixth century. Salviati is the principal -philosopher of the work; it is to him that the others apply for -solutions of their doubts and difficulties, and on him the principal -task falls of explaining the tenets of the Copernican theory. Sagredo is -only a half convert, but an acute and ingenious one; to him are allotted -the objections which seem to have some real difficulty in them, as well -as lively illustrations and digressions, which might have been thought -inconsistent with the gravity of Salviati's character. Simplicio, though -candid and modest, is of course a confirmed Ptolemaist and Aristotelian, -and is made to produce successively all the popular arguments of that -school in support of his master's system. Placed between the wit and the -philosopher, it may be guessed that his success is very indifferent, and -in fact he is alternately ridiculed and confuted at every turn. As -Galileo racked his memory and invention to leave unanswered no argument -which was or could be advanced against Copernicus, it unfortunately -happened, that he introduced some which Urban himself had urged upon him -in their former controversies on this subject; and Galileo's opponents -found means to make His Holiness believe that the character of Simplicio -had been sketched in personal derision of him. We do not think it -necessary to exonerate Galileo from this charge; the obvious folly of -such an useless piece of ingratitude speaks sufficiently for itself. But -self-love is easily irritated; and Urban, who aspired to a reputation -for literature and science, was peculiarly sensitive on this point. His -own expressions almost prove his belief that such had been Galileo's -design, and it seems to explain the otherwise inexplicable change which -took place in his conduct towards his old friend, on account of a book -which he had himself undertaken to examine, and of which he had -authorised the publication. - -One of the earliest notices of what was approaching, is found in the -dispatches, dated August 24, 1632, from Ferdinand's minister, Andrea -Cioli, to Francesco Nicolini, the Tuscan ambassador at the court of -Rome. - -"I have orders to signify to Your Excellency that His Highness remains -greatly astonished that a book, placed by the author himself in the -hands of the supreme authority in Rome, read and read again there most -attentively, and in which every thing, not only with the consent, but at -the request of the author, was amended, altered, added, or removed at -the will of his superiors, which was again subjected here to the same -examination, agreeably to orders from Rome, and which finally was -licensed both there and here, and here printed and published, should now -become an object of suspicion at the end of two years, and the author -and printer be prohibited from publishing any more."--In the sequel is -intimated Ferdinand's desire that the charges, of whatever nature they -might be, either against Galileo or his book, might be reduced to -writing and forwarded to Florence, that he might prepare for his -justification; but this reasonable demand was utterly disregarded. It -appears to have been owing to the mean subserviency of Cioli to the -court of Rome, that Ferdinand refrained from interfering more -strenuously to protect Galileo. Cioli's words are: "The Grand Duke is so -enraged with this business of Galileo, that I do not know what will be -done. I know, at least, that His Holiness shall have no reason to -complain of his ministers, or of their bad advice."[81] - -A letter from Galileo's Venetian friend Micanzio, dated about a month -later, is in rather a bolder and less formal style:--"The efforts of -your enemies to get your book prohibited will occasion no loss either to -your reputation, or to the intelligent part of the world. As to -posterity, this is just one of the surest ways to hand the book down to -them. But what a wretched set this must be to whom every good thing, and -all that is founded in nature, necessarily appears hostile and odious! -The world is not restricted to a single corner; you will see the book -printed in more places and languages than one; and just for this reason, -I wish they would prohibit all good books. My disgust arises from seeing -myself deprived of what I most desire of this sort, I mean your other -dialogues; and if, from this cause, I fail in having the pleasure of -seeing them, I shall devote to a hundred thousand devils these unnatural -and godless hypocrites." - -At the same time, Thomas Campanella, a monk, who had already -distinguished himself by an apology for Galileo (published in 1622), -wrote to him from Rome:--"I learn with the greatest disgust, that a -congregation of angry theologians is forming to condemn your Dialogues, -and that no single member of it has any knowledge of mathematics, or -familiarity with abstruse speculations. I should advise you to procure a -request from the Grand Duke that, among the Dominicans and Jesuits and -Theatins, and secular priests whom they are putting on this congregation -against your book, they should admit also Castelli and myself." It -appears, from subsequent letters both from Campanella and Castelli, that -the required letter was procured and sent to Rome, but it was not -thought prudent to irritate the opposite party by a request which it was -then clearly seen would have been made in vain. Not only were these -friends of Galileo not admitted to the congregation, but, upon some -pretext, Castelli was even sent away from Rome, as if Galileo's enemies -desired to have as few enlightened witnesses as possible of their -proceedings; and on the contrary, Scipio Chiaramonte, who had been long -known for one of the staunchest and most bigoted defenders of the old -system, and who, as Montucla says, seems to have spent a long life in -nothing but retarding, as far as he was able, the progress of discovery, -was summoned from Pisa to complete their number. From this period we -have a tolerably continuous account of the proceedings against Galileo -in the dispatches which Nicolini sent regularly to his court. It appears -from them that Nicolini had several interviews with the Pope, whom he -found highly incensed against Galileo, and in one of the earliest he -received an intimation to advise the Duke "not to engage himself in this -matter as he had done in the other business of Alidosi,[82] because he -would not get through it with honour." Finding Urban in this humour, -Nicolini thought it best to temporize, and to avoid the appearance of -any thing like direct opposition. On the 15th of September, probably as -soon as the first report on Galileo's book had been made, Nicolini -received a private notice from the Pope, "in especial token of the -esteem in which he held the Grand Duke," that he was unable to do less -than consign the work to the consideration of the Inquisition. Nicolini -was permitted to communicate this to the Grand Duke only, and both were -declared liable to "the usual censures" of the Inquisition in case of -divulging the secret. - -The next step was to summon Galileo to Rome, and the only answer -returned to all Nicolini's representations of his advanced age of -seventy years, the very infirm state of his health, and the discomforts -which he must necessarily suffer in such a journey, and in keeping -quarantine, was that he might come at leisure, and that the quarantine -should be relaxed as much as possible in his favour, but that it was -indispensably necessary that he should be personally examined before the -Inquisition at Rome. Accordingly, on the 14th of February, 1633, -Nicolini announces Galileo's arrival, and that he had officially -notified his presence to the Assessor and Commissary of the Holy Office. -Cardinal Barberino, Urban's nephew, who seems on the whole to have acted -a friendly part towards Galileo, intimated to him that his most prudent -course would be to keep himself as much at home and as quiet as -possible, and to refuse to see any but his most intimate friends. With -this advice, which was repeated to him from several quarters, Galileo -thought it best to comply, and kept himself entirely secluded in -Nicolini's palace, where he was as usual maintained at the expense of -the Grand Duke. Nelli quotes two letters, which passed between -Ferdinand's minister Cioli and Nicolini, in which the former intimated -that Galileo's expenses were to be defrayed only during the first month -of his residence at Rome. Nicolini returned a spirited answer, that in -that case, after the time specified, he should continue to treat him as -before at his own private cost. - -The permission to reside at the ambassador's palace whilst his cause was -pending, was granted and received as an extraordinary indulgence on the -part of the Inquisition, and indeed if we estimate the proceedings -throughout against Galileo by the usual practice of that detestable -tribunal, it will appear that he was treated with unusual consideration. -Even when it became necessary in the course of the inquiry to examine -him in person, which was in the beginning of April, although his removal -to the Holy Office was then insisted upon, yet he was not committed to -close or strictly solitary confinement. On the contrary, he was -honourably lodged in the apartments of the Fiscal of the Inquisition, -where he was allowed the attendance of his own servant, who was also -permitted to sleep in an adjoining room, and to come and go at pleasure. -His table was still furnished by Nicolini. But, notwithstanding the -distinction with which he was thus treated, Galileo was annoyed and -uneasy at being (though little more than nominally) within the walls of -the Inquisition. He became exceedingly anxious that the matter should be -brought to a conclusion, and a severe attack of his constitutional -complaints rendered him still more fretful and impatient. On the last -day of April, about ten days after his first examination, he was -unexpectedly permitted to return to Nicolini's house, although the -proceedings were yet far from being brought to a conclusion. Nicolini -attributes this favour to Cardinal Barberino, who, he says, liberated -Galileo on his own responsibility, in consideration of the enfeebled -state of his health. - -In the society of Nicolini and his family, Galileo recovered something -of his courage and ordinary cheerfulness, although his return appears to -have been permitted on express condition of a strict seclusion; for at -the latter end of May, Nicolini was obliged to apply for permission that -Galileo should take that exercise in the open air which was necessary -for his health; on which occasion he was permitted to go into the public -gardens in a half-closed carriage. - -On the evening of the 20th of June, rather more than four months after -Galileo's arrival in Rome, he was again summoned to the Holy Office, -whither he went the following morning; he was detained there during the -whole of that day, and on the next day was conducted in a penitential -dress[83] to the Convent of Minerva, where the Cardinals and Prelates, -his judges, were assembled for the purpose of passing judgment upon him, -by which this venerable old man was solemnly called upon to renounce and -abjure, as impious and heretical, the opinions which his whole existence -had been consecrated to form and strengthen. As we are not aware that -this remarkable record of intolerance and bigoted folly has ever been -printed entire in English, we subjoin a literal translation of the whole -sentence and abjuration. - - -_The Sentence of the Inquisition on Galileo._ - - "We, the undersigned, by the Grace of God, Cardinals of the Holy - Roman Church, Inquisitors General throughout the whole Christian - Republic, Special Deputies of the Holy Apostolical Chair against - heretical depravity, - - "Whereas you, Galileo, son of the late Vincenzo Galilei of Florence, - aged seventy years, were denounced in 1615 to this Holy Office, for - holding as true a false doctrine taught by many, namely, that the - sun is immoveable in the centre of the world, and that the earth - moves, and also with a diurnal motion; also, for having pupils whom - you instructed in the same opinions; also, for maintaining a - correspondence on the same with some German mathematicians; also for - publishing certain letters on the solar spots, in which you - developed the same doctrine as true; also, for answering the - objections which were continually produced from the Holy Scriptures, - by glozing the said Scriptures according to your own meaning; and - whereas thereupon was produced the copy of a writing, in form of a - letter, professedly written by you to a person formerly your pupil, - in which, following the hypotheses of Copernicus, you include - several propositions contrary to the true sense and authority of the - Holy Scripture: therefore this holy tribunal being desirous of - providing against the disorder and mischief which was thence - proceeding and increasing to the detriment of the holy faith, by the - desire of His Holiness, and of the Most Eminent Lords Cardinals of - this supreme and universal Inquisition, the two propositions of the - stability of the sun, and motion of the earth, were _qualified_ by - the _Theological Qualifiers_ as follows: - - "_1st. The proposition that the Sun is in the centre of the world - and immoveable from its place, is absurd, philosophically false, and - formally heretical; because it is expressly contrary to the Holy - Scripture._ - - "_2dly. The proposition that the Earth is not the centre of the - world, nor immoveable, but that it moves, and also with a diurnal - motion, is also absurd, philosophically false, and, theologically - considered, at least erroneous in faith._ - - "But whereas being pleased at that time to deal mildly with you, it - was decreed in the Holy Congregation, held before His Holiness on - the 25th day of February, 1616, that His Eminence the Lord Cardinal - Bellarmine should enjoin you to give up altogether the said false - doctrine; if you should refuse, that you should be ordered by the - Commissary of the Holy Office to relinquish it, not to teach it to - others, nor to defend it, nor ever mention it, and in default of - acquiescence that you should be imprisoned; and in execution of this - decree, on the following day at the palace, in presence of His - Eminence the said Lord Cardinal Bellarmine, after you had been - mildly admonished by the said Lord Cardinal, you were commanded by - the acting Commissary of the Holy Office, before a notary and - witnesses, to relinquish altogether the said false opinion, and in - future neither to defend nor teach it in any manner, neither - verbally nor in writing, and upon your promising obedience you were - dismissed. - - "And in order that so pernicious a doctrine might be altogether - rooted out, nor insinuate itself farther to the heavy detriment of - the Catholic truth, a decree emanated from the Holy Congregation of - the Index[84] prohibiting the books which treat of this doctrine; - and it was declared false, and altogether contrary to the Holy and - Divine Scripture. - - "And whereas a book has since appeared, published at Florence last - year, the title of which shewed that you were the author, which - title is: _The Dialogue of Galileo Galilei, on the two principal - systems of the world, the Ptolemaic and Copernican_; and whereas the - Holy Congregation has heard that, in consequence of the printing of - the said book, the false opinion of the earth's motion and stability - of the sun is daily gaining ground; the said book has been taken - into careful consideration, and in it has been detected a glaring - violation of the said order, which had been intimated to you; - inasmuch as in this book you have defended the said opinion, - already and in your presence condemned; although in the said book - you labour with many circumlocutions to induce the belief that it is - left by you undecided, and in express terms probable: which is - equally a very grave error, since an opinion can in no way be - probable which has been already declared and finally determined - contrary to the divine Scripture. Therefore by Our order you have - been cited to this Holy Office, where, on your examination upon - oath, you have acknowledged the said book as written and printed by - you. You also confessed that you began to write the said book ten or - twelve years ago, after the order aforesaid had been given. Also, - that you demanded license to publish it, but without signifying to - those who granted you this permission that you had been commanded - not to hold, defend, or teach the said doctrine in any manner. You - also confessed that the style of the said book was, in many places, - so composed that the reader might think the arguments adduced on the - false side to be so worded as more effectually to entangle the - understanding than to be easily solved, alleging in excuse, that you - have thus run into an error, foreign (as you say) to your intention, - from writing in the form of a dialogue, and in consequence of the - natural complacency which every one feels with regard to his own - subtilties, and in showing himself more skilful than the generality - of mankind in contriving, even in favour of false propositions, - ingenious and apparently probable arguments. - - "And, upon a convenient time being given to you for making your - defence, you produced a certificate in the hand-writing of His - Eminence the Lord Cardinal Bellarmine, procured, as you said, by - yourself, that you might defend yourself against the calumnies of - your enemies, who reported that you had abjured your opinions, and - had been punished by the Holy Office; in which certificate it is - declared, that you had not abjured, nor had been punished, but - merely that the declaration made by His Holiness, and promulgated by - the Holy Congregation of the Index, had been announced to you, which - declares that the opinion of the motion of the earth, and stability - of the sun, is contrary to the Holy Scriptures, and, therefore, - cannot be held or defended. Wherefore, since no mention is there - made of two articles of the order, to wit, the order 'not to teach,' - and 'in any manner,' you argued that we ought to believe that, in - the lapse of fourteen or sixteen years, they had escaped your - memory, and that this was also the reason why you were silent as to - the order, when you sought permission to publish your book, and that - this is said by you not to excuse your error, but that it may be - attributed to vain-glorious ambition, rather than to malice. But - this very certificate, produced on your behalf, has greatly - aggravated your offence, since it is therein declared that the said - opinion is contrary to the Holy Scripture, and yet you have dared to - treat of it, to defend it, and to argue that it is probable; nor is - there any extenuation in the licence artfully and cunningly extorted - by you, since you did not intimate the command imposed upon you. But - whereas it appeared to Us that you had not disclosed the whole truth - with regard to your intentions, We thought it necessary to proceed - to the rigorous examination of you, in which (without any prejudice - to what you had confessed, and which is above detailed against you, - with regard to your said intention) you answered like a good - Catholic. - - "Therefore, having seen and maturely considered the merits of your - cause, with your said confessions and excuses, and every thing else - which ought to be seen and considered, We have come to the - underwritten final sentence against you. - - "Invoking, therefore, the most holy name of Our Lord Jesus Christ, - and of His Most Glorious Virgin Mother Mary, by this Our final - sentence, which, sitting in council and judgment for the tribunal of - the Reverend Masters of Sacred Theology, and Doctors of both Laws, - Our Assessors, We put forth in this writing touching the matters and - controversies before Us, between The Magnificent Charles Sincerus, - Doctor of both Laws, Fiscal Proctor of this Holy Office of the one - part, and you, Galileo Galilei, an examined and confessed criminal - from this present writing now in progress as above of the other - part, We pronounce, judge, and declare, that you, the said Galileo, - by reason of these things which have been detailed in the course of - this writing, and which, as above, you have confessed, have rendered - yourself vehemently suspected by this Holy Office of heresy: that is - to say, that you believe and hold the false doctrine, and contrary - to the Holy and Divine Scriptures, namely, that the sun is the - centre of the world, and that it does not move from east to west, - and that the earth does move, and is not the centre of the world; - also that an opinion can be held and supported as probable after it - has been declared and finally decreed contrary to the Holy - Scripture, and consequently that you have incurred all the censures - and penalties enjoined and promulgated in the sacred canons, and - other general and particular constitutions against delinquents of - this description. From which it is Our pleasure that you be - absolved, provided that, first, with a sincere heart and unfeigned - faith, in Our presence, you abjure, curse, and detest the said - errors and heresies, and every other error and heresy contrary to - the Catholic and Apostolic Church of Rome, in the form now shown to - you. - - "But, that your grievous and pernicious error and transgression may - not go altogether unpunished, and that you may be made more cautious - in future, and may be a warning to others to abstain from - delinquencies of this sort, We decree that the book of the dialogues - of Galileo Galilei be prohibited by a public edict, and We condemn - you to the formal prison of this Holy Office for a period - determinable at Our pleasure; and, by way of salutary penance, We - order you, during the next three years, to recite once a week the - seven penitential psalms, reserving to Ourselves the power of - moderating, commuting, or taking off the whole or part of the said - punishment and penance. - - "And so We say, pronounce, and by Our sentence declare, decree, and - reserve, in this and in every other better form and manner, which - lawfully We may and can use. - - "So We, the subscribing Cardinals, pronounce. - - Felix, Cardinal di Ascoli, - Guido, Cardinal Bentivoglio, - Desiderio, Cardinal di Cremona, - Antonio, Cardinal S. Onofrio, - Berlingero, Cardinal Gessi, - Fabricio, Cardinal Verospi, - Martino, Cardinal Ginetti." - -We cannot suppose that Galileo, even broken down as he was with age and -infirmities, and overawed by the merciless tribunal to whose power he -was subjected, could without extreme reluctance thus formally give the -lie to his whole life, and call upon God to witness his renunciation of -the opinions which even his bigoted judges must have felt that he still -clung to in his heart. - -We know indeed that his friends were unanimous in recommending an -unqualified acquiescence in whatever might be required, but some persons -have not been able to find an adequate explanation of his submission, -either in their exhortations, or in the mere dread of the alternative -which might await him in case of non-compliance. It has in short been -supposed, although the suspicion scarcely rests upon grounds -sufficiently strong to warrant the assertion, that Galileo did not -submit to this abjuration until forced to it, not merely by the -apprehension, but by the actual experience of personal violence. The -arguments on which this horrible idea appears to be mainly founded are -the two following: First, the Inquisitors declare in their sentence -that, not satisfied with Galileo's first confession, they judged it -necessary to proceed "to the rigorous examination of him, in which he -answered like a good Catholic."[85] It is pretended by those who are -more familiar with inquisitorial language than we can profess to be, -that the words _il rigoroso esame_, form the official phrase for the -application of the torture, and accordingly they interpret this passage -to mean, that the desired answers and submission had thus been extorted -from Galileo, which his judges had otherwise failed to get from him. -And, secondly, the partisans of this opinion bring forward in -corroboration of it, that Galileo immediately on his departure from -Rome, in addition to his old complaints, was found to be afflicted with -hernia, and this was a common consequence of the torture of the cord, -which they suppose to have been inflicted. It is right to mention that -no other trace can be found of this supposed torturing in all the -documents relative to the proceedings against Galileo, at least Venturi -was so assured by one who had inspected the originals at Paris.[86] - -Although the arguments we have mentioned appear to us slight, yet -neither can we attach much importance to the contrast which the -favourers of the opposite opinion profess to consider so incredible -between the honourable manner in which Galileo was treated throughout -the rest of the inquiry, and the suspected harsh proceeding against him. -Whether Galileo should be lodged in a prison or a palace, was a matter -of far other importance to the Inquisitors and to their hold upon public -opinion, than the question whether or not he should be suffered to -exhibit a persevering resistance to the censures which they were -prepared to cast upon him. Nor need we shrink from the idea, as we might -from suspecting of some gross crime, on trivial grounds, one of hitherto -unblemished innocence and character. The question may be disencumbered -of all such scruples, since one atrocity more or less can do little -towards affecting our judgment of the unholy Office of the Inquisition. - -Delambre, who could find so much to reprehend in Galileo's former -uncompromising boldness, is deeply penetrated with the insincerity of -his behaviour on the present occasion. He seems to have forgotten that a -tribunal which finds it convenient to carry on its inquiries in secret, -is always liable to the suspicion of putting words into the mouth of its -victims; and if it were worth while, there is sufficient internal -evidence that the language which Galileo is made to hold in his defence -and confession, is rather to be read as the composition of his judges -than his own. For instance, in one of the letters which we have -extracted[87], it may be seen that this obnoxious work was already in -forward preparation as early as 1610, and yet he is made to confess, and -the circumstance appears to be brought forward in aggravation of his -guilt, that he began to write it after the prohibition which he had -received in 1616. - -The abjuration was drawn up in the following terms:-- - - _The Abjuration of Galileo._ - - "I Galileo Galilei, son of the late Vincenzo Galilei, of Florence, - aged 70 years, being brought personally to judgment, and kneeling - before you, Most Eminent and Most Reverend Lords Cardinals, General - Inquisitors of the universal Christian republic against heretical - depravity, having before my eyes the Holy Gospels, which I touch - with my own hands, swear, that I have always believed, and now - believe, and with the help of God will in future believe, every - article which the Holy Catholic and Apostolic Church of Rome holds, - teaches, and preaches. But because I had been enjoined by this Holy - Office altogether to abandon the false opinion which maintains that - the sun is the centre and immoveable, and forbidden to hold, defend, - or teach, the said false doctrine in any manner, and after it had - been signified to me that the said doctrine is repugnant with the - Holy Scripture, I have written and printed a book, in which I treat - of the same doctrine now condemned, and adduce reasons with great - force in support of the same, without giving any solution, and - therefore have been judged grievously suspected of heresy; that is - to say, that I held and believed that the sun is the centre of the - world and immoveable, and that the earth is not the centre and - moveable. Willing, therefore, to remove from the minds of Your - Eminences, and of every Catholic Christian, this vehement suspicion - rightfully entertained towards me, with a sincere heart and - unfeigned faith, I abjure, curse, and detest, the said errors and - heresies, and generally every other error and sect contrary to the - said Holy Church; and I swear, that I will never more in future say - or assert anything verbally, or in writing, which may give rise to a - similar suspicion of me: but if I shall know any heretic, or any one - suspected of heresy, that I will denounce him to this Holy Office, - or to the Inquisitor and Ordinary of the place in which I may be. I - swear, moreover, and promise, that I will fulfil, and observe fully, - all the penances which have been, or shall be laid on me by this - Holy Office. But if it shall happen that I violate any of my said - promises, oaths, and protestations, (which God avert!) I subject - myself to all the pains and punishments, which have been decreed and - promulgated by the sacred canons, and other general and particular - constitutions, against delinquents of this description. So may God - help me, and his Holy Gospels, which I touch with my own hands. I, - the above-named Galileo Galilei, have abjured, sworn, promised, and - bound myself, as above, and in witness thereof with my own hand have - subscribed this present writing of my abjuration, which I have - recited word for word. At Rome in the Convent of Minerva, 22d June, - 1633. I, Galileo Galilei, have abjured as above with my own hand." - -It is said that Galileo, as he rose from his knees, stamped on the -ground, and whispered to one of his friends, _E pur si muove_--(It does -move though). - -Copies of Galileo's sentence and abjuration were immediately promulgated -in every direction, and the professors at several universities received -directions to read them publicly. At Florence this ceremony took place -in the church of Sta. Croce, whither Guiducci, Aggiunti, and all others -who were known in that city as firm adherents to Galileo's opinions, -were specially summoned. The triumph of the "Paper Philosophers" was so -far complete, and the alarm occasioned by this proof of their dying -power extended even beyond Italy. "I have been told," writes Descartes -from Holland to Mersenne at Paris, "that Galileo's system was printed in -Italy last year, but that every copy has been burnt at Rome, and himself -condemned to some sort of penance, which has astonished me so much that -I have almost determined to burn all my papers, or at least never to let -them be seen by any one. I cannot collect that he, who is an Italian and -even a friend of the Pope, as I understand, has been criminated on any -other account than for having attempted to establish the motion of the -earth. I know that this opinion was formerly censured by some Cardinals, -but I thought I had since heard, that no objection was now made to its -being publicly taught, even at Rome." - -The sentiments of all who felt themselves secured against the -apprehension of personal danger could take but one direction, for, as -Pascal well expressed it in one of his celebrated letters to the -Jesuits--"It is in vain that you have procured against Galileo a decree -from Rome condemning his opinion of the earth's motion. Assuredly, that -will never prove it to be at rest; and if we have unerring observations -proving that it turns round, not all mankind together can keep it from -turning, nor themselves from turning with it." - -The assembly of doctors of the Sorbonne at Paris narrowly escaped from -passing a similar sentence upon the system of Copernicus. The question -was laid before them by Richelieu, and it appears that their opinion was -for a moment in favour of confirming the Roman decree. It is to be -wished that the name had been preserved of one of its members, who, by -his strong and philosophical representations, saved that celebrated body -from this disgrace. - -Those who saw nothing in the punishment of Galileo but passion and -blinded superstition, took occasion to revert to the history of a -similar blunder of the Court of Rome in the middle of the eighth -century. A Bavarian bishop, named Virgil, eminent both as a man of -letters and politician, had asserted the existence of Antipodes, which -excited in the ignorant bigots of his time no less alarm than did the -motion of the earth in the seventeenth century. Pope Zachary, who was -scandalized at the idea of another earth, inhabited by another race of -men, and enlightened by another sun and moon (for this was the shape -which Virgil's system assumed in his eyes), sent out positive orders to -his legate in Bavaria. "With regard to Virgil, the philosopher, (I know -not whether to call him priest,) if he own these perverse opinions, -strip him of his priesthood, and drive him from the church and altars of -God." But Virgil had himself occasionally acted as legate, and was -moreover too necessary to his sovereign to be easily displaced. He -utterly disregarded these denunciations, and during twenty-five years -which elapsed before his death, retained his opinions, his bishopric of -Salzburg, and his political power. He was afterwards canonized.[88] - -Even the most zealous advocates of the authority of Rome were -embarrassed in endeavouring to justify the treatment which Galileo -experienced. Tiraboschi has attempted to draw a somewhat subtle -distinction between the bulls of the Pope and the inquisitorial decrees -which were sanctioned and approved by him; he dwells on the reflection -that no one, even among the most zealous Catholics, has ever claimed -infallibility as an attribute of the Inquisition, and looks upon it as a -special mark of grace accorded to the Roman Catholic Church, that during -the whole period in which most theologians rejected the opinions of -Copernicus, as contrary to the Scriptures, the head of that Church was -never permitted to compromise his infallible character by formally -condemning it.[89] - -Whatever may be the value of this consolation, it can hardly be -conceded, unless it be at the same time admitted that many scrupulous -members of the Church of Rome have been suffered to remain in singular -misapprehension of the nature and sanction of the authority to which -Galileo had yielded. The words of the bull of Sixtus V., by which the -Congregation of the Index was remodelled in 1588, are quoted by a -professor of the University of Louvain, a zealous antagonist of Galileo, -as follows: "They are to examine and expose the books which are -repugnant to the Catholic doctrines and Christian discipline, and after -reporting on them to us, they are to condemn them by our authority."[90] -Nor does it appear that the learned editors of what is commonly called -the Jesuit's edition of Newton's "Principia" were of opinion, that in -adopting the Copernican system they should transgress a mandate -emanating from any thing short of infallible wisdom. The remarkable -words which they were compelled to prefix to their book, show how -sensitive the court of Rome remained, even so late as 1742, with regard -to this rashly condemned theory. In their preface they say: "Newton in -this third book supposes the motion of the earth. We could not explain -the author's propositions otherwise than by making the same supposition. -We are therefore forced to sustain a character which is not our own; but -we profess to pay the obsequious reverence which is due to the decrees -pronounced by the supreme Pontiffs against the motion of the earth."[91] - -This coy reluctance to admit what nobody any longer doubts has survived -to the present time; for Bailli informs us,[92] that the utmost -endeavours of Lalande, when at Rome, to obtain that Galileo's work -should be erased from the Index, were entirely ineffectual, in -consequence of the decree which had been fulminated against him; and in -fact both it, and the book of Copernicus, "Nisi Corrigatur," are still -to be seen on the forbidden list of 1828. - -The condemnation of Galileo and his book was not thought sufficient. -Urban's indignation also vented itself upon those who had been -instrumental in obtaining the licence for him. The Inquisitor at -Florence was reprimanded; Riccardi, the master of the sacred palace, and -Ciampoli, Urban's secretary, were both dismissed from their situations. -Their punishment appears rather anomalous and inconsistent with the -proceedings against Galileo, in which it was assumed that his book was -not properly licensed; yet the others suffered on account of granting -that very licence, which he was accused of having surreptitiously -obtained from them, by concealing circumstances with which they were not -bound to be otherwise acquainted. Riccardi, in exculpation of his -conduct, produced a letter in the hand-writing of Ciampoli, in which was -contained that His Holiness, in whose presence the letter professed to -be written, ordered the licence to be given. Urban only replied that -this was a Ciampolism; that his secretary and Galileo had circumvented -him; that he had already dismissed Ciampoli, and that Riccardi must -prepare to follow him. - -As soon as the ceremony of abjuration was concluded, Galileo was -consigned, pursuant to his sentence, to the prison of the Inquisition. -Probably it was never intended that he should long remain there, for at -the end of four days, he was reconducted on a very slight representation -of Nicolini to the ambassador's palace, there to await his further -destination. Florence was still suffering under the before-mentioned -contagion; and Sienna was at last fixed on as the place of his -relegation. He would have been shut up in some convent in that city, if -Nicolini had not recommended as a more suitable residence, the palace of -the Archbishop Piccolomini, whom he knew to be among Galileo's warmest -friends. Urban consented to the change, and Galileo finally left Rome -for Sienna in the early part of July. - -Piccolomini received him with the utmost kindness, controlled of course -by the strict injunctions which were dispatched from Rome, not to suffer -him on any account to quit the confines of the palace. Galileo continued -at Sienna in this state of seclusion till December of the same year, -when the contagion having ceased in Tuscany, he applied for permission -to return to his villa at Arcetri. This was allowed, subject to the same -restrictions under which he had been residing with the archbishop. - - -FOOTNOTES: - -[79] Delambre quotes this sentence from a passage which is so obviously -ironical throughout, as an instance of Galileo's mis-statement of -facts!--_Hist. de l'Astr. Mod._, vol, i. p. 666. - -[80] Page 54. - -[81] Galuzzi. Storia di Toscana. Firenze, 1822. - -[82] Alidosi was a Florentine nobleman, whose estate Urban wished to -confiscate on a charge of heresy.--_Galuzzi._ - -[83] S'irrito il Papa, e lo fece abjurare, comparendo il pover uomo con -uno straccio di camicia indosso, che faceva compassione, MS. nella Bibl. -Magliab. Venturi. - -[84] The Index is a list of books, the reading of which is prohibited to -Roman Catholics. This list, in the early periods of the Reformation, was -often consulted by the curious, who were enlarging their libraries; and -a story is current in England, that, to prevent this mischief, the Index -itself was inserted in its own forbidden catalogue. The origin of this -story is, that an Index was published in Spain, particularizing the -objectionable passages in such books as were only partially condemned; -and although compiled with the best intentions, this was found to be so -racy, that it became necessary to forbid the circulation of this edition -in subsequent lists. - -[85] Giudicassimo esser necessario venir contro di te al rigoroso esame -nel quale rispondesti cattolicamente. - -[86] The fate of these documents is curious; after being long preserved -at Rome, they were carried away in 1809, by order of Buonaparte, to -Paris, where they remained till his first abdication. Just before the -hundred days, the late king of France, wishing to inspect them, ordered -that they should be brought to his own apartments for that purpose. In -the hasty flight which soon afterwards followed, the manuscripts were -forgotten, and it is not known what became of them. A French -translation, begun by Napoleon's desire, was completed only down to the -30th of April, 1633, the date of Galileo's first return to Nicolini's -palace. - -[87] Page 18. - -[88] Annalium Bolorum, libri vii. Ingolstadii, 1554. - -[89] La Chiesa non ha mai dichiarati eretici i sostenitori del Sistema -Copernicano, e questa troppo rigorosa censura non usci che dal tribunale -della Romana Inquisizione a cui niuno tra Cattolici ancor piu zelanti ha -mai attribuito it diritto dell'infallibilita. Anzi in cio ancora e d' -ammirarsi la providenza di Dio a favor della Chiesa, percioche in un -tempo in cui la maggior parte dei teologi fermamente credavano che il -Sistema Copernicano fosse all' autorita delle sacre Carte contrario, pur -non permise che dalla Chiesa si proferisse su cio un solenne -giudizio.--Stor. della Lett. Ital. - -[90] Lib. Fromondi Antaristarchus, Antwerpiae, 1631. - -[91] Newtoni Principia, Coloniae, 1760. - -[92] Histoire de l'Astronomie Moderne. - - - - -CHAPTER XIV. - - _Extracts from the Dialogues on the System._ - - -AFTER narrating the treatment to which Galileo was subject on account of -his admirable Dialogues, it will not be irrelevant to endeavour, by a -few extracts, to convey some idea of the style in which they are -written. It has been mentioned, that he is considered to surpass all -other Italian writers (unless we except Machiavelli) in the purity and -beauty of his language, and indeed his principal followers, who avowedly -imitated his style, make a distinguished group among the classical -authors of modern Italy. He professed to have formed himself from the -study of Ariosto, whose poems he passionately admired, insomuch that he -could repeat the greater part of them, as well as those of Berni and -Petrarca, all which he was in the frequent habit of quoting in -conversation. The fashion and almost universal practice of that day was -to write on philosophical subjects in Latin; and although Galileo wrote -very passably in that language, yet he generally preferred the use of -Italian, for which he gave his reasons in the following characteristic -manner:-- - -"I wrote in Italian because I wished every one to be able to read what I -wrote; and for the same cause I have written my last treatise in the -same language: the reason which has induced me is, that I see young men -brought together indiscriminately to study to become physicians, -philosophers, &c., and whilst many apply to such professions who are -most unfit for them, others who would be competent remain occupied -either with domestic business, or with other employments alien to -literature; who, although furnished, as Ruzzante might say, with a -_decent set of brains_, yet, not being able to understand things written -in _gibberish_, take it into their heads, that in these crabbed folios -there must be some grand _hocus pocus_ of logic and philosophy much too -high up for them to think of jumping at. I want them to know, that as -Nature has given eyes to them just as well as to philosophers for the -purpose of seeing her works, she has also given them brains for -examining and understanding them." - -The general structure of the dialogues has been already described;[93] -we shall therefore premise no more than the judgment pronounced on them -by a highly gifted writer, to supply the deficiencies of our necessarily -imperfect analysis. - -"One forms a very imperfect idea of Galileo, from considering the -discoveries and inventions, numerous and splendid as they are, of which -he was the undisputed author. It is by following his reasonings, and by -pursuing the train of his thoughts, in his own elegant, though somewhat -diffuse exposition of them, that we become acquainted with the fertility -of his genius--with the sagacity, penetration, and comprehensiveness of -his mind. The service which he rendered to real knowledge is to be -estimated, not only from the truths which he discovered, but from the -errors which he detected--not merely from the sound principles which he -established, but from the pernicious idols which he overthrew. The -dialogues on the system are written with such singular felicity, that -one reads them at the present day, when the truths contained in them are -known and admitted, with all the delight of novelty, and feels one's -self carried back to the period when the telescope was first directed to -the heavens, and when the earth's motion, with all its train of -consequences, was proved for the first time."[94] - -The first Dialogue is opened by an attack upon the arguments by which -Aristotle pretended to determine _a priori_ the necessary motions -belonging to different parts of the world, and on his favourite -principle that particular motions belong naturally to particular -substances. Salviati (representing Galileo) then objects to the -Aristotelian distinctions between the corruptible elements and -incorruptible skies, instancing among other things the solar spots and -newly appearing stars, as arguments that the other heavenly bodies may -probably be subjected to changes similar to those which are continually -occurring on the earth, and that it is the great distance alone which -prevents their being observed. After a long discussion on this point, -Sagredo exclaims, "I see into the heart of Simplicio, and perceive that -he is much moved by the force of these too conclusive arguments; but -methinks I hear him say--'Oh, to whom must we betake ourselves to settle -our disputes if Aristotle be removed from the chair? What other author -have we to follow in our schools, our studies, and academies? What -philosopher has written on all the parts of Natural Philosophy, and so -methodically as not to have overlooked a single conclusion? Must we then -desolate this fabric, by which so many travellers have been sheltered? -Must we destroy this asylum, this Prytaneum wherein so many students -have found a convenient resting-place, where without being exposed to -the injuries of the weather, one may acquire an intimate knowledge of -nature, merely by turning over a few leaves? Shall we level this -bulwark, behind which we are safe from every hostile attack?' I pity him -no less than I do one who at great expense of time and treasure, and -with the labour of hundreds, has built up a very noble palace; and then, -because of insecure foundations, sees it ready to fall--unable to bear -that those walls be stripped that are adorned with so many beautiful -pictures, or to suffer those columns to fall that uphold the stately -galleries, or to see ruined the gilded roofs, the chimney-pieces, the -friezes, and marble cornices erected at so much cost, he goes about it -with girders and props, with shores and buttresses, to hinder its -destruction." - -Salviati proceeds to point out the many points of similarity between the -earth and moon, and among others which we have already mentioned, the -following remark deserves especial notice:-- - -"Just as from the mutual and universal tendency of the parts of the -earth to form a whole, it follows that they all meet together with equal -inclination, and that they may unite as closely as possible, assume the -spherical form; why ought we not to believe that the moon, the sun, and -other mundane bodies are also of a round figure, from no other reason -than from a common instinct and natural concourse of all their component -parts; of which if by accident any one should be violently separated -from its whole, is it not reasonable to believe that spontaneously, and -of its natural instinct, it would return? It may be added that if any -centre of the universe may be assigned, to which the whole terrene globe -if thence removed would seek to return, we shall find most probable that -the sun is placed in it, as by the sequel you shall understand." - -Many who are but superficially acquainted with the History of Astronomy, -are apt to suppose that Newton's great merit was in his being the first -to suppose an attractive force existing in and between the different -bodies composing the solar system. This idea is very erroneous; Newton's -discovery consisted in conceiving and proving the identity of the force -with which a stone falls, and that by which the moon falls, towards the -earth (on an assumption that this force becomes weaker in a certain -proportion as the distance increases at which it operates), and in -generalizing this idea, in applying it to all the visible creation, and -tracing the principle of universal gravitation with the assistance of a -most refined and beautiful geometry into many of its most remote -consequences. But the general notion of an attractive force between the -sun, moon, and planets, was very commonly entertained before Newton was -born, and may be traced back to Kepler, who was probably the first -modern philosopher who suggested it. The following extraordinary -passages from his "Astronomy" will shew the nature of his conceptions on -this subject:-- - -"The true doctrine of gravity is founded on these axioms: every -corporeal substance, so far forth as it is corporeal, has a natural -fitness for resting in every place where it may be situated by itself -beyond the sphere of influence of its cognate body. Gravity is a mutual -affection between cognate bodies towards union or conjunction (similar -in kind to the magnetic virtue), so that the earth attracts a stone much -rather than the stone seeks the earth. Heavy bodies (if in the first -place we put the earth in the centre of the world) are not carried to -the centre of the world in its quality of centre of the world, but as to -the centre of a cognate round body, namely the earth. So that -wheresoever the earth may be placed or whithersoever it may be carried -by its animal faculty, heavy bodies will always be carried towards it. -If the earth were not round heavy bodies would not tend from every side -in a straight line towards the centre of the earth, but to different -points from different sides. If two stones were placed in any part of -the world near each other and beyond the sphere of influence of a third -cognate body, these stones, like two magnetic needles, would come -together in the intermediate point, each approaching the other by a -space proportional to the comparative mass of the other. If the moon -and earth were not retained in their orbits by their animal force or -some other equivalent, the earth would mount to the moon by a -fifty-fourth part of their distance, and the moon fall towards the earth -through the other fifty-three parts, and would there meet, assuming -however that the substance of both is of the same density. If the earth -should cease to attract its waters to itself, all the waters of the sea -would be raised, and would flow to the body of the moon."[95] - -He also conjectured that the irregularities in the moon's motion were -caused by the joint action of the sun and earth, and recognized the -mutual action of the sun and planets, when he declared the mass and -density of the sun to be so great that the united attraction of the -other planets cannot remove it from its place. Among these bold and -brilliant ideas, his temperament led him to introduce others which show -how unsafe it was to follow his guidance, and which account for, if they -do not altogether justify, the sarcastic remark of Ross, that "Kepler's -opinion that the planets are moved round by the sunne, and that this is -done by sending forth a magnetic virtue, and that the sun-beames are -like the teethe of a wheele taking hold of the planets, are senslesse -crotchets fitter for a wheeler or a miller than a philosopher."[96] -Roberval took up Kepler's notions, especially in the tract which he -falsely attributed to Aristarchus, and it is much to be regretted that -Roberval should deserve credit for anything connected with that impudent -fraud. The principle of universal gravitation, though not the varying -proportion, is distinctly assumed in it, as the following passages will -sufficiently prove: "In every single particle of the earth, and the -terrestrial elements, is a certain property or accident which we suppose -common to the whole system of the world, by virtue of which all its -parts are forced together, and reciprocally attract each other; and this -property is found in a greater or less degree in the different -particles, according to their density. If the earth be considered by -itself, its centres of magnitude and virtue, or gravity, as we usually -call it, will coincide, to which all its parts tend in a straight line, -as well by their own exertion or gravity, as by the reciprocal -attraction of all the rest." In a subsequent chapter, Roberval repeats -these passages nearly in the same words, applying them to the whole -solar system, adding, that "the force of this attraction is not to be -considered as residing in the centre itself, as some ignorant people -think, but in the whole system whose parts are equally disposed round -the centre."[97] This very curious work was reprinted in the third -volume of the _Reflexiones Physico-Mathematicae_ of Mersenne, from whom -Roberval pretended to have received the Arabic manuscript, and who is -thus irretrievably implicated in the forgery.[98] The last remark, -denying the attractive force to be due to any property of the central -point, seems aimed at Aristotle, who, in a no less curious passage, -maintaining exactly the opposite opinion, says, "Hence, we may better -understand what the ancients have related, that like things are wont to -have a tendency to each other. For this is not absolutely true; for if -the earth were to be removed to the place now occupied by the moon, no -part of the earth would then have a tendency towards that place, but -would still fall towards the point which the earth's centre now -occupies."[99] Mersenne considered the consequences of the attractive -force of each particle of matter so far as to remark, that if a body -were supposed to fall towards the centre of the earth, it would be -retarded by the attraction of the part through which it had already -fallen.[100] Galileo had not altogether neglected to speculate on such a -supposition, as is plain from the following extract. It is taken from a -letter to Carcaville, dated from Arcetri, in 1637. "I will say farther, -that I have not absolutely and clearly satisfied myself that a heavy -body would arrive sooner at the centre of the earth, if it began to fall -from the distance only of a single yard, than another which should start -from the distance of a thousand miles. I do not affirm this, but I offer -it as a paradox."[101] - -It is very difficult to offer any satisfactory comment upon this -passage; it may be sufficient to observe that this paradoxical result -was afterwards deduced by Newton, as one of the consequences of the -general law with which all nature is pervaded, but with which there is -no reason to believe that Galileo had any acquaintance; indeed the idea -is fully negatived by other passages in this same letter. This is one of -the many instances from which we may learn to be cautious how we invest -detached passages of the earlier mathematicians with a meaning which in -many cases their authors did not contemplate. The progressive -development of these ideas in the hands of Wallis, Huyghens, Hook, Wren, -and Newton, would lead us too far from our principal subject. There is -another passage in the third dialogue connected with this subject, which -it may be as well to notice in this place. "The parts of the earth have -such a propensity to its centre, that when it changes its place, -although they may be very distant from the globe at the time of the -change, yet must they follow. An example similar to this is the -perpetual sequence of the Medicean stars, although always separated from -Jupiter. The same may be said of the moon, obliged to follow the earth. -And this may serve for those simple ones who have difficulty in -comprehending how these two globes, not being chained together, nor -strung upon a pole, mutually follow each other, so that on the -acceleration or retardation of the one, the other also moves quicker or -slower." - -The second Dialogue is appropriated chiefly to the discussion of the -diurnal motion of the earth; and the principal arguments urged by -Aristotle, Ptolemy, and others, are successively brought forward and -confuted. The opposers of the earth's diurnal motion maintained, that if -it were turning round, a stone dropped from the top of a tower would not -fall at its foot; but, by the rotation of the earth to the eastward -carrying away the tower with it, would be left at a great distance to -the westward; it was common to compare this effect to a stone dropped -from the mast-head of a ship, and without any regard to truth it was -boldly asserted that this would fall considerably nearer the stern than -the foot of the mast, if the ship were in rapid motion. The same -argument was presented in a variety of forms,--such as that a -cannon-ball shot perpendicularly upwards would not fall at the same -spot; that if fired to the eastward it would fly farther than to the -westward; that a mark to the east or west would never be hit, because of -the rising or sinking of the horizon during the flight of the ball; that -ladies' ringlets would all stand out to the westward,[102] with other -conceits of the like nature: to which the general reply is given, that -in all these cases the stone, or ball, or other body, participates -equally in the motion of the earth, which, therefore, so far as regards -the relative motion of its parts, may be disregarded. The manner in -which this is illustrated, appears in the following extract from the -dialogue:--"_Sagredo._ If the nib of a writing pen which was in the ship -during my voyage direct from Venice to Alexandria, had had the power of -leaving a visible mark of all its path, what trace, what mark, what line -would it have left?--_Simplicio._ It would have left a line stretched -out thither from Venice not perfectly straight, or to speak more -correctly, not perfectly extended in an exact circular arc, but here and -there more and less curved accordingly as the vessel had pitched more or -less; but this variation in some places of one or two yards to the right -or left, or up or down in a length of many hundred miles, would have -occasioned but slight alteration in the whole course of the line, so -that it would have been hardly sensible, and without any great error we -may speak of it as a perfectly circular arc.--_Sagred._ So that the true -and most exact motion of the point of the pen would also have been a -perfect arc of a circle if the motion of the vessel, abstracting from -the fluctuations of the waves, had been steady and gentle; and if I had -held this pen constantly in my hand, and had merely moved it an inch or -two one way or the other, what alteration would that have made in the -true and principal motion?--_Simpl._ Less than that which would be -occasioned in a line a thousand yards long, by varying here and there -from perfect straightness by the quantity of a flea's eye.--_Sagred._ If -then a painter on our quitting the port had begun to draw with this pen -on paper, and had continued his drawing till we got to Alexandria, he -would have been able by its motion, to produce an accurate -representation of many objects perfectly shadowed, and filled up on all -sides with landscapes, buildings, and animals, although all the true, -real, and essential motion of the point of his pen would have been no -other but a very long and very simple line; and as to the peculiar work -of the painter, he would have drawn it exactly the same if the ship had -stood still. Therefore, of the very protracted motion of the pen, there -remain no other traces than those marks drawn upon the paper, the reason -of this being that the great motion from Venice to Alexandria was common -to the paper, the pen, and everything that was in the ship; but the -trifling motion forwards and backwards, to the right and left, -communicated by the painter's fingers to the pen, and not to the paper, -from being peculiar to the pen, left its mark upon the paper, which as -to this motion was immoveable. Thus it is likewise true that in the -supposition of the earth's rotation, the motion of a falling stone is -really a long track of many hundreds and thousands of yards; and if it -could have delineated its course in the calm air, or on any other -surface, it would have left behind it a very long transversal line; but -that part of all this motion which is common to the stone, the tower, -and ourselves, is imperceptible by us and the same as if not existing, -and only that part remains to be observed of which neither we nor the -tower partake, which in short is the fall of the stone along the tower." - -The mechanical doctrines introduced into this second dialogue will be -noticed on another occasion; we shall pass on to other extracts, -illustrative of the general character of Galileo's reasoning:-- -"_Salviati._ I did not say that the earth has no principle, either -internal or external, of its motion of rotation, but I do say that I -know not which of the two it has, and that my ignorance has no power to -take its motion away; but if this author knows by what principle other -mundane bodies, of the motion of which we are certain, are turned round, -I say that what moves the Earth is something like that by which Mars and -Jupiter, and, as he believes, the starry sphere, are moved round; and if -he will satisfy me as to the cause of their motion, I bind myself to be -able to tell him what moves the earth. Nay more; I undertake to do the -same if he can teach me what it is which moves the parts of the earth -downwards.--_Simpl._ The cause of this effect is notorious, and every -one knows that it is Gravity.--_Salv._ You are out, Master Simplicio; -you should say that every one knows that it is called Gravity; but I do -not ask you the name but the nature of the thing, of which nature you do -not know one tittle more than you know of the nature of the moving cause -of the rotation of the stars, except it be the name which has been given -to the one, and made familiar and domestic, by the frequent experience -we have of it many thousand times in a day; but of the principle or -virtue by which a stone falls to the ground, we really know no more than -we know of the principle which carries it upwards when thrown into the -air, or which carries the moon round its orbit, except, as I have said, -the name of gravity which we have peculiarly and exclusively assigned to -it; whereas we speak of the other with a more generic term, and talk of -the virtue impressed, and call it either an assisting or an informing -intelligence, and are content to say that Nature is the cause of an -infinite number of other motions." - -Simplicio is made to quote a passage from Scheiner's book of Conclusions -against Copernicus, to the following effect:--"'If the whole earth and -water were annihilated, no hail or rain would fall from the clouds, but -would only be naturally carried round in a circle, nor would any fire or -fiery thing ascend, since, according to the not improbable opinion of -these others, there is no fire in the upper regions.'--_Salv._ The -foresight of this philosopher is most admirable and praiseworthy, for he -is not content with providing for things that might happen during the -common course of nature, but persists in shewing his care for the -consequences of what he very well knows will never come to pass. -Nevertheless, for the sake of hearing some of his notable conceits, I -will grant that if the earth and water were annihilated there would be -no more hail or rain, nor would fiery matter ascend any more, but would -continue a motion of revolution. What is to follow? What conclusion is -the philosopher going to draw?--_Simpl._ This objection is in the very -next words--'Which nevertheless (says he) is contrary to experience and -reason.'--_Salv._ Now I must yield: since he has so great an advantage -over me as experience, with which I am quite unprovided. For hitherto I -have never happened to see the terrestrial earth and water annihilated, -so as to be able to observe what the hail and fire did in the confusion. -But does he tell us for our information at least what they did?--_Simp._ -No, he does not say any thing more.--_Salv._ I would give something to -have a word or two with this person, to ask him whether, when this globe -vanished, it also carried away the common centre of gravity, as I fancy -it did, in which case I take it that the hail and water would remain -stupid and confounded amongst the clouds, without knowing what to do -with themselves.... And lastly, that I may give this philosopher a less -equivocal answer, I tell him that I know as much of what would follow -after the annihilation of the terrestrial globe, as he could have known -what was about to happen in and about it, before it was created." - -Great part of the third Dialogue is taken up with discussions on the -parallax of the new stars of 1572 and 1604, in which Delambre notices -that Galileo does not employ logarithms in his calculations, although -their use had been known since Napier discovered them in 1616: the -dialogue then turns to the annual motion "first taken from the Sun and -conferred upon the Earth by Aristarchus Samius, and afterwards by -Copernicus." Salviati speaks of his contemporary philosophers with great -contempt--"If you had ever been worn out as I have been many and many a -time with hearing what sort of stuff is sufficient to make the obstinate -vulgar unpersuadable, I do not say to agree with, but even to listen to -these novelties, I believe your wonder at finding so few followers of -these opinions would greatly fall off. But little regard in my judgment -is to be had of those understandings who are convinced and immoveably -persuaded of the fixedness of the earth, by seeing that they are not -able to breakfast this morning at Constantinople, and sup in the evening -in Japan, and who feel satisfied that the earth, so heavy as it is, -cannot climb up above the sun, and then come tumbling in a breakneck -fashion down again!"[103] This remark serves to introduce several -specious arguments against the annual motion of the earth, which are -successively confuted, and it is shewn how readily the apparent stations -and retrogradations of the planets are accounted for on this -supposition. - -The following is one of the frequently recurring passages in which -Galileo, whilst arguing in favour of the enormous distances at which the -theory of Copernicus necessarily placed the fixed stars, inveighs -against the arrogance with which men pretend to judge of matters removed -above their comprehension. "_Simpl._ All this is very well, and it is -not to be denied that the heavens may surpass in bigness the capacity of -our imaginations, as also that God might have created it yet a thousand -times larger than it really is, but we ought not to admit anything to be -created in vain, and useless in the universe. Now whilst we see this -beautiful arrangement of the planets, disposed round the earth at -distances proportioned to the effects they are to produce on us for our -benefit, to what purpose should a vast vacancy be afterwards interposed -between the orbit of Saturn and the starry spheres, containing not a -single star, and altogether useless and unprofitable? to what end? for -whose use and advantage?--_Salv._ Methinks we arrogate too much to -ourselves, Simplicio, when we will have it that the care of us alone is -the adequate and sufficient work and bound, beyond which the divine -wisdom and power does and disposes of nothing. I feel confident that -nothing is omitted by the Divine Providence of what concerns the -government of human affairs; but that there may not be other things in -the universe dependant upon His supreme wisdom, I cannot for myself, by -what my reason holds out to me, bring myself to believe. So that when I -am told of the uselessness of an immense space interposed between the -orbits of the planets and the fixed stars, empty and valueless, I reply -that there is temerity in attempting by feeble reason to judge the works -of God, and in calling vain and superfluous every part of the universe -which is of no use to us.--_Sagr._ Say rather, and I believe you would -say better, that we have no means of knowing what is of use to us; and I -hold it to be one of the greatest pieces of arrogance and folly that can -be in this world to say, because I know not of what use Jupiter or -Saturn are to me, that therefore these planets are superfluous; nay -more, that there are no such things in nature. To understand what effect -is worked upon us by this or that heavenly body (since you will have it -that all their use must have a reference to us), it would be necessary -to remove it for a while, and then the effect which I find no longer -produced in me, I may say that it depended upon that star. Besides, who -will dare say that the space which they call too vast and useless -between Saturn and the fixed stars is void of other bodies belonging to -the universe. Must it be so because we do not see them: then I suppose -the four Medicean planets, and the companions of Saturn, came into the -heavens when we first began to see them, and not before! and, by the -same rule, the other innumerable fixed stars did not exist before men -saw them. The nebulae were till lately only white flakes, till with the -telescope we have made of them constellations of bright and beautiful -stars. Oh presumptuous! rather, Oh rash ignorance of man!" - -After a discussion on Gilbert's Theory of Terrestrial Magnetism, -introduced by the parallelism of the earth's axis, and of which Galileo -praises very highly both the method and results, the dialogue proceeds -as follows:--"_Simpl._ It appears to me that Sig. Salviati, with a fine -circumlocution, has so clearly explained the cause of these effects, -that any common understanding, even though unacquainted with science, -may comprehend it: but we, confining ourselves to the terms of art, -reduce the cause of these and other similar natural phenomena to -sympathy, which is a certain agreement and mutual appetency arising -between things which have the same qualities, just as, on the other -hand, that disagreement and aversion, with which other things naturally -repel and abhor each other, we style antipathy.--_Sagr._ And thus with -these two words they are able to give a reason for the great number of -effects and accidents which we see, not without admiration, to be -produced in Nature. But it strikes me that this mode of philosophising -has a great sympathy with the style in which one of my friends used to -paint: on one part of the canvas he would write with chalk--there I will -have a fountain, with Diana and her nymphs; here some harriers; in this -corner I will have a huntsman, with a stag's head; the rest may be a -landscape of wood and mountain; and what remains to be done may be put -in by the colourman: and thus he flattered himself that he had painted -the story of Actaeon, having contributed nothing to it beyond the names." - -The fourth Dialogue is devoted entirely to an examination of the tides, -and is a development and extension of the treatise already mentioned to -have been sent to the Archduke Leopold, in 1618.[104] Galileo was -uncommonly partial to his theory of the tides, from which he thought to -derive a direct proof of the earth's motion in her orbit; and although -his theory was erroneous, it required a farther advance in the science -of motion than had been attained even at a much later period to point -out the insufficiency of it. It is well known that the problem of -explaining the cause of this alternate motion of the waters had been -considered from the earliest ages one of the most difficult that could -be proposed, and the solutions with which different inquirers were -obliged to rest contented, shew that it long deserved the name given to -it, of "the grave of human curiosity."[105] Riccioli has enumerated -several of the opinions which in turn had their favourers and -supporters. One party supposed the rise of the waters to be occasioned -by the influx of rivers into the sea; others compared the earth to a -large animal, of which the tides indicated the respiration; a third -theory supposed the existence of subterraneous fires, by which the sea -was periodically made to boil; others attributed the cause of a similar -change of temperature to the sun and moon. - -There is an unfounded legend, that Aristotle drowned himself in despair -of being able to invent a plausible explanation of the extraordinary -tides in the Euripus. His curiosity on the subject does not appear to -have been so acute (judging from his writings) as this story would -imply. In one of his books he merely mentions a rumour, that there are -great elevations or swellings of the seas, which recur periodically, -according to the course of the moon. Lalande, in the fourth volume of -his Astronomy, has given an interesting account of the opinion of the -connection of the tides with the moon's motion. Pytheas of Marseilles, a -contemporary of Aristotle, was the first who has been recorded as -observing, that the full tides occur at full moon, and the ebbs at new -moon.[106] This is not quite correctly stated; for the tide of new moon -is known to be still higher than the rise at the full, but it is likely -enough, that the seeming inaccuracy should be attributed, not to -Pytheas, but to his biographer Plutarch, who, in many instances, -appears to have viewed the opinions of the old philosophers through the -mist of his own prejudices and imperfect information. The fact is, that, -on the same day when the tide rises highest, it also ebbs lowest; and -Pytheas, who, according to Pliny, had recorded a tide in Britain of -eighty cubits, could not have been ignorant of this. Posidonius, as -quoted by Strabo, maintained the existence of three periods of the tide, -daily, monthly, and annual, "in sympathy with the moon."[107] Pliny, in -his vast collection of natural observations, not unaptly styled the -Encyclopaedia of the Antients, has the following curious passages:--"The -flow and ebb of the tide is very wonderful; it happens in a variety of -ways, but the cause is in the sun and moon."[108] He then very -accurately describes the course of the tide during a revolution of the -moon, and adds: "The flow takes place every day at a different hour; -being waited on by the star, which rises every day in a different place -from that of the day before, and with greedy draught drags the seas with -it."[109] "When the moon is in the north, and further removed from the -earth, the tides are more gentle than when digressing to the south, she -exerts her force with a closer effort."[110] - -The College of Jesuits at Coimbra appears to deserve the credit of first -clearly pointing out the true relation between the tides and the moon, -which was also maintained a few years later by Antonio de Dominis and -Kepler. In the Society's commentary on Aristotle's book on Meteors, -after refuting the notion that the tides are caused by the light of the -sun and moon, they say, "It appears more probable to us, without any -rarefaction, of which there appears no need or indication, that the moon -raises the waters by some inherent power of impulsion, in the same -manner as a magnet moves iron; and according to its different aspects -and approaches to the sea, and the obtuse or acute angles of its -bearing, at one time to attract and raise the waters along the shore, -and then again to leave them to sink down by their own weight, and to -gather into a lower level."[111] The theory of Universal Gravitation -seems here within the grasp of these philosophers, but unfortunately it -did not occur to them that possibly the same attraction might be exerted -on the earth as well as the water, and that the tide was merely an -effect of the diminution of force, owing to the increase of distance, -with which the centre of the earth is attracted, as compared with that -exerted on its surface. This idea, so happily seized afterwards by -Newton, might at once have furnished them with a satisfactory -explanation of the tide, which is observed on the opposite side of the -earth as well as immediately under the moon. They might have seen that -in the latter case the centre of the earth is pulled away from the -water, just as in the former the water is pulled away from the centre of -the earth, the sensible effect to us being in both cases precisely the -same. For want of this generalization, the inferior tide as it is called -presented a formidable obstacle to this theory, and the most plausible -explanation that was given was, that this magnetic virtue radiated out -from the moon was reflected by the solid heavens, and concentrated again -as in a focus on the opposite side of the earth. The majority of modern -astronomers who did not admit the existence of any solid matter fit for -producing the effect assigned to it, found a reasonable difficulty in -acquiescing in this explanation. Galileo, who mentions the Archbishop of -Spalatro's book, treated the theory of attraction by the moon as absurd. -"This motion of the seas is local and sensible, made in an immense mass -of water, and cannot be brought to obey light, and warmth, and -predominancy of occult qualities, and such like vain fancies; all which -are so far from being the cause of the tide, that on the contrary the -tide is the cause of them, inasmuch as it gives rise to these ideas in -brains which are more apt for talkativeness and ostentation, than for -speculation and inquiry into the secrets of Nature; who, rather than see -themselves driven to pronounce these wise, ingenuous, and modest -words--_I do not know_,--will blurt out from their tongues and pens all -sorts of extravagancies." - -Galileo's own theory is introduced by the following illustration, which -indeed probably suggested it, as he was in the habit of suffering no -natural phenomena, however trivial in appearance, to escape him. He felt -the advantage of this custom in being furnished on all occasions with a -stock of homely illustrations, to which the daily experience of his -hearers readily assented, and which he could shew to be identical in -principle with the phenomena under discussion. That he was mistaken in -applying his observations in the present instance cannot be urged -against the incalculable value of such a habit. - -"We may explain and render sensible these effects by the example of one -of those barks which come continually from Lizza Fusina, with fresh -water for the use of the city of Venice. Let us suppose one of these -barks to come thence with moderate velocity along the canal, carrying -gently the water with which it is filled, and then, either by touching -the bottom, or from some other hindrance which is opposed to it, let it -be notably retarded; the water will not on that account lose like the -bark the impetus it has already acquired, but will forthwith run on -towards the prow where it will sensibly rise, and be depressed at the -stern. If on the contrary the said vessel in the middle of its steady -course shall receive a new and sensible increase of velocity, the -contained water before giving into it will persevere for some time in -its slowness, and will be left behind that is to say towards the stern -where consequently it will rise, and sink at the head.--Now, my masters, -that which the vessel does in respect of the water contained in it, and -that which the water does in respect of the vessel containing it, is the -same to a hair as what the Mediterranean vase does in respect of the -water which it contains, and that the waters do in respect of the -Mediterranean vase which contains them. We have now only to demonstrate -how, and in what manner it is true that the Mediterranean, and all other -gulfs, and in short all the parts of the earth move with a motion -sensibly not uniform, although no motion results thence to the whole -globe which is not perfectly uniform and regular." - -This unequable motion is derived from a combination of the earth's -motion on her axis, and in her orbit, the consequence of which is that a -point turned from the sun is carried in the same direction by the annual -and diurnal velocities, whereas a point on the opposite side of the -globe is carried in opposite directions by the annual and diurnal -motions, so that in every twenty-four hours the absolute motion through -space of every point in the earth completes a cycle of varying -swiftness. Those readers who are unacquainted with the mathematical -theory of motion must be satisfied with the assurance that this specious -representation is fallacious, and that the oscillation of the water does -not in the least result from the causes here assigned to it: the -reasoning necessary to prove this is not elementary enough to be -introduced here with propriety. - -Besides the principal daily oscillation of the water, there is a monthly -inequality in the rise and fall, of which the extremes are called the -spring and neap tides: the manner in which Galileo attempted to bring -his theory to bear upon these phenomena is exceedingly curious. - -"It is a natural and necessary truth, that if a body be made to revolve, -the time of revolution will be greater in a greater circle than in a -less: this is universally allowed, and fully confirmed by experiments, -such for instance as these:--In wheel clocks, especially in large ones, -to regulate the going, the workmen fit up a bar capable of revolving -horizontally, and fasten two leaden weights to the ends of it; and if -the clock goes too slow, by merely approaching these weights somewhat -towards the centre of the bar, they make its vibrations more frequent, -at which time they are moving in smaller circles than before.[112]--Or, -if you fasten a weight to a cord which you pass round a pulley in the -ceiling, and whilst the weight is vibrating draw in the cord towards -you, the vibrations will become sensibly accelerated as the length of -the string diminishes. We may observe the same rule to hold among the -celestial motions of the planets, of which we have a ready instance in -the Medicean planets, which revolve in such short periods round Jupiter. -We may therefore safely conclude, that if the moon for instance shall -continue to be forced round by the same moving power, and were to move -in a smaller circle, it would shorten the time of its revolution. Now -this very thing happens in fact to the moon, which I have just advanced -on a supposition. Let us call to mind that we have already concluded -with Copernicus, that it is impossible to separate the moon from the -earth, round which without doubt it moves in a month: we must also -remember that the globe of the earth, accompanied always by the moon, -revolves in the great circle round the sun in a year, in which time the -moon revolves round the earth about thirteen times, whence it follows -that the moon is sometimes near the sun, that is to say between the -earth and sun, sometimes far from it, when she is on the outside of the -earth. Now if it be true that the power which moves the earth and the -moon round the sun remains of the same efficacy, and if it be true that -the same moveable, acted on by the same force, passes over similar arcs -of circles in a time which is least when the circle is smallest, we are -forced to the conclusion that at new moon, when in conjunction with the -sun, the moon passes over greater arcs of the orbit round the sun, than -when in opposition at full moon; and this inequality of the moon will be -shared by the earth also. So that exactly the same thing happens as in -the balance of the clocks; for the moon here represents the leaden -weight, which at one time is fixed at a greater distance from the centre -to make the vibrations slower, and at another time nearer to accelerate -them." - -Wallis adopted and improved this theory in a paper which he inserted in -the Philosophical Transactions for 1666, in which he declares, that the -circular motion round the sun should be considered as taking place at a -point which is the centre of gravity of the earth and moon. "To the -first objection, that it appears not how two bodies that have no tie can -have one common centre of gravity, I shall only answer, that it is -harder to show how they have it, than that they have it."[113] As Wallis -was perfectly competent from the time at which he lived, and his -knowledge of the farthest advances of science in his time, to appreciate -the value of Galileo's writings, we shall conclude this chapter with the -judgment that he has passed upon them in the same paper. "Since Galileo, -and after him Torricelli and others have applied mechanical principles -to the solving of philosophical difficulties, natural philosophy is well -known to have been rendered more intelligible, and to have made a much -greater progress in less than a hundred years than before for many -ages." - - -FOOTNOTES: - -[93] See page 56. - -[94] Playfair's Dissertation, Supp. Encyc. Brit. - -[95] Astronomia Nova. Pragae. 1609. - -[96] The new Planet no Planet, or the Earth no wandering Star, except in -the wandering heads of Galileans. London, 1646. - -[97] Aristarchi Samii de Mundi Systemate. Parisiis 1644. - -[98] See page 12. - -[99] De Coelo, lib. iv. cap. 3. - -[100] Reflexiones Physico-Mathematicae, Parisiis, 1647. - -[101] Venturi. - -[102] Riccioli. - -[103] The notions commonly entertained of 'up' and 'down,' as connected -with the observer's own situation, had long been a stumbling-block in -the way of the new doctrines. When Columbus held out the certainty of -arriving in India by sailing to the westward on account of the earth's -roundness, it was gravely objected, that it might be well enough to sail -down to India, but that the chief difficulty would consist in climbing -up back again. - -[104] See page 50. - -[105] Riccioli Almag. Nov. - -[106] Plutarch, De placit. Philos. lib. iii. c. 17. - -[107] [sympatheos te selene]. Geographiae, lib. iii. - -[108] Historia Naturalis, lib. ii. c, 97. - -[109] Ut ancillante sidere, trahenteque secum avido haustu maria. - -[110] Eadem Aquilonia, et a terris longius recedente, mitiores quam cum, -in Austros digressa, propiore nisu vim suam exercet. - -[111] Commentarii Collegii Conimbricensis. Coloniae, 1603. - -[112] See fig. 1. p. 96. - -[113] Phil. Trans., No. 16, August 1666. - - - - -CHAPTER XV. - - _Galileo at Arcetri--Becomes Blind--Moon's Libration--Publication of - the Dialogues on Motion._ - - -WE have already alluded to the imperfect state of the knowledge -possessed with regard to Galileo's domestic life and personal habits; -there is reason however to think that unpublished materials exist from -which these outlines might be in part filled up. Venturi informs us that -he had seen in the collection from which he derived a great part of the -substance of his Memoirs of Galileo, about one hundred and twenty -manuscript letters, dated between the years 1623 and 1633, addressed to -him by his daughter Maria, who with her sister had attached herself to -the convent of St. Matthew, close to Galileo's usual place of residence. -It is difficult not to think that much interesting information might be -obtained from these, with respect to Galileo's domestic character. The -very few published extracts confirm our favourable impressions of it, -and convey a pleasing idea of this his favourite daughter. Even when, in -her affectionate eagerness to soothe her father's wounded feelings at -the close of his imprisonment in Rome, she dwells with delight upon her -hopes of being allowed to relieve him, by taking on herself the -penitential recitations which formed a part of his sentence, the -prevalent feeling excited in every one by the perusal must surely be -sympathy with the filial tenderness which it is impossible to -misunderstand. - -The joy she had anticipated in again meeting her parent, and in -compensating to him by her attentive affection the insults of his -malignant enemies, was destined to be but of short duration. Almost in -the same month in which Galileo returned to Arcetri she was seized with -a fatal illness; and already in the beginning of April, 1634, we learn -her death from the fruitless condolence of his friends. He was deeply -and bitterly affected by this additional blow, which came upon him when -he was himself in a weak and declining state of health, and his answers -breathe a spirit of the most hopeless and gloomy despondency. - -In a letter written in April to Bocchineri, his son's father-in-law, he -says: "The hernia has returned worse than at first: my pulse is -intermitting, accompanied with a palpitation of the heart; an -immeasurable sadness and melancholy; an entire loss of appetite; I am -hateful to myself; and in short I feel that I am called incessantly by -my dear daughter. In this state, I do not think it advisable that -Vincenzo should set out on his journey, and leave me, when every hour -something may occur, which would make it expedient that he should be -here." In this extremity of ill health, Galileo requested leave to go to -Florence for the advantage of medical assistance; but far from obtaining -permission, it was intimated that any additional importunities would be -noticed by depriving him of the partial liberty he was then allowed to -enjoy. After several years confinement at Arcetri, during the whole of -which time he suffered from continual indisposition, the inquisitor -Fariano wrote to him in 1638, that the Pope permitted his removal to -Florence, for the purpose of recovering his health; requiring him at the -same time to present himself at the Office of the Inquisition, where he -would learn the conditions on which this favour had been granted. These -were that he should neither quit his house nor receive his friends -there; and so closely was the letter of these instructions adhered to, -that he was obliged to obtain a special permission to go out to attend -mass during Passion week. The strictness with which all personal -intercourse with his friends was interrupted, is manifest from the -result of the following letter from the Duke of Tuscany's secretary of -state to Nicolini, his ambassador at Rome. "Signor Galileo Galilei, from -his great age and the illnesses which afflict him, is in a condition -soon to go to another world; and although in this the eternal memory of -his fame and value is already secured, yet his Highness is greatly -desirous that the world should sustain as little loss as possible by his -death; that his labours may not perish, but for the public good may be -brought to that perfection which he will not be able to give them. He -has in his thoughts many things worthy of him, which he cannot be -prevailed on to communicate to any but Father Benedetto Castelli, in -whom he has entire confidence. His Highness wishes therefore that you -should see Castelli, and induce him to procure leave to come to Florence -for a few months for this purpose, which his Highness has very much at -heart; and if he obtains permission, as his Highness hopes, you will -furnish him with money and every thing else he may require for his -journey." Castelli, it will be remembered, was at this time salaried by -the court of Rome. Nicolini answered that Castelli had been himself to -the Pope to ask leave to go to Florence. Urban immediately intimated his -suspicions that his design was to see Galileo, and upon Castelli's -stating that certainly it would be impossible for him to refrain from -attempting to see him, he received permission to visit him in the -company of an officer of the Inquisition. At the end of some months -Galileo was remanded to Arcetri, which he never again quitted. - -In addition to his other infirmities, a disorder which some years before -had affected the sight of his right eye returned in 1636; in the course -of the ensuing year the other eye began to fail also, and in a few -months he became totally blind. It would be difficult to find any even -among those who are the most careless to make a proper use of the -invaluable blessing of sight, who could bear unmoved to be deprived of -it, but on Galileo the loss fell with peculiar and terrible severity; on -him who had boasted that he would never cease from using the senses -which God had given him, in declaring the glory of his works, and the -business of whose life had been the splendid fulfilment of that -undertaking. "The noblest eye is darkened," said Castelli, "which nature -ever made: an eye so privileged, and gifted with such rare qualities, -that it may with truth be said to have seen more than all of those who -are gone, and to have opened the eyes of all who are to come." His own -patience and resignation under this fatal calamity are truly wonderful; -and if occasionally a word of complaint escaped him, it was in the -chastened tone of the following expressions--"Alas! your dear friend and -servant Galileo has become totally and irreparably blind; so that this -heaven, this earth, this universe, which with wonderful observations I -had enlarged a hundred and thousand times beyond the belief of by-gone -ages, henceforward for me is shrunk into the narrow space which I myself -fill in it.--So it pleases God: it shall therefore please me also." -Hopes were at first entertained by Galileo's friends, that the -blindness was occasioned by cataracts, and that he might look forward to -relief from the operation of couching; but it very soon appeared that -the disorder was not in the humours of the eye, but in a cloudiness of -the cornea, the symptoms of which all external remedies failed to -alleviate. - -As long as the power was left him, he had indefatigably continued his -astronomical observations. Just before his sight began to decay, he had -observed a new phenomenon in the moon, which is now known by the name of -the moon's libration, the nature of which we will shortly explain. A -remarkable circumstance connected with the moon's motion is, that the -same side is always visible from the earth, showing that the moon turns -once on her own axis in exactly the time of her monthly revolution.[114] -But Galileo, who was by this time familiar with the whole of the moon's -visible surface, observed that the above-mentioned effect does not -accurately take place, but that a small part on either side comes -alternately forward into sight, and then again recedes, according to the -moon's various positions in the heavens. He was not long in detecting -one of the causes of this apparent libratory or rocking motion. It is -partly occasioned by our distance as spectators from the centre of the -earth, which is also the centre of the moon's motion. In consequence of -this, as the moon rises in the sky we get an additional view of the -lower half, and lose sight of a small part of the upper half which was -visible to us while we were looking down upon her when low in the -horizon. The other cause is not quite so simple, nor is it so certain -that Galileo adverted to it: it is however readily intelligible even to -those who are unacquainted with astronomy, if they will receive as a -fact that the monthly motion of the moon is not uniform, but that she -moves quicker at one time than another, whilst the motion of rotation on -her own axis, like that of the earth, is perfectly uniform. A very -little reflection will show that the observed phenomenon will -necessarily follow. If the moon did not turn on her axis, every side of -her would be successively presented, in the course of a month, towards -the earth; it is the motion of rotation which tends to carry the newly -discovered parts out of sight. - -Let us suppose the moon to be in that part of her orbit where she moves -with her average motion, and that she is moving towards the part where -she moves most quickly. If the motion in the orbit were to remain the -same all the way round, the motion of rotation would be just sufficient -at every point to bring round the same part of the moon directly in -front of the earth. But since, from the supposed point, the moon is -moving for some time round the earth with a motion continually growing -quicker, the motion of rotation is not sufficiently quick to carry out -of sight the entire part discovered by the motion of translation. We -therefore get a glimpse of a narrow strip on the side _from_ which the -moon is moving, which strip grows broader and broader, till she passes -the point where she moves most swiftly, and reaches the point of average -swiftness on the opposite side of her orbit. Her motion is now -continually growing slower, and therefore from this point the motion of -rotation is too swift, and carries too much out of sight, or in other -words, brings into sight a strip on the side _towards_ which the moon is -moving. This increases till she passes the point of least swiftness, and -arrives at the point from which we began to trace her course, and the -phenomena are repeated in the same order. - -This interesting observation closes the long list of Galileo's -discoveries in the heavens. After his abjuration, he ostensibly withdrew -himself in a great measure from his astronomical pursuits, and employed -himself till 1636 principally with his Dialogues on Motion, the last -work of consequence that he published. In that year he entered into -correspondence with the Elzevirs, through his friend Micanzio, on the -project of printing a complete edition of his writings. Among the -letters which Micanzio wrote on the subject is one intimating that he -had enjoyed the gratification, in his quality of Theologian to the -Republic of Venice, of refusing his sanction to a work written against -Galileo and Copernicus. The temper however in which this refusal was -announced, contrasts singularly with that of the Roman Inquisitors. "A -book was brought to me which a Veronese Capuchin has been writing, and -wished to print, denying the motion of the earth. I was inclined to let -it go, to make the world laugh, for the ignorant beast entitles every -one of the twelve arguments which compose his book, 'An irrefragable and -undeniable demonstration,' and then adduces nothing but such childish -trash as every man of sense has long discarded. For instance, this poor -animal understands so much geometry and mathematics, that he brings -forward as a demonstration, that if the earth could move, having nothing -to support it, it must necessarily fall. He ought to have added that -then we should catch all the quails. But when I saw that he speaks -indecently of you, and has had the impudence to put down an account of -what passed lately, saying that he is in possession of the whole of your -process and sentence, I desired the man who brought it to me to go and -be hanged. But you know the ingenuity of impertinence; I suspect he will -succeed elsewhere, because he is so enamoured of his absurdities, that -he believes them more firmly than his Bible." - -After Galileo's condemnation at Rome, he had been placed by the -Inquisition in the list of authors the whole of whose writings, '_edita -et edenda_,' were strictly forbidden. Micanzio could not even obtain -permission to reprint the Essay on Floating Bodies, in spite of his -protestations that it did not in any way relate to the Copernican -theory. This was the greatest stigma with which the Inquisition were in -the habit of branding obnoxious authors; and, in consequence of it, when -Galileo had completed his Dialogues on Motion, he found great difficulty -in contriving their publication, the nature of which may be learned from -the account which Pieroni sent to Galileo of his endeavours to print -them in Germany. He first took the manuscript to Vienna, but found that -every book printed there must receive the approbation of the Jesuits; -and Galileo's old antagonist, Scheiner, happening to be in that city, -Pieroni feared lest he should interfere to prevent the publication -altogether, if the knowledge of it should reach him. Through the -intervention of Cardinal Dietrichstein, he therefore got permission to -have it printed at Olmutz, and that it should be approved by a -Dominican, so as to keep the whole business a secret from Scheiner and -his party; but during this negociation the Cardinal suddenly died, and -Pieroni being besides dissatisfied with the Olmutz type, carried back -the manuscript to Vienna, from which he heard that Scheiner had gone -into Silesia. A new approbation was there procured, and the work was -just on the point of being sent to press, when the dreaded Scheiner -re-appeared in Vienna, on which Pieroni again thought it advisable to -suspend the impression till his departure. In the mean time his own duty -as a military architect in the Emperor's service carried him to Prague, -where Cardinal Harrach, on a former occasion, had offered him the use of -the newly-erected University press. But Harrach happened not to be at -Prague, and this plan like the rest became abortive. In the meantime -Galileo, wearied with these delays, had engaged with Louis Elzevir, who -undertook to print the Dialogues at Amsterdam. - -It is abundantly evident from Galileo's correspondence that this edition -was printed with his full concurrence, although, in order to obviate -further annoyance, he pretended that it was pirated from a manuscript -copy which he sent into France to the Comte de Noailles, to whom the -work is dedicated. The same dissimulation had been previously thought -necessary, on occasion of the Latin translation of "The Dialogues on the -System," by Bernegger, which Galileo expressly requested through his -friend Deodati, and of which he more than once privately signified his -approbation, presenting the translator with a valuable telescope, -although he publicly protested against its appearance. The story which -Bernegger introduced in his preface, tending to exculpate Galileo from -any share in the publication, is by his own confession a mere fiction. -Noailles had been ambassador at Rome, and, by his conduct there, well -deserved the compliment which Galileo paid him on the present occasion. - -As an introduction to the account of this work, which Galileo considered -the best he had ever produced, it will become necessary to premise a -slight sketch of the nature of the mechanical philosophy which he found -prevailing, nearly as it had been delivered by Aristotle, with the same -view with which we introduced specimens of the astronomical opinions -current when Galileo began to write on that subject: they serve to show -the nature and objects of the reasoning which he had to oppose; and, -without some exposition of them, the aim and value of many of his -arguments would be imperfectly understood and appreciated. - - -FOOTNOTES: - -[114] Frisi says that Galileo did not perceive this conclusion (Elogio -del Galileo); but see The Dial. on the System, Dial. 1. pp. 61, 62, 85. -Edit. 1744. Plutarch says, (De Placitis Philos. lib. ii. c. 28,) that -the Pythagoreans believed the moon to have inhabitants fifteen times as -large as men, and that their day is fifteen times as long as ours. It -seems probable, that the former of these opinions was engrafted on the -latter, which is true, and implies a perception of the fact in the text. - - - - -CHAPTER XVI. - - _State of the Science of Motion before Galileo._ - - -IT is generally difficult to trace any branch of human knowledge up to -its origin, and more especially when, as in the case of mechanics, it is -very closely connected with the immediate wants of mankind. Little has -been told to us when we are informed that so soon as a man might wish to -remove a heavy stone, "he would be led, by natural instinct, to slide -under it the end of some long instrument, and that the same instinct -would teach him either to raise the further end, or to press it -downwards, so as to turn round upon some support placed as near to the -stone as possible."[115] - -Montucla's history would have lost nothing in value, if, omitting "this -philosophical view of the birth of the art," he had contented himself -with his previous remark, that there can be little doubt that men were -familiar with the use of mechanical contrivances long before the idea -occurred of enumerating or describing them, or even of examining very -closely the nature and limits of the aid they are capable of affording. -The most careless observer indeed could scarcely overlook that the -weights heaved up with a lever, or rolled along a slope into their -intended places, reached them more slowly than those which the workmen -could lift directly in their hands; but it probably needed a much longer -time to enable them to see the exact relation which, in these and all -other machines, exists between the increase of the power to move, and -the decreasing swiftness of the thing moved. - -In the preface to Galileo's Treatise on Mechanical Science, published in -1592, he is at some pains to set in a clear light the real advantages -belonging to the use of machines, "which (says he) I have thought it -necessary to do, because, if I mistake not, I see almost all mechanics -deceiving themselves in the belief that, by the help of a machine, they -can raise a greater weight than they are able to lift by the exertion of -the same force without it.--Now if we take any determinate weight, and -any force, and any distance whatever, it is beyond doubt that we can -move the weight to that distance by means of that force; because even -although the force may be exceedingly small, if we divide the weight -into a number of fragments, each of which is not too much for our force, -and carry these pieces one by one, at length we shall have removed the -whole weight; nor can we reasonably say at the end of our work, that -this great weight has been moved and carried away by a force less than -itself, unless we add that the force has passed several times over the -space through which the whole weight has gone but once. From which it -appears that the velocity of the force (understanding by velocity the -space gone through in a given time) has been as many times greater than -that of the weight, as the weight is greater than the force: nor can we -on that account say that a great force is overcome by a small one, -contrary to nature: then only might we say that nature is overcome when -a small force moves a great weight as swiftly as itself, which we assert -to be absolutely impossible with any machine either already or hereafter -to be contrived. But since it may occasionally happen that we have but a -small force, and want to move a great weight without dividing it into -pieces, then we must have recourse to a machine by means of which we -shall remove the given weight, with the given force, through the -required space. But nevertheless the force as before will have to travel -over that very same space as many times repeated as the weight surpasses -its power, so that, at the end of our work, we shall find that we have -derived no other benefit from our machine than that we have carried away -the same weight altogether, which if divided into pieces we could have -carried without the machine, by the same force, through the same space, -in the same time. This is one of the advantages of a machine, because it -often happens that we have a lack of force but abundance of time, and -that we wish to move great weights all at once." - -This compensation of force and time has been fancifully personified by -saying that Nature cannot be cheated, and in scientific treatises on -mechanics, is called the "principle of virtual velocities," consisting -in the theorem that two weights will balance each other on any machine, -no matter how complicated or intricate the connecting contrivances may -be, when one weight bears to the other the same proportion that the -space through which the latter would be raised bears to that through -which the former would sink, in the first instant of their motion, if -the machine were stirred by a third force. The whole theory of machines -consists merely in generalizing and following out this principle into -its consequences; combined, when the machines are in a state of motion, -with another principle equally elementary, but to which our present -subject does not lead us to allude more particularly. - -The credit of making known the principle of virtual velocities is -universally given to Galileo; and so far deservedly, that he undoubtedly -perceived the importance of it, and by introducing it everywhere into -his writings succeeded in recommending it to others; so that five and -twenty years after his death, Borelli, who had been one of Galileo's -pupils, calls it "that mechanical principle with which everybody is so -familiar[116]," and from that time to the present it has continued to be -taught as an elementary truth in most systems of mechanics. But although -Galileo had the merit in this, as in so many other cases, of -familiarizing and reconciling the world to the reception of truth, there -are remarkable traces before his time of the employment of this same -principle, some of which have been strangely disregarded. Lagrange -asserts[117] that the ancients were entirely ignorant of the principle -of virtual velocities, although Galileo, to whom he refers it, -distinctly mentions that he himself found it in the writings of -Aristotle. Montucla quotes a passage from Aristotle's Physics, in which -the law is stated generally, but adds that he did not perceive its -immediate application to the lever, and other machines. The passage to -which Galileo alludes is in Aristotle's Mechanics, where, in discussing -the properties of the lever, he says expressly, "the same force will -raise a greater weight, in proportion as the force is applied at a -greater distance from the fulcrum, and the reason, as I have already -said, is because it describes a greater circle; and a weight which is -farther removed from the centre is made to move through a greater -space."[118] - -It is true, that in the last mentioned treatise, Aristotle has given -other reasons which belong to a very different kind of philosophy, and -which may lead us to doubt whether he fully saw the force of the one we -have just quoted. It appeared to him not wonderful that so many -mechanical paradoxes (as he called them) should be connected with -circular motion, since the circle itself seemed of so paradoxical a -nature. "For, in the first place, it is made up of an immoveable centre, -and a moveable radius, qualities which are contrary to each other. 2dly. -Its circumference is both convex and concave. 3dly. The motion by which -it is described is both forward and backward, for the describing radius -comes back to the place from which it started. 4thly. The radius is -_one_; but every point of it moves in describing the circle with a -different degree of swiftness." - -Perhaps Aristotle may have borrowed the idea of virtual velocities, -contrasting so strongly with his other physical notions, from some older -writer; possibly from Archytas, who, we are told, was the first to -reduce the science of mechanics to methodical order;[119] and who by the -testimony of his countrymen was gifted with extraordinary talents, -although none of his works have come down to us. The other principles -and maxims of Aristotle's mechanical philosophy, which we shall have -occasion to cite, are scattered through his books on Mechanics, on the -Heavens, and in his Physical Lectures, and will therefore follow rather -unconnectedly, though we have endeavoured to arrange them with as much -regularity as possible. - -After defining a body to be that which is divisible in every direction, -Aristotle proceeds to inquire how it happens that a body has only the -three dimensions of length, breadth, and thickness; and seems to think -he has given a reason in saying that, when we speak of two things, we do -not say "all," but "both," and three is the first number of which we say -"all."[120] When he comes to speak of motion, he says, "If motion is not -understood, we cannot but remain ignorant of Nature. Motion appears to -be of the nature of continuous quantities, and in continuous quantity -infinity first makes its appearance; so as to furnish some with a -definition who say that continuous quantity is that which is infinitely -divisible.--Moreover, unless there be time, space, and a vacuum, it is -impossible that there should be motion."[121]--Few propositions of -Aristotle's physical philosophy are more notorious than his assertion -that nature abhors a vacuum, on which account this last passage is the -more remarkable, as he certainly did not go so far as to deny the -existence of motion, and therefore asserts here the necessity of that of -which he afterwards attempts to show the absurdity.--"Motion is the -energy of what exists in power so far forth as so existing. It is that -act of a moveable which belongs to its power of moving."[122] After -struggling through such passages as the preceding we come at last to a -resting-place.--"It is difficult to understand what motion is."--When -the same question was once proposed to another Greek philosopher, he -walked away, saying, "I cannot tell you, but I will show you;" an answer -intrinsically worth more than all the subtleties of Aristotle, who was -not humble-minded enough to discover that he was tasking his genius -beyond the limits marked out for human comprehension. - -He labours in the same manner and with the same success to vary the idea -of space. He begins the next book with declaring, that "those who say -there is a vacuum assert the existence of space; for a vacuum is space, -in which there is no substance;" and after a long and tedious reasoning -concludes that, "not only what space is, but also whether there be such -a thing, cannot but be doubted."[123] Of time he is content to say -merely, that "it is clear that time is not motion, but that without -motion there would be no time;"[124] and there is perhaps little fault -to be found with this remark, understanding motion in the general sense -in which Aristotle here applies it, of every description of change. - -Proceeding after these remarks on the nature of motion in general to the -motion of bodies, we are told that "all local motion is either straight, -circular, or compounded of these two; for these two are the only simple -sorts of motion. Bodies are divided into simple and concrete; simple -bodies are those which have naturally a principle of motion, as fire and -earth, and their kinds. By simple motion is meant the motion of a simple -body."[125] By these expressions Aristotle did not mean that a simple -body cannot have what he calls a compound motion, but in that case he -called the motion violent or unnatural; this division of motion into -natural and violent runs through the whole of the mechanical philosophy -founded upon his principles. "Circular motion is the only one which can -be endless;"[126] the reason of which is given in another place: for -"that cannot be doing, which cannot be done; and therefore it cannot be -that a body should be moving towards a point (_i.e._ the end of an -infinite straight line) whither no motion is sufficient to bring -it."[127] Bacon seems to have had these passages in view when he -indulged in the reflections which we have quoted in page 14. "There are -four kinds of motion of one thing by another: Drawing, Pushing, -Carrying, Rolling. Of these, Carrying and Rolling may be referred to -Drawing and Pushing.[128]--The prime mover and the thing moved are -always in contact." - -The principle of the composition of motions is stated very plainly: -"when a moveable is urged in two directions with motions bearing an -indefinitely small ratio to each other, it moves necessarily in a -straight line, which is the diameter of the figure formed by drawing the -two lines of direction in that ratio;"[129] and adds, in a singularly -curious passage, "but when it is urged for any time with two motions -which have an indefinitely small ratio one to another, the motion cannot -be straight, so that a body describes a curve, when it is urged by two -motions bearing an indefinitely small ratio one to another, and lasting -an indefinitely small time."[130] - -He seemed on the point of discovering some of the real laws of motion, -when he was led to ask--"Why are bodies in motion more easily moved than -those which are at rest?--And why does the motion cease of things cast -into the air? Is it that the force has ceased which sent them forth, or -is there a struggle against the motion, or is it through the disposition -to fall, does it become stronger than the projectile force, or is it -foolish to entertain doubts on this question, when the body has quitted -the principle of its motion?" A commentator at the close of the -sixteenth century says on this passage: "They fall because every thing -recurs to its nature; for if you throw a stone a thousand times into the -air, it will never accustom itself to move upwards." Perhaps we shall -now find it difficult not to smile at the idea we may form of this -luckless experimentalist, teaching stones to fly; yet it may be useful -to remember that it is only because we have already collected an opinion -from the results of a vast number of observations in the daily -experience of life, that our ridicule would not be altogether misplaced, -and that we are totally unable to determine by any kind of reasoning, -unaccompanied by experiment, whether a stone thrown into the air would -fall again to the earth, or move for ever upwards, or in any other -conceivable manner and direction. - -The opinion which Aristotle held, that motion must be caused by -something in contact with the body moved, led him to his famous theory -that falling bodies are accelerated by the air through which they pass. -We will show how it was attempted to explain this process when we come -to speak of more modern authors. He classed natural bodies into heavy -and light, remarking at the same time that it is clear that there are -some bodies possessing neither gravity nor levity."[131] By light bodies -he understood those which have a natural tendency to move from the -earth, observing that "that which is lighter is not always light."[132] -He maintained that the heavenly bodies were altogether devoid of -gravity; and we have already had occasion to mention his assertion, that -a large body falls faster than a small one in proportion to its -weight.[133] With this opinion may be classed another great mistake, in -maintaining that the same bodies fall through different mediums, as air -or water, with velocities reciprocally proportional to their densities. -By a singular inversion of experimental science, Cardan, relying on this -assertion, proposed in the sixteenth century to determine the densities -of air and water by observing the different times taken by a stone in -falling through them.[134] Galileo inquired afterwards why the -experiment should not be made with a cork, which pertinent question put -an end to the theory. - -There are curious traces still preserved in the poem of Lucretius of a -mechanical philosophy, of which the credit is in general given to -Democritus, where many principles are inculcated strongly at variance -with Aristotle's notions. We find absolute levity denied, and not only -the assertion that in a vacuum all things would fall, but that they -would fall with the same velocity; and the inequalities which we observe -are attributed to the right cause, the impediment of the air, although -the error remains of believing the velocity of bodies falling through -the air to be proportional to their weight.[135] Such specimens of this -earlier philosophy may well indispose us towards Aristotle, who was as -successful in the science of motion as he was in astronomy in -suppressing the knowledge of a theory so much sounder than that which he -imposed so long upon the credulity of his blinded admirers. - -An agreeable contrast to Aristotle's mystical sayings and fruitless -syllogisms is presented in Archimedes' book on Equilibrium, in which he -demonstrates very satisfactorily, though with greater cumbrousness of -apparatus than is now thought necessary, the principal properties of the -lever. This and the Treatise on the Equilibrium of Floating Bodies are -the only mechanical works which have reached us of this writer, who was -by common consent one of the most accomplished mathematicians of -antiquity. Ptolemy the astronomer wrote also a Treatise on Mechanics, -now lost, which probably contained much that would be interesting in the -history of mechanics; for Pappus says, in the Preface to the Eighth Book -of his Mathematical Collections: "There is no occasion for me to explain -what is meant by a heavy, and what by a light body, and why bodies are -carried up and down, and in what sense these very words 'up' and 'down' -are to be taken, and by what limits they are bounded; for all this is -declared in Ptolemy's Mechanics."[136] This book of Ptolemy's appears to -have been also known by Eutocius, a commentator of Archimedes, who lived -about the end of the fifth century of our era; he intimates that the -doctrines contained in it are grounded upon Aristotle's; if so, its loss -is less to be lamented. Pappus's own book deserves attention for the -enumeration which he makes of the mechanical powers, namely, the wheel -and axle, the lever, pullies, the wedge and the screw. He gives the -credit to Hero and Philo of having shown, in works which have not -reached us, that the theory of all these machines is the same. In Pappus -we also find the first attempt to discover the force necessary to -support a given weight on an inclined plane. This in fact is involved in -the theory of the screw; and the same vicious reasoning which Pappus -employs on this occasion was probably found in those treatises which he -quotes with so much approbation. Numerous as are the faults of his -pretended demonstration, it was received undoubtingly for a long period. - -[Illustration: Chain.] - -The credit of first giving the true theory of equilibrium on the -inclined plane is usually ascribed to Stevin, although, as we shall -presently show, with very little reason. Stevin supposed a chain to be -placed over two inclined planes, and to hang down in the manner -represented in the figure. He then urged that the chain would be in -equilibrium; for otherwise, it would incessantly continue in motion, if -there were any cause why it should begin to move. This being conceded, -he remarks further, that the parts AD and BD are also in equilibrium, -being exactly similar to each other; and therefore if they are taken -away, the remaining parts AC and BC will also be in equilibrium. The -weights of these parts are proportional to the lengths AC and BC; and -hence Stevin concluded that two weights would balance on two inclined -planes, which are to each other as the lengths of the planes included -between the same parallels to the horizon.[137] This conclusion is the -correct one, and there is certainly great ingenuity in this contrivance -to facilitate the demonstration; it must not however be mistaken for an -_a priori_ proof, as it sometimes seems to have been: we should remember -that the experiments which led to the principle of virtual velocities -are also necessary to show the absurdity of supposing a perpetual -motion, which is made the foundation of this theorem. That principle had -been applied directly to determine the same proportion in a work written -long before, where it has remained singularly concealed from the notice -of most who have written on this subject. The book bears the name of -Jordanus, who lived at Namur in the thirteenth century; but Commandine, -who refers to it in his Commentary on Pappus, considers it as the work -of an earlier period. The author takes the principle of virtual -velocities for the groundwork of his explanations, both of the lever and -inclined plane; the latter will not occupy much space, and in an -historical point of view is too curious to be omitted. - -"_Quaest. 10._--If two weights descend by paths of different -obliquities, and the proportion be the same of the weights and the -inclinations taken in the same order, they will have the same descending -force. By the inclinations, I do not mean the angles, but the paths up -to the point in which both meet the same perpendicular.[138] Let, -therefore, _e_ be the weight upon _dc_, and _h_ upon _da_, and let _e_ -be to _h_ as _dc_ to _da_. I say these weights, in this situation, are -equally effective. Take _dk_ equally inclined with _dc_, and upon it a -weight equal to _e_, which call 6. If possible let _e_ descend to _l_, -so as to raise _h_ to _m_, and take 6_n_ equal to _hm_ or _el_, and draw -the horizontal and perpendicular lines as in the figure. - -[Illustration] - - Then _nz_:_n_6 :: _db_:_dk_ - and _mh_:_mx_ :: _da_:_db_ - -therefore _nz_:_mx_ :: _da_:_dk_ :: _h_:6, _and therefore since er is -not able to raise_ 6 _to n, neither will it be able to raise h to m_; -therefore they will remain as they are."[139] The passage in Italics -tacitly assumes the principle in question. Tartalea, who edited -Jordanus's book in 1565, has copied this theorem _verbatim_ into one of -his own treatises, and from that time it appears to have attracted no -further attention. The rest of the book is of an inferior description. -We find Aristotle's doctrine repeated, that the velocity of a falling -body is proportional to its weight; that the weight of a heavy body -changes with its form; and other similar opinions. The manner in which -falling bodies are accelerated by the air is given in detail. "By its -first motion the heavy body will drag after it what is behind, and move -what is just below it; and these when put in motion move what is next to -them, so that by being set in motion they less impede the falling body. -In this manner it has the effect of being heavier, and impels still more -those which give way before it, until at last they are no longer -impelled, but begin to drag. And thus it happens that its gravity is -increased by their attraction, and their motion by its gravity, whence -we see that its velocity is continually multiplied." - -In this short review of the state of mechanical science before Galileo, -the name of Guido Ubaldi ought not to be omitted, although his works -contain little or nothing original. We have already mentioned Benedetti -as having successfully attacked some of Aristotle's statical doctrines, -but it is to be noticed that the laws of motion were little if at all -examined by any of these writers. There are a few theorems connected -with this latter subject in Cardan's extraordinary book "On -Proportions," but for the most part false and contradictory. In the -seventy-first proposition of his fifth book, he examines the force of -the screw in supporting a given weight, and determines it accurately on -the principle of virtual velocities; namely, that the power applied at -the end of the horizontal lever must make a complete circuit at that -distance from the centre, whilst the weight rises through the -perpendicular height of the thread. The very next proposition in the -same page is to find the same relation between the power and weight on -an inclined plane; and although the identity of principle in these two -mechanical aids was well known, yet Cardan declares the necessary -sustaining force to vary as the angle of inclination of the plane, for -no better reason than that such an expression will properly represent it -at the two limiting angles of inclination, since the force is nothing -when the plane is horizontal, and equal to the weight when -perpendicular. This again shows how cautious we should be in attributing -the full knowledge of general principles to these early writers, on -account of occasional indications of their having employed them. - - -FOOTNOTES: - -[115] Histoire des Mathematiques, vol. i. p. 97. - -[116] De vi Percussionis, Bononiae, 1667. - -[117] Mec. Analyt. - -[118] Mechanica. - -[119] Diog. Laert. In vit. Archyt. - -[120] De Coelo, lib. i. c. 1. - -[121] Phys. lib. i. c. 3. - -[122] Lib. iii. c. 2. The Aristotelians distinguished between things as -existing in act or energy ([energeia]) and things in capacity or power -([dynamis]). For the advantage of those who may think the distinction -worth attending to, we give an illustration of Aristotle's meaning, from -a very acute and learned commentator:--"It (motion) is something more -than dead capacity; something less than perfect actuality; capacity -roused, and striving to quit its latent character; not the capable -brass, nor yet the actual statue, but the capacity in energy; that is to -say, the brass in fusion while it is becoming the statue and is not yet -become."--"The bow moves not because it may be bent, nor because it is -bent; but the motion lies between; lies in an imperfect and obscure -union of the two together; is the actuality (if I may so say) even of -capacity itself: imperfect and obscure, because such is capacity to -which it belongs."--Harris, Philosophical Arrangements. - -[123] Lib. iv. c. 1. - -[124] Lib. iv. c. 11. - -[125] De Coelo, lib. i. c. 2. - -[126] Phys. lib. vii. c. 8. - -[127] De Coelo, lib. i. c. 6. - -[128] Phys. lib. vii. c. 2. - -[129] Mechanica. - -[130] [Ean de en medeni logo pheretai duo phoras kata medena chronon, -adynaton eutheian einai ten phoran. Ean gar tina logon enechthe en -chrono tini touton anagke ton chronon eutheian einai phoran dia ta -proeiremena, hoste peripheres ginetai duo pheromenon phoras en medeni -logo medena chronon.]--_i.e._ v = ds/dt - -[131] De Coelo, lib. i. c. 3. - -[132] Lib. iv. c. 2. - -[133] Phys., lib. iv. c. 8. - -[134] De Proport. Basileae, 1570. - -[135] - - "Nunc locus est, ut opinor, in his illud quoque rebus - Confirmare tibi, nullam rem posse sua vi - Corpoream sursum ferri, sursumque meare.-- - Nec quom subsiliunt ignes ad tecta domorum, - Et celeri flamma degustant tigna trabeisque - Sponte sua facere id sine vi subicente putandum est. - --Nonne vides etiam quanta vi tigna trabeisque - Respuat humor aquae? Nam quod magi' mersimus altum - Directa et magna vi multi pressimus aegre:-- - Tam cupide sursum revomit magis atque remittit - Plus ut parte foras emergant, exsiliantque: - --Nec tamen haec, quantu'st in sedubitamus, opinor, - Quinvacuum per inane deorsum cuncta ferantur, - Sic igitur debent flammae quoque posse per auras - Aeris expressae sursum subsidere, quamquam - Pondera quantum in se est deorsum deducere pugnent. - --Quod si forte aliquis credit Graviora potesse - Corpora, quo citius rectum per Inane feruntur, - --Avius a vera longe ratione recedit. - Nam per Aquas quaecunque cadunt atque Aera deorsum - Haec pro ponderibus casus celerare necesse 'st - Propterea quia corpus Aquae, naturaque tenuis - Aeris haud possunt aeque rem quamque morari: - Sed citius cedunt Gravioribus exsuperata. - At contra nulli de nulla parte, neque ullo - Tempore Inane potest Vacuum subsistere reii - Quin, sua quod natura petit, considere pergat: - Omnia qua propter debent per Inane quietum - AEque ponderibus non aequis concita ferri." - - De Rerum Natura, lib. ii, v. 184-239. - -[136] Math. Coll. Pisani, 1662. - -[137] Oeuvres Mathematiques. Leyde, 1634. - -[138] This is not a literal translation, but by what follows, is -evidently the Author's meaning. His words are, "Proportionem igitur -declinationum dico non angulorum, sed linearum usque ad aequidistantem -resecationem in qua aequaliter sumunt de directo." - -[139] Opusculum De Ponderositate. Venetiis, 1565. - - - - -CHAPTER XVII. - - _Galileo's theory of Motion--Extracts from the Dialogues._ - - -DURING Galileo's residence at Sienna, when his recent persecution had -rendered astronomy an ungrateful, and indeed an unsafe occupation for -his ever active mind, he returned with increased pleasure to the -favourite employment of his earlier years, an inquiry into the laws and -phenomena of motion. His manuscript treatises on motion, written about -1590, which are mentioned by Venturi to be in the Ducal library at -Florence, seem, from the published titles of the chapters, to consist -principally of objections to the theory of Aristotle; a few only appear -to enter on a new field of speculation. The 11th, 13th, and 17th -chapters relate to the motion of bodies on variously inclined planes, -and of projectiles. The title of the 14th implies a new theory of -accelerated motion, and the assertion in that of the 16th, that a body -falling naturally for however great a time would never acquire more than -an assignable degree of velocity, shows that at this early period -Galileo had formed just and accurate notions of the action of a -resisting medium. It is hazardous to conjecture how much he might have -then acquired of what we should now call more elementary knowledge; a -safer course will be to trace his progress through existing documents in -their chronological order. In 1602 we find Galileo apologizing in a -letter addressed to his early patron the Marchese Guido Ubaldi, for -pressing again upon his attention the isochronism of the pendulum, which -Ubaldi had rejected as false and impossible. It may not be superfluous -to observe that Galileo's results are not quite accurate, for there is a -perceptible increase in the time occupied by the oscillations in larger -arcs; it is therefore probable that he was induced to speak so -confidently of their perfect equality, from attributing the increase of -time which he could not avoid remarking to the increased resistance of -the air during the larger vibrations. The analytical methods then known -would not permit him to discover the curious fact, that the time of a -total vibration is not sensibly altered by this cause, except so far as -it diminishes the extent of the swing, and thus in fact, (paradoxical as -it may sound) renders each oscillation successively more rapid, though -in a very small degree. He does indeed make the same remark, that the -resistance of the air will not affect the time of the oscillation, but -that assertion was a consequence of his erroneous belief that the time -of vibration in all arcs is the same. Had he been aware of the -variation, there is no reason to think that he could have perceived that -this result is not affected by it. In this letter is the first mention -of the theorem, that the times of fall down all the chords drawn from -the lowest point of a circle are equal; and another, from which Galileo -afterwards deduced the curious result, that it takes less time to fall -down the curve than down the chord, notwithstanding the latter is the -direct and shortest course. In conclusion he says, "Up to this point I -can go without exceeding the limits of mechanics, but I have not yet -been able to demonstrate that all arcs are passed in the same time, -which is what I am seeking." In 1604 he addressed the following letter -to Sarpi, suggesting the false theory sometimes called Baliani's, who -took it from Galileo. - -[Illustration: - - A-+ - | - | - B-+ - | - | - C-+ - | - | - D-+ ] - -"Returning to the subject of motion, in which I was entirely without a -fixed principle, from which to deduce the phenomena I have observed, I -have hit upon a proposition, which seems natural and likely enough; and -if I take it for granted, I can show that the spaces passed in natural -motion are in the double proportion of the times, and consequently that -the spaces passed in equal times are as the odd numbers beginning from -unity, and the rest. The principle is this, that the swiftness of the -moveable increases in the proportion of its distance from the point -whence it began to move; as for instance,--if a heavy body drop from A -towards D, by the line ABCD, I suppose the degree of velocity which it -has at B to bear to the velocity at C the ratio of AB to AC. I shall be -very glad if your Reverence will consider this, and tell me your opinion -of it. If we admit this principle, not only, as I have said, shall we -demonstrate the other conclusions, but we have it in our power to show -that a body falling naturally, and another projected upwards, pass -through the same degrees of velocity. For if the projectile be cast up -from D to A, it is clear that at D it has force enough to reach A, and -no farther; and when it has reached C and B, it is equally clear that it -is still joined to a degree of force capable of carrying it to A: thus -it is manifest that the forces at D, C and B decrease in the proportion -of AB, AC, and AD; so that if, in falling, the degrees of velocity -observe the same proportion, that is true which I have hitherto -maintained and believed." - -We have no means of knowing how early Galileo discovered the fallacy of -this reasoning. In his Dialogues on Motion, which contain the correct -theory, he has put this erroneous supposition in the mouth of Sagredo, -on which Salviati remarks, "Your discourse has so much likelihood in it, -that our author himself did not deny to me when I proposed it to him, -that he also had been for some time in the same mistake. But that which -I afterwards extremely wondered at, was to see discovered in four plain -words, not only the falsity, but the impossibility of a supposition -carrying with it so much of seeming truth, that although I proposed it -to many, I never met with any one but did freely admit it to be so; and -yet it is as false and impossible as that motion is made in an instant: -for if the velocities are as the spaces passed, those spaces will be -passed in equal times, and consequently all motion must be -instantaneous." The following manner of putting this reasoning will -perhaps make the conclusion clearer. The velocity at any point is the -space that would be passed in the next moment of time, if the motion be -supposed to continue the same as at that point. At the beginning of the -time, when the body is at rest, the motion is none; and therefore, on -this theory, the space passed in the next moment is none, and thus it -will be seen that the body cannot begin to move according to the -supposed law. - -A curious fact, noticed by Guido Grandi in his commentary on Galileo's -Dialogues on Motion, is that this false law of acceleration is precisely -that which would make a circular arc the shortest line of descent -between two given points; and although in general Galileo only declared -that the fall down the arc is made in less time than down the chord (in -which he is quite correct), yet in some places he seems to assert that -the circular arc is absolutely the shortest line of descent, which is -not true. It has been thought possible that the law, which on reflection -he perceived to be impossible, might have originally recommended itself -to him from his perception that it satisfied his prejudice in this -respect. - -John Bernouilli, one of the first mathematicians in Europe at the -beginning of the last century, has given us a proof that such a reason -might impose even on a strong understanding, in the following argument -urged by him in favour of Galileo's second and correct theory, that the -spaces vary as the squares of the times. He had been investigating the -curve of swiftest descent, and found it to be a cycloid, the same curve -in which Huyghens had already proved that all oscillations are made in -accurately equal times. "I think it," says he, "worthy of remark that -this identity only occurs on Galileo's supposition, so that this alone -might lead us to presume it to be the real law of nature. For nature, -which always does everything in the very simplest manner, thus makes one -line do double work, whereas on any other supposition, we must have had -two lines, one for equal oscillations, the other for the shortest -descent."[140] - -Venturi mentions a letter addressed to Galileo in May 1609 by Luca -Valerio, thanking him for his experiments on the descent of bodies on -inclined planes. His method of making these experiments is detailed in -the Dialogues on Motion:--"In a rule, or rather plank of wood, about -twelve yards long, half a yard broad one way, and three inches the -other, we made upon the narrow side or edge a groove of little more than -an inch wide: we cut it very straight, and, to make it very smooth and -sleek, we glued upon it a piece of vellum, polished and smoothed as -exactly as possible, and in that we let fall a very hard, round, and -smooth brass ball, raising one of the ends of the plank a yard or two at -pleasure above the horizontal plane. We observed, in the manner that I -shall tell you presently, the time which it spent in running down, and -repeated the same observation again and again to assure ourselves of the -time, in which we never found any difference, no, not so much as the -tenth part of one beat of the pulse. Having made and settled this -experiment, we let the same ball descend through a fourth part only of -the length of the groove, and found the measured time to be exactly half -the former. Continuing our experiments with other portions of the -length, comparing the fall through the whole with the fall through half, -two-thirds, three-fourths, in short, with the fall through any part, we -found by many hundred experiments that the spaces passed over were as -the squares of the times, and that this was the case in all inclinations -of the plank; during which, we also remarked that the times of descent, -on different inclinations, observe accurately the proportion assigned to -them farther on, and demonstrated by our author. As to the estimation of -the time, we hung up a great bucket full of water, which by a very small -hole pierced in the bottom squirted out a fine thread of water, which we -caught in a small glass during the whole time of the different descents: -then weighing from time to time, in an exact pair of scales, the -quantity of water caught in this way, the differences and proportions of -their weights gave the differences and proportions of the times; and -this with such exactness that, as I said before, although the -experiments were repeated again and again, they never differed in any -degree worth noticing." In order to get rid of the friction, Galileo -afterwards substituted experiments with the pendulum; but with all his -care he erred very widely in his determination of the space through -which a body would fall in 1'', if the resistance of the air and all -other impediments were removed. He fixed it at 4 _braccia_: Mersenne has -engraved the length of the '_braccia_' used by Galileo, in his "Harmonie -Universelle," from which it appears to be about 231/2 English inches, so -that Galileo's result is rather less than eight feet. Mersenne's own -result from direct observation was thirteen feet: he also made -experiments in St. Peter's at Rome, with a pendulum 325 feet long, the -vibrations of which were made in 10''; from this the fall in 1'' might -have been deduced rather more than sixteen feet, which is very close to -the truth. - -From another letter also written in the early part of 1609, we learn -that Galileo was then busied with examining the strength and resistance -"of beams of different sizes and forms, and how much weaker they are in -the middle than at the ends, and how much greater weight they can -support laid along their whole length, than if sustained on a single -point, and of what form they should be so as to be equally strong -throughout." He was also speculating on the motion of projectiles, and -had satisfied himself that their motion in a vertical direction is -unaffected by their horizontal velocity; a conclusion which, combined -with his other experiments, led him afterwards to determine the path of -a projectile in a non-resisting medium to be parabolical. - -Tartalea is supposed to have been the first to remark that no bullet -moves in a horizontal line; but his theory beyond this point was very -erroneous, for he supposed the bullet's path through the air to be made -up of an ascending and descending straight line, connected in the middle -by a circular arc. - -Thomas Digges, in his treatise on the Newe Science of Great Artillerie, -came much nearer the truth; for he remarked[141], that "The bullet -violentlye throwne out of the peece by the furie of the poulder hath two -motions: the one violent, which endeuoreth to carry the bullet right out -in his line diagonall, according to the direction of the peece's axis, -from whence the violent motion proceedeth; the other naturall in the -bullet itselfe, which endeuoreth still to carrye the same directlye -downeward by a right line perpendiculare to the horizon, and which dooth -though insensiblye euen from the beginning by little and little drawe it -from that direct and diagonall course." And a little farther he observes -that "These middle curve arkes of the bullet's circuite, compounded of -the violent and naturall motions of the bullet, albeit they be indeed -mere helicall, yet have they a very great resemblance of the Arkes -Conical. And in randons above 45 deg. they doe much resemble the Hyperbole, -and in all vnder the Ellepsis. But exactlye they neuer accorde, being -indeed Spirall mixte and Helicall." - -Perhaps Digges deserves no greater credit from this latter passage than -the praise of a sharp and accurate eye, for he does not appear to have -founded this determination of the form of the curve on any theory of the -direct fall of bodies; but Galileo's arrival at the same result was -preceded, as we have seen, by a careful examination of the simplest -phenomena into which this compound motion may be resolved. But it is -time to proceed to the analysis of his "Dialogues on Motion," these -preliminary remarks on their subject matter having been merely intended -to show how long before their publication Galileo was in possession of -the principal theories contained in them. - -Descartes, in one of his letters to Mersenne, insinuates that Galileo -had taken many things in these Dialogues from him: the two which he -especially instances are the isochronism of the pendulum, and the law of -the spaces varying as the squares of the times.[142] Descartes was born -in 1596: we have shown that Galileo observed the isochronism of the -pendulum in 1583, and knew the law of the spaces in 1604, although he -was then attempting to deduce it from an erroneous principle. As -Descartes on more than one occasion has been made to usurp the credit -due to Galileo, (in no instance more glaringly so than when he has been -absurdly styled the forerunner of Newton,) it will not be misplaced to -mention a few of his opinions on these subjects, recorded in his letters -to Mersenne in the collection of his letters just cited:--"I am -astonished at what you tell me of having found by experiment that bodies -thrown up in the air take neither more nor less time to rise than to -fall again; and you will excuse me if I say that I look upon the -experiment as a very difficult one to make accurately. This proportion -of increase according to the odd numbers 1, 3, 5, 7, &c., which is in -Galileo, and which I think I wrote to you some time back, cannot be -true, as I believe I intimated at the same time, unless we make two or -three suppositions which are entirely false. One is Galileo's opinion, -that motion increases gradually from the slowest degree; and the other -is, that the air makes no resistance." In a later letter to the same -person he says, apparently with some uneasiness, "I have been revising -my notes on Galileo, in which I have not said expressly, that falling -bodies do not pass through every degree of slowness, but I said that -this cannot be determined without knowing what weight is; _which comes -to the same thing_. As to your example, I grant that it proves that -every degree of velocity is infinitely divisible, but not that a falling -body actually passes through all these divisions.--It is certain that a -stone is not equally disposed to receive a new motion or increase of -velocity, when it is already moving very quickly, and when it is moving -slowly. But I believe that I am now able to determine in what proportion -the velocity of a stone increases, not when falling in a vacuum, but in -this substantial atmosphere.--However I have now got my mind full of -other things, and I cannot amuse myself with hunting this out, _nor is -it a matter of much utility_." He afterwards returns once more to the -same subject:--"As to what Galileo says, that falling bodies pass -through every degree of velocity, I do not believe that it generally -happens, but I allow it is not impossible that it may happen -occasionally." After this the reader will know what value to attach to -the following assertion by the same Descartes:--"I see nothing in -Galileo's books to envy him, and hardly any thing which I would own as -mine;" and then may judge how far Salusbury's blunt declaration is borne -out, "Where or when did any one appear that durst enter the lists with -our Galileus? save only one bold and unfortunate Frenchman, who yet no -sooner came within the ring but he was hissed out again."[143] - -The principal merit of Descartes must undoubtedly be derived from the -great advances he made in what are generally termed Abstract or Pure -Mathematics; nor was he slow to point out to Mersenne and his other -friends the acknowledged inferiority of Galileo to himself in this -respect. We have not sufficient proof that this difference would have -existed if Galileo's attention had been equally directed to that object; -the singular elegance of some of his geometrical constructions indicates -great talent for this as well as for his own more favourite -speculations. But he was far more profitably employed: geometry and pure -mathematics already far outstripped any useful application of their -results to physical science, and it was the business of Galileo's life -to bring up the latter to the same level. He found abstract theorems -already demonstrated in sufficient number for his purpose, nor was there -occasion to task his genius in search of new methods of inquiry, till -all was exhausted which could be learned from those already in use. The -result of his labours was that in the age immediately succeeding -Galileo, the study of nature was no longer in arrear of the abstract -theories of number and measure; and when the genius of Newton pressed it -forward to a still higher degree of perfection, it became necessary to -discover at the same time more powerful instruments of investigation. -This alternating process has been successfully continued to the present -time; the analyst acts as the pioneer of the naturalist, so that the -abstract researches, which at first have no value but in the eyes of -those to whom an elegant formula, in its own beauty, is a source of -pleasure as real and as refined as a painting or a statue, are often -found to furnish the only means for penetrating into the most intricate -and concealed phenomena of natural philosophy. - -Descartes and Delambre agree in suspecting that Galileo preferred the -dialogistic form for his treatises, because it afforded a ready -opportunity for him to praise his own inventions: the reason which he -himself gave is, the greater facility for introducing new matter and -collateral inquiries, such as he seldom failed to add each time that he -reperused his work. We shall select in the first place enough to show -the extent of his knowledge on the principal subject, motion, and shall -then allude as well as our limits will allow to the various other points -incidentally brought forward. - -The dialogues are between the same speakers as in the "System of the -World;" and in the first Simplicio gives Aristotle's proof,[144] that -motion in a vacuum is impossible, because according to him bodies move -with velocities in the compound proportion of their weights and the -rarities of the mediums through which they move. And since the density -of a vacuum bears no assignable ratio to that of any medium in which -motion has been observed, any body which should employ time in moving -through the latter, would pass through the same distance in a vacuum -instantaneously, which is impossible. Salviati replies by denying the -axioms, and asserts that if a cannon ball weighing 200 lbs., and a -musket ball weighing half a pound, be dropped together from a tower 200 -yards high, the former will not anticipate the latter by so much as a -foot; "and I would not have you do as some are wont, who fasten upon -some saying of mine that may want a hair's breadth of the truth, and -under this hair they seek to hide another man's blunder as big as a -cable. Aristotle says that an iron ball weighing 100 lbs. will fall from -the height of 100 yards while a weight of one pound falls but one yard: -I say they will reach the ground together. They find the bigger to -anticipate the less by two inches, and under these two inches they seek -to hide Aristotle's 99 yards." In the course of his reply to this -argument Salviati formally announces the principle which is the -foundation of the whole of Galileo's theory of motion, and which must -therefore be quoted in his own words:--"A heavy body has by nature an -intrinsic principle of moving towards the common centre of heavy things; -that is to say, to the centre of our terrestrial globe, with a motion -continually accelerated in such manner that in equal times there are -always equal additions of velocity. This is to be understood as holding -true only when all accidental and external impediments are removed, -amongst which is one that we cannot obviate, namely, the resistance of -the medium. This opposes itself, less or more, accordingly as it is to -open more slowly or hastily to make way for the moveable, which being by -its own nature, as I have said, continually accelerated, consequently -encounters a continually increasing resistance in the medium, until at -last the velocity reaches that degree, and the resistance that power, -that they balance each other; all further acceleration is prevented, and -the moveable continues ever after with an uniform and equable motion." -That such a limiting velocity is not greater than some which may be -exhibited may be proved as Galileo suggested by firing a bullet upwards, -which will in its descent strike the ground with less force than it -would have done if immediately from the mouth of the gun; for he argued -that the degree of velocity which the air's resistance is capable of -diminishing must be greater than that which could ever be reached by a -body falling naturally from rest. "I do not think the present occasion a -fit one for examining the cause of this acceleration of natural motion, -on which the opinions of philosophers are much divided; some referring -it to the approach towards the centre, some to the continual diminution -of that part of the medium remaining to be divided, some to a certain -extrusion of the ambient medium, which uniting again behind the moveable -presses and hurries it forwards. All these fancies, with others of the -like sort, we might spend our time in examining, and with little to gain -by resolving them. It is enough for our author at present that we -understand his object to be the investigation and examination of some -phenomena of a motion so accelerated, (no matter what may be the cause,) -that the momenta of velocity, from the beginning to move from rest, -increase in the simple proportion in which the time increases, which is -as much as to say, that in equal times are equal additions of velocity. -And if it shall turn out that the phenomena demonstrated on this -supposition are verified in the motion of falling and naturally -accelerated weights, we may thence conclude that the assumed definition -does describe the motion of heavy bodies, and that it is true that their -acceleration varies in the ratio of the time of motion." - -When Galileo first published these Dialogues on Motion, he was obliged -to rest his demonstrations upon another principle besides, namely, that -the velocity acquired in falling down all inclined planes of the same -perpendicular height is the same. As this result was derived directly -from experiment, and from that only, his theory was so far imperfect -till he could show its consistency with the above supposed law of -acceleration. When Viviani was studying with Galileo, he expressed his -dissatisfaction at this chasm in the reasoning; the consequence of which -was, that Galileo, as he lay the same night, sleepless through -indisposition, discovered the proof which he had long sought in vain, -and introduced it into the subsequent editions. The third dialogue is -principally taken up with theorems on the direct fall of bodies, their -times of descent down differently inclined planes, which in planes of -the same height he determined to be as the lengths, and with other -inquiries connected with the same subject, such as the straight lines of -shortest descent under different data, &c. - -[Illustration] - -The fourth dialogue is appropriated to projectile motion, determined -upon the principle that the horizontal motion will continue the same as -if there were no vertical motion, and the vertical motion as if there -were no horizontal motion. "Let AB represent a horizontal line or plane -placed on high, on which let a body be carried with an equable motion -from A towards B, and the support of the plane being taken away at B, -let the natural motion downwards due to the body's weight come upon it -in the direction of the perpendicular BN. Moreover let the straight line -BE drawn in the direction AB be taken to represent the flow, or measure, -of the time, on which let any number of equal parts BC, CD, DE, &c. be -marked at pleasure, and from the points C, D, E, let lines be drawn -parallel to BN; in the first of these let any part CI be taken, and let -DF be taken four times as great as CI, EH nine times as great, and so -on, proportionally to the squares of the lines BC, BD, BE, &c., or, as -we say, in the double proportion of these lines. Now if we suppose that -whilst by its equable horizontal motion the body moves from B to C, it -also descends by its weight through CI, at the end of the time denoted -by BC it will be at I. Moreover in the time BD, double of BC, it will -have fallen four times as far, for in the first part of the Treatise it -has been shewn that the spaces fallen through by a heavy body vary as -the squares of the times. Similarly at the end of the time BE, or three -times BC, it will have fallen through EH, and will be at H. And it is -plain that the points I, F, H, are in the same parabolical line BIFH. -The same demonstration will apply if we take any number of equal -particles of time of whatever duration." - -The curve called here a Parabola by Galileo, is one of those which -results from cutting straight through a Cone, and therefore is called -also one of the Conic Sections, the curious properties of which curves -had drawn the attention of geometricians long before Galileo thus began -to point out their intimate connexion with the phenomena of motion. -After the proposition we have just extracted, he proceeds to anticipate -some objections to the theory, and explains that the course of a -projectile will not be accurately a parabola for two reasons; partly on -account of the resistance of the air, and partly because a horizontal -line, or one equidistant from the earth's centre, is not straight, but -circular. The latter cause of difference will, however, as he says, be -insensible in all such experiments as we are able to make. The rest of -the Dialogue is taken up with different constructions for determining -the circumstances of the motion of projectiles, as their range, greatest -height, &c.; and it is proved that, with a given force of projection, -the range will be greatest when a ball is projected at an elevation of -45 deg., ranges of all angles equally inclined above and below 45 deg. -corresponding exactly to each other. - -[Illustration] - -One of the most interesting subjects discussed in these dialogues is the -famous notion of Nature's horror of a vacuum or empty space, which the -old school of philosophy considered as impossible to be obtained. -Galileo's notions of it were very different; for although he still -unadvisedly adhered to the old phrase to denote the resistance -experienced in endeavouring to separate two smooth surfaces, he was so -far from looking upon a vacuum as an impossibility, that he has -described an apparatus by which he endeavoured to measure the force -necessary to produce one. This consisted of a cylinder, into which is -tightly fitted a piston; through the centre of the piston passes a rod -with a conical valve, which, when drawn down, shuts the aperture -closely, supporting a basket. The space between the piston and cylinder -being filled full of water poured in through the aperture, the valve is -closed, the vessel reversed, and weights are added till the piston is -drawn forcibly downwards. Galileo concluded that the weight of the -piston, rod, and added weights, would be the measure of the force of -resistance to the vacuum which he supposed would take place between the -piston and lower surface of the water. The defects in this apparatus for -the purpose intended are of no consequence, so far as regards the -present argument, and it is perhaps needless to observe that he was -mistaken in supposing the water would not descend with the piston. This -experiment occasions a remark from Sagredo, that he had observed that a -lifting-pump would not work when the water in the cistern had sunk to -the depth of thirty-five feet below the valve; that he thought the pump -was injured, and sent for the maker of it, who assured him that no pump -upon that construction would lift water from so great a depth. This -story is sometimes told of Galileo, as if he had said sneeringly on this -occasion that Nature's horror of a vacuum does not extend beyond -thirty-five feet; but it is very plain that if he had made such an -observation, it would have been seriously; and in fact by such a -limitation he deprived the notion of the principal part of its -absurdity. He evidently had adopted the common notion of suction, for he -compares the column of water to a rod of metal suspended from its upper -end, which may be lengthened till it breaks with its own weight. It is -certainly very extraordinary that he failed to observe how simply these -phenomena may be explained by a reference to the weight of the elastic -atmosphere, which he was perfectly well acquainted with, and endeavoured -by the following ingenious experiment to determine:--"Take a large glass -flask with a bent neck, and round its mouth tie a leathern pipe with a -valve in it, through which water may be forced into the flask with a -syringe without suffering any air to escape, so that it will be -compressed within the bottle. It will be found difficult to force in -more than about three-fourths of what the flask will hold, which must be -carefully weighed. The valve must then be opened, and just so much air -will rush out as would in its natural density occupy the space now -filled by the water. Weigh the vessel again; the difference will show -the weight of that quantity of air."[145] By these means, which the -modern experimentalist will see were scarcely capable of much accuracy, -Galileo found that air was four hundred times lighter than water, -instead of ten times, which was the proportion fixed on by Aristotle. -The real proportion is about 830 times. - -The true theory of the rise of water in a lifting-pump is commonly dated -from Torricelli's famous experiment with a column of mercury, in 1644, -when he found that the greatest height at which it would stand is -fourteen times less than the height at which water will stand, which is -exactly the proportion of weight between water and mercury. The -following curious letter from Baliani, in 1630, shows that the original -merit of suggesting the real cause belongs to him, and renders it still -more unaccountable that Galileo, to whom it was addressed, should not at -once have adopted the same view of the subject:--"I have believed that a -vacuum may exist naturally ever since I knew that the air has sensible -weight, and that you taught me in one of your letters how to find its -weight exactly, though I have not yet succeeded with that experiment. -From that moment I took up the notion that it is not repugnant to the -nature of things that there should be a vacuum, but merely that it is -difficult to produce. To explain myself more clearly: if we allow that -the air has weight, there is no difference between air and water except -in degree. At the bottom of the sea the weight of the water above me -compresses everything round my body, and it strikes me that the same -thing must happen in the air, we being placed at the bottom of its -immensity; we do not feel its weight, nor the compression round us, -because our bodies are made capable of supporting it. But if we were in -a vacuum, then the weight of the air above our heads would be felt. It -would be felt very great, but not infinite, and therefore determinable, -and it might be overcome by a force proportioned to it. In fact I -estimate it to be such that, to make a vacuum, I believe we require a -force greater than that of a column of water thirty feet high."[146] - -[Illustration] - -This subject is introduced by some observations on the force of -cohesion, Galileo seeming to be of opinion that, although it cannot be -adequately accounted for by "the great and principal resistance to a -vacuum, yet that perhaps a sufficient cause may be found by considering -every body as composed of very minute particles, between every two of -which is exerted a similar resistance." This remark serves to lead to a -discussion on indivisibles and infinite quantities, of which we shall -merely extract what Galileo gives as a curious paradox suggested in the -course of it. He supposes a basin to be formed by scooping a hemisphere -out of a cylinder, and a cone to be taken of the same depth and base as -the hemisphere. It is easy to show, if the cone and scooped cylinder be -both supposed to be cut by the same plane, parallel to the one on which -both stand, that the area of the ring CDEF thus discovered in the -cylinder is equal to the area of the corresponding circular section AB -of the cone, wherever the cutting plane is supposed to be.[147] He then -proceeds with these remarkable words:--"If we raise the plane higher and -higher, one of these areas terminates in the circumference of a circle, -and the other in a point, for such are the upper rim of the basin and -the top of the cone. Now since in the diminution of the two areas they -to the very last maintain their equality to one another, it is in my -thoughts proper to say that the highest and ultimate terms[148] of such -diminutions are equal, and not one infinitely bigger than the other. It -seems therefore that the circumference of a large circle may be said to -be equal to one single point. And why may not these be called equal if -they be the last remainders and vestiges left by equal magnitudes[149]?" - -We think no one can refuse to admit the probability, that Newton may -have found in such passages as these the first germ of the idea of his -prime and ultimate ratios, which afterwards became in his hands an -instrument of such power. As to the paradoxical result, Descartes -undoubtedly has given the true answer to it in saying that it only -proves that the line is not a greater area than the point is. Whilst on -this subject, it may not be uninteresting to remark that something -similar to the doctrine of fluxions seems to have been lying dormant in -the minds of the mathematicians of Galileo's era, for Inchoffer -illustrates his argument in the treatise we have already mentioned, that -the Copernicans may deduce some true results from what he terms their -absurd hypothesis, by observing, that mathematicians may deduce the -truth that a line is length without breadth, from the false and -physically impossible supposition that a point flows, and that a line is -the fluxion of a point.[150] - -A suggestion that perhaps fire dissolves bodies by insinuating itself -between their minute particles, brings on the subject of the violent -effects of heat and light; on which Sagredo inquires, whether we are to -take for granted that the effect of light does or does not require time. -Simplicio is ready with an answer, that the discharge of artillery -proves the transmission of light to be instantaneous, to which Sagredo -cautiously replies, that nothing can be gathered from that experiment -except that light travels more swiftly than sound; nor can we draw any -decisive conclusion from the rising of the sun. "Who can assure us that -he is not in the horizon before his rays reach our sight?" Salviati then -mentions an experiment by which he endeavoured to examine this question. -Two observers are each to be furnished with a lantern: as soon as the -first shades his light, the second is to discover his, and this is to be -repeated at a short distance till the observers are perfect in the -practice. The same thing is to be tried at the distance of several -miles, and if the first observer perceive any delay between shading his -own light and the appearance of his companion's, it is to be attributed -to the time taken by the light in traversing twice the distance between -them. He allows that he could discover no perceptible interval at the -distance of a mile, at which he had tried the experiment, but recommends -that with the help of a telescope it should be tried at much greater -distances. Sir Kenelm Digby remarks on this passage: "It may be objected -(if there be some observable tardity in the motion of light) that the -sunne would never be truly in that place in which unto our eyes he -appeareth to be; because that it being seene by means of the light which -issueth from it, if that light required time to move in, the sunne -(whose motion is so swifte) would be removed from the place where the -light left it, before it could be with us to give tidings of him. To -this I answer, allowing peradventure that it may be so, who knoweth the -contrary? Or what inconvenience would follow if it be admitted[151]?" - -The principal thing remaining to be noticed is the application of the -theory of the pendulum to musical concords and dissonances, which are -explained, in the same manner as by Kepler in his "Harmonices Mundi," to -result from the concurrence or opposition of vibrations in the air -striking upon the drum of the ear. It is suggested that these vibrations -may be made manifest by rubbing the finger round a glass set in a large -vessel of water; "and if by pressure the note is suddenly made to rise -to the octave above, every one of the undulations which will be seen -regularly spreading round the glass, will suddenly split into two, -proving that the vibrations that occasion the octave are double those -belonging to the simple note." Galileo then describes a method he -discovered by accident of measuring the length of these waves more -accurately than can be done in the agitated water. He was scraping a -brass plate with an iron chisel, to take out some spots, and moving the -tool rapidly upon the plate, he occasionally heard a hissing and -whistling sound, very shrill and audible, and whenever this occurred, -and then only, he observed the light dust on the plate to arrange itself -in a long row of small parallel streaks equidistant from each other. In -repeated experiments he produced different tones by scraping with -greater or less velocity, and remarked that the streaks produced by the -acute sounds stood closer together than those from the low notes. Among -the sounds produced were two, which by comparison with a viol he -ascertained to differ by an exact fifth; and measuring the spaces -occupied by the streaks in both experiments, he found thirty of the one -equal to forty-five of the other, which is exactly the known proportion -of the lengths of strings of the same material which sound a fifth to -each other.[152] - -Salviati also remarks, that if the material be not the same, as for -instance if it be required to sound an octave to a note on catgut, on a -wire of the same length, the weight of the wire must be made four times -as great, and so for other intervals. "The immediate cause of the forms -of musical intervals is neither the length, the tension, nor the -thickness, but the proportion of the numbers of the undulations of the -air which strike upon the drum of the ear, and make it vibrate in the -same intervals. Hence we may gather a plausible reason of the different -sensations occasioned to us by different couples of sounds, of which we -hear some with great pleasure, some with less, and call them accordingly -concords, more or less perfect, whilst some excite in us great -dissatisfaction, and are called discords. The disagreeable sensation -belonging to the latter probably arises from the disorderly manner in -which the vibrations strike the drum of the ear; so that for instance a -most cruel discord would be produced by sounding together two strings, -of which the lengths are to each other as the side and diagonal of a -square, which is the discord of the false fifth. On the contrary, -agreeable consonances will result from those strings of which the -numbers of vibrations made in the same time are commensurable, "to the -end that the cartilage of the drum may not undergo the incessant torture -of a double inflexion from the disagreeing percussions." Something -similar may be exhibited to the eye by hanging up pendulums of different -lengths: "if these be proportioned so that the times of their vibrations -correspond with those of the musical concords, the eye will observe with -pleasure their crossings and interweavings still recurring at -appreciable intervals; but if the times of vibration be incommensurate, -the eye will be wearied and worn out with following them." - -The second dialogue is occupied entirely with an investigation of the -strength of beams, a subject which does not appear to have been examined -by any one before Galileo beyond Aristotle's remark, that long beams are -weaker, because they are at once the weight, the lever, and the fulcrum; -and it is in the development of this observation that the whole theory -consists. The principle assumed by Galileo as the basis of his inquiries -is, that the force of cohesion with which a beam resists a cross -fracture in any section may all be considered as acting at the centre of -gravity of the section, and that it breaks always at the lowest point: -from this he deduced that the effect of the weight of a prismatic beam -in overcoming the resistance of one end by which it is fastened to a -wall, varies directly as the square of the length, and inversely as the -side of the base. From this it immediately follows, that if for instance -the bone of a large animal be three times as long as the corresponding -one in a smaller beast, it must be nine times as thick to have the same -strength, provided we suppose in both cases that the materials are of -the same consistence. An elegant result which Galileo also deduced from -this theory, is that the form of such a beam, to be equally strong in -every part, should be that of a parabolical prism, the vertex of the -parabola being the farthest removed from the wall. As an easy mode of -describing the parabolic curve for this purpose, he recommends tracing -the line in which a heavy flexible string hangs. This curve is not an -accurate parabola: it is now called a catenary; but it is plain from the -description of it in the fourth dialogue, that Galileo was perfectly -aware that this construction is only approximately true. In the same -place he makes the remark, which to many is so paradoxical, that no -force, however great, exerted in a horizontal direction, can stretch a -heavy thread, however slender, into an accurately straight line. - -The fifth and sixth dialogues were left unfinished, and annexed to the -former ones by Viviani after Galileo's death: the fragment of the fifth, -which is on the subject of Euclid's Definition of Ratio, was at first -intended to have formed a part of the third, and followed the first -proposition on equable motion: the sixth was intended to have embodied -Galileo's researches on the nature and laws of Percussion, on which he -was employed at the time of his death. Considering these solely as -fragments, we shall not here make any extracts from them. - - -FOOTNOTES: - -[140] Joh. Bernouilli, Opera Omnia, Lausannae, 1744. tom. i. p. 192. - -[141] Pantometria, 1591. - -[142] Lettres de Descartes. Paris, 1657. - -[143] Math. Coll. vol. ii. - -[144] Phys. Lib. iv. c. 8. - -[145] It has been recently proposed to determine the density of -high-pressure steam by a process analogous to this. - -[146] Venturi, vol. ii. - -[147] Galileo also reasons in the same way on the equality of the solids -standing on the cutting plane, but one is sufficient for our present -purpose. - -[148] Gli altissimi e ultimi termini. - -[149] Le ultime reliquie e vestigie lasciate da grandezze eguali. - -[150] Punctum fluere, et lineam esse fluxum puncti. Tract. Syllept. -Romae, 1633. - -[151] "Treatise of the Nature of Bodies. London, 1665." - -[152] This beautiful experiment is more easily tried by drawing the bow -of a violin across the edge of glass strewed with fine dry sand. Those -who wish to see more on the subject may consult Chladni's 'Acoustique.' - - - - -CHAPTER XVIII. - - _Correspondence on Longitudes.--Pendulum Clock._ - - -IN the spring of 1636, having finished his Dialogues on Motion, Galileo -resumed the plan of determining the longitude by means of Jupiter's -satellites. Perhaps he suspected something of the private intrigue which -thwarted his former expectations from the Spanish government, and this -may have induced him on the present occasion to negotiate the matter -without applying for Ferdinand's assistance and recommendation. -Accordingly he addressed himself to Lorenz Real, who had been Governor -General of the Dutch possessions in India, freely and unconditionally -offering the use of his theory to the States General of Holland. Not -long before, his opinion had been requested by the commissioners -appointed at Paris to examine and report on the practicability of -another method proposed by Morin,[153] which consisted in observing the -distance of the moon from a known star. Morin was a French philosopher, -principally known as an astrologer and zealous Anti-Copernican; but his -name deserves to be recorded as undoubtedly one of the first to -recommend a method, which, under the name of a Lunar distance, is now in -universal practice. - -The monthly motion of the moon is so rapid, that her distance from a -given star sensibly varies in a few minutes even to the unassisted eye; -and with the aid of the telescope, we can of course appreciate the -change more accurately. Morin proposed that the distances of the moon -from a number of fixed stars lying near her path in the heavens should -be beforehand calculated and registered for every day in the year, at a -certain hour, in the place from which the longitudes were to be -reckoned, as for instance at Paris. Just as in the case of the eclipses -of Jupiter's satellites, the observer, when he saw that the moon had -arrived at the registered distance, would know the hour at Paris: he -might also make allowance for intermediate distances. Observing at the -same instant the hour on board his ship, the difference between the two -would show his position in regard of longitude. In using this method as -it is now practised, several modifications are to be attended to, -without which it would be wholly useless, in consequence of the -refraction of the atmosphere, and the proximity of the moon to the -earth. Owing to the latter cause, if two spectators should at the same -instant of time, but in different places, measure the distance of the -moon in the East, from a star still more to the eastward, it would -appear greater to the more easterly spectator than to the other -observer, who as seen from the star would be standing more directly -behind the moon. The mode of allowing for these alterations is taught by -trigonometry and astronomy. - -The success of this method depends altogether upon the exact knowledge -which we now have of the moon's course, and till that knowledge was -perfected it would have been found altogether illusory. Such in fact was -the judgment which Galileo pronounced upon it. "As to Morin's book on -the method of finding the longitude by means of the moon's motion, I say -freely that I conceive this idea to be as accurate in theory, as -fallacious and impossible in practice. I am sure that neither you nor -any one of the other four gentlemen can doubt the possibility of finding -the difference of longitude between two meridians by means of the moon's -motion, provided we are sure of the following requisites: First, an -Ephemeris of the moon's motion exactly calculated for the first meridian -from which the others are to be reckoned; secondly, exact instruments, -and convenient to handle, in taking the distance between the moon and a -fixed star; thirdly, great practical skill in the observer; fourthly, -not less accuracy in the scientific calculations, and astronomical -computations; fifthly, very perfect clocks to number the hours, or other -means of knowing them exactly, &c. Supposing, I say, all these elements -free from error, the longitude will be accurately found; but I reckon it -more easy and likely to err in all of these together, than to be -practically right in one alone. Morin ought to require his judges to -assign, at their pleasure, eight or ten moments of different nights -during four or six months to come, and pledge himself to predict and -assign by his calculations the distances of the moon at those determined -instants from some star which would then be near her. If it is found -that the distances assigned by him agree with those which the quadrant -or sextant[154] will actually show, the judges would be satisfied of his -success, or rather of the truth of the matter, and nothing would remain -but to show that his operations were such as could be performed by men -of moderate skill, and also practicable at sea as well as on land. I -incline much to think that an experiment of this kind would do much -towards abating the opinion and conceit which Morin has of himself, -which appears to me so lofty, that I should consider myself the eighth -sage, if I knew the half of what Morin presumes to know." - -It is probable that Galileo was biassed by a predilection for his own -method, on which he had expended so much time and labour; but the -objections which he raises against Morin's proposal in the foregoing -letter are no other than those to which at that period it was -undoubtedly open. With regard to his own, he had already, in 1612, given -a rough prediction of the course of Jupiter's satellites, which had been -found to agree tolerably well with subsequent observations; and since -that time, amid all his other employments, he had almost -unintermittingly during twenty-four years continued his observations, -for the sake of bringing the tables of their motions to as high a state -of perfection as possible. This was the point to which the inquiries of -the States in their answer to Galileo's frank proposal were principally -directed. They immediately appointed commissioners to communicate with -him, and report the various points on which they required information. -They also sent him a golden chain, and assured him that in the case of -the design proving successful, he should have no cause to complain of -their want of gratitude and generosity. The commissioners immediately -commenced an active correspondence with him, in the course of which he -entered into more minute details with regard to the methods by which he -proposed to obviate the practical difficulties of the necessary -observations. - -It is worth noticing that the secretary to the Prince of Orange, who was -mainly instrumental in forming this commission, was Constantine -Huyghens, father of the celebrated mathematician of that name, of whom -it has been said that he seemed destined to complete the discoveries of -Galileo; and it is not a little remarkable, that Huyghens nowhere in his -published works makes any allusion to this connexion between his father -and Galileo, not even during the discussion that arose some years later -on the subject of the pendulum clock, which must necessarily have forced -it upon his recollection. - -The Dutch commissioners had chosen one of their number to go into Italy -for the purpose of communicating personally with Galileo, but he -discouraged this scheme, from a fear of its giving umbrage at Rome. The -correspondence being carried on at so great a distance necessarily -experienced many tedious delays, till in the very midst of Galileo's -labours to complete his tables, he was seized with the blindness which -we have already mentioned. He then resolved to place all the papers -containing his observations and calculations for this purpose in the -hands of Renieri, a former pupil of his, and then professor of -mathematics at Pisa, who undertook to finish and to forward them into -Holland. Before this was done, a new delay was occasioned by the deaths -which speedily followed each other of every one of the four -commissioners; and for two or three years the correspondence with -Holland was entirely interrupted. Constantine Huyghens, who was capable -of appreciating the value of the scheme, succeeded after some trouble in -renewing it, but only just before the death of Galileo himself, by which -of course it was a second time broken off; and to complete the singular -series of obstacles by which the trial of this method was impeded, just -as Renieri, by order of the Duke of Tuscany, was about to publish the -ephemeris and tables which Galileo had entrusted to him, and which the -Duke told Viviani he had seen in his possession, he also was attacked -with a mortal malady; and upon his death the manuscripts were nowhere to -be found, nor has it since been discovered what became of them. Montucla -has intimated his suspicions that Renieri himself destroyed them, from a -consciousness that they were insufficient for the purpose to which it -was intended to apply them; a bold conjecture, and one which ought to -rest upon something more than mere surmise: for although it may be -considered certain, that the practical value of these tables would be -very inconsiderable in the present advanced state of knowledge, yet it -is nearly as sure that they were unique at that time, and Renieri was -aware of the value which Galileo himself had set upon them, and should -not be lightly accused of betraying his trust in so gross a manner. In -1665, Borelli calculated the places of the satellites for every day in -the ensuing year, which he professed to have deduced (by desire of the -Grand Duke) from Galileo's tables;[155] but he does not say whether or -not these tables were the same that had been in Renieri's possession. - -We have delayed till this opportunity to examine how far the invention -of the pendulum clock belongs to Galileo. It has been asserted that the -isochronism of the pendulum had been noticed by Leonardo da Vinci, but -the passage on which this assertion is founded (as translated from his -manuscripts by Venturi) scarcely warrants this conclusion. "A rod which -engages itself in the opposite teeth of a spur-wheel can act like the -arm of the balance in clocks, that is to say, it will act alternately, -first on one side of the wheel, then on the opposite one, without -interruption." If Da Vinci had constructed a clock on this principle, -and recognized the superiority of the pendulum over the old balance, he -would surely have done more than merely mention it as affording an -unintermitted motion "like the arm of the balance." The use of the -balance is supposed to have been introduced at least as early as the -fourteenth century. Venturi mentions the drawing and description of a -clock in one of the manuscripts of the King's Library at Paris, dated -about the middle of the fifteenth century, which as he says nearly -resembles a modern watch. The balance is there called "The circle -fastened to the stem of the pallets, and moved by the force with -it."[156] In that singularly wild and extravagant book, entitled "A -History of both Worlds," by Robert Flud, are given two drawings of the -wheel-work of the clocks and watches in use before the application of -the pendulum. An inspection of them will show how little remained to be -done when the isochronism of the pendulum was discovered. _Fig. 1._ -represents "the large clocks moved by a weight, such as are put up in -churches and turrets; _fig. 2._ the small ones moved by a spring, such -as are worn round the neck, or placed on a shelf or table. The use of -the chain is to equalize the spring, which is strongest at the beginning -of its motion."[157] This contrivance of the chain is mentioned by -Cardan, in 1570, and is probably still older. In both figures the name -given to the cross bar, with the weight attached to it, is "the time or -balance (_tempus seu libratio_) by which the motion is equalized." The -manner in which Huyghens first applied the pendulum is shown in _fig. -3._[158] The action in the old clocks of the balance, or _rake_, as it -was also called, was by checking the motion of the descending weight -till its inertia was overcome; it was then forced round till the -opposite pallet engaged in the toothed wheel. The balance was thus -suddenly and forcibly reduced to a state of rest, and again set in -motion in the opposite direction. It will be observed that these -balances wanted the spiral spring introduced in all modern watches, -which has a property of isochronism similar to that of the pendulum. -Hooke is generally named as the discoverer of this property of springs, -and as the author of its application to the improvement of watches, but -the invention is disputed with him by Huyghens. Lahire asserts[159] that -the isochronism of springs was communicated to Huyghens at Paris by -Hautefeuille, and that this was the reason why Huyghens failed to obtain -the patent he solicited for the construction of spring watches. A great -number of curious contrivances at this early period in the history of -Horology, may be seen in Schott's Magia Naturae, published at Nuremberg -in 1664. - -[Illustration: _Fig. 2. Fig. 1. Fig. 3._] - -Galileo was early convinced of the importance of his pendulum to the -accuracy of astronomical observations; but the progress of invention is -such that the steps which on looking back seem the easiest to make, are -often those which are the longest delayed. Galileo recognized the -principle of the isochronism of the pendulum, and recommended it as a -measurer of time in 1583; yet fifty years later, although constantly -using it, he had not devised a more convenient method of doing so, than -is contained in the following description taken from his "Astronomical -Operations." - -"A very exact time-measurer for minute intervals of time, is a heavy -pendulum of any size hanged by a fine thread, which, if removed from the -perpendicular and allowed to swing freely, always completes its -vibrations, be they great or small, in exactly the same time."[160] - -The mode of finding exactly by means of this the quantity of any time -reduced to hours, minutes, seconds, &c., which are the divisions -commonly used among astronomers, is this:--"Fit up a pendulum of any -length, as for instance about a foot long, and count patiently (only for -once) the number of vibrations during a natural day. Our object will be -attained if we know the exact revolution of the natural day. The -observer must then fix a telescope in the direction of any star, and -continue to watch it till it disappears from the field of view. At that -instant he must begin to count the vibrations of the pendulum, -continuing all night and the following day till the return of the same -star within the field of view of the telescope, and its second -disappearance, as on the first night. Bearing in recollection the total -number of vibrations thus made in twenty-four hours, the time -corresponding to any other number of vibrations will be immediately -given by the Golden Rule." - -A second extract out of Galileo's Dutch correspondence, in 1637, will -show the extent of his improvements at that time:--"I come now to the -second contrivance for increasing immensely the exactness of -astronomical observations. I allude to my time-measurer, the precision -of which is so great, and such, that it will give the exact quantity of -hours, minutes, seconds, and even thirds, if their recurrence could be -counted; and its constancy is such that two, four, or six such -instruments will go on together so equably that one will not differ from -another so much as the beat of a pulse, not only in an hour, but even in -a day or a month."--"I do not make use of a weight hanging by a thread, -but a heavy and solid pendulum, made for instance of brass or copper, in -the shape of a circular sector of twelve or fifteen degrees, the radius -of which may be two or three palms, and the greater it is the less -trouble will there be in attending it. This sector, such as I have -described, I make thickest in the middle radius, tapering gradually -towards the edges, where I terminate it in a tolerably sharp line, to -obviate as much as possible the resistance of the air, which is the sole -cause of its retardation."--[These last words deserve notice, because, -in a previous discussion, Galileo had observed that the parts of the -pendulum nearest the point of suspension have a tendency to vibrate -quicker than those at the other end, and seems to have thought -erroneously that the stoppage of the pendulum is partly to be attributed -to this cause.]--"This is pierced in the centre, through which is passed -an iron bar shaped like those on which steelyards hang, terminated below -in an angle, and placed on two bronze supports, that they may wear away -less during a long motion of the sector. If the sector (when accurately -balanced) be removed several degrees from its perpendicular position, it -will continue a reciprocal motion through a very great number of -vibrations before it will stop; and in order that it may continue its -motion as long as is wanted, the attendant must occasionally give it a -smart push, to carry it back to large vibrations." Galileo then -describes as before the method of counting the vibrations in the course -of a day, and gives the rule that the lengths of two similar pendulums -will have the same proportion as the squares of their times of -vibration. He then continues: "Now to save the fatigue of the assistant -in continually counting the vibrations, this is a convenient -contrivance: A very small and delicate needle extends out from the -middle of the circumference of the sector, which in passing strikes a -rod fixed at one end; this rod rests upon the teeth of a wheel as light -as paper, placed in a horizontal plane near the pendulum, having round -it teeth cut like those of a saw, that is to say, with one side of each -tooth perpendicular to the rim of the wheel and the other inclined -obliquely. The rod striking against the perpendicular side of the tooth -moves it, but as the same rod returns against the oblique side, it does -not move it the contrary way, but slips over it and falls at the foot of -the following tooth, so that the motion of the wheel will be always in -the same direction. And by counting the teeth you may see at will the -number of teeth passed, and consequently the number of vibrations and of -particles of time elapsed. You may also fit to the axis of this first -wheel a second, with a small number of teeth, touching another greater -toothed wheel, &c. But it is superfluous to point out this to you, who -have by you men very ingenious and well skilled in making clocks and -other admirable machines; and on this new principle, that the pendulum -makes its great and small vibrations in the same time exactly, they will -invent contrivances more subtle than any I can suggest; and as the error -of clocks consists principally in the disability of workmen hitherto to -adjust what we call the balance of the clock, so that it may vibrate -regularly, my very simple pendulum, which is not liable to any -alteration, affords a mean of maintaining the measures of time always -equal." The contrivance thus described would be somewhat similar to the -annexed representation, but it is almost certain that no such instrument -was actually constructed. - -[Illustration] - -It must be owned that Galileo greatly overrated the accuracy of his -timekeeper; and in asserting so positively that which he had certainly -not experienced, he seems to depart from his own principles of -philosophizing. It will be remarked that in this passage he still is of -the erroneous opinion, that all the vibrations great or small of the -same pendulum take exactly the same time; and we have not been able to -find any trace of his having ever held a different opinion, unless -perhaps in the Dialogues, where he says, "If the vibrations are not -exactly equal, they are at least insensibly different." This is very -much at variance with the statement in the Memoirs of the Academia del -Cimento, edited by their secretary Magalotti, on the credit of which -Galileo's claim to the pendulum-clock chiefly rests. It is there said -that experience shows that the smallest vibrations are rather the -quickest, "as Galileo announced after the observation, which in 1583 he -was the first to make of their approximate equality." It is not possible -immediately in connexion with so glaring a misstatement, to give -implicit credence to the assertion in the next sentence, that "_to -obviate this inconvenience_" Galileo was the first to contrive a clock, -constructed in 1649, by his son Vincenzo, in which, by the action of a -weight or spring, the pendulum was constrained to move always from the -same height. Indeed it appears as if Magalotti did not always tell this -story in the same manner, for he is referred to as the author of the -account given by Becher, "that Galileo himself made a pendulum-clock one -of which was sent to Holland," plainly insinuating that Huyghens was a -mere copyist.[161] These two accounts therefore serve to invalidate each -other's credibility. Tiraboschi[162] asserts that, at the time he wrote, -the mathematical professor at Pisa was in possession of the identical -clock constructed by Treffler under Vincenzo's directions; and quotes a -letter from Campani, to whom it was shown by Ferdinand, "old, rusty, and -unfinished as Galileo's son made it before 1649." Viviani on the other -hand says that Treffler constructed this same clock some time after -Vincenzo's death (which happened in 1649), on a different principle from -Vincenzo's ideas, although he says distinctly that he heard Galileo -describe an application of the pendulum to a clock similar to Huyghens' -contrivance. Campani did not actually see this clock till 1659, which -was three years after Huyghens' invention, so that perhaps Huyghens was -too easily satisfied when, on occasion of the answer which Ferdinand -sent to his complaints of the Memorie del Cimento he wrote to Bouillaud, -"I must however believe, since such a prince assures me, that Galileo -had this idea before me." - -There is another circumstance almost amounting to a proof that it was an -afterthought to attribute the merit of constructing the pendulum-clock -to Galileo, for on the reverse of a medal struck by Viviani, and -inscribed "to the memory of his excellent instructor,"[163] is a rude -exhibition of the principal objects to which Galileo's attention was -directed. The pendulum is represented simply by a weight attached to a -string hanging on the face of a rock. It is probable that, in a design -expressly intended to commemorate Galileo's inventions, Viviani would -have introduced the timekeeper in the most perfect form to which it had -been brought by him. Riccioli,[164] whose industry was unwearied in -collecting every fact and argument which related in any way to the -astronomical and mechanical knowledge and opinions of his time, -expressly recommends swinging a pendulum, or perpendicular as it was -often called (only a few years before Huyghens' publication), as much -more accurate _than any clock_.[165] Join to all these arguments -Huyghens' positive assertion, that if Galileo had conceived any such -idea, he at least was entirely ignorant of it,[166] and no doubt can -remain that the merit of the original invention (such as it was) rests -entirely with Huyghens. The step indeed seems simple enough for a less -genius than his: for the property of the pendulum was known, and the -conversion of a rotatory into a reciprocating motion was known; but the -connexion of the one with the other having been so long delayed, we must -suppose that difficulties existed where we are not now able to perceive -them, for Huyghens' improvement was received with universal admiration. - -There may be many who will consider the pendulum as undeserving so long -a discussion; who do not know or remember that the telescope itself has -hardly done more for the precision of astronomical observations than -this simple instrument, not to mention the invaluable convenience of an -uniform and accurate timekeeper in the daily intercourse of life. The -patience and industry of modern observers are often the theme of -well-merited praise, but we must look with a still higher degree of -wonder on such men as Tycho Brahe and his contemporaries, who were -driven by the want of any timekeeper on which they could depend to the -most laborious expedients, and who nevertheless persevered to the best -of their ability, undisgusted either by the tedium of such processes, or -by the discouraging consciousness of the necessary imperfection of their -most approved methods and instruments. - -The invariable regularity of the pendulum's motion was soon made -subservient to ulterior purposes beyond that of merely registering time. -We have seen the important assistance it afforded in establishing the -laws of motion; and when the theory founded on those laws was extended -and improved, the pendulum was again instrumental, by a species of -approximate reasoning familiar to all who are acquainted with physical -inquiries, in pointing out by its minute irregularities in different -parts of the earth, a corresponding change in the weight of all bodies -in those different situations, supposed to be the consequence of a -greater distance from the axis of the earth's rotation; since that would -occasion the force of attraction to be counterbalanced by an increased -centrifugal force. The theory which kept pace with the constantly -increasing accuracy of such observations, proving consistent in all -trials of it, has left little room for future doubts; and in this manner -the pendulum in intelligent hands became the simplest instrument for -ascertaining the form of the globe which we inhabit. An English -astronomer, who corresponded with Kepler under the signature of Brutius -(whose real name perhaps might be Bruce), had already declared his -belief in 1603, that "the earth on which we tread is neither round nor -globular, but more nearly of an oval figure."[167] There is nothing to -guide us to the grounds on which he formed this opinion, which was -perhaps only a lucky guess. Kepler's note upon it is: "This is not -altogether to be contemned." - -A farther use of the pendulum is in furnishing a general and unperishing -standard of measure. This application is suggested in the third volume -of the 'Reflections' of Mersenne, published in 1647, where he observes -that it may be best for the future not to divide time into hours, -minutes, and seconds, but to express its parts by the number of -vibrations of a pendulum of given length, swinging through a given arc. -It was soon seen that it would be more convenient to invert this -process, and to choose as an unit of length the pendulum which should -make a certain number of vibrations in the unit of time, naturally -determined by the revolution of the earth on its axis. Our Royal -Society took an active part in these experiments, which seem, -notwithstanding their utility, to have met from the first with much of -the same ridicule which was lavished upon them by the ignorant, when -recently repeated for the same purpose. "I contend," says Graunt[168] in -a dedication to the Royal Society, dated 1662, "against the envious -schismatics of your society (who think you do nothing unless you -presently transmute metals, make butter and cheese without milk, and, as -their own ballad hath it, make leather without hides), by asserting the -usefulness of even all your preparatory and luciferous experiments, -being not the ceremonies, but the substance and principles of useful -arts. For I find in trade the want of an universal measure, and have -heard musicians wrangle about the just and uniform keeping of time in -their consorts, and therefore cannot with patience hear that your -labours about vibrations, eminently conducing to both, should be -slighted, nor your pendula called swing-swangs with scorn."[169] - - -FOOTNOTES: - -[153] One of the Commissioners was the father of Blaise Pascal. - -[154] These instruments were very inferior to those now in use under the -same name. See "Treatise on Opt. Instrum." - -[155] Theoricae Mediceorum Planetarum, Florentiae, 1666. - -[156] Circulus affixus virgae paletorum qui cum ea de vi movetur. - -[157] Utriusque Cosmi Historia. Oppenhemii, 1617. - -[158] Huygenii Opera. Lugduni, 1724. - -[159] Memoires de l'Academie, 1717. - -[160] See page 84. - -[161] De nova Temporis dimetiendi ratione. Londini, 1680. - -[162] Storia della Lett. Ital. - -[163] Museum Mazuchellianum, vol. ii. Tab. cvii. p. 29. - -[164] Almagestum Novum, vol. i. - -[165] Quovis horologio accuratius. - -[166] Clarorum Belgarum ad Ant. Magliabech. Epistolae. Florence, 1745, -tom. i. p. 235. - -[167] Kepleri Epistolae. - -[168] Natural and Political Observations. London, 1665. - -[169] See also Hudibras, Part II. Cant. III. - - They're guilty by their own confessions - Of felony, and at the Sessions - Upon the bench I will so handle 'em, - That the vibration of this pendulum - Shall make all taylors' yards of one - Unanimous opinion; - A thing he long has vaunted of, - But now shall make it out of proof. - -Hudibras was certainly written before 1663: ten years later Huyghens -speaks of the idea of so employing the pendulum as a common one. - - - - -CHAPTER XIX. - - _Character of Galileo--Miscellaneous details--his - Death--Conclusion._ - - -THE remaining years of Galileo's life were spent at Arcetri, where -indeed, even if the Inquisition had granted his liberty, his increasing -age and infirmities would probably have detained him. The rigid caution -with which he had been watched in Florence was in great measure relaxed, -and he was permitted to see the friends who crowded round him to express -their respect and sympathy. The Grand Duke visited him frequently, and -many distinguished strangers, such as Gassendi and Deodati, came into -Italy solely for the purpose of testifying their admiration of his -character. Among other visitors the name of Milton will be read with -interest: we may probably refer to the effects of this interview the -allusions to Galileo's discoveries, so frequently introduced into his -poem. Milton mentions in his 'Areopagitica,' that he saw Galileo whilst -in Italy, but enters into no details of his visit. - -Galileo was fond of society, and his cheerful and popular manners -rendered him an universal favourite among those who were admitted to his -intimacy. Among these, Viviani, who formed one of his family during the -three last years of his life, deserves particular notice, on account of -the strong attachment and almost filial veneration with which he ever -regarded his master and benefactor. His long life, which was prolonged -to the completion of his 81st year in 1703, enabled him to see the -triumphant establishment of the truths on account of which Galileo had -endured so many insults; and even in his old age, when in his turn he -had acquired a claim to the reverence of a younger generation, our Royal -Society, who invited him among them in 1696, felt that the complimentary -language in which they addressed him as the first mathematician of the -age would have been incomplete and unsatisfactory without an allusion to -the friendship that gained him the cherished title of "The last pupil of -Galileo."[170] - -Torricelli, another of Galileo's most celebrated followers, became a -member of his family in October, 1641: he first learned mathematics from -Castelli, and occasionally lectured for him at Rome, in which manner he -was employed when Galileo, who had seen his book 'On Motion,' and -augured the greatest success from such a beginning, invited him to his -house--an offer which Torricelli eagerly embraced, although he enjoyed -the advantages of it but for a short time. He afterwards succeeded -Galileo in his situation at the court of Florence,[171] but survived him -only a few years. - -It is from the accounts of Viviani and Gherardini that we principally -draw the following particulars of Galileo's person and character:--Signor -Galileo was of a cheerful and pleasant countenance, especially in his -old age, square built, and well proportioned in stature, and rather -above the middle size. His complexion was fair and sanguine, his eyes -brilliant, and his hair of a reddish cast. His constitution was -naturally strong, but worn out by fatigue of mind and body, so as -frequently to be reduced to a state of the utmost weakness. He was -subject to attacks of hypochondria, and often molested by severe and -dangerous illnesses, occasioned in great measure by his sleepless -nights, the whole of which he frequently spent in astronomical -observations. During upwards of forty-eight years of his life, he was -tormented with acute rheumatic pains, suffering particularly on any -change of weather. He found himself most free from these pains whilst -residing in the country, of which consequently he became very fond: -besides, he used to say that in the country he had greater freedom to -read the book of Nature, which lay there open before him. His library -was very small, but well chosen, and open to the use of the friends whom -he loved to see assembled round him, and whom he was accustomed to -receive in the most hospitable manner. He ate sparingly himself; but was -particularly choice in the selection of his wines, which in the latter -part of his life were regularly supplied out of the Grand Duke's -cellars. This taste gave an additional stimulus to his agricultural -pursuits, and many of his leisure hours were spent in the cultivation -and superintendence of his vineyards. It should seem that he was -considered a good judge of wine; for Viviani has preserved one of his -receipts in a collection of miscellaneous experiments. In it he strongly -recommends that for wine of the first quality, that juice only should be -employed, which is pressed out by the mere weight of the heaped grapes, -which would probably be that of the ripest fruit. The following letter, -written in his 74th year, is dated, "From my prison at Arcetri.--I am -forced to avail myself of your assistance and favour, agreeably to your -obliging offers, in consequence of the excessive chill of the weather, -and of old age, and from having drained out my grand stock of a hundred -bottles, which I laid in two years ago; not to mention some minor -particulars during the last two months, which I received from my Serene -Master, the Most Eminent Lord Cardinal, their Highnesses the Princes, -and the Most Excellent Duke of Guise, besides cleaning out two barrels -of the wine of this country. Now, I beg that with all due diligence and -industry, and with consideration, and taking counsel with the most -refined palates, you will provide me with two cases, that is to say, -with forty flasks of different wines, the most exquisite that you can -find: take no thought of the expense, because I stint myself so much in -all other pleasures that I can afford to lay out something at the -request of Bacchus, without giving offence to his two companions Ceres -and Venus. You must be careful to leave out neither Scillo nor Carino (I -believe they meant to call them Scylla and Charybdis), nor the country -of my master, Archimedes of Syracuse, nor Greek wines, nor clarets, &c. -&c. The expense I shall easily be able to satisfy, but not the infinite -obligation." - -In his expenditure Galileo observed a just mean between avarice and -profusion: he spared no cost necessary for the success of his many and -various experiments, and spent large sums in charity and hospitality, -and in assisting those in whom he discovered excellence in any art or -profession, many of whom he maintained in his own house. His temper was -easily ruffled, but still more easily pacified. He seldom conversed on -mathematical or philosophical topics except among his intimate friends; -and when such subjects were abruptly brought before him, as was often -the case by the numberless visitors he was in the habit of receiving, he -showed great readiness in turning the conversation into more popular -channels, in such manner however that he often contrived to introduce -something to satisfy the curiosity of the inquirers. His memory was -uncommonly tenacious, and stored with a vast variety of old songs and -stories, which he was in the constant habit of quoting and alluding to. -His favourite Italian authors were Ariosto, Petrarca, and Berni, great -part of whose poems he was able to repeat. His excessive admiration of -Ariosto determined the side which he took against Tasso in the virulent -and unnecessary controversy which has divided Italy so long on the -respective merits of these two great poets; and he was accustomed to say -that reading Tasso after Ariosto was like tasting cucumbers after -melons. When quite a youth, he wrote a great number of critical remarks -on Tasso's Gerusalemme Liberata, which one of his friends borrowed, and -forgot to return. For a long time it was thought that the manuscript had -perished, till the Abbe Serassi discovered it, whilst collecting -materials for his Life of Tasso, published at Rome in 1785. Serassi -being a violent partizan of Tasso, but also unwilling to lose the credit -of the discovery, copied the manuscript, but without any intention of -publishing it, "till he could find leisure for replying properly to the -sophistical and unfounded attacks of a critic so celebrated on other -accounts." He announced his discovery as having been made "in one of the -famous libraries at Rome," which vague indication he with some reason -considered insufficient to lead to a second discovery. On Serassi's -death his copy was found, containing a reference to the situation of the -original; the criticisms were published, and form the greatest part of -the last volume of the Milan edition of Galileo's works. The manuscript -was imperfect at the time of this second discovery, several leaves -having been torn out, it is not known by whom. - -The opinion of the most judicious Italian critics appears to be, that it -would have been more for Galileo's credit if these remarks had never -been made public: they are written in a spirit of flippant violence, -such as might not be extraordinary in a common juvenile critic, but -which it is painful to notice from the pen of Galileo. Two or three -sonnets are extant written by Galileo himself, and in two instances he -has not scrupled to appropriate the conceits of the poet he affected to -undervalue.[172] It should be mentioned that Galileo's matured taste -rather receded from the violence of his early prejudices, for at a later -period of his life he used to shun comparing the two; and when forced to -give an opinion he said, "that Tasso's appeared the finer poem, but that -Ariosto gave him the greater pleasure." Besides these sonnets, there is -extant a short burlesque poem written by him, "In abuse of Gowns," when, -on his first becoming Professor at Pisa, he found himself obliged by -custom to wear his professional habit in every company. It is written -not without humour, but does not bear comparison with Berni, whom he -imitated. - -There are several detached subjects treated of by Galileo, which may be -noticed in this place. A letter by him containing the solution of a -problem in Chances is probably the earliest notice extant of the -application of mathematics to that interesting subject: the -correspondence between Pascal and Fermat, with which its history is -generally made to begin, not having taken place till at least twelve -years later. There can be little doubt after the clear account of Carlo -Dati, that Galileo was the first to examine the curve called the -Cycloid, described by a point in the rim of a wheel rolling on a -straight line, which he recommended as a graceful form for the arch of a -bridge at Pisa. He even divined that the area contained between it and -its base is exactly three times that of the generating circle. He seems -to have been unable to verify this guess by strict geometrical -reasoning, for Viviani tells an odd story, that in order to satisfy his -doubts he cut out several large cycloids of pasteboard, but finding the -weight in every trial to be rather less than three times that of the -circle, he suspected the proportion to be irrational, and that there was -some error in his estimation; the inquiry he abandoned was afterwards -resumed with success by his pupil Torricelli.[173] - -The account which Lagalla gives of an experiment shown in his presence -by Galileo, carries the observation of the phosphorescence of the -Bologna stone at least as far back as 1612.[174] Other writers mention -the name of an alchymist, who according to them discovered it -accidentally in 1603. Cesi, Lagalla, and one or two others, had passed -the night at Galileo's house, with the intention of observing Venus and -Saturn; but, the night being cloudy, the conversation turned on other -matters, and especially on the nature of light, "on which Galileo took a -small wooden box at daybreak before sunrise, and showed us some small -stones in it, desiring us to observe that they were not in the least -degree luminous. Having then exposed them for some time to the twilight, -he shut the window again; and in the midst of the dark room showed us -the stones, shining and glistening with a faint light, which we saw -presently decay and become extinguished." In 1640, Liceti attempted to -refer the effect of the earthshine upon the moon to a similar -phosphorescent quality of that luminary, to which Galileo, then aged 76, -replied by a long and able letter, enforcing the true explanation he had -formerly given. - -Although quite blind, and nearly deaf, the intellectual powers of -Galileo remained to the end of his life; but he occasionally felt that -he was overworking himself, and used to complain to his friend Micanzio -that he found his head too busy for his body. "I cannot keep my restless -brain from grinding on, although with great loss of time; for whatever -idea comes into my head with respect to any novelty, drives out of it -whatever I had been thinking of just before." He was busily engaged in -considering the nature of the force of percussion, and Torricelli was -employed in arranging his investigations for a continuation of the -'Dialogues on Motion,' when he was seized with an attack of fever and -palpitation of the heart, which, after an illness of two months, put an -end to his long, laborious, and useful life, on the 8th of January, -1642, just one year before his great successor Newton was born. - -The malice of his enemies was scarcely allayed by his death. His right -of making a will was disputed, as having died a prisoner to the -Inquisition, as well as his right to burial in consecrated ground. These -were at last conceded, but Urban anxiously interfered to prevent the -design of erecting a monument to him in the church of Santa Croce, in -Florence, for which a large sum had been subscribed. His body was -accordingly buried in an obscure corner of the church, which for upwards -of thirty years after his death was unmarked even by an inscription to -his memory. It was not till a century later that the splendid monument -was erected which now covers his and Viviani's remains. When their -bodies were disinterred in 1737 for the purpose of being removed to -their new resting-place, Capponi, the president of the Florentine -Academy, in a spirit of spurious admiration, mutilated Galileo's body, -by removing the thumb and forefinger of the right-hand, and one of the -vertebrae of the back, which are still preserved in some of the Italian -museums. The monument was put up at the expense of his biographer, -Nelli, to whom Viviani's property descended, charged with the condition -of erecting it. Nor was this the only public testimony which Viviani -gave of his attachment. The medal which he struck in honour of Galileo -has already been mentioned; he also, as soon as it was safe to do so, -covered every side of the house in which he lived with laudatory -inscriptions to the same effect. A bust of Galileo was placed over the -door, and two bas-reliefs on each side representing some of his -principal discoveries. Not less than five other medals were struck in -honour of him during his residence at Padua and Florence, which are all -engraved in Venturi's Memoirs. - -There are several good portraits of Galileo extant, two of which, by -Titi and Subtermanns, are engraved in Nelli's Life of Galileo. Another -by Subtermanns is in the Florentine Gallery, and an engraving from a -copy of this is given by Venturi. There is also a very fine engraving -from the original picture. An engraving from another original picture is -in the frontispiece of the Padua edition of his works. Salusbury seems -in the following passage to describe a portrait of Galileo painted by -himself: "He did not contemn the other inferior arts, for he had a good -hand in sculpture and carving; but his particular care was to paint -well. By the pencil he described what his telescope discovered; in one -he exceeded art, in the other, nature. Osorius, the eloquent bishop of -Sylva, esteems one piece of Mendoza the wise Spanish minister's -felicity, to have been this, that he was contemporary to Titian, and -that by his hand he was drawn in a fair tablet. And Galilaeus, lest he -should want the same good fortune, made so great a progress in this -curious art, that he became his own _Buonarota_; and because there was -no other copy worthy of his pencil, drew himself." No other author makes -the slightest allusion to such a painting; and it appears more likely -that Salusbury should be mistaken than that so interesting a portrait -should have been entirely lost sight of. - -Galileo's house at Arcetri was standing in 1821, when Venturi visited -it, and found it in the same state in which Galileo might be supposed to -have left it. It is situated nearly a mile from Florence, on the -south-eastern side, and about a gun-shot to the north-west of the -convent of St. Matthew. Nelli placed a suitable inscription over the -door of the house, which belonged in 1821 to a Signor Alimari.[175] - -Although Nelli's Life of Galileo disappointed the expectations that had -been formed of it, it is impossible for any admirer of Galileo not to -feel the greatest degree of gratitude towards him, for the successful -activity with which he rescued so many records of the illustrious -philosopher from destruction. After Galileo's death, the principal part -of his books, manuscripts, and instruments, were put into the charge of -Viviani, who was himself at that time an object of great suspicion; most -of them he thought it prudent to conceal, till the superstitious -outcries against Galileo should be silenced. At Viviani's death, he left -his library, containing a very complete collection of the works of all -the mathematicians who had preceded him (and amongst them those of -Galileo, Torricelli, and Castelli, all which were enriched with notes -and additions by himself), to the hospital of St. Mary at Florence, -where an extensive library already existed. The directors of the -hospital sold this unique collection in 1781, when it became entirely -dispersed. The manuscripts in Viviani's possession passed to his nephew, -the Abbe Panzanini, together with the portraits of the chief personages -of the Galilean school, Galileo's instruments, and, among other -curiosities, the emerald ring which he wore as a member of the Lyncean -Academy. A great number of these books and manuscripts were purchased at -different times by Nelli, after the death of Panzanini, from his -relations, who were ignorant or regardless of their value. One of his -chief acquisitions was made by an extraordinary accident, related by -Tozzetti with the following details, which we repeat, as they seem to -authenticate the story:--"In the spring of 1739, the famous Doctor Lami -went out according to his custom to breakfast with some of his friends -at the inn of the Bridge, by the starting-place; and as he and Sig. -Nelli were passing through the market, it occurred to them to buy some -Bologna sausages from the pork-butcher, Cioci, who was supposed to excel -in making them. They went into the shop, had their sausages cut off and -rolled in paper, which Nelli put into his hat. On reaching the inn, and -calling for a plate to put them in, Nelli observed that the paper in -which they had been rolled was one of Galileo's letters. He cleaned it -as well as he could with his napkin, and put it into his pocket without -saying a word to Lami; and as soon as he returned into the city, and -could get clear of him, he flew to the shop of Cioci, who told him that -a servant whom he did not know brought him from time to time similar -letters, which he bought by weight as waste paper. Nelli bought all that -remained, and on the servant's next reappearance in a few days, he -learned the quarter whence they came, and after some time succeeded at a -small expense in getting into his own possession an old corn-chest, -containing all that still remained of the precious treasures which -Viviani had concealed in it ninety years before."[176] - -The earliest biographical notice of Galileo is that in the Obituary of -the Mercurio Italico, published at Venice in 1647, by Vittorio Siri. It -is very short, but contains an exact enumeration of his principal works -and discoveries. Rossi, who wrote under the name of Janus Nicius -Erythraeus, introduced an account of Galileo in his Pinacotheca Imaginum -Illustrium, in which the story of his illegitimacy first made its -appearance. In 1664, Salusbury published a life of Galileo in the second -volume of his Mathematical Collections, the greater part of which is a -translation of Galileo's principal works. Almost the whole edition of -the second volume of Salusbury's book was burnt in the great fire of -London. Chauffepie says that only one copy is known to be extant in -England: this is now in the well-known library of the Earl of -Macclesfield, to whose kindness the author is much indebted for the use -he has been allowed to make of this unique volume. A fragment of this -second volume is in the Bodleian Library at Oxford. The translations in -the preceding pages are mostly founded upon Salusbury's version. -Salusbury's account, although that of an enthusiastic admirer of -Galileo, is too prolix to be interesting: the general style of the -performance may be guessed from the title of the first chapter--'Of Man -in general, and how he excelleth all the other Animals.' After informing -his readers that Galileo was born at Pisa, he proceeds:--"Italy is -affirmed to have been the first that peopled the world after the -universal deluge, being governed by Janus, Cameses, and Saturn, &c." His -description of Galileo's childhood is somewhat quaint. "Before others -had left making of dirt pyes, he was framing of diagrams; and whilst -others were whipping of toppes, he was considering the cause of their -motion." It is on the whole tolerably correct, especially if we take -into account that Salusbury had not yet seen Viviani's Life, though -composed some years earlier. - -The Life of Galileo by Viviani was first written as an outline of an -intended larger work, but this latter was never completed. This sketch -was published in the Memoirs of the Florentine Academy, of which Galileo -had been one of the annual presidents, and afterwards prefixed to the -complete editions of Galileo's works; it is written in a very agreeable -and flowing style, and has been the groundwork of most subsequent -accounts. Another original memoir by Niccolo Gherardini, was published -by Tozzetti. A great number of references to authors who have treated of -Galileo is given by Sach in his Onomasticon. An approved Latin memoir by -Brenna is in the first volume of Fabroni's Vitae Italorum Illustrium; he -has however fallen into several errors: this same work contains the -lives of several of his principal followers. - -The article in Chauffepie's Continuation of Bayle's Dictionary does not -contain anything which is not in the earlier accounts. - -Andres wrote an essay entitled 'Saggio sulla Filosofia del Galileo,' -published at Mantua 1776; and Jagemann published his 'Geschichte des -Leben des Galileo' at Leipzig, in 1787;[177] neither of these the author -has been able to meet with. An analysis of the latter may be seen in -Kaestner's 'Geschichte der Mathematik, Goettingen, 1800,' from which it -does not appear to contain any additional details. The 'Elogio del -Galileo' by Paolo Frisi, first published at Leghorn in 1775, is, as its -title expresses, rather in the nature of a panegyric than of a -continuous biographical account. It is written with very great elegance -and intimate knowledge of the subjects of which it treats. Nelli gave -several curious particulars with respect to Galileo in his 'Saggio di -Storia Letteraria Fiorentina, Lucca, 1759;' and in 1793 published his -large work entitled 'Vita e Commercio Letterario di Galileo Galilei.' So -uninteresting a book was probably never written from such excellent -materials. Two thick quarto volumes are filled with repetitions of the -accounts that were already in print, the bulky preparation of which -compelled the author to forego the publication of the vast collection of -original documents which his unwearied zeal and industry had collected. -This defect has been in great measure supplied by Venturi in 1818 and -1821, who has not only incorporated in his work many of Nelli's -manuscripts, but has brought together a number of scattered notices of -Galileo and his writings from a variety of outlying sources--a service -which the writer is able to appreciate from having gone through the -greatest part of the same labour before he was fortunate enough to meet -with Venturi's book. Still there are many letters cited by Nelli, which -do not appear either in his book or Venturi's. Carlo Dati, in 1663, -quotes "the registers of Galileo's correspondence arranged in -alphabetical order, in ten large volumes."[178] The writer has no means -of ascertaining what collection this may have been; it is difficult to -suppose that one so arranged should have been lost sight of. It is -understood that a life of Galileo is preparing at this moment in -Florence, by desire of the present Grand Duke, which will probably throw -much additional light on the character and merits of this great and -useful philosopher. - -The first editions of his various treatises, as mentioned by Nelli, are -given below. Clement, in his 'Bibliotheque Curieuse,' has pointed out -such among them, and the many others which have been printed, as have -become rare. - -The Florentine edition is the one used by the Academia della Crusca for -their references; for which reason its paging is marked in the margin of -the edition of Padua, which is much more complete, and is the one which -has been on the present occasion principally consulted. - -The latter contains the Dialogue on the System, which was not suffered -to be printed in the former editions. The twelve first volumes of the -last edition of Milan are a mere transcript of that of Padua: the -thirteenth contains in addition the Letter to the Grand Duchess, the -Commentary on Tasso, with some minor pieces. A complete edition is still -wanted, embodying all the recently discovered documents, and omitting -the verbose commentaries, which, however useful when they were written, -now convey little information that cannot be more agreeably and more -profitably learned in treatises of a later date. - -Such was the life, and such were the pursuits, of this extraordinary -man. The numberless inventions of his acute industry; the use of the -telescope, and the brilliant discoveries to which it led; the patient -investigation of the laws of weight and motion; must all be looked upon -as forming but a part of his real merits, as merely particular -demonstrations of the spirit in which he everywhere withstood the -despotism of ignorance, and appealed boldly from traditional opinions to -the judgments of reason and common sense. He claimed and bequeathed to -us the right of exercising our faculties in examining the beautiful -creation which surrounds us. Idolized by his friends, he deserved their -affection by numberless acts of kindness; by his good humour, his -affability, and by the benevolent generosity with which he devoted -himself and a great part of his limited income to advance their talents -and fortunes. If an intense desire of being useful is everywhere worthy -of honour; if its value is immeasurably increased, when united to genius -of the highest order; if we feel for one who, notwithstanding such -titles to regard, is harassed by cruel persecution,--then none deserve -our sympathy, our admiration, and our gratitude, more than Galileo. - - -_List of Galileo's Works._ - - Le Operazioni del Compasso Geom. e Milit. - Padova, 1606. - Fol. Difesa di Gal. Galilei contr. all. cal. et impost. di Bald. Capra - Venezza, 1607. 4to. - Sydereus Nuncius Venetiis, 1610. 4to. - Discorso int. alle cose che stanno in su l'Acqua - Firenze, 1612. 4to. - Novantiqua SS. PP. Doctrina de S. Scripturae Testimoniis - Argent, 1612. 4to. - Istoria e Demostr. int. alle Macchie Solari - Roma, 1613. 4to. - Risp. alle oppos. del S. Lod. delle Colombe e del S. Vinc. di Grazia - Firenze, 1615. 4to. - Discorso delle Comete di Mario Guiducci - Firenze, 1619. 4to. - Dialogo sopra i due Massimi Sistemi del Mondo - Firenze, 1632. 4to. - Discorso e Demostr. intorno alle due nuove Scienze - Leida, 1638. 4to. - Della Scienza Meccanica Ravenna, 1649. 4to. - Trattato della Sfera Roma, 1655. 4to. - Discorso sopra il Flusso e Reflusso. (Scienze Fisiche di Tozzetti.) - Firenze, 1780. 4to. - Considerazioni sul Tasso Roma, 1793. - Trattato della Fortificazione. (Memorie di Venturi.) - Modena, 1818. 4to. - -The editions of his collected works (in which is contained much that was -never published separately) are-- - - Opere di Gal. Galilei, Linc. Nob. Fior. &c. - Bologna, 1656. 2 vols. 4to. - Opere di Gal. Galilei, Nob. Fior. Accad. Linc. &c. - Firenze, 1718. 3 vols. 4to. - Opere di Gal. Galilei Padova, 1744. 4 vols. 4to. - Opere di Gal. Galilei Milano, 1811. 13 vols. 8vo. - - -CORRECTIONS. - - _Page Co. Line._ - - 5 1 2, - _Add_: His instructor was the celebrated botanist, Andreas - Caesalpinus, who was professor of medicine at Pisa from 1567 to 1592. - Hist. Acad. Pisan.; Pisis, 1791. - - 8 2 18, - _Add_: According to Kaestner, his German name was Wursteisen. - - 8 2 21, _for_ 1588 _read_ 1586. - 15 1 57, _for_ 1632 _read_ 1630. - 17 1 29, - Salusbury alludes to the instrument described and figured in "The - Use of the Sector, Crosse Staffe, and other Instruments. London, - 1624." It is exactly Galileo's Compass. - - 17 1 52, _for_ Burg, a German, _read_ Burgi, a Swiss. - 27 2 17, - The author here called Brutti was an Englishman: his real name, - perhaps, was Bruce. See p. 99. - - 50 1 14, - Kepler's Epitome was not published till 1619: it was then inserted - in the Index. - - 73 1 60, _for_ under _read_ turned from. - 80 2 44, _for_ any _read_ an indefinitely small. - - -FOOTNOTES: - -[170] The words of his diploma are: Galilaei in mathematicis disciplinis -discipulus, in aerumnis socius, Italicum ingenium ita perpolivit optimis -artibus ut inter mathematicos saeculi nostri facile princeps per orbem -litterarium numeretur.--Tiraboschi. - -[171] On this occasion the taste of the time showed itself in the -following anagram:-- - - Evangelista Torricellieus, - En virescit Galilaeus alter. - -[172] Compare Son. ii. v. 8 & 9; and Son. iii. v. 2 & 3, with Ger. Lib. -c. iv. st. 76, and c. vii. st. 19.--The author gladly owns his -obligation for these remarks to the kindness of Sig. Panizzi, Professor -of Italian in the University of London. - -[173] Lettera di Timauro Antiate. Firenze, 1663. - -[174] De phaenomenis in orbe Lunae. Venetiis, 1612. - -[175] Venturi. - -[176] Notizie sul Ingrandimento delle Scienze Fisiche. Firenze, 1780. - -[177] Venturi. - -[178] Lettera di Timauro Antiate. - - - - -LIFE OF KEPLER. - - - - -CHAPTER I. - - _Introduction--Birth and Education of Kepler--He is appointed - Astronomical Professor at Gratz--Publishes the 'Mysterium - Cosmographicum.'_ - - -IN the account of the life and discoveries of Galileo, we have -endeavoured to inculcate the safety and fruitfulness of the method -followed by that great reformer in his search after physical truth. As -his success furnishes the best instance of the value of the inductive -process, so the failures and blunders of his adversaries supply equally -good examples of the dangers and the barrenness of the opposite course. -The history of JOHN KEPLER might, at the first view, suggest conclusions -somewhat inconsistent with this remark. Every one who is but moderately -acquainted with astronomy is familiar with the discoveries which that -science owes to him; the manner in which he made them is, perhaps, not -so generally known. This extraordinary man pursued, almost invariably, -the hypothetical method. His life was passed in speculating on the -results of a few principles assumed by him, from very precarious -analogies, as the causes of the phenomena actually observed in Nature. -We nevertheless find that he did, in spite of this unphilosophical -method, arrive at discoveries which have served as guides to some of the -most valuable truths of modern science. - -The difficulty will disappear if we attend more closely to the details -of Kepler's investigations. We shall perceive that to an unusual degree -of rashness in the formation of his systems, he added a quality very -rarely possessed by philosophers of the hypothetical school. One of the -greatest intellectual vices of the latter was a wilful blindness to the -discrepancy of facts from their creed, a perverse and obstinate -resistance to physical evidence, leading not unfrequently to an attempt -at disguising the truth. From this besetting sin of the school, which -from an intellectual fault often degenerated into a moral one, Kepler -was absolutely free. Scheme after scheme, resting originally upon little -beyond his own glowing imagination, but examined and endeared by the -ceaseless labour of years, was unhesitatingly sacrificed, as soon as its -insufficiency became indisputable, to make room for others as little -deserving support. The history of philosophy affords no more remarkable -instance of sincere uncompromising love of truth. To this virtue he owed -his great discoveries: it must be attributed to his unhappy method that -he made no more. - -In considering this opinion upon the real nature of Kepler's title to -fame, it ought not to be forgotten that he has exposed himself at a -disadvantage on which certainly very few philosophers would venture. His -singular candour allowed him to comment upon his own errors with the -same freedom as if scrutinizing the work of a stranger; careless whether -the impression on his readers were favourable or otherwise to himself, -provided it was instructive. Few writers have spoken so much, and so -freely of themselves, as Kepler. He records, on almost every occasion, -the train of thought by which he was led to each of the discoveries that -eventually repaid his perseverance; and he has thus given us a most -curious and interesting view of the workings of a mind of great, though -eccentric power. "In what follows," says he (when introducing a long -string of suppositions, of which he had already discovered the fallacy), -"let the reader pardon my credulity, whilst working out all these -matters by my own ingenuity. For it is my opinion that the occasions by -which men have acquired a knowledge of celestial phenomena are not less -admirable than the discoveries themselves." Agreeing altogether with -this opinion in its widest application, we have not scrupled, in the -following sketch, to introduce at some length an account even of -Kepler's erroneous speculations; they are in themselves very amusing, -and will have the additional utility of proving the dangerous tendency -of his method; they will show by how many absurd theories, and how many -years of wasted labour, his real discoveries and services to science lie -surrounded. - -JOHN KEPLER was born (as we are assured by his earliest biographer -Hantsch) in long. 29 deg. 7', lat. 48 deg. 54', on the 21st day of December, -1571. On this spot stands the imperial city of Weil, in the duchy of -Wirtemberg. His parents were Henry Kepler and Catherine Guldenmann, both -of noble, though decayed families. Henry Kepler, at the time of his -marriage, was a petty officer in the Duke of Wirtemberg's service; and a -few years after the birth of his eldest son John, he joined the army -then serving in the Netherlands. His wife followed him, leaving their -son, then in his fifth year, at Leonberg, under the care of his -grandfather. He was a seven months child, very weak and sickly; and -after recovering with difficulty from a severe attack of small-pox, he -was sent to school in 1577. Henry Kepler's limited income was still -farther reduced on his return into Germany, the following year, in -consequence of the absconding of one of his acquaintance, for whom he -had incautiously become surety. His circumstances were so much narrowed -by this misfortune, that he was obliged to sell his house, and nearly -all that he possessed, and for several years he supported his family by -keeping a tavern at Elmendingen. This occasioned great interruption to -young Kepler's education; he was taken from school, and employed in -menial services till his twelfth year, when he was again placed in the -school at Elmendingen. In the following year he was again seized with a -violent illness, so that his life was almost despaired of. In 1586, he -was admitted into the monastic school of Maulbronn, where the cost of -his education was defrayed by the Duke of Wirtemberg. This school was -one of those established on the suppression of the monasteries at the -Reformation, and the usual course of education followed there required -that the students, after remaining a year in the superior classes, -should offer themselves for examination at the college of Tubingen for -the degree of bachelor: they then returned to their school with the -title of veterans; and after completing the studies taught there, they -were admitted as resident students at Tubingen, proceeded in about a -year to the degree of master, and were then allowed to commence their -course of theology. The three years of Kepler's life following his -admission to Maulbronn, were marked by periodical returns of several of -the disorders which had well nigh proved fatal to him in his childhood. -During the same time disagreements arose between his parents, in -consequence of which his father quitted his home, and soon after died -abroad. After his father's departure, his mother also quarrelled with -her relations, having been treated, says Hantsch, "with a degree of -barbarity by her husband and brother-in-law that was hardly exceeded -even by her own perverseness:" one of his brothers died, and the -family-affairs were in the greatest confusion. Notwithstanding these -disadvantages, Kepler took his degree of master in August 1591, -attaining the second place in the annual examination. The first name on -the list was John Hippolytus Brentius. - -Whilst he was thus engaged at Tubingen, the astronomical lectureship at -Gratz, the chief town of Styria, became vacant by the death of George -Stadt, and the situation was offered to Kepler. Of this first occasion -of turning his thoughts towards astronomy, he has himself given the -following account: "As soon as I was of an age to feel the charms of -philosophy, I embraced every part of it with intense desire, but paid no -especial regard to astronomy. I had indeed capacity enough for it, and -learned without difficulty the geometrical and astronomical theorems -occurring in the usual course of the school, being well grounded in -figures, numbers, and proportions. But those were compulsory -studies--there was nothing to show a particular turn for astronomy. I -was educated at the expense of the Duke of Wirtemberg, and when I saw -such of my companions as the duke selected to send abroad shrink in -various ways from their employments, out of fondness for home, I, who -was more callous, had early made up my mind to go with the utmost -readiness whithersoever I might be sent. The first offering itself was -an astronomical post, which I was in fact forced to accept by the -authority of my tutors; not that I was alarmed, in the manner I had -condemned in others, by the remoteness of the situation, but by the -unexpected and contemptible nature of the office, and by the slightness -of my information in this branch of philosophy. I entered on it, -therefore, better furnished with talent than knowledge: with many -protestations that I was not abandoning my claim to be provided for in -some other more brilliant profession. What progress I made in the first -two years of my studies, may be seen in my 'Mysterium Cosmographicum;' -and the encouragement given me by my tutor, Maestlin, to take up the -science of astronomy, may be read in the same book, and in his letter -which is prefixed to the 'Narrative of Rheticus.' I looked on that -discovery as of the highest importance, and still more so, because I saw -how greatly it was approved by Maestlin." - -The nature of the singular work to which Kepler thus refers with so much -complacency, will be best shown by quoting some of the most remarkable -parts of it, and especially the preface, in which he briefly details -some of the theories he successively examined and rejected, before -detecting (as he imagined he had here done) the true cause of the number -and order of the heavenly bodies. The other branches of philosophy with -which he occupied himself in his younger years, were those treated by -Scaliger in his 'Exoteric Exercises,' to the study of which book Kepler -attributed the formation of many of his opinions; and he tells us that -he devoted much time "to the examination of the nature of heaven, of -souls, of genii, of the elements, of the essence of fire, of the cause -of fountains, the ebb and flow of the tide, the shape of the continents, -and inland seas, and things of this sort." He also says, that by his -first success with the heavens, his hopes were greatly inflamed of -discovering similar analogies in the rest of the visible world, and for -this reason, named his book merely a Prodromus, or Forerunner, meaning, -at some future period, to subjoin the Aftercomer, or Sequel. But this -intention was never fulfilled; either his imagination failed him, or, -what is more likely, the laborious calculations in which his -astronomical theories engaged him, left him little time for turning his -attention to objects unconnected with his first pursuit. - -It is seldom that we are admitted to trace the progress of thought in -those who have distinguished themselves by talent and originality; and -although the whole of the following speculations begin and end in error, -yet they are so characteristic, and exhibit such an extraordinary -picture of the extravagances into which Kepler's lively imagination was -continually hurrying him, that we cannot refrain from citing nearly the -whole preface. From it, better than from any enumeration of -peculiarities, the reader will at once apprehend the nature of his -disposition. - -"When I was attending the celebrated Maestlin, six years ago, at -Tubingen, I was disturbed by the manifold inconveniences of the common -theory of the universe, and so delighted with Copernicus, whom Maestlin -was frequently in the habit of quoting with great respect, that I not -only often defended his propositions in the physical disputations of the -candidates, but also wrote a correct essay on the primary motion, -maintaining, that it is caused by the rotation of the earth. And I was -then at that point that I attributed to the earth the motion of the sun -on physical (or, if you will, on metaphysical) grounds, as Copernicus -had done for mathematical reasons. And, by this practice, I came by -degrees, partly from Maestlin's instructions, and partly from my own -efforts, to understand the superior mathematical convenience of the -system of Copernicus beyond Ptolemy's. This labour might have been -spared me, by Joachim Rheticus, who has shortly and clearly explained -everything in his first Narrative. While incidentally engaged in these -labours, in the intermission of my theology, it happened conveniently -that I succeeded George Stadt in his situation at Gratz, where the -nature of my office connected me more closely with these studies. -Everything I had learned from Maestlin, or had acquired of myself, was -there of great service to me in explaining the first elements of -astronomy. And, as in Virgil, '_Fama mobilitate viget, viresque acquirit -eundo_,' so it was with me, that the diligent thought on these things -was the occasion of still further thinking: until, at last, in the year -1595, when I had some intermission of my lectures allowed me, I brooded -with the whole energy of my mind on this subject. There were three -things in particular, of which I pertinaciously sought the causes why -they are not other than they are: the number, the size, and the motion -of the orbits. I attempted the thing at first with numbers, and -considered whether one of the orbits might be double, triple, quadruple, -or any other multiple of the others, and how much, according to -Copernicus, each differed from the rest. I spent a great deal of time in -that labour, as if it were mere sport, but could find no equality either -in the proportions or the differences, and I gained nothing from this -beyond imprinting deeply in my memory the distances as assigned by -Copernicus; unless, perhaps, reader, this record of my various attempts -may force your assent, backwards and forwards, as the waves of the sea; -until tired at length, you will willingly repose yourself, as in a safe -haven, on the reasons explained in this book. However, I was comforted -in some degree, and my hopes of success were supported as well by other -reasons which will follow presently, as by observing that the motions in -every case seemed to be connected with the distances, and that where -there was a great gap between the orbits, there was the same between the -motions. And I reasoned, that if God had adapted motions to the orbits -in some relation to the distances, it was probable that he had also -arrayed the distances themselves in relation to something else. - -"Finding no success by this method, I tried another, of singular -audacity. I inserted a new planet between Mars and Jupiter, and another -between Venus and Mercury, both of which I supposed invisible, perhaps -on account of their smallness, and I attributed to each a certain period -of revolution.[179] I thought that I could thus contrive some equality -of proportions, increasing between every two, from the sun to the fixed -stars. For instance, the Earth is nearer Venus in parts of the -terrestrial orbit, than Mars is to the Earth in parts of the orbit of -Mars. But not even the interposition of a new planet sufficed for the -enormous gap between Mars and Jupiter; for the proportion of Jupiter to -the new planet was still greater than that of Saturn to Jupiter. And -although, by this supposition, I got some sort of a proportion, yet -there was no reasonable conclusion, no certain determination of the -number of the planets either towards the fixed stars, till we should get -as far as them, nor ever towards the Sun, because the division in this -proportion of the residuary space within Mercury might be continued -without end. Nor could I form any conjecture, from the mobility of -particular numbers, why, among an infinite number, so few should be -moveable. The opinion advanced by Rheticus in his Narrative is -improbable, where he reasons from the sanctity of the number six to the -number of the six moveable heavens; for he who is inquiring of the frame -of the world itself, must not derive reasons from these numbers, which -have gained importance from things of later date. - -"I sought again, in another way, whether the distance of every planet is -not as the residuum of a sine; and its motion as the residuum of the -sine of the complement in the same quadrant. - -[Illustration] - -"Conceive the square AB to be constructed, whose side AC is equal to the -semidiameter of the universe. From the angle B opposite to A the place -of the sun, or centre of the world, describe the quadrant DC with the -radius BC. Then in AC, the true radius of the world, let the sun, fixed -stars, and planets be marked at their respective distances, and from -these points draw lines parallel to BC, meeting the quadrant. I imagined -the moving force acting on each of the planets to be in the proportion -of these parallels. In the line of the sun is infinity, because AD is -touched, and not cut, by the quadrant: therefore the moving force is -infinite in the sun, as deriving no motion except from its own act. In -Mercury the infinite line is cut off at K, and therefore at this point -the motion is comparable with the others. In the fixed stars the line is -altogether lost, and compressed into a mere point C; therefore at that -point there is no moving force. This was the theorem, which was to be -tried by calculation; but if any one will reflect that two things were -wanting to me, first, that I did not know the size of the _Sinus Totus_, -that is, the radius of the proposed quadrant; secondly, that the -energies of the motions were not thus expressed otherwise than in -relation one to another; whoever, I say, well considers this, will -doubt, not without reason, as to the progress I was likely to make in -this difficult course. And yet, with unremitting labour, and an infinite -reciprocation of sines and arcs, I did get so far as to be convinced -that this theory could not hold. - -"Almost the whole summer was lost in these annoying labours; at last, by -a trifling accident, I lighted more nearly on the truth. I looked on it -as an interposition of Providence, that I should obtain by chance, what -I had failed to discover with my utmost exertions; and I believed this -the more, because I prayed constantly that I might succeed, if -Copernicus had really spoken the truth. It happened on the 9th or -19th[180] day of July, in the year 1595, that, having occasion to show, -in my lecture-room, the passages of the great conjunctions through eight -signs, and how they pass gradually from one trine aspect to another, I -inscribed in a circle a great number of triangles, or quasi-triangles, -so that the end of one was made the beginning of another. In this manner -a smaller circle was shadowed out by the points in which the lines -crossed each other. - -[Illustration: A Scheme of the great Conjunctions of SATURN & JUPITER, -their leaps through eight Signs, and their passages through all the four -Triplicities of the Zodiac.] - -"The radius of a circle inscribed in a triangle is half the radius of -that described about it; therefore the proportion between these two -circles struck the eye as almost identical with that between Saturn and -Jupiter, and the triangle is the first figure, just as Saturn and -Jupiter are the first planets. On the spot I tried the second distance -between Jupiter and Mars with a square, the third with a pentagon, the -fourth with a hexagon. And as the eye again cried out against the second -distance between Jupiter and Mars, I combined the square with a triangle -and a pentagon. There would be no end of mentioning every trial. The -failure of this fruitless attempt was the beginning of the last -fortunate one; for I reflected, that in this way I should never reach -the sun, if I wished to observe the same rule throughout; nor should I -have any reason why there were six, rather than twenty or a hundred -moveable orbits. And yet figures pleased me, as being quantities, and as -having existed before the heavens; for quantity was created with matter, -and the heavens afterwards. But if (this was the current of my -thoughts), in relation to the quantity and proportion of the six orbits, -as Copernicus has determined them among the infinite other figures, five -only could be found having peculiar properties above the rest, my -business would be done. And then again it struck me, what have plane -figures to do among solid orbits? Solid bodies ought rather to be -introduced. This, reader, is the invention and the whole substance of -this little work; for if any one, though but moderately skilled in -geometry, should hear these words hinted, the five regular solids will -directly occur to him with the proportions of their circumscribed and -inscribed spheres: he has immediately before his eyes that scholium of -Euclid to the 18th proposition of his 13th Book, in which it is proved -to be impossible that there should be, or be imagined, more than five -regular bodies. - -"What is worthy of admiration (since I had then no proof of any -prerogatives of the bodies with regard to their order) is, that -employing a conjecture which was far from being subtle, derived from the -distances of the planets, I should at once attain my end so happily in -arranging them, that I was not able to change anything afterwards with -the utmost exercise of my reasoning powers. In memory of the event, I -write down here for you the sentence, just as it fell from me, and in -the words in which it was that moment conceived:--The Earth is the -circle, the measurer of all; round it describe a dodecahedron, the -circle including this will be Mars. Round Mars describe a tetrahedron, -the circle including this will be Jupiter. Describe a cube round -Jupiter, the circle including this will be Saturn. Now, inscribe in the -Earth an icosahedron, the circle inscribed in it will be Venus. Inscribe -an octahedron in Venus, the circle inscribed in it will be Mercury. This -is the reason of the number of the planets. - -[Illustration] - -"This was the cause, and such the success, of my labour: now read my -propositions in this book. The intense pleasure I have received from -this discovery never can be told in words. I regretted no more the time -wasted; I tired of no labour; I shunned no toll of reckoning; days and -nights I spent in calculations; until I could see whether this opinion -would agree with the orbits of Copernicus, or whether my joy was to -vanish into air. I willingly subjoin that sentiment of Archytas, as -given by Cicero: 'If I could mount up into heaven, and thoroughly -perceive the nature of the world, and beauty of the stars, that -admiration would be without a charm for me, unless I had some one like -you, reader, candid, attentive, and eager for knowledge, to whom to -describe it.' If you acknowledge this feeling, and are candid, you will -refrain from blame, such as not without cause I anticipate; but if, -leaving that to itself, you fear lest these things be not ascertained, -and that I have shouted triumph before victory, at least approach these -pages, and learn the matter in consideration: you will not find, as just -now, new and unknown planets interposed; that boldness of mine is not -approved, but those old ones very little loosened, and so furnished by -the interposition (however absurd you may think it) of rectilinear -figures, that in future you may give a reason to the rustics when they -ask for the hooks which keep the skies from falling.--Farewell." - -In the third chapter Kepler mentions, that a thickness must be allowed -to each orb sufficient to include the greatest and least distance of -the planet from the sun. The form and result of his comparison with the -real distances are as follows:-- - - Book V. - If the {Saturn } be taken {Jupiter = 577} {635 Ch. 9 - inner {Jupiter} at 1000 {Mars = 333} According to {333--14 - Surface {Mars } then the {Earth = 795} Copernicus {757--19 - of the {Earth } outer {Venus = 795} they are {794--21, 22 - orbit of {Venus } one of {Mercury = 577} {723--27 - -It will be observed, that Kepler's results were far from being entirely -satisfactory; but he seems to have flattered himself, that the -differences might be attributed to erroneous measurements. Indeed, the -science of observation was then so much in its infancy, that such an -assertion might be made without incurring much risk of decisive -refutation. - -Kepler next endeavoured to determine why the regular solids followed in -this rather than any other order; and his imagination soon created a -variety of essential distinctions between the cube, pyramid, and -dodecahedron, belonging to the superior planets, and the other two. - -The next question examined in the book, is the reason why the zodiac is -divided into 360 degrees; and on this subject, he soon becomes enveloped -in a variety of subtle considerations, (not very intelligible in the -original, and still more difficult to explain shortly to others -unacquainted with it,) in relation to the divisions of the musical -scale; the origin of which he identifies with his five favourite solids. -The twentieth chapter is appropriated to a more interesting inquiry, -containing the first traces of his finally successful researches into -the proportion between the distances of the planets, and the times of -their motions round the sun. He begins with the generally admitted fact, -that the more distant planets move more slowly; but in order to show -that the proportion, whatever it may be, is not the simple one of the -distances, he exhibits the following little Table:-- - - [Saturn] - +---------+--------+ - | |D. Scr. |[Jupiter] - +---------+--------+---------+ - |[Saturn] |10759.12| D. Scr. |[Mars] - +---------+--------+---------+--------+ - |[Jupiter]| 6159 | 4332.37 |D. Scr. |[Earth] - +---------+--------+---------+--------+-------+ - |[Mars] | 1785 | 1282 | 686.59 |D. Scr.|[Venus] - +---------+--------+---------+--------+-------+-------+ - |[Earth] | 1174 | 843 | 452 |365.15 |D. Scr.| [Mercury] - +---------+--------+---------+--------+-------+-------+----------+ - |[Venus] | 844 | 606 | 325 |262.30 |224.42 | D. Scr. | - +---------+--------+---------+--------+-------+-------+----------+ - |[Mercury]| 434 | 312 | 167 |135 |115 | 87.58 | - -At the head of each vertical column is placed the real time (in days and -sexagesimal parts) of the revolution of the planet placed above it, and -underneath the days due to the other inferior planets, if they observed -the proportion of distance. Hence it appears that this proportion in -every case gives a time greater than the truth; as for instance, if the -earth's rate of revolution were to Jupiter's in the proportion of their -distances, the second column shows that the time of her period would be -843 instead of 3651/4 days; so of the rest. His next attempt was to -compare them by two by two, in which he found that he arrived at a -proportion something like the proportion of the distances, although as -yet far from obtaining it exactly. This process amounts to taking the -quotients obtained by dividing the period of each planet by the period -of the one next beyond. - - { [Saturn] 10759.27} be successively { [Jupiter] 403 - For if { [Jupiter] 4332.37} taken to consist of { [Mars] 159 - each { } 1000 equal parts, { - of the { [Mars] 686.59} the periods of { [Earth] 532 - periods { [Earth] 365.15} the planet next { [Venus] 615 - of { } below will contain { - { [Venus] 244.42} of those parts in { [Mercury] 392 - - But if the distance of each planet in {[Jupiter] 572 - succession be taken to consist of {[Mars] 290 - 1000 equal parts, the distance of {[Earth] 658 - the next below will contain, according {[Venus] 719 - to Copernicus, in {[Mercury] 500 - -From this table he argued that to make the proportions agree, we must -assume one of two things, "either that the moving intelligences of the -planets are weakest in those which are farthest from the Sun, or that -there is one moving intelligence in the Sun, the common centre forcing -them all round, but those most violently which are nearest, and that it -languishes in some sort, and grows weaker at the most distant, because -of the remoteness and the attenuation of the virtue." - -We stop here to insert a note added by Kepler to the later editions, and -shall take advantage of the same interruption to warn the reader not to -confound this notion of Kepler with the theory of a gravitating force -towards the Sun, in the sense in which we now use those words. According -to our theory, the effect of the presence of the Sun upon the planet is -to pull it towards the centre in a straight line, and the effect of the -motion thus produced combined with the motion of the planet, which if -undisturbed would be in a straight line inclined to the direction of the -radius, is, that it describes a curve round the Sun. Kepler considered -his planets as perfectly quiet and unwilling to move when left alone; -and that this virtue supposed by him to proceed in every direction out -of the Sun, swept them round, just as the sails of a windmill would -carry round anything which became entangled in them. In other parts of -his works Kepler mentions having speculated on a real attractive force -in the centre; but as he knew that the planets are not always at the -same distance from the Sun, and conceived erroneously, that to remove -them from their least to their greatest distance a repulsive force must -be supposed alternating with an attractive one, he laid aside this -notion as improbable. In a note he acknowledges that when he wrote the -passage just quoted, imbued as he then was with Scaliger's notions on -moving intelligences, he literally believed "that each planet was moved -by a living spirit, but afterwards came to look on the moving cause as a -corporeal though immaterial substance, something in the nature of light -which is observed to diminish similarly at increased distances." He then -proceeds as follows in the original text. - -"Let us then assume, as is very probable, that motion is dispensed by -the sun in the same manner as light. The proportion in which light -emanating from a centre is diminished, is taught by optical writers: for -there is the same quantity of light, or of the solar rays, in the small -circles as in the large; and therefore, as it is more condensed in the -former, more attenuated in the latter, a measure of the attenuation may -be derived from the proportion of the circles themselves, both in the -case of light and of the moving virtue. Therefore, by how much the orbit -of Venus is greater than that of Mercury, in the same proportion will -the motion of the latter be stronger, or more hurried, or more swift, or -more powerful, or by whatever other word you like to express the fact, -than that of the former. But a larger orbit would require a -proportionably longer time of revolution, even though the moving force -were the same. Hence it follows that the one cause of a greater distance -of the planet from the Sun, produces a double effect in increasing the -period, and conversely the increase of the periods will be double the -difference of the distances. Therefore, half the increment added to the -shorter period ought to give the true proportion of the distances, so -that the sum should represent the distance of the superior planet, on -the same scale on which the shorter period represents the distance of -the interior one. For instance, the period of Mercury is nearly 88 days; -that of Venus is 224-2/3, the difference is 136-2/3: half of this is -68-1/3, which, added to 88, gives 156-1/3. The mean distance of Venus -ought, therefore, to be, in proportion to that of Mercury, as 156-1/3 to -88. If this be done with all the planets, we get the following results, -taking successively, as before, the distance of each planet at 1000. - - The distance in } [Jupiter] 574 But according { 572 - parts of which } [Mars] 274 to Copernicus { 290 - the distance of } [Earth] 694 they are { 658 - the next superior } [Venus] 762 respectively { 719 - planet contains } { - 1000, is at } [Mercury] 563 { 500 - -As you see, we have now got nearer the truth." - -Finding that this theory of the rate of diminution would not bring him -quite close to the result he desired to find, Kepler immediately -imagined another. This latter occasioned him a great deal of perplexity, -and affords another of the frequently recurring instances of the waste -of time and ingenuity occasioned by his impetuous and precipitate -temperament. Assuming the distance of any planet, as for instance of -Mars, to be the unit of space, and the virtue at that distance to be the -unit of force, he supposed that as many particles as the virtue at the -Earth gained upon that of Mars, so many particles of distance did the -Earth lose. He endeavoured to determine the respective positions of the -planets upon this theory, by the rules of false position, but was much -astonished at finding the same exactly as on his former hypothesis. The -fact was, as he himself discovered, although not until after several -years, that he had become confused in his calculation; and when half -through the process, had retraced his steps so as of course to arrive -again at the numbers from which he started, and which he had taken from -his former results. This was the real secret of the identity of the two -methods; and if, when he had taken the distance of Mars at 1000, instead -of assuming the distance of the earth at 694, as he did, he had taken -any other number, and operated upon it in the same manner, he would -have had the same reason for relying on the accuracy of his supposition. -As it was, the result utterly confounded him; and he was obliged to -leave it with the remark, that "the two theories are thus proved to be -the same in fact, and only different in form; although how that can -possibly be, I have never to this day been able to understand."--His -perplexity was very reasonable; they are by no means the same; it was -only his method of juggling with the figures which seemed to connect -them. - -Notwithstanding all its faults, the genius and unwearied perseverance -displayed by Kepler in this book, immediately ranked him among -astronomers of the first class; and he received the most flattering -encomiums from many of the most celebrated; among others, from Galileo -and Tycho Brahe, whose opinion he invited upon his performance. Galileo -contented himself with praising in general terms the ingenuity and good -faith which appeared so conspicuously in it. Tycho Brahe entered into a -more detailed criticism of the work, and, as Kepler shrewdly remarked, -showed how highly he thought of it by advising him to try to adapt -something of the same kind to the Tychonic system. Kepler also sent a -copy of his book to the imperial astronomer, Raimar, with a -complimentary letter, in which he exalted him above all other -astronomers of the age. Raimar had surreptitiously acquired a notion of -Tycho Brahe's theory, and published it as his own; and Tycho, in his -letter, complained of Kepler's extravagant flattery. This drew a long -apologetical reply from Kepler, in which he attributed the admiration he -had expressed of Raimar to his own want of information at that time, -having since met with many things in Euclid and Regiomontanus, which he -then believed original in Raimar. With this explanation, Tycho professed -himself perfectly satisfied. - - -FOOTNOTES: - -[179] The following scrupulous note added by Kepler in 1621 to a -subsequent edition of this work, deserves to be quoted. It shows how -entirely superior he was to the paltriness of attempting to appropriate -the discoveries of others, of which many of his contemporaries had -exhibited instances even on slighter pretences than this passage might -have afforded him. The note is as follows: "Not circulating round -Jupiter like the Medicaean stars. Be not deceived. I never had them in my -thoughts, but, like the other primary planets, including the sun in the -centre of the system within their orbits." - -[180] This inconvenient mode of dating was necessary before the new or -Gregorian style was universally adopted. - - - - -CHAPTER II. - - _Kepler's Marriage--He joins Tycho Brahe at Prague--Is appointed - Imperial Mathematician--Treatise on the New Star._ - - -THE publication of this extraordinary book, early as it occurs in the -history of Kepler's life, was yet preceded by his marriage. He had -contemplated this step so early as 1592; but that suit having been -broken off, he paid his addresses, in 1596, to Barbara Muller von -Muhleckh. This lady was already a widow for the second time, although -two years younger than Kepler himself. On occasion of this alliance he -was required to prove the nobility of his family, and the delay -consequent upon the inquiry postponed the marriage till the following -year. He soon became involved in difficulties in consequence of this -inconsiderate engagement: his wife's fortune was less than he had been -led to expect, and he became embroiled on that account with her -relations. Still more serious inconvenience resulted to him from the -troubled state in which the province of Styria was at that time, arising -out of the disputes in Bohemia and the two great religious parties into -which the empire was now divided, the one headed by Rodolph, the feeble -minded emperor,--the other by Matthias, his ambitious and enterprising -brother. - -In the year following his marriage, he thought it prudent, on account of -some opinions he had unadvisedly promulgated, (of what nature does not -very distinctly appear,) to withdraw himself from Gratz into Hungary. -Thence he transmitted several short treatises to his friend Zehentmaier, -at Tubingen--"On the Magnet," "On the Cause of the Obliquity of the -Ecliptic," and "On the Divine Wisdom, as shown in the Creation." Little -is known of these works beyond the notice taken of them in Zehentmaier's -answers. Kepler has himself told us, that his magnetic philosophy was -built upon the investigations of Gilbert, of whom he always justly spoke -with the greatest respect. - -About the same time a more violent persecution had driven Tycho Brahe -from his observatory of Uraniburg, in the little island of Hueen, at the -entrance of the Baltic. This had been bestowed on him by the munificence -of Frederick I. of Denmark, who liberally furnished him with every means -of prosecuting his astronomical observations. After Frederick's death, -Tycho found himself unable to withstand the party which had constantly -opposed him, and was forced, at a great loss and much inconvenience, to -quit his favourite island. On the invitation of the emperor, Rudolph -II., he then betook himself, after a short stay at Hamburg, to the -castle of Benach, near Prague, which was assigned to him with an annual -pension of three thousand florins, a truly munificent provision in those -times and that country. - -Kepler had been eager to see Tycho Brahe since the latter had intimated -that his observations had led him to a more accurate determination of -the excentricities of the orbits of the planets. By help of this, Kepler -hoped that his theory might be made to accord more nearly with the -truth; and on learning that Tycho was in Bohemia, he immediately set out -to visit him, and arrived at Prague in January, 1600. From thence he -wrote a second letter to Tycho, not having received the answer to his -former apology, again excusing himself for the part he had appeared to -take with Raimar against him. Tycho replied immediately in the kindest -manner, and begged he would repair to him directly:--"Come not as a -stranger, but as a very welcome friend; come and share in my -observations with such instruments as I have with me, and as a dearly -beloved associate." During his stay of three or four months at Benach, -it was settled that Tycho should apply to the emperor, to procure him -the situation of assistant in the observatory. Kepler then returned to -Gratz, having previously received an intimation, that he might do so in -safety. The plan, as it had been arranged between them was, that a -letter should be procured from the emperor to the states of Styria, -requesting that Kepler might join Tycho Brahe for two years, and retain -his salary during that time: a hundred florins were to be added annually -by the emperor, on account of the greater dearness of living at Prague. -But before everything was concluded, Kepler finally threw up his -situation at Gratz, in consequence of new dissensions. Fearing that this -would utterly put an end to his hopes of connecting himself with Tycho, -he determined to revive his claims on the patronage of the Duke of -Wirtemberg. With this view he entered into correspondence with Maestlin -and some of his other friends at Tubingen, intending to prosecute his -medical studies, and offer himself for the professorship of medicine in -that university. He was dissuaded from this scheme by the pressing -instances of Tycho, who undertook to exert himself in procuring a -permanent settlement for him from the emperor, and assured him, even if -that attempt should fail, that the language he had used when formerly -inviting him to visit him at Hamburg, should not be forgotten. In -consequence of this encouragement, Kepler abandoned his former scheme, -and travelled again with his wife to Prague. He was detained a long time -on the road by violent illness, and his money became entirely exhausted. -On this he wrote complainingly to Tycho, that he was unable without -assistance to travel even the short distance which still separated them, -far less to await much longer the fulfilment of the promises held out to -him. - -By his subsequent admissions, it appears that for a considerable time he -lived entirely on Tycho's bounty, and by way of return, he wrote an -essay against Raimar, and against a Scotchman named Liddell, professor -at Rostoch and Helmstadt, who, like Raimar, had appropriated to himself -the credit of the Tychonic system. Kepler never adopted this theory, and -indeed, as the question merely regarded priority of invention, there -could be no occasion, in the discussion, for an examination of its -principles. - -This was followed by a transaction, not much to Kepler's credit, who in -the course of the following year, and during a second absence from -Prague, fancied that he had some reason to complain of Tycho's -behaviour, and wrote him a violent letter, filled with reproaches and -insults. Tycho appears to have behaved in this affair with great -moderation: professing to be himself occupied with the marriage of his -daughter, he gave the care of replying to Kepler's charges, to Ericksen, -one of his assistants, who, in a very kind and temperate letter, pointed -out to him the ingratitude of his behaviour, and the groundlessness of -his dissatisfaction. His principal complaint seems to have been, that -Tycho had not sufficiently supplied his wife with money during his -absence. Ericksen's letter produced an immediate and entire change in -Kepler's temper, and it is only from the humble recantation which he -instantaneously offered that we learn the extent of his previous -violence. "Most noble Tycho," these are the words of his letter, "how -shall I enumerate or rightly estimate your benefits conferred on me! For -two months you have liberally and gratuitously maintained me, and my -whole family; you have provided for all my wishes; you have done me -every possible kindness; you have communicated to me everything you hold -most dear; no one, by word or deed, has intentionally injured me in -anything: in short, not to your children, your wife, or yourself have -you shown more indulgence than to me. This being so, as I am anxious to -put upon record, I cannot reflect without consternation that I should -have been so given up by God to my own intemperance, as to shut my eyes -on all these benefits; that, instead of modest and respectful gratitude, -I should indulge for three weeks in continual moroseness towards all -your family, in headlong passion, and the utmost insolence towards -yourself, who possess so many claims on my veneration from your noble -family, your extraordinary learning, and distinguished reputation. -Whatever I have said or written against the person, the fame, the -honour, and the learning of your excellency; or whatever, in any other -way, I have injuriously spoken or written, (if they admit no other more -favourable interpretation,) as to my grief I have spoken and written -many things, and more than I can remember; all and everything I recant, -and freely and honestly declare and profess to be groundless, false, and -incapable of proof." Hoffmann, the president of the states of Styria, -who had taken Kepler to Prague on his first visit, exerted himself to -perfect the reconciliation, and this hasty quarrel was entirely passed -over. - -On Kepler's return to Prague, in September, 1601, he was presented to -the Emperor by Tycho, and honoured with the title of Imperial -Mathematician, on condition of assisting Tycho in his calculations. -Kepler desired nothing more than this condition, since Tycho was at that -time probably the only person in the world who possessed observations -sufficient for the reform which he now began to meditate in the theory -of astronomy. Rudolph appears to have valued both Tycho Brahe and Kepler -as astrologers rather than astronomers; but although unable to -appreciate rightly the importance of the task they undertook, of -compiling a new set of astronomical tables founded upon Tycho's -observations, yet his vanity was flattered with the prospect of his name -being connected with such a work, and he made liberal promises to defray -the expense of the new Rudolphine Tables. Tycho's principal assistant at -this time was Longomontanus, who altered his name to this form, -according to the prevalent fashion of giving to every name a Latin -termination. Lomborg or Longbierg was the name, not of his family, but -of the village in Denmark, where he was born, just as Mueller was seldom -called by any other name than Regiomontanus, from his native town -Koenigsberg, as George Joachim Rheticus was so surnamed from Rhetia, the -country of the Grisons, and as Kepler himself was sometimes called -Leonmontanus, from Leonberg, where he passed his infancy. It was agreed -between Longomontanus and Kepler, that in discussing Tycho's -observations, the former should apply himself especially to the Moon, -and the latter to Mars, on which planet, owing to its favourable -position, Tycho was then particularly engaged. The nature of these -labours will be explained when we come to speak of the celebrated book -"On the Motions of Mars." - -This arrangement was disturbed by the return of Longomontanus into -Denmark, where he had been offered an astronomical professorship, and -still more by the sudden death of Tycho Brahe himself in the following -October. Kepler attended him during his illness, and after his death -undertook to arrange some of his writings. But, in consequence of a -misunderstanding between him and Tycho's family, the manuscripts were -taken out of his hands; and when, soon afterwards, the book appeared, -Kepler complained heavily that they had published, without his consent -or knowledge, the notes and interlineations added by him for his own -private guidance whilst preparing it for publication. - -On Tycho's death, Kepler succeeded him as principal mathematician to the -emperor; but although he was thus nominally provided with a liberal -salary, it was almost always in arrear. The pecuniary embarrassments in -which he constantly found himself involved, drove him to the resource of -gaining a livelihood by casting nativities. His peculiar temperament -rendered him not averse from such speculations, and he enjoyed -considerable reputation in this line, and received ample remuneration -for his predictions. But although he did not scruple, when consulted, to -avail himself in this manner of the credulity of his contemporaries, he -passed over few occasions in his works of protesting against the -futility of this particular genethliac astrology. His own astrological -creed was in a different strain, more singular, but not less -extravagant. We shall defer entering into any details concerning it, -till we come to treat of his book on Harmonics, in which he has -collected and recapitulated the substance of his scattered opinions on -this strange subject. - -His next works deserving notice are those published on occasion of the -new star which shone out with great splendour in 1604, in the -constellation Cassiopeia.[181] Immediately on its appearance, Kepler -wrote a short account of it in German, marked with all the oddity which -characterises most of his productions. We shall see enough of his -astronomical calculations when we come to his book on Mars; the -following passage will probably be found more amusing. - -After comparing this star with that of 1572, and mentioning that many -persons who had seen it maintained this to be the brighter of the two, -since it was nearly twice the size of its nearest neighbour, Jupiter, he -proceeds as follows:--"Yonder one chose for its appearance a time no way -remarkable, and came into the world quite unexpectedly, like an enemy -storming a town, and breaking into the market-place before the citizens -are aware of his approach; but ours has come exactly in the year of -which astrologers have written so much about the fiery trigon that -happens in it;[182] just in the month in which (according to Cyprian) -Mars comes up to a very perfect conjunction with the other two superior -planets; just in the day when Mars has joined Jupiter, and just in the -place where this conjunction has taken place. Therefore the apparition -of this star is not like a secret hostile irruption, as was that one of -1572, but the spectacle of a public triumph, or the entry of a mighty -potentate; when the couriers ride in some time before, to prepare his -lodgings, and the crowd of young urchins begin to think the time -over-long to wait: then roll in, one after another, the ammunition, and -money, and baggage waggons, and presently the trampling of horse, and -the rush of people from every side to the streets and windows; and when -the crowd have gazed with their jaws all agape at the troops of knights; -then at last, the trumpeters, and archers, and lackeys, so distinguish -the person of the monarch, that there is no occasion to point him out, -but every one cries out of his own accord--'Here we have him!'--What it -may portend is hard to determine, and thus much only is certain, that it -comes to tell mankind either nothing at all, or high and weighty news, -quite beyond human sense and understanding. It will have an important -influence on political and social relations; not indeed by its own -nature, but, as it were, accidentally through the disposition of -mankind. First, it portends to the booksellers great disturbances, and -tolerable gains; for almost every _Theologus_, _Philosophicus_, -_Medicus_, and _Mathematicus_, or whoever else, having no laborious -occupation intrusted to him, seeks his pleasure _in studiis_, will make -particular remarks upon it, and will wish to bring these remarks to the -light. Just so will others, learned and unlearned, wish to know its -meaning, and they will buy the authors who profess to tell them. I -mention these things merely by way of example, because, although thus -much can be easily predicted without great skill, yet may it happen just -as easily, and in the same manner, that the vulgar, or whoever else is -of easy faith, or it may be, crazy, may wish to exalt himself into a -great prophet; or it may even happen that some powerful lord, who has -good foundation and beginning of great dignities, will be cheered on by -this phenomenon to venture on some new scheme, just as if God had set up -this star in the darkness merely to enlighten them." - -It would hardly be supposed, from the tenor of this last passage, that -the writer of it was not a determined enemy to astrological predictions -of every description. In 1602 he had published a disputation, not now -easily met with, "On the Principles of Astrology," in which it seems -that he treated the professed astrologers with great severity. The -essence of this book is probably contained in the second treatise on the -new star, which he published in 1606.[183] In this volume he inveighs -repeatedly against the vanity and worthlessness of ordinary astrology, -declaring at the same time, that the professors of that art know that -this judgment is pronounced by one well acquainted with its principles. -"For if the vulgar are to pronounce who is the best astrologer, my -reputation is known to be of the highest order; if they prefer the -judgment of the learned, they are already condemned. Whether they stand -with me in the eyes of the populace, or I fall with them before the -learned, in both cases I am in their ranks; I am on a level with them; I -cannot be renounced." - -The theory which Kepler proposed to substitute is intimated shortly in -the following passage: "I maintain that the colours and aspects, and -conjunctions of the planets, are impressed on the natures or faculties -of sublunary things, and when they occur, that these are excited as well -in forming as in moving the body over whose motion they preside. Now let -no one conceive a prejudice that I am anxiously seeking to mend the -deplorable and hopeless cause of astrology by far-fetched subtilties and -miserable quibbling. I do not value it sufficiently, nor have I ever -shunned having astrologers for my enemies. But a most unfailing -experience (as far as can be hoped in natural phenomena) of the -excitement of sublunary natures by the conjunctions and aspects of the -planets, has instructed and compelled my unwilling belief." - -After exhausting other topics suggested by this new star, he examines -the different opinions on the cause of its appearance. Among others he -mentions the Epicurean notion, that it was a fortuitous concourse of -atoms, whose appearance in this form was merely one of the infinite -number of ways in which, since the beginning of time, they have been -combined. Having descanted for some time on this opinion, and declared -himself altogether hostile to it, Kepler proceeds as follows:--"When I -was a youth, with plenty of idle time on my hands, I was much taken with -the vanity, of which some grown men are not ashamed, of making anagrams, -by transposing the letters of my name, written in Greek, so as to make -another sentence: out of [Ioannes Kepleros] I made [Seirenon -kapelos];[184] in Latin, out of _Joannes Keplerus_ came _Serpens in -akuleo_.[185] But not being satisfied with the meaning of these words, -and being unable to make another, I trusted the thing to chance, and -taking out of a pack of playing cards as many as there were letters in -the name, I wrote one upon each, and then began to shuffle them, and at -each shuffle to read them in the order they came, to see if any meaning -came of it. Now, may all the Epicurean gods and goddesses confound this -same chance, which, although I spent a good deal of time over it, never -showed me anything like sense even from a distance.[186] So I gave up my -cards to the Epicurean eternity, to be carried away into infinity, and, -it is said, they are still flying about there, in the utmost confusion -among the atoms, and have never yet come to any meaning. I will tell -these disputants, my opponents, not my own opinion, but my wife's. -Yesterday, when weary with writing, and my mind quite dusty with -considering these atoms, I was called to supper, and a salad I had asked -for was set before me. It seems then, said I aloud, that if pewter -dishes, leaves of lettuce, grains of salt, drops of water, vinegar, and -oil, and slices of egg, had been flying about in the air from all -eternity, it might at last happen by chance that there would come a -salad. Yes, says my wife, but not so nice and well dressed as this of -mine is." - - -FOOTNOTES: - -[181] See Life of Galileo, p. 16. - -[182] The fiery trigon occurs about once in every 800 years, when -Saturn, Jupiter, and Mars are in the three fiery signs, Aries, Leo, and -Sagittarius. - -[183] The copy of this work in the British Museum is Kepler's -presentation copy to our James I. On the blank leaf, opposite the -title-page, is the following inscription, apparently in the author's -hand-writing:--"Regi philosophanti, philosophus serviens, Platoni -Diogenes, Britannias tenenti, Pragae stipem mendicans ab Alexandro, e -dolio conductitio, hoc suum philosophema misit et commendavit." - -[184] The tapster of the Sirens. - -[185] A serpent in his sting. - -[186] In one of his anonymous writings Kepler has anagrammatized his -name, _Joannes Keplerus_, in a variety of other forms, probably selected -from the luckiest of his shuffles:--"_Kleopas Herennius, Helenor -Kapuensis, Raspinus Enkeleo, Kanones Pueriles._" - - - - -CHAPTER III. - - _Kepler publishes his Supplement to Vitellion--Theory of - Refraction._ - - -DURING several years Kepler remained, as he himself forcibly expressed -it, begging his bread from the emperor at Prague, and the splendour of -his nominal income served only to increase his irritation, at the real -neglect under which he nevertheless persevered in his labours. His -family was increasing, and he had little wherewith to support them -beyond the uncertain proceeds of his writings and nativities. His salary -was charged partly on the states of Silesia, partly on the imperial -treasury; but it was in vain that repeated orders were procured for the -payment of the arrears due to him. The resources of the empire were -drained by the constant demands of an engrossing war, and Kepler had not -sufficient influence to enforce his claims against those who thought -even the smallest sum bestowed upon him ill spent, in fostering -profitless speculations. In consequence of this niggardliness, Kepler -was forced to postpone the publication of the Rudolphine Tables, which -he was engaged in constructing from his own and Tycho Brahe's -observations, and applied himself to other works of a less costly -description. Among these may be mentioned a "Treatise on Comets," -written on occasion of one which appeared in 1607: in this he suggests -that they are planets moving in straight lines. The book published in -1604, which he entitles "A Supplement to Vitellion," may be considered -as containing the first reasonable and consistent theory of optics, -especially in that branch of it usually termed dioptrics, which relates -to the theory of vision through transparent substances. In it was first -explained the true use of the different parts of the eye, to the -knowledge of which Baptista Porta had already approached very nearly, -though he stopped short of the accurate truth. Kepler remarked the -identity of the mechanism in the eye with that beautiful invention of -Porta's, the camera obscura; showing, that the light which falls from -external objects on the eye is refracted through a transparent -substance, called, from its form and composition, the crystalline lens, -and makes a picture on the fine net-work of nerves, called the retina, -which lies at the back of the eye. The manner in which the existence of -this coloured picture on the retina causes to the individual the -sensation of sight, belongs to a theory not purely physical; and beyond -this point Kepler did not attempt to go. - -The direction into which rays of light (as they are usually called) are -bent or refracted in passing through the air and other transparent -substances or mediums, is discussed in this treatise at great length. -Tycho Brahe had been the first astronomer who recognized the necessity -of making some allowance on this account in the observed heights of the -stars. A long controversy arose on this subject between Tycho Brahe and -Rothman, the astronomer at Hesse Cassel, a man of unquestionable talent, -but of odd and eccentric habits. Neither was altogether in the right, -although Tycho had the advantage in the argument. He failed however to -establish the true law of refraction, and Kepler has devoted a chapter -to an examination of the same question. It is marked by precisely the -same qualities as those appearing so conspicuously in his astronomical -writings:--great ingenuity; wonderful perseverance; bad philosophy. That -this may not be taken solely upon assertion, some samples of it are -subjoined. The writings of the authors of this period are little read or -known at the present day; and it is only by copious extracts that any -accurate notion can be formed of the nature and value of their labours. -The following tedious specimen of Kepler's mode of examining physical -phenomena is advisedly selected to contrast with his astronomical -researches: though the luck and consequently the fame that attended his -divination were widely different on the two occasions, the method -pursued was the same. After commenting on the points of difference -between Rothman and Tycho Brahe, Kepler proceeds to enumerate his own -endeavours to discover the law of refraction. - -"I did not leave untried whether, by assuming a horizontal refraction -according to the density of the medium, the rest would correspond with -the sines of the distances from the vertical direction, but calculation -proved that it was not so: and indeed there was no occasion to have -tried it, for thus the refractions would increase according to the same -law in all mediums, which is contradicted by experiment. - -"The same kind of objection may be brought against the cause of -refraction alleged by Alhazen and Vitellion. They say that the light -seeks to be compensated for the loss sustained at the oblique impact; so -that in proportion as it is enfeebled by striking against the denser -medium, in the same degree does it restore its energy by approaching the -perpendicular, that it may strike the bottom of the denser medium with -greater force; for those impacts are most forcible which are direct. And -they add some subtle notions, I know not what, how the motion of -obliquely incident light is compounded of a motion perpendicular and a -motion parallel to the dense surface, and that this compound motion is -not destroyed, but only retarded by meeting the denser medium. - -[Illustration] - -"I tried another way of measuring the refraction, which should include -the density of the medium and the incidence: for, since a denser medium -is the cause of refraction, it seems to be the same thing as if we were -to prolong the depth of the medium in which the rays are refracted into -as much space as would be filled by the denser medium under the force of -the rarer one. - -"Let A be the place of the light, BC the surface of the denser medium, -DE its bottom. Let AB, AG, AF be rays falling obliquely, which would -arrive at D, I, H, if the medium were uniform. But because it is denser, -suppose the bottom to be depressed to KL, determined by this that there -is as much of the denser matter contained in the space DC as of the -rarer in LC: and thus, on the sinking of the whole bottom DE, the points -D, I, H, E will descend vertically to L, M, N, K. Join the points BL, -GM, FN, cutting DE in O, P, Q; the refracted rays will be ABO, AGP, -AFQ."--"This method is refuted by experiment; it gives the refractions -near the perpendicular AC too great in respect of those near the -horizon. Whoever has leisure may verify this, either by calculation or -compasses. It may be added that the reasoning itself is not very -sure-footed, and, whilst seeking to measure other things, scarcely takes -in and comprehends itself." This reflection must not be mistaken for the -dawn of suspicion that his examination of philosophical questions began -not altogether at the right end: it is merely an acknowledgment that he -had not yet contrived a theory with which he was quite satisfied before -it was disproved by experiment. - -After some experience of Kepler's miraculous good fortune in seizing -truths across the wildest and most absurd theories, it is not easy to -keep clear of the opposite feeling of surprise whenever any of his -extravagancies fail to discover to him some beautiful law of nature. But -we must follow him as he plunges deeper in this unsuccessful inquiry; -and the reader must remember, in order fully to appreciate this method -of philosophizing, that it is almost certain that Kepler laboured upon -every one of the gratuitous suppositions that he makes, until positive -experiment satisfied him of their incorrectness. - -"I go on to other methods. Since density is clearly connected with the -cause of the refractions, and refraction itself seems a kind of -compression of light, as it were, towards the perpendicular, it occurred -to me to examine whether there was the same proportion between the -mediums in respect of density and the parts of the bottom illuminated by -the light, when let into a vessel, first empty, and afterwards filled -with water. This mode branches out into many: for the proportion may be -imagined, either in the straight lines, as if one should say that the -line EQ, illuminated by refraction, is to EH illuminated directly, as -the density of the one medium is to that of the other--Or another may -suppose the proportion to be between FC and FH--Or it may be conceived -to exist among surfaces, or so that some power of EQ should be to some -power of EH in this proportion, or the circles or similar figures -described on them. In this manner the proportion of EQ to EP would be -double that of EH to EI--Or the proportion may be conceived existing -among the solidities of the pyramidal frustums FHEC, FQEC--Or, since the -proportion of the mediums involves a threefold consideration, since they -have density in length, breadth, and thickness, I proceeded also to -examine the cubic proportions among the lines EQ, EH. - -"I also considered other lines. From any of the points of refraction as -G, let a perpendicular GY be dropped upon the bottom. It may become a -question whether possibly the triangle IGY, that is, the base IY, is -divided by the refracted ray GP, in the proportion of the densities of -the mediums. - -"I have put all these methods here together, because the same remark -disproves them all. For, in whatever manner, whether as line, plane, or -pyramid, EI observes a given proportion to EP, or the abbreviated line -YI to YP, namely, the proportion of the mediums, it is sure that EI, the -tangent of the distance of the point A from the vertex, will become -infinite, and will, therefore make EP or YP, also infinite. Therefore, -IGP, the angle of refraction, will be entirely lost; and, as it -approaches the horizon, will gradually become less and less, which is -contrary to experiment. - -"I tried again whether the images are equally removed from their points -of refraction, and whether the ratio of the densities measures the least -distance. For instance, supposing E to be the image, C the surface of -the water, K the bottom, and CE to CK in the proportion of the densities -of the mediums. Now, let F, G, B, be three other points of refraction -and images at S, T, V, and let CE be equal to FS, GT, and BV. But -according to this rule an image E would still be somewhat raised in the -perpendicular AK, which is contrary to experiment, not to mention other -contradictions. Thirdly, whether the proportion of the mediums holds -between FH and FX, supposing H to be the place of the image? Not at all. -For so, CE would be in the same proportion to CK, so that the height of -the image would always be the same, which we have just refuted. -Fourthly, whether the raising of the image at E is to the raising at H, -as CE to FH? Not in the least; for so the images either would never -begin to be raised, or, having once begun, would at last be infinitely -raised, because FH at last becomes infinite. Fifthly, whether the images -rise in proportion to the sines of the inclinations? Not at all; for so -the proportion of ascent would be the same in all mediums. Sixthly, are -then the images raised at first, and in perpendicular radiation, -according to the proportion of the mediums, and do they subsequently -rise more and more according to the sines of the inclinations? For so -the proportion would be compound, and would become different in -different mediums. There is nothing in it: for the calculation disagreed -with experiment. And generally it is in vain to have regard to the image -or the place of the image, for that very reason, that it is imaginary. -For there is no connexion between the density of the medium or any real -quality or refraction of the light, and an accident of vision, by an -error of which the image happens. - -"Up to this point, therefore, I had followed a nearly blind mode of -inquiry, and had trusted to good fortune; but now I opened the other -eye, and hit upon a sure method, for I pondered the fact, that the image -of a thing seen under water approaches closely to the true ratio of the -refraction, and almost measures it; that it is low if the thing is -viewed directly from above; that by degrees it rises as the eye passes -towards the horizon of the water. Yet, on the other hand, the reason -alleged above, proves that the measure is not to be sought in the image, -because the image is not a thing actually existing, but arises from a -deception of vision which is purely accidental. By a comparison of these -conflicting arguments, it occurred to me at length, to seek the causes -themselves of the existence of the image under water, and in these -causes the measure of the refractions. This opinion was strengthened in -me by seeing that opticians had not rightly pointed out the cause of the -image which appears both in mirrors and in water. And this was the -origin of that labour which I undertook in the third chapter. Nor, -indeed, was that labour trifling, whilst hunting down false opinions of -all sorts among the principles, in a matter rendered so intricate by the -false traditions of optical writers; whilst striking out half a dozen -different paths, and beginning anew the whole business. How often did it -happen that a rash confidence made me look upon that which I sought with -such ardour, as at length discovered! - -"At length I cut this worse than Gordian knot of catoptrics by analogy -alone, by considering what happens in mirrors, and what must happen -analogically in water. In mirrors, the image appears at a distance from -the real place of the object, not being itself material, but produced -solely by reflection at the polished surface. Whence it followed in -water also, that the images rise and approach the surface, not according -to the law of the greater or less density in the water, as the view is -less or more oblique, but solely because of the refraction of the ray of -light passing from the object to the eye. On which assumption, it is -plain that every attempt I had hitherto made to measure refractions by -the image, and its elevation, must fall to the ground. And this became -more evident when I discovered the true reason why the image is in the -same perpendicular line with the object both in mirrors and in dense -mediums. When I had succeeded thus far by analogy in this most difficult -investigation, as to the place of the image, I began to follow out the -analogy further, led on by the strong desire of measuring refraction. -For I wished to get hold of some measure of some sort, no matter how -blindly, having no fear but that so soon as the measure should be -accurately known, the cause would plainly appear. I went to work as -follows. In convex mirrors the image is diminished, and just so in rarer -mediums; in denser mediums it is magnified, as in concave mirrors. In -convex mirrors the central parts of the image approach, and recede in -concave farther than towards the circumference; the same thing happens -in different mediums, so that in water the bottom appears depressed, and -the surrounding parts elevated. Hence it appears that a denser medium -corresponds with a concave reflecting surface, and a rarer one with a -convex one: it was clear, at the same time, that the plane surface of -the water affects a property of curvature. I was, therefore, to -excogitate causes consistent with its having this effect of curvature, -and to see if a reason could be given, why the parts of the water -surrounding the incident perpendicular should represent a greater -density than the parts just under the perpendicular. And so the thing -came round again to my former attempts, which being refuted by reason -and experiment, I was forced to abandon the search after a cause. I then -proceeded to measurements." - -Kepler then endeavoured to connect his measurements of different -quantities of refraction with the conic sections, and was tolerably well -pleased with some of his results. They were however not entirely -satisfactory, on which he breaks off with the following sentence: "Now, -reader, you and I have been detained sufficiently long whilst I have -been attempting to collect into one faggot the measure of different -refractions: I acknowledge that the cause cannot be connected with this -mode of measurement: for what is there in common between refractions -made at the plane surfaces of transparent mediums, and mixtilinear conic -sections? Wherefore, _quod Deus bene vortat_, we will now have had -enough of the causes of this measure; and although, even now, we are -perhaps erring something from the truth, yet it is better, by working -on, to show our industry, than our laziness by neglect." - -Notwithstanding the great length of this extract, we must add the -concluding paragraph of the Chapter, directed, as we are told in the -margin, against the "Tychonomasticks:"-- - -"I know how many blind men at this day dispute about colours, and how -they long for some one to give some assistance by argument to their rash -insults of Tycho, and attacks upon this whole matter of refractions; -who, if they had kept to themselves their puerile errors and naked -ignorance, might have escaped censure; for that may happen to many great -men. But since they venture forth publicly, and with thick books and -sounding titles, lay baits for the applause of the unwary, (for -now-a-days there is more danger from the abundance of bad books, than -heretofore from the lack of good ones,) therefore let them know that a -time is set for them publicly to amend their own errors. If they longer -delay doing this, it shall be open, either to me or any other, to do to -these unhappy meddlers in geometry as they have taken upon themselves to -do with respect to men of the highest reputation. And although this -labour will be despicable, from the vile nature of the follies against -which it will be directed, yet so much more necessary than that which -they have undertaken against others, as he is a greater public nuisance, -who endeavours to slander good and necessary inventions, than he who -fancies he has found what is impossible to discover. Meanwhile, let them -cease to plume themselves on the silence which is another word for their -own obscurity." - -Although Kepler failed, as we have seen, to detect the true law of -refraction, (which was discovered some years later by Willibrord Snell, -a Flemish mathematician,) there are many things well deserving notice in -his investigations. He remarked, that the quantity of refraction would -alter, if the height of the atmosphere should vary; and also, that it -would be different at different temperatures. Both these sources of -variation are now constantly taken into account, the barometer and -thermometer giving exact indications of these changes. There is also a -very curious passage in one of his letters to Bregger, written in 1605, -on the subject of the colours in the rainbow. It is in these -words:--"Since every one sees a different rainbow, it is possible that -some one may see a rainbow in the very place of my sight. In this case, -the medium is coloured at the place of my vision, to which the solar ray -comes to me through water, rain, or aqueous vapours. For the rainbow is -seen when the sun is shining between rain, that is to say, when the sun -also is visible. Why then do I not see the sun green, yellow, red, and -blue, if vision takes place according to the mode of illumination? I -will say something for you to attack or examine. The sun's rays are not -coloured, except with a definite quantity of refraction. Whether you are -in the optical chamber, or standing opposite glass globes, or walking in -the morning dew, everywhere it is obvious that a certain and definite -angle is observed, under which, when seen in dew, in glass, in water, -the sun's splendour appears coloured, and under no other angle. There is -no colouring by mere reflexion, without the refraction of a denser -medium." How closely does Kepler appear, in this passage, to approach -the discovery which forms not the least part of Newton's fame! - -We also find in this work a defence of the opinion that the planets are -luminous of themselves; on the ground that the inferior planets would, -on the contrary supposition, display phases like those of the moon when -passing between us and the sun. The use of the telescope was not then -known; and, when some years later the form of the disk of the planets -was more clearly defined with their assistance, Kepler had the -satisfaction of finding his assertions verified by the discoveries of -Galileo, that these changes do actually take place. In another of his -speculations, connected with the same subject, he was less fortunate. In -1607 a black spot appeared on the face of sun, such as may almost always -be seen with the assistance of the telescope, although they are seldom -large enough to be visible to the unassisted eye. Kepler saw it for a -short time, and mistook it for the planet Mercury, and with his usual -precipitancy hastened to publish an account of his observation of this -rare phenomenon. A few years later, Galileo discovered with his glasses, -a great number of similar spots; and Kepler immediately retracted the -opinion announced in his treatise, and acknowledged his belief that -previous accounts of the same occurrence which he had seen in old -authors, and which he had found great difficulty in reconciling with his -more accurate knowledge of the motions of Mercury, were to be referred -to a like mistake. On this occasion of the invention of the telescope, -Kepler's candour and real love of truth appeared in a most favourable -light. Disregarding entirely the disagreeable necessity, in consequence -of the discoveries of this new instrument, of retracting several -opinions which he had maintained with considerable warmth, he ranged -himself at once on the side of Galileo, in opposition to the bitter and -determined hostility evinced by most of those whose theories were -endangered by the new views thus offered of the heavens. Kepler's -quarrel with his pupil, Horky, on this account, has been mentioned in -the "Life of Galileo;" and this is only a selected instance from the -numerous occasions on which he espoused the same unpopular side of the -argument. He published a dissertation to accompany Galileo's -"Intelligencer of the Stars," in which he warmly expressed his -admiration of that illustrious inquirer into nature. His conduct in this -respect was the more remarkable, as some of his most intimate friends -had taken a very opposite view of Galileo's merit, and seem to have -laboured much to disturb their mutual regard; Maestlin especially, -Kepler's early instructor, seldom mentioned to him the name of Galileo, -without some contemptuous expression of dislike. These statements have -rather disturbed the chronological order of the account of Kepler's -works. We now return to the year 1609, in which he published his great -and extraordinary book, "On the Motions of Mars;" a work which holds the -intermediate place, and is in truth the connecting link, between the -discoveries of Copernicus and Newton. - - - - -CHAPTER IV. - - _Sketch of the Astronomical Theories before Kepler._ - - -KEPLER had begun to labour upon these commentaries from the moment when -he first made Tycho's acquaintance; and it is on this work that his -reputation should be made mainly to rest. It is marked in many places -with his characteristic precipitancy, and indeed one of the most -important discoveries announced in it (famous among astronomers by the -name of the Equable Description of Areas) was blundered upon by a lucky -compensation of errors, of the nature of which Kepler remained ignorant -to the very last. Yet there is more of the inductive method in this than -in any of his other publications; and the unwearied perseverance with -which he exhausted years in hunting down his often renewed theories, -till at length he seemed to arrive at the true one, almost by having -previously disproved every other, excites a feeling of astonishment -nearly approaching to awe. It is wonderful how he contrived to retain -his vivacity and creative fancy amongst the clouds of figures which he -conjured up round him; for the slightest hint or shade of probability -was sufficient to plunge him into the midst of the most laborious -computations. He was by no means an accurate calculator, according to -the following character which he has given of himself:--"Something of -these delays must be attributed to my own temper, for _non omnia -possumus omnes_, and I am totally unable to observe any order; what I do -suddenly, I do confusedly, and if I produce any thing well arranged, it -has been done ten times over. Sometimes an error of calculation -committed by hurry, delays me a great length of time. I could indeed -publish an infinity of things, for though my reading is confined, my -imagination is abundant, but I grow dissatisfied with such confusion: I -get disgusted and out of humour, and either throw them away, or put them -aside to be looked at again; or, in other words, to be written again, -for that is generally the end of it. I entreat you, my friends, not to -condemn me for ever to grind in the mill of mathematical calculations: -allow me some time for philosophical speculations, my only delight." - -He was very seldom able to afford the expense of maintaining an -assistant, and was forced to go through most of the drudgery of his -calculations by himself; and the most confirmed and merest arithmetician -could not have toiled more doggedly than Kepler did in the work of which -we are about to speak. - -In order that the language of his astronomy may be understood, it is -necessary to mention briefly some of the older theories. When it had -been discovered that the planets did not move regularly round the earth, -which was supposed to be fixed in the centre of the world, a mechanism -was contrived by which it was thought that the apparent irregularity -could be represented, and yet the principle of uniform motion, which was -adhered to with superstitious reverence, might be preserved. This, in -its simplest form, consisted in supposing the planet to move uniformly -in a small circle, called an _epicycle_, the centre of which moved with -an equal angular motion in the opposite direction round the earth.[187] -The circle D_d_, described by D, the centre of the epicycle, was called -the _deferent_. For instance, if the planet was supposed to be at A when -the centre of the epicycle was at D, its position, when the centre of -the epicycle had removed to _d_, would be at _p_, found by drawing _dp_ -parallel to DA. Thus, the angle _adp_, measuring the motion of the -planet in its epicycle, would be equal to DE_d_, the angle described by -the centre of the epicycle in the deferent. The angle _p_E_d_ between -E_p_, the direction in which a planet so moving would be seen from the -earth, supposed to be at E, and E_d_ the direction in which it would -have been seen had it been moving in the centre of the deferent, was -called the equation of the orbit, the word equation, in the language of -astronomy, signifying what must be added or taken from an irregularly -varying quantity to make it vary uniformly. - -[Illustration] - -As the accuracy of observations increased, minor irregularities were -discovered, which were attempted to be accounted for by making a second -deferent of the epicycle, and making the centre of a second epicycle -revolve in the circumference of the first, and so on, or else by -supposing the revolution in the epicycle not to be completed in exactly -the time in which its centre is carried round the deferent. Hipparchus -was the first to make a remark by which the geometrical representation -of these inequalities was considerably simplified. In fact, if EC be -taken equal to _pd_, C_d_ will be a parallelogram, and consequently -C_p_ equal to E_d_, so that the machinery of the first deferent and -epicycle amounts to supposing that the planet revolves uniformly in a -circle round the point C, not coincident with the place of the earth. -This was consequently called the excentric theory, in opposition to the -former or concentric one, and was received as a great improvement. As -the point _d_ is not represented by this construction, the equation to -the orbit was measured by the angle C_p_E, which is equal to _p_E_d_. It -is not necessary to give any account of the manner in which the old -astronomers determined the magnitudes and positions of these orbits, -either in the concentric or excentric theory, the present object being -little more than to explain the meaning of the terms it will be -necessary to use in describing Kepler's investigations. - -To explain the irregularities observed in the other planets, it became -necessary to introduce another hypothesis, in adopting which the -severity of the principle of uniform motion was somewhat relaxed. The -machinery consisted partly of an excentric deferent round E, the earth, -and on it an epicycle, in which the planet revolved uniformly; but the -centre of the epicycle, instead of revolving uniformly round C, the -centre of the deferent, as it had hitherto been made to do, was -supposed to move in its circumference with an uniform angular motion -round a third point, Q; the necessary effect of which supposition was, -that the linear motion of the centre of the epicycle ceased to be -uniform. There were thus three points to be considered within the -deferent; E, the place of the earth; C, the centre of the deferent, and -sometimes called the centre of the orbit; and Q, called the centre of -the equant, because, if any circle were described round Q, the planet -would appear to a spectator at Q, to be moving equably in it. It was -long uncertain what situation should be assigned to the centre of the -equant, so as best to represent the irregularities to a spectator on the -earth, until Ptolemy decided on placing it (in every case but that of -Mercury, the observations on which were very doubtful) so that C, the -centre of the orbit, lay just half way in the straight line, joining Q, -the centre of equable motion, and E, the place of the earth. This is the -famous principle, known by the name of the bisection of the -excentricity. - -[Illustration] - -The first equation required for the planet's motion was thus supposed to -be due to the displacement of E, the earth, from Q, the centre of -uniform motion, which was called the excentricity of the equant: it -might be represented by the angle _d_EM, drawing EM parallel to Q_d_; -for clearly M would have been the place of the centre of the epicycle at -the end of a time proportional to D_d_, had it moved with an equable -angular motion round E instead of Q. This angle _d_EM, or its equal -E_d_Q, was called the equation of the centre (_i.e._ of the centre of -the epicycle); and is clearly greater than if EQ, the excentricity of -the equant, had been no greater than EC, called the excentricity of the -orbit. The second equation was measured by the angle subtended at E by -_d_, the centre of the epicycle, and _p_ the planet's place in its -circumference: it was called indifferently the equation of the orbit, or -of the argument. In order to account for the apparent stations and -retrogradations of the planets, it became necessary to suppose that many -revolutions in the latter were completed during one of the former. The -variations of latitude of the planets were exhibited by supposing not -only that the planes of their deferents were oblique to the plane of the -ecliptic, and that the plane of the epicycle was also oblique to that of -the deferent, but that the inclination of the two latter was continually -changing, although Kepler doubts whether this latter complication was -admitted by Ptolemy. In the inferior planets, it was even thought -necessary to give to the plane of the epicycle two oscillatory motions -on axes at right angles to each other. - -The astronomers at this period were much struck with a remarkable -connexion between the revolutions of the superior planets in their -epicycles, and the apparent motion of the sun; for when in conjunction -with the sun, as seen from the earth, they were always found to be in -the apogee, or point of greatest distance from the earth, of their -epicycle; and when in opposition to the Sun, they were as regularly in -the perigee, or point of nearest approach of the epicycle. This -correspondence between two phenomena, which, according to the old -astronomy, were entirely unconnected, was very perplexing, and it seems -to have been one of the facts which led Copernicus to substitute the -theory of the earth's motion round the sun. - -As time wore on, the superstructure of excentrics and epicycles, which -had been strained into representing the appearances of the heavens at a -particular moment, grew out of shape, and the natural consequence of -such an artificial system was, that it became next to impossible to -foresee what ruin might be produced in a remote part of it by any -attempt to repair the derangements and refit the parts to the changes, -as they began to be remarked in any particular point. In the ninth -century of our era, Ptolemy's tables were already useless, and all those -that were contrived with unceasing toil to supply their place, rapidly -became as unserviceable as they. Still the triumph of genius was seen in -the veneration that continued to be paid to the assumptions of Ptolemy -and Hipparchus; and even when the great reformer, Copernicus, appeared, -he did not for a long time intend to do more than slightly modify their -principles. That which he found difficult in the Ptolemaic system, was -none of the inconveniences by which, since the establishment of the new -system, it has become common to demonstrate the inferiority of the old -one; it was the displacement of the centre of the equant from the centre -of the orbit that principally indisposed him against it, and led him to -endeavour to represent the appearances by some other combinations of -really uniform circular motions. - -There was an old system, called the Egyptian, according to which Saturn, -Jupiter, Mars, and the Sun circulated round the earth, the sun carrying -with it, as two moons or satellites, the other two planets, Venus and -Mercury. This system had never entirely lost credit: it had been -maintained in the fifth century by Martianus Capella[188], and indeed it -was almost sanctioned, though not formally taught, by Ptolemy himself, -when he made the mean motion of the sun the same as that of the centres -of the epicycles of both these planets. The remark which had also been -made by the old astronomers, of the connexion between the motion of the -sun and the revolutions of the superior planets in their epicycles, led -him straight to the expectation that he might, perhaps, produce the -uniformity he sought by extending the Egyptian system to these also, and -this appears to have been the shape in which his reform was originally -projected. It was already allowed that the centre of the orbits of all -the planets was not coincident with the earth, but removed from it by -the space EC. This first change merely made EC the same for all the -planets, and equal to the mean distance of the earth from the sun. This -system afterwards acquired great celebrity through its adoption by Tycho -Brahe, who believed it originated with himself. It might perhaps have -been at this period of his researches, that Copernicus was struck with -the passages in the Latin and Greek authors, to which he refers as -testifying the existence of an old belief in the motion of the earth -round the sun. He immediately recognised how much this alteration would -further his principles of uniformity, by referring all the planetary -motions to one centre, and did not hesitate to embrace it. The idea of -explaining the daily and principal apparent motions of the heavenly -bodies by the revolution of the earth on its axis, would be the -concluding change, and became almost a necessary consequence of his -previous improvements, as it was manifestly at variance with his -principles to give to all the planets and starry worlds a rapid daily -motion round the centre of the earth, now that the latter was removed -from its former supposed post in the centre of the universe, and was -itself carried with an annual motion round another fixed point. - -[Illustration] - -The reader would, however, form an inaccurate notion of the system of -Copernicus, if he supposed that it comprised no more than the theory -that each planet, including the earth among them, revolved in a simple -circular orbit round the sun. Copernicus was too well acquainted with -the motions of the heavenly bodies, not to be aware that such orbits -would not accurately represent them; the motion he attributed to the -earth round the sun, was at first merely intended to account for those -which were called the second inequalities of the planets, according to -which they appear one while to move forwards, then backwards, and at -intermediate periods, stationary, and which thenceforward were also -called the optical equations, as being merely an optical illusion. With -regard to what were called the first inequalities, or physical -equations, arising from a real inequality of motion, he still retained -the machinery of the deferent and epicycle; and all the alteration he -attempted in the orbits of the superior planets was an extension of the -concentric theory to supply the place of the equant, which he considered -the blot of the system. His theory for this purpose is shown in the -accompanying diagram, where S represents the sun, D_d_, the deferent or -mean orbit of the planet, on which revolves the centre of the great -epicycle, whose radius, DF, was taken at 3/4 of Ptolemy's excentricity of -the equant; and round the circumference of this revolved, in the -opposite direction, the centre of the little epicycle, whose radius, FP, -was made equal to the remaining 1/4 of the excentricity of the equant. - -The planet P revolved in the circumference of the little epicycle, in -the same direction with the centre of the great epicycle in the -circumference of the deferent, but with a double angular velocity. The -planet was supposed to be in the perigee of the little epicycle, when -its centre was in the apogee of the greater; and whilst, for instance, D -moved equably though the angle DS_d_, F moved through _hdf_ = DS_d_, -and P through _rfp_ = 2 DS_d_. - -It is easy to show that this construction gives nearly the same result -as Ptolemy's; for the deferent and great epicycle have been already -shown exactly equivalent to an excentric circle round S, and indeed -Copernicus latterly so represented it: the effect of his construction, -as given above, may therefore be reproduced in the following simpler -form, in which only the smaller epicycle is retained: - -[Illustration] - -In this construction, the place of the planet is found at the end of any -time proportional to F _f_ by drawing _fr_ parallel to SF, and taking -_rfp_ = 2F _of_. Hence it is plain, if we take OQ, equal to FP, (already -assumed equal to 1/4 of Ptolemy's excentricity of the equant,) since SO is -equal to 3/4 of the same, that SQ is the whole of Ptolemy's excentricity -of the equant; and therefore, that Q is the position of the centre of -his equant. It is also plain if we join Q_p_, since _rfp_ = 2F _of_, and -_o_Q = _fp_, that _p_Q is parallel to _fo_, and, therefore, _p_QP is -proportional to the time; so that the planet moves uniformly about the -same point Q, as in Ptolemy's theory; and if we bisect SQ in C, which is -the position of the centre of Ptolemy's deferent, the planet will, -according to Copernicus, move very nearly, though not exactly, in the -same circle, whose radius is CP, as that given by the simple excentric -theory. - -The explanation offered by Copernicus, of the motions of the inferior -planets, differed again in form from that of the others. He here -introduced what was called a _hypocycle_, which, in fact, was nothing -but a deferent not including the sun, round which the centre of the -orbit revolved. An epicycle in addition to the hypocycle was introduced -into Mercury's orbit. In this epicycle he was not supposed to revolve, -but to librate, or move up and down in its diameter. Copernicus had -recourse to this complication to satisfy an erroneous assertion of -Ptolemy with regard to some of Mercury's inequalities. He also retained -the oscillatory motions ascribed by Ptolemy to the planes of the -epicycles, in order to explain the unequal latitudes observed at the -same distance from the nodes, or intersections of the orbit of the -planet with the ecliptic. Into this intricacy, also, he was led by -placing too much confidence in Ptolemy's observations, which he was -unable to satisfy by an unvarying obliquity. Other very important -errors, such as his belief that the line of nodes always coincided with -the line of apsides, or places of greatest and least distance from the -central body, (whereas, at that time, in the case of Mars, for instance, -they were nearly 90 deg. asunder,) prevented him from accurately -representing many of the celestial phenomena. - -These brief details may serve to show that the adoption or rejection of -the theory of Copernicus was not altogether so simple a question as -sometimes it may have been considered. It is, however, not a little -remarkable, while it is strongly illustrative of the spirit of the -times, that these very intricacies, with which Kepler's theories have -enabled us to dispense, were the only parts of the system of Copernicus -that were at first received with approbation. His theory of Mercury, -especially, was considered a masterpiece of subtle invention. Owing to -his dread of the unfavourable judgment he anticipated on the main -principles of his system, his work remained unpublished during forty -years, and was at last given to the world only just in time to allow -Copernicus to receive the first copy of it a few hours before his -death. - - -FOOTNOTES: - -[187] By "the opposite direction" is meant, that while the motion in the -circumference of one circle appeared, as viewed from its centre, to be -from left to right, the other, viewed from its centre, appeared from -right to left. This must be understood whenever these or similar -expressions are repeated. - -[188] Venus Mercuriusque, licet ortus occasusque quotidianos ostendunt, -tamen eorum circuli terras omnino non ambiunt, sed circa solem laxiore -ambitu circulantur. Denique circulorum suorum centron in sole -constituunt.--De Nuptiis Philologiae et Mercurii. Vicentiae. 1499. - - - - -CHAPTER V. - - _Account of the Commentaries on the motions of Mars--Discovery of - the Law of the equable description of Areas, and of Elliptic - Orbits._ - - -WE may now proceed to examine Kepler's innovations, but it would be -doing injustice to one of the brightest points of his character, not to -preface them by his own animated exhortation to his readers. "If any one -be too dull to comprehend the science of astronomy, or too feeble-minded -to believe in Copernicus without prejudice to his piety, my advice to -such a one is, that he should quit the astronomical schools, and -condemning, if he has a mind, any or all of the theories of -philosophers, let him look to his own affairs, and leaving this worldly -travail, let him go home and plough his fields: and as often as he lifts -up to this goodly heaven those eyes with which alone he is able to see, -let him pour out his heart in praises and thanksgiving to God the -Creator; and let him not fear but he is offering a worship not less -acceptable than his to whom God has granted to see yet more clearly with -the eyes of his mind, and who both can and will praise his God for what -he has so discovered." - -Kepler did not by any means underrate the importance of his labours, as -is sufficiently shewn by the sort of colloquial motto which he prefixed -to his work. It consists in the first instance of an extract from the -writings of the celebrated and unfortunate Peter Ramus. This -distinguished philosopher was professor of mathematics in Paris, and in -the passage in question, after calling on his contemporaries to turn -their thoughts towards the establishment of a system of Astronomy -unassisted by any hypothesis, he promised as an additional inducement to -vacate his own chair in favour of any one who should succeed in this -object. Ramus perished in the massacre of St. Bartholomew, and Kepler -apostrophizes him as follows:--"It is well, Ramus, that you have -forfeited your pledge, by quitting your life and professorship together: -for if you still held it, I would certainly claim it as of right -belonging to me on account of this work, as I could convince you even -with your own logic." It was rather bold in Kepler to assert his claim -to a reward held out for a theory resting on no hypothesis, by right of -a work filled with hypotheses of the most startling description; but of -the vast importance of this book there can be no doubt; and throughout -the many wild and eccentric ideas to which we are introduced in the -course of it, it is fit always to bear in mind that they form part of a -work which is almost the basis of modern Astronomy. - -The introduction contains a curious criticism of the commonly-received -theory of gravity, accompanied with a declaration of Kepler's own -opinions on the same subject. Some of the most remarkable passages in it -have been already quoted in the life of Galileo; but, nevertheless, they -are too important to Kepler's reputation to be omitted here, containing -as they do a distinct and positive enunciation of the law of universal -gravitation. It does not appear, however, that Kepler estimated rightly -the importance of the theory here traced out by him, since on every -other occasion he advocated principles with which it is scarcely -reconcileable. The discussion is introduced in the following terms:-- - -"The motion of heavy bodies hinders many from believing that the earth -is moved by an animal motion, or rather a magnetic one. Let such -consider the following propositions. A mathematical point, whether the -centre of the universe or not, has no power, either effectively or -objectively, to move heavy bodies to approach it. Let physicians prove -if they can, that such power can be possessed by a point, which, neither -is a body, nor is conceived unless by relation alone. It is impossible -that the form[189] of a stone should, by moving its own body, seek a -mathematical point, or in other words, the centre of the universe, -without regard of the body in which that point exists. Let physicians -prove if they can, that natural things have any sympathy with that which -is nothing. Neither do heavy bodies tend to the centre of the universe -by reason that they are avoiding the extremities of the round universe; -for their distance from the centre is insensible, in proportion to their -distance from the extremities of the universe. And what reason could -there be for this hatred? How strong, how wise must those heavy bodies -be, to be able to escape so carefully from an enemy lying on all sides -of them: what activity in the extremities of the world to press their -enemy so closely! Neither are heavy bodies driven into the centre by the -whirling of the first moveable, as happens in revolving water. For if we -assume such a motion, either it would not be continued down to us, or -otherwise we should feel it, and be carried away with it, and the earth -also with us; nay, rather, we should be hurried away first, and the -earth would follow; all which conclusions are allowed by our opponents -to be absurd. It is therefore plain that the vulgar theory of gravity is -erroneous. - -"The true theory of gravity is founded on the following axioms:--Every -corporeal substance, so far forth as it is corporeal, has a natural -fitness for resting in every place where it may be situated by itself -beyond the sphere of influence of a body cognate with it. Gravity is a -mutual affection between cognate bodies towards union or conjunction -(similar in kind to the magnetic virtue), so that the earth attracts a -stone much rather than the stone seeks the earth. Heavy bodies (if we -begin by assuming the earth to be in the centre of the world) are not -carried to the centre of the world in its quality of centre of the -world, but as to the centre of a cognate round body, namely, the earth; -so that wheresoever the earth may be placed, or whithersoever it may be -carried by its animal faculty, heavy bodies will always be carried -towards it. If the earth were not round, heavy bodies would not tend -from every side in a straight line towards the centre of the earth, but -to different points from different sides. If two stones were placed in -any part of the world near each other, and beyond the sphere of -influence of a third cognate body, these stones, like two magnetic -needles, would come together in the intermediate point, each approaching -the other by a space proportional to the comparative mass of the other. -If the moon and earth were not retained in their orbits by their animal -force or some other equivalent, the earth would mount to the moon by a -fifty-fourth part of their distance, and the moon fall towards the earth -through the other fifty-three parts and they would there meet; assuming -however that the substance of both is of the same density. If the earth -should cease to attract its waters to itself, all the waters of the sea -would be raised and would flow to the body of the moon. The sphere of -the attractive virtue which is in the moon extends as far as the earth, -and entices up the waters; but as the moon flies rapidly across the -zenith, and the waters cannot follow so quickly, a flow of the ocean is -occasioned in the torrid zone towards the westward. If the attractive -virtue of the moon extends as far as the earth, it follows with greater -reason that the attractive virtue of the earth extends as far as the -moon, and much farther; and in short, nothing which consists of earthly -substance any how constituted, although thrown up to any height, can -ever escape the powerful operation of this attractive virtue. Nothing -which consists of corporeal matter is absolutely light, but that is -comparatively lighter which is rarer, either by its own nature, or by -accidental heat. And it is not to be thought that light bodies are -escaping to the surface of the universe while they are carried upwards, -or that they are not attracted by the earth. They are attracted, but in -a less degree, and so are driven outwards by the heavy bodies; which -being done, they stop, and are kept by the earth in their own place. But -although the attractive virtue of the earth extends upwards, as has been -said, so very far, yet if any stone should be at a distance great enough -to become sensible, compared with the earth's diameter, it is true that -on the motion of the earth such a stone would not follow altogether; its -own force of resistance would be combined with the attractive force of -the earth, and thus it would extricate itself in some degree from the -motion of the earth." - -Who, after perusing such passages in the works of an author, whose -writings were in the hands of every student of astronomy, can believe -that Newton waited for the fall of an apple to set him thinking for the -first time on the theory which has immortalized his name? An apple may -have fallen, and Newton may have seen it; but such speculations as those -which it is asserted to have been the cause of originating in him had -been long familiar to the thoughts of every one in Europe pretending to -the name of natural philosopher. - -As Kepler always professed to have derived his notion of a magnetic -attraction among the planetary bodies from the writings of Gilbert, it -may be worth while to insert here an extract from the "New Philosophy" -of that author, to show in what form he presented a similar theory of -the tides, which affords the most striking illustration of that -attraction. This work was not published till the middle of the -seventeenth century, but a knowledge of its contents may, in several -instances, be traced back to the period in which it was written:-- - -"There are two primary causes of the motion of the seas--the moon, and -the diurnal revolution. The moon does not act on the seas by its rays or -its light. How then? Certainly by the common effort of the bodies, and -(to explain it by something similar) by their magnetic attraction. It -should be known, in the first place, that the whole quantity of water is -not contained in the sea and rivers, but that the mass of earth (I mean -this globe) contains moisture and spirit much deeper even than the sea. -The moon draws this out by sympathy, so that they burst forth on the -arrival of the moon, in consequence of the attraction of that star; and -for the same reason, the quicksands which are in the sea open themselves -more, and perspire their moisture and spirits during the flow of the -tide, and the whirlpools in the sea disgorge copious waters; and as the -star retires, they devour the same again, and attract the spirits and -moisture of the terrestrial globe. Hence the moon attracts, not so much -the sea as the subterranean spirits and humours; and the interposed -earth has no more power of resistance than a table or any other dense -body has to resist the force of a magnet. The sea rises from the -greatest depths, in consequence of the ascending humours and spirits; -and when it is raised up, it necessarily flows on to the shores, and -from the shores it enters the rivers."[190] - -This passage sets in the strongest light one of the most notorious -errors of the older philosophy, to which Kepler himself was remarkably -addicted. If Gilbert had asserted, in direct terms, that the moon -attracted the water, it is certain that the notion would have been -stigmatized (as it was for a long time in Newton's hands) as arbitrary, -occult, and unphilosophical: the idea of these subterranean humours was -likely to be treated with much more indulgence. A simple statement, that -when the moon was over the water the latter had a tendency to rise -towards it, was thought to convey no instruction; but the assertion that -the moon draws out subterranean spirits by sympathy, carried with it a -more imposing appearance of theory. The farther removed these humours -were from common experience, the easier it became to discuss them in -vague and general language; and those who called themselves philosophers -could endure to hear attributes bestowed on these fictitious elements -which revolted their imaginations when applied to things of whose -reality at least some evidence existed. - -It is not necessary to dwell upon the system of Tycho Brahe, which was -identical, as we have said, with one rejected by Copernicus, and -consisted in making the sun revolve about the earth, carrying with it -all the other planets revolving about him. Tycho went so far as to deny -the rotation of the earth to explain the vicissitudes of day and night, -but even his favourite assistant Longomontanus differed from him in this -part of his theory. The great merit of Tycho Brahe, and the service he -rendered to astronomy, was entirely independent of any theory; -consisting in the vast accumulation of observations made by him during a -residence of fifteen years at Uraniburg, with the assistance of -instruments, and with a degree of care, very far superior to anything -known before his time in practical astronomy. Kepler is careful -repeatedly to remind us, that without Tycho's observations he could have -done nothing. The degree of reliance that might be placed on the results -obtained by observers who acknowledged their inferiority to Tycho Brahe, -maybe gathered from an incidental remark of Kepler to Longomontanus. He -had been examining Tycho's registers, and had occasionally found a -difference amounting sometimes to 4' in the right ascensions of the same -planet, deduced from different stars on the same night. Longomontanus -could not deny the fact, but declared that it was impossible to be -always correct within such limits. The reader should never lose sight of -this uncertainty in the observations, when endeavouring to estimate the -difficulty of finding a theory that would properly represent them. - -When Kepler first joined Tycho Brahe at Prague, he found him and -Longomontanus very busily engaged in correcting the theory of Mars, and -accordingly it was this planet to which he also first directed his -attention. They had formed a catalogue of the mean oppositions of Mars -during twenty years, and had discovered a position of the equant, which -(as they said) represented them with tolerable exactness. On the other -hand, they were much embarrassed by the unexpected difficulties they met -in applying a system which seemed on the one hand so accurate, to the -determination of the latitudes, with which it could in no way be made to -agree. Kepler had already suspected the cause of this imperfection, and -was confirmed in the view he took of their theory, when, on a more -careful examination, he found that they overrated the accuracy even of -their longitudes. The errors in these, instead of amounting as they -said, nearly to 2', rose sometimes above 21'. In fact they had reasoned -ill on their own principles, and even if the foundations of their theory -had been correctly laid, could not have arrived at true results. But -Kepler had satisfied himself of the contrary, and the following diagram -shews the nature of the first alteration he introduced, not perhaps so -celebrated as some of his later discoveries, but at least of equal -consequence to astronomy, which could never have been extricated from -the confusion into which it had fallen, till this important change had -been effected. - -[Illustration] - -The practice of Tycho Brahe, indeed of all astronomers till the time of -Kepler, had been to fix the position of the planet's orbit and equant -from observations on its mean oppositions, that is to say, on the times -when it was precisely six signs or half a circle distant from the mean -place of the sun. In the annexed figure, let S represent the sun, C the -centre of the earth's orbit, T_t_. Tycho Brahe's practice amounted to -this, that if Q were supposed the place of the centre of the planet's -equant, the centre of P_p_ its orbit was taken in QC, and not in QS, as -Kepler suggested that it ought to be taken. The consequence of this -erroneous practice was, that the observations were deprived of the -character for which oppositions were selected, of being entirely free -from the second inequalities. It followed therefore that as part of the -second inequalities were made conducive towards fixing the relative -position of the orbit and equant, to which they did not naturally -belong, there was an additional perplexity in accounting for the -remainder of them by the size and motion of the epicycle. As the line of -nodes of every planet was also made to pass through C instead of S, -there could not fail to be corresponding errors in the latitudes. It -would only be in the rare case of an opposition of the planet in the -line CS, that the time of its taking place would be the same, whether O, -the centre of the orbit, was placed in CQ or SQ. Every other opposition -would involve an error, so much the greater as it was observed at a -greater distance from the line CS. - -It was long however before Tycho Brahe could be made to acquiesce in the -propriety of the proposed alteration; and, in order to remove his doubts -as to the possibility that a method could be erroneous which, as he -still thought, had given him such accurate longitudes, Kepler undertook -the ungrateful labour of the first part of his "Commentaries." He there -shewed, in the three systems of Copernicus, Tycho Brahe, and Ptolemy, -and in both the concentric and excentric theories, that though a false -position were given to the orbit, the longitudes of a planet might be so -represented, by a proper position of the centre of the equant, as never -to err in oppositions above 5' from those given by observation; though -the second inequalities and the latitudes would thereby be very greatly -deranged. - -The change Kepler introduced, of observing apparent instead of mean -oppositions, made it necessary to be very accurate in his reductions of -the planet's place to the ecliptic; and in order to be able to do this, -a previous knowledge of the parallax of Mars became indispensable. His -next labour was therefore directed to this point; and finding that the -assistants to whom Tycho Brahe had previously committed this labour had -performed it in a negligent and imperfect manner, he began afresh with -Tycho's original observations. Having satisfied himself as to the -probable limits of his errors in the parallax on which he finally fixed, -he proceeded to determine the inclination of the orbit and the position -of the line of nodes. In all these operations his talent for -astronomical inquiries appeared pre-eminent in a variety of new methods -by which he combined and availed himself of the observations; but it -must be sufficient merely to mention this fact, without entering into -any detail. One important result may be mentioned, at which he arrived -in the course of them, the constancy of the inclination of the planet's -orbit, which naturally strengthened him in his new theory. - -Having gone through these preliminary inquiries, he came at last to fix -the proportions of the orbit; and, in doing so, he determined, in the -first instance, not to assume, as Ptolemy appeared to have done -arbitrarily, the bisection of the excentricity, but to investigate its -proportion along with the other elements of the orbit, which resolution -involved him in much more laborious calculations. After he had gone over -all the steps of his theory no less than seventy times--an appalling -labour, especially if we remember that logarithms were not then -invented--his final result was, that in 1587, on the 6th of March, at -7^{h} 23', the longitude of the aphelion of Mars was 4^{s} 28 deg. 48' 55''; -that the planet's mean longitude was 6^{s} 0 deg. 51' 35''; that if the -semidiameter of the orbit was taken at 100000, the excentricity was -11332; and the excentricity of the equant 18564. He fixed the radius of -the greater epicycle at 14988, and that of the smaller at 3628. - -When he came to compare the longitudes as given by this, which he -afterwards called the _vicarious_ theory, with the observations at -opposition, the result seemed to promise him the most brilliant success. -His greatest error did not exceed 2'; but, notwithstanding these -flattering anticipations, he soon found by a comparison of longitudes -out of opposition and of latitudes, that it was yet far from being so -complete as he had imagined, and to his infinite vexation he soon found -that the labour of four years, which he had expended on this theory, -must be considered almost entirely fruitless. Even his favourite -principle of dividing the excentricity in a different ratio from -Ptolemy, was found to lead him into greater error than if he had -retained the old bisection. By restoring that, he made his latitudes -more accurate, but produced a corresponding change for the worse in his -longitudes; and although the errors of 8', to which they now amounted, -would probably have been disregarded by former theorists, Kepler could -not remain satisfied till they were accounted for. Accordingly he found -himself forced to the conclusion that one of the two principles on which -this theory rested must be erroneous; either the orbit of the planet is -not a perfect circle, or there is no fixed point within it round which -it moves with an uniform angular motion. He had once before admitted the -possibility of the former of these facts, conceiving it possible that -the motion of the planets is not at all curvilinear, but that they move -in polygons round the sun, a notion to which he probably inclined in -consequence of his favourite harmonics and geometrical figures. - -In consequence of the failure of a theory conducted with such care in -all its practical details, Kepler determined that his next trial should -be of an entirely different complexion. Instead of first satisfying the -first inequalities of the planet, and then endeavouring to account for -the second inequalities, he resolved to reverse the process, or, in -other words, to ascertain as accurately as possible what part of the -planet's apparent motion should be referred solely to the optical -illusion produced by the motion of the earth, before proceeding to any -inquiry of the real inequality of the planet's proper motion. It had -been hitherto taken for granted, that the earth moved equably round the -centre of its orbit; but Kepler, on resuming the consideration of it, -recurred to an opinion he had entertained very early in his astronomical -career (rather from his conviction of the existence of general laws, -than that he had then felt the want of such a supposition), that it -required an equant distinct from its orbit no less than the other -planets. He now saw, that if this were admitted, the changes it would -everywhere introduce in the optical part of the planet's irregularities -might perhaps relieve him from the perplexity in which the vicarious -theory had involved him. Accordingly he applied himself with renewed -assiduity to the examination of this important question, and the result -of his calculations (founded principally on observations of Mars' -parallax) soon satisfied him not only that the earth's orbit does -require such an equant, but that its centre is placed according to the -general law of the bisection of the excentricity which he had previously -found indispensable in the other planets. This was an innovation of the -first magnitude, and accordingly Kepler did not venture to proceed -farther in his theory, till by evidence of the most varied and -satisfactory nature, he had established it beyond the possibility of -cavil. - -It may be here remarked, that this principle of the bisection of the -eccentricity, so familiar to the Ptolemaic astronomers, is identical -with the theory afterwards known by the name of the simple elliptic -hypothesis, advocated by, Seth Ward and others. That hypothesis -consisted in supposing the sun to be placed in one focus of the elliptic -orbit of the planet, whose angular motion was uniform round the other -focus. In Ptolemaic phraseology, that other focus was the centre of the -equant, and it is well known that the centre of the ellipse lies in the -middle point between the two foci. - -It was at this period also, that Kepler first ventured upon the new -method of representing inequalities which terminated in one of his most -celebrated discoveries. We have already seen, in the account of the -"Mysterium Cosmographicum," that he was speculating, even at that time, -on the effects of a whirling force exerted by the sun on the planets -with diminished energy at increased distances, and on the proportion -observed between the distances of the planets from the sun, and their -periods of revolution. He seems even then to have believed in the -possibility of discovering a relation between the times and distances in -different planets. Another analogous consequence of his theory of the -radiation of the whirling force would be, that if the same planet should -recede to a greater distance from the central body, it would be acted on -by a diminished energy of revolution, and consequently, a relation might -be found between the velocity at any point of its orbit, and its -distance at that point from the sun. Hence he expected to derive a more -direct and natural method of calculating the inequalities, than from the -imaginary equant. But these ingenious ideas had been checked in the -outset by the erroneous belief which Kepler, in common with other -astronomers, then entertained of the coincidence of the earth's equant -with its orbit; in other words, by the belief that the earth's linear -motion was uniform, though it was known not to remain constantly at the -same distance from the sun. As soon as this prejudice was removed, his -former ideas recurred to him with increased force, and he set himself -diligently to consider what relation could be found between the velocity -and distance of a planet from the sun. The method he adopted in the -beginning of this inquiry was to assume as approximately correct -Ptolemy's doctrine of the bisection of the excentricity, and to -investigate some simple relation nearly representing the same effect. - -In the annexed figure, S is the place of the sun, C the centre of the -planet's orbit AB_ab_, Q the centre of the equant represented by the -equal circle DE_de_, AB, _ab_, two equal small arcs described by the -planet at the apsides of its orbit: then, according to Ptolemy's -principles, the arc DE of the equant would be proportional to the time -of passing along AB, on the same scale on which _de_ would represent the -time of passing through the equal arc _ab_. - -[Illustration] - -QD:QA :: DE:AB, nearly; and because QS is bisected in C, QA, CA or QD, -and SA, are in arithmetical proportion: and, therefore, since an -arithmetical mean, when the difference is small, does not differ much -from a geometrical mean, QD:QA :: SA:QD, nearly. Therefore, DE:AB :: S -A:QD, nearly, and in the same manner _de_:_ab_ :: S_a_:Q_d_ nearly; and -therefore DE:_de_ :: SA:S_a_ nearly. Therefore at the apsides, the -times of passing over equal spaces, on Ptolemy's theory, are nearly as -the distances from the sun, and Kepler, with his usual hastiness, -immediately concluded that this was the accurate and general law, and -that the errors of the old theory arose solely from having departed from -it. - -It followed immediately from this assumption, that after leaving the -point A, the time in which the planet would arrive at any point P of -its orbit would be proportional to, and might be represented by, the -sums of all the lines that could be drawn from S to the arc AP, on the -same scale that the whole period of revolution would be denoted by the -sum of all the lines drawn to every point of the orbit. Kepler's first -attempt to verify this supposition approximately, was made by dividing -the whole circumference of the orbit into 360 equal parts, and -calculating the distances at every one of the points of division. Then -supposing the planet to move uniformly, and to remain at the same -distance from the sun during the time of passing each one of these -divisions, (a supposition which manifestly would not differ much from -the former one, and would coincide with it more nearly, the greater was -the number of divisions taken) he proceeded to add together these -calculated distances, and hoped to find that the time of arriving at any -one of the divisions bore the same ratio to the whole period, as the sum -of the corresponding set of distances did to the sum of the whole 360. - -This theory was erroneous; but by almost miraculous good fortune, he was -led by it in the following manner to the true measure. The discovery was -a consequence of the tediousness of his first method, which required, in -order to know the time of arriving at any point, that the circle should -be subdivided, until one of the points of division fell exactly upon the -given place. Kepler therefore endeavoured to discover some shorter -method of representing these sums of the distances. The idea then -occurred to him of employing for that purpose the area inclosed between -the two distances, SA, SP, and the arc AP, in imitation of the manner in -which he remembered that Archimedes had found the area of the circle, by -dividing it into an infinite number of small triangles by lines drawn -from the centre. He hoped therefore to find, that the time of passing -from A to P bore nearly the same ratio to the whole period of revolution -that the area ASP bore to the whole circle. - -This last proportion is in fact accurately observed in the revolution of -one body round another, in consequence of an attractive force in the -central body. Newton afterwards proved this, grounding his demonstration -upon laws of motion altogether irreconcileable with Kepler's opinions; -and it is impossible not to admire Kepler's singular good fortune in -arriving at this correct result in spite, or rather through the means, -of his erroneous principles. It is true that the labour which he -bestowed unsparingly upon every one of his successive guesses, joined -with his admirable candour, generally preserved him from long retaining -a theory altogether at variance with observations; and if any relation -subsisted between the times and distances which could any way be -expressed by any of the geometrical quantities under consideration, he -could scarcely have failed--it might be twenty years earlier or twenty -years later,--to light upon it at last, having once put his -indefatigable fancy upon this scent. But in order to prevent an -over-estimate of his merit in detecting this beautiful law of nature, -let us for a moment reflect what might have been his fate had he -endeavoured in the same manner, and with the same perseverance, to -discover a relation, where, in reality, none existed. Let us take for -example the inclinations or the excentricities of the planetary orbits, -among which no relation has yet been discovered; and if any exists, it -is probably of too complicated a nature to be hit at a venture. If -Kepler had exerted his ingenuity in this direction, he might have wasted -his life in fruitless labour, and whatever reputation he might have left -behind him as an industrious calculator, it would have been very far -inferior to that which has procured for him the proud title of the -"Legislator of the Heavens." - -However this may be, the immediate consequence of thus lighting upon the -real law observed by the earth in its passage round the sun was, that he -found himself in possession of a much more accurate method of -representing its inequalities than had been reached by any of his -predecessors; and with renewed hopes he again attacked the planet Mars, -whose path he was now able to consider undistorted by the illusions -arising out of the motion of the earth. Had the path of Mars been -accurately circular, or even as nearly approaching a circle as that of -the earth, the method he chose of determining its position and size by -means of three distances carefully calculated from his observed -parallaxes, would have given a satisfactory result; but finding, as he -soon did, that almost every set of three distances led him to a -different result, he began to suspect another error in the long-received -opinion, that the orbits of the planets must consist of a combination -of circles; he therefore, determined, in the first instance, to fix the -distances of the planet at the apsides without any reference to the form -of the intermediate orbit. Half the difference between these would, of -course, be the excentricity of the orbit; and as this quantity came out -very nearly the same as had been determined on the vicarious theory, it -seemed clear that the error of that theory, whatever it might be, did -not lie in these elements. - -Kepler also found that in the case of this planet likewise, the times of -describing equal arcs at the apsides were proportional to its distances -from the sun, and he naturally expected that the method of areas would -measure the planet's motion with as much accuracy as he had found in the -case of the earth. This hope was disappointed: when he calculated the -motion of the planet by this method, he obtained places too much -advanced when near the apsides, and too little advanced at the mean -distances. He did not, on that account, immediately reject the opinion -of circular orbits, but was rather inclined to suspect the principle of -measurement, at which he felt that he had arrived in rather a precarious -manner. He was fully sensible that his areas did not accurately -represent the sums of any distances except those measured from the -centre of the circle; and for some time he abandoned the hope of being -able to use this substitution, which he always considered merely as an -approximate representation of the true measure, the sum of the -distances. But on examination he found that the errors of this -substitution were nearly insensible, and those it did in fact produce, -were in the contrary direction of the errors he was at this time -combating. As soon as he had satisfied himself of this, he ventured once -more on the supposition, which by this time had, in his eyes, almost -acquired the force of demonstration, that the orbits of the planets are -not circular, but of an oval form, retiring within the circle at the -mean distances, and coinciding with it at the apsides. - -This notion was not altogether new; it had been suggested in the case of -Mercury, by Purbach, in his "Theories of the Planets." In the edition of -this work published by Reinhold, the pupil of Copernicus, we read the -following passage. "Sixthly, it appears from what has been said, that -the centre of Mercury's epicycle, by reason of the motions -above-mentioned, does not, as is the case with the other planets, -describe the circumference of a circular deferent, but rather the -periphery of a figure resembling a plane oval." To this is added the -following note by Reinhold. "The centre of the Moon's epicycle describes -a path of a lenticular shape; Mercury's on the contrary is egg-shaped, -the big end lying towards his apogee, and the little end towards his -perigee."[191] The excentricity of Mercury's orbit is, in fact, much -greater than that of any of the other planets, and the merit of making -this first step cannot reasonably be withheld from Purbach and his -commentator, although they did not pursue the inquiry so far as Kepler -found himself in a condition to do. - -Before proceeding to the consideration of the particular oval which -Kepler fixed upon in the first instance, it will be necessary, in order -to render intelligible the source of many of his doubts and -difficulties, to make known something more of his theory of the moving -force by which he supposed the planets to be carried round in their -orbits. In conformity with the plan hitherto pursued, this shall be done -as much as possible in his own words. - -"It is one of the commonest axioms in natural philosophy, that if two -things always happen together and in the same manner, and admit the same -measure, either the one is the cause of the other, or both are the -effect of a common cause. In the present case, the increase or languor -of motion invariably corresponds with an approach to or departure from -the centre of the universe. Therefore, either the languor is the cause -of the departure of the star, or the departure of the languor, or both -have a common cause. But no one can be of opinion that there is a -concurrence of any third thing to be a common cause of these two -effects, and in the following chapters it will be made clear that there -is no occasion to imagine any such third thing, since the two are of -themselves sufficient. Now, it is not agreeable to the nature of things -that activity or languor in linear motion should be the cause of -distance from the centre. For, distance from the centre is conceived -anteriorly to linear motion. In fact linear motion cannot exist without -distance from the centre, since it requires space for its -accomplishment, but distance from the centre can be conceived without -motion. Therefore distance is the cause of the activity of motion, and a -greater or less distance of a greater or less delay. And since distance -is of the kind of relative quantities, whose essence consists in -boundaries, (for there is no efficacy in relation _per se_ without -regard to bounds,) it follows that the cause of the varying activity of -motion rests in one of the boundaries. But the body of the planet -neither becomes heavier by receding, nor lighter by approaching. -Besides, it would perhaps be absurd on the very mention of it, that an -animal force residing in the moveable body of the planet for the purpose -of moving it, should exert and relax itself so often without weariness -or decay. It remains, therefore, that the cause of this activity and -languor resides at the other boundary, that is, in the very centre of -the world, from which the distances are computed.--Let us continue our -investigation of this moving virtue which resides in the sun, and we -shall presently recognize its very close analogy to light. And although -this moving virtue cannot be identical with the light of the sun, let -others look to it whether the light is employed as a sort of instrument, -or vehicle, to convey the moving virtue. There are these seeming -contradictions:--first, light is obstructed by opaque bodies, for which -reason if the moving virtue travelled on the light, darkness would be -followed by a stoppage of the moveable bodies. Again, light flows out in -right lines spherically, the moving virtue in right lines also, but -cylindrically; that is, it turns in one direction only, from west to -east; not in the opposite direction, not towards the poles, &c. But -perhaps we shall be able presently to reply to these objections. In -conclusion, since there is as much virtue in a large and remote circle -as in a narrow and close one, nothing of the virtue perishes in the -passage from its source, nothing is scattered between the source and the -moveable. Therefore the efflux, like that of light, is not material, and -is unlike that of odours, which are accompanied by a loss of substance, -unlike heat from a raging furnace, unlike every other emanation by which -mediums are filled. It remains, therefore, that as light which -illuminates all earthly things, is the immaterial species of that fire -which is in the body of the sun, so this virtue, embracing and moving -all the planetary bodies, is the immaterial species of that virtue which -resides in the sun itself, of incalculable energy, and so the primary -act of all mundane motion.--I should like to know who ever said that -there was anything material in light!--Guided by our notion of the -efflux of this species (or archetype), let us contemplate the more -intimate nature of the source itself. For it seems as if something -divine were latent in the body of the sun, and comparable to our own -soul, whence that species emanates which drives round the planets; just -as from the mind of a slinger the species of motion sticks to the -stones, and carries them forward, even after he who cast them has drawn -back his hand. But to those who wish to proceed soberly, reflections -differing a little from these will be offered." - -Our readers will, perhaps, be satisfied with the assurance, that these -sober considerations will not enable them to form a much more accurate -notion of Kepler's meaning than the passages already cited. We shall -therefore proceed to the various opinions he entertained on the motion -of the planets. - -He considered it as established by his theory, that the centre E of the -planet's epicycle (see fig. p. 33.) moved round the circumference of the -deferent D_d_, according to the law of the planet's distances; the point -remaining to be settled was the motion of the planet in the epicycle. If -it were made to move according to the same law, so that when the centre -of the epicycle reached E, the planet should be at F, taking the angle -BEF equal to BSA, it has been shewn (p. 19) that the path of F would -still be a circle, excentric from D_d_ by DA the radius of the epicycle. - -But Kepler fancied that he saw many sound reasons why this could not be -the true law of motion in the epicycle, on which reasons he relied much -more firmly than on the indisputable fact, which he mentions as a -collateral proof, that it was contradicted by the observations. Some of -these reasons are subjoined: "In the beginning of the work it has been -declared to be most absurd, that a planet (even though we suppose it -endowed with mind) should form any notion of a centre, and a distance -from it, if there be no body in that centre to serve for a -distinguishing mark. And although you should say, that the planet has -respect to the sun, and knows beforehand, and remembers the order in -which the distances from the sun are comprised, so as to make a perfect -excentric; in the first place, this is rather far-fetched, and requires, -in any mind, means for connecting the effect of an accurately circular -path with the sign of an increasing and diminishing diameter of the sun. -But there are no such means, except the position of the centre of the -excentric at a given distance from the sun; and I have already said, -that this is beyond the power of a mere mind. I do not deny that a -centre may be imagined, and a circle round it; but this I do say, if the -circle exists only in imagination, with no external sign or division, -that it is not possible that the path of a moveable body should be -really ordered round it in an exact circle. Besides, if the planet -chooses from memory its just distances from the sun, so as exactly to -form a circle, it must also take from the same source, as if out of the -Prussian or Alphonsine tables, equal excentric arcs, to be described in -unequal times, and to be described by a force extraneous from the sun; -and thus would have, from its memory, a foreknowledge of what effects a -virtue, senseless and extraneous from the sun, was about to produce: all -these consequences are absurd. - -"It is therefore more agreeable to reason that the planet takes no -thought, either of the excentric or epicycle; but that the work which it -accomplishes, or joins in effecting, is a libratory path in the diameter -B_b_ of the epicycle, in the direction towards the sun. The law is now -to be discovered, according to which the planet arrives at the proper -distances in any time. And indeed in this inquiry, it is easier to say -what the law is not than what it is."--Here, according to his custom, -Kepler enumerates several laws of motion by which the planet might -choose to regulate its energies, each of which is successively -condemned. Only one of them is here mentioned, as a specimen of the -rest. "What then if we were to say this? Although the motions of the -planet are not epicyclical, perhaps the libration is so arranged that -the distances from the sun are equal to what they would have been in a -real epicyclical motion.--This leads to more incredible consequences -than the former suppositions, and yet in the dearth of better opinions, -let us for the present content ourselves with this. The greater number -of absurd conclusions it will be found to involve, the more ready will a -physician be, when we come to the fifty-second chapter, to admit what -the observations testify, that the path of the planet is not circular." - -The first oval path on which Kepler was induced to fix, by these and -many other similar considerations, was in the first instance very -different from the true elliptical form. Most authors would have thought -it unnecessary to detain their readers with a theory which they had once -entertained and rejected; but Kepler's work was written on a different -plan. He thus introduces an explanation of his first oval. "As soon as I -was thus taught by Brahe's very accurate observations that the orbit of -a planet is not circular, but more compressed at the sides, on the -instant I thought that I understood the natural cause of this -deflection. But the old proverb was verified in my case;--the more haste -the less speed.--For having violently laboured in the 39th chapter, in -consequence of my inability to find a sufficiently probable cause why -the orbit of the planet should be a perfect circle, (some absurdities -always remaining with respect to that virtue which resides in the body -of the planet,) and having now discovered from the observations, that -the orbit is not a perfect circle, I felt furiously inclined to believe -that if the theory which had been recognized as absurd, when employed in -the 39th chapter for the purpose of fabricating a circle, were modulated -into a more probable form, it would produce an accurate orbit agreeing -with the observations. If I had entered on this course a little more -warily, I might have detected the truth immediately. But, being blinded -by my eagerness, and not sufficiently regardful of every part of the -39th chapter, and clinging to my first opinion, which offered itself to -me with a wonderful show of probability, on account of the equable -motion in the epicycle, I got entangled in new perplexities, with which -we shall now have to struggle in this 45th chapter and the following -ones as far as the 50th chapter." - -In this theory, Kepler supposed that whilst the centre of the epicycle -was moving round a circular deferent according to the law of the -planets' distances (or areas) the planet itself moved equably in the -epicycle, with the mean angular velocity of its centre in the deferent. -In consequence of this supposition, since at D, when the planet is at A -the aphelion, the motion in the deferent is less than the mean motion, -the planet will have advanced through an angle BEP greater than BEF or -BSA, through which the centre of the epicycle has moved; and -consequently, the path will lie everywhere within the circle A_a_, -except at the apsides. Here was a new train of laborious calculations to -undergo for the purpose of drawing the curve AP_a_ according to this -law, and of measuring the area of any part of it. After a variety of -fruitless attempts, for this curve is one of singular complexity, he was -reduced, as a last resource, to suppose it insensibly different from an -ellipse on the same principal axes, as an approximate means of -estimating its area. Not content even with the results so obtained, and -not being able to see very clearly what might be the effect of his -alteration in substituting the ellipse for the oval, and in other -simplifications introduced by him, he had courage enough to obtain the -sums of the 360 distances by direct calculation, as he had done in the -old circular theory. - -[Illustration] - -In the preface to his book he had spoken of his labours under the -allegory of a war carried on by him against the planet; and when -exulting in the early prospects of success this calculation seemed to -offer, he did not omit once more to warn his readers, in his peculiar -strain, that this exultation was premature. - -"Allow me, gentle reader, to enjoy so splendid a triumph for one little -day (I mean through the five next chapters), meantime be all rumours -suppressed of new rebellion, that our preparations may not perish, -yielding us no delight. Hereafter if anything shall come to pass, we -will go through it in its own time and season; now let us be merry, as -then we will be bold and vigorous." At the time foretold, that is to -say, at the end of the five merry chapters, the bad news could no longer -be kept a secret. It is announced in the following bulletin:--"While -thus triumphing over Mars, and preparing for him, as for one altogether -vanquished, tabular prisons, and equated eccentric fetters, it is buzzed -here and there that the victory is vain, and that the war is raging anew -as violently as before. For the enemy, left at home a despised captive, -has burst all the chains of the equations, and broken forth of the -prisons of the tables. For no method of geometrically administering the -theory of the 45th chapter was able to come near the accuracy of -approximation of the vicarious theory of the 16th chapter, which gave me -true equations derived from false principles. Skirmishers, disposed all -round the circuit of the excentric, (I mean the true distances,) routed -my forces of physical causes levied out of the 45th chapter, and shaking -off the yoke, regained their liberty. And now there was little to -prevent the fugitive enemy from effecting a junction with his rebellious -supporters, and reducing me to despair, had I not suddenly sent into the -field a reserve of new physical reasonings on the rout and dispersion of -the veterans, and diligently followed, without allowing him the -slightest respite, in the direction in which he had broken out." - -In plainer terms, Kepler found, after this labour was completed, that -the errors in longitude he was still subject to were precisely of an -opposite nature to those he had found with the circle; instead of being -too quick at the apsides, the planet was now too slow there, and too -much accelerated in the mean distances; and the distances obtained from -direct observation were everywhere greater, except at the apsides, than -those furnished by this oval theory. It was in the course of these -tedious investigations that he established, still more satisfactorily -than he had before done, that the inclinations of the planets' orbits -are invariable, and that the lines of their nodes pass through the -centre of the Sun, and not, as before his time had been supposed, -through the centre of the ecliptic. - -When Kepler found with certainty that this oval from which he expected -so much would not satisfy the observations, his vexation was extreme, -not merely from the mortification of finding a theory confuted on which -he had spent such excessive labour, for he was accustomed to -disappointments of that kind, but principally from many anxious and -fruitless speculations as to the real physical causes why the planet did -not move in the supposed epicycle, that being the point of view, as has -been already shewn, from which he always preferred to begin his -inquiries. One part of the reasoning by which he reconciled himself to -the failure exhibits much too curious a view of the state of his mind to -be passed over in silence. The argument is founded on the difficulty -which he met with, as above mentioned, in calculating the proportions of -the oval path he had imagined. "In order that you may see the cause of -the impracticability of this method which we have just gone through, -consider on what foundations it rests. The planet is supposed to move -equably in the epicycle, and to be carried by the Sun unequably in the -proportion of the distances. But by this method it is impossible to be -known how much of the oval path corresponds to any given time, although -the distance at that part is known, unless we first know the length of -the whole oval. But the length of the oval cannot be known, except from -the law of the entry of the planet within the sides of the circle. But -neither can the law of this entry be known before we know how much of -the oval path corresponds to any given time. Here you see that there is -a _petitio principii_; and in my operations I was assuming that of which -I was in search, namely, the length of the oval. This is at least not -the fault of my understanding, but it is also most alien to the primary -Ordainer of the planetary courses: I have never yet found so -ungeometrical a contrivance in his other works. Therefore we must either -hit upon some other method of reducing the theory of the 45th chapter to -calculation; or if that cannot be done, the theory itself, suspected on -account of this _petitio principii_, will totter." Whilst his mind was -thus occupied, one of those extraordinary accidents which it has been -said never occur but to those capable of deriving advantage from them -(but which, in fact, are never noticed when they occur to any one else), -fortunately put him once more upon the right path. Half the extreme -breadth between the oval and the circle nearly represented the errors of -his distances at the mean point, and he found that this half was 429 -parts of a radius, consisting of 100000 parts; and happening to advert -to the greatest optical inequality of Mars, which amounts to about 5 deg. -18', it struck him that 429 was precisely the excess of the secant of 5 deg. -18' above the radius taken at 100000. This was a ray of light, and, to -use his own words, it roused him as out of sleep. In short, this single -observation was enough to produce conviction in his singularly -constituted mind, that instead of the distances SF, he should everywhere -substitute FV, determined by drawing SV perpendicular on the line FC, -since the excess of SF above FV is manifestly that of the secant above -the radius in the optical equation SFC at that point. It is still more -extraordinary that a substitution made for such a reason should have the -luck, as is again the case, to be the right one. This substitution in -fact amounted to supposing that the planet, instead of being at the -distance SP or SF, was at S_n_; or, in other words, that instead of -revolving in the circumference, it librated in the diameter of the -epicycle, which was to him an additional recommendation. Upon this new -supposition a fresh set of distances was rapidly calculated, and to -Kepler's inexpressible joy, they were found to agree with the -observations within the limits of the errors to which the latter were -necessarily subject. Notwithstanding this success, he had to undergo, -before arriving at the successful termination of his labours, one more -disappointment. Although the distance corresponding to a time from the -aphelion represented approximately by the area ASF, was thus found to be -accurately represented by the line S_n_, there was still an error with -regard to the direction in which that distance was to be measured. -Kepler's first idea was to set it off in the direction SF, but this he -found to lead to inaccurate longitudes; and it was not until after much -perplexity, driving him, as he tells us, "almost to insanity," that he -satisfied himself that the distance SQ equal to FV ought to be taken -terminating in F_m_, the line from F perpendicular to A_a_, the line of -apsides, and that the curve so traced out by Q would be an accurate -ellipse. - -[Illustration] - -He then found to his equal gratification and amazement, a small part of -which he endeavoured to express by a triumphant figure on the side of -his diagram, that the error he had committed in taking the area ASF to -represent the sums of the distances SF, was exactly counterbalanced; for -this area does accurately represent the sums of the distances FV or SQ. -This compensation, which seemed to Kepler the greatest confirmation of -his theory, is altogether accidental and immaterial, resulting from the -relation between the ellipse and circle. If the laws of planetary -attraction had chanced to have been any other than those which cause -them to describe ellipses, this last singular confirmation of an -erroneous theory could not have taken place, and Kepler would have been -forced either to abandon the theory of the areas, which even then would -have continued to measure and define their motions, or to renounce the -physical opinions from which he professed to have deduced it as an -approximative truth. - -These are two of the three celebrated theorems called Kepler's laws: the -first is, that the planets move in ellipses round the sun, placed in the -focus; the second, that the time of describing any arc is proportional -in the same orbit to the area included between the arc and the two -bounding distances from the sun. The third will be mentioned on another -occasion, as it was not discovered till twelve years later. On the -establishment of these two theorems, it became important to discover a -method of measuring such elliptic areas, but this is a problem which -cannot be accurately solved. Kepler, in offering it to the attention of -geometricians, stated his belief that its solution was unattainable by -direct processes, on account of the incommensurability of the arc and -sine, on which the measurement of the two parts AQ_m_, SQ_m_ depends. -"This," says he in conclusion, "this is my belief, and whoever shall -shew my mistake, and point out the true solution, - - _Is erit mihi magnus Apollonius._" - - -FOOTNOTES: - -[189] It is not very easy to carry the understanding aright among these -Aristotelian ideas. Many at the present day might think they understood -better what is meant, if for "form" had been written "nature." - -[190] De mundo nostro sublunari, Philosophia Nova. Amstelodami, 1651. - -[191] Theoricae novae planetarum. G. Purbachii, Parisiis, 1553. - - - - -CHAPTER VI. - - _Kepler appointed Professor at Linz--His second marriage--Publishes - his new Method of Gauging--Refuses a Professorship at Bologna._ - - -WHEN presenting this celebrated book to the emperor, Kepler gave notice -that he contemplated a farther attack upon Mars's relations, father -Jupiter, brother Mercury, and the rest; and promised that he would be -successful, provided the emperor would not forget the sinews of war, and -order him to be furnished anew with means for recruiting his army. The -death of his unhappy patron, the Emperor Rodolph, which happened in -1612, barely in time to save him from the last disgrace of deposition -from the Imperial throne, seemed to put additional difficulties in the -way of Kepler's receiving the arrears so unjustly denied to him; but on -the accession of Rodolph's brother, Matthias, he was again named to his -post of Imperial Mathematician, and had also a permanent professorship -assigned to him in the University of Linz. He quitted Prague without -much regret, where he had struggled against poverty during eleven years. -Whatever disinclination he might feel to depart, arose from his -unwillingness to loosen still more the hold he yet retained upon the -wreck of Tycho Brahe's instruments and observations. Tengnagel, -son-in-law of Tycho, had abandoned astronomy for a political career, and -the other members of his family, who were principally females, suffered -the costly instruments to lie neglected and forgotten, although they had -obstructed with the utmost jealousy Kepler's attempts to continue their -utility. The only two instruments Kepler possessed of his own property, -were "An iron sextant of 21/2 feet diameter, and a brass azimuthal -quadrant, of 31/2 feet diameter, both divided into minutes of a degree." -These were the gift of his friend and patron, Hoffman, the President of -Styria, and with these he made all the observations which he added to -those of Tycho Brahe. His constitution was not favourable to these -studies, his health being always delicate, and suffering much from -exposure to the night air; his eyes also were very weak, as he mentions -himself in several places. In the summary of his character which he drew -up when proposing to become Tycho Brahe's assistant, he describes -himself as follows:--"For observations my sight is dull; for mechanical -operations my hand is awkward; in politics and domestic matters my -nature is troublesome and choleric; my constitution will not allow me, -even when in good health, to remain a long time sedentary (particularly -for an extraordinary time after dinner); I must rise often and walk -about, and in different seasons am forced to make corresponding changes -in my diet." - -The year preceding his departure to Linz was denounced by him as -pregnant with misfortune and misery. "In the first place I could get no -money from the court, and my wife, who had for a long time been -suffering under low spirits and despondency, was taken violently ill -towards the end of 1610, with the Hungarian fever, epilepsy, and -phrenitis. She was scarcely convalescent when all my three children were -at once attacked with small-pox. Leopold with his army occupied the town -beyond the river, just as I lost the dearest of my sons, him whose -nativity you will find in my book on the new star. The town on this side -of the river where I lived was harassed by the Bohemian troops, whose -new levies were insubordinate and insolent: to complete the whole, the -Austrian army brought the plague with them into the city. I went into -Austria, and endeavoured to procure the situation which I now hold. -Returning in June, I found my wife in a decline from her grief at the -death of her son, and on the eve of an infectious fever; and I lost her -also, within eleven days after my return. Then came fresh annoyance, of -course, and her fortune was to be divided with my step-sisters. The -Emperor Rodolph would not agree to my departure; vain hopes were given -me of being paid from Saxony; my time and money were wasted together, -till on the death of the emperor, in 1612, I was named again by his -successor, and suffered to depart to Linz. These, methinks, were reasons -enough why I should have overlooked not only your letters, but even -astronomy itself." - -Kepler's first marriage had not been a happy one; but the necessity in -which he felt himself of providing some one to take charge of his two -surviving children, of whom the eldest, Susanna, was born in 1602, and -Louis in 1607, determined him on entering a second time into the married -state. The account he has left us of the various negotiations which -preceded his final choice, does not, in any point, belie the oddity of -his character. His friends seem to have received a general commission to -look out for a suitable match, and in a long and most amusing letter to -the Baron Strahlendorf, we are made acquainted with the pretensions and -qualifications of no less than eleven ladies among whom his inclinations -wavered. - -The first on the list was a widow, an intimate friend of his first -wife's, and who, on many accounts, appeared a most eligible match. "At -first she seemed favourably inclined to the proposal; it is certain that -she took time to consider it, but at last she very quietly excused -herself." It must have been from a recollection of this lady's good -qualities that Kepler was induced to make his offer; for we learn rather -unexpectedly, after being informed of her decision, that when he soon -afterwards paid his respects to her, it was for the first time that he -had seen her during the last six years; and he found, to his great -relief, that "there was no single pleasing point about her." The truth -seems to be that he was nettled by her answer, and he is at greater -pains than appear necessary, considering this last discovery, to -determine why she would not accept his offered hand. Among other reasons -he suggested her children, among whom were two marriageable daughters; -and it is diverting afterwards to find them also in the catalogue which -Kepler appeared to be making of all his female acquaintance. He seems to -have been much perplexed in attempting to reconcile his astrological -theory with the fact of his having taken so much trouble about a -negotiation not destined to succeed. "Have the stars exercised any -influence here? For just about this time the direction of the Mid-Heaven -is in hot opposition to Mars, and the passage of Saturn, through the -ascending point of the zodiac, in the scheme of my nativity, will happen -again next November and December. But if these are the causes, how do -they act? Is that explanation the true one which I have elsewhere given? -For I can never think of handing over to the stars the office of deities -to produce effects. Let us therefore suppose it accounted for by the -stars, that at this season I am violent in my temper and affections, in -rashness of belief, in a shew of pitiful tender-heartedness; in catching -at reputation by new and paradoxical notions, and the singularity of my -actions; in busily inquiring into, and weighing and discussing, various -reasons; in the uneasiness of my mind with respect to my choice. I thank -God that that did not happen which might have happened; that this -marriage did not take place: now for the others." Of these others, one -was too old, another in bad health, another too proud of her birth and -quarterings; a fourth had learned nothing but shewy accomplishments, -"not at all suitable to the sort of life she would have to lead with -me." Another grew impatient, and married a more decided admirer, whilst -he was hesitating. "The mischief (says he) in all these attachments was, -that whilst I was delaying, comparing, and balancing conflicting -reasons, every day saw me inflamed with a new passion." By the time he -reached the eighth, he found his match in this respect. "Fortune at -length has avenged herself on my doubtful inclinations. At first she was -quite complying, and her friends also: presently, whether she did or did -not consent, not only I, but she herself did not know. After the lapse -of a few days, came a renewed promise, which however had to be confirmed -a third time; and four days after that, she again repented her -confirmation, and begged to be excused from it. Upon this I gave her up, -and this time all my counsellors were of one opinion." This was the -longest courtship in the list, having lasted three whole months; and -quite disheartened by its bad success, Kepler's next attempt was of a -more timid complexion. His advances to No. 9, were made by confiding to -her the whole story of his recent disappointment, prudently determining -to be guided in his behaviour, by observing whether the treatment he had -experienced met with a proper degree of sympathy. Apparently the -experiment did not succeed; and almost reduced to despair, Kepler betook -himself to the advice of a friend, who had for some time past complained -that she was not consulted in this difficult negotiation. When she -produced No. 10, and the first visit was paid, the report upon her was -as follows:--"She has, undoubtedly, a good fortune, is of good family, -and of economical habits: but her physiognomy is most horribly ugly; she -would be stared at in the streets, not to mention the striking -disproportion in our figures. I am lank, lean, and spare; she is short -and thick: in a family notorious for fatness she is considered -superfluously fat." The only objection to No. 11 seems to have been her -excessive youth; and when this treaty was broken of on that account, -Kepler turned his back upon all his advisers, and chose for himself one -who had figured as No. 5 in the list, to whom he professes to have felt -attached throughout, but from whom the representations of his friends -had hitherto detained him, probably on account of her humble station. - -The following is Kepler's summary of her character. "Her name is -Susanna, the daughter of John Reuthinger and Barbara, citizens of the -town of Eferdingen; the father was by trade a cabinet-maker, but both -her parents are dead. She has received an education well worth the -largest dowry, by favour of the Lady of Stahrenberg, the strictness of -whose household is famous throughout the province. Her person and -manners are suitable to mine; no pride, no extravagance; she can bear to -work; she has a tolerable knowledge how to manage a family; middle-aged, -and of a disposition and capability to acquire what she still wants. Her -I shall marry by favour of the noble baron of Stahrenberg at twelve -o'clock on the 30th of next October, with all Eferdingen assembled to -meet us, and we shall eat the marriage-dinner at Maurice's at the Golden -Lion." - -Hantsch has made an absurd mistake with regard to this marriage, in -stating that the bride was only twelve years old. Kaestner and other -biographers have been content to repeat the same assertion without any -comment, notwithstanding its evident improbability. The origin of the -blunder is to be found in Kepler's correspondence with Bernegger, to -whom, speaking of his wife, he says "She has been educated for twelve -years by the Lady of Stahrenberg." This is by no means a single instance -of carelessness in Hantsch; Kaestner has pointed out others of greater -consequence. It was owing to this marriage, that Kepler took occasion to -write his new method of gauging, for as he tells us in his own peculiar -style "last November I brought home a new wife, and as the whole course -of Danube was then covered with the produce of the Austrian vineyards, -to be sold at a reasonable rate, I purchased a few casks, thinking it my -duty as a good husband and a father of a family, to see that my -household was well provided with drink." When the seller came to -ascertain the quantity, Kepler objected to his method of gauging, for -he allowed no difference, whatever might be the proportion of the -bulging parts. The reflections to which this incident gave rise, -terminated in the publication of the above-mentioned treatise, which -claims a place among the earliest specimens of what is now called the -modern analysis. In it he extended several properties of plane figures -to segments of cones and cylinders, from the consideration that "these -solids are incorporated circles," and, therefore, that those properties -are true of the whole which belong to each component part. That the book -might end as oddly as it began, Kepler concluded it with a parody of -Catullus: - - "Et cum pocula mille mensi erimus - Conturbabimus illa, ne sciamus." - -His new residence at Linz was not long undisturbed. He quarrelled there, -as he had done in the early part of his life at Gratz, with the Roman -Catholic party, and was excommunicated. "Judge," says he to Peter -Hoffman, "how far I can assist you, in a place where the priest and -school-inspector have combined to brand me with the public stigma of -heresy, because in every question I take that side which seems to me to -be consonant with the word of God." The particular dogma which -occasioned his excommunication, was connected with the doctrine of -transubstantiation. He published his creed in a copy of Latin verses, -preserved by his biographer Hantsch. - -Before this occurrence, Kepler had been called to the diet at Ratisbon -to give his opinion on the propriety of adopting the Gregorian -reformation of the calendar, and he published a short essay, pointing -out the respective convenience of doing so, or of altering the old -Julian Calendar in some other manner. Notwithstanding the readiness of -the diet to avail themselves of his talents for the settlement of a -difficult question, the arrears of his salary were not paid much more -regularly than they had been in Rodolph's time, and he was driven to -provide himself with money by the publication of his almanac, of which -necessity he heavily and justly complained. "In order to pay the expense -of the Ephemeris for these two years, I have also written a vile -prophesying almanac, which is scarcely more respectable than begging; -unless it be because it saves the emperor's credit, who abandons me -entirely; and with all his frequent and recent orders in council, would -suffer me to perish with hunger." Kepler published this Ephemeris -annually till 1620; ten years later he added those belonging to the -years from 1620 to 1628. - -In 1617 Kepler was invited into Italy, to succeed Magini as Professor of -Mathematics at Bologna. The offer tempted him; but, after mature -consideration, he rejected it, on grounds which he thus explained to -Roffini:--"By birth and spirit I am a German, imbued with German -principles, and bound by such family ties, that even if the emperor -should consent, I could not, without the greatest difficulty, remove my -dwelling-place from Germany into Italy. And although the glory of -holding so distinguished a situation among the venerable professors of -Bologna stimulates me, and there appears great likelihood of notably -increasing my fortune, as well from the great concourse to the public -lectures, as from private tuition; yet, on the other hand, that period -of my life is past which was once excited by novelty, or which might -promise itself a long enjoyment of these advantages. Besides, from a boy -up to my present years, living a German among Germans, I am accustomed -to a degree of freedom in my speech and manners, which, if persevered in -on my removal to Bologna, seems likely to draw upon me, if not danger, -at least notoriety, and might expose me to suspicion and party malice. -Notwithstanding this answer, I have yet hopes that your most honourable -invitation will be of service to me, and may make the imperial treasurer -more ready than he has hitherto been to fulfil his master's intentions -towards me. In that case I shall the sooner be able to publish the -Rudolphine Tables and the Ephemerides, of which you had the scheme so -many years back; and in this manner you and your advisers may have no -reason to regret this invitation, though for the present it seems -fruitless." - -In 1619, the Emperor Matthias died, and was succeeded by Ferdinand III., -who retained Kepler in the post he had filled under his two predecessors -on the imperial throne. Kaestner, in his "History of Mathematics," has -corrected a gross error of Hantsch, in asserting that Kepler -prognosticated Matthias's death. The letter to which Hantsch refers, in -support of his statement, does indeed mention the emperor's death, but -merely as a notorious event, for the purpose of recalling a date to the -memory of his correspondent. - - - - -CHAPTER VII. - - _Kepler publishes his Harmonics--Account of his Astrological - Opinions and Discovery of the Law of the Periods of the Planetary - Revolutions--Sketch of Newton's proof of Kepler's Laws._ - - -THE "Cosmographical Mystery" was written, as has been already mentioned, -when Kepler was only twenty-six, and the wildness of its theories might -be considered as due merely to the vivacity of a young man; but as if -purposely to shew that his maturer age did not renounce the creations of -his youthful fancy, he reprinted the "Mystery" in 1619, nearly at the -same time when he published his celebrated work on Harmonics; and the -extravagance of the latter publication does not at all lose in -comparison with its predecessor. It is dedicated to James I. of England, -and divided into five books: "The first, Geometrical, on the origin and -demonstration of the laws of the figures which produce harmonious -proportions;--the second, Architectonical, on figurate geometry, and the -congruence of plane and solid regular figures;--the third, properly -Harmonic, on the derivation of musical proportions from figures, and on -the nature and distinction of things relating to song, in opposition to -the old theories;--the fourth, Metaphysical, Psychological, and -Astrological, on the mental essence of harmonies, and of their kinds in -the world, especially on the harmony of rays emanating on the earth from -the heavenly bodies, and on their effect in nature, and on the sublunary -and human soul;--the fifth, Astronomical and Metaphysical, on the very -exquisite harmonies of the celestial motions, and the origin of the -excentricities in harmonious proportions." - -The two first books are almost strictly, as Kepler styles them, -geometrical, relating in great measure to the inscription of regular -polygons in a circle. The following passage is curious, presenting an -analogous idea to that contained in one of the extracts already given -from the Commentaries on Mars. "The heptagon, and all other polygons and -stars beyond it, which have a prime number of sides, and all other -figures derived from them, cannot be inscribed geometrically in a -circle; although their sides have a necessary magnitude, it is equally a -matter of necessity that we remain ignorant of it. This is a question of -great importance, for on this account is it that the heptagon, and other -figures of this kind, have not been employed by God in the adornment of -the world, as the other intelligible figures are employed which have -been already explained." Kepler then introduces the algebraical -equation, on the solution of which this problem depends, and makes a -remark which is curious at this period of the history of algebra--that -the root of an equation which cannot be accurately found, may yet be -found within any degree of approximation by an expert calculator. In -conclusion he again remarks that "the side of the heptagon has no place -among scientific existences, since its formal description is impossible, -and therefore it cannot be known by the human mind, since the -possibility of description precedes the possibility of knowledge; nor is -it known even by the simple eternal act of an omniscient mind, because -its nature belongs to things which cannot be known. And yet this -scientific nonentity has some scientific properties, for if a heptagon -were described in a circle, the proportion of its sides would have -analogous proportions." - -The third book is a treatise on music, in the confined and ordinary -sense in which we now use that word, and apparently a sober and rational -one, at least as nearly so as Kepler could be trusted to write on a -subject so dangerous to his discretion. All the extravagance of the work -seems reserved for the fourth book, the title of which already conveys -some notion of the nature of its contents. In this book he has collected -the substance of the astrological opinions scattered through his other -works. We shall content ourselves with merely citing his own words, -without any attempt to explain the difference between the astrology -which he believed, and that which he contemptuously rejected. The -distinctive line seems very finely drawn, and as both one and the other -are now discarded by all who enjoy the full use of their reasoning -powers, it is not of much consequence that it should be accurately -traced. - -It is to be observed, that he does not in this treatise modify or recant -anything of his earlier opinions, but refers to the favourable judgment -of his contemporary philosophers as a reason for embodying them in a -regular form. "Since many very celebrated professors of philosophy and -medicine are of opinion that I have created a new and most true -philosophy, this tender plant, like all novelties, ought to be carefully -nursed and cherished, so that it may strike root in the minds of -philosophers, and not be choked by the excessive humours of vain -sophistications, or washed away by the torrents of vulgar prejudices, or -frozen by the chill of public neglect; and if I succeed in guarding it -from these dangers, I have no fear that it will be crushed by the storms -of calumny, or parched by the sun of sterling criticism." - -One thing is very remarkable in Kepler's creed, that he whose candour is -so indisputable in every other part of his conduct, professed to have -been forced to adopt his astrological opinions from direct and positive -observation.--"It is now more than twenty years since I began to -maintain opinions like these on the predominant nature of the elements, -which, adopting the common name, I call sublunary. I have been driven to -this not by studying or admiring Plato, but singly and solely by -observing seasons, and noting the aspects by which they are produced. I -have seen the state of the atmosphere almost uniformly disturbed as -often as the planets are in conjunction, or in the other configurations -so celebrated among astrologers. I have noticed its tranquil state, -either when there are none or few such aspects, or when they are -transitory and of short duration. I have not formed an opinion on this -matter without good grounds, like the common herd of prophesiers, who -describe the operations of the stars as if they were a sort of deities, -the lords of heaven and earth, and producing everything at their -pleasure. They never trouble themselves to consider what means the stars -have of working any effects among us on the earth, whilst they remain in -the sky, and send down nothing to us which is obvious to the senses -except rays of light. This is the principal source of the filthy -astrological superstitions of that vulgar and childish race of dreamers, -the prognosticators." - -The real manner in which the configurations of the stars operate, -according to Kepler, is as follows:--"Like one who listens to a sweet -melodious song, and by the gladness of his countenance, by his voice, -and by the beating of his hand or foot attuned to the music, gives token -that he perceives and approves the harmony: just so does sublunary -nature, with the notable and evident emotion of the bowels of the earth, -bear like witness to the same feelings, especially at those times when -the rays of the planets form harmonious configurations on the -earth."--"I have been confirmed in this theory by that which might have -deterred others; I mean, by observing that the emotions do not agree -nicely with the instants of the configurations; but the earth sometimes -appears lazy and obstinate, and at another time (after important and -long-continued configurations) she becomes exasperated, and gives way to -her passion, even without the continuation of aspects. For in fact the -earth is not an animal like a dog, ready at every nod; but more like a -bull, or an elephant, slow to become angry, and so much the more furious -when incensed." - -This singular doctrine must not be mistaken for one of Kepler's -favourite allegories; he actually and literally professed to believe -that the earth was an enormous living animal; and he has enumerated, -with a particularity of details into which we forbear to follow him, the -analogies he recognized between its habits and those of men and other -animals. A few samples of these may speak for the rest. "If any one who -has climbed the peaks of the highest mountains throw a stone down their -very deep clefts, a sound is heard from them; or if he throw it into one -of the mountain lakes, which beyond doubt are bottomless, a storm will -immediately arise, just as when you thrust a straw into the ear or nose -of a ticklish animal, it shakes its head, or runs shuddering away. What -so like breathing, especially of those fish who draw water into their -mouths and spout it out again through their gills, as that wonderful -tide! For although it is so regulated according to the course of the -moon, that, in the preface to my 'Commentaries on Mars,' I have -mentioned it as probable that the waters are attracted by the moon as -iron is by the loadstone; yet, if any one uphold that the earth -regulates its breathing according to the motion of the sun and moon, as -animals have daily and nightly alternations of sleep and waking, I shall -not think his philosophy unworthy of being listened to; especially if -any flexible parts should be discovered in the depths of the earth to -supply the functions of lungs or gills." - -From the next extract, we must leave the reader to learn as well as he -may, how much Kepler did, and how much he did not believe on the -subject of genethliac astrology.--"Hence it is that human spirits, at -the time of celestial aspects, are particularly urged to complete the -matters which they have in hand. What the goad is to the ox, what the -spur or the rowel is to the horse, to the soldier the bell and trumpet, -an animated speech to an audience, to a crowd of rustics a performance -on the fife and bagpipes, that to all, and especially in the aggregate, -is a heavenly configuration of suitable planets; so that every single -one is excited in his thoughts and actions, and all become more ready to -unite and associate their efforts. For instance, in war you may see that -tumults, battles, fights, invasions, assaults, attacks, and panic fears, -generally happen at the time of the aspects of Mars and Mercury, Mars -and Jupiter, Mars and the Sun, Mars and Saturn, &c. In epidemic -diseases, a greater number of persons are attacked at the times of the -powerful aspects, they suffer more severely, or even die, owing to the -failure of nature in her strife with the disease, which strife (and not -the death) is occasioned by the aspect. It is not the sky which does all -these things immediately, but the faculty of the vital soul, associating -its operation with the celestial harmonies, is the principal agent in -this so-called influence of the heavens. Indeed this word influence has -so fascinated some philosophers that they prefer raving with the -senseless vulgar, to learning the truth with me. This essential property -is the principal foundation of that admirable genethliac art. For when -anything begins to have its being when that is working harmonies, the -sensible harmony of the rays of the planets has peculiar influence on -it. This then is the cause why those who are born under a season of many -aspects among the planets, generally turn out busy and industrious, -whether they accustom themselves from childhood to amass wealth, or are -born or chosen to direct public affairs, or finally, have given their -attention to study. If any one think that I might be taken as an -instance of this last class, I do not grudge him the knowledge of my -nativity. I am not checked by the reproach of boastfulness, -notwithstanding those who, by speech or conduct, condemn as folly all -kinds of writing on this subject; the idiots, the half-learned, the -inventors of titles and trappings, to throw dust in the eyes of the -people, and those whom Picus calls the plebeian theologians: among the -true lovers of wisdom, I easily clear myself of this imputation, by the -advantage of my reader; for there is no one whose nativity or whose -internal disposition and temper I can learn so well as I know my own. -Well then, Jupiter nearest the nonagesimal had passed by four degrees -the trine of Saturn; the Sun and Venus, in conjunction, were moving from -the latter towards the former, nearly in sextiles with both: they were -also removing from quadratures with Mars, to which Mercury was closely -approaching: the moon drew near the trine of the same planet, close to -the Bull's Eye, even in latitude. The 25th degree of Gemini was rising, -and the 22d of Aquarius culminating. That there was this triple -configuration on that day--namely, the sextile of Saturn and the Sun, -the sextile of Mars and Jupiter, the quadrature of Mercury and Mars, is -proved by the change of weather; for, after a frost of some days, that -very day became warmer, there was a thaw and a fall of rain.[192] - -"I do not wish this single instance to be taken as a defence and proof -of all the aphorisms of astrologers, nor do I attribute to the heavens -the government of human affairs: what a vast interval still separates -these philosophical observations from that folly or madness as it should -rather be called. For, following up this example, I knew a lady[193], -born under nearly the same aspects, whose disposition, indeed, was -exceedingly restless, but who not only makes no progress in literature -(that is not strange in a woman), but troubles her whole family, and is -the cause to herself of deplorable misery. What, in my case, assisted -the aspects was--firstly, the fancy of my mother when pregnant with me, -a great admirer of her mother-in-law, my grandmother, who had some -knowledge of medicine, my grandfather's profession; a second cause is, -that I was born a male, and not a female, for astrologers have sought -in vain to distinguish sexes in the sky; thirdly, I derive from my -mother a habit of body, more fit for study than other kinds of life; -fourthly, my parents' fortune was not large, and there was no landed -property to which I might succeed and become attached; fifthly, there -were the schools, and the liberality of the magistracy towards such boys -as were apt for learning. But now if I am to speak of the result of my -studies, what I pray can I find in the sky, even remotely alluding to -it. The learned confess that several not despicable branches of -philosophy have been newly extricated or amended or brought to -perfection by me: but here my constellations were, not Mercury from the -east, in the angle of the seventh, and in quadratures with Mars, but -Copernicus, but Tycho Brahe, without whose books of observations -everything now set by me in the clearest light must have remained buried -in darkness; not Saturn predominating Mercury, but my Lords the Emperors -Rodolph and Matthias; not Capricorn, the house of Saturn, but Upper -Austria, the home of the Emperor, and the ready and unexampled bounty of -his nobles to my petition. Here is that corner, not the western one of -the horoscope, but on the Earth, whither, by permission of my imperial -master, I have betaken myself from a too uneasy court; and whence, -during these years of my life, which now tends towards its setting, -emanate these Harmonies, and the other matters on which I am engaged. - -"However, it may be owing to Jupiter's ascendancy that I take greater -delight in the application of geometry to physics, than in that abstract -pursuit which partakes of the dryness of Saturn; and it is perhaps the -gibbous moon, in the bright constellation of the Bull's forehead, which -fills my mind with fantastic images." - -The most remarkable thing contained in the 5th Book, is the announcement -of the celebrated law connecting the mean distances of the planets with -the periods of their revolution about the Sun. This law is expressed in -mathematical language, by saying that the squares of the times vary as -the cubes of the distances.[194] Kepler's rapture on detecting it was -unbounded, as may be seen from the exulting rhapsody with which he -announced it. "What I prophecied two-and-twenty years ago, as soon as I -discovered the five solids among the heavenly orbits--what I firmly -believed long before I had seen Ptolemy's 'Harmonics'--what I had -promised my friends in the title of this book, which I named before I -was sure of my discovery--what, sixteen years ago, I urged as a thing to -be sought--that for which I joined Tycho Brahe, for which I settled in -Prague, for which I have devoted the best part of my life to -astronomical contemplations, at length I have brought to light, and have -recognized its truth beyond my most sanguine expectations. Great as is -the absolute nature of Harmonics with all its details, as set forth in -my third book, it is all found among the celestial motions, not indeed -in the manner which I imagined, (that is not the least part of my -delight,) but in another very different, and yet most perfect and -excellent. It is now eighteen months since I got the first glimpse of -light, three months since the dawn, very few days since the unveiled -sun, most admirable to gaze on, burst out upon me. Nothing holds me; I -will indulge in my sacred fury; I will triumph over mankind by the -honest confession, that I have stolen the golden vases of the -Egyptians[195], to build up a tabernacle for my God far away from the -confines of Egypt. If you forgive me, I rejoice; if you are angry, I can -bear it: the die is cast, the book is written; to be read either now or -by posterity, I care not which: it may well wait a century for a reader, -as God has waited six thousand years for an observer." - -He has told, with his usual particularity, the manner and precise moment -of the discovery. "Another part of my 'Cosmographical Mystery,' -suspended twenty-two years ago, because it was then undetermined, is -completed and introduced here, after I had discovered the true intervals -of the orbits, by means of Brahe's observations, and had spent the -continuous toil of a long time in investigating the true proportion of -the periodic times to the orbits, - - Sera quidem respexit inertem, - Respexit tamen, et longo post tempore venit. - -If you would know the precise moment, the first idea came across me on -the 8th March of this year, 1618; but chancing to make a mistake in the -calculation, I rejected it as false. I returned again to it with new -force on the 15th May, and it has dissipated the darkness of my mind by -such an agreement between this idea and my seventeen years' labour on -Brahe's observations, that at first I thought I must be dreaming, and -had taken my result for granted in my first assumptions. But the fact is -perfect, the fact is certain, that the proportion existing between the -periodic times of any two planets is exactly the sesquiplicate -proportion of the mean distances of the orbits." - -There is high authority for not attempting over anxiously to understand -the rest of the work. Delambre sums it up as follows:--"In the music of -the celestial bodies it appears that Saturn and Jupiter take the bass, -Mars the tenor, the Earth and Venus the counter-tenor, and Mercury the -treble." If the patience of this indefatigable historian gave way, as he -confesses, in the perusal, any further notice of it here may be well -excused. Kepler became engaged, in consequence of this publication, in -an angry controversy with the eccentric Robert Fludd, who was at least -Kepler's match in wild extravagance and mysticism, if far inferior to -him in genius. It is diverting to hear each reproaching the other with -obscurity. - -In the "Epitome of the Copernican Astronomy," which Kepler published -about the same time, we find the manner in which he endeavoured to -deduce the beautiful law of periodic times, from his principles of -motion and radiation of whirling forces. This work is in fact a summary -of all his astronomical opinions, drawn up in a popular style in the -form of question and answer. We find there a singular argument against -believing, as some did, that each planet is carried round by an angel, -for in that case, says Kepler, "the orbits would be perfectly circular; -but the elliptic form, which we find in them, rather smacks of the -nature of the lever and material necessity." - -The investigation of the relation between the periodic times and -distances of the planets is introduced by a query whether or not they -are to be considered heavy. The answer is given in the following -terms:--"Although none of the celestial globes are heavy, in the sense -in which we say on earth that a stone is heavy, nor light as fire is -light with us, yet have they, by reason of their materiality, a natural -inability to move from place to place: they have a natural inertness or -quietude, in consequence of which they remain still in every situation -where they are placed alone. - -"_P._ Is it then the sun, which by its turning carries round the -planets? How can the sun do this, having no hands to seize the planet at -so great a distance, and force it round along with itself?--Its bodily -virtue, sent forth in straight lines into the whole space of the world, -serves instead of hands; and this virtue, being a corporeal species, -turns with the body of the sun like a very rapid vortex, and travels -over the whole of that space which it fills as quickly as the sun -revolves in its very confined space round the centre. - -"_P._ Explain what this virtue is, and belonging to what class of -things?--As there are two bodies, the mover and the moved, so are there -two powers by which the motion is obtained. The one is passive, and -rather belonging to matter, namely, the resemblance of the body of the -planet to the body of the sun in its corporeal form, and so that part of -the planetary body is friendly, the opposite part hostile to the sun. -The other power is active, and bearing more relation to form, namely, -the body of the sun has a power of attracting the planet by its friendly -part, of repelling it by the hostile part, and finally, of retaining it -if it be placed so that neither the one nor the other be turned directly -towards the sun. - -"_P._ How can it be that the whole body of the planet should be like or -cognate to the body of the sun, and yet part of the planet friendly, -part hostile to the sun?--Just as when one magnet attracts another, the -bodies are cognate; but attraction takes place only on one side, -repulsion on the other. - -"_P._ Whence, then, arises that difference of opposite parts in the same -body?--In magnets the diversity arises from the situation of the parts -with respect to the whole. In the heavens the matter is a little -differently arranged, for the sun does not, like the magnet, possess -only on one side, but in all the parts of its substance, this active and -energetic faculty of attracting, repelling, or retaining the planet. So -that it is probable that the centre of the solar body corresponds to one -extremity or pole of the magnet, and its whole surface to the other -pole. - -"_P._ If this were so, all the planets would be restored[196] in the -same time with the sun?--True, if this were all: but it has been said -already that, besides this carrying power of the sun, there is also in -the planets a natural inertness to motion, which causes that, by reason -of their material substance, they are inclined to remain each in its -place. The carrying power of the sun, and the impotence or material -inertness of the planet, are thus in opposition. Each shares the -victory; the sun moves the planet from its place, although in some -degree it escapes from the chains with which it was held by the sun, and -so is taken hold of successively by every part of this circular virtue, -or, as it may be called, solar circumference, namely, by the parts which -follow those from which it has just extricated itself. - -"_P._ But how does one planet extricate itself more than another from -this violence--First, because the virtue emanating from the sun has the -same degree of weakness at different distances, as the distances or the -width of the circles described on these distances.[197] This is the -principal reason. Secondly, the cause is partly in the greater or less -inertness or resistance of the planetary globes, which reduces the -proportions to one-half; but of this more hereafter. - -"_P._ How can it be that the virtue emanating from the sun becomes -weaker at a greater distance? What is there to hurt or weaken -it?--Because that virtue is corporeal, and partaking of quantity, which -can be spread out and rarefied. Then, since there is as much virtue -diffused in the vast orb of Saturn as is collected in the very narrow -one of Mercury, it is very rare and therefore weak in Saturn's orbit, -very dense and therefore powerful at Mercury. - -"_P._ You said, in the beginning of this inquiry into motion, that the -periodic times of the planets are exactly in the sesquiplicate -proportion of their orbits or circles: pray what is the cause of -this?--Four causes concur for lengthening the periodic time. First, the -length of the path; secondly, the weight or quantity of matter to be -carried; thirdly, the degree of strength of the moving virtue; fourthly, -the bulk or space into which is spread out the matter to be moved. The -circular paths of the planets are in the simple ratio of the distances; -the weights or quantities of matter in different planets are in the -subduplicate ratio of the same distances, as has been already proved; so -that with every increase of distance, a planet has more matter, and -therefore is moved more slowly, and accumulates more time in its -revolution, requiring already as it did more time by reason of the -length of the way. The third and fourth causes compensate each other in -a comparison of different planets: the simple and subduplicate -proportion compound the sesquiplicate proportion, which therefore is the -ratio of the periodic times." - -Three of the four suppositions here made by Kepler to explain the -beautiful law he had detected, are now indisputably known to be false. -Neither the weights nor the sizes of the different planets observe the -proportions assigned by him, nor is the force by which they are retained -in their orbits in any respect similar in its effects to those -attributed by him to it. The wonder which might naturally be felt that -he should nevertheless reach the desired conclusion, will be -considerably abated on examining the mode in which he arrived at and -satisfied himself of the truth of these three suppositions. It has been -already mentioned that his notions on the existence of a whirling force -emanating from the sun, and decreasing in energy at increased distances, -are altogether inconsistent with all the experiments and observations we -are able to collect. His reason for asserting that the sizes of the -different planets are proportional to their distances from the sun, was -simply because he chose to take for granted that either their -solidities, surfaces, or diameters, must necessarily be in that -proportion, and of the three, the solidities appeared to him least -liable to objection. The last element of his precarious reasoning rested -upon equally groundless assumptions. Taking as a principle, that where -there is a number of different things they must be different in every -respect, he declared that it was quite unreasonable to suppose all the -planets of the same density. He thought it indisputable that they must -be rarer as they were farther from the sun, "and yet not in the -proportion of their distances, for thus we should sin against the law of -variety in another way, and make the quantity of matter (according to -what he had just said of their bulk) the same in all. But if we assume -the ratio of the quantities of matter to be half that of the distances, -we shall observe the best mean of all; for thus Saturn will be half as -heavy again as Jupiter, and Jupiter half again as dense as Saturn. And -the strongest argument of all is, that unless we assume this proportion -of the densities, the law of the periodic times will not answer." This -is the _proof_ alluded to, and it is clear that by such reasoning any -required result might be deduced from any given principles. - -It may not be uninstructive to subjoin a sketch of the manner in which -Newton established the same celebrated results, starting from principles -of motion diametrically opposed to Kepler's, and it need scarcely be -added, reasoning upon them in a manner not less different. For this -purpose, a very few prefatory remarks will be found sufficient. - -The different motions seen in nature are best analysed and classified by -supposing that every body in motion, if left to itself, will continue to -move forward at the same rate in a straight line, and by considering all -the observed deviations from this manner of moving, as exceptions and -disturbances occasioned by some external cause. To this supposed cause -is generally given the name of Force, and it is said to be the first law -of motion, that, unless acted on by some force, every body at rest -remains at rest, and every body in motion proceeds uniformly in a -straight line. Many employ this language, without perceiving that it -involves a definition of force, on the admission of which, it is reduced -to a truism. We see common instances of force in a blow, or a pull from -the end of a string fastened to the body: we shall also have occasion -presently to mention some forces where no visible connexion exists -between the moving body and that towards which the motion takes place, -and from which the force is said to proceed. - -[Illustration: - - _c_ C - +-------------+ - \ / \ - \ / \ - \ / \ - \ / \ - \ / \ - \ / \ - +-------------+ - B C' ] - -A second law of motion, founded upon experiment, is this: if a body have -motion communicated to it in two directions, by one of which motions -alone it would have passed through a given space in a given time, as for -instance, through BC' in one second, and by the other alone through any -other space B_c_ in the same time, it will, when both are given to it at -the same instant, pass in the same time (in the present instance in one -second) through BC the diagonal of the parallelogram of which BC' and -B_c_ are sides. - -[Illustration: - - / S \ - / /|\ \ - / / | \ \ - / / | \ \ - / / | \ \ - / / | \ \ - / / | \ \ - --------+-+------+------+-+ - A B C D E ] - -Let a body, acted upon by no force, be moving along the line AE; that -means, according to what has been said, let it pass over the equal -straight lines AB, BC, CD, DE, &c., in equal times. If we take any point -S not in the line AE, and join AS, BS, &c., the triangles ASB, BSC, &c. -are also equal, having a common altitude and standing on equal bases, so -that if a string were conceived reaching from S to the moving body -(being lengthened or shortened in each position to suit its distance -from S), this string, as the body moved along AE, would sweep over equal -triangular areas in equal times. - -[Illustration] - -Let us now examine how far these conclusions will be altered if the body -from time to time is forced towards S. We will suppose it moving -uniformly from A to B as before, no matter for the present how it got to -A, or into the direction AB. If left to itself it would, in an equal -time (say 1'') go through BC' in the same straight line with and equal -to AB. But just as it reaches B, and is beginning to move along BC', let -it be suddenly pulled towards S with a motion which, had it been at -rest, would have carried it in the same time, 1'' through any other -space B_c_. According to the second law of motion, its direction during -this 1'', in consequence of the two motions combined, will be along BC, -the diagonal of the parallelogram of which BC', B_c_, are sides. In -this case, as this figure is drawn, BC, though passed in the same time, -is longer than AB; that is to say, the body is moving quicker than at -first. How is it with the triangular areas, supposed as before to be -swept by a string constantly stretched between S and the body? It will -soon be seen that these still remain equal, notwithstanding the change -of direction, and increased swiftness. For since CC' is parallel to -B_c_, the triangles SCB, SC'B are equal, being on the same base SB, and -between the same parallels SB, CC', and SC'B is equal to SBA as before, -therefore SCB, SBA are equal. The body is now moving uniformly (though -quicker than along AB) along BC. As before, it would in a time equal to -the time of passing along BC, go through an equal space CD' in the same -straight line. But if at C it has a second pull towards S, strong enough -to carry it to _d_ in the same time, its direction will change a second -time to CD, the diagonal of the parallelogram, whose sides are CD', -C_d_; and the circumstances being exactly similar to those at the first -pull, it is shewn in the same manner that the triangular area SDC = SCB -= SBA. - -Thus it appears, that in consequence of these intermitting pulls towards -S, the body may be moving round, sometimes faster, sometimes slower, but -that the triangles formed by any of the straight portions of its path -(which are all described in equal times), and the lines joining S to the -ends of that portion, are all equal. The path it will take depends of -course, in other respects, upon the frequency and strength of the -different pulls, and it might happen, if they were duly proportionate, -that when at H, and moving off in the direction HA', the pull H_a_ -might be such as just to carry the body back to A, the point from which -it started, and with such a motion, that after one pull more, A_b_, at -A, it might move along AB as it did at first. If this were so, the body -would continue to move round in the same polygonal path, alternately -approaching and receding from S, as long as the same pulls were repeated -in the same order, and at the same intervals. - -It seems almost unnecessary to remark, that the same equality which -subsists between any two of these triangular areas subsists also between -an equal number of them, from whatever part of the path taken; so that, -for instance, the four paths AB, BC, CD, DE, corresponding to the four -areas ASB, BSC, CSD, DSE, that is, to the area ABCDES, are passed in the -same time as the four EF, FG, GH, HA, corresponding to the equal area -EFGHAS. Hence it may be seen, if the whole time of revolution from A -round to A again be called a year, that in half a year the body will -have got to E, which in the present figure is more than half way round, -and so of any other periods. - -The more frequently the pulls are supposed to recur, the more frequently -will the body change its direction; and if the pull were supposed -constantly exerted in the direction towards S, the body would move in a -curve round S, for no three successive positions of it could be in a -straight line. Those who are not familiar with the methods of measuring -curvilinear spaces must here be contented to observe, that the law -holds, however close the pulls are brought together, and however closely -the polygon is consequently made to resemble a curve: they may, if they -please, consider the minute portions into which the curve is so divided, -as differing insensibly from little rectilinear triangles, any equal -number of which, according to what has been said above, wherever taken -in the curve, would be swept in equal times. The theorem admits, in this -case also, a rigorous proof; but it is not easy to make it entirely -satisfactory, without entering into explanations which would detain us -too long from our principal subject. - -The proportion in which the pull is strong or weak at different -distances from the central spot, is called "_the law of the central or -centripetal force_," and it may be observed, that after assuming the -laws of motion, our investigations cease to have anything hypothetical -or experimental in them; and that if we wish, according to these -principles of motion, to determine the law of force necessary to make a -body move in a curve of any required form, or conversely to discover the -form of the curve described, in consequence of any assumed law of force, -the inquiry is purely geometrical, depending upon the nature and -properties of geometrical quantities only. This distinction between what -is hypothetical, and what necessary truth, ought never to be lost sight -of. - -As the object of the present treatise is not to teach geometry, we shall -describe, in very general terms, the manner in which Newton, who was -the first who systematically extended the laws of motion to the heavenly -bodies, identified their results with the two remaining laws of Kepler. -His "Principles of Natural Philosophy" contain general propositions with -regard to any law of centripetal force, but that which he supposed to be -the true one in our system, is expressed in mathematical language, by -saying that the centripetal force varies inversely as the square of the -distance, which means, that if the force at any distance be taken for -the unit of force, at half that distance, it is two times twice, or four -times as strong; at one-third the distance, three times thrice, or nine -times as strong, and so for other distances. He shewed the probability -of this law in the first instance by comparing the motion of the moon -with that of heavy bodies at the surface of the earth. Taking LP to -represent part of the moon's orbit described in one minute, the line PM -between the orbit and the tangent at L would shew the space through -which the central force at the earth (assuming the above principles of -motion to be correct) would draw the moon. From the known distance and -motion of the moon, this line PM is found to be about sixteen feet. The -distance of the moon is about sixty times the radius of the earth, and -therefore if the law of the central force in this instance were such as -has been supposed, the force at the earth's surface would be 60 times -60, or 3600 times stronger, and at the earth's surface, the central -force would make a body fall through 3600 times 16 feet in one minute. -Galileo had already taught that the spaces through which a body would be -made to fall, by the constant action of the same unvarying force, would -be proportional to the squares of the times during which the force was -exerted, and therefore according to these laws, a body at the earth's -surface ought (since there are sixty seconds in a minute) to fall -through 16 feet in one second, which was precisely the space previously -established by numerous experiments. - -[Illustration] - -With this confirmation of the supposition, Newton proceeded to the -purely geometrical calculation of the law of centripetal[198] force -necessary to make a moving body describe an ellipse round its focus, -which Kepler's observations had established to be the form of the orbits -of the planets round the sun. The result of the inquiry shewed that this -curve required the same law of the force, varying inversely as the -square of the distance, which therefore of course received additional -confirmation. His method of doing this may, perhaps, be understood by -referring to the last figure but one, in which C_d_, for instance, -representing the space fallen from any point C towards S, in a given -time, and the area CSD being proportional to the corresponding time, the -space through which the body would have fallen at C in any other time -(which would be greater, by Galileo's law, in proportion to the squares -of the times), might be represented by a quantity varying directly as -C_d_, and inversely in the duplicate proportion of the triangular area -CSD, that is to say, proportional to C_d_/(SC x D_k_) squared, if D_k_ be drawn -from D perpendicular on SC. If this polygon represent an ellipse, so -that CD represents a small arc of the curve, of which S is the focus, it -is found by the nature of that curve, that C_d_/(D_k_) squared is the same at -all points of the curve, so that the law of variation of the force in -the same ellipse is represented solely by 1/(SC) squared. If C_d_, &c. are -drawn so that C_d_/(D_k_) squared is not the same at every point, the curve -ceases to be an ellipse whose focus is at S, as Newton has shewn in the -same work. The line to which (Dk) squared/Cd is found to be equal, is one drawn -through the focus at right angles to the longest axis of the ellipse -till it meets the curve;--this line is called the _latus rectum_, and is -a third proportional to the two principal axes. - -Kepler's third law follows as an immediate consequence of this -determination; for, according to what has been already shown, the time -of revolution round the whole ellipse, or, as it is commonly called, -the periodic time, bears the same ratio to the unit of time as the whole -area of the ellipse does to the area described in that unit. The area of -the whole ellipse is proportional in different ellipses to the rectangle -contained by the two principal axes, and the area described in an unit -of time is proportional to SC x D_k_, that is to say, is in the -subduplicate ratio of SC squared x D_k_ squared, or D_k_ squared/C_d_, when the force varies -inversely as the square of the distance SC; and in the ellipse, as we -have said already, this is equal to a third proportional to the -principal axes; consequently the periodic times in different ellipses, -which are proportional to the whole areas of the ellipses directly, and -the areas described in the unit of time inversely, are in the compound -ratio of the rectangle of the axes directly, and subduplicately as a -third proportional to the axes inversely; that is to say, the squares of -these times are proportional to the cubes of the longest axes, which is -Kepler's law. - - -FOOTNOTES: - -[192] This mode of verifying configurations, though something of the -boldest, was by no means unusual. On a former occasion Kepler, wishing -to cast the nativity of his friend Zehentmaier, and being unable to -procure more accurate information than that he was born about three -o'clock in the afternoon of the 21st of October, 1751, supplied the -deficiency by a record of fevers and accidents at known periods of his -life, from which he deduced a more exact horoscope. - -[193] Kepler probably meant his own mother, whose horoscope he in many -places declared to be nearly the same as his own. - -[194] See Preliminary Treatise, p. 13. - -[195] In allusion to the Harmonics of Ptolemy. - -[196] This is a word borrowed from the Ptolemaic astronomy, according to -which the sun and planets are hurried from their places by the daily -motion of the _primum mobile_, and by their own peculiar motion seek to -regain or be restored to their former places. - -[197] In other parts of his works, Kepler assumes the diminution to be -proportional to the circles themselves, not to the diameters. - -[198] In many curves, as in the circle and ellipse, there is a point to -which the name of centre is given, on account of peculiar properties -belonging to it: but the term "centripetal force" always refers to the -place towards which the force is directed, whether or not situated in -the centre of the curve. - - - - -CHAPTER VIII. - - _The Epitome prohibited at Rome--Logarithmic Tables--Trial of - Catharine Kepler--Kepler invited to England--Rudolphine - Tables--Death--Conclusion._ - - -KEPLER'S "Epitome," almost immediately on its appearance, enjoyed the -honour of being placed by the side of the work of Copernicus, on the -list of books prohibited by the congregation of the Index at Rome. He -was considerably alarmed on receiving this intelligence, anticipating -that it might occasion difficulties in publishing his future writings. -His words to Remus, who had communicated the news to him, are as -follows:--"I learn from your letter, for the first time, that my book is -prohibited at Rome and Florence. I particularly beg of you, to send me -the exact words of the censure, and that you will inform me whether that -censure would be a snare for the author, if he were caught in Italy, or -whether, if taken, he would be enjoined a recantation. It is also of -consequence for me to know whether there is any chance of the same -censure being extended into Austria. For if this be so, not only shall I -never again find a printer there, but also the copies which the -bookseller has left in Austria at my desire will be endangered, and the -ultimate loss will fall upon me. It will amount to giving me to -understand, that I must cease to profess Astronomy, after I have grown -old in the belief of these opinions, having been hitherto gainsayed by -no one,--and, in short, I must give up Austria itself, if room is no -longer to be left in it for philosophical liberty." He was, however, -tranquillized, in a great degree, by the reply of his friend, who told -him that "the book is only prohibited as contrary to the decree -pronounced by the holy office two years ago. This has been partly -occasioned by a Neapolitan monk (Foscarini), who was spreading these -notions by publishing them in Italian, whence were arising dangerous -consequences and opinions: and besides, Galileo was at the same time -pleading his cause at Rome with too much violence. Copernicus has been -corrected in the same manner for some lines, at least in the beginning -of his first book. But by obtaining a permission, they may be read (and, -as I suppose, this "Epitome" also) by the learned and skilful in this -science, both at Rome and throughout all Italy. There is therefore no -ground for your alarm, either in Italy or Austria; only keep yourself -within bounds, and put a guard upon your own passions." - -We shall not dwell upon Kepler's different works on comets, beyond -mentioning that they were divided, on the plan of many of his other -publications, into three parts, Astronomical, Physical, and -Astrological. He maintained that comets move in straight lines, with a -varying degree of velocity. Later theories have shewn that they obey the -same laws of motion as the planets, differing from them only in the -extreme excentricity of their orbits. In the second book, which contains -the Physiology of Comets, there is a passing remark that comets come out -from the remotest parts of ether, as whales and monsters from the depth -of the sea; and the suggestion is thrown out that perhaps comets are -something of the nature of silkworms, and are wasted and consumed in -spinning their own tails. - -Among his other laborious employments, Kepler yet found time to -calculate tables of logarithms, he having been one of the first in -Germany to appreciate the full importance of the facilities they afford -to the numerical calculator. In 1618 he wrote to his friend Schickhard: -"There is a Scottish Baron (whose name has escaped my memory), who has -made a famous contrivance, by which all need of multiplication and -division is supplied by mere addition and subtraction; and he does it -without sines. But even he wants a table of tangents[199], and the -variety, frequency, and difficulty of the additions and subtractions, in -some cases, is greater than the labour of multiplying and dividing." - -Kepler dedicated his "Ephemeris" for 1620 to the author of this -celebrated invention, Baron Napier, of Merchistoun; and in 1624, -published what he called "Chilias Logarithmorum," containing the -Napierian logarithms of the quotients of 100,000 divided by the first -ten numbers, then proceeding by the quotients of every ten to 100, and -by hundreds to 100,000. In the supplement published the following year, -is a curious notice of the manner in which this subtle contrivance was -at first received: "In the year 1621, when I had gone into Upper -Austria, and had conferred everywhere with those skilled in mathematics, -on the subject of Napier's logarithms, I found that those whose prudence -had increased, and whose readiness had diminished, through age, were -hesitating whether to adopt this new sort of numbers, instead of a table -of sines; because they said it was disgraceful to a professor of -mathematics to exult like a child at some compendious method of working, -and meanwhile to admit a form of calculation, resting on no legitimate -proof, and which at some time might entangle us in error, when we least -feared it. They complained that Napier's demonstration rested on a -fiction of geometrical motion, too loose and slippery for a sound method -of reasonable demonstration to be founded on it.[200] "This led me -forthwith to conceive the germ of a legitimate demonstration, which -during that same winter I attempted, without reference to lines or -motion, or flow, or any other which I may call sensible quality. - -"Now to answer the question; what is the use of logarithms? Exactly what -ten years ago was announced by their author, Napier, and which may be -told in these words.--Wheresoever in common arithmetic, and in the Rule -of Three, come two numbers to be multiplied together, there the sum of -the logarithms is to be taken; where one number is to be divided by -another, the difference; and the number corresponding to this sum or -difference, as the case may be, will be the required product or -quotient. This, I say, is the use of logarithms. But in the same work in -which I gave the demonstration of the principles, I could not satisfy -the unfledged arithmetical chickens, greedy of facilities, and gaping -with their beaks wide open, at the mention of this use, as if to bolt -down every particular gobbet, till they are crammed with my -precepticles." - -The year 1622 was marked by the catastrophe of a singular adventure -which befell Kepler's mother, Catharine, then nearly seventy years old, -and by which he had been greatly harassed and annoyed during several -years. From her youth she had been noted for a rude and passionate -temper, which on the present occasion involved her in serious -difficulties. One of her female acquaintance, whose manner of life had -been by no means unblemished, was attacked after a miscarriage by -violent headaches, and Catharine, who had often taken occasion to sneer -at her notorious reputation, was accused with having produced these -consequences, by the administration of poisonous potions. She repelled -the charge with violence, and instituted an action of scandal against -this person, but was unlucky (according to Kepler's statement) in the -choice of a young doctor, whom she employed as her advocate. Considering -the suit to be very instructive, he delayed its termination during five -years, until the judge before whom it was tried was displaced. He was -succeeded by another, already indisposed against Catharine Kepler, who -on some occasion had taunted him with his sudden accession to wealth -from a very inferior situation. Her opponent, aware of this advantage, -turned the tables on her, and in her turn became the accuser. The end -of the matter was, that in July, 1620, Catharine was imprisoned, and -condemned to the torture. Kepler was then at Linz, but as soon as he -learned his mother's danger, hurried to the scene of trial. He found the -charges against her supported only by evidence which never could have -been listened to, if her own intemperate conduct had not given advantage -to her adversaries. He arrived in time to save her from the question, -but she was not finally acquitted and released from prison till November -in the following year. Kepler then returned to Linz, leaving behind him -his mother, whose spirit seemed in no degree broken by the unexpected -turn in the course of her litigation. She immediately commenced a new -action for costs and damages against the same antagonist, but this was -stopped by her death, in April 1622, in her seventy-fifth year. - -In 1620 Kepler was visited by Sir Henry Wotton, the English ambassador -at Venice, who finding him, as indeed he might have been found at every -period of his life, oppressed by pecuniary difficulties, urged him to go -over to England, where he assured him of a welcome and honourable -reception; but Kepler could not resolve upon the proposed journey, -although in his letters he often returned to the consideration of it. In -one of them, dated a year later, he says, "The fires of civil war are -raging in Germany--they who are opposed to the honour of the empire are -getting the upper hand--everything in my neighbourhood seems abandoned -to flame and destruction. Shall I then cross the sea, whither Wotton -invites me? I, a German? a lover of firm land? who dread the confinement -of an island? who presage its dangers, and must drag along with me my -little wife and flock of children? Besides my son Louis, now thirteen -years old, I have a marriageable daughter, a two-year old son by my -second marriage, an infant daughter, and its mother but just recovering -from her confinement." Six years later, he says again,--"As soon as the -Rudolphine Tables are published, my desire will be to find a place where -I can lecture on them to a considerable assembly; if possible, in -Germany; if not, why then in Italy, France, the Netherlands, or England, -provided the salary is adequate for a traveller." - -In the same year in which he received this invitation an affront was put -upon Kepler by his early patrons, the States of Styria, who ordered all -the copies of his "Calendar," for 1624, to be publicly burnt. Kepler -declares that the reason of this was, that he had given precedence in -the title-page to the States of Upper Ens, in whose service he then was, -above Styria. As this happened during his absence in Wirtemberg, it was -immediately coupled by rumour with his hasty departure from Linz: it was -said that he had incurred the Emperor's displeasure, and that a large -sum was set upon his head. At this period Matthias had been succeeded by -Ferdinand III., who still continued to Kepler his barren title of -imperial mathematician. - -In 1624 Kepler went to Vienna, in the hopes of getting money to complete -the Rudolphine Tables, but was obliged to be satisfied with the sum of -6000 florins and with recommendatory letters to the States of Suabia, -from whom he also collected some money due to the emperor. On his return -he revisited the University of Tubingen, where he found his old -preceptor, Maestlin, still alive, but almost worn out with old age. -Maestlin had well deserved the regard Kepler always appears to have -entertained for him; he had treated him with great liberality whilst at -the University, where he refused to receive any remuneration for his -instruction. Kepler took every opportunity of shewing his gratitude; -even whilst he was struggling with poverty he contrived to send his old -master a handsome silver cup, in acknowledging the receipt of which -Maestlin says,--"Your mother had taken it into her head that you owed me -two hundred florins, and had brought fifteen florins and a chandelier -towards reducing the debt, which I advised her to send to you. I asked -her to stay to dinner, which she refused: however, we handselled your -cup, as you know she is of a thirsty temperament." - -The publication of the Rudolphine Tables, which Kepler always had so -much at heart, was again delayed, notwithstanding the recent grant, by -the disturbances arising out of the two parties into which the -Reformation had divided the whole of Germany. Kepler's library was -sealed up by desire of the Jesuits, and nothing but his connexion with -the Imperial Court secured to him his own personal indemnity. Then -followed a popular insurrection, and the peasantry blockaded Linz, so -that it was not until 1627 that these celebrated tables finally made -their appearance, the earliest calculated on the supposition that the -planets move in elliptic orbits. Ptolemy's tables had been succeeded by -the "Alphonsine," so called from Alphonso, King of Castile, who, in the -thirteenth century, was an enlightened patron of astronomy. After the -discoveries of Copernicus, these again made way for the Prussian, or -Prutenic tables, calculated by his pupils Reinhold and Rheticus. These -remained in use till the observations of Tycho Brahe showed their -insufficiency, and Kepler's new theories enabled him to improve upon -them. The necessary types for these tables were cast at Kepler's own -expense. They are divided into four parts, the first and third -containing a variety of logarithmic and other tables, for the purpose of -facilitating astronomical calculations. In the second are tables of the -elements of the sun, moon, and planets. The fourth gives the places of -1000 stars as determined by Tycho, and also at the end his table of -refractions, which appears to have been different for the sun, moon, and -stars. Tycho Brahe assumed the horizontal refraction of the sun to be 7' -30'', of the moon 8', and of the other stars 3'. He considered all -refraction of the atmosphere to be insensible above 45 deg. of altitude, and -even at half that altitude in the case of the fixed stars. A more -detailed account of these tables is here obviously unsuitable: it will -be sufficient to say merely, that if Kepler had done nothing in the -course of his whole life but construct these, he would have well earned -the title of a most useful and indefatigable calculator. - -Some copies of these tables have prefixed to them a very remarkable map, -divided by hour lines, the object of which is thus explained:-- - -"The use of this nautical map is, that if at a given hour the place of -the moon is known by its edge being observed to touch any known star, or -the edges of the sun, or the shadow of the earth; and if that place -shall (if necessary) be reduced from apparent to real by clearing it of -parallax; and if the hour at Uraniburg be computed by the Rudolphine -tables, when the moon occupied that true place, the difference will show -the observer's meridian, whether the picture of the shores be accurate -or not, for by this means it may come to be corrected." - -This is probably one of the earliest announcements of the method of -determining longitudes by occultations; the imperfect theory of the moon -long remained a principal obstacle to its introduction in practice. -Another interesting passage connected with the same object may be -introduced here. In a letter to his friend Cruger, dated in 1616, Kepler -says: "You propose a method of observing the distances of places by -sundials and automata. It is good, but needs a very accurate practice, -and confidence in those who have the care of the clocks. Let there be -only one clock, and let it be transported; and in both places let -meridian lines be drawn with which the clock may be compared when -brought. The only doubt remaining is, whether a greater error is likely -from the unequal tension in the automaton, and from its motion, which -varies with the state of the air, or from actually measuring the -distances. For if we trust the latter, we can easily determine the -longitudes by observing the differences of the height of the pole." - -In an Appendix to the Rudolphine Tables, or, as Kepler calls it, "an -alms doled out to the nativity casters," he has shown how they may use -his tables for their astrological predictions. Everything in his hands -became an allegory; and on this occasion he says,--"Astronomy is the -daughter of Astrology, and this modern Astrology, again, is the daughter -of Astronomy, bearing something of the lineaments of her grandmother; -and, as I have already said, this foolish daughter, Astrology, supports -her wise but needy mother, Astronomy, from the profits of a profession -not generally considered creditable." - -Soon after the publication of these tables, the Grand Duke of Tuscany -sent him a golden chain; and if we remember the high credit in which -Galileo stood at this time in Florence, it does not seem too much to -attribute this honourable mark of approbation to his representation of -the value of Kepler's services to astronomy. This was soon followed by a -new and final change in his fortunes. He received permission from the -emperor to attach himself to the celebrated Duke of Friedland, Albert -Wallenstein, one of the most remarkable men in the history of that -time. Wallenstein was a firm believer in astrology, and the reception -Kepler experienced by him was probably due, in great measure, to his -reputation in that art. However that may be, Kepler found in him a more -munificent patron than any one of his three emperors; but he was not -destined long to enjoy the appearance of better fortune. Almost the last -work which he published was a commentary on the letter addressed, by the -missionary Terrentio, from China, to the Jesuits at Ingolstadt. The -object of this communication was to obtain from Europe means for -carrying into effect a projected scheme for improving the Chinese -calendar. In this essay Kepler maintains the opinion, which has been -discussed with so much warmth in more modern times, that the pretended -ancient observations of the Chinese were obtained by computing them -backwards from a much more recent date. Wallenstein furnished him with -an assistant for his calculations, and with a printing press; and -through his influence nominated him to the professorship in the -University of Rostoch, in the Duchy of Mecklenburg. His claims on the -imperial treasury, which amounted at this time to 8000 crowns, and which -Ferdinand would gladly have transferred to the charge of Wallenstein, -still remained unsatisfied. Kepler made a last attempt to obtain them at -Ratisbon, where the imperial meeting was held, but without success. The -fatigue and vexation occasioned by his fruitless journey brought on a -fever, which unexpectedly put an end to his life, in the early part of -November, 1630, in his fifty-ninth year. His old master, Maestlin, -survived him for about a year, dying at the age of eighty-one. - -Kepler left behind him two children by his first wife, Susanna and -Louis; and three sons and two daughters, Sebald, Cordelia, Friedman, -Hildebert, and Anna Maria, by his widow. Susanna married, a few months -before her father's death, a physician named Jacob Bartsch, the same who -latterly assisted Kepler in preparing his "Ephemeris." He died very -shortly after Kepler himself. Louis studied medicine, and died in 1663, -whilst practising as a physician at Konigsberg. The other children died -young. - -Upon Kepler's death the Duke of Friedland caused an inventory to be -taken of his effects, when it appeared that near 24,000 florins were due -to him, chiefly on account of his salary from the emperor. His daughter -Susanna, Bartsch's widow, managed to obtain a part of these arrears by -refusing to give up Tycho Brahe's observations till her claims were -satisfied. The widow and younger children were left in very straightened -circumstances, which induced Louis, Kepler's eldest son, to print, for -their relief, one of his father's works, which had been left by him -unpublished. It was not without much reluctance, in consequence of a -superstitious feeling which he did not attempt to conceal or deny. -Kepler himself, and his son-in-law, Bartsch, had been employed in -preparing it for publication at the time of their respective deaths; and -Louis confessed that he did not approach the task without apprehension -that he was incurring some risk of a similar fate. This little rhapsody -is entitled a "Dream on Lunar Astronomy;" and was intended to illustrate -the appearances which would present themselves to an astronomer living -upon the moon. - -The narrative in the dream is put into the mouth of a personage, named -Duracoto, the son of an Icelandic enchantress, of the name of -Fiolxhildis. Kepler tells us that he chose the last name from an old map -of Europe in his house, in which Iceland was called Fiolx: Duracoto -seemed to him analogous to the names he found in the history of -Scotland, the neighbouring country. Fiolxhildis was in the habit of -selling winds to mariners, and used to collect herbs to use in her -incantations on the sides of Mount Hecla, on the Eve of St. John. -Duracoto cut open one of his mother's bags, in punishment of which she -sold him to some traders, who brought him to Denmark, where he became -acquainted with Tycho Brahe. On his return to Iceland, Fiolxhildis -received him kindly, and was delighted with the progress he had made in -astronomy. She then informed him of the existence of certain spirits, or -demons, from whom, although no traveller herself, she acquired a -knowledge of other countries, and especially of a very remarkable -country, called Livania. Duracoto requesting further information, the -necessary ceremonies were performed for invoking the demon; Duracoto and -his mother enveloped their heads in their clothing, and presently "the -screaking of a harsh dissonant voice began to speak in the Icelandic -tongue." The island of Livania is situated in the depths of ether, at -the distance of about 250000 miles; the road thence or thither is very -seldom open, and even when it is passable, mankind find the journey a -most difficult and dangerous one. The demon describes the method -employed by his fellow spirits to convey such travellers as are thought -fit for the undertaking: "We bring no sedentary people into our company, -no corpulent or delicate persons; but we pick out those who waste their -life in the continual use of post-horses, or who sail frequently to the -Indies; who are accustomed to live upon biscuit, garlic, dried fish, and -such abominable feeding. Those withered old hags are exactly fit for us, -of whom the story is familiar that they travel immense distances by -night on goats, and forks, and old petticoats. The Germans do not suit -us at all; but we do not reject the dry Spaniards." This extract will -probably be sufficient to show the style of the work. The inhabitants of -Livania are represented to be divided into two classes, the Privolvans -and Subvolvans, by whom are meant those supposed to live in the -hemisphere facing the earth, which is called the Volva, and those on the -opposite half of the moon: but there is nothing very striking in the -account given of the various phenomena as respects these two classes. In -some notes which were added some time after the book was first written, -are some odd insights into Kepler's method of composing. Fiolxhildis had -been made to invoke the daemon with twenty-one characters; Kepler -declares, in a note, that he cannot remember why he fixed on this -number, "except because that is the number of letters in _Astronomia -Copernicana_, or because there are twenty-one combinations of the -planets, two together, or because there are twenty-one different throws -upon two dice." The dream is abruptly terminated by a storm, in which, -says Kepler, "I suddenly waked; the Demon, Duracoto, and Fiolxhildis -were gone, and instead of their covered heads, I found myself rolled up -among the blankets." - -Besides this trifle, Kepler left behind him a vast mass of unpublished -writings, which came at last into the hands of his biographer, Hantsch. -In 1714, Hantsch issued a prospectus for publishing them by -subscription, in twenty-two folio volumes. The plan met no -encouragement, and nothing was published but a single folio volume of -letters to and from Kepler, which seem to have furnished the principal -materials for the memoir prefixed to them. After various unavailing -attempts to interest different learned bodies in their appearance, the -manuscripts were purchased for the library at St. Petersburg, where -Euler, Lexell, and Kraft, undertook to examine them, and select the most -interesting parts for publication. The result of this examination does -not appear. - -Kepler's body was buried in St. Peter's churchyard at Ratisbon, and a -simple inscription was placed on his tombstone. This appears to have -been destroyed not long after, in the course of the wars which still -desolated the country. In 1786, a proposal was made to erect a marble -monument to his memory, but nothing was done. Kaestner, on whose -authority it is mentioned, says upon this, rather bitterly, that it -matters little whether or not Germany, having almost refused him bread -during his life, should, a century and a half after his death, offer him -a stone. - -Delambre mentions, in his History of Astronomy, that this design was -resumed in 1803 by the Prince Bishop of Constance, and that a monument -has been erected in the Botanical Garden at Ratisbon, near the place of -his interment. It is built in the form of a temple, surmounted by a -sphere; in the centre is placed a bust of Kepler, in Carrara marble. -Delambre does not mention the original of the bust; but says it is not -unlike the figure engraved in the frontispiece of the Rudolphine Tables. -That frontispiece consists of a portico of ten pillars, supporting a -cupola covered with astronomical emblems. Copernicus, Tycho Brahe, -Ptolemy, Hipparchus, and other astronomers, are seen among them. In one -of the compartments of the common pedestal is a plan of the observatory -at Uraniburg; in another, a printing press; in a third is the figure of -a man, meant for Kepler, seated at a table. He is identified by the -titles of his works, which are round him; but the whole is so small as -to convey very little idea of his figure or countenance. The only -portrait known of Kepler was given by him to his assistant Gringallet, -who presented it to Bernegger; and it was placed by the latter in the -library at Strasburg. Hantsch had a copy taken for the purpose of -engraving it, but died before it was completed. A portrait of Kepler is -engraved in the seventh part of Boissard's Bibliotheca Chalcographica. -It is not known whence this was taken, but it may, perhaps, be a copy of -that which was engraved by desire of Bernegger in 1620. The likeness is -said not to have been well preserved. "His heart and genius," says -Kaestner, "are faithfully depicted in his writings; and that may console -us, if we cannot entirely trust his portrait." In the preceding pages, -it has been endeavoured to select such passages from his writings as -might throw the greatest light on his character, with a subordinate -reference only to the importance of the subjects treated. In conclusion, -it may be well to support the opinion which has been ventured on the -real nature of his triumphs, and on the danger of attempting to follow -his method in the pursuit of truth, by the judgment pronounced by -Delambre, as well on his failures as on his success. "Considering these -matters in another point of view, it is not impossible to convince -ourselves that Kepler may have been always the same. Ardent, restless, -burning to distinguish himself by his discoveries, he attempted -everything; and having once obtained a glimpse of one, no labour was too -hard for him in following or verifying it. All his attempts had not the -same success, and, in fact, that was impossible. Those which have failed -seem to us only fanciful; those which have been more fortunate appear -sublime. When in search of that which really existed, he has sometimes -found it; when he devoted himself to the pursuit of a chimera, he could -not but fail; but even there he unfolded the same qualities, and that -obstinate perseverance that must triumph over all difficulties but those -which are insurmountable."[201] - - -_List of Kepler's published Works._ - - Ein Calender _Gratz_, 1594 - Prodromus Dissertat. Cosmograph. _Tubingae_, 1596, 4to. - De fundamentis Astrologiae _Pragae_, 1602, 4to. - Paralipomena ad Vitellionem _Francofurti_, 1604, 4to. - Epistola de Solis deliquio 1605 - De stella nova _Pragae_, 1606, 4to. - Vom Kometen _Halle_, 1608, 4to. - Antwort an Roeslin _Pragae_, 1609, 4to. - Astronomia Nova _Pragae_, 1609, fol. - Tertius interveniens _Frankfurt_, 1610, 4to. - Dissertatio cum Nuncio Sidereo _Francofurti_, 1610, 4to. - Strena, seu De dive sexangula _Frankfurt_, 1611, 4to. - Dioptrica _Francofurti_, 1611, 4to. - Vom Geburts Jahre des Heylandes _Strasburg_, 1613, 4to. - Respons. ad epist S. Calvisiii _Francofurti_, 1614, 4to. - Eclogae Chronicae _Frankfurt_, 1615, 4to. - Nova Stereometria _Lincii_, 1615, 4to. - Ephemerides 1617-1620 _Lincii_, 1616, 4to. - Epitomes Astron. Copern. Libri i. ii. iii. _Lentiis_, 1618, 8vo. - De Cometis _Aug. Vindelic._ 1619, 4to. - Harmonice Mundi _Lincii_, 1619, fol. - Kanones Pueriles _Ulmae_, 1620 - Epitomes Astron. Copern. Liber iv. _Lentiis_, 1622, 8vo. - Epitomes Astron. Copern. Libri v. vi. vii. _Francofurti_, 1622, 8vo. - Discurs von der grossen Conjunction _Linz._ 1623, 4to. - Chilias Logarithmorum _Marpurgi_, 1624, fol. - Supplementum _Lentiis_, 1625, 4to. - Hyperaspistes _Francofurti_, 1625, 8vo. - Tabulae Rudolphinae _Ulmae_, 1627, fol. - Resp. ad epist. J. Bartschii _Sagani_, 1629, 4to. - De anni 1631 phaenomenis _Lipsae_, 1629, 4to. - Terrentii epistolium cum commentatiuncula _Sagani_, 1630, 4to. - Ephemerides. _Sagani_, 1630, 4to. - - Somnium _Francofurti_, 1634, 4to. - Tabulae mannales _Argentorati_, 1700, 12mo. - - -FOOTNOTES: - -[199] The meaning of this passage is not very clear: Kepler evidently -had seen and used logarithms at the time of writing this letter; yet -there is nothing in the method to justify this expression,--"_At tamen -opus est ipsi Tangentium canone._" - -[200] This was the objection originally made to Newton's "Fluxions," and -in fact, Napier's idea of logarithms is identical with that method of -conceiving quantities. This may be seen at once from a few of his -definitions, - - 1 Def. A line is said to increase uniformly, when the point by which - it is described passes through equal intervals, in equal times. - - 2 Def. A line is said to diminish to a shorter one proportionally, - when the point passing along it cuts off in equal times segments - proportional to the remainder. - - 6 Def. The logarithm of any sine is the number most nearly denoting - the line, which has increased uniformly, whilst the radius has - diminished to that sine proportionally, the initial velocity being - the same in both motions. (Mirifici logarithmorum canonis - descriptio, Edinburgi 1614.) - -This last definition contains what we should now call the differential -equation between a number and the logarithm of its reciprocal. - -[201] Histoire del'Astronomie Moderne, Paris, 1821. - - - - -Transcriber's Notes. - -Corrections. - -The first line indicates the original, the second the correction. - - -Life of Galileo Galilei - -p. 20: - - success very inadeqnate to the zeal - success very inadequate to the zeal - -p. 20: - - "New method of Guaging, - "New method of Gauging, - -p. 23: - - the knowlege, if it existed - the knowledge, if it existed - -p. 30, note: - - to represent terrestial objects correctly. - to represent terrestrial objects correctly. - -p. 64: - - the palace of the Archishop Piccolomini - the palace of the Archbishop Piccolomini - -p. 68: - - that ladies ringlets - that ladies' ringlets - -p. 69: - - For hitherto I have never happened to see the terrestial earth - For hitherto I have never happened to see the terrestrial earth - -p. 106: - - 80 1 50, _for_ any _read_ an indefinitely small. - 80 2 44, _for_ any _read_ an indefinitely small. - - -Life of Kepler - -p. 6: - - Now, inscribe in the Earth an icosaedron, the circle inscribed in it - will be Venus. - - Now, inscribe in the Earth an icosahedron, the circle inscribed in - it will be Venus. - - Inscribe an octaedron in Venus, the circle inscribed in it will be - Mercury. - - Inscribe an octahedron in Venus, the circle inscribed in it will be - Mercury. - -p. 32: - - Butthere are no such means - But there are no such means - -p. 48: - - the compound ratio of the rectangle of the axes directly, and - subduplicatly - - the compound ratio of the rectangle of the axes directly, and - subduplicately - -p. 52: - - and was in-intended to illustrate the appearances - and was intended to illustrate the appearances - - - - - - -End of the Project Gutenberg EBook of The Life of Galileo Galilei, with -Illustrations of the Advancement of Experimental Philosophy, by John Elliot Drinkwater Bethune - -*** END OF THIS PROJECT GUTENBERG EBOOK THE LIFE OF GALILEO GALILEI *** - -***** This file should be named 43877.txt or 43877.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/3/8/7/43877/ - -Produced by David Garcia, Bryan Ness, Eleni Christofaki -and the Online Distributed Proofreading Team at -http://www.pgdp.net - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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