THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 PRESENTED BY 
 
 PROF. CHARLES A. KOFOID AND 
 MRS. PRUDENCE W. KOFOID 
 

THE 
 
 LIFE 
 
 OF 
 
 GALILEO GALILEI, 
 
 WITH 
 
 ILLUSTRATIONS OF THE ADVANCEMENT 
 
 OF 
 
 EXPERIMENTAL PHILOSOPHY. 
 
 
 MDCCCXXX. 
 
 LONDON. 
 
GIFT 
 
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 acquire- 
 ments of eastern nations at a remote 
 period, it is certain that some among 
 the early Greeks were in possession of 
 several truths, however acquired, con- 
 nected with the economy of the universe, 
 which were afterwards suffered to fall 
 into neglect and oblivion. But the phi- 
 losophers of the old school appear in 
 general to have confined themselves at 
 the best to observations ; very few traces 
 remain of their having instituted experi- 
 ments, properly so called. This putting 
 of nature to the tor.ture, as Bacon calls 
 it, has occasioned the principal part of 
 modern philosophical discoveries. The 
 experimentalist may so order his exami- 
 nation of nature as to vary at pleasure 
 the circumstances in which it is made, 
 often to discard accidents which com- 
 plicate the general appearances, and 
 at once to bring any theory which he 
 may form to a decisive test. The pro- 
 vince of the mere observer is necessarily 
 limited : the power of selection among 
 the phenomena to be presented is in 
 great measure denied to him, arid he 
 may consider himself fortunate if they 
 are such as to lead him readily to a 
 knowledge of the laws which they fol- 
 low. 
 
 Perhaps to this imperfection of me- 
 thod 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 cen- 
 turies 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 insu- 
 lated facts, such as might first happen 
 
 to be noticed, often inaccurately ob- 
 served and always too hastily general- 
 ized, were found sufficient to excite the 
 naturalist's lively imagination ; and hav- 
 ing once pleased his fancy with the sup- 
 posed fitness of his artificial scheme, 
 his perverted ingenuity was thencefor- 
 ward 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 cor- 
 recting 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 benefi- 
 cent design in the structure of the uni- 
 verse, so much as for the fertile topics 
 which the favourite mode of viewing the 
 subject supplied to the spirit of scholas- 
 tic disputation : and it is a humiliating 
 reflection that mankind never reasoned 
 so ill as when they most professed to 
 cultivate the art of reasoning. How- 
 ever specious the objects, and alluring 
 the announcements of this art, the then 
 prevailing manner ot studying it curbed 
 and corrupted all that is free and noble 
 in the human mind. Innumerable falla- 
 cies lurked every where among the 
 most generally received opinions, and 
 crowds of dogmatic and self-sufficient 
 pedants fully justified the lively defini- 
 tion, that " logic is the art of talking un- 
 intelligibly on things of which we are 
 ignorant."* 
 
 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 ab- 
 surd to begin with the effect instead of 
 the cause ; whereas the real choice lay 
 between proceeding from particular facts 
 
 * Menage. 
 
 M8797'77 
 
GALILEO. 
 
 to general facts, or from general facts 
 to particular facts ; and it was under 
 this misrepresentation of the real ques- 
 tion 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 phe- 
 nomena, 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 in- 
 vestigation 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 coun- 
 try, to name Bacon as the founder of 
 the present school of experimental phi- 
 losophy ; we speak of the Baconian or 
 inductive method of reasoning as syno- 
 nimous 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 com- 
 parison 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 con- 
 stantly 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. Dis- 
 cussing 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 pre- 
 sent, 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 phi- 
 losophy : 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 posi- 
 tive disdain the system of Copernicus: 
 the latter fortified it with new proofs 
 derived both from reason and the 
 senses."* 
 
 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 indis- 
 putable. The fate of the two writers is 
 directly opposed the one to the other ; 
 Bacon's works seem te 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 inde- 
 pendently 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 coun- 
 trymen 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 ce- 
 lebrated universities, and were busily en- 
 gaged 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 influ- 
 ence of Galileo's example. Unlike Ba- 
 con's, his reputation, and the value of 
 his writings, were higher among his 
 contemporaries than they have since be- 
 come. This judgment perhaps awards 
 the highest intellectual prize to him 
 whose disregarded services rise in esti- 
 mation with the advance of knowledge ; 
 but the praise due to superior usefulness 
 belongs to him who succeeded in train- 
 ing round him a school of imitators, 
 and thereby enabled his imitators to 
 surpass himself. 
 
 The biography of men who have de- 
 voted themselves to philosophical pur- 
 suits seldom affords so various and stri- 
 king a succession of incidents as that 
 
 * Hume's England, James I. 
 
GALILEO. 
 
 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 labora- 
 tory supplies but scanty materials for 
 personal details ; and the lapse of time 
 rapidly removes from us the opportuni- 
 ties 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 suc- 
 ceeding 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 trans- 
 ferred 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 in- 
 sipid 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 pe- 
 ripatetics 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 throwaaway, 
 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 magnifi- 
 cent philosophy, never to be overthrown, 
 that will empirically and sensibly can- 
 vass 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."* 
 
 CHAPTER II. 
 
 Galileo 's Birth Family Education 
 Observation of the Pendulum Pul- 
 silogies Hydrostatical Balance 
 Lecturer at Pisa. 
 
 GALILEO GALILEI was born at Pisa, on 
 the 15th day ot February, 1564, of a noble 
 
 * Power's Experimental Philosophy, 1663, 
 
 and ancient Florentine family, which, 
 in the middle of the fourteenth century, 
 adopted this surname instead of Bona- 
 juti, under which several of their an- 
 cestors filled distinguished offices in the 
 Florentine state. Some misapprehen- 
 sion has occasionally existed, in conse- 
 quence 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 Ita- 
 lian custom ; just as Sanzio, Buonarotti, 
 Sarpi, Reni, Vecelli, are universally 
 known by their Christian names of Ra- 
 phael, Michel Angelo, Fra Paolo, Gui- 
 do, 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 inspec- 
 tion 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.* 
 
 His father, Vmcenzo Galilei, was a 
 man of considerable talent and learning, 
 with a competent knowledge of mathe- 
 matics, 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 pas- 
 sage 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 ar- 
 gument 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 adula- 
 tion, 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 
 
 * Erythraeus, Pinacotheca, vol. i. ; Salusbury's 
 Life of Galileo. Nelli, Vita di Gal. Galilei. 
 13 2 
 
GALILEO. 
 
 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, Vir- 
 ginia, and Livia. After Vincenzo's death 
 the chief support of the family devolved 
 upon Galileo, who seems to have as- 
 sisted 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 ad- 
 vantageous 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 Ihis 
 letter in a convent, the last expression 
 seems to denote that she had been 
 destined to take the veil. This pro- 
 posed 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 Bellos- 
 guardo. Michel Angelo is probably the 
 same brother of Galileo who is men- 
 tioned by Liceti as having communi- 
 cated from Germany some observations 
 on natural history.* 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 
 
 * De his quae diu vivunt, Patavii, 1612. 
 
 he was then living. These two were 
 then the only survivors of Michel An- 
 gelo'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 in- 
 genious toys and models of machinery, 
 supplying the deficiencies of his infor- 
 mation from the resources of his own 
 invention ; and he conciliated the uni- 
 versal 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 bur- 
 dened with a large family, and was 
 unable to provide expensive instructors 
 for his son ; but. Galileo's own ener- 
 getic industry rapidly supplied the want 
 of better opportunities ; and he acquired, 
 under considerable disadvantages, the 
 ordinary rudiments of a classical educa- 
 tion, 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, espe- 
 cially 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 scru- 
 ple to own publicly their deference to 
 young Galileo's criticism. 
 
 When he had reached his nineteenth 
 year, his father, becomingdailymore sen- 
 sible 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 
 
GALILEO. 
 
 he should adopt the profession of me- 
 dicine. In the matriculation lists at Pisa, 
 he is styled Galileo, the son of Vincenzo 
 Galilei, a Florentine, Scholar in Arts. 
 It is dated 5th November, 1581. Vi- 
 viani, his pupil, friend, and panegy- 
 rist, 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 lis- 
 tened to the dogmas of the Aristote- 
 lian 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 irrecon- 
 cileable with the mental quietude of 
 his instructors, whose philosophic 
 doubts, when they ventured to entertain 
 any, were speedily lulled by a quota- 
 tion from Aristotle. Galileo thought 
 himself capable of giving the world 
 an example of a sounder and more 
 original mode of thinking; he felt him- 
 self destined to be the founder of a new 
 school of rational and experimental 
 philosophy. Of this we are now se- 
 curely enjoying the benefits ; and it 
 is difficult at this time fully to appre- 
 ciate the obstacles which then pre- 
 sented themselves to free inquiry : but 
 we shall see, in the course of this nar- 
 rative, how arduous their struggle was 
 who happily effected this important re- 
 volution. The vindictive rancour with 
 which the partisans of the old phi- 
 losophy 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 disco- 
 very, to the superficial observer appa- 
 rently 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 em- 
 ployed for measuring time were very 
 imperfect : Galileo attempted to bring 
 his observation to the test before quit- 
 ting the church, by comparing the vi- 
 brations with the beatings of his own 
 pulse, and his mind being then princi- 
 pally employed upon his intended pro- 
 fession, it occurred to him, when he had 
 further satisfied himself of their regula- 
 rity by repeated and varied experiments, 
 that the process he at first adopted 
 might be reversed, and that an instru- 
 ment 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 pen- 
 dulum 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. 
 
 Santorio, who was professor of medi- 
 cine at Padua, has given representa- 
 tions of four different forms of these 
 
 .TV? 2. i 
 
 7 
 
 =^z:z^f- 
 
 -\ro o ^-rrrrrr^ 
 
 instruments, which he calls pulsilogies, 
 (pulsilogias,) and strongly recommends 
 to medical practitioners.* These instru- 
 ments 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 gather 
 ed up into the hand till the vibrations of 
 the weight coincided with the beatings of 
 the patient's pulse, the length was ascer- 
 tained from the scale, which, of course, 
 if great, indicated a languid, if shorter, 
 a more lively action. In No. 2 the im- 
 provement 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 short- 
 ened by winding upon an axle at the 
 back of the dial-plate. The construc- 
 tion of No. 4, which Santorio claims as 
 his own improvement, is not given, but 
 it is probable that the principal index, 
 by its motion, shitted a weight to differ- 
 ent distances from the point of suspen- 
 sion, and that the period of vibration 
 
 * Comment, in Avicennam. Venetiis, 1625. 
 
GALILEO. 
 
 was still more accurately adjusted by a 
 smaller weight connected with the se- 
 cond 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 Gali- 
 leo's principle to that purpose* ; 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 con- 
 sideration of the invention of pendulum 
 clocks, and the examination of the dif- 
 ferent claims to the honour of their first 
 construction. 
 
 At the time of which we are speaking, 
 Galileo was entirely ignorant of mathe- 
 matics, the study of which was then at a 
 low ebb, not only in Italy, but in every 
 part of Europe. Commandine had re- 
 cently revived a taste for the writings of 
 Euclid and Archimedes, and Vieta Tar- 
 talea 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 incon- 
 siderable exceptions the application of 
 mathematics to the phenomena of na- 
 ture 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 the- 
 ory. His father, fearful lest he should 
 relax his medical studies, refused 
 openly to encourage him in this new 
 pursuit ; but he connived at the instruc- 
 tion 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 pro- 
 fessors 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 veri- 
 fied, began to repent his indirect sanc- 
 tion, and privately requested Ricci to in- 
 vent 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 mathe- 
 matical volumes on which the whole of 
 his time was really employed. His pro- 
 
 * Essai sur les Ouvrages de Leonard da Vinci. 
 Paris, 1797. 
 
 gress soon revealed the tine 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 wri- 
 ters, Galileo proceeded to the study of 
 Archimedes, and, whilst perusing the 
 Hydrostatics of that author, composed 
 his earliest work, an Essay on the Hy- 
 drostatical Balance. In this he explains 
 the method probably adopted by Archi- 
 medes for the solution of Hiero's cele- 
 brated question*, 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 ap- 
 plied 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 disconti- 
 nued these researches on meeting with 
 Lucas Valerie'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 in- 
 troduced him to his brother, the Cardi- 
 nal 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 insigni- 
 ficant sum of sixty crowns annually, but 
 he had an opportunity of greatly adding 
 to his income by private tuition. 
 
 CHAPTER III. 
 
 Galileo at Pisa Aristotle Leonardo 
 da Vinci Galileo becomes a Coper - 
 nican Urstisius Bruno Experi- 
 ments 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 in- 
 creased diligence. He instituted a course 
 
 * See Treatise on HYDROSTATICS. 
 
GALILEO. 
 
 of experiments for the purpose of put- 
 ting to the test the mechanical doctrines 
 of Aristotle, most of which he found un- 
 supported even by the pretence of ex- 
 perience. It is to be regretted that we 
 do not more frequently find detailed his 
 method of experimenting, than occasion- 
 ally 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. Ven- 
 turi has found several unpublished pa- 
 pers 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 au- 
 thority 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 ] 6th century, had condemned 
 Aristotle's philosophy, especially his Phy- 
 sics, in very unequivocal and forcible 
 terms, declaring that, although there 
 were many excellent truths in his wri- 
 tings, the number was scarcely less of 
 false, useless, and ridiculous proposi- 
 tions*. 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. f 
 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 ascer- 
 taining the fact) that Galileo may have 
 been acquainted with Leonardo's inves- 
 tigations, although they remained, till 
 very lately, almost unknown to the ma- 
 thematical world. This supposition is 
 rendered more probable from the fact, 
 that Mazenta, the preserver of Leonardo's 
 manuscripts, was, at the very time of 
 
 * Antibarbarus Philosophicus. Francofurti, 1674. 
 t Speculationum liber. Venetiis, 1585. 
 
 their discovery, a contemporary student 
 with Galileo at Pisa. Kopernik, or, as 
 he is usually called, Copernicus, a na- 
 tive 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 attri- 
 butes 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 re- 
 ferring to any additional sources of in- 
 formation, and in most instances merely 
 transcribing Voss's words, so as to shew 
 indisputably whence they derived their 
 account. Voss himself gives no author- 
 ity, 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 sub- 
 sisted between Maestlin, and his sup- 
 posed pupil, such as in fact we find 
 subsisting between Maestlin and his ac- 
 knowledged pupil Kepler, the devoted 
 friend of Galileo ; but, on the contrary, 
 we find Maestlin writing to Kepler him- 
 self 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 compre- 
 hend 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 Salus- 
 bury, in his life of Galileo, haying appa- 
 rently an imperfect recollection of its 
 tenor, refers to this very passage in con- 
 firmation of Voss's statement. In the 
 second part of the dialogue on the Co- 
 pernican system, Galileo makes Sagredo, 
 one of the speakers in it, give the fol- 
 lowing 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 cer- 
 tain foreigner of Rostoch, whose name, 
 as I remember, was Christianus Ursli- 
 sius, 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 
 
GALILEO. 
 
 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 alto- 
 gether 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 w r hether they were well pos- 
 sessed 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 acute- 
 ness of their wits. On the contrary, of 
 as many of the Peripatetics and Ptole- 
 means as I have asked, (and out of cu- 
 riosity 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 under- 
 stood 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. Where- 
 upon, considering that there was no 
 man who followed the opinion of Coper- 
 nicus 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 con- 
 trary, that there was not one of the follow- 
 ers of Ptolemy that had ever been of the 
 judgment of Copernicus, and had left 
 that to embrace this of Aristotle ; con- 
 sidering, 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 opi- 
 nion 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 him- 
 self, the account cannot refer to him. 
 The circumstance mentioned of the in- 
 termission of his philosophical studies, 
 though in itself trivial, agrees very well 
 with Galileo's original medical destina- 
 tion. 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. In 1568 Voss informs us 
 that he published some new questions on 
 Purbach's Theory of the Planets. He 
 died at Bale in 1588, when Galileo was 
 about twenty-two years old. 
 
 It is not unlikely that Galileo also, in 
 part, owed his emancipation from popu- 
 lar prejudices to the writings of Gior- 
 dano Bruno, an unfortunate man, whose 
 unsparing boldness in exposing fallacies 
 and absurdities was rewarded by a judi- 
 cial murder, and by the character of 
 heretic and infidel, with which his exe- 
 cutioners endeavoured to stigmatize him 
 for the purpose of covering over their 
 own atrocious crime. Bruno was burnt 
 at Home 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 slight- 
 est degree relate. Bruno attacked the 
 fashionable philosophy alternately with 
 reason and ridicule, and numerous pas- 
 sages 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 opi- 
 nions, he believed that the universe con- 
 sisted 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 re- 
 marked 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 re- 
 mote distance from us." He declined 
 asserting that all the apparently fixed 
 stars are really so, considering this as 
 riot sufficiently proved, " because at such 
 enormous distances the motions become 
 difficult to estimate, and it is only by 
 
GALILEO. 
 
 9 
 
 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 them- 
 selves, and heat themselves, and embroil 
 themselves for Aristotle ; they call them- 
 selves 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 dis- 
 believe 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 re- 
 served for later observations to furnish 
 complete verification of his most daring 
 speculations, yet there was enough, ab- 
 stractedly taken, in the wild freedom of 
 his remarks, to attract a mind like Gali- 
 leo'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 Gali- 
 leo'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 
 JEneid 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 experi- 
 ment, either directly in confirmation of 
 it, or tending to show its probability and 
 consistency. We have already seen that 
 
 * De 1'Infinito Universe. Dial. 3. La Cena de le 
 Cenere, 1584. 
 
 he engaged in a series of experiments 
 to investigate the truth of some of Aris- 
 totle's positions. As fast as he suc- 
 ceeded 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 stub- 
 born opposition which he encountered 
 in establishing the truth of his mecha- 
 nical theorems, still more stupidly ab- 
 surd than in the ill will to which, at 
 a later period of his life, his astrono- 
 mical opinions exposed him: it is in- 
 telligible 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 dif- 
 ferent 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 con- 
 sequently this assertion had been long 
 received, upon his word, among the 
 axioms of the science of motion. Gali- 
 leo ventured to appeal from the au- 
 thority of Aristotle to that of his own 
 senses, and maintained that, with the 
 exception of an inconsiderable differ- 
 ence, which he attributed to the dis- 
 proportionate resistance of the air, they 
 would fall in the same time. The Aris- 
 totelians 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 ma- 
 lice of these men soon found the means 
 of making Galileo desirous of quitting 
 
10 
 
 GALILEO. 
 
 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 cleans- 
 ing the port of Leghorn, on the effi- 
 ciency of which Galileo was consulted. 
 His opinion was unfavourable, and the 
 violence of the inventor's disappoint- 
 ment, (for Galileo's judgment was veri- 
 fied by the result,) took the somewhat 
 unreasonable direction of hatred to- 
 wards the man whose penetration had 
 foreseen the failure. Galileo's situation 
 was rendered so unpleasant by the ma- 
 chinations of this person, that he de- 
 cided on accepting overtures elsewhere, 
 which had already been made to him ; 
 accordingly, under the negotiation of his 
 staunch iriend Guido Ubaldi, and with 
 the consent of Ferdinand, he procured 
 from the republic of Venice a nomina- 
 tion for six years to the professorship of 
 mathematics in the university of Padua, 
 whither he removed in September 1592. 
 Galileo's predecessor in the mathe- 
 matical chair at Padua was Moleti, who 
 died in 1588, and the situation had re- 
 mained unfilled during the intervening 
 four years. This seems to show that 
 the directors attributed but little im- 
 portance to the knowledge which it was 
 the professor's duty to impart. This in- 
 ference is strengthened by the fact, that 
 the amount of the annual salary at- 
 tached to it did not exceed 1 80 florins, 
 whilst the professors of philosophy and 
 civil law, in the same university, were 
 rated at. the annual stipends of 1400 
 and 1680 florins.* 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 edu- 
 cation into the hands of their own 
 body.t 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 1C 06, 
 by a second more peremptory, which 
 banished them entirely from the Vene- 
 tian territory. Galileo would of course 
 find his fellow-professors much embit- 
 
 Riccuboni, Comment arii de Gymnasio Patavino, 
 
 
 Nelii. 
 
 tered against ttyat society, and would 
 naturally feel inclined to make common 
 cause with them, so that it is not un- 
 likely 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 cir- 
 culation 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 author- 
 ship 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 resent- 
 ing affronts of this nature ottered 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 ther- 
 mometer. The original idea of this 
 useful instrument belongs to the Greek 
 mathematician Hero; and Santorio him- 
 self, who has been named as the in- 
 ventor by Italian writers, and at one 
 time claimed it himself, refers it to 
 him. In 1633, Castelli wrote to Ce- 
 sarini that " he remembered an experi- 
 ment 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 ves- 
 sel, and Galileo employed this principle 
 in the construction of an instrument for 
 measuring heat and cold."* 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 : " 1 have 
 brought the instrument which you in- 
 vented for measuring heat into several 
 convenient and perfect forms, so that 
 the difference of temperature between 
 two rooms is seen as far as 100 de- 
 
 Nelli. 
 
GALILEO. 
 
 11 
 
 grees."* 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 ^lir, although Galileo did not 
 intend it for this purpose, and when 
 he attempted to determine the relative 
 weight of the air, employed a contri- 
 vance still more imperfect than this rude 
 barometer would have been. A passage 
 among his posthumous fragments inti- 
 mates 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 Gali- 
 leo, and, after the death of his father 
 Cosmo, reigning duke of Florence. It 
 was still further improved by Ferdi- 
 nand'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 
 earty as 1670, on account of its equable 
 expansion.-!* For further details on the 
 history and use of this instrument, the 
 reader may consult the Treatises on the 
 THERMOMETER and PYROMETER. 
 
 CHAPTER IV. 
 
 Astronomy before Copernicus Fracas- 
 tor o Bacon Kepler Galileo 's 
 Treatise on the Sphere. 
 THIS period of Galileo's lectureship at 
 Padua derives interest from its inclu- 
 
 * Venturi. Memurie e Lettere di Gal. Galilei. 
 Modena, 1821. 
 f Prodromo all' Arte Maestra. Brescia, 16?0. 
 
 ding 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 num- 
 ber of those who possess much know- 
 ledge of the cumbrous and unwieldy 
 system which it superseded is perhaps 
 more limited. The present is not a tit 
 .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 in- 
 telligible. 
 
 The earth was supposed to be im- 
 moveably fixed in the centre of the uni- 
 verse, 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 pre- 
 ceding Copernicus, whether the Sun 
 was not nearer the Earth than Mer- 
 cury, or at least than Venus ; and this 
 'question was one on which the astro- 
 nomical theorists were then chiefly 
 divided. 
 
 We possess at this time a curious 
 record of a former belief in this arrange- 
 ment 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 siipposed to exert its influence in 
 succession, reckoning from the most 
 distant down to the nearest, over each 
 hour of the tw r enty-four. The planet 
 which was supposed to predominate 
 over the first hour, gave its name to 
 that day.* 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 be- 
 ginning, 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, 
 
 * Dion Cassius, lib. 3?. 
 
12 
 
 GALILEO. 
 
 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 fol- 
 lowing 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 man- 
 ner the whole week will be found to 
 complete the 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 phir 
 losophers 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 insuf- 
 ficient to account for all the irregu- 
 larities of motion observed, two hy- 
 potheses were introduced. First, that 
 to each planet belonged several con- 
 centric 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 epicy- 
 clical motions, so as to represent with 
 tolerable fidelity the ever varying phe- 
 nomena 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.* Aris- 
 totle'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 mo- 
 tion, with which it is carried about the 
 centre." It might be doubtful, upon 
 this passage alone, whether the Pytha- 
 gorean theory embraced more than the 
 diurnal motion of the earth, but a lit- 
 tle 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."t From 
 
 The pretended translation by Roberval of an 
 Arabic version of Aristarchus, " De Systemate Mun- 
 di," in which the Copernican system is fully deve- 
 loped, is spurious. Menage asserts this in his observa- 
 tions on Diogen. Laert. lib. 8, sec. 85, torn, ii., p. 389. 
 (Kd. Atnst. 169 J.) The commentary contains many 
 authorities well worth consulting. Delambre, His- 
 toire de 1'Astronomie, infers it from its nor 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 Aris- 
 tarchus the credit of havint? known this, and intro- 
 duced 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 apo- 
 gee (or place of greatest distaneefrom 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 equi- 
 noxes. 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 Rol*rval, and he accordingly has introduced 
 the proper value which it had in Aristarchus's time. 
 
 t De Crelo. lib. 2. 
 
GALILEO. 
 
 \vhich, in conjunction with the former 
 extract, it very plainly appears that the 
 Pythagoreans maintained both the diur- 
 nal and annual motions of the earth. 
 
 Some idea of the supererogatory la- 
 bour 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 pass- 
 ing through a thickly planted wood, 
 in how complicated a manner the re- 
 lative positions of the trees appear at 
 each step to be continually changing, 
 and by considering the difficulty with 
 which the laws of their apparent mo- 
 tions could be traced, if we were to 
 attempt to refer these changes to a real 
 motion of the trees instead of the tra- 
 veller. 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 con- 
 tributes to perplex and complicate the 
 general appearances. Accordingly the 
 heavens rapidly became, under this sys- 
 tem, 
 
 " With centric and eccentric scribbled o'er, 
 Cycle and epicycle, orb in orb ;"* 
 
 crossing and penetrating each other 
 in every direction. Maestlin has given 
 a concise enumeration of the prin- 
 cipal orbs which belonged to this 
 theory. After warning the readers that 
 " they are not mere iictions which 
 have nothing to correspond with them 
 out of the imagination, but that they 
 exist really, and bodily in the hea- 
 vens,"i 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 re- 
 volutions, motions of the apogee, and 
 nodes, &c. &c. In what manner this 
 multitude of solid and crystalline orbs 
 were secured from injuring or interfe- 
 ring with each other was not very closely 
 inquired into. 
 
 The reader will cease 1o 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 Fra- 
 
 * Paradise Lost, b. viii. v. 83. 
 
 f Itaque tarn circulosprimi motus quam orbes s-e- 
 cundoruin mobilinm revera in coelesti corpore essecon- 
 cludimus, &c. Non ergo sunt meratigmenta, quibus 
 extra mentem nibil correspondeat. M. Maestlini, 
 De Astronomies Hypothesibu-, disputatio, Heidelbergse, 
 
 castoro, who lived in the sixteenth cen- 
 tury, 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 " rea- 
 soning" which appeared to him so in- 
 controvertible. " The planets are ob- 
 served 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 com- 
 pound 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 hea- 
 vens 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 alto- 
 gether impossible that the stars of them- 
 selves 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 mo- 
 tion 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 him- 
 self 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 
 
14 
 
 GALILEO. 
 
 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 bewjlder them- 
 selves 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 eiforts of 
 matured reason to erase them, and con- 
 sider 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 pe- 
 rusal of his works, every line of which 
 will then increase our admiration of 
 the penetrating acuteness of his inven- 
 tion and unswerving accuracy of his 
 judgment. In almost every page we 
 discover an allusion to some new ex- 
 periment, 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 soundprinciples of induc- 
 tive 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 see.i:s 
 transitory, and to move towards a limit 
 of cessation or rest, and that it may 
 reach some point, and then put off' its 
 motion."* Bacon rejected ail the ma- 
 chinery 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 ab- 
 surdity could have driven theorists to 
 the extravagant supposition of the mo- 
 tion ot the earth, which, said he, " we 
 
 Opusoula Philosophic*, Thema Coeli, 
 
 know to be most false."* Instances of 
 extravagant suppositions and premature 
 generalizations are to be found in al- 
 most every page of his other great con- 
 temporary, Kepler. 
 
 It is with pain that we observe De- 
 lambre taking every opportunity, in his 
 admirable History of Astronomy, to un- 
 dervalue and sneer at Galileo, seem- 
 ingly 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 illus- 
 trious contemporary. Delambre is es- 
 pecially dissatisfied with Galileo, for 
 taking no notice, in his *' System of 
 the World," of the celebrated laws 
 of the planetary motions which Kep- 
 ler discovered, and which are now 
 inseparably connected with his name. 
 The analysis of Newton and his suc- 
 cessors has now identified those ap- 
 parently mysterious laws with the ge- 
 neral phenomena of motion, and has 
 thus entitled them to an attention of 
 which,beforethat 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 disco- 
 vered between the distances of the planets 
 from the sun and the periods of their 
 revolutions around him were neces- 
 sarily to be received as demonstrated 
 truths; and Galileo surely acted most 
 prudently and philosophically in hold- 
 ing himself altogether aloof from Kep- 
 ler's fanciful devices and numeral con- 
 cinnities, although, with all the extra- 
 vagance, they possessed much of the 
 genius of the Platonic reveries, and al- 
 though it did happen that Galileo, by 
 systematically avoiding them, failed to 
 recognise some important truths. Ga- 
 lileo 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 turther 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 
 
 * "Nobis constat falsissiuiu'm esse." De AUK. Sci 
 eat.Ub, m, c.3, 1623. 
 
GALILEO. 
 
 15 
 
 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, how- 
 ever 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 Kep- 
 ler's Mysterium Cosmographicum, " I 
 have as yet read nothing beyond the 
 preface of your book, from which how- 
 ever 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 me- 
 lancholy 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* and by that theory have 
 succeeded in fully explaining many phe- 
 nomena, which on the contrary hypo- 
 thesis 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 ven- 
 ture to publish my speculations; but, 
 since that is not so, I shall lake time to 
 consider of it." This interesting letter 
 was the beginning of the friendship of 
 these two great men, which lasted un- 
 interruptedly till 1632, the date of 
 Kepler's death. That extraordinary ge- 
 nius never omitted an opportunity of 
 testifying his admiration of Galileo, 
 
 * Id autum eo libentius faciam, quod in Copernici 
 sententiam muHis abhinc annis yen erim. Kepi. 
 Epistolae. 
 
 although there were not wanting per- 
 sons envious of their good understand- 
 ing, who exerted themselves to provoke 
 coolness and quarrel between them. 
 Thus Brutlus writes to Kepler in 1602*: 
 " 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 qualifi- 
 cations. 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 ap- 
 pear 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. 
 
 CHAPTER V. 
 
 Galileo re-elected Professor at Padua 
 New star Compass of propor- 
 tion Capra Gilbert Proposals to 
 return to Pisa Lost writings Ca- 
 valieri. 
 
 GALILEO'S reputation was now rapidly 
 increasing: his lectures were attended 
 by many persons of the highest rank ; 
 among whom w r eie the Archduke Fer- 
 dinand, afterwards Emperor of Ger- 
 many, the Landgrave of Hesse, and 
 the Princes of Alsace and Mantua. On 
 the exphrtion 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 aug- 
 mentation is said by Fabronit, to have 
 arisen out of the malice of an ill wisher 
 of Galileo, who, hoping to do him dis- 
 service, 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 in- 
 quire into the morality of his private 
 life, it was probably from a wish to 
 mark their sense of the informer's im- 
 pertinence, 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 Viviam's intimation, 
 towards the thirtieth year of his age, 
 that is to say in 1594, he experienced 
 
 * Kepleri Epistolae. 
 
 j- Vitae Italorum IJlustrium. 
 
GALILEO. 
 
 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 blow- 
 ing 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 ap- 
 petite ; and this painful disorder thence- 
 forward never left him entirely, but re- 
 curred 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 how- 
 ever 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 inRiccioli* a catalogue of the 
 principal new stars which have at dif- 
 ferent times appeared. There is a tra- 
 dition 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 ca- 
 talogue of the stars ; and only thirty-two 
 years before, in 1572, the same remark- 
 able 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 astro- 
 nomy. Tycho's star disappeared at the 
 
 * Alnrtgestuui Nyvuui, vol. i. 
 
 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 em- 
 bodied the results of his observations 
 in three lectures, which have been un- 
 fortunately lost. Only the exordium of 
 the first has been preserved : in this he 
 reproaches his auditors with their ge- 
 neral insensibility to the magnificent 
 wonders of creation daily exposed to 
 their view, in no respect less admirable 
 than the new prodigy, to hear an ex- 
 planation 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 re- 
 mote heavenly bodies. This was in- 
 conceivable to the Aristotelians, whose 
 notions of a perfect, simple, and un- 
 changeable sky were quite at variance 
 with the introduction of any such new 
 body; and we may perhaps consider 
 these lectures as the first public decla- 
 ration 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 in- 
 vented 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 as- 
 tronomical discoveries ; but on this oc- 
 casion, 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 in- 
 strument is of simple construction, con- 
 sisting 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 
 
GALILEO. 
 
 17 
 
 case of mathematical instruments. In- 
 stead of the tri:ono metrical and logarith- 
 mic lines which are now generally en- 
 graved 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 multipli- 
 cations, divisions, and the extraction of 
 roots ; for finding the dimensions of 
 equally heavy balls of different ma- 
 terials, &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 mul- 
 titude 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 diffi- 
 cult to understand on what grounds 
 Salusbury charges Gunter with plagi- 
 arism from Galileo's Compass. He de- 
 clares that he has closely compared the 
 two, and can find no difference between 
 them.* There has also been some con- 
 fusion, 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 po- 
 sitions. 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 inex- 
 cusable error of confounding Galileo's 
 with the Mariner's Compass. He re- 
 fers to a treatise by Hulsius for his 
 authority in attributing the Proportional 
 Compass to Burg, a German astrono- 
 mer 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.f To the description which Ga- 
 lileo published of his compass, he added 
 
 * M.-ith. Coll. vol. ii. 
 
 f Constructio Circini Proportionum. Moguntiae, 
 1605. 
 
 a short treatise on the method of mea- 
 suring 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 Com- 
 pass was of much more importance 
 before the grand discovery of loga- 
 rithms than it can now be considered : 
 however it acquires an additional in- 
 terest from the value which he himself 
 set on it. In 1607, Capra, at the insti- 
 gation 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 Im- 
 postures of Balthasar Capra." His prin- 
 cipal 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 com- 
 mitted on that occasion, to add a com- 
 plete proof of his piracy of the geo- 
 metrical 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 expo- 
 sure, and of the report of the famous 
 Fra Paolo Sarpi, to whom the matter 
 had been referred, was a formal prohi- 
 bition by the university of Capra' s pub- 
 lication, and all copies of the book then 
 on hand were seized, and probably de- 
 stroyed, though Galileo has preserved 
 it from oblivion by incorporating it in 
 his own publication. 
 
 Nearly at the same time, 1607, or im- 
 mediately after, he first turned his atten- 
 tion towards the loadstone, on which our 
 c 
 
18 
 
 GALILEO. 
 
 countryman Gilbert had already pub- 
 lished 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 success- 
 ful. Sir Kenelm Digby* 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 
 
 ? raise, admire, and envy this author ; 
 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, with- 
 out attempting to satisfy themselves of 
 the same by experience, perhaps that 
 they may not dimmish the size of their 
 books." 
 
 Galileo's reputation being now greatly 
 increased, proposals were made to him, 
 in 1609, to return to his original situ- 
 ation at Pisa. He had been in the 
 habit of passing over to Florence du- 
 ring the academic vacation, for the pur- 
 pose of giving mathematical instruc- 
 tion to the younger members of Ferdi- 
 nand'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 Ga- 
 lileo'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 anybody, the 
 little talent which God has granted to 
 my assiduity in my profession, that my 
 wish certainly would be to have suffi- 
 cient rest and leisure to enable me, be- 
 fore my life comes to its close, to conclude 
 three great works which I have in hand, 
 and to publish them ; which might per- 
 haps bring some credit to me, and to 
 those who had favoured me in this 
 undertaking, and possibly may be of 
 
 Treatise of the Nature of Bodies, London, 1665. 
 
 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) never- 
 theless 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 1 am almost certain will be ad- 
 vanced to as many crowns upon my re- 
 election, and these I can greatly increase 
 by receiving pupils, and from private lec- 
 tures, 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 do- 
 mestic 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 coun- 
 try, I should wish the first object of his 
 Serene Highness to be, that leisure and 
 opportunity should be given me to com- 
 plete my works without employing my- 
 self in lecturing. And, in short, I 
 should wish to gain my bread from my 
 writings, which I would always dedi- 
 cate to my Serene Master. The works 
 which I have to finish are principally 
 two books on the system or struc- 
 ture of the Universe, an immense work, 
 full of philosophy, astronomy, and geo- 
 metry ; three books on Local Motion, 
 a science entirely new, no one, either 
 ancient or modern, having discovered 
 any of the very many admirable acci- 
 dents 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 com- 
 position of continuous quantity ; On the 
 
GALILEO. 
 
 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 teach- 
 ing with very exact rules every thing 
 which it is his duty to know that de- 
 pends upon mathematics ; as the know- 
 ledge of castrametation, drawing up 
 battalions, fortifications, assaults, plan- 
 ning, surveying, the knowledge of artil- 
 lery, the use of instruments, &c. I 
 also wish to reprint the ' Use of my Geo- 
 metrical 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 con- 
 vinced that as I am to live upon it, 
 the graciousness of his highness would 
 not deprive me of any of those com- 
 forts, which, however, I feel the want 
 of less than many others ; and there- 
 fore 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 num- 
 ber 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 high- 
 nesses see as often as it shall please 
 them to give me an opportunity of dis- 
 cussing 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 under- 
 value 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 per- 
 haps almost impossible for him to have 
 remained entirely blind to his vast supe- 
 riority 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 sub- 
 mitted to this expurgation. It is also 
 
 supposed that many were burnt by his 
 infatuated grandson Cosimo, who con- 
 ceived he was thus offering a proper 
 and pious sacrifice before devoting him- 
 self to the life of a missionary. A Trea- 
 tise 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 read- 
 ers a compendium of the most approved 
 Erinciples then already known. It has 
 een 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 de- 
 serves notice only from its having been 
 made the subject of controversy. 
 
 The loss of Galileo's Essay on Conti- 
 nuous Quantity is particularly to be 
 regretted, as it. would be highly interest- 
 ing to see how far he succeeded in 
 methodizing his thoughts on this import- 
 ant 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 Indivisi- 
 bles," which is universally recognized as 
 one of the first germs of the powerful 
 methods of modern analysis. Through- 
 out Galileo's works we find many indi- 
 cations of his having thought much on 
 the subject, but his remarks are vague, 
 and bear little, if at all, on the appli- 
 cation 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, sur- 
 faces 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 pro- 
 found view of the subject than is implied 
 in this superficial exposition, and had 
 approached very closely to the appa- 
 rently mure exact theories of his suc- 
 cessors. Anticipating the objections to 
 his hypothesis, he argues, that " there 
 is no necessity to suppose the conti- 
 nuous quantities made up of these in- 
 divisible 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 
 c 2 
 
20 
 
 GALILEO. 
 
 Cavalieri in his " New method of Gua- 
 ging," which is the earliest work with 
 which we are acquainted, where prin- 
 ciples of this sort are employed.* 
 
 CHAPTER VI. 
 
 Invention of the telesccpeFracastoro 
 Porta Reflecting telescope Ro- 
 ger Bacon Digges De Dominis 
 Jans en Lipperhey Galileo con- 
 structs 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 prin- 
 cipal, 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 astro- 
 nomical discoveries; yet Lagrangef 
 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 MpntuclaJ omits an im- 
 portant 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 re- 
 curring, 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 con- 
 tradict, and a strong one to bear down, 
 a party, who, when invited to look on 
 any object in the heavens which Aris- 
 totle had never suspected, immediately 
 refused all credit to those senses, to 
 which, on other occasions, they so confi- 
 dently appealed. It surely is a real 
 and solid part of Galileo's glory that he 
 consumed his life in laborious and inde- 
 fatigable observations, and that he per- 
 severed in announcing his discoveries 
 undisgusted by the invectives, and un- 
 dismayed by the persecutions, to which 
 they subjected him. Plagiarist ! liar ! 
 impostor ! heretic ! were among the ex- 
 pressions 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- 
 
 * Nova Stercometria Doliorum Lincii, 1615. 
 
 + Mecanique Analytiqne. 
 
 $ HUtoire des Matheuiatiques, torn. ii. 
 
 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, arid 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 prac- 
 tice. After the discovery of the tele- 
 scope, 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 promulga- 
 tion of the discovery, as containing the 
 germ of it in their works. These are 
 Baptista Porta, and Gerolamo Fracas - 
 toro. We have already had occasion 
 to quote the Homocentrica of Fracas- 
 toro, who died in 1553 ; the follow- 
 ing 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 ex- 
 plaining and commenting on some phe- 
 nomena 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 rea- 
 son, 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." * It should 
 seem that this passage (asDelambrehas 
 already remarked) rather refers to the 
 close application of one glass upon an- 
 other, and it may fairly be doubted 
 whether any thing 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 
 
 * " Per dno specilla ocularia si quis perspiciat, 
 alteroalteri snperposito, majora multo et propinqniora 
 videtitomnia." Fracast. Homocentrica, *2, c. 8. 
 
GALILEO. 
 
 21 
 
 know rightly how to combine one of 
 each sort, you will see both far and near 
 objects larger and clearer," * These 
 words show, if Porta really was then 
 unacquainted with the telescope, how 
 close it is possible to pass by an inven- 
 tion without lighting on it, for of pre- 
 cisely 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 repu- 
 tation of the invention, but he then pro- 
 fesses 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 prin- 
 ciples, nor is it at all difficult of execu- 
 tion ; 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 in- 
 deed every writer who has hitherto 
 quoted it has merely given the passage 
 in its original Latin, apparently despair. 
 ing of an intelligible translation. With 
 some alterations in the punctuation, 
 which; appear necessary to bring it into 
 any grammatical construction,-}- 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, arid 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 
 
 * Si utrumqne recte componere noveris, et longin- 
 qua et proxima majora et clara videbis. Mag. Nat. 
 lib. 17. 
 
 t The passage in the original, which is printed 
 alike in the editions of 1598, 1607, 16L9, and 1650, is 
 as follows : Visus constituatur centre valentissimus 
 speculi, ubi fief, et valentissime universales solares 
 radii disperguntur, et coeunt minime, sed centro prae- 
 dicti speculi in illius medio, ubi diametri transver- 
 sales, omnium ibi concursus. Constituitur hoc modo 
 speculum concavum columnare sequidistantibus late- 
 ribus, sed lateri uno obliquo sectionibus illis accomo- 
 detur, trianguli vero obtusiauguli, vel orthogonii 
 secentur, hijic inde duobus transversy-libus lineis, ex- 
 centro eductis. Et coijfectum erit speciUum, ad. id, 
 
 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 
 aglass (specillum) will be completed.fit for 
 the purposes we mentioned. 1 ' If it were not 
 for the word " specillum" which, in the 
 passage immediately preceding this, 
 Porta* 1 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 in- 
 strument. It is in the 5th chapter 
 of the 17th book, where Porta explains 
 by what device exceedingly minute let- 
 ters 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 Na- 
 tural Magic, which was published in 
 1611, under his own superintendence; 
 but the English translator of 1(558 
 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 hap- 
 pened 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,t but which contains 
 no allusion to Porta's claim, and pos- 
 sibly Stelliola may have thought it most 
 for his friend's reputation to suppress 
 it. Schott^ says, a friend of his had 
 
 * Diximusde Ptolemaei speculo,sive specillo potius, 
 quo per saxcentena millia pervementes naves conspi : 
 oiebat. ) II Telescopio, itiJj?. 
 
GALILEO. 
 
 seen Porta's book in manuscript, and 
 that it did at that time contain the as- 
 sertion of Porta's title to the invention. 
 After all it is not improbable that he 
 may have derived his notions of mag- 
 nifying distant objects from our cele- 
 brated 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 re- 
 cognised the use of single lenses in 
 producing distinct vision, and he has 
 some expressions with respect to their 
 combination which promise effects ana- 
 logous to those held out by Porta. In 
 " The Admirable Force of Art and Na- 
 ture," 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 
 moanes, 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 incredi- 
 ble 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, be- 
 cause in the first and last of these asser- 
 tions he is, to a certain extent, borne out 
 by facts, that he therefore was in posses- 
 sion 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 Mar- 
 quis of Worcester's Century of Inven- 
 tions) which if we can really persuade 
 ourselves that he was capable of accom- 
 plishing, we must allow the present age 
 to be still immeasurably interior to him 
 in science. 
 
 Thomas Digges, in the preface to 
 his Pantometria, (published in 159 1 ) de- 
 clares, " My father, by his continuall 
 painfull practises, assisted with de- 
 monstrations mathematical!, was able, 
 and sundry times hath by proportional! 
 glasses, duely situate in convenient 
 angles, not only discouered things farre 
 off, read letters, numbered peeces of 
 money, with the verye coyne and super- 
 
 scription 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 im- 
 pertinent to this place." 
 
 We find another pretender to the ho- 
 nour 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 suffi- 
 ciently 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 im- 
 prisoned 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 ac- 
 knowledged invention of the telescope 
 by Galileo ; but Bartolo tells us, in the 
 preface, that the manuscript was com- 
 municated to him from a collection of 
 papers written 20 years before, on his 
 inquiring the Archbishop's opinion with 
 respect to the newly discovered instru- 
 ment, 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 im- 
 probable that he would have suffered 
 an acknowledgment of additions, pre- 
 vious 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 Mon- 
 
GALILEO. 
 
 tucla calls him, conspicuous for igno- 
 rance even among the ignorant men of 
 his age. He gives a drawing of a con- 
 vex 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 re- 
 fracted rays, and to magnify the object 
 by increasing the visible angle under 
 which it is viewed. These, among the 
 many claimants, are certainly the au- 
 thors who approached the most nearly 
 to the discovery: and the reader may 
 judire, from the passages ciled, whether 
 the knowledge of the telescope can with 
 probability be referred to a period ear- 
 lier 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 knowlege, 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 ge- 
 neral 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 him- 
 self 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 con- 
 sistent with Galileo's statement ; and 
 in fact the question, whether or not 
 Galileo saw the original instrument, 
 becomes important only from his ex- 
 pressly asserting the contrary, and pro- 
 fessing 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 Pignona to Paolo 
 Gualdo, that one at least of the Dutch 
 glasses had been sent to Italy. It is 
 
 dated Padua, 31st August, 1609.* 
 " 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 Car- 
 dinal 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 dis- 
 puted. According to one account, 
 which appears consistent and probable, 
 it had been made for sometime before 
 its importance was in the slightest de- 
 gree understood or appreciated, but 
 was set up in the optician's shop as 
 a curious philosophical toy, show- 
 ing a large and inverted image of a 
 weathercock, towards which it was di- 
 rected. The Marquis Spinola, chancing 
 to see it, was struck with the phenome- 
 non, 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 Lipper- 
 hey, two spectacle-makers, living close 
 to each other, near the church of Mid- 
 dleburg, have both had strenuous sup- 
 porters 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 .f It seems that the truth 
 lies between them, and that one, pro- 
 bably Jansen, was the inventor of the 
 microscope, which application of the 
 principle was unquestionably of an ear r 
 lier 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 
 
 * Lettere d'Uomini illustri. Venezia, 1?44. 
 t Borelli, De vero Telescopii inventore, 1655, 
 
24 
 
 GALILEO. 
 
 mentioned) saw it many years after- 
 wards, when ambassador from the 
 United Provinces to England, and got 
 from Drebbel this account of the quar- 
 ter whence it came. Lipperhey after- 
 wards, 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 in- 
 dependently 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 sub- 
 ject, some of whom do not seem to 
 distinguish very accurately whether the 
 telescope or microscope is the instru- 
 ment to which their evidence refers. 
 Borelli arrives at the conclusion, that 
 Jansen was the inventor ; but not satis- 
 fied with this, he endeavours, with a 
 glaring partiality which makes his for- 
 mer determination suspicious, to secure 
 for him and his son the more solid re- 
 putation of having anticipated Galileo in 
 the useful employment of the invention. 
 He has however inserted in his collec- 
 tions a letter from John the son of Za- 
 charias, 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,* 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 in- 
 formed 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 intelli- 
 gible account of the process of reason- 
 ing, 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 con- 
 cave diminishes them : it is true that the 
 
 * gncyclopsodia BriUnuica, Art, TELESCOPE, 
 
 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 de- 
 termined 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 expe- 
 riments 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 ;* but it is plain, from 
 this statement, that he does not profess 
 to have theorized beyond the determi- 
 nation 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 some- 
 thing 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 lan- 
 guage bears a resemblance to the first 
 passage which we quoted from Bap- 
 tista Porta, sufficiently close to make it 
 not improbable that he might be as- 
 sisted in his inquiries by some recollec- 
 tion 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 con- 
 sisted of a plano-convex and plano-con- 
 cave lens, the latter nearest the eye, 
 distant from each other by the differ- 
 ence of their focal lengths, being, in 
 principle, exactly the same with the mo- 
 dern 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 in- 
 verted 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 de- 
 monstrative proof of the falsehood of 
 Fuccarius's insinuation : in that case 
 the Dutch glass must have been similar 
 to what was afterwards called the astro- 
 nomical telescope, consisting of two 
 
 Ibid, 
 
GALILEO. 
 
 25 
 
 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 after- 
 wards ; for the fame of Galileo's obser- 
 vations, and the superior excellence of 
 the instruments constructed under his 
 superintendence, induced every one in 
 the first instance to imitate his con- 
 structions as closely as possible. The 
 astronomical telescope was however 
 eventually found to possess superior ad- 
 vantages over that which Galileo ima- 
 gined, 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 intro- 
 duction of a second pair of similar 
 glasses, which restore the inverted 
 image to its original position. For fur- 
 ther 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 INSTRU- 
 MENTS. 
 
 Galileo, about the same time, con- 
 structed microscopes on the same prin- 
 ciple, for we find that, in 1612, he pre- 
 sented one to Sigisraund, King of Po- 
 land ; but his attention being principally 
 devoted to the employment and perfec- 
 tion 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 perfec- 
 tion, having experienced some difficulty 
 in working the glasses. Schott tells an 
 amusing story, in his " Magic of Na- 
 ture," 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 pos- 
 session of his baggage, and were pro- 
 ceeding 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 sor- 
 cerer who was in the habit of using 
 a portable familiar, was declared un- 
 worthy of Christian burial. Fortu- 
 nately 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 Ve- 
 nice, 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 inhabit- 
 ants 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 in- 
 timated 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 flo- 
 rins. 
 
 It was long before the phrenzy of 
 public curiosity abated. Sirturi de- 
 scribes 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. Un- 
 luckily 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 se- 
 veral hours till their curiosity was sa- 
 tiated, 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.* In- 
 struments 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 him- 
 self, Hortensius, assuring Galileo that 
 none could be met with in Holland suf- 
 ficiently good to show Jupiter's disc 
 well defined ; and in 1634 Gassendi begs 
 for a telescope from Galileo, informing 
 
 iiiw, V<meti}, 1619, . 
 
26 
 
 GALILEO. 
 
 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 dou- 
 ble eye-glass : the names of telescope 
 and microscope were suggested by 
 Demisiano, as we are told by Lagalla 
 in his treatise on the Moon.* 
 
 CHAPTER VII. 
 
 Discovery of Jupiter s satellites Kepler 
 Sizzi Astrologers Mcestlin 
 Horky Mayer. 
 
 As soon as Galileo had provided him- 
 self with a second instrument, he began 
 a careful examination of the heavenly 
 bodies, and a series of splendid discove- 
 ries 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 ap- 
 peared 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 re- 
 fuse to believe that these small stars 
 were four moons, revolving round Ju- 
 piter in the same manner in which our 
 earth is accompanied by its single at- 
 tendant. In honour of his patron Cos- 
 mo, 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 Gali- 
 leo 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 
 
 * De phsenomeais in orbe Lunse. Venetiis, 1612. 
 
 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 bril- 
 liant 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 op- 
 portunity 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 differ- 
 ent 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 pro- 
 duced. Many doubted, many positively 
 refused to believe, so novel an announce- 
 ment ; all were struck with the greatest 
 astonishment, according to their respec- 
 tive opinions, either at the new view of 
 the universe thus offered to them, or at 
 the daring audacity of Galileo in in- 
 venting such fables. We shall proceed 
 to extract a few passages from contem- 
 porary 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 in- 
 telligence : "I was sitting idle at 
 home, thinking of you, most excellent 
 Galileo, and your letters, when the 
 news was brought me of the dis- 
 covery 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 be- 
 tween 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 cele- 
 brated men, far removed by their learn- 
 ing, weight, and character, above vulgar 
 folly ; that the book was actually in the 
 press, and would be published immedi- 
 ately. On our separating, the authority 
 of Galileo had the greatest influence on 
 
GALILEO. 
 
 27 
 
 me, earned by the accuracy of his judg- 
 ment, and excellence of his understand- 
 ing ; so I immediately fell to thinking 
 how there could he any addition to the 
 number of the planets without over- 
 turning my Mysterium Cosmographi- 
 cum, published thirteen years ago, ac- 
 cording to which Euclid's five regular 
 solids do not allow more than six pla- 
 nets 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 dodecahe- 
 dron. The sphere including this will be 
 that of Mars. About Mars' orbit de- 
 scribe a tetrahedron : the sphere contain- 
 ing this will be Jupiter's orbit. Round 
 Jupiter's describe a cube: the sphere in- 
 cluding this will be Saturn's. Within the 
 earth's orbit inscribe an icosahedron: 
 the sphere inscribed in it will beVenus's 
 orbit. In Venus inscribe an octahedron : 
 the sphere inscribed in it will be Mer- 
 cury'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 pos- 
 sible, 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 dif- 
 fered 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 indis- 
 pensable assistance, if he neglect from 
 time to time to consolidate his observa- 
 tions, and thence to conjecture the course 
 of future observation most likely to re- 
 ward his assiduity. This cannot be 
 more forcibly expressed than in the 
 words of Leonardo da Vinci :* " Theory 
 is the general, experiments are the 
 soldiers. The interpreter of the works 
 of nature is experiment ; that is never 
 
 * Venturi, Essai sur les ouvrages de Leo, da 
 Vinci. 
 
 wrong; it is our judgment whteh is 
 sometimes deceived, because we are ex- 
 pecting 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 pro- 
 mising ourselves results which we can 
 never obtain." 
 
 In the instance before us, it is well 
 known that, adopting some of the opi- 
 nions of Bruno and Brutti, Galileo, even 
 before he had seen the satellites of Jupi- 
 ter, 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 exa- 
 mining the other heavenly bodies. Kep- 
 ler on the contrary had taken the op- 
 posite 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 ac- 
 count 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 esta- 
 blish ; but so far as regards the progress 
 of the science of inductive reasoning, it 
 is perhaps to be regretted, that the se- 
 venteen years which he wasted in ran- 
 dom and unconnected guesses should 
 have been finally rewarded, by disco- 
 veries splendid enough to shed deceitful 
 lustre upon the method by which he ar- 
 rived 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 know- 
 ledge of God ; as if that alone were per- 
 fect, which they understand to be so. 
 But J, on the contrary, observe that 
 
28 
 
 GALILEO. 
 
 Nature has other scales of perfection, 
 which we cannot comprehend, and rather 
 seem disposed to class among imper- 
 fections. For instance, among the re- 
 lations of different numbers, those ap- 
 pear to us most perfect which exist be- 
 tween numbers nearly related to each 
 other , as the double, the triple, the pro- 
 portion of three to two, &c. ; those appear 
 less perfect which exist between num- 
 bers 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 incommen- 
 surable quantities, which by us are 
 nameless and inexplicable. Conse- 
 quently, 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 pro- 
 portions, I doubt not that he would have 
 arranged them according to the former 
 rational proportions ; but, on the con- 
 trary, God, with no regard to our ima- 
 ginary symmetries, has ordered them in 
 proportions not only incommeasurable 
 and irrational, but altogether inappre- 
 ciable 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, thou- 
 sands 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 
 \vould not be quadruple of a great cir- 
 cle, nor the cylinder be to the sphere as 
 three to^two : in short, no part of geo- 
 metry 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 dan- 
 gerous 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 in- 
 contestably established, and Huyghens 
 had discovered a similar satellite near 
 Saturn, he was so rash as to declare his 
 belief, (unwarned by the vast pro- 
 gress 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 num- 
 ber 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 astro- 
 nomer, took the matter up in a some- 
 what different strain from Kepler.* 
 " 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 
 ftixzoxofffto; (or little world) ; two nostrils, 
 two eyes, two ears, and a mouth ; so 
 in the heavens, as in a petxcoxtrpos (or 
 great world), there are two favourable 
 stars, two unpropitious, two luminaries, 
 and Mercury alone undecided and in- 
 different. From which and many other 
 similar phenomena of nature, such as 
 the seven metak, Sec., 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 exer- 
 cise no influence on the earth, and there- 
 fore would be useless, and therefore do 
 not exist. Besides, as well the Jews and 
 other ancient nations as modern Euro- 
 peans have [adopted the division of the 
 week into se'ven 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 dis- 
 covered, 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 con- 
 tented themselves, and satisfied others, 
 
 * Pmnoia Astronomies, Yejjetijs, 16J.Q. 
 
GALILEO. 
 
 29 
 
 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 suf- 
 ficiently ludicrous. " Oh, my dear 
 Kepler,"* says Galileo, "how I wish 
 that we could have one hearty laugh 
 together. Here, at Padua, is the prin- 
 cipal professor of philosophy, whom I 
 have repeatedly and urgently requested 
 to look at the moon and planets through 
 my srlass, 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 pro- 
 fessor of philosophy at Pisa labouring 
 before the grand duke with logical ar- 
 guments, 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 sin- 
 gular impudence of the charge he 
 ventures to bring against him. " We 
 are not to think," says Christmann, 
 in the Appendix to his Nodus Gor- 
 dius, " that Jupiter has four satellites 
 given him by nature, in order, by re- 
 volving 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 in- 
 dustrious correction of the heavens. 
 Nature abhors so horrible a chaos, and 
 to the truly wise such vanity is detest- 
 able. 
 
 Galileo was also urged by the astro- 
 logers to attribute some influence, ac- 
 cording 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 extract- 
 ing, as a specimen of his method of 
 uniting sarcasm with serious expostula- 
 tion; " 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 impor- 
 tunity ; 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 super- 
 fluous. I believe this set of men to be 
 of Sizzi's opinion, that astronomers dis- 
 covered the other seven planets, not by 
 seeing them corporally in the skies, but 
 only from their effects on earth, much 
 
 * Kepleri Epistolae. 
 
 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 recon- 
 sider 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 con- 
 formably 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 con- 
 trary, he should find the events depend- 
 ing 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 cal- 
 culating the constitution of the four 
 Jovial circulators at every bygone mo- 
 merit, and, perhaps, from the diversity of 
 their aspects, he would be able, with ac- 
 curate observations and multiplied con- 
 junctions, 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 excel- 
 lent 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 phi- 
 losophy, 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 
 
30 
 
 GALILEO. 
 
 (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 ac- 
 quainted 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 admi- 
 ration of his friend. " Some might 
 wish I had spoken in more moderate 
 terms in praise of Galileo, in conside- 
 ration 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 in- 
 tentions : the Martin Horky of whom 
 he speaks, a young German, also sig- 
 nalized himself by a vain attack upon 
 the book which he thought his patron 
 Kepler condemned. He was then travel- 
 ling 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." * He seems 
 soon to have decided that most repu- 
 tation 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 tele- 
 scope, which, he says, " does wonders 
 upon the earth, but represents celestial 
 objects falsely ;"t he concludes with 
 
 * Kepleri Epistolse. 
 
 fit may seem extraordinary that any one could 
 support an argument by this partial disbelief in thein- 
 btrumeiit, whicu wa allowed on aii hands to if present 
 terresliai objects correctly. A similar instance of 
 obstinacy, in au almost identical case though in a 
 
 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 know- 
 ledge 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 pla- 
 nets to that Italian from Padua though 
 I die for it," followed up this declara- 
 tion by publishing a book against Ga- 
 lileo, 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 ex- 
 amination of four principal questions 
 touching the alleged planets ; 1st, Whe- 
 ther 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 ob- 
 servations. 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.* 
 
 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 Wed- 
 derburn, then a student at Padua, and 
 afterwards a physician at the Court of 
 Vienna. In the latter reply we find it men- 
 tioned, that Galileo was also using his 
 telescope for the examination of insects, 
 
 more unpretending station, once came under the 
 writer's own observation. A farmer in Cambridge- 
 shire, who had acquired some confused notions of 
 the use of the quadrant, consulted him. ou 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, cer- 
 tainly sufficiently gross, appeared to be that he had 
 confounded the angular measure of a degree, with 
 69 miles, the linear measure of a degree on the 
 earth's surface. As a short way of showing his.mis- 
 take, he was desired to determine, in the same man- 
 ner, the height of his barn which stood about 30 yards 
 distant ; he lifted the quadrant to his eye, but per- 
 ceiving, probably, the monstrous size to which his 
 principles were forcing him, he said, " Oh, Sir, the 
 quadrant's only true lor the sky." He must have 
 been an objector of this kind, wiio said to Galileo. 
 " Uh,',Sir, the telescope's only true for the earth." 
 * Venturi. 
 
GALILEO. 
 
 31 
 
 &c.* Horky sent his performance tri- 
 umphantly to Kepler, and, as he returned 
 home before receiving an answer, he 
 presented himself before his patron in 
 1he same misapprehension under which 
 he had written, but the philosopher re- 
 ceived 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 ac- 
 count, 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 fa- 
 vour 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 confi- 
 dence in the truth of Galileo's asser- 
 tions, 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 correspon- 
 dence with Florence, part of which we 
 have already extracted, t " In the first 
 place, I return you my thanks that you 
 first, and almost alone, before the ques- 
 tion had been sifted (such is your can- 
 dour 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 ob- 
 jects 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 mu- 
 seum, among his most rare and precious 
 curiosities, in eternal remembrance of 
 the invention : I have made no other of 
 equal excellence, for the mechanical la- 
 bour is very great : I have, however, 
 devised some instruments for figuring 
 and polishing them which I am un- 
 willing 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 testi- 
 monies : I produce, for one, the 
 Grand Duke, who, after observing the 
 Medicsean planets several times with 
 
 * Quatuor probl. confut. per J. Wedderboraiuju, 
 Scotobritannum. Patayii, 1610. 
 t See page 18. 
 
 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 com- 
 plete my Treatises on Mechanics, on 
 the Constitution of the Universe, and 
 on Natural and Violent Local Motion, 
 of which I have demonstrated geo- 
 metrically many new and admirable 
 phenomena. I produce, for another wit- 
 ness, myself, who, although already en- 
 dowed 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 pla- 
 nets had deceived me and should dis- 
 appear, yet quit this situation, and be- 
 take 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 advan- 
 tageously employed in his own hands, 
 than pompously laid up in a museum ; 
 for in 1637 we find him saying, in an- 
 swer to a request from his friend Mi- 
 canzio 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 whicl: 
 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 fa- 
 ther'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 al- 
 ways 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 un- 
 polished, 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 
 
GALILEO. 
 
 of these observations." A telescope 
 was in existence, though with the object 
 glass broken, at the end of the last cen- 
 tury, 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 New- 
 ton's own hands, and scarcely possess- 
 ing 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 sluggish- 
 ness of their perception, by its acute- 
 ness when brought into action. Simon . 
 Mayer published his ".Mundus Jovialis" 
 in 1614, in which he claims to have 
 been an original observer of the satel- 
 lites, but, with an affectation of candour, 
 allows that Galileo observed them pro- 
 bably 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, .1 6 1 0, of 
 the new style, which was the date of 
 Galileo's second observation, and Gali- 
 leo 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 an- 
 nouncements, carried the number as 
 high as twelve.* In imitation of Gali- 
 leo's nomenclature, and to honour the 
 sovereigns of the respective observers, 
 these supposed additional satellites were 
 dignified with the names of Vladisla- 
 vian, 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 him- 
 self from the neighbourhood of the 
 fixed stars, which gave rise to these 
 pretended discoveries, carryingwith 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 Jupi- 
 ter's satellites, and of the intense interest 
 
 * Sherbunie's sphere of Mauilius. London, 1675. , 
 
 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 bril- 
 liant results of the invention of the tele- 
 scope ; 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 vast- 
 ness and nicer mechanism of those 
 other bodies, which had before been dis- 
 tinguished from the stars only by their 
 motion, and wherein none but the bold- 
 est thinkers had ventured to suspect a 
 community of nature with our own 
 globe. This discovery gave the holding 
 turn to the opinions of mankind respect- 
 ing 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 revo- 
 lutions 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 sub- 
 ject naturally inspired. The eclipses of 
 the satellites speedily attracled 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, si- 
 multaneously made. Thus the first 
 astronomical solution of the great pro- 
 blem 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 em- 
 pires, 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 some- 
 thing moving among the stars, they knew 
 not what, nor why : perhaps only to 
 perplex the wise with fruitless conjec- 
 tures, and harass the weak with fears 
 as idle as their theories."* 
 
 * Hersehel'a Address to the Astronomical So- 
 ciety, 1&27. 
 
GALILEO. 
 
 33 
 
 CHAPTER VIII. 
 
 Observations on the Moon Nebulce 
 Saturn Venus Mars. 
 
 THERE were other discoveries an- 
 nounced 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 addi- 
 tional light on the constitution of the 
 solar system, and cleared up the difficul- 
 ties 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 my- 
 thological poem, by Marini.* 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 gene- 
 rally taken for granted, really resembled 
 our earth in its structure ; he was able dis- 
 tinctly to trace on it the outlines of moun- 
 tains 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 pre- 
 conceived notion of what the moon 
 ought to be, and they loathed the doc- 
 trines 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 
 
 * Adone di Marini, Venetiis, 1G23, Cant. x. 
 
 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 sphe- 
 ricity would make it not only less per- 
 fect, 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 inac- 
 tion; 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 : no- 
 thing could console them for the de- 
 struction 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 evi- 
 dence of the sensible inequalities of the 
 moon's surface, attempted to reconcile 
 the old doctrine with the new observa- 
 tions, 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 im- 
 perceptible 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 re- 
 fute absurd opinions with too much 
 curiosity." " Truly," says he, " the 
 idea is admirable, its only fault is that 
 it is neither demonstrated nor demonstra- 
 ble : 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 pro- 
 ceed to such extremities, he seems to 
 have scared the opposite party into mo- 
 deration, for we do not find that the 
 crystalline theory was persevered in. 
 
 In the same essay, Galileo also ex- 
 plained 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 be- 
 fore him Leonardo da Vinci, had already 
 declared this ; to arise from what may 
 be called earthshine, or the reflec- 
 
34 
 
 GALILEO. 
 
 tion of the sun's light from the terres- 
 trial globe, exactly similar to that, which 
 the moon affords us when we are simi- 
 larly placed between her and the sun ; but 
 the notion had not been favourably re- 
 ceived, because one of the arguments 
 against the earth being a planet, revolv- 
 ing 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, point- 
 ing 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 atmo- 
 sphere.* 
 
 Galileo also announced the detection 
 of innumerable stars, invisible to the 
 unassisted sight; and those remark- 
 able appearances in the heavens, ge- 
 nerally called nebulae, the most con- 
 siderable 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 collec- 
 tion of minute stars, too closely congre- 
 gated to produce a separate impression 
 upon the unassisted eye.t Benedetti, 
 who divined that the dark shades on the 
 moon's surface arose from the constitu- 
 tion of those parts which suffered much 
 of the light to pass into them, and con- 
 sequently 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^lan- 
 guage 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 eter- 
 nally renewed discussions and disputes, 
 they could have occupied Galileo's time 
 
 * Speculat. Lib Venetiis, 1585, Epistolae. 
 j- This opinion, with respect to the milky way, had 
 been held by some of the ancient astronomers. See 
 Manillas. Lib. i. v. 753. 
 
 " Anne mngis densu stcllarum turba corona 
 ~ Cuntexitjtaittmas, et cnmsu lumine candct, 
 JUtfulgore nitet collato clarior orbis." 
 
 sufficiently to detain his attention from 
 his telescope and astronomical observa- 
 tions ; but he knew too well where his 
 real strength lay, and they had scarcely 
 time to compound any thing like an ar- 
 gument against him and his theories, 
 before they found him in possession of 
 some new facts, which they were un- 
 prepared to meet, otherwise than by 
 the never*- failing resource of abuse and 
 affected contempt. The year had not 
 expired before Galileo had new intelli- 
 gence to communicate of the highest im- 
 portance. Perhaps he had been taught 
 caution irom the numerous piracies which 
 had been committed upon his discoveries, 
 and he first announced his new disco- 
 veries enigmatically, veiling their real 
 import by transpositions of the letters in 
 the words which described them, (a prac- 
 tice 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 Ro- 
 dolph, Galileo speedily sent to him the 
 real reading 
 
 Altissimum planetam tcrgeminum 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 oQo the middle being some- 
 what 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 ob- 
 long appearance, like the appearance of 
 an olive, thus O. Now 1 have dis- 
 covered a court for Jupiter, and two 
 servants for this old man, who aid his 
 
GALILEO. 
 
 35 
 
 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." Gali- 
 leo'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 com- 
 pletely distinct from the body of Saturn ;* 
 and the still more accurate observations 
 of Herschel have ascertained that it 
 consists of two concentric rings revolv- 
 ing 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 pla- 
 nets nothing new was to be observed ;" 
 but a month had scarcely elapsed, before 
 he communicated to the world another 
 enigma, 
 
 Hcec immatura d me jamfrustra leguntur oy, 
 
 which, as he said, contained the an- 
 nouncement of a new phenomenon, in 
 the highest degree important to the truth 
 of the Copernican system. The inter- 
 pretation of this is, 
 
 Cynthice Jiguras cemulatur muter amorum, 
 
 that is to say, Venus rivals the ap- 
 pearances 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 sur- 
 face turned towards the earth, the tele- 
 scope shewed her in a crescent form, like 
 the moon in a similar position, and tra- 
 cing 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 
 
 * Huyghens announced his discovery in this form : 
 aaaaaaac ccccdeee e eg hii i iiiil 1 1 1 mmnn 
 nnnnnnnoouoppqrrstttttuuuu K, which he 
 afterwards recomposed inlo the sentence. Annulu 
 cingitur, tcnui, piano, nusquam cohcerente, ad cclipti- 
 -cam inclinato. De Saturui Luna. Hagae, 1656. 
 
 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 im- 
 portance 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 there- 
 fore 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 commen- 
 tator of Aristotle, under the name of 
 Lucillus Philalthaeas, 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 re- 
 ceded 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 fur- 
 ther remarks, " that Mercury and Ve- 
 nus 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, ex- 
 pressly to shew the ignorance and pre- 
 sumption of the author. Copernicus, 
 whose want of instruments had pre- 
 vented him from observing the horned 
 appearance of Venus when between 
 the earth and sun, had perceived how 
 formidable an obstacle the non-appear- 
 ance 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 
 D 2 
 
36 
 
 GALILEO'. 
 
 adopting the system, which, on the whole, 
 appeared to agree best with the phe- 
 nomena, by meeting with some \vhich it 
 did not enable him to explain. Milton, 
 whose poem is filled with allusions to 
 Galileo and his astronomy, has not suf- 
 fered 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.* " 
 
 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 an- 
 nounces these last observations to his 
 pupil Castelli, with the following ex- 
 pressions, shewing how justly he esti- 
 mated the opposition they encounter- 
 ed : " 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 rea- 
 soning, and those who wish to learn 
 the truth ; but that to convince the ob- 
 stinate, and those who care for nothing 
 beyond the vain applause of the stupid 
 and senseless vulgar, not even the testi- 
 mony 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 satis- 
 faction ; but of advancing in popular 
 opinion, or gaining the assent of the 
 book-philosophers, let us abandon both 
 the hope and the desire." 
 
 CHAPTER IX. 
 Account of the Academia Lincea Del 
 
 Cimento Royal Society. 
 GALILEO'S resignation of the mathema- 
 tical professorship at Padua occasioned 
 
 "*~B vii. v. 364. Other passages maybe examined 
 in B. i. 286 ; in. 565590, 722733 ; iv, 589 ; v. 
 2b'l, 414; vii. 577; via. 1178. 
 
 much dissatisfaction to all -those who 
 were connected with that university. 
 Perhaps not fully appreciating his de- 
 sire of returning to his native country, 
 and the importance to him and to the 
 scientific world in general, of the com- 
 plete leisure which Cosmo secured to 
 him at Florence, (for by the terms of his 
 diploma he was not even required to re- 
 side 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 ho- 
 nourable 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 de- 
 cree, 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 communica- 
 tion 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 peremptoiy 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 contem- 
 plating 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 pri- 
 vate friends."* Among other distinc- 
 tions he was solicited to become a mem- 
 ber 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 sci- 
 ence has not been by any means re- 
 warded 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 ap- 
 peared more prominently on the page of 
 history. Cesi had scarcely completed 
 
 Salusbury, Math. Coll. 
 
GALILEO. 
 
 37 
 
 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 phy- 
 sician, 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 de- 
 sign by the most violent and unjusti- 
 fiable 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 suc- 
 cess he renewed the plan which he had 
 sketched six years before. A few extracts 
 from the Regulations will serve to shew 
 the spirit ill which this distinguished 
 society was conceived : 
 
 " The Lyncean Society desires for its 
 academicians, philosophers eager for 
 real knowledge, who will give them- 
 selves to the study of nature, and espe- 
 cially to mathematics ; at the same time 
 it will not neglect the ornaments of ele- 
 gant 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 Lyn- 
 ceans give their minds, first to obser- 
 vation and reflection, and afterwards 
 to writing and publishing. It is not 
 within the Lyncean plan to find leisure 
 for recitations and declamatory assem- 
 blies ; the meetings will neither be fre- 
 quent nor full, and chiefly for transact- 
 ing the necessary business of the society: 
 but those who wish to enj oy 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 everyone 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 assist- 
 ance. 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 sin- 
 cere 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 sti- 
 mulus, especially when they write on 
 any literary subject, also in their private 
 letters to their associates, and in gene- 
 ral when any work comes from them 
 wisely and well performed. The Lyn- 
 ceans will pass over in silence all poli 
 tical 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 molesta- 
 tion, and to avoid every sort of disturb- 
 ance. And if any one by command of 
 his superiors, or from some other ne- 
 cessity, is reduced to handle such mat- 
 ters, since they are foreign to physical 
 and mathematical science, and conse- 
 quently alien to the object of the Aca- 
 demy, let them be printed without the 
 Lyncean name." * 
 
 The society which was eventually or- 
 ganized formed but a very trifling part 
 of the comprehensive scheme which 
 Cesi originally proposed to himself; it 
 had been his wish to establish a scien- 
 tific Order which should have corre- 
 sponding lodges in the principal towns of 
 Europe, and in other parts of the glcrbe, 
 each consisting of not more than five nor 
 less than three members, besides an un- 
 limited 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 admi- 
 rable 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 re- 
 searches, and also to defray the charges 
 
 * Perhaps it was to deprecate the hostility of the 
 Jesuits that, at the close of these Regulations, the 
 Lyuceans are directed to address their prayers, 
 among other Saints, especially to Ignatius Loyola, 
 as to one who greatly favoured the interests of learn- 
 ing. Odescalchi, Memorie dell' Acad. de' Lincei, 
 Roma. 1806. 
 
38 
 
 GALILEO. 
 
 of publishing such of their" works as 
 should be thought worthy of appearing 
 with the common sanction. Such libe- 
 ral offers were not likely to meet with 
 an unfavourable reception : they were 
 thankfully accepted by many well quali 
 fied 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 quaint- 
 ness may be thought to belong to the 
 Lyncean name. The Inflamed the 
 Transformed the Uneasy the Hu- 
 morists the Fantastic the Intricate 
 the Indolent the Senseless the Un- 
 deceived the Valiant the ^Etherial 
 Societies are selected from a vast num- 
 ber of similar institutions, the names of 
 which, now almost their sole remains, 
 are collected by the industry of Morhof 
 and Tiraboschi*. 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 ag- 
 mine duld ; 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 presi- 
 dency for his life, and the celebrated 
 Baptista Porta was appointed vice pre- 
 sident 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 Aca- 
 demy, 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 Co- 
 
 * PolyhistorLiterarius, &e. Storia della Letterat. 
 Ital. The still existing: society of Chaff, more pene- 
 rally known by its Italian title, DeflaCrusca, belongs 
 to the same period. 
 
 lonna, Lucas Valeric, Guiducci, Welser, 
 Giovanni Fabro, Terrentio, Vira^nio Ce- 
 sarini, Ciampoli, Molitor, Cardinal Bar- 
 berino, (nephew of Pope Urban VIII.) 
 Stelliola, Salviati, &c. 
 
 The principal monument still remain- 
 ing 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 Her- 
 nandez ; and Reecho, who often has the 
 credit of the whole work, made great ad- 
 ditions to it. During fifty years the ma- 
 nuscript 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 Tdbulce Phytosophicce, and a Disser- 
 tation on Bees entitled Apiarium, the 
 only known copy of which last is in the 
 library of the Vatican. His great work, 
 Theatrum Natures, was never printed ; 
 a circumstance which tends to shew that 
 he did not assemble the society round 
 him for the purpose of minist'ering to his 
 own vanity, but postponed the publica- 
 tion of his own productions to the la- 
 bours 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 li- 
 brary for the use of the academy, (which 
 was afterwards augmented on the pre- 
 mature death of Cesarini by the dona- 
 tion of his books) ; he filled a botanical 
 garden with the rarer specimens of 
 plants, and arranged a museum of natu- 
 ral 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 fin his place in the 
 princely manner to which the academi- 
 cians were accustomed, and the society, 
 after lingering some years under the no- 
 minal patronage of Urban VIII., gra- 
 dually decayed, till, by the death of its 
 principal members, and dispersion of the 
 rest, it became entirely extinct*. Bianchi, 
 
 * F. Colonnae Phytobasanus Jano Planco Auctore. 
 Florent, 1?44. 
 
GALILEO. 
 
 39 
 
 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 flourish- 
 ing in Rome. Before leaving the sub- 
 ject 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 sug- 
 gests 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, Torri- 
 celli, and Aggiunti formed the plan of es- 
 tablishing 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 Ex- 
 perimental 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 deve- 
 lopement of Galileo's experiments, it 
 kept up a correspondence with the prin- 
 cipal philosophers in every part of Eu- 
 rope, but when Leopold was, in 1666, 
 created a cardinal, it appears to have 
 been dissolved, scarcely ten years after 
 its institutiont. 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 Lon- 
 don, and Acade" mie Franchise of Paris. 
 
 These latter two are mentioned toge- 
 ther, probably for the first time, by Sa- 
 lusbury. The passage is curious in an his- 
 torical point of view, and worth extract- 
 ing: "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 Ms sacred 
 Majesty that now is. The Beaux Esprits 
 have published sundry volumes of their 
 moral and physiological conferences, 
 
 * Nelli Saggio di Storia Literaria Fiorentina, 
 Lucca, 1759. 
 
 with the laws and history of their fellow- 
 ship; 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 de- 
 tractions and expectations." * 
 
 CHAPTER X. 
 
 Spots on the Sun Essay on Floating 
 Bodies Scheiner Change in Sa- 
 turn. 
 
 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 ap- 
 peared 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 Mer- 
 cury t. Kepler, whose astronomical 
 knowledge would not suffer him to over- 
 look 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 barba- 
 rous 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 men- 
 tioned 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 con- 
 tented with it. In 1609, he himself ob- 
 served upon the sun a black spot, which 
 he in like manner mistook for Mercury, 
 and unluckily the day, being cloudy, did 
 
 * Salisbury's Math. Coll. vol. ii. London, 1664. 
 j Aimoini Hist. Francorum. Parisiis. 1567. 
 
40 
 
 GALILEO. 
 
 not allow him to contemplate it suffici- 
 ently long to discover his error, which 
 the slowness of its apparent motion would 
 soon have pointed out.* 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 pos- 
 sess 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 unfor- 
 tunate, as in the course of the contro- 
 versy in which they engaged him, he first 
 became personally embroiled with the 
 powerful party, whose prevailing influ- 
 ence 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 com- 
 mencement, he thought it necessary to 
 apologize for writing on a subject so dif- 
 ferent from that which chiefly occupied 
 the public attention, and declared that he 
 had been too closely occupied in calcu- 
 lating the periods of the revolutions of 
 Jupiter's satellites to permit him to pub- 
 lish 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, 18 
 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 con- 
 tinue 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 dis- 
 tance to which they are removed from 
 
 * Mercurius in sole visits. 1609. 
 
 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 ground 
 with the sun, which turned upon its axis 
 in about the time of a lunar month. 
 
 Having by these prefatory observa- 
 tions assuaged the public thirst for as- 
 tronomical novelties, he ventures to in- 
 troduce the principal subject of the trea- 
 tise 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 com- 
 pany appearing to be that the floating 
 or sinking of a body depended princi- 
 pally 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 ; " * which is exactly the 
 distinction which those who called them- 
 selves Aristotelians were unable to per- 
 ceive, and to which the opinions of Aris- 
 totle himself were not always true. Ga- 
 lileo states the discussion to have imme- 
 diately 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 con- 
 densed, the proof of which is, that ice 
 always floats upon water/}- It was re- 
 plied, 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 
 
 i * De Coelo. lib. 4. 
 
 t 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 ex- 
 periment. 
 
GALILEO. 
 
 41 
 
 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 perti- 
 nent to commence his Essay with the 
 following observation on the advantage 
 of delivering scientific opinions in writ- 
 ing, " because in conversational argu- 
 ments, either one or other party, or per- 
 haps 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 ori- 
 ginal 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 occa- 
 sion to state the famous hydrostatical 
 paradox, of which the earliest notice is 
 to be found in Stevin's works, a contem- 
 porary 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 expe- 
 rimental 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 be- 
 coming more familiar with Galileo's 
 mode of conducting an argument, it is 
 fortunate that such a series of experi- 
 ments 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 forc- 
 ing conviction. They also present an ad- 
 mirable specimen of the talent for which 
 Galileo was so deservedly famous, of in- 
 venting ingenious arguments in favour 
 of his adversaries' absurd opinions before 
 he condescended to crush them, shew- 
 ing 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 doc- 
 trines 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 sink- 
 ing 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 shew- 
 ing that the ball in water sinks to the 
 bottom*, and that the board if put lightly 
 on the surface floats, have held and con- 
 firmed 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 pur- 
 pose of these experiments, Galileo re- 
 commends 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 re- 
 move 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 
 
 * Ebony is one of the few -\voods heavier than 
 water. See Treatise on Hydrostatics. 
 
GALILEO. 
 
 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 in- 
 stance, 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, in- 
 stead 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 hard- 
 ness of the wood and bread. And there- 
 fore, 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 visco- 
 sity 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 fehe corpo- 
 real substance, nor have I ever alleged 
 them to be stript of sensible matter: 
 and also 1 freely admit, that in our en- 
 deavours 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 1 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 mat- 
 ter; nay, in such matters, the wax is 
 more convenient than steel for finding 
 the difference depending on the acute- 
 ness 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 dif- 
 ferent figures, are to divide some mat- 
 ters asunder; but also, oji the other 
 
 hand, to the resistance of the matter to 
 be penetrated. And, since I have chosen 
 a matter which does penetrate the resist- 
 ance of the water, and in all figures de- 
 scends to the bottom, my antagonists 
 can charge me with no defect ; nor (to 
 revert to their illustration) have I at- 
 tempted to test the efficacy of acuteness 
 by cutting with matters unable to cut. 
 I subjoin withal, that all caution, dis- 
 tinction, 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 thick- 
 ness ; 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 thick- 
 ness under the surface of it ; and that 
 more and more, according as the float- 
 ing 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 pene- 
 tration, Galileo then directs a cone 
 to be made of wood or wax, and as- 
 serts 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 resist- 
 ance 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, 
 
GALILEO. 
 
 43 
 
 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 dif- 
 fering in nothing but in figure, they 
 affirm that with all perspicuity they 
 have demonstrated and sensibly mani- 
 fested what they undertook. Neverthe- 
 less 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 en- 
 vironed by the surface of the am,bient 
 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 im- 
 pediment (of which more anon) it is sur- 
 rounded, 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, conclu- 
 sive against the notion that figure, and 
 the resistance of the water to" penetra- 
 tion have anything to do with the buoy- 
 ancy 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 ques- 
 tion, 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 attri- 
 bute 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 consi- 
 derable 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 an- 
 nexed figure, in which B D L F repre- 
 
 sents the surface of the water, and 
 A E I O 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 there- 
 fore have the goodness to remove this 
 air, which may be done simply by wash- 
 ing 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 wul 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." 
 
 " To this I answer first, that nobody 
 can suppose bodies to be put into the 
 water without their being wet, nor do I 
 
44 
 
 GALILEO. 
 
 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 sur- 
 face 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 ac- 
 quires 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 sur- 
 face of the board, might beget an opinion 
 in a third person of a poverty of argu- 
 ments 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. 1 ' 
 
 " 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 sus- 
 taining heavy bodies with which it is 
 in contact. To satisfy all these doubts, 
 I have contrived the following experi- 
 ment 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 sus- 
 tained 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 care- 
 fully part the glass and water without 
 too much disturbing it*. 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 exceed- 
 ingly ingenious and convincing experi- 
 ment, 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 py- 
 ramidal or conical figure may be made 
 of any substance, such that by help of 
 the air, it shall rest upon the water with- 
 out wetting more than its base ; and 
 that we may so form a cone of any sub- 
 stance 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 ex- 
 tracts 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 ap- 
 peared as the ostensible author of a de- 
 
 * 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 con- 
 ducted. 
 
GALILEO. 
 
 fence against the attacks made by Vin- 
 cenzio di Grasia and by Lodovico delle 
 Columbe (the author of the crystalline 
 composition of the moon) on the ob- 
 noxious 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.* 
 
 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 mathe- 
 matics at Ingolstadt, in imitation of Ga- 
 lileo had commenced a series of obser- 
 vations on them, but adopted the theory 
 which, as we have seen, Galileo had exa- 
 mined 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 astrono- 
 mei, who in honour of the reigning fa- 
 mily called them Borbonian stars. 
 Scheiner promulgated his notions in 
 three letters, addressed to their common 
 friend Welser, under the quaint signature 
 of " Apelles latenspost tabulam." Galileo 
 replied to Schemer's letters by three 
 others, also addressed to Welser, and 
 although the dispute was carried on amid 
 mutual professions of respect and es- 
 teem, 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, writ- 
 ten in December, 1612, is annexed a 
 table of the expected positions of Ju- 
 piter'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 ap- 
 pendages of this planet had disappeared, 
 and the accompanying extract will show 
 the uneasiness which Galileo could not 
 conceal at the sight of this phenome- 
 
 .* Nelli. Saggio di Stor. Liter, Fiorent. 
 
 non, although it is admirable to see 
 the contempt with which, even in that 
 trying moment, he expresses his con- 
 sciousness that his adversaries were 
 unworthy of the triumph they appeared 
 on the point of celebrating. " Looking 
 on Saturn within these few days, 1 found 
 it solitary, without the assistance of its 
 accustomed stars, and in short, per- 
 fectly 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 con- 
 sumed, 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. J 
 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 ob- 
 servations and recognised their impossi- 
 bility ! 1 cannot resolve what to say in 
 a chance so strange, so new, and so un- 
 expected ; the shortness of the time, the 
 unexampled occurrence, the weakness of 
 my intellect, and the terror of being mis- 
 taken, have greatly confounded me." 
 These first expressions of alarm are not 
 to be wondered at; however, he soon 
 recovered courage, and ventured to fore- 
 tel the periods at which the lateral stars 
 would again show themselves, protest- 
 ing at the same time, that he was in no 
 respect to be understood as classing this 
 prediction among the results which de- 
 pend on certain principles and sound 
 conclusions, but merely on some conjec- 
 tures which appeared to him probable. 
 From one of the Dialogues on the Sys- 
 tem, 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 ac- 
 count for a phenomenon of which Galileo 
 had not rightly apprehended the cha- 
 racter. 
 
 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 dis- 
 sent 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 ; 
 
46 
 
 GALILEO. 
 
 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 appear- 
 ance, 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." 
 
 CHAPTER XI. 
 
 Letter to Christina, Arch-Duchess of 
 Tuscany Caccini Galileo revisits 
 Rome Inchoffer Problem of Lon- 
 gitudes. 
 
 THE uncompromising boldness with 
 which Galileo published and supported 
 his opinions, with little regard to the 
 power and authority of those who ad- 
 vocated the contrary doctrines, had 
 raised against Mm 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 ad- 
 herents. The alarm became greater 
 every day, inasmuch as Galileo had 
 succeeded in training round him a nu- 
 merous band of followers who all ap- 
 peared imbued with the same dangerous 
 spirit of innovation, and his favourite 
 scholars were successful candidates for 
 professorships in many of the most cele- 
 brated universities of Italy. 
 
 At the close of 1 6 13, 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 ex- 
 
 pressions contained in the Scriptures , 
 and asserted, that the object of the Scrip- 
 tures not being to teach astronomy, suoh 
 expressions are there used as would be 
 intelligible and conformable to the vulgar 
 belief, without regard to the true struc- 
 ture of the universe ; which argument 
 he afterwards amplified in a letter ad- 
 dressed 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, in- 
 tended 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 de- 
 monstrations : 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 ac- 
 count 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 pro- 
 fessors of astronomy that they of them- 
 selves 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 contraiy of that 
 which they happen to meet with. I would 
 entreat these wise and prudent fathers, 
 that they would with all diligence consi- 
 
GALILEO. 
 
 47 
 
 der the difference that is between Opinion- 
 ative and demonstrative doctrines: to 
 the end that well weighing in their minds 
 with what force necessary inferences urge 
 us, they might the better assure them- 
 selves 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 be- 
 tween 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 can- 
 not 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 be- 
 longeth ; 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 them- 
 selves 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 ex- 
 tracting these passages, because it has 
 been advanced by a writer of high re- 
 putation, that the treatment which 
 Galileo subsequently experienced was 
 solely in consequence of his persisting in 
 the endeavour to prove that the Scrip- 
 tures were reconcileable with the Co- 
 pernican theory*, 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 
 
 * Ce philosophe (Galilee) ne fut point persecute 
 comme bon astronome, mais comme mauvais theo- 
 logien. C'est son entetement a vsuloir concilier la 
 Bible avec Copernic qui lui donna des juges. Mais 
 vingt auteurs, surtout parmi les p-rotestans, ontecrit 
 quo Galilee fut persecute et imprisonne pour avqir 
 soutenu que la tcrre tourne autour du solei], que ce 
 systeme aetecondanne par 1'inquisition comme faux, 
 errone et contraire a la Bible, &c. Bergier, Ency- 
 clopedic Methodique, Paris, 1790, Art. SCIENCES 
 HUMAINES. 
 
 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 pur- 
 pose ^of attacking Galileo and his parti- 
 sans with more personality*. Galileo 
 complained formally of Caccini' s con- 
 duct 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 col- 
 lecting evidence against Galileo. Lorini, 
 a brother Dominican of Caccini, had 
 given them notice of the letter to Cas- 
 telli 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 per- 
 mission 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 contempo- 
 rary 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 secre- 
 tary, he expresses himself well satisfied 
 with the results of this step, whether 
 forced or not, and Querenghi thus de- 
 scribes to the Cardinal d'Este the public 
 effect of his appearance : " Your Emi- 
 nence 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 en- 
 tire persuasion, at least he convicts of 
 emptiness most of the arguments with 
 which his adversaries endeavour to over- 
 whelm him. He was particularly admi- 
 
 * Viri Galilsei, quid statis adspicientes in ccelora, 
 Acts I. II. 
 
GALILEO. 
 
 rable 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 adversanes in a more ridicu- 
 lous plight when he afterwards over- 
 turned them all." 
 
 Among the malicious stories which 
 were put into circulation, it had been 
 said, that the Grand Duke had with- 
 drawn 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 correspon- 
 dence 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 im- 
 mediately ; but although this new ques- 
 tion regards me no more than all those 
 who for the last eighty years have sup- 
 ported these opinions both in public and 
 private, yet, as perhaps I may be of 
 some assistance in that part of the dis- 
 cussion 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 ungrate- 
 fully remarks on this part of his life, that 
 " it was scarcely worth while to compro- 
 mise 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 con- 
 sider 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 obnox- 
 ious. 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 mathe- 
 maticians and philosophers, who alter- 
 nately 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 reli- 
 gious 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 se- 
 lect 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 refu- 
 tation of the letters to Castelli and the 
 Archduchess Christina*. 
 
 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 exami- 
 nation of this purely geometrical diffi- 
 culty 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 conse- 
 quence 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 argumen- 
 
 * Tractatus Syllepticns. Roma;, "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 corner*, 
 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 " Hisjixa quiescit," ."Fixed by these it is at 
 rest." 
 
GALILEO. 
 
 49 
 
 tative 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 argu- 
 ment. 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 re- 
 lied in proof of this part of the argu- 
 ment.) "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 en- 
 dowed with action. I answer, even 
 allowing that hell is in the centre of the 
 earth, and a fire in it, I deny the conse- 
 quence : and for proof I say, if the ar- 
 gument is worth any thing, it proves 
 also that lime-kilns, ovens, and fire-grates 
 are animated and spontaneously move- 
 able. 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 solici- 
 tous about such things, either in assert- 
 ing or denying them. And Opusc. 1 1 , 
 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. 1 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 per- 
 sons 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 immo- 
 bility ; 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 dis- 
 regards 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 ad- 
 herents, and it is scarcely possible that 
 he could seriously persuade himself that 
 he was stating and overturning argu- 
 ments similar to those by which Galileo 
 had made so many converts to the opi- 
 nions of Copernicus. Whatever may be 
 our judgment of his candour, we may at 
 least feel assured that if this had in- 
 deed 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 spin- 
 ning 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 de- 
 cree 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 op- 
 posed 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 pro- 
 bably 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 hu- 
 mour to listen lightly to calumnies 
 against him, and that so long as he oc- 
 cupied the papal chair, Galileo might 
 think himself out of all danger. But 
 nevertheless he was not allowed to re- 
 turn home, without receiving formal 
 notice not to teach the opinions of Co- 
 E 
 
50 
 
 GALILEO. 
 
 pernicus, 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 Car- 
 melite friar a commentary on the book 
 of Joshua by a Spaniard named Diego 
 Zuniga Kepler's Epitome of the Co- 
 pernican Theory and Copernicus' sown 
 work, were inserted in the list of for- 
 bidden books, nor was it till four years 
 afterwards, in 1620, that, on reconsidera- 
 tion, 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 fol- 
 lowing remarks : " This theory occurred 
 to me when in Rome, whilst the theolo- 
 gians were debating on the prohibition 
 of Copernicus's book, and of the opi- 
 nion maintained in it of the motion of 
 the earth, which I at that time believed ; 
 until it pleased those gentlemen to sus- 
 pend the book, and declare the opinion 
 false and repugnant to the Holy Scrip- 
 tures. Now, as I know how well it be- 
 comes me to obey and believe the deci- 
 sions of my superiors, which proceed 
 out of more profound knowledge than 
 the weakness of my intellect can attain 
 to, this theory which 1 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 far- 
 ther, 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 in- 
 deed 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 lon- 
 gitudes at sea, for the solution of which 
 important problem Philip 111. had 
 ottered a considerable reward, an exam- 
 ple 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 Flo- 
 rence 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 1 5 in each hour, the 
 hours, minutes, and seconds of time 
 which express this difference must be 
 multiplied by 15, and the respective pro- 
 ducts 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 embar- 
 rassed 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 
 
GALILEO. 
 
 51 
 
 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 suffi- 
 ciently, during the interval which must 
 necessarily occur between the two ob- 
 servations. This consideration led Ga- 
 lileo to reflect on the use which might 
 be made of his pendulum for this pur- 
 pose ; and, with respect to the other diffi- 
 culty, he contrived a peculiar kind of 
 telescope, with which he flattered him- 
 self, 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 com- 
 municate directly with the Duke of 
 Lerma, the Spanish minister, and in- 
 structions 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 be- 
 lieve 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 person- 
 ages, 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 
 1 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, ho- 
 nours, 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 want- 
 ing on the part of those who are to re- 
 ceive it, and who should solicit and foster 
 it." But he could not, with all his en- 
 thusiasm, rouse the attention of the 
 Spanish court. The negotiation lan- 
 guished, and although occasionally re- 
 newed during the next ten or twelve 
 years, was never brought to a satisfactory 
 issue. Some explanation of this other- 
 wise 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 re- 
 quired privately from Spain, (in return 
 for the permission granted for Galileo to 
 leave Florence, m pursuance of this de- 
 sign,) the privilege of sending every year 
 from Leghorn two merchantmen, duty 
 free, to the Spanish Indies. 
 
 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 de- 
 livered 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 ap- 
 pearance of these comets, was confined 
 to his bed by severe illness. This essay 
 was printed in Florence at the sign of 
 The Medicean Stars.* What princi- 
 pally deserves notice in it, is the opinion 
 of Galileo, that the distance of a comet 
 cannot be safely determined by its paral- 
 lax, 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 dis- 
 tance 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 
 
 * In Firenze nella Stamperia di Pietro Cecconcelli 
 alle stelle Medicee, 1619. 
 
 E2 
 
GALILEO. 
 
 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 per- 
 fectly 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 qua- 
 lity, 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 ani- 
 mosity in so many quarters that none 
 of his published opinions, whether cor- 
 rect or incorrect, ever wanted a ready 
 antagonist. The champion on the pre- 
 sent 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 fre- 
 quent illnesses occasioned so many in- 
 terruptions, that it was not until the au- 
 tumn of 1623 that II Saggiatore (or The 
 Assayer) as he called his answer, was 
 ready for publication. This was printed 
 by the Lvncean Academy, and as Cardi- 
 nal Mafrco Barberino, wno 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*, 
 when eulogizing Galileo as one of the 
 earliest who adorned philosophical truths 
 with the graces and ornaments of lan- 
 guage, expressly instances the Saggia- 
 
 * Dell' Origine d'ogai Literatura : Parma, 1787. 
 
 tore, 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 preemi- 
 nent reputation. It is a prolix and ra- 
 ther tedious examination of Grassi 1 s 
 Essay; nor do the arguments seem so 
 satisfactory, nor the reasonings so com- 
 pact 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 Coperni- 
 can 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, con- 
 sider 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 de- 
 scends 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 pheno- 
 mena of comets." 
 
 Sarsi had quoted a story from Suidas 
 in support of his argument that motion 
 always produces heat, how the Babylo- 
 nians used to cook their eggs by whirl- 
 ing them in a sling ; to which Galileo 
 replies : " I cannot refrain from mar- 
 velling that Sarsi will persist in proving 
 to me, by authorities, that which at any 
 moment I can bring to the test of ex- 
 periment. 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 she wing that we rea- 
 son better than many men of established 
 reputation. If Sarsi insists that I believe, 
 
GALILEO. 
 
 53 
 
 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 be- 
 cause, 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 un- 
 grateful 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 what- 
 ever 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 acci- 
 dent, affection, and quality, really inherent 
 in the substance by which we feel our- 
 selves 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 condi- 
 tions, 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 in- 
 clined 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 ; inso- 
 much 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 be- 
 lieve that there exists any thing in ex- 
 ternal 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 publica- 
 tion of the " Saggiatore," that is to say, 
 about the time of Easter, in 1624, Gali- 
 leo 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 ap- 
 pears 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 Oc- 
 tober, 1 623, 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 1 will visit 
 you at Acqua Sparta, that I may bq 
 
54 
 
 GALILEO. 
 
 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 re- 
 ceived 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, Cardi- 
 nal 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 con- 
 demned 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 ad- 
 dressed a letter to Ferdinand, who had 
 succeeded his father Cosmo as Grand 
 Duke of Tascany, expressly for the pur- 
 pose 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 ob- 
 tained. 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 whicti you shall confer upon 
 him, imitating, or even surpassing your 
 father's liberality, will conduce to Our 
 gratification." Honoured with these un- 
 equivocal 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 con- 
 sisted 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 Vin- 
 cenzo'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 superin- 
 tendence, 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 Vincenzp's conduct, characterizing 
 him as "dissolute, obstinate, and im- 
 pudent ;" in consequence of which be- 
 haviour, 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 em- 
 ploying 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 de- 
 privation of his stipend as extraordi- 
 nary 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 esta- 
 blishment in Florence, but probably 
 those who now raised it reckoned upon 
 finding in Ferdinand II., then scarcely 
 
GALILEO. 
 
 55 
 
 of age, a less firm supporter of Galileo 
 than his father Cosmo had been. But 
 the matler 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 sti- 
 pend and privileges. 
 
 CHAPTKR XIII. 
 
 Publication of Galileo's ' System of the 
 World' His Condemnation and Ab- 
 juration. 
 
 IN the year 1630, Galileo brought to its 
 conclusion his great work, " The Dia- 
 logue on the Ptolemaic and Copernican 
 Systems," and began to take the neces- 
 sary 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, re- 
 turned home, where he intended to com- 
 plete 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 discon- 
 certed by the premature death of that 
 accomplished nobleman, in August 1630, 
 in whom Galileo lost one of his steadiest 
 and most effective friends and pro- 
 tectors. This unfortunate event de- 
 termined 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 in- 
 specting the commencement and conclu- 
 sion, 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 pre- 
 vented the publication of the work till 
 late in 1632; it then appeared, with a 
 dedication to Ferdinand, under the fol- 
 lowing 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 Co- 
 pernican, indeterminately proposing the 
 Philosophical Arguments as well on 
 one side as on the other." The begin- 
 ning of the introduction, which is ad- 
 dressed "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 Py- 
 thagorean opinion of the earth's motion. 
 Some were not wanting, who rashly as- 
 serted that this decree originated, not in 
 a judicious examination, but in ill in- 
 formed passion ; and complaints were 
 heard that counsellors totally inexpe- 
 rienced 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 determi- 
 nation, 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 au- 
 diences, 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.* 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 par- 
 ticularly 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 
 
 * Delambre quotes this sentence from a passage 
 which is so obviously ironical throughout, as an in- 
 stance of Galileo's mis-statement of facts I Hint, 
 de I'Astr. Mod., vol. i. p. 666. 
 
56 
 
 GALILEO. 
 
 country proceed not only dogmas for 
 the salvation of the soul, but also inge- 
 nious discoveries for the gratification of 
 the understanding. With this object, I 
 have taken up in the Dialogue the Co- 
 pernican 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 in- 
 deed profess to be Peripatetics, but re- 
 tain only the name, and are contented 
 without improvement to worship sha- 
 dows, 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 go- 
 vernment 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 conve- 
 nient, but in fact unreal supposition. 
 So long as this decree remained in force, 
 a due regard to consistency would com- 
 pel 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 Gali- 
 leo.* There were not wanting circum- 
 stances 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 at- 
 tained his father's energy, showed him- 
 self as friendly as possible to Galileo. 
 Cardinal Bellarmine, who had been 
 mainly instrumental in procuring the 
 decree of 16 1 6, was dead ; Urban on the 
 contrary, who had been among the few 
 Cardinals who then opposed it as un- 
 called for and ill-advised, was now pos- 
 sessed of supreme power, and his recent 
 affability~s^eTned~~to~j)n)ve that the in- 
 creased 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 him- 
 
 * Page 54. 
 
 self mistaken in this estimate of his 
 position, but for an unlucky circum- 
 stance, of which his enemies imme- 
 diately saw the importance, and which 
 they were not slow in making available 
 against him. The dialogue of Galileo's 
 work is conducted between three per- 
 sonages ; 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 solu- 
 tions of their doubts and difficulties, and 
 on him the principal task falls of ex- 
 plaining 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 digres- 
 sions, 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 indiffer- 
 ent, and in fact he is alternately ridi- 
 culed and confuted at every turn. As 
 Galileo racked his memory and inven- 
 tion 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 exone- 
 rate Galileo from this charge ; the ob- 
 vious 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 sen- 
 sitive on this point. His own expres- 
 sions 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 autho- 
 rised the publication. 
 
 One of the earliest notices of what was 
 approaching, is found in the dispatches, 
 
GALILEO. 
 
 57 
 
 dated August 24, 1 632, from Ferdinand's 
 minister, Andrea Cioli, to Francesco 
 Nicolini, the Tuscan ambassador at the 
 court of Rome. 
 
 " I have orders to signify toYour Excel- 
 lency that His Highness remains greatly 
 astonished that a book, placed by the au- 
 thor 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 justifi- 
 cation ; 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 Ferdi- 
 nand refrained from interfering more 
 strenuously to protect Galileo. Cioli's 
 words are : " The Grand Duke is so en- 
 raged 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 mi- 
 nisters, or of their bad advice."* 
 
 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 ene- 
 mies to get your book prohibited will 
 occasion no loss either to your reputa- 
 tion, 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 
 
 * Galuzzi. Storia di Toscana. Firenze, 1822. 
 
 pleasure of seeing them, I shall devote 
 to a hundred thousand devils these un- 
 natural and godless hypocrites." 
 
 At the same time, Thomas Campanella, 
 a monk, who had already distinguished 
 himself by an apology for Galileo (pub- 
 lished 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 ma- 
 thematics, or familiarity with abstruse 
 speculations. I should advise you to 
 procure a request from the Grand Duke 
 that, among the Dominicans and Je- 
 suits and Theatins, and secular priests 
 whom they are putting on this congre- 
 gation 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 Gali- 
 leo not admitted to the congrega- 
 tion, 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 sys- 
 tem, 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 re- 
 ceived an intimation to advise the Duke 
 " not to engage himself in this matter 
 as he had done in the other business of 
 Alidosi,* 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 op- 
 position. On the 15th of September, 
 probably as soon as the first report on 
 
 * Alidosi was a Florentine nobleman, whose estate 
 Urban wished to confiscate on a charge of heresy. r 
 Galuzzi. 
 
58 
 
 GALILEO. 
 
 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 Inqui- 
 sition. Nicolini was permitted to com- 
 municate this to the Grand Duke pnly, 
 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 ad- 
 vanced age of seventy years, the very in- 
 firm state of his health, and the discom- 
 forts which he must necessarily suffer in 
 such a journey, and in keeping quaran- 
 tine, 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 him- 
 self 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 se- 
 cluded in Nicolini's palace, where he was 
 as usual maintained at the expense of 
 the Grand Duke. Nelli quotes two let- 
 ters, which passed between Ferdinand's 
 minister Cioli and Nicolini, in which 
 the former intimated that Galileo's ex- 
 penses 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 am- 
 bassador'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 es- 
 timate the proceedings throughout 
 against Galileo by 'the usual practice of 
 that detestable tribunal, it will appear 
 that he was treated with unusual consi- 
 deration. Even when it became neces- 
 sary in the course of the inquiry to 
 examine him in person, which was in 
 the beginning of April, although his re- 
 
 moval to the Holy Office was then in- 
 sisted 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 adjoin- 
 ingroom.andto 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 fret- 
 ful and impatient. On the last day of 
 April, about ten days after his first ex- 
 amination, he was unexpectedly per- 
 mitted to return to Nicolini's house, 
 although the proceedings were yet far 
 from being brought to a conclusion. 
 Nicolini attributes this favour to Cardi- 
 nal 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 cheerful- 
 ness, although his return appears to 
 have been permitted on express condi- 
 tion 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 * 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 ab- 
 jure, as impious and heretical, the opi- 
 nions which his whole existence had 
 been consecrated to form and strengthen. 
 
 * S' irrito il Papa, e lo fece abjurare, comparendo 
 il pover uome con uno straccio di camicia iiidosso, 
 che faceva compassione, MS. nella Bibl. Magliab. 
 Venturi. 
 
GALILEO. 
 
 59 
 
 As we are not aware that this remark- 
 able record of intolerance and bigoted 
 folly has ever been printed entire in Eng- 
 lish, 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 through- 
 out the whole Christian Republic, Spe- 
 cial Deputies of the Holy Apostolical 
 Chair against heretical depravity, 
 
 " Whereas you, Galileo, son of the late 
 Vincenzo Galilei of Florence, aged^seven- 
 ty 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 maintain- 
 ing 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 an- 
 swering the objections which were con- 
 tinually produced from the Holy Scrip- 
 tures, 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, follow- 
 ing 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 detri- 
 ment 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 proposi- 
 tions 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 immove- 
 able from its place, is absurd, philoso- 
 phically false, and formally heretical; 
 because it is expressly contrary to the 
 Holy Scripture. 
 
 " Idly. The proposition that the Earth 
 is not the centre of the world, nor im- 
 moveable, 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 de- 
 creed 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 ac- 
 quiescence that you should be im- 
 prisoned ; and in execution of this de- 
 cree, on the following day at the pa- 
 lace, in presence of His Eminence the 
 said Lord Cardinal Bellarmine, after 
 you had been mildly admonished by the 
 said Lord Cardinal, you were com- 
 manded by the acting Commissary of the 
 Holy Office, before a notary and wit- 
 nesses, to relinquish altogether the said 
 false opinion, and in future neither to 
 defend nor teach it in any manner, nei- 
 ther verbally nor in writing, and upon 
 your promising obedience you were dis- 
 missed. 
 
 " 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 Congre- 
 gation of the Index* prohibiting the 
 books which treat of this doctrine ; and 
 it was declared false, and altogether con- 
 trary to the Holy and Divine Scripture, j 
 
 " And whereas a book has since ap- 
 peared, 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 conse- 
 quence 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 
 
 * 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, par- 
 ticularizing 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. 
 
60 
 
 GALILEO. 
 
 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 ex- 
 press 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. There- 
 fore by Our order you have been cited to 
 this Holy Office, where, on your exami- 
 nation upon oath, you have acknow- 
 ledged 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 argu- 
 ments 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 conse- 
 quence of the natural complacency 
 which every one feels with regard to his 
 own subtilties, and in showing himself 
 more skilful than the generality of man- 
 kind in contriving, even in favour of 
 false propositions, ingenious and appa- 
 rently 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^Car- 
 dinalBellarmine, procured, as you said, 
 by yourself, that you might defend 
 yourself against the calumnies of your 
 enemies, who reported that you had ab- 
 jured your opinions, and had been pun- 
 ished by the Holy Office ; in which cer- 
 tificate 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 de- 
 clares 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 rea- 
 son 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 am- 
 bition, rather than to malice. But this 
 very certificate, produced on your behalf, 
 has greatly aggravated yo'ur 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 thai it is 
 probable ; nor is there any extenuation 
 in the licence artfully and cunningly 
 extorted by you, since you did not inti- 
 mate 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 exa- 
 mination 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 con- 
 fessed 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 arid hold the 
 false doctrine, and contrary to the Holy 
 
GALILEO. 
 
 ft 
 
 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 pe- 
 nalties enjoined and promulgated in the 
 sacred canons, and other general! and 
 particular constitutions against delin- 
 quents 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 Ca- 
 tholic and Apostolic Church of Rome, 
 in the form now shown to you. 
 
 " But, that your grievous and per- 
 nicious 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 plea- 
 sure ; 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 Our- 
 selves the power of moderating, com- 
 muting, 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 re- 
 serve, 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 merci- 
 less tribunal to wjiose power he was 
 subjected, could without extreme reluc- 
 tance 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 ade- 
 quate explanation of his submission, 
 either in their exhortations, or in the 
 mere dread of the alternative which 
 might await him in case of non-com- 
 pliance. It has in short been supposed, 
 although the suspicion scarcely rests 
 upon grounds sufficiently strong to war- 
 rant 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.*" 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 opi- 
 nion bring forward in corroboration of 
 it, that Galileo immediately on his de- 
 parture from Rome, in addition to his 
 old complaints, was found to be afflicted 
 with hernia, and this was a common con- 
 sequence 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. t 
 
 * Giudicassimo esser necessario venir contro di 
 te al rigoroso esame nel quale rispondesti cattolica- 
 mente. 
 
 f 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 tirst re- 
 turn to Nicolini's palace. 
 
GALILEO. 
 
 Although the arguments we have 
 mentioned appear to us slight, yet nei- 
 ther can we attach much importance to 
 the contrast which the favourers of the 
 opposite opinion profess to consider so in- 
 credible between the honourable manner 
 in which Galileo was treated throughout 
 the rest of the inquiry, and the suspected 
 harsh proceeding against him. Whe- 
 ther Galileo should be lodged in a pri- 
 son 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 hither- 
 to unblemished innocence and charac- 
 ter. The question may be disencum- 
 bered of all such scruples, since one 
 atrocity more or less can do little to- 
 wards affecting our judgment of the 
 unholy Office of the Inquisition. 
 
 Delambre, who could find so much to 
 reprehend in Galileo's former uncom- 
 promising 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 in- 
 quiries 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 con- 
 fession, is rather to be read as the com- 
 position of his judges than his own. For 
 instance, in one of the letters which we 
 have extracted*, 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 aggra- 
 vation of his guilt, that he began to write 
 it after the prohibition which he had re- 
 ceived in 1616. 
 
 The abjuration was drawn up in the 
 following terms : 
 
 The Abjuration of Galileo. 
 
 " I Galileo Galilei, son of the late Vin- 
 cenzo 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 re- 
 
 * Page 18. 
 
 public against heretical depravity, having 
 before my eyes the Holy Gospels, which 
 I touch with my own hands, swear, that 
 I hare 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 be- 
 cause 1 had been enjoined by this Holy 
 Office altogether to abandon the false 
 opinion which maintains that the sun is 
 the centre and immoveable, and forbid- 
 den 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 doc- 
 trine now condemned, and adduce rea- 
 sons 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 ve- 
 hement suspicion rightfully entertained 
 towards me, with a sincere heart and 
 unfeigned faith, I abjure, curse, and de- 
 test, the said errors and .heresies, and 
 generally every other error and sect con- 
 trary 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 simi- 
 lar 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 Or- 
 dinary 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 de- 
 linquents 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 tliis 
 present writing of my abjuration, which 
 
GALILEO. 
 
 I have .' recited word for word. At 
 Rome in the Convent of Minerva, 22d 
 June, 1633. I, Galileo Galilei, have ab- 
 jured as above with my own hand." 
 
 IL.is..-SaJd that Galileo, as he rose 
 from his knees, stamped on the ground, 
 and whispered to one of his friends, E 
 pur simuove (It does move though). 
 
 Copies of Galileo's sentence and abju- 
 ration 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 Mer- 
 senne 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 pe- 
 nance, 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 col- 
 lect 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 them- 
 selves 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 toge- 
 ther can keep it from turning, nor them- 
 selves from turning with it." 
 
 The assembly of doctors of the Sor- 
 bonne at Paris narrowly escaped from 
 passing a similar sentence upon the 
 system of Copernicus. The question was 
 laid before them by .Richelieu, and it ap- 
 pears that their opinion was for a mo- 
 ment in fay our of confirming the Roman 
 decree. It is to be wished that the name 
 
 had been preserved of one of its mem- 
 bers, who, by his strong and philoso- 
 phical representations, saved that cele- 
 brated body from this disgrace. 
 
 Those who saw nothing in the punish- 
 ment 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 Za- 
 chary, 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 le- 
 gate 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*. 
 
 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 attri- 
 bute 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 theolo- 
 gians rejected the opinions of Copernicus, 
 as contrary to the Scriptures, the head of 
 that Church was never permitted to com- 
 promise his infallible character by for- 
 mally condemning it t. 
 
 Whatever may be the value of this 
 
 * Annalium Bolorum, libri vii. Ingolstadii, 1554. 
 
 t La Chiesa non ha mai dichiarati eretici i soste- 
 nitori del Sistema Copernicano, e questa troppo ri- 
 gorosa censura non usci che dal tribunale della 
 Romana Inquisizione a cui niuno tra Cattolici ancor 
 piu zelanti ha mai attribuito U diritto dell' infalli- 
 
64 
 
 GALILEO. 
 
 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 remo- 
 delled in 1588, are quoted by a pro- 
 fessor of the University of Louvain, 
 a zealous antagonist of Galileo, as fol- 
 lows : " They are to examine and ex- 
 pose the books which are repugnant 
 to the Catholic doctrines 'and Chris- 
 tian discipline, and after reporting on 
 them to us, they are to condemn them 
 by our authority.*" Nor does it ap- 
 pear 'that the learned editors of what 
 is commonly called the Jesuit's edi- 
 tion of Newton's "Principia" were of 
 opinion, that in adopting the Copernican 
 system they should transgress a mandate 
 emanating from any thing short of infal- 
 lible 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 riot 
 explain the author's propositions other- 
 wise than by making the same supposi- 
 tion. We are therefore forced to sus- 
 tain 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."-{- 
 
 This coy reluctance to admit what 
 nobody any longer doubts has sur- 
 vived to the present time; for Bailli 
 informs us,$ that the utmost endea- 
 vours of Lalande, when at Rome, to 
 obtain that Galileo's work should be 
 erased from the Index, were entirely in- 
 effectual, 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. Ur- 
 
 bilita. Anzi in cio ancora e d' ammirarsi la provi- 
 denza di Dip a favor della Chiesa, percioche in un 
 tempo in cni la maggior parte dei teologi ferma- 
 mente credavano che il Sistema Copernicano fosse 
 all* autorita delle sacre Carte contrario, pur non 
 pennise che dalla Chiesa si proferisse su cio un 
 solenne giudizio. Stor. della Lett. Ital. 
 
 * Lib. Frpmondi Antaristarchus, Antwerpiae, 1631. 
 
 t Newtpni Principia, Colonise, 1760. 
 
 J Histoire de 1'Astronomie Moderce, 
 
 ban's indignation also vented itself upon 
 those who had been instrumental in ob- 
 taining the licence for him. The Inquisi- 
 tor at Florence was reprimanded ; Ric- 
 cardi, the master of the sacred palace, 
 and Ciampoli, Urban's secretary, were 
 both dismissed from their situations. 
 Their punishment appears rather ano- 
 malous and inconsistent with the pro- 
 ceedings 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 sur- 
 reptitiously obtained from them,, by con- 
 cealing circumstances with which they 
 were not bound to be otherwise ac- 
 quainted. 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 writ- 
 ten, ordered the licence to be given. 
 Urban only replied that this was a 
 Ciampolism ; that his secretary and Ga- 
 lileo had circumvented him ; that' he had 
 already dismissed Ciampoli, and that 
 Riccardi must prepare to follow him. 
 
 As soon as the ceremony of abju- 
 ration was concluded, Galileo was con- 
 signed, pursuant to his sentence, to 
 the prison of the Inquisition. Pro- 
 bably 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 recom- 
 mended as a more suitable residence, the 
 palace of the Archishop 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 ut- 
 most kindness, controlled of course by 
 the strict injunctions which were dis- 
 patched 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 re- 
 siding with the archbishop. 
 
GALILEO. 
 
 65 
 
 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 con- 
 sidered to surpass all other Italian 
 writers (unless we except Machiavelli) 
 in the purity and beauty of his lan- 
 guage, and indeed his principal fol- 
 lowers, 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 sub- 
 jects 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 to- 
 gether indiscriminately to study to be- 
 come 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 ^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 examin- 
 ing and understanding them." 
 
 The general structure of the dialogues 
 has been already described*; we shall 
 
 * See page 56. 
 
 therefore premise no more than the 
 judgment pronounced on them by a 
 highly gifted writer, to supply the de- 
 ficiencies 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 undis- 
 puted 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 ren- 
 dered to real knowledge is to be esti- 
 mated, 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 ad- 
 mitted, with all the delight of novelty, 
 and feels one's self carried back to the 
 period when the telescope was first di- 
 rected to the heavens, and when the 
 earth's motion, with all its train of con- 
 sequences, was proved for the first 
 time."* 
 
 The first Dialogue is opened by an at- 
 tack upon the arguments by which Aris- 
 totle 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. Sal- 
 viati (representing Galileo) then objects 
 to the Aristotelian distinctions between 
 the corruptible elements and incorrupti- 
 ble skies, instancing among other things 
 the solar spots and newly appearing 
 stars, as arguments that the other hea- 
 venly 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 Sim- 
 plicio, and perceive that he is much 
 moved by the force of these too conclu- 
 sive arguments; but methinks I hear 
 him say ' Oh, to whom must we betake 
 ourselves to settle our disputes if Aris- 
 totle be removed from the chair ? What 
 
 * Playfair's Dissertation, Supp. Encyc. Brit. 
 
66 
 
 GALILEO. 
 
 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 with- 
 out 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 ex- 
 pense 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 
 fail 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 no- 
 tice: 
 
 " Just as from the mutual and uni- 
 versal 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 rea- 
 sonable to believe that spontaneously, 
 and of its natural instinct, it would re- 
 turn? 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 ac- 
 
 quainted with the History of Astro- 
 nomy, are apt to suppose that New- 
 ton'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 apply- 
 ing it to all the visible creation, and 
 tracing the principle of universal gravi- 
 tation with the assistance of a most re- 
 fined 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 pas- 
 sages from his "Astronomy" will shew 
 the nature of his conceptions on this 
 subject : 
 
 "The true doctrine of gravity is 
 founded on these axioms : every corpo- 
 real substance, so far forth as it is cor- 
 poreal, 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 to- 
 wards 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 bo- 
 dies (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 whitherso- 
 ever it may be carried by its animal fa- 
 culty, 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 to- 
 gether in the intermediate point, each 
 approaching the other by a space pro- 
 
GALILEO. 
 
 67 
 
 portional 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 sub- 
 stance of both is of the same density. If 
 the earth should cease to attract its wa>- 
 ters to itself, all the waters of the sea 
 would be raised, and would flow to the 
 body of the moon*." 
 
 He also conjectured that the irregu- 
 larities 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 attrac- 
 tion 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 al- 
 together 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." t Roberval took up Kep- 
 ler'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 con- 
 nected 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 acci- 
 dent 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, ac- 
 cording 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 
 
 * Astronomia Nova. Pragae. 1609. 
 
 f The new Planet no Planet, or the Earth no wan- 
 dering Star, except in the wandering heads of Gali- 
 leans. London, 1646. 
 
 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*". This very curious 
 work was reprinted in the third volume, 
 of the Reflexiones Physico-Mathematicce 
 of Mersenne, from whom Roberval pre- 
 tended to have received the Arabic ma- 
 nuscript, and who is thus irretrievably 
 implicated in the r forgery.t 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, maintain- 
 ing 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 abso- 
 lutely 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.''^ 
 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. Galileo 
 had not altogether neglected to specu- 
 late on such a supposition, as is plain 
 from the following extract. It is taken 
 from a letter to Carcaville, dated from 
 Aicetri, 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 dis- 
 tance 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." f 
 
 It is very difficult to offer any satis- 
 factory comment upon this passage ; it 
 may be sufficient to observe that this 
 paradoxical result was afterwards de- 
 
 * Aristarchi Samii de Mundi Systemate. Parisiis 
 1644. 
 
 f See page 12. 
 I De Coelo.lib. iv. cap. 3. 
 
 Reflexiones Fhysico-Mathematicse, Pansiis,167 
 If Yeutuvi. 
 
68 GALILEO. 
 
 duced by Newton, as one of the conse- 
 quences 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 mathemati- 
 cians with a meaning which in many 
 cases their authors did not contem- 
 plate. The progressive development of 
 these ideas in the hands of Wallis, 
 Huyghens, Hook, Wren, and New- 
 ton, 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 pro- 
 pensity 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 ex- 
 ample 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,* 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 altera- 
 tion 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, ab- 
 stracting 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 alter- 
 ation 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 draw- 
 ing till we got to Alexandria, he would 
 have been able by its motion, to produce 
 an accurate representation of many ob- 
 jects 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 
 
 Jliccioli. 
 
GALILEO. 
 
 69 
 
 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 mo- 
 tion was immoveable. Thus it is like- 
 wise 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 im- 
 perceptible 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 ge- 
 neral character of Galileo's reasoning : 
 " Salviati. I did not say that the earth 
 has no principle, either" internal or ex- 
 ternal, 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 no- 
 torious, and every one knows that it is 
 Gravity. Salv. You are out, Master 
 
 ture 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 ge- 
 neric term, and talk of the virtue im- 
 pressed, and call it either an assisting or 
 an informing intelligence, and are con- 
 tent to say that Nature is the cause of 
 an infinite number of other motions." 
 
 Simplicio is made to quote a passage 
 from Schemer's book of Conclusions 
 against Copernicus, to the following ef- 
 fect : " ' 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 fore- 
 sight of this philosopher is most ad- 
 mirable and praiseworthy, for he is not 
 content with providing for things that 
 might happen during the common 
 course of nature, but persists in shew- 
 ing 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 con- 
 ceits, 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 con- 
 tinue a motion of revolution. What is 
 to follow ? What conclusion is the phi- 
 losopher going to draw ? Simpl. This 
 objection is in the very next words 
 4 Which nevertheless (says he) is con- 
 trary to experience and reason.' Salv. 
 Now I must yield: since he has so 
 great an advantage over me as ex- 
 perience, with which I am quite unpro- 
 vided. For hitherto I have never hap- 
 pened to see the terrestial earth and 
 water annihilated, so as to be able to 
 observe what the hail and fire did in the 
 
 Simplicio ; you should say that every confusion. But does he.tell us for our in- 
 ane knows that it is called Gravity ; but formation at least what they did ISimp. 
 I do not ask you the name but the na- No, he does not say any thing more. 
 
GALILEO. 
 
 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 equivo- 
 cal 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 paral- 
 lax of the new stars of 1572 and 1604, 
 in which Delambre notices that Galileo 
 does not employ logarithms in his cal- 
 culations, although their use had been 
 known since Napier discovered them in 
 1616 : the dialogue then turns to the an- 
 nual motion " first taken from the Sun 
 and conferred upon the Earth by Aris- 
 tarchus Samius, and afterwards by Co- 
 pernicus." Salviati speaks of his con- 
 temporary philosophers with great con- 
 tempt " If you had ever been worn out 
 as I have been many and many a time 
 with hearing what sort of stuff is suf- 
 ficient to make the obstinate vulgar un- 
 persuadable, 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 satis- 
 fied that the earth, so heavy as it is, 
 cannot climb up above the sun, and then 
 come tumbling in a breakneck fashion 
 down again ! " * 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 sta- 
 tions and retrogradations of the planets 
 are accounted for on this supposition. 
 
 * The notions commonly entertained of ' up' and 
 * down,' as connected with the observer's own situ- 
 ation, 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 west- 
 ward 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. 
 
 The following is one of the frequently 
 recurring passages in which Galileo, 
 whilst arguing in favour of the enor- 
 mous distances at which the theory of 
 Copernicus necessarily placed the fixed 
 stars, inveighs against the arrogance 
 with which men pretend to judge of mat- 
 ters 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 be- 
 nefit, to what purpose should a vast 
 vacancy be afterwards interposed be- 
 tween 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 advan- 
 tage ? 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 con- 
 cerns the government of human affairs ; 
 but that there may not be other things 
 in the universe dependant upon His su- 
 preme 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 teme- 
 rity 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 know- 
 ing what is of use to us ; and I hold it 
 to be one of the greatest pieces of arro- 
 gance and folly that can be in this world 
 to say, because I know not of what use 
 Jupiter or Saturn are to me, that there- 
 fore 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 
 
GALILEO. 
 
 71 
 
 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 Medi- 
 cean 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 innu- 
 merable 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 con- 
 stellations 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 ap- 
 pears to me that Sig. Salviati, with a 
 fine circumlocution, has so clearly ex- 
 plained the cause of these effects, that 
 any common understanding, even though 
 unacquainted with science, may compre- 
 hend it : but we, confining ourselves to 
 the terms of art, reduce the cause of 
 these and other similar natural pheno- 
 mena 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 num- 
 ber of effects and accidents which we 
 see, not without admiration, to be pro- 
 duced 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 har- 
 riers ; in this corner I will have a hunts- 
 man, 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 en- 
 tirely 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*. 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 consi- 
 dered 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 cu- 
 riosity!'." Riccioli has enumerated se- 
 veral 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 indi- 
 cated 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 expla- 
 nation 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, accord- 
 ing 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 moonj. 
 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 in- 
 accuracy should be attributed, not to 
 
 * See page 50. i Riccioli Almag. Nov. 
 
 K. Plutarch, De placit, Philos. lib. iii. c. 1?. 
 
72 
 
 GALILEO. 
 
 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 informa- 
 tion. 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." * 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 
 moont." He then very accurately de- 
 scribes 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$." " When the moon is in the north, 
 and further removed from the earth, the 
 tides are more gentle than when digress- 
 ing to the south, she exerts her^force 
 with a closer effort^." 
 
 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 
 
 eix; ry fft^vr,. Geographic, lib. iii. 
 
 | Historia Naturalis, lit. ii. c, 97. 
 
 t Ut ancillante sidere, trahenteque secum avido 
 hausm maria. 
 
 Eadem Aquilonia, et a terris longius recedente, 
 mitiores qaam cum, in Austros digressa, propiore 
 nisuvim suam exercet. 
 
 to gather into a lower level.*" The 
 theory of Universal Gravitation seems 
 here within the grasp of these philo- 
 sophers, 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 dis- 
 tance, 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 formi- 
 dable obstacle to this theory, and the 
 most plausible explanation that was 
 given was, that this magnetic virtue ra- 
 diated 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 men- 
 tions 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 them- 
 selves driven to pronounce these wise, 
 ingenuous, and modest words 1 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, \Mhich indeed 
 
 * Commentarii Collegii Conimbricensis. Colcmiae t 
 
GALILEO. 
 
 73 
 
 probably suggested it, as he was in 
 the habit of suffering no natural phe- 
 nomena, 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 illus- 
 trations, 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 ac- 
 quired, 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 con- 
 sequently 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 con- 
 taining 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 Medi- 
 terranean 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 conse- 
 quence of which is that a point under 
 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 direc- 
 tions 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 repre- 
 sentation is fallacious, and that the 
 oscillation of the water does not in the 
 least result from the causes here as- 
 signed 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 ine- 
 quality 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 revolv- 
 ing horizontally, and fasten two leaden 
 weights to the ends of it; and if the 
 clock goes too slow, by merely ap- 
 proaching these weights somewhat to- 
 wards the centre of the bar, they make 
 its vibrations more frequent, at which 
 time they are moving in smaller circles 
 than before*. 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 ac- 
 celerated as the length of the string 
 diminishes. W r e 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 revolu- 
 tion. Now this very thing happens 
 in fact to the moon, which I have just 
 advanced on a supposition. Let us call 
 
 * See fig. 1, p. 96. 
 
GALILEO. 
 
 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 conclu- 
 sion that at new moon, when in con- 
 junction 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 mo- 
 tion 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*. M 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 appre- 
 ciate 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 ap- 
 plied mechanical principles to the solv- 
 ing of philosophical difficulties, natural 
 philosophy is well known to have been 
 rendered more intelligible, and to have 
 
 Phil. Trans., No. 16, August 1666. 
 
 made a much greater progress in less 
 than a hundred years than before for 
 many ages." 
 
 CHAPTER XV. 
 
 Galileo at Arcetri Becomes Blind 
 Moon's Librarian Publication of 
 the Dialogues on Motion. 
 
 WE have already alluded to the imper- 
 fect 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 in- 
 forms us that he had seen in the collec- 
 tion 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 sis- 
 ter 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 fa- 
 vourable impressions of it, and convey 
 a pleasing idea of this his favourite 
 daughter. Even when, in her affec- 
 tionate eagerness to soothe her father's 
 wounded feelings at the close of his im- 
 prisonment 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 feel- 
 ing excited in every one by the perusal 
 must surely be sympathy with the filial 
 tenderness which it is impossible to mis- 
 understand. 
 
 The joy she had anticipated in again 
 meeting her parent, and in compensat- 
 ing 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 con- 
 dolence 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 Boe- 
 
GALILEO. 
 
 ehineri, his son's father-in-law, he says : 
 "The hernia has returned worse than 
 at first : my pulse is intermitting, ac- 
 companied 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 extre- 
 mity of ill health, Galileo requested leave 
 to go to Florence for the advantage of 
 medical assistance; but far from obtain- 
 ing permission, it was intimated that any 
 additional importunities would be no- 
 ticed by depriving him of the partial 
 liberty he was then allowed to enjoy. 
 After several years confinement at Ar- 
 cetri, during the whole of which time 
 he suffered from continual indisposi- 
 tion, 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 instruc- 
 tions 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 inter- 
 rupted, is manifest from the result of 
 the following letter from the Duke of 
 Tuscany 's secretary of state to Nicolini, 
 his ambassador at Rome. " Signer 
 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 per- 
 fection 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 ob- 
 tains 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 remem- 
 bered, 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 suspi- 
 cions 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 re- 
 manded 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 re- 
 turned in 1636 ; in the course of the en- 
 suing 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 pe- 
 culiar 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 ex- 
 pressions " 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, hencefor- 
 ward 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 enter- 
 
76 
 
 GALILEO. 
 
 tained 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 symp- 
 toms of which all external remedies 
 failed to alleviate. 
 
 As long as the power was left him, he 
 had indefatigably continued his astrono- 
 mical 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 circum- 
 stance connected with the moon's mo- 
 tion is, that the same side is always 
 visible from the earth, showing that the 
 moon turns once on her own axis in ex- 
 actly the time of her monthly revolu- 
 tion.* 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 accu- 
 rately take place, but that a small part 
 on either side comes alternately forward 
 into sight, and then again recedes, ac- 
 cording to the moon's various positions 
 in the heavens. He was not long in de- 
 tecting one of the causes of this appa- 
 rent 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 ad- 
 ditional 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 in- 
 telligible even to those who are unac- 
 quainted with astronomy, if they will re- 
 ceive 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 
 
 * 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, Ue Placitis Philos. lib. ii. c. 28,) 
 that the Pythagoreans believed the moon to have in- 
 habitants 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 en- 
 grafted on the latter, which is true, and implies a 
 2**&ejition of the fact ia the text. 
 
 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 mov- 
 ing, 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 oppo- 
 site 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 re- 
 peated 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 pur- 
 suits, and employed himself till 1636 
 principally with his Dialogues on Mo- 
 tion, the last work of consequence that 
 he published. In that year he entered 
 into correspondence with the Elzevirs^ 
 through his friend Micanzio, on the pro- 
 ject 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 gra- 
 tification, 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 an- 
 
GALILEO. 
 
 nounced, contrasts singularly with that 
 of the Roman Inquisitors. " A book was 
 brought to me which a Veronese Capu- 
 chin 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 en- 
 titles every one of the twelve arguments 
 which compose his book, ' An irrefra- 
 gable and undeniable demonstration,' 
 and then adduces nothing but such 
 childish trash as every man of sense 
 has long discarded. For instance, this 
 poor animai understands so much geo- 
 metry 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, say- 
 ing 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 be- 
 lieves 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 ob- 
 tain permission to reprint the Essay on 
 Floating Bodies, in spite of his protes- 
 tations that it did not in any way relate 
 to the Copernican theory. This was the 
 greatest stigma with which the Inqui- 
 sition were in the habit of branding ob- 
 noxious 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 manu- 
 script to Vienna, but found that every 
 book printed there must receive the ap- 
 probation of the Jesuits ; and Galileo's 
 old antagonist, Scheiner, happening to 
 be in that city, Pieroni feared lest he 
 should interfere to prevent the publi- 
 cation altogether, if the knowledge of it 
 should reach him. Through the inter- 
 vention of Cardinal Dietrich stein, 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 Sile- 
 sia. A new approbation was there pro- 
 cured, 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 ad- 
 visable to suspend the impression till his 
 departure. In the mean time his own 
 duty as a military architect in the Em- 
 peror'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, al- 
 though, in order to obviate further an- 
 noyance, 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 Gali- 
 leo expressly requested through his 
 friend Deodati, and of which he more 
 than once privately signified his appro- 
 bation, 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 spe- 
 cimens of the astronomical opinions cur- 
 rent when Galileo began to write on that 
 subject : they serve to show the nature 
 
GALILEO. 
 
 and objects of the reasoning which he 
 had to oppose ; and, without some expo- 
 sition of them, the aim and value of 
 many of his arguments would be imper- 
 fectly understood and appreciated. 
 
 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 im- 
 mediate wants of mankind. Little has 
 been told to us when we are in- 
 formed 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*." 
 
 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 enu- 
 merating or describing them, or even 
 of examining very closely the nature and 
 limits of the aid they are capable of af- 
 fording. 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, be- 
 cause, 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 
 
 * Histoire des Alatk^matiques, vol. i. p. 97. 
 
 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 ac- 
 count say that a great force is over- 
 come 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 here- 
 after 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 ma- 
 chine by means of which we shall re- 
 move 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 sur- 
 passes its power, so that, at the end of 
 our work, we shall find that we have 
 derived no other benefit from our ma- 
 chine than that we have carried away 
 the same weight altogether, which if 
 divided into pieces we could have car- 
 ried without the machine, by the same 
 force, through the same space, in the 
 same time. This is one of the advan- 
 tages of a machine, because it often hap- 
 pens 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 an mechanics, is 
 called the " principle of virtual velocities," 
 consisting in the theorem that two 
 weights will balance each other on any 
 
GALILEO. 
 
 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 prin- 
 ciple into its consequences ; combined, 
 when the machines are in a state of mo- 
 tion, 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 prin- 
 ciple of virtual velocities is universally 
 given to Galileo ; and so far deservedly, 
 Siat he undoubtedly perceived the im- 
 portance 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 prin- 
 ciple with which everybody is so fa- 
 miliar*," 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 dis- 
 regarded. Lagrange assertsf that the 
 ancients were entirely ignorant of the 
 principle of virtual velocities, although 
 Galileo, to whom he refers it, dis- 
 tinctly mentions that he himself found 
 it in the writings of Aristotle. Montu- 
 cla 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 pas- 
 sage to which Galileo alludes is in 
 Aristotle's Mechanics, where, in dis- 
 cussing 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."$ 
 
 * De vi Percussionis, Bcmoniae, 1667. 
 t Mec, Aaalyt. J Mechanica, 
 
 It is true, that in the last mentioned 
 treatise, Aristotle has given other rea- 
 sons 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 de- 
 scribing the circle with a different degree 
 of swiftness/' 
 
 Perhaps Aristotle may have borrowed 
 the idea of virtual velocities," contrast- 
 ing so strongly with his other physi- 
 cal notions, from some older writer; 
 possibly from Archytas, who, we are 
 told, was the first to reduce the science 
 of mechanics to methodical order ; * 
 and who by the testimony of his coun- 
 trymen was gifted with extraordinary 
 talents, although none of his works have 
 come down to us. The other principles and 
 maxims of Aristotle's mechanical phi- 
 losophy, 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 
 sayingthat, when we speak of two things, 
 we do not say " all," but " both," and 
 three is the first number of which we 
 say " all." t When he comes to speak 
 of motion, he says, "If motion is not 
 understood, we cannot but remain igno- 
 rant 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 con- 
 
 * Diog. Laert. In vit. Archyt. 
 t De Coelo, lib. i. e. 1.^ 
 
80 
 
 GALILEO. 
 
 tinuous quantity is that which is infi- 
 . nitely divisible. Moreover, unless there 
 v be time, space, and a vacuum, it is im- 
 possible that there should be motion*." 
 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. " Mo- 
 tion 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." f 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 sub- 
 tleties 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 
 ^vith 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."j 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 ; " and there 
 is perhaps little fault to be found with 
 this remark, understanding motion in 
 
 * Phys. lib. i. c. 3. 
 
 -j- Lib. Hi. c. 2. The Aristotelians distinguished 
 between things as existing in act or energy (m^- 
 ytttt) and things in capacity or power (i/va^/j). 
 For the advantage of those who may think the 
 distinction worth attending to, we give an illus- 
 tration of Aristotle's meaning, from a very acute and 
 learned commentator: " It (motion) is something 
 more than dead capacity ; something less than per- 
 fect 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 actu- 
 ality (if I may so say) even of capacity itself: im- 
 perfect and obscure, because such is capacity to 
 which it belongs." Harris, Philosophical Arrange- 
 
 J Lib. iv. c. 1. Lib. iv. c. 11. 
 
 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 con- 
 crete ; 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." * 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 unnatu- 
 ral; this division of motion into na- 
 tural and violent runs through the 
 whole of the mechanical philosophy 
 founded upon his principles. " Circular 
 motion is the only one which can be 
 endless ;"f 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." $ Ba- 
 con seems to have had these passages 
 in view when he indulged in the reflec- 
 tions 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.^ 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 any 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 di- 
 rection in that ratio ;"|| 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.' ' [ 
 
 * De Coelo, lib. i. c. 2. 
 % De Ccelp, lib. i. c. 6. 
 || Mechanica. 
 
 Ev $i iv tifitvi 
 
 f Phys. lib. viii. c. 8. 
 Phys. lib. vii. c. 2. 
 
GALILEO. 
 
 81 
 
 He seemed on the point of discover- 
 ing 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 com- 
 mentator 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 experimen- 
 talist, 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, unaccompa- v/ 
 niecl 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 au- 
 thors. 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*." By light bodies he under- 
 stood those which have a natural ten- 
 dency to move from the earth, observing 
 that " that which is lighter is not al- 
 ways lightf." He maintained that the 
 
 x&ra, ftydtvx %govov, aSuvaiTov ivfaiav uvcci vnt 
 Qogxv. EOS.V yocp rivx Xoyov ivi%-6'/i &y wovcu nvt 
 
 ret 
 
 VOV 
 
 d s 
 
 dt 
 
 *DeCcelo,lib,i.c.3, fLib,iv.c,2 
 
 heavenly bodies were altogether devoid 
 of gravity ; and we have already had 
 occasion to mention his assertion, that 
 f a large body falls faster than a small 
 one in proportion to its weight*. With 
 this opinion may be classed another 
 great mistake, in maintaining that the 
 same bodies fall through different me- , 
 diums, as air or water, with velocities ^ 
 reciprocally proportional to their densi- 
 ties. By a singular inversion of expe- 
 rimental science, Cardan, relying on this 
 assertion, proposed in the sixteenth cen- 
 tury to determine the densities of air 
 and water by observing the different 
 times taken by a stone in falling through 
 themf. 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 pre- 
 served 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 no- 
 tions. 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^. Such 
 specimens of this earlier philosophy 
 
 * Phys., lib. iv. c. 8. f De Propprt.Basileae, 1570. 
 j " Nunc locus est, ut opinor, in his illud quoque 
 
 rebus 
 
 Confirmare tibi, nullam rem posse su. vi 
 Corpoream sursum ferri,- sursumque meare. 
 Nee quom subsiliunt ignes ad tecta domorura, 
 Et celeri flamml 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' mersi- 
 
 mus altum 
 
 Directa et magna vi multi pressimus segre : 
 Tarn cupide sursum revomit magis atque remittit 
 Plus ut parte foras emergant, exsiliantque : 
 Nee tamen haec, quantu'st in sedubitamus, opinor, 
 Quinvacuum per inane deorsum cuncta ferantur, 
 Sic igitur debent flammse quoque posse per auras 
 Aeris expresses sursum subsidere, quamquam 
 Pondera quantum in se est deorsum deducere pug- 
 
 nent. 
 
 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 baud 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 qu& propter debent per Inane quietum 
 ,3que ponderibus non sequis concita ferri." 
 
 De Rerura Natura, lib, U, v. 184239. 
 G 
 
S2 
 
 GALILEO. 
 
 may well indispose us towards Aris- 
 totle, who was as successful in the 
 science of motion as he was in astro- 
 nomy in suppressing the knowledge 
 of a theory so much sounder than that 
 which he imposed so long upon the cre- 
 dulity 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 pro- 
 perties of the lever. This and the Trea- 
 tise 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."* 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 enume- 
 ration 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 Pap- 
 pus 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 demon- 
 
 Math. Coll.Pisani, 16(52. 
 
 stration, it was received undoubtingly 
 for a long period. 
 
 The credit of first giving the true 
 theory of equilibrium on the inclined 
 plane is usually ascribed to Stevin, al- 
 though, 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 conti- 
 nue in motion, if there were any cause 
 why it should begin to move. This being 
 conceded, he remarks further, that the 
 parts A D and BD are also in equili- 
 brium, being exactly similar to each 
 other; and therefore 
 if they are taken 
 away, the remaining 
 parts A C and B C 
 will also be in equi- 
 librium. 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.* This 
 conclusion is the correct one, and there is 
 certainly great ingenuity in this contriv- 
 ance 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 prin- 
 ciple had been applied directly to deter- 
 mine the same proportion in a work 
 written long before, where it has re- 
 mained 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. 
 
 * (Euvres Math6mati<iues, Leyde. 1634, 
 
GALILEO. 
 
 83 
 
 " Qucest. 10. If two weights descend 
 bypaths 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 descend- 
 ing force. By the inclinations, 1 do 
 not mean the angles, but the paths up 
 to the point in which both meet the same 
 perpendicular.* Let, therefore, e be 
 the weight upon d c, and h upon d a, 
 and let e be to h as d c to d a. I say 
 these weights, in this situation, are 
 equally effective. Take d k equally in- 
 clined with d c, and upon it a weight 
 equal to e, which call 6. If possible let 
 e descend to I, so as to raise h to m, and 
 
 take 6 n equal to h m or e I, and draw 
 the horizontal and perpendicular lines as 
 in the figure. 
 
 Then n z\n 6::d b:d k 
 and m h:m x::d a:d b 
 therefore n z : m x\ \d a : d k: :h : 6, and 
 therefore since e r 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."t The passage in Italics 
 tacitly assumes the principle in ques- 
 tion. Tartalea, who edited Jorda- 
 nus'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 doc- 
 trine 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 
 \vhen put in motion move what is next 
 to them, so that by being set in motion 
 they less impede the falling body. In 
 
 * This is not a literal translation, but by what 
 follows, is evidently the Author's meaning. His 
 words are, "Proportionem igitur declination urn dico 
 uon angulorum, sed iinearum usque ad aequidis- 
 tantem resecationem in qu& aequaltter suinunt de 
 directo." 
 
 t Opusculum. De Ponderositate. Venetiis, 1565. 
 
 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 ex- 
 traordinary 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 horizon- 
 tal lever must make a complete circuit 
 at that distance from the centre, whilst 
 the weight rises through the perpen- 
 dicular 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 neces- 
 sary sustaining force to vary as the 
 angle of inclination of the plane, for no 
 better reason than that such an expres- 
 sion 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 attribut- 
 ing the full knowledge of general prin- 
 ciples to these early writers, on account 
 of occasional indications of their having 
 employed them. 
 
 CHAPTER XVII. 
 Galileo's theory of Motion Extracts 
 
 from the Dialogues. 
 DURING Galileo's residence at Sienna, 
 when his recent persecution had ren- 
 dered astronomy an ungrateful, and in- 
 deed an unsafe occupation for his ever 
 active mind, he returned with increased 
 pleasure to the favourite employment of 
 G2 
 
84 
 
 GALILEO. 
 
 his earlier years, an inquiry into the laws 
 and phenomena of motion. His manu- 
 script 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 objec- 
 tions to the theory of Aristotle ; a few 
 only appear to enter on a new field of 
 speculation. The llth, 13th, and 17th 
 chapters relate to the motion of bodies 
 on variously inclined planes, and of pro- 
 jectiles. 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 know- 
 ledge ; a safer course will be to trace 
 his progress through existing documents 
 in their chronological Older. In 1602 
 we find Galileo apologizing in a letter 
 addressed to his early patron the Mar- 
 chese Guido Ubaldi, for pressing again 
 upon his attention the isochronism of 
 the pendulum, which Ubaldi had re- 
 jected 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 
 x 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 resist- 
 ance of the air during the larger vibra- 
 tions. The analytical methods then 
 known would not permit him to dis- 
 cover the c\irious fact, that the time of 
 a total vibration is not sensibly altered 
 by this cause, except so far as it dimi- 
 nishes 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 oscilla- 
 * tion, but that assertion was a conse- 
 quence 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. 
 
 " 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 1 take it for 
 granted, I can show that the spaces 
 passed in natural motion are in the 
 double proportion of the times, and con- 
 sequently 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 move- 
 able 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 
 A - D, by the line A BCD, I 
 suppose the degree of velo- 
 city which it has at B to 
 bear to the velocity at C the 
 ratio of A B to AC. I shall 
 be very glad if your Rever- 
 ence will consider this, and 
 n _ tell me your opinion of it. 
 If we admit this principle, 
 not only, as I have said, shall 
 we demonstrate the other 
 D - 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 pro- 
 jectile 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, A C, 
 and A D ; so that if, in falling, the degrees 
 of velocity observe the same proportion, 
 that is true which I have hitherto main- 
 tained and believed." 
 
GALILEO. 
 
 85 
 
 We have no means of knowing how 
 early Galileo discovered the fallacy of 
 this reasoning. In his Dialogues on Mo- 
 tion, 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 pro- 
 posed 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 v 
 will be passed in equal times, and con- 
 sequently all motion must be instanta- 
 neous." The following manner of put- 
 ting 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 ac- 
 cording 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), 
 
 of Galileo's second and correct theory, 
 that the spaces vary as the squares of 
 the times. He had been investigating 
 the curye 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 accu- 
 rately equal times. " I think it," says 
 he, " worthy of remark that this iden- 
 tity only occurs on Galileo's supposition, 
 so that this alone might lead us to pre- 
 sume it to be the real law of nature. 
 For nature, which always does every- 
 thing 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."* 
 
 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 experi- 
 ments 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, po- 
 lished and smoothed as exactly as pos- 
 sible, 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 
 
 ?lane. We observed, in the manner that 
 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 
 
 yet in some places he seems to assert 'Ahe length of the groove, and found the 
 that the circular arc is absolutely the measured time to be exactly half the 
 shortest line of descent, which is not former. Continuing our experiments 
 true. It has been thought possible that with other portions of the length, com- 
 the law, which on reflection he per- paring 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 
 
 ceived 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 ma- 
 thematicians 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 follow- 
 ing argument urged by him in favour 
 
 were as the squares of the times, and 
 that this was the case in all inclinations 
 of the plank ; during which, we also re- 
 
 Job. Bernoulli!, Opera Omnia, Lausannae, 1744. 
 torn. i. p. 192. 
 
GALILEO. 
 
 marked 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 dif- 
 ferent 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 propor- 
 tions 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 substi- 
 tuted 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 l", if 
 the resistance of the air and all other im- 
 pediments were removed. He fixed it 
 at 4 braccia: Mersenne has engraved 
 the length of the * braccia ' used by Ga- 
 lileo, in his " Harmonie Universelle," 
 from which it appears to be about 23 
 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 velo- 
 city ; a conclusion which, combined with 
 his other experiments, led him after- 
 wards to determine the path of a pro- 
 jectile in a non-resisting medium to be 
 parabolical. 
 
 Tartaleais 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*, 
 that " The bullet violentlye throwne 
 out of the peece by the furie of the 
 poulder hath two motions : the one vio- 
 lent, which endeuoreth to carry the bul- 
 let right out in his line diagonall, accord- 
 ing to the direction of the peece's axis, 
 from whence the violent motion proceed- 
 eth; 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 insensiblyeeuen 
 from the beginning by little and little 
 drawe it from that direct and diagonall 
 course." And a little farther he ob- 
 serves 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 heli- 
 call, yet have they a very great resem- 
 blance of the Arkes Conical. And in 
 randons above 45 they doe much re- 
 semble the Hyperbole, and in all vnder 
 the Ellepsis. But exactly e 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 phe- 
 nomena into which this compound mo- 
 tion 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 Mer- 
 senne, insinuates that Galileo had taken 
 many things in these Dialogues from 
 him: the two which he especially in- 
 stances are the isochronism of the pen- 
 dulum, and the law of the spaces varying 
 
 Pantometria, 1591. 
 
GALILEO. 
 
 as the squares of the times.* 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 erro- 
 neous principle. As Descartes on more 
 than one occasion has been made to 
 usurp the credit due to Galileo, (in no in- 
 stance more glaringly so than when he 
 has been absurdly styled the forerunner of 
 Newton,) it will not be misplaced to men- 
 tion a few of his opinions on these sub- 
 jects, recorded in his letters to Mersenne 
 in the collection of his letters just cited : 
 " 1 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 
 
 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 Salisbury'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."* 
 
 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 
 
 time, unless we make two or three sup- 
 positions which are entirely false. One constructions indicates great talent for 
 is Galileo's opinion, that motion in- this as well as for his own more fa- 
 creases gradually from the slowest^ de- vourite speculations. But he was far 
 gree; and the other is, that the air -/more profitably employed: geometry 
 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 velo- 
 city 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. 
 
 and pure mathematics already far out- 
 stripped 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 imme- 
 diately succeeding Galileo, the study of 
 nature was no longer in arrear of the 
 abstract theories of number and mea- 
 sure ; and when the genius of Newton 
 pressed it forward to a still higher de- 
 gree of perfection, it became necessary 
 to discover at the same time more power- 
 ful instruments of investigation. This 
 alternating process has been successfully 
 continued to the present time ; the analyst 
 
 However I have now got my mind full of acts as the pioneer of the naturalist, 
 
 other things, and I cannot amuse myself so that the abstract researches, which at 
 with hunting this out, nor is it a matter ^"first have no value but in the eyes of 
 
 of much utility :" He afterwards returns those to whom an elegant formula, in 
 
 once more to the same subject : " As its own beauty, is a source of pleasure 
 
 to what Galileo says, that falling bodies as real and as refined as a painting or 
 
 pass through every degree of velocity, I a statue, are often found to furnish the 
 
 * Lettres de Descartes. Paris, 1657. * Math. Coll. vol. ii, 
 f Atti+* a*i f <v /-* ^ 
 w/. m t /* <t 
 
88 
 
 GALILEO. 
 
 only means for penetrating into the 
 most intricate and concealed pheno- 
 mena 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 for- 
 ward. 
 
 The dialogues are between the same 
 speakers as in the " System of the 
 World ;" and in the first Simplicio gives 
 Aristotle's proof,* that motion in a va- 
 cuum 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 Ibs., and a 
 musket ball weighing half a pound, be 
 dropped together from a tower 200 
 yards high, the former will not antici- 
 pate 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 1 00 Ibs. will fall from 
 the height of 1 00 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 mo- 
 tion, and which must therefore be 
 quoted in his own words : " A heavy 
 
 * Pbys. Lib. ir. c. 8. 
 
 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 v / 
 when all accidental and external impe- 
 diments 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, continu- 
 ally accelerated, consequently encoun- 
 ters 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 pre- 
 vented, and the moveable continues ever 
 after with an uniform and equable mo- 
 tion." That such a limiting velocity is not 
 greater than some which may be exhi- 
 bited may be proved as Galileo suggested / 
 by firing a bullet upwards, which will in v 
 its descent strike the ground with less 
 force than it would have done if imme- 
 diately from the mouth of the gun ; for he 
 argued that the degree of velocity which 
 the air's resistance is capable of dimi- 
 nishing 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 ex- 
 amining 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 extru- 
 sion 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 acce- 
 lerated, (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 hit-reuses, 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 de- 
 
GALILEO. 
 
 monstrated on this supposition are veri- 
 fied in the motion of falling and natu- 
 rally accelerated weights, we may thence 
 conclude that the assumed definition 
 does describe the motion of heavy bo- 
 dies, and that it is true that their acce- 
 leration 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 velo- 
 city 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 
 
 t ^ , t / C^ L- 
 
 in the direction of the perpendicular 
 B N. Moreover let the straight line 
 B E drawn in the direction A B be taken 
 to represent the flow, or measure, of the 
 time, on which let any number of equal 
 parts B C, C D, D E, &c. be marked at 
 pleasure, and from the points C, D, E, 
 let lines be drawn parallel to B N ; in 
 the first of these let any part C I be 
 taken, and let D F be taken four times 
 as great as C I, E H nine times as 
 great, and so on, proportionally to the 
 squares of the lines B C, B D, B E, &c., 
 or, as we say, in the double proportion 
 of these lines. Now if we suppose 
 that whilst by its equable horizontal 
 
 only, his theory was so far imperfect >/ motion the body moves from B to C, it 
 till he could show its consistency with also descends by its weight through C I, 
 the above supposed law of acceleration - A " ' * * ~ ~ 
 
 When Viviani was studying with Galileo, 
 he expressed his dissatisfaction at this 
 chasm in the reasoning; the conse- 
 quence 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 in- 
 troduced it into the subsequent edi- 
 tions. The third dialogue is princi- 
 pally 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 deter- 
 mined 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. 
 
 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 mo- 
 tion as if there were no horizontal mo- 
 tion. " Let A B represent a horizontal 
 
 E D C B A. 
 
 N 
 
 line or plane placed on high, on which 
 let a body be carried with an equable 
 motion from A towards B, and the sup- 
 port of the plane being taken away at 
 B, let the natural motion downwards 
 due to the body's weight come upon it 
 
 at the end of the time denoted by B C 
 it will be at I. Moreover in the time 
 B D, double of B C, 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. Simi- 
 larly at the end of the time B E, or 
 three times B C, it will have fallen 
 through E H, and will be at H. And it 
 is plain that the points I, F, H, are in 
 the same parabolical line B I F H. 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 mo- 
 tion. After the proposition we have 
 just extracted, he proceeds to anticipate 
 some objections to the theory, and ex- 
 plains 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 be- 
 cause a horizontal line, or one equi- 
 distant 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 con- 
 structions for determining the circum- 
 stances 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 
 
90 
 
 GALILEO. 
 
 of 45, the ranges of all angles equally 
 inclined above and below 45 corre- 
 sponding exactly to each other. 
 
 One of the most interesting subjects 
 discussed in these dialogues is the fa- 
 mous notion of Nature's horror of a 
 vacuum or empty space, which the old 
 school of philosophy considered as im- 
 possible 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 expe- 
 rienced in endeavouring to separate two 
 smooth surfaces, he was so far from 
 looking upon a vacuum as an impossi- 
 bility, that he has described an appa- 
 ratus by which he endeavoured to mea- 
 -sure the force necessary to produce one. 
 This consisted of a cylin- 
 der, into which is tightly 
 fitted a piston ; through 
 the centre of the piston 
 passes a rod with a coni- 
 cal valve, which, when 
 drawn down, shuts the 
 aperture closely, support- 
 ing 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 be- 
 tween the piston and lower surface of 
 the water. The defects in this appa- 
 ratus for the purpose intended are of no 
 consequence, so far as regards the pre- 
 sent argument, and it is perhaps need- 
 less to observe that he was mistaken in 
 supposing the water would not descend 
 with the piston. This experiment occa- 
 sions 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 
 itjs very plain that if he had made such 
 an observation, it would have been se- 
 riously ; and in fact by such a limi- 
 tation he deprived the notion of the 
 principal part of its absurdity. He evi- 
 
 dently 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 length- 
 ened till it breaks with its own weight. 
 It is certainly very extraordinary that 
 he failed to observe how simply these phe- 
 nomena may be explained by a refer- 
 ence to the weight of the elastic atmo- 
 sphere, which he was perfectly well ac- 
 quainted with, and endeavoured by the 
 following ingenious experiment to de- 
 termine : " 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 suffer- 
 ing 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 oc- 
 cupy the space now filled by the water. 
 Weigh the vessel again ; the differ- 
 ence will show the weight of that quan- 
 tity of air*." By these means, which 
 the modern experimentalist will see were 
 scarcely capable of much accuracy, Ga- 
 lileo 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 propor- 
 tion of weight between water and mer- 
 cury. The following curious letter from 
 Baliani, in 1630, shows that the original 
 merit of suggesting the real cause be- 
 longs 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 
 
 * It has been recently proposed to determine the 
 density of high-pressure steam by a process analo- 
 gous to this. 
 
GALILEO. 
 
 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 com- 
 presses 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 infi- 
 nite, and therefore determinable, and it 
 might be overcome by a force propor- 
 tioned 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*." 
 
 This subject is introduced by some ob- 
 servations on the force of cohesion, Ga- 
 lileo seeming to be of opinion that, al- 
 though it cannot be adequately ac- 
 counted for by " the great and principal 
 resistance to a vacuum, yet that per- 
 haps 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 resist- 
 ance." This remark serves to lead to a 
 discussion on indivisibles and infinite 
 quantities, of which we shall merely ex- 
 tract 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 C D E F thus discovered 
 in the cylinder is equal to the area of the 
 corresponding circular section AB of the 
 cone, wherever the cutting plane is sup- 
 
 * Yeuturi, vol. ii. 
 
 posed to be*. 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 f 
 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 $ ?" 
 
 We think no one can refuse to ad- 
 mit 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 paradoxi- 
 cal 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 unin- 
 teresting 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 . 
 
 A suggestion that perhaps fire dis- 
 solves bodies by insinuating itself be- 
 tween 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 re- 
 quire time. Simplicio is ready with art 
 answer, that the discharge of artillery- 
 proves the transmission of light to be 
 
 * 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. 
 
 t Gli altissimi e ultimi termini. 
 
 j Le ultimo reliquie e vestigie lasciate da grandezze 
 eguali. 
 
 Punctum fluere, et lineani esse fluxum puncti. 
 Tract. Syllept. Romae, 1633. 
 
92 
 
 GALILEO. 
 
 instantaneous, to which Sagredo cau- 
 tiously replies, that nothing can be ga- 
 thered 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?" Sal- 
 viati 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 dis- 
 tance 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 pas- 
 sage : " 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 re- 
 quired tima 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 per- 
 adventure that it may be so, who 
 knoweth the contrary? Or what in- 
 convenience would follow if it be ad- 
 mitted * ?" 
 
 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 vibra- 
 tions 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 pres- 
 sure the note is suddenly made to rise 
 to the octave above, every one of the 
 
 * " Treatise of the Nature of Bodies. London, 
 1665." 
 
 undulations which will be seen regu- 
 larly spreading round the glass, will 
 suddenly split into two, proving that 
 the vibrations that occasion the octave 
 are double those belonging to the sim- 
 ple 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 agi- 
 tated 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 occur- 
 red, 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 re- 
 peated experiments he produced differ- 
 ent 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 pro- 
 duced were two, which by compari- 
 son 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 *. 
 
 Salyiati also remarks, that if the 
 material be not the same, as for in- 
 stance 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 musi- 
 cal intervals is neither the length, the 
 tension, nor the thickness, but the pro- 
 portion of the numbers of the undula- 
 tions 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 differ- 
 ent sensations occasioned to us by dif- 
 ferent 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 disagree- 
 able sensation belonging to the latter 
 
 * 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.' 
 
GALILEO. 
 
 93 
 
 probably arises from the disorderly 
 manner in which the vibrations strike 
 the drum of the ear ; so that for in- 
 stance 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 con- 
 sonances 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 cor- 
 respond with those of the musical con- 
 cords, the eye will observe with pleasure 
 their crossings and interweavings still 
 recurring at appreciable intervals ; but 
 if the times of vibration be incommen- 
 surate, the eye will be wearied and worn 
 out with following them." 
 
 The second dialogue is occupied en- 
 tirely with an investigation of the 
 strength of beams, a subject which does 
 not appear to have been examined by 
 any one before Galileo beyond Aris- 
 totle'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 obser- 
 vation 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 over- 
 coming 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 consist- 
 ence. 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 para- 
 bolical 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 dia- 
 logue, that Galileo was perfectly aware 
 that this construction is only approxi- 
 mately true. In the same place he makes 
 the remark, which to many is so para- 
 doxical, 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. 
 
 . CHAPTER XVIII. 
 
 Correspondence on Longitudes. Pen- 
 dulum Clock. 
 
 IN the spring of 1636, having finished 
 his Dialogues on Motion, Galileo re- 
 sumed the plan of determining the lon- 
 gitude 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 Ferdi- 
 nand'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 offer- 
 ing 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,* 
 which consisted in observing the dis- 
 tance of the moon from a known star. 
 Morin was a French philosopher, prin- 
 
 * One of the Commissioners was the father of 
 Blaise Pascal, 
 
94 
 
 GALILEO. 
 
 cipally known as an astrologer and zea- 
 lous Anti-Copernican ; but his name de- 
 serves to be recorded as undoubtedly one 
 of the first to recommend a method, 
 which, under the nwne of a Lunar dis- 
 tance, 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 appre- 
 ciate 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 be- 
 forehand 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 al- 
 lowance for intermediate distances. 
 Observing at the same instant the hour 
 on board his ship, the difference between 
 the two would show his position in re- 
 gard of longitude. In using this 
 method as it is now practised, several 
 modifications are to be attended to, 
 without which it would be wholly use- 
 less, 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 di- 
 rectly behind the moon. The mode 
 of allowing for these alterations is taught 
 by trigonometry and astronomy. 
 
 The success of this method depends al- 
 together 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 il- 
 lusory. Such in fact was the judgment 
 which Galileo pronounced upon it. " As 
 to Morin' s book on the method of find- 
 ing 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 dif- 
 ference of longitude between two me- 
 
 ridians 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 in- 
 struments, and convenient to handle, in 
 taking the distance between the moon 
 and a fixed star ; thirdly, great prac- 
 tical skill in the observer ; fourthly, not 
 less accuracy in the scientific calcula- 
 tions, 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 prac- 
 tically right in one alone. Morin ought 
 to require his judges to assign, at their 
 pleasure, eight or ten moments of dif- 
 ferent nights during four or six months 
 to come, and pledge himself to predict 
 and assign by his calculations the dis- 
 tances 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 sex- 
 tant* will actually sho\v, 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 con- 
 ceit 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 ob- 
 jections 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 sub- 
 sequent observations ; and since that 
 
 * These instruments were very inferior to those 
 now in use under the same name. See " Treatise on 
 Opt. Instrum." 
 
GALILEO. 
 
 95 
 
 time, amid all his other employments, 
 he had almost unmtermittingly during 
 twenty-four years continued his obser- 
 vations, 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 pro- 
 posal 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 success- 
 ful, he should have no cause to com- 
 plain of their want of gratitude and ge- 
 nerosity. The commissioners immedi- 
 ately commenced an active correspon- 
 dence 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 dif- 
 ficulties of the necessary observations. 
 It is worth noticing that the secretary 
 to the Prince of Orange, who was mainly 
 instrumental in forming this commis- 
 sion, was Constantine Huyghens, father 
 of the celebrated mathematician of that 
 name, of whom it has been said that he 
 seemed destined to complete the disco- 
 veries 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 sub- 
 ject of the pendulum clock, which must 
 necessarily have forced it upon his re- 
 collection. 
 
 The Dutch commissioners had chosen 
 one of their number to go into Italy for 
 the purpose of communicating person- 
 ally 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 de- 
 lays, 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 for- 
 mer pupil of his, and then professor 
 of mathematics at Pisa, who under- 
 took 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 cor- 
 respondence 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 Tus- 
 cany, was about to publish the ephe- 
 meris and tables which Galileo had en- 
 trusted to him, and which the Duke 
 told Viviani he had seen in his pos- 
 session, 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 inti- 
 mated his suspicions that Renieri him- 
 self destroyed them, from a conscious- 
 ness that they were insufficient for the 
 purpose to which it was intended to ap- 
 ply 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 ad- 
 vanced 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 betray ing 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;* 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 trans- 
 lated 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 
 
 * Theoricae Mediceorum Planetarum, Florentise, 
 1666. 
 
96 
 
 GALILEO. 
 
 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 flian 
 merely mention it as affording an un- 
 intermitted 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 de- 
 scription of a clock in one of the manu- 
 scripts of the King's Library at Paris, 
 dated about the middle of the fifteenth 
 century, which as he says nearly re- 
 sembles a modern watch. The balance 
 is there called " The circle fastened to 
 the stem of the pallets, and moved by 
 the force with it.* 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 pen- 
 dulum. 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 ; 
 
 Circnlus affrxus virgaa paletorum qui cum e& de 
 vi movetur. 
 
 Jig. 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 begin- 
 ning of its motion."* 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 sen libra- 
 tio) by which the motion is equalized." 
 The manner in which Huyghens first 
 applied the pendulum is shown in 
 Jig. 3.t 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 pro- 
 perty of isochronism similar to that of 
 the pendulum. Hooke is generally 
 named as the discoverer of this pro- 
 perty 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^ 
 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 construc- 
 tion of spring watches. A great num- 
 ber 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. 
 
 Galileo was early convinced of the im- 
 portance of his pendulum to the ac- 
 curacy 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 re- 
 cognized 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." 
 
 * Utriusque Cosmi Historia. Oppenhemii, 1617. 
 f Huygenii Opera. Lugduni, 1724. 
 t Memoires de 1' Academic, 171?. 
 
GALILEO. 
 
 97 
 
 " A very exact time-measurer for mi- 
 nute intervals of time, is a heavy pendu- 
 lum of any size hanged by a fine thread, 
 which, if removed from the perpendicular 
 and allowed to swing freely, always com- 
 pletes its vibrations, be they great or 
 small, in exactly the same time/'* 
 
 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 pen- 
 dulum of any length, as for instance 
 about a foot long, and count pa- 
 tiently (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 disap- 
 pears 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 im- 
 mediately 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 con- 
 trivance fpr increasing immensely the ex- 
 actness 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 hang- 
 ing by a thread, but a heavy arid 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,-! 
 make thickest in the middle radius, 
 
 * See page 84. 
 
 tapering gradually towards the edges, 
 where I terminate it in a tolerably 
 sharp line, to obviate as much as pos- 
 sible the resistance of the air, which 
 is the sole cause of its retardation." 
 [These last words deserve notice, be- 
 cause, in a previous discussion, Galileo 
 had observed that the parts of the 
 pendulum nearest the point of sus- 
 pension 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, termi- 
 nated 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 accu- 
 rately balanced) be removed several 
 degrees from its perpendicular position, 
 it will continue a reciprocal motion 
 through a very great number of vibra- 
 tions before it will stop ; and in order 
 that it may continue its motion as long 
 as is wanted, the attendant must occa- 
 sionally give it a smart push, to carry it 
 back to large vibrations." Galileo then 
 describes as before the method of count- 
 ing 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 assist- 
 ant in continually counting the vibra- 
 tions, this is a convenient contrivance: 
 A very small and delicate needle extends 
 out from the middle of the circumfer- 
 ence 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 perpen- 
 dicular 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 nmy also fit to the axis 
 
98 
 
 GALILEO. 
 
 of this first wheel a second, with a small 
 number of teeth, touching another 
 greater toothed wheel, &c. But it is su- 
 perfluous 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 contri- 
 vances 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 pen- 
 dulum, which is not liable to any altera- 
 tion, affords a mean of maintaining the 
 measures of time always equal." The 
 contrivance thus described would be 
 somewhat similar to the annexed repre- 
 sentation, but it is almost certain that 
 no such instrument was actually con- 
 structed. 
 
 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 vibra- 
 tions great or small of the same pen- 
 dulum take exactly the same time ; and 
 we have not been able to find any trace 
 of his having ever held a different opi- 
 nion, unless perhaps in the Dialogues, 
 where he says, " If the vibrations are 
 not exactly equal, they are at least in- 
 sensibly 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 immedi- 
 ately 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 Vin- 
 cenzo, in which, by the action of a weight 
 or spring, the pendulum was con- 
 strained to move always from the same 
 height. Indeed it appears as if Maga- 
 lotti 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 Hol- 
 land," plainly insinuating that Huyghens 
 was a mere copyist.* These two ac- 
 counts therefore serve to invalidate 
 each other's credibility. Tiraboschit 
 asserts that, at the time he wrote, the 
 mathematical professor at Pisa was 
 in possession of the identical clock 
 constructed by Treffler under Vincen- 
 zo'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 prin- 
 ciple from Vincenzo's ideas, although he 
 says distinctly that he heard Galileo de- 
 scribe 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 Ferdi- 
 nand sent to his complaints of the Me- 
 morie del Cimento he wrote to Bouil- 
 laud, " 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 after- 
 thought to attribute the merit of construct- 
 ing the pendulum-clock to Galileo, for on 
 the reverse of a medal struck by Viviani, 
 and inscribed " to the memory of his 
 excellent instructor,"^ is a rude exhibi- 
 tion 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, 
 
 * De nova Temporis dimetiendi ratione. Londini, 
 1630. 
 
 f StoriadellaLett. Ital. 
 
 * Museum Mazuchelliaimm, vol. ii. Tab. cvii, p. 29, 
 
GALILEO. 
 
 99 
 
 in a design expressly intended to com- 
 memorate Galileo's s inventions, Viviani 
 would have introduced the timekeeper 
 in the most perfect form to which it had 
 been brought by him. Riccioli,* whose 
 industry was unwearied in collecting 
 every fact and argument which related in 
 any way to the astronomical and mecha- 
 nical knowledge and opinions of his time, 
 expressly recommends swinging a pen- 
 dulum, or perpendicular as it was often 
 called (only a few years before Huyghens' 
 publication), as much more accurate 
 than any clock. -'r Join to all these argu- 
 ments Huyghens 1 positive assertion, that 
 if Galileo had conceivedany such idea, he 
 at least was entirely ignorant of it,| 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 : tor the property of the 
 pendulum was known, and the conver- 
 sion 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' im- 
 provement was received with universal 
 admiration. 
 
 There may be many who will con- 
 sider the pendulum as undeserving so 
 long a discussion ; who do not know 
 or remember that the telescope itself 
 has hardly done more for the preci- 
 sion of astronomical observations than 
 this simple instrument, not to mention 
 the invaluable convenience of an uni- 
 form 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 de- 
 gree 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 neverthe- 
 less persevered to the best of their abi- 
 lity, undisgusted either by the tedium of 
 such processes, or by the discouraging 
 consciousness of the necessary imper- 
 fection of .their most approved methods 
 and instruments. 
 
 The invariable regularity of the pen- 
 dulum's motion was soon made subser- 
 vient to ulterior purposes beyond that of 
 
 * AliTiagestum Novum, vol. i. 
 t Quovis horologin accuratius;. 
 j Clarorum Bel^aram ad Ant. Magliabech. Epis- 
 tolee. Florence, 1713, torn. i. p. 235. 
 
 merely registering time. We have seen 
 the important assistance it afforded in es- 
 tablishing 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 in- 
 quiries, 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 conse- 
 quence 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 astro- 
 nomer, 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."* There is 
 nothing to guide us to the grounds on 
 which he formed this opinion, which 
 was perhaps only a lucky guess. Kep- 
 ler's note upon it is : " This is not alto- 
 gether 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 ex- 
 press its parts by the number of vibra- 
 tions of a pendulum of given length, 
 swinging through a given arc. It was 
 soon seen that it would be more con- 
 venient 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 
 
 * Kepleri Epistolae. 
 
 H2 
 
100 
 
 GALILEO. 
 
 upon them by the ignorant, when re- 
 cently repeated for the same purpose. 
 *' I contend," says Graunt* in a dedica- 
 tion 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 s\ving-swangs with scorn."t 
 
 CHAPTER XIX. 
 
 deta 
 
 ter of 
 ils hi 
 
 is Death Conclusion. 
 
 THE remaining years of Galileo's life 
 were spent at Arcetri, where indeed, even 
 if the Inquisition had granted his li- 
 berty, .his increasing age and infirmities 
 would probably have detained him. The 
 rigid caution with which he had been 
 watched in Florence was in great mea- 
 sure 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 testify- 
 ing their admiration of his character. 
 Among other visitors the name of Mil- 
 ton will be read with interest : we may 
 probably refer to the effects of this in- 
 terview the allusions to Galileo's disco- 
 veries, so frequently introduced into his 
 poem. Milton mentions in his ' Areo- 
 pagitica,' that he saw Galileo whilst in 
 Italy, but enters into no details of his 
 visit. 
 
 * Natural and Political Observations. London, 
 1664. 
 
 f 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 put of proof. 
 Hudibras was certainly written before 1663 : ten 
 years later Huyghens speaks of the idea of SO employ- 
 ing the pendulum aaa common one. 
 
 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 bene- 
 factor. His long life, which was pro- 
 longed to the completion of his 81st year 
 in 1703, enabled him to see the tri- 
 umphant establishment of the truths 
 on account of which Galileo had en- 
 dured 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 So 
 ciety, who invited him among them in 
 1696, felt that the complimentary lan- 
 guage 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."* 
 
 Torricelli, another of Galileo's most ce- 
 lebrated 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 suc- 
 cess 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 Flo- 
 rence,t 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 : Signer 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 
 
 * The words of his diploma are : Galilaui in ma- 
 thematicis disciplinis discipulus, in aerumnis socius, 
 Italicum ingenium ita perpolivit optimis artibus ut 
 inter mathematicos sseculi nostri facile princeps per 
 orbem litterarium numeretur. Tiraboschi. 
 
 t On this occasion the taste of the time showed 
 itself in the following anagram : , 
 
 Evangelista Torricellieus, 
 Kn yirescit Gulilwus alter. 
 
GALILEO. 
 
 101 
 
 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 dan- 
 gerous illnesses, occasioned in great 
 measure by his sleepless nights, the 
 whole of which he frequently spent 
 in astronomical observations. Curing 
 upwards of forty-eight years of his life, 
 he was tormented with" acute rheuma- 
 tic pains, suffering particularly on any 
 change of weather. He found himself 
 most free from these pains whilst re- 
 siding in the country, of which conse- 
 quently 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 accus- 
 tomed 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 agri- 
 cultural 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 pre- 
 served 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 fa- 
 vour, 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 parti- 
 culars 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 pro- 
 
 vide 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 Charyb- 
 dis), nor the country of my master, Ar- 
 chimedes 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 profu- 
 sion : he spared no cost necessary for the 
 success of his many and various experi- 
 ments, 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 tem- 
 per 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 conver- 
 sation 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 tena- 
 cious, and stored with a vast variety of old 
 songs and stories, which he was ire 
 the constant habit of quoting and allu- 
 ding to. His favourite Italian authors 
 were Ariosto, Petrarca, and Berni, 
 great part of whose poems he was 
 able to repeat. His excessive admira- 
 tion 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 Geru- 
 salemme 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 Abb6 
 Serassi discovered it, whilst collecting 
 materials for his Life of Tasso, pub- 
 
102 
 
 GALILEO. 
 
 lishecl at Rome in 1785. Serassi being 
 a violent partizan of Tasso, but also un- 
 willing to lose the credit of the disco- 
 very, 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 ac- 
 counts." He announced his discovery 
 as Tiaving been made " in one of the 
 famous libraries at Rome," which vague 
 indication he with some reason consi- 
 dered 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 manu- 
 script 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 Ita- 
 lian critics appears to be, that it would 
 have been more for Galileo's credit if 
 these remarks had never been made pub- 
 lic : they are written in a spirit of flippant 
 violence, such as might not be extra- 
 ordinary in a common juvenile critic, 
 but which it is painful to notice from 
 the pen of Galileo. Two or three son- 
 nets are extant written by Galileo 
 himself, and in two instances he has not 
 scrupled to appropriate the conceits 
 of the poet he affected to under- 
 value.* 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 plea- 
 sure." 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 fpund himself obliged by custom to 
 wear his professional habit in every com- 
 
 Eany. It is written not without humour, 
 ut 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 no- 
 
 * 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 )-in<!ne*s of Sig. Panizzi, Profesior of Italian 
 in the University of London. 
 
 tice extant of the application of ma- 
 thematics to that interesting subject : 
 the correspondence between Pascal and 
 Fermat, with which its history is gene- 
 rally 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 be- 
 tween 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.* 
 
 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.t 
 Other writers mention the name of an 
 alchymist, who according to them dis- 
 covered 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, desir- 
 ing us to observe that they were not in 
 the least degree luminous. Having then 
 exposed them for some time to the twi- 
 light, 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 qua- 
 lity of that luminary, to which Galileo, 
 then aged 76, replied by a long and able 
 letter, enforcing the true explanation he 
 had formerly given. 
 
 * Lettera di Timauro Antiate. Firenze, 1663. 
 j- De phaenomenis in orbe Lunae. Venetiis, 1612; 
 
GALILEO. 
 
 103 
 
 Although quite blind, and nearly deaf, 
 the intellectual powers of Galileo re- 
 mained to the end of his life ; but he oc- 
 casionally 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 rest- 
 less 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 what- 
 ever t had been thinking of just be- 
 fore." He was busily engaged in consi- 
 dering the nature of the force of percus- 
 sion, and Torricelli was employed in 
 arranging his investigations for a conti- 
 nuation 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 spu- 
 rious admiration, mutilated Galileo's 
 body, by removing the thumb and fore- 
 finger of the right-hand, and one of the 
 vertebrae of the back, which are still pre- 
 served in some of the Italian museums. 
 The monument was put up at the ex- 
 pense 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 str uck in honour o f 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 fron- 
 tispiece of the Padua edition of his 
 works. Salusbury seems in the fol- 
 lowing 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 Sylya, 
 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 Baonarota; 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 mis- 
 taken than that so interesting a portrait 
 should have been entirely lost sight of. 
 Galileo's house at Arcetri was stand- 
 ing 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 Alimarl* 
 
 Although Nelli's Life of Galileo dis- 
 appointed 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 
 
 * Veaturi. 
 
104 
 
 GALILEO. 
 
 him, for the successful activity with 
 which he rescued so many records of 
 the illustrious philosopher from destruc- 
 tion. After Galileo's death, the prin- 
 cipal 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, con- 
 taining 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 dis- 
 persed. The manuscripts in Viviani's 
 possession passed to his nephew, the 
 Abbe Panzanini, together with the por- 
 traits of the chief personages of the Gali- 
 lean school, Galileo's instruments, and, 
 among other curiosities, the emerald ring 
 which he wore as a member of the Lyn- 
 cean 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 bi ought him from time to time, 
 
 similar letters,whichhe 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 posses- 
 sion an old corn-chest, containing all 
 that still remained of the precious trea- 
 sures which Viviani had concealed in it 
 ninety years before."* 
 
 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 Erythraeu*?, 
 introduced an account of Galileo in his 
 Pinacotheca Imaginum Illustrium, in 
 which the story of his illegitimacy first 
 made its appearance. In 1664, Salus- 
 bury 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. Almoit the whole edition of 
 the second volume of Salisbury's 
 book was burnt in the great fire of 
 London. Chauffepi6 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 kind- 
 ness 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 Li- 
 brary at Oxford. The translations in the 
 preceding pages are mostly founded upon 
 Salusbury's version. Salisbury's ac- 
 count, although that of an enthusiastic 
 admirer of Galileo, is too prolix to be 
 interesting : the general style of the per- 
 formance may be guessed from the title 
 of the first chapter ' Of ..Man in gene- 
 ral, and how he excelleth all the other 
 Animals.' After informing his readers 
 that Galileo was born at Pisa, he pro- 
 ceeds : " 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 
 
 * Xotizie sul Ingrandimento dello Scienze Fisiche. 
 Fireoze, 1780. 
 
GALILEO. 
 
 105 
 
 whole tolerably correct, especially if we 
 take into account that Salusbury had 
 not yet seen Viviani's Life, though com- 
 posed 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 Aca- 
 demy, of which Galileo had been one of 
 the annual presidents, and afterwards 
 prefixed to the complete editions of Gali- 
 leo's works ; it is written in a very 
 agreeable and flowing style, and has 
 been the groundwork of most subse- 
 quent accounts. Another original me- 
 moir by Niccolo Gherardini, was pub- 
 lished 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 Ita- 
 lorum 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 Continua- 
 tion of Bayle's Dictionary does not con- 
 tain anything which is not in the earlier 
 accounts. 
 
 Andres wrote an essay entitled ' Sag- 
 gio sulla Filosofi a del Galileo,' published 
 at 'Mantua 1776; and Jagemann pub- 
 lished his * Geschichte des Leben des 
 Galileo 1 at Leipzig, in 1787;* neither 
 of these the author has been able to 
 meet with. An analysis of the latter 
 may be seen in Kastner's ' Geschichte 
 der Mathematik, Gottingen, 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 ex- 
 presses, rather in the nature of a pa- 
 negyric than of a continuous biogra- 
 phical 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 Com- 
 mercio 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 
 
 * Venturi. 
 
 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 sup- 
 plied 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 ser- 
 vice which the writer is able to appre- 
 ciate from having gone through th 
 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 ap- 
 pear either in his book or Venturi's... 
 Carlo Dati, in 1663, quotes " the regis- 
 ters of Galileo's correspondence arranged 
 in alphabetical order, in ten large vo- 
 lumes."* 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 me- 
 rits of this great and useful philosopher. 
 
 The first editions of his various trea- 
 tises, 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 thirtee-nth contains in addi- 
 tion the Letter to the Grand Duchess, 
 the Commentary on Tasso, with some 
 minor pieces . A complete edition is still 
 wanted, embodying all the recently dis- 
 covered 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. 
 
 * Lettera di Timauro Antiate. 
 
106 
 
 GALILEO. 
 
 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 demonstra- 
 tions of the spirit in which he every- 
 where withstood the despotism of igno- 
 rance, and appealed boldly from tradi- 
 tional 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 gene- 
 rosity 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 gra- 
 titude, more than Galileo. 
 
 List of Galileo's Works. 
 
 Le Operazioni del Compasso Geom. e Milit. 
 Difesa di Gal. Galilei contr. all. cal. et impost, di Bald. Capra 
 Sydereus Nuucius ..... 
 
 Discorso int. alle cose che stanno in su 1' Acqua . . 
 
 Novantiqua SS. PP. Doctrina de S. Scripturse Testimoniis . 
 Istoria e Demostr. int. alle Macchie Solari 
 
 Risp. alle oppos. del S. Led. delle Colombe e del S. Vine, di Grazia 
 Discorso delle Comete di Mario Guiducci . , 
 
 Dialogo sopra i due Massimi Sistemi del Moudo . 
 
 Discorso e Demostr. intorno alle due nuove Scienze 
 Delia Scienza Meccanica ..... 
 
 Trattato della Sfera ..... 
 
 Discorso sopra il Flusso e Reflusso. (Scienze Fisiche di Tozzetti.) 
 Considerazioni sul Tasso ..... 
 Trattato della Fortificazione. (Memorie di Venturi.) 
 
 The editions of his collected works (in which is contained much that was 
 published separately) are 
 
 Opere di Gal. Galilei, Line. Nob. Fior. &c. . Bologna, 1G5G. 
 
 Opere di Gal. Galilei, Nob. Fior. Accad. Line. &c. . Firenze, 1718. 
 Opere di Gal. Galilei '';'*' '' : Paclova, 1744. 
 
 Padova, 
 
 1606. 
 
 Fol. 
 
 Venezza, 
 
 1607. 
 
 4 to. 
 
 Venetiis, 
 
 1610. 
 
 4to. 
 
 Firenze, 
 
 1612. 
 
 4to. 
 
 Argent, 
 
 1612. 
 
 4to. 
 
 Roma, 
 
 1613. 
 
 4to. 
 
 Firenze, 
 
 1615. 
 
 4to. 
 
 Firenze, 
 
 1619. 
 
 4 to. 
 
 Firenze, 
 
 1632. 
 
 4to. 
 
 Leida, 
 
 1638. 
 
 4 to. 
 
 Ravenna, 
 
 1649. 
 
 4to. 
 
 Roma, 
 
 1655. 
 
 4to. 
 
 Firenze, 
 
 1780. 
 
 4to. 
 
 Roma, 
 
 1793. 
 
 
 Modena, 
 
 1818. 
 
 4to. 
 
 much that was 
 
 never 
 
 Opere di Gal. Galilei 
 
 4to. 
 4to. 
 4to. 
 Milano, 1811. 13 vols. 8vo. 
 
 2 vols. 
 
 3 vols. 
 
 4 vols. 
 
 CORRECTIONS. 
 
 Page Co . Line. 
 512, Add : Hia instructor was the celebrated botanist, Andreas Ceesalpinus, who was professor 
 
 of medicine at Pisa from 1567 to 1592. Hist. Acad. Pisan. ; Pisis, 1/91. 
 8 2 18, Add: According to Kiistner, 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. 
 [60 1 50, for any read an indefinitely small. 
 

LIFE OF KEPLER. 
 
 CHAPTER I. 
 
 Introduction Birth and Education of 
 Kepler He is appointed Astronomi- 
 cal Professor at Gratz Publishes 
 the * Mysterium Cosmographicum." 
 
 IN the account of the life and discoveries 
 of Galileo, we have endeavoured to in- 
 culcate 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 adversa- 
 ries supply equally good examples of the 
 dangers and the barrenness of the oppo- 
 site course. The history of JOHN KEP- 
 LER might, at the first view, suggest con- 
 clusions somewhat inconsistent with this 
 remark. Every one who is but mode- 
 rately 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 imphilosophical me- 
 thod, 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 per- 
 ceive that to an unusual degree of 
 rashness in the formation of his sys- 
 tems, he added a quality very rarely 
 possessed by philosophers of the hypo- 
 thetical school. One of the greatest in- 
 tellectual vices of the latter was a wilful 
 blindness to the discrepancy of facts 
 from their creed, a perverse and obsti- 
 nate resistance to physical evidence, 
 leading not unfrequently to an attempt 
 at disguising the truth. From this be- 
 setting 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 ima- 
 gination, but examined and endeared by 
 the 'ceaseless labour of years, was unhe- 
 sitatingly sacrificed, as soon as its in- 
 sufficiency became indisputable, to make 
 room for others as little deserving sup- 
 port. 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 me- 
 thod 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 ex- 
 posed 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 favour- 
 able 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 persever- 
 ance ; and he has thus given us "a 
 most curious and interesting view of the 
 workings of a mind of great, though ec- 
 centric 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 inge- 
 nuity. For it is my opinion that the oc- 
 casions by which men have acquired 
 a knowledge of celestial phenomena 
 are not less admirable than the disco- 
 veries 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 spe- 
 culations ; they are in themselves very 
 amusing, and will have the additional 
 utility of proving the dangerous ten- 
 dency of his method ; they will show by 
 how many absurd theories, and how 
 
KEPLER. 
 
 many years of 'wasted labour, his real 
 discoveries and services to science lie 
 surrounded. 
 
 JOHN KEPLER was born (as we are as- 
 sured by his earliest biographer Hantsch) 
 in long. 29 7', lat. 48 54', on the 21 st 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,bpth 
 of noble, though decayed families. 
 Henry Kepler, at the time of his mar- 
 riage, 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 
 Jiad incautiously become surety. His 
 circumstances were 'so much nar- 
 rowed 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 wkh 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 fol- 
 lowed there required that the students, 
 after remaining a year in the superior 
 classes, should offer themselves for ex- 
 lamination 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, pro- 
 ceeded in about a year to the degree of 
 master, and were then allowed to com- 
 mence 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 dis- 
 orders 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 depar- 
 ture, 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 bro- 
 thers died, and the family-affairs were 
 in the greatest confusion. Notwith- 
 standing 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 Tu- 
 bingen, the astronomical lectureship at 
 Grate, the chief town of Styria, be- 
 came vacant by the death of George 
 Stadf, and the situation was offered to 
 Kepler. Of this first occasion of turn- 
 ing 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 learn- 
 ed 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 phi- 
 losophy. I entered on it, therefore, bet- 
 ter furnished with talent than knowledge : 
 with many protestations that I was 
 
KEPLER. 
 
 not abandoning my claim to be provided 
 for in some other more brilliant pro- 
 fession. What progress I made in the 
 first two years of my studies, may be 
 seen in my ' Mysterium Cosmogra- 
 phicurn ;' and the encouragement given 
 me by my tutor, Mastlin, 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 ap- 
 proved by Mastlin." 
 
 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 for- 
 mation 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 discover- 
 ing similar analogies in the rest of the 
 visible world, and for this reason, named 
 his book merely a Prpdromus, or Fore- 
 runner, 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 calcu- 
 lations in which his astronomical theories,, 
 engaged him, left him little time for 
 turning his attention to objects uncon- 
 nected 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 be- 
 gin and end in error, yet they are so 
 characteristic, and exhibit such an extra- 
 ordinary 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 
 Mastlin, six years ago, at Tubingen, 
 I was disturbed by the manifold incon- 
 veniences of the common theory of the 
 universe, and so delighted with Coper- 
 nicus, whom Mastlin was frequently in 
 the habit of quoting with great respect, 
 that I not only often defended his pro- 
 positions in the physical disputations of 
 the candidates, but also wrote a correct 
 essay on the primary motion, maintain- 
 ing, 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 de- 
 grees, partly from Miistlin's instructions, 
 and partly from my own efforts, to un- 
 derstand the superior mathematical con- 
 venience of the system of Copernicus 
 beyond Ptolemy's. This labour might 
 have been spared me, by Joachim Rhe- 
 ticus, who has shortly and clearly ex- 
 plained everything in his first Narra- 
 tive. 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 Mastlin, 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 eitn- 
 do,' so it was with me, that the diligent 
 thought on these things was the occasion 
 of still further thinking : until, at last, 
 in the ye'ar 1595, when I had some in- 
 termission 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 aye not 
 other than they are : the number, the 
 size, and the motion of the orbits. I 
 attempted the thing at first with num- 
 bers, and considered whether one of the 
 orbits might be double, triple, quadru- 
 ple, or any other multiple of the others, 
 and how much, according to Coper- 
 nicus, 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 
 
KEPLER. 
 
 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 for- 
 wards, as the waves of the sea; until 
 tired at length, you will willingly repose 
 yourself, as in a safe haven, on the rea- 
 sons 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 pre- 
 sently, as by observing that the motions 
 in every case seemed to be connected 
 with the distances, and that where there 
 was a great gap bet ween 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 them- 
 selves in relation to something else. 
 
 " Finding no success by this method, 
 I tried another, of singular auda- 
 city. 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.* I 
 thought that I could thus contrive some 
 equality of proportions, increasing be- 
 tween 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, be- 
 cause the division in this proportion of 
 the residuary space within Mercury 
 might be continued without end. Nor 
 
 * The following scrupulous note added by Kepler 
 in 1621 to a subsequent edition of this work, de- 
 serves 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 con- 
 temporaries had exhibited instances even on 
 slighter pretences than this passage might have 
 afforded him. The note is as follows : " Not cir- 
 culating round Jupiter like the Jfedicoean stars. lie 
 not deceived. I never had them in rny thoughts, 
 but, like the other primary planets, including the 
 sun in the centre of tli system within their orbits." 
 
 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 impro- 
 bable, where he reasons from the sanctity 
 of the number six to the number of the 
 six moveable heavens ; for he who is in- 
 quiring 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, whe- 
 ther the distance of every planet is not 
 as the residuum of a sine ; and its mo- 
 tion as the residuum of the sine of the 
 complement in the same quadrant. 
 
 " Conceive the square A B to be con- 
 structed, whose side A. C is equal to the 
 sernidiameter of the universe. From the 
 angle B opposite to A the place of the 
 sun, or centre of the world, describe the 
 quadrant D C with the radius B C. 
 Then in A C, the true radius of the 
 world, let the sun, fixed stars, and pla- 
 nets be marked at their respective dis- 
 tances, and from these points draw lines 
 parallel toB C, meeting the quadrant. I 
 imagined the moving force acting on 
 each of the planets to be in the propor- 
 tion of these parallels. In the line of the 
 sun is infinity, because A D 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, arid 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 cal- 
 
KEPLER. 
 
 dilation ; 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 consi- 
 ders 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 re- 
 ciprocation 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 in- 
 terposition 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 1 9th * 
 day of July, in the year 1595, that, 
 having occasion to show, in my lecture- 
 room, the passages of the great con- 
 junctions through eight signs, and how 
 they pass gradually from one trine as- 
 pect to another, I inscribed in a circle 
 
 A Scheme of the 
 great Conjunctions of 
 SATURN & JUPITER, 
 their leaps through eight 
 Signs, and their passa- 
 ges through all the 
 four Triplicities 
 of the Zodiac. 
 
 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. 
 
 " The radius of a circle inscribed in 
 a triangle is half the radius of that 
 described about it; therefore the pro- 
 
 * This inconvenient mode of dating was neces- 
 sary before the new or Gregorian style was uni- 
 versally adopted. 
 
 portion 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 Sa- 
 turn 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 pen- 
 tagon. There would be no end of men- 
 tioning 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 quan- 
 tity and proportion of the six orbits, as 
 Copernicus has determined them among 
 the infinite ether 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 intro- 
 duced. This, reader, is the invention 
 and the whole substance of this little 
 work; for if any one, though but mo- 
 derately 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 imme- 
 diately 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 arrang- 
 ing them, that I was not able to change 
 anything afterwards with the utmost ex- 
 ercise of my reasoning powers. In me- 
 mory 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 
 
6 
 
 KEPLER. 
 
 circle, the measurer of all ; round it de- 
 scribe a dodecahedron, the circle in- 
 cluding this will be Mars. Round Mars 
 describe a tetrahedron, the circle includ- 
 ing this will be Jupiter. Describe a 
 cube round Jupiter, the circle including 
 
 this will be Saturn. Now, inscribe in 
 the Earth an icosaedron, the circle in- 
 scribed in it will beVenus. Inscribe an 
 octaedron in Venus, the circle inscribed 
 in it will be Mercury. This is the reason 
 of the number of the planets. 
 
 " This was the cause, and such the suc- 
 cess, of my labour : now read my propo- 
 sitions in this book. The intense plea- 
 sure 1 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 toil of reckoning ; 
 days and nights I spent in calculations, 
 until I could see whether this opinion 
 would agree with the orbits of Coper- 
 nicus, or whether my joy was to vanish 
 into air. I willingly subjoin that senti- 
 ment 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 ad- 
 miration 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 vic- 
 tory, at least approach these pages, and 
 learn the matter in consideration : you 
 will not find, as just now, new and un- 
 known 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 
 
KEPLER. 7 
 
 each orb sufficient to include the greatest parison with the real distances are as 
 and least distance of the planet from the follows : 
 sun. The form and result of his com- 
 
 
 
 
 
 Book V. 
 
 If the 
 inner 
 surface 
 of the 
 
 Saturn 
 Jupiter 
 Mars 
 Earth 
 
 be taken at 
 1000, then 
 
 the outer 
 e 
 
 1 Jupiter = 577 
 Mars = 333 
 Earth = 79") 
 Venus = 795 
 
 1 According to 
 Copernicus 
 they are 
 
 i635 Ch. 9 
 333 14 
 757 19 
 794 21,22 
 
 orbit of 
 
 Venus 
 
 one 01 
 
 Mercury = 577 
 
 
 723 27 
 
 It will he observed, that Kepler's re- 
 sults were far from being entirely satis- 
 factory ; 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 in- 
 curring much risk of decisive refutation. 
 Kepler next endeavoured to deter- 
 mine why the regular solids followed in 
 Ihis rather than any other order; and 
 his imagination soon created a variety of 
 assential distinctions between the cube, 
 pyramid, and dodecahedron, belonging 
 to the superior planets, and the other two. 
 
 The next question examined in the 
 t>pok, is the reason why the zodiac is 
 divided into 3GO 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 fa- 
 vourite 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 : 
 
 <? 
 
 D. Scr. 
 
 % 
 
 <? 
 
 4j 
 
 $ 
 
 S 
 
 10759.12 
 
 D. Scr. 
 
 % 
 
 3 
 
 
 6151) 
 
 4382.37 
 
 D.Scr. 
 
 1785 
 
 1282 
 
 686.59 
 
 D.Scr. 
 
 1174 
 
 843 
 
 482 
 
 3(55.15 
 
 D.Scr. 
 
 ? 
 
 844 
 
 COS 
 
 325 
 
 202.30 
 
 224.42 
 
 D.Scr. 
 
 5 
 
 434 
 
 312 
 
 1(57 
 
 >135 
 
 115 
 
 87. 5 S 
 
 At the head of each vertical column 
 is placed the real time (in days and sex- 
 agesimal parts) of the revolution of the 
 
 planet placed above it, and underneath 
 the days due to the other inferior pla- 
 nets, 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 dis- 
 tances, the second column shows thafc 
 the time of her period would be 843 in- 
 stead of 3G5| 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. 
 
 9.27 ^ be successively 
 ,- I taken to consist of I 
 ^ 61 1000 equal parts, 
 6.59 V the periods of J 
 
 the planet next 
 below will contain I 
 of those parts in I 
 
 But if the distance of each planet in 
 succession be taken to consist of 
 1000 equal parts, the distance of 
 the next below will contain, ac- 
 cording to Copernicus, in ^ $ 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, be- 
 cause of the remoteness and the atte- 
 nuation of the virtue." 
 
 We stop here to insert a note added 
 by Kepler to the later editions, and 
 shall take advantage of the same in- 
 terruption 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 
 
KEPLER. 
 
 centre in a straight line, and the'effect of 
 the motion thus produced combined with 
 the motion of the planet, which if un- 
 disturbed 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 per- 
 fectly 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 attrac- 
 tive 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 intelli- 
 gences, 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 simi- 
 larly at increased distances." He then 
 proceeds as follows in the original text. 
 " Let us then assume, as is very pro- 
 bable, 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 : foj 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 de- 
 rived 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 mere 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 pe- 
 riods will be double the difference of the 
 distances. Therefore, half the incre- 
 ment added to the shorter period ought 
 to give the true proportion of the dis- 
 tances, 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^ in- 
 terior one. For instance, the period of 
 Mercury is nearly 88 days ; that of Ve- 
 nus is 224f, the difference is 136 2 3 : half 
 of this is 683% which, added to 88, gives 
 156i. The mean distance of Venus 
 ought, therefore, to be, in proportion to 
 that of Mercury, as 156 to 88. If this be 
 done with all the planets, we get. the fol- 
 lowing results, taking successively, as be- 
 fore, the distance of each planet at 1000. 
 
 The distance iin 1 574 But accordr(572 
 
 parts of which ^ 274 in ? * c - 290 
 
 the distance of U fiq , pernicus J ( . .g 
 
 the next superior Hf they are ) 
 
 planet contains < G2 respectively 
 
 1000, is at 
 
 < G2 
 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 ^ occa- 
 sioned 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 de- 
 termine 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 
 
KEPLEP. 
 
 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 dis- 
 played by Kepler in this book, immedi- 
 ately 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 ge- 
 neral terms the ingenuity and good faith 
 which appeared so conspicuously in it. 
 Tycho Brahe entered into a more de- 
 tailed 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 ac- 
 quired a notion of Tycho Brahe's theory, 
 and published it as his own ; and Tycho, 
 in his letter, complained of Kepler's ex- 
 travagant flattery. This drew a long 
 apologetical reply from Kepler, in which 
 he attributed the admiration he had ex- 
 pressed 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 explana- 
 tion, Tycho professed himself perfectly 
 satisfied. 
 
 CHAPTER II. 
 
 Kepler's Marriage He joins Tycho 
 Brahe at Prague Is appointed Im- 
 perial 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 ad- 
 
 dresses, in 1596, to Barbara Muller von 
 Muhleckh. This lady was already a 
 widow for the second time, although two 
 years younger than Kepler himself. n 
 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 follow*- 
 ing 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 Bohe- 
 mia 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 promul- 
 gated, (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 Crea- 
 tion." Little is known of these works 
 beyond the notice taken of them in Ze- 
 hentmaier'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 Fre- 
 derick's death, Tycho found himself un- 
 able 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 in- 
 vitation of the emperor, Rudolph II.,. 
 he then betook himself, after a short 
 stay at Hamburg, to the castle of Be- 
 nach, near Prague, which was assigned 
 to him with an annual pension of three 
 thousand florins, a truly munificent pro- 
 vision in those times and that country. 
 12 
 
10 
 
 KEPLER. 
 
 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 ex- 
 centricities 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 imme- 
 diately 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, aj;am excusing himself 
 for the part he had appeared to take with 
 Raimar against him. Tycho replied im- 
 mediately 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 instru- 
 ments 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. Kep- 
 ler then returned to Gratz, having pre- 
 viously 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, Kep- 
 ler finally threw up his situation at 
 Gratz, in consequence of new dissen- 
 sions. 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 
 Mastlin 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 set- 
 tlement 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 en- 
 
 couragement," Kepler abandoned his 
 former scheme, and travelled again 
 with his wife to Prague. He was 
 detained along 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 ap- 
 pears 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 Helm- 
 stadt, who, like Raimar, had appropri- 
 ated to himself the credit of the Ty- 
 chonic system. Kepler never adopted 
 this theory, and indeed, as the question 
 merely regarded priority of invention, 
 there could be no occasion, in the dis- 
 cussion, for an examination of its prin- 
 ciples. 
 
 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 Ty- 
 cho'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 reply- 
 ing 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 recanta- 
 tion 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 
 1 enumerate or rightly estimate your 
 benefits conferred on me ! For two 
 months you have liberally and gratui- 
 tously maintained me, and my whole 
 family ; you have provided for all my 
 wishes ; you have done me every pos- 
 sible kindness ; you have communicated 
 to me everything you hold most dear ; 
 no one, by word o'r deed, has intention- 
 ally injured me in any thing: in short, 
 
KEPLER. 
 
 11 
 
 not to your children, your wife, or your- 
 self 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 mo- 
 roseness towards all your family, in head- 
 long 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 fa- 
 vourable 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 ho- 
 nestly declare and profess to be ground- 
 less, false, and incapable of proof." Hoff- 
 mann, the president of the states of 
 Styria, who had taken Kepler to Prague 
 on his first visit, exerted himself to per- 
 fect 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 per- 
 son in the world who possessed obser- 
 vations 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 observa- 
 tions, yet his vanity was flattered with 
 the prospect of his name being con- 
 nected with such a work, and he made 
 liberal promises to defray the expense of 
 the new Hudolphine 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 Miiller was seldom called 
 by any other name than Regiomontanus, 
 from 'his native town Konigsberg, as 
 George Joachim Rheticus was so sur- 
 named from Rhetia, the country of the 
 Grisons, and as Kepler himself was 
 sometimes called Leonmontanus, from 
 Leonberg, where he passed his in- 
 fancy. It was agreed between Longo- 
 montanus and Kepler, that in discuss- 
 ing Tycho's observations, the former 
 should apply himself especially to the 
 Moon, and the latter to Mars, o*n which 
 planet, owing to its favourable position, 
 Tycho was then particularly engaged. 
 The nature of these labours will be ex- 
 plained when we come to speak of the 
 celebrated book " On the Motions of 
 Mars." 
 
 This arrangement was disturbed by 
 the return of Longomontanus into Den- 
 mark, where he had been offered an as- 
 tronomical professorship, and still more 
 by the sudden death of Tycho Brahe 
 himself in the following October. Kep- 
 ler attended him during his illness, and 
 after his death undertook -to arrange 
 some of his writings. But, in conse- 
 quence 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 know- 
 ledge, 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 liveli- 
 hood 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 pre- 
 dictions. But although he did not scruple, 
 when consulted, to avail himself in this 
 manner of the credulity of his contem- 
 poraries, he passed over few occasions 
 in his works of protesting against the 
 futility of this particular genethliac as- 
 trology. His own astrological creed was 
 in a different strain, more singular, but 
 not less extravagant. We shall defer en- 
 tering into any details concerning it, till 
 we come to treat of his book on Har- 
 monics, in which he has collected and 
 
12 
 
 KEPLEP. 
 
 recapitulated the substance of his scat- 
 tered opinions on this strange subject. 
 
 His next works deserving notice are 
 those published on occasion of the new 
 star which shone out with great splen- 
 dour in 1 604, in the constellation Cassio- 
 peia *. Immediately on its appearance, 
 Kepler wrote a short account of it in 
 German, marked with all the oddity 
 which characterises most of his pro- 
 ductions. 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 break- 
 ing 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 hap- 
 pens in it t ; 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 con- 
 junction has taken place. Therefore the 
 apparition of this star is not like a secret 
 hostile irruption, as was that one of 1 572, 
 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 mo- 
 ney, 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, afld 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 
 
 * See Life of Galileo, p. 16. 
 t 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. 
 
 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, acci- 
 dentally through the disposition of man- 
 kind. First, it portends to the book- 
 sellers great disturbances, and tolerable 
 gains ; for almost every Theologus, Phi' 
 losophicus, Medicus, and Mathematicus* 
 or whoever else, having no laborious oc- 
 cupation intrusted to him, seeks his plea- 
 sure in studiis, will make particular re- 
 marks 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 foun- 
 dation 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 dark- 
 ness 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 descrip- 
 tion. In 1602 he had published a dis- 
 putation, 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 con- 
 tained in the second treatise on the 
 new star, which he published in 1606*. 
 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 
 
 * 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 follow- 
 ing inscription, apparently in the author's hand- 
 writing :" Regi philosophanti, philosophus ser- 
 viens, Platoni Diogenes, Britannias tenenti, Pragae 
 stipem mendicans ab Alexandro, e dolio conduc- 
 titio, hoc stium philosophema misit et coimnen- 
 darit," 
 
KEPLER. 
 
 13 
 
 prefer the judgment of the learned, they 
 are already condemned. Whether they 
 stand with me in the eyes of the popu- 
 lace, or I fall with them before the 
 learned, in both cases I am in their 
 ranks ; I am on a level with them ; T 
 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 con- 
 junctions of the planets, are impressed 
 on the natures or faculties of sub- 
 lunary 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 hope- 
 less 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 ene- 
 mies. But a most unfailing experience 
 (as .far as can be hoped in natural phe- 
 nomena) of the excitement of sublunary 
 natures by the conjunctions and aspects 
 of the planets, has instructed and com- 
 pelled my unwilling belief." 
 
 After exhausting other topics sug- 
 gested by this new star, he examines the 
 different opinions on the cause of its ap- 
 pearance. Among others he mentions 
 the Epicurean notion, that it was a for- 
 tuitous concourse of atoms, whose ap- 
 pearance 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 pro- 
 ceeds 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 
 
 Lwavvjjj KssrX^oj I made "Slipway x.dtf'/iXo;'* ', 
 
 in Latin, out of Joannes Keplerus came 
 Serpens in akule&\. But not being satis- 
 fied 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 
 
 * The tapster of the Sirens, 
 t A serpent in his sting. 
 
 this same chance, which, although I 
 spent a good deal of time over it, never 
 showed me anything like sense even from 
 a distance *. So 1 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 confu- 
 sion 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, 
 1 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." 
 
 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 nomi- 
 nal 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 Si- 
 lesia, 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 profit- 
 less speculations. In consequence of 
 this niggardliness, Kepler was ^forced to 
 postpone the publication of the Rudol- 
 phine Tables, which he was engaged in 
 constructing from his own and Tycho 
 Brahe's observations, and applied him- 
 self to other works of a less costly de- 
 scription. Among these may be men- 
 
 * 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, 
 tielenor Kapuensis, Raspinus Enkeleo, Kanones 
 Pueriles," 
 
14 
 
 KEPLER. 
 
 tioned a " Treatise on Comets," written 
 on occasion of one which appeared in 
 3607 : in this h? suggests that they are 
 planets moving in straight lines. The 
 book published in 1G04, which he en- 
 titles " 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 re- 
 lates to the theory of vision through trans- 
 parent substances. In it was first ex- 
 plained 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 
 \vith 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 transpa- 
 rent 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 me- 
 diums, 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 theargument. 
 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 writ- 
 Ings : great' ingenuity ; wonderful per- 
 severance ; 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 forrrted 
 of the nature and value of their labours. 
 
 The following tedious specimen of Kep- 
 ler's mode of examining physical pheno- 
 mena is advisedly selected to contrast 
 with his astronomical researches : though 
 the luck and consequently the fame that 
 attended his divination were widely dif- 
 ferent on the two occasions, the method 
 pursued was the same. After comment- 
 ing on ,the points of difference between 
 Rothman and Tycho Brahe, Kepler pro- 
 ceeds 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 direc- 
 tion, but calculation proved that it w r as 
 not so : and indeed there was no occa- 
 sion to have tried it, for thus the refrac- 
 tions would increase according to the 
 same law in all mediums, which is con- 
 tradicted 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 compen- 
 sated for the loss sustained at the ob- 
 lique 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 bot- 
 tom of the denser medium with greater 
 force ; for those impacts are most for- 
 cible 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 perpen- 
 dicular and a motion parallel to the dense 
 surface, and that this compound motion 
 is not destroyed, but only retarded by 
 meeting the denser medium. 
 
 " I tried another way of measuring the 
 refraction, which should include the den- 
 sity of the medium and the incidence : 
 
 for, since a denser medium is the causa 
 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 re- 
 
KEPLER. 
 
 fracted 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, B C 
 the surface of the denser medium, D E 
 its bottom . Let A B , A G, A F 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 K L, deter- 
 mined by this that there is as much of 
 the denser matter contained in the space 
 DC as of the rarer in LG : 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 B L, 
 GM, FN, cutting D E in O,P, Q ; 
 the refracted rays will be A B O, A G P, 
 AFQ." ''This method is refuted by 
 experiment ; it gives the refractions near 
 the perpendicular A C too great in re- 
 spect of those near the horizon. Who- 
 ever 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 reflec- 
 tion must not be mistaken for the dawn 
 of suspicion that his examination of phi- 
 losophical questions began not altogether 
 at the right end : it is merely an acknow- 
 ledgment 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 theo- 
 ries, it is not easy to keep clear of the op- 
 posite 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 appre- 
 ciate this method of philosophizing, that 
 it is almost certain that Kepler laboured 
 upon every one of the gratuitous sup- 
 positions that he makes, until positive 
 experiment satisfied him of their incor- 
 rectness. 
 
 " 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 perpendi- 
 cular, it occurred to me to examine whe- 
 ther there was the same proportion be- 
 tween 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 E Q, 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 E Q should be to some 
 power of E H in this proportion, or 
 the circles or similar figures described 
 on them. In this manner the proportion- 
 of E Q to E P would be double that of 
 E H to El 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 con- 
 sideration, since they have density in 
 length, breadth, and thickness, 1 pro- 
 ceeded also to examine the 1 cubic propor- 
 tions among the lines E Q, EH. 
 
 " I also considered other lines. From 
 any of the points of refraction as GV 
 let a perpendicular GY be dropped upon/ 
 the bottom. It may become a question 
 whether possibly the triangle I G Y, 
 that, is, the base I Y, is divided by the 
 refracted ray G P, in the proportion of 
 the densities of the mediums. 
 
 " I have put all these methods here 
 together, because the same remark dis- 
 proves them all. For, in whatever manner, 
 whether as line, plane, or pyramid, E I 
 observes a given proportion to E P, or 
 the abbreviated line Y I to YP, namely, 
 the proportion of the mediums, it is sure 
 that E I, the tangent of the distance of 
 the point A from the vertex, will be- 
 come infinite, and will, therefore make 
 E P or Y P, also infinite. Therefore, 
 I G P, 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 dis- 
 tance. For instance, supposing E to 
 be the imaije, C the surface of the water, 
 K the bottom, and C E to C K in the 
 proportion of the densities of the me 
 diums. Now, let F, G, B, be three 
 other points of refraction and images at 
 S, T, V, and let C E be equal to F S, GT, 
 and B V. But according to this rule an 
 image E would still be somewhat raised 
 in the perpendicular A K, which is con- 
 trary to experiment, not to mention other 
 
16 
 
 KEPLER. 
 
 contradictions. Thirdly, whether the 
 proportion of the mediums holds be- 
 tween F H and F X, supposing H to be 
 the place of the image? Not at all. 
 For so, C E would be in the same pro- 
 portion to C K, 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 CEtoFH? 
 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 perpen- 
 dicular radiation, according to the pro- 
 portion of the mediums, and do they 
 subsequently rise more and more ac- 
 cording to the sines of the inclinations ? 
 For so the proportion would be com- 
 pound, 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 con- 
 nexion between the density of the me- 
 dium 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 fol- 
 lowed 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 mea- 
 sures it ; that it is low if the thing is 
 viewed directly from above ; that by de- 
 grees 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 them- 
 selves of the existence of the image un- 
 der water, and in these causes the mea- 
 sure 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 under- 
 took 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 hap- 
 pen 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 analo- 
 gically 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 J less or more 
 oblique, but solely because of the re- 
 fraction of the ray of light passing 
 from the object to the eye. On which 
 assumption, it is plain that every attempt 
 I had hi!herto made to measure refrac- 
 tions by the image, and its elevation, 
 must fall to the ground. And this be- 
 came 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 investiga- 
 tion, as to the place of the image, I be- 
 gan 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 con- 
 cave farther than towards the circumfe- 
 rence ; 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 con- 
 cave reflecting surface, and a rarer one 
 with a convex one : it was clear, at the 
 same time, that the plane surface of the 
 
KEPLER. 
 
 17 
 
 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 at- 
 tempting to collect into one faggot the 
 measure of different refractions : I ac- 
 knowledge that the cause cannot be con- 
 nected 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 
 benevortat, we will now have had enough 
 of the causes of this measure ; and al- 
 though, even now, we are perhaps err- 
 ing something from the truth, yet it is 
 better, by working on, to show our in- 
 dustry, 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 assist- 
 ance 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 sound- 
 ing 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 ne- 
 cessary than that which they have un- 
 dertaken 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." 1 
 
 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 mathe- 
 matician,) there are many things well 
 deserving notice in his investigations. 
 He remarked, that the quantity of re- 
 fraction would alter, if the height of the 
 atmosphere should vary ; and also, that 
 it would be different at different tempe- 
 ratures. Both these sources of varia- 
 tion are now n constantly taken into ac- 
 count, the barometer and thermometer 
 fiving exact indications of these changes, 
 here 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 rain- 
 bow, it is possible that some one may 
 see a rainbow in the very place of my 
 sight. In this case, the medium is co- 
 loured 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 1 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 cham- 
 ber, or standing opposite glass globes', 
 or walking in the morning dew, every- 
 where it is obvious that a certain and de- 
 finite 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 pas- 
 sage, 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 lumi 
 
18 
 
 KEPLER. 
 
 nous 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. 1 he 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 precipi- 
 tancy 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 recon- 
 ciling with his more accurate knowledge 
 of the motions of Mercury, were to be 
 referred to a like mistake. On this occa- 
 sion 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 dis- 
 coveries of this new instrument, of retract- 
 ing several opinions which he had main- 
 tained with considerable warmth, he 
 ranged himself at once on the side of Gali- 
 leo, in opposition to the bitter and deter- 
 mined 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 se- 
 lected instance from the numerous occa.- 
 sions 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 ad- 
 miration 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 mu- 
 tual regard : Mastlin especially, Kepler's 
 
 early instructor, seldom mentioned to him 
 the name of Galrleo, without some con- 
 temptuous 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 disco- 
 veries 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 acquaint- 
 ance ; and it is on this work that his re- 
 putation 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 astro- 
 nomers 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 ex- 
 hausted 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 ap- 
 proaching 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 proba- 
 bility was sufficient to plunge him into 
 the midst of the most laborious compu- 
 tations. He was by no means an accu- 
 rate calculator, according to the follow- 
 ing character which he has given of him- 
 self : " 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 pro- 
 duce 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 
 
KEPLER. 
 
 19 
 
 l>e 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 assist- 
 ant, 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 as- 
 tronomy may be understood, it is neces- 
 sary 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 me- 
 chanism was contrived by which it was 
 thought that the apparent irregularity 
 could be represented, and yet the prin- 
 ciple of uniform motion, which was ad- 
 hered to with superstitious reverence, 
 might be preserved. This, in its sim- 
 plest 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*. 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 D A. Thus, 
 the angle a dp, measuring the motion of 
 the planet in its epicycle, would be equal 
 
 * 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 under- 
 stood whenever these or similar expressions are 
 repeated. 
 
 to DEd, the angle described by the 
 centre of the epicycle in the deferent. 
 The angle pE d between Ejo, the direc- 
 tion 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 mov- 
 ing in the centre of the deferent, was 
 called the equation of the orbit, the 
 word equation, in the language of astro- 
 nomy, signifying what must be added 
 or taken from an irregularly varying 
 quantity to make it vary uniformly. 
 
 As the accuracy of ^observations in- 
 creased, minor irregularities were dis- 
 covered, 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 revo- 
 lution in the epicycle not to be com- 
 pleted in exactly the time in which its 
 centre is carried round the deferent. 
 Hipparchus was the first to make a re- 
 mark by which the geometrical repre- 
 sentation of these inequalities was consi- 
 derably simplified. In fact, if EC be 
 taken equal to p d, Cd will be a paral- 
 lelogram, and consequently Cp equal 
 to E d, so that the machinery of the 
 first deferent and epicycle amounts to 
 supposing that Ihe planet revolves uni- 
 formly 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 CpE, 
 which is equal top Ed. It is not ne- 
 cessary to give any account of the man- 
 ner in which the old astronomers de- 
 termined 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 neces- 
 sary to use in describing Kepler's in- 
 vestigations. 
 
 To explain the irregularities observed 
 in the other planets, it became neces- 
 sary to introduce another hypothesis, in 
 adopting which the severity of the prin- 
 ciple 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 uni- 
 formly round C, the centre of the deferent, 
 
KEPLER. 
 
 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 some- 
 times called the centre of the orbit ; and 
 Q, called the centre of the equant, be- 
 cause, if any circle were described round 
 Q, the planet would appear to a spec- 
 tator 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 ir- 
 regularities 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 doubt- 
 ful) 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. 
 
 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 E M, drawing E M 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 angu- 
 lar motion round E instead of Q. This 
 angle dE M, or its equal Erf Q, was called 
 the equation of the centre (i. e. of the 
 centre of the epicycle) ; and is clearly 
 greater than if E Q, the excentri- 
 city of the equant, had been "no greater 
 than E C, called the excentricity of the 
 orbit. The second equation was mea- 
 sured 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 be- 
 came necessary to suppose that many 
 revolutions in the latter were completed 
 during one of the former. The va- 
 riations 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 chang- 
 ing, 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 mo- 
 tions 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 peri- 
 gee, or point of nearest approach of the 
 epicycle. This correspondence between 
 two phenomena, which, according to 
 the old astronomy, were entirely uncon- 
 nected, 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 
 ofexcentrics and epicycles, which had 
 been strained into representing the ap- 
 pearances of the heavens at a particular 
 moment, grew out of shape, and the 
 natural consequence of such an artifi- 
 cial 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 par- 
 ticular point. In the ninth century of 
 our era, Ptolemy's tables were already 
 useless, and all those that were con- 
 trived with unceasing toil to supply 
 their place, rapidly became as unser- 
 viceable as they. Still the triumph of 
 genius was seen in the veneration that 
 continued to be paid to the assump- 
 tions of Ptolemy and Hipparchus ; and 
 even when the great reformer, Coper- 
 
KEPLER. 
 
 21 
 
 nicus, appeared, he did not for along 
 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 sys- 
 tem, it has become common to demon- 
 strate 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 combina- 
 tions 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 cen- 
 tury by Martianus Capella*, and in- 
 deed 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 be- 
 tween the motion of the sun and the revo- 
 lutions of the superior planets in their 
 epicycles, led him straight to the expec- 
 tation 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 coin- 
 cident with the earth, but removed from 
 it by the space E C. This first change 
 merely made E C the same for all the 
 planets, and equal to the mean distance 
 of the earth from the sun. This sys- 
 tem ^afterwards acquired great cele- 
 brity 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 pas- 
 sages in the Latin and Greek authors, 
 to which he refers as testifying the ex- 
 istence of an old belief in the motion 
 of the earth round the sun. He im- 
 mediately recognised how much this 
 alteration would further his princi- 
 ples of uniformity, by referring all the 
 
 * Venus Mercuriusque, licet ortus occasusque 
 quotidianos ostendunt, tamen eorum circuli terras 
 omnino non ambiunt, sed circa solem laxiore am- 
 bitu circulantur. Denique circulorura suorum 
 centron in sole constituunt. De Nuptiis Philolo- 
 gise et Mercurii. Vicentije. 1499. 
 
 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 con- 
 sequence of his previous improvements, 
 as it was manifestly at variance with 
 his principles to give to all the pla- 
 nets 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. 
 
 The reader would, however, form an 
 inaccurate notion of the system of Co- 
 pernicus, if he supposed that it com- 
 prised 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 hea- 
 venly 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 ap- 
 pear 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 al- 
 teration 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 accompany- 
 ing diagram, where S represents the sun,. 
 
 D d, the deferent or mean orbit of the 
 
KEPLER. 
 
 planet, on \vhich revolves the centre of 
 the great epicycle, whose radius, D F, 
 \vas taken at | of Ptolemy's excentricity 
 of the equant ; and round the circum- 
 ference of this revolved, in the opposite 
 direction, the centre of the little epicycle, 
 \vhose radius, F P, \vas made equal to 
 the remaining of the excentricity of the 
 equant. 
 
 The planet P revolved in the circum- 
 ference^of the little epicycle, in the same 
 direction with the centre of the great epi- 
 cycle in the circumference of the defe- 
 rent, 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 DSd, F moved through 
 h d f= D S d, and P through r f p = 
 
 It is easy to show that this construc- 
 tion gives nearly the same result as 
 Ptolemy's ; for the deferent and great 
 epicycle have been already shown ex- 
 actly equivalent to an excentric circle 
 round S, and indeed Copernicus latterly 
 so represented it: the effect of his con- 
 struction, as given above, may therefore 
 be reproduced in the following simpler 
 form, in which only the smaller epicycle 
 is retained : 
 
 In this construction, the place of the 
 "planet is found at the end of any time 
 proportional to F /, by drawing / r 
 parallel to SF, and taking rfp = 2 F of. 
 Hence it is plain, if we take O Q, equal 
 to F P, (already assumed equal to of 
 Ptolemy's excentricity of the equant,) 
 since S O is equal to f cf the same, 
 that S Q is the whole of Ptolemy's ex- 
 centricity of the equant ; and therefore, 
 that Q is the position of the centre of 
 his equant. It is also plain if we join 
 Qp, since rfp = 2Fo/, and oQ = 
 .fp,'\ that p Q is parallel to fo, and, 
 therefore, p Q P is proportional to the 
 time ; so that the planet moves uni- 
 formly about the same point Q, as in 
 Plolwiry's theory ; and if we bisect S Q 
 
 in C, which is the position of tVie centre 
 of Ptolemy's deferent, the planet will, 
 according to Copernicus, move very 
 nearly, though not exactly, in the same 
 circle, whose radius is C P, as that 
 given by the simple excentric theory. 
 
 The explanation offered by Coperni- 
 cus, of the motions of the inferior pla- 
 nets, 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 re- 
 tained the oscillatory motions ascribed 
 by Ptolemy to the planes of the epicy- 
 cles, 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 obser- 
 vations, 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 phe- 
 nomena. 
 
 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, how- 
 ever, 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 urifavourable 
 judgment he anticipated on the main 
 principles of his system, his work re- 
 mained unpublished during forty years, 
 and was at last given to the world only 
 just in time to allow Copernicus to re- 
 ceive the first copy of it a few hours 
 before his death. 
 
KEPLER. 
 
 CHAPTER V. 
 
 Account of the Commentaries on the 
 motions of Mars Discovery of the 
 Law of 'the equable description of 
 ' A reas, and of Elliptic Orbits. 
 WE may now proceed to examine Kep- 
 ler'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 com- 
 prehend 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 ac- 
 ceptable 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 under- 
 rate the importance of his labours, as is 
 sufficiently shewn by the sort of collo- 
 quial 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 pro- 
 fessor 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 hypo- 
 thesis, he promised as an additional in- 
 ducement to vacate his own chair in fa- 
 vour 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 profes- 
 sorship together :"for if you still held it, 
 I would certainly claim it as of right be- 
 longing 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 
 light of a work filled with hypotheses of 
 the most startling description ; but ot" 
 
 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 uni- 
 versal gravitation. It does not appear, 
 however, that Kepler estimated rightly 
 the importance of the theory here traced 
 out by him, since on every other occa- 
 sion he advocated principles with which 
 it is scarcely reconcileable. The dis- 
 cussion 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 pos- 
 sessed by a point, which neither is a 
 body, nor is conceived unless by rela- 
 tion alone. It is impossible that the 
 form* of a stone should, by moving its 
 own body, seek a mathematical point, 
 or in other words, the centre of the uni- 
 verse, 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 propor- 
 tion to their distance from the extremi- 
 ties 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 care- 
 fully from an enemy lying on all sides of 
 
 * 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." 
 
 ~K 
 
24 
 
 KEPLER. 
 
 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 revolv- 
 ing water. For if we assume such a 
 motion, either it would not be con- 
 tinued 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 oppo- 
 nents to be absurd. It is therefore plain 
 that the vulgar theory of gravity is erro- 
 neous. 
 
 The true theory of gravity is founded 
 on the following axioms : Every corpo- 
 real substance, so far forth as it is corpo- 
 real, 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 mu- 
 tual 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 whitherso- 
 ever 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. I f 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 ani- 
 mal force or some other equivalent, the 
 earth would mount to the moon by a 
 lifty-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 1he 
 body Of the moon. The sphere of the at- 
 
 tractive virtue which is in the moon ex- 
 tends 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 at- 
 tracted, 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 sen- 
 sible, compared with the earth's dia- 
 meter, 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 as- 
 tronomy, can believe that Newton waited 
 for the fall of an apple to set him think- 
 ing 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 ritinu 
 of natural philosopher. 
 
 As Kepler always professed to have 
 derived his notion of a magnetic attrac- 
 tion 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 lie presented a simi- 
 lar theory of the tides, winch aiibuls the 
 
KEPLER. 
 
 25 
 
 most striking illustration of that attrac- 
 tion. 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 writlen : 
 
 " 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 ex- 
 plain it by something similar) by their 
 magnetic attraction. It should be known, 
 in the first place, that the whole quan- 
 tity 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 at- 
 traction of that star ; and for the same 
 reason, the quicksands which are in the 
 sea open themselves more, and per- 
 spire 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 mois- 
 ture 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/'* 
 
 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) jas 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 ten- 
 dency to rise towards it, was thought 
 to convey no instruction ; but the asser- 
 tion that the moon draws out subterra- 
 nean spirits by sympathy, carried with it 
 
 * De mundo nostro sublunari, Philosophia 
 
 Nova, Amsteiodami, JCoi, 
 
 a more imposing appearance of theory. 
 The farther removed these humoms 
 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^ iden- 
 tical, 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 Longomon- 
 tanus 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 accu- 
 mulation of observations made by him 
 during a residence of fifteen years at 
 Uraniburg, with the assistance of instru- 
 ments, 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 with- 
 out 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 in- 
 feriority to Tycho Brahe', maybe gathered 
 from an incidental remark of Kepler to 
 Longomontanus. He had been examin- 
 ing Tycho' s registers, and had occasion- 
 ally found a difference amounting some- 
 times 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 Longomon- 
 tanus very busily engaged in correct- 
 ing 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 disco- 
 vered a position of the equant, which (as 
 they said) represented them with tolerable 
 
KEPLER. 
 
 exactness. On the other hand, they were 
 much embarrassed by the unexpected 
 difficulties they met in applying a sys- 
 tem which seemed on the one hand so 
 accurate, to the determination of the lati- 
 tudes, with which it could in no way be 
 made to agree. Kepler had already sus- 
 pected 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 over- 
 rated the accuracy even of their longi- 
 tudes. 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 Kepkr 
 had satisfied himself of the contrary, 
 and the following diagram shews the na- 
 ture 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. 
 The practice of Tycho Brahe, indeed 
 of all astronomers till the time of Kepler, 
 had been to fix the position of the pla- 
 net's orbit and equant from observa- 
 tions 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 /. 
 
 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 Q C, and not 
 in Q S, as Kepler suggested that it ought 
 to Le taken. The consequence of this 
 erroneous practice was, that the observa- 
 
 tions were deprived of the character for 
 which oppositions were selected, of being 
 entirely tree from the second inequalities. 
 It followed therefore that as part of 
 the second inequalities were made con- 
 ducive towards fixing the relative posi- 
 tion 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 C S, that the time of .its taking 
 place would be the same, whether O, the 
 centre of the orbit, was placed in C Q or 
 S Q. Every other opposition would in- 
 volve an error, so much the greater as 
 it was observed at a greater distance 
 from the line G S. 
 
 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 erro- 
 neous 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 observa- 
 tion ; though the second inequalities and 
 the latitudes would thereby be very 
 greatly deranged. 
 
 The change Kepler introduced, of ob- 
 serving apparent instead of mean oppo- 
 sitions, made it necessary to be very ac- 
 curate 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 indispen- 
 sable. 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 imper- 
 fect 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 de- 
 termine the inclination of the orbit and 
 
KEPLER. 
 
 Ihe position of the line of nodes. In 
 all these operations his talent for as- 
 tronomical inquiries appeared pre-emi- 
 nent in a variety of new methods by 
 which he combined and availed him- 
 self 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 orbil, which naturally strength- 
 ened him in his new theory. 
 
 Having gone through these preliminary 
 inquiries, he came at last to fix the pro- 
 portions of the orbit ; and, in doing so, he 
 determined, in the first instance, not to as- 
 sume, as Ptolemy appeared to have done 
 arbitrarily, the bisection of the excen- 
 tricity, 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 la- 
 bo ur,especially if we remember that loga- 
 rithms 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 51' 35 7 ; that if the semidiameter of 
 the orbit was taken at 1000UO, the excen- 
 tricity was 1 1 332 ; 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 longi- 
 tudes as given by this, which he after- 
 wards called the vicarious theory, with 
 the observations at opposition, the result 
 seemed to promise him the most bril- 
 liant 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 com- 
 plete as he had imagined, and to his in- 
 finite vexation he soon found that the 
 labour of four years, which he had ex- 
 pended on this theory, must be consi- 
 dered 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 pro- 
 duced 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 ad- 
 mitted the possibility of the former of 
 these facts, conceiving it possible that the 
 motion of the planets is not at all curvi- 
 linear, but that they move in polygons 
 round the sun, a notion to which he pro- 
 bably inclined in consequence of his fa- 
 vourite 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 en- 
 tirely different complexion. Instead of 
 first satisfying the first inequalities of 
 the planet, and then endeavouring to ac- 
 count for the second inequalities, he re- 
 solved 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 pro- 
 ceeding to any inquiry of the real in- 
 equality 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 re- 
 suming 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 Jess than the other planets. 
 He now saw, that if this were admitted, 
 the changes it would everywhere intro- 
 duce in the optical part of the planet's 
 irregularities might perhaps relieve him 
 from the perplexity "in which the vica- 
 rious theory had involved him. Ac- 
 cordingly he applied himself with re- 
 newed 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 ex- 
 centricity which he had previously found 
 
23 
 
 KEPLER. 
 
 indispensable in the other planets. This 
 \v as an innovation of the first magni- 
 tude, 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 eccen- 
 tricity, so familiar to the Ptolemaic as- 
 tronomers, 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 termi- 
 nated in one of his most celebrated dis- 
 coveries. We have already seen, in the 
 account of the " Mysterium Cosmogra- 
 phicum," 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 dis- 
 tances, 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 tinges and distances in dif- 
 ferent planets. Another analogous con- 
 sequence 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 in- 
 equalities, than from th.3 imaginary 
 equant. But these ingenious ideas had 
 been checked in the outset by the errone- 
 ous belief which Kepler, in common with 
 other astronomers, then entertained of 
 the coincidence of the earth's equantr 
 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 re- 
 lation could be found between the ve- 
 locity and distance of a planet from tli3 
 sun. The method he adopted in the be- 
 ginning of this inquiry was to assume 
 as approximately correct Ptolemy's doc- 
 trine 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 A B a b, Q the centre of the equant 
 represented by the equal circle D E d e, 
 AB, ab, two equal small arcs described 
 by the planet at the apsides of its orbit : 
 then, according to Ptolemy's principles, 
 the arc D E of the equant would be pro- 
 portional to the time of passing along 
 A B, on the same scale on which de would 
 represent the time of passing through 
 the equal arc a b. 
 
 Q D ; Q A : : D E : A B, nearly ; and 
 because Q S is bisected in C, Q A, CA 
 or Q D, and S A, are in arithmetical 
 proportion: and, therefore, since an 
 arithmetical mean, when the difference 
 is small, does not differ much from a 
 geometrical mean, Q D : Q A : : S A : 
 Q D, nearly. Therefore, D E : A B :.: 
 S A : Q D, nearly, and in the same man- 
 ner d e : a b : : S a : Qd nearly ; and 
 therefore DE: c?e : : S A : 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 ii. 
 
 It followed immediately from this 
 assumption, that after leaving the point 
 A, the time in which the planet would 
 
KEPLER. 
 
 29 
 
 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 
 A P, 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 at- 
 tempt to verify this supposition ap- 
 proximately, 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 al- 
 most miraculous good fortune, he was 
 led by it in the following manner to the 
 true measure. The discovery was aeon- 
 sequence 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 dis- 
 tances, S A, S P, and the arc A P, 
 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 tri- 
 angles 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 accu- 
 rately observed in the revolution of one 
 body round another, in consequence of 
 an attractive force in the central body. 
 Newton afterwards proved this, ground- 
 ing 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 unspar- 
 ingly upon every one of his successive 
 guesses, joined with his admirable can- 
 dour, generally preserved him from long 
 retaining a theory altogether at variance 
 with observations ; and if any relation 
 subsisted between the times and dis- 
 tances which could any way be express- 
 ed 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 in- 
 defatigable 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 exist- 
 ed. Let us take for example the incli- 
 nations or the excentricities of the 
 planetary orbits, among which no rela- 
 tion has yet been discovered ; and if any 
 exists, it is probably of too complicated 
 a nature to be hit at a venture. If Kep- 
 ler had exerted his ingenuity in this 
 direction, he might have wasted his life 
 in fruitless labour, and whatever repu- 
 tation 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 pas- 
 sage round the sun was, that he found 
 himself in possession of a much more ac- 
 curate method of representing its inequa- 
 lities 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 opi- 
 
30 
 
 KEPLER. 
 
 nion, that the orbits of the planets must 
 consist of a combination of circles ; he 
 therefore determined, in the first in- 
 stance, 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 describ- 
 ing equal arcs at the apsides were pro- 
 portional to its distances from the sun, 
 and he naturally expected that the me- 
 thod 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 beino; able to use this substitu- 
 tion, 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 pro- 
 duce, 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 sup- 
 position, which by this time had, in his 
 eyes, almost acquired the force of demon- 
 stration, 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, \ve read the following 
 passage. " Sixthly, it appears from 
 what lias 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, de- 
 scribe 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 de- 
 scribes 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*." 
 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 com- 
 mentator, although they did not pursue 
 the inquiry so far as Kepler found him- 
 self in a condition to do. 
 
 Before proceeding to the considera- 
 tion of the particular oval which Kepler 
 fixed upon in the first instance, it will 
 be necessary, in order to render intelli- 
 gible the source of many of his doubts 
 and difficulties, to make known some- 
 thing 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 pur- 
 sued, this shall be done as much as pos- 
 sible in his own words. 
 
 " It is one of the commonest axioms in 
 natural philosophy, that if two things al- 
 ways 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 lan- 
 guor 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 chap- 
 ters 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 dis- 
 
 * Theories novre plauetarum. G. Purbachii, 
 rurisiis, K>'>o. 
 
KEPLER. 
 
 31 
 
 
 tance from the centre, since it requires 
 space for its accomplishment, but dis- 
 tance 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 es- 
 sence 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 ap- 
 proaching. 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 pur- 
 pose of moving it, should exert and re- 
 lax itself so often without weariness or 
 decay. It remains, therefore, that the 
 cause of this activity and languor re- 
 sides 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 mov- 
 ing 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 con- 
 vey 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 eveiy other ema- 
 nation by which mediums are filled. It 
 remains, therefore, that as %ht which . 
 illuminates all earthly things, is the im- 
 material species of that fire which is in 
 
 the body of the sun, so this virtue, em- 
 bracing 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 con- 
 template 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 car- 
 ries 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 pro- 
 ceed to the various opinions he enter- 
 tained 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 ~Dd, 
 according to the law of the planet's dis- 
 tances ; the point remaining to be settled 
 was the motion of the planet in the 
 epicycle. If it were made to move ac- 
 cording 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 Dd 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 observa- 
 tions. Some of these reasons are sub- 
 joined : " 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 
 
32 
 
 KEPLER. 
 
 has respect to the sun, and knows be- 
 forehand, and remembers the order in 
 which the distances from the sun are 
 comprised, so as to make a perfect ex- 
 centric ; 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 dia- 
 meter of the sun. Butthere are no 
 such means, except the position of the 
 centre of the excentric at a given dis- 
 tance 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 de- 
 scribed in unequal times, and to be de- 
 scribed 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 anytime. 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 spe- 
 cimen 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 dis- 
 tances from the sun are equal to what 
 they would have been in a real epicycli- 
 cal motion. This leads to more incredi- 
 ble consequences than the former suppo- 
 sitions, and yet in the dearth of better 
 opinions, let us for the present content 
 ourselves with this. The greater num- 
 
 ber of absurd conclusions it will be found 
 to involve, the more ready will a physi- 
 cian 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 explana- 
 tion of his first oval. " As soon as I 
 was thus taught by Brahe's very accu- 
 rate observations that the orbit of a pla- 
 net is not circular, but more compressed 
 at the sides, on the instant 1 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 la- 
 boured in the 39th chapter, in conse- 
 quence of my inability to find a suffi- 
 ciently 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 fu- 
 riously 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 pro- 
 bable 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 re- 
 gardful 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 en- 
 tangled 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 accord- 
 ing 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.supposjtion, since 
 
KEPLER. 
 
 33 
 
 at D, when the planet is at A. the aphe- 
 lion, the motion in the deferent is less than 
 the mean motion, the planet will have ad- 
 vanced through an angle B E P greater 
 than B E F or B S A, through which the 
 centre of the epicycle has moved ; and 
 consequently, the path will lie every- 
 where 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 sup- 
 pose 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. 
 
 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 pur 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 accu- 
 racy 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 rea- 
 sonings on the rout and dispersion of the 
 veterans, and diligently followed, with- 
 out allowing him the slightest respite, in 
 the direction in which he had broken 
 out.' 7 
 
 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 ap- 
 sides, the planet was now too slow there, 
 and too much accelerated in the mean 
 distances ; and the distances obtained 
 from direct observation were every- 
 where 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 obser- 
 vations, his vexation was extreme, not 
 merely from the mortification of finding 
 a theory confuted on which he had spent 
 
KEPLER. 
 
 such excessive labour, for he was accus- 
 tomed to disappointments of that kind, 
 but principally from many anxious and 
 fruitless speculations as to the real phy- 
 sical 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 reason- 
 ing 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 abovementioned, in calcu- 
 lating the proportions of the oval path 
 he had imagined. "In order that 
 you may see the cause of the impracti- 
 cability of this method which we have 
 just gone through, consider on what 
 foundations it rests. The planet is sup- 
 posed 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 cor- 
 responds to any given time, although 
 the distance at that part is known, un- 
 less 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 cor- 
 responds to any given time. Here you 
 see that there is a petitio principii ; and 
 in my operations I was assuming that of 
 which [ 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 
 {\\ispetitioprincipii, 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 
 
 Sit him once more upon the right path, 
 alf 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 S F, he should every- 
 where substitute F V, determined by 
 drawing S V perpendicular on the line 
 F C, since the excess of S F above F V 
 is manifestly that of the secant above 
 the radius in the optical equation S F C 
 at that point. It is still more extraor- 
 dinary 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 S P or S F, 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; Not- 
 withstanding this success, he had to 
 undergo, before arriving at the success- 
 ful termination of his labours, one more 
 disappointment. Although the distance 
 corresponding to a time from the aphe- 
 lion represented approximately by the 
 area ASF, was thus found to be accu- 
 rately represented by the line S n, there 
 was still an error with regard to the di- 
 rection in which that distance was to be 
 measured. Kepler's fir.^t idea was to set 
 it off in the direction S F, but this he 
 found to lead to inaccurate longitudes ; 
 
KEPLEtt. 
 
 35 
 
 and it was not until after much per- 
 plexity, driving him, as he tells us, 
 "almost to insanity," that he satisfied 
 himself that the distance S Q tqual to 
 FV ought to betaken 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. 
 
 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 A S F to represent the sums of the 
 distances S F, was exactly counterba- 
 lanced ; for this area does accurately 
 represent the sums of the distances F V or 
 S Q. 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 mea- 
 sure and define their motions, or to re- 
 nounce 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 establish- 
 ment of these two theorems, it became 
 important to discover a method of mea- 
 suring such elliptic areas, but this is a 
 problem which cannot be accurately 
 solved. Kepler, in offering it to the 
 attention of geometricians, stated his be- 
 lief that its solution was unattainable by 
 direct processes, on account of the in- 
 commensurability of the arc and sine, on 
 which the measurement of the two parts 
 AQm, SQm depends. " This," says 
 he in conclusion, " this is my belief, and 
 whoever shall shew my mistake, and 
 point out the true solution, 
 
 /* Grit mihi magnus Apollonius" 
 
 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 recruit- 
 ing 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 Kep- 
 ler'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 Ma- 
 thematician, and had also a permanent 
 professorship assigned to him in the Uni- 
 versity of Linz. He quitted Prague with- 
 out 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 yetretained 
 upon the wreck of Tycho Brahe's instru- 
 ments and observations. Tengnagel, 
 son-in-law of Tycho, had abandoned as- 
 tronomy for a political career, and the 
 other members of his family, who were 
 principally females, suffered the costly 
 instruments to lie neglected and for- 
 gotten, although they had obstructed 
 with the utmost jealousy Kepler's at- 
 tempts to continue their utility. The 
 only two instruments Kepler possessed 
 of his own property, were " An iron 
 sextant of 2 feet diameter, and a brass 
 azimuthal quadrant, of 3 4 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 obser- 
 vations 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 men- 
 tions himself in several places. In the 
 summary of his character which he 
 drew up when proposing to beco.ne 
 Tycho Brahe's assistant, he describes 
 himself as follows : " For observations 
 
36 
 
 KEPLER. 
 
 my sight is dull ; for mechanical opera- 
 tions my hand is awkward ; in politics 
 and domestic matters my nature is 
 troublesome and choleric ; my constitu- 
 tion will not allow me, even when in 
 good health, to remain a long time 
 sedentary (particularly for an extraor- 
 dinary time after dinner); 1 must rise 
 often and walk ahout, and in different 
 seasons am forced to make correspond- 
 ing 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 phre- 
 nitis. 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. Return- 
 ing 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 an- 
 noyance, 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 histwo 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 hi* final choice, does not, in 
 
 any point, belie the oddity of his charac 
 ter. 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 pre- 
 tensions and qualifications of no less 
 than eleven ladies among whom his in- 
 clinations 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 pro- 
 posal ; 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 after- 
 wards 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, consider- 
 ing this last discovery, to determine 
 why she would not accept his offered 
 hand. Among other reasons he sug- 
 gested 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 acquaint- 
 ance. 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 there- 
 fore 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 pititul tender- 
 heartedness ; in catching at reputation 
 by new and paradoxical notions, and the 
 
KEPLER. 
 
 37 
 
 singularity of my actions ; in busily in- 
 quiring into, and weighing and dis- 
 cussing, various reasons ; in the un T 
 easiness 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 Ihe others." Of these others, 
 one was too old, another in bad health, 
 another too proud of her birth and 
 quarterings; a fourth had learned no- 
 thing 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 hesitat- 
 ing. "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 anew passion." By the 
 time he reached the eighth, he found 
 his match in this respect. " Fortune at 
 length has avenged herself on my doubt- 
 ful inclinations. At first she was quite 
 complying, and her friends also : pre- 
 sently, whether she did or did not con- 
 sent, not only I, but she herself did not 
 know. After the lapse of a few days, 
 came a renewed promise, which how- 
 ever had to be confirmed a third time ; 
 and four clays after that, she again re- 
 pented 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 com- 
 plexion. His advances to No. 9, were 
 made by confiding to her the whole 
 story of his recent disappointment, pru- 
 dently determining to be guided in his 
 behaviour, by observing whether the 
 treatment he had experienced met with 
 a proper degree of sympathy. Appa- 
 rently 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 diffi- 
 cult 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 dis- 
 proportion 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. 1 1 seems to have been 
 her excessive youth ; and when this 
 treaty was broken of on that account, 
 Kepler turned his back upon -all his ad- 
 visers, 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 repre- 
 sentations 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 Bar- 
 bara, 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 extra- 
 vagance ; 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. 
 Kastner and other biographers have 
 been content to repeat the same asser- 
 tion without any comment, notwith- 
 standing its evident improbability. 
 The origin of the blunder is to be found 
 in Kepler's correspondence with Berneg- 
 ger, to whom, speaking of his wife, he 
 says " She has been educated for twelve 
 
 >ars by the Lady of Stahrenberg." 
 his is by no means a single instance of 
 carelessness in Hantsch ; Kastner 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 Aus- 
 trian vineyards, to be sold at a rea- 
 sonable 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 
 
38 
 
 KEPLER. 
 
 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 cylin- 
 ders, from the consideration that " these 
 solids are incorporated circles," and, 
 therefore, that those properties are true 
 of the whole which belong to each com- 
 ponent 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 ilia, ne sciamus. " 
 
 His new residence at Linz was not 
 long undisturbed. He quarrelled there, 
 as he had done in the early part ef 
 his life at Gratz, with the Roman Ca- 
 tholic 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 oc- 
 casioned his excommunication, was con- 
 nected with the doctrine of transubstan- 
 tiation. 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 con- 
 venience of doing so, or of altering 
 the old Julian Calendar in some other 
 manner. Notwithstanding the readi- 
 ness of the diet to avail themselves of 
 his talents for the. settlement of a dif- 
 ficult 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 ex- 
 pense of the Ephemeris for these two 
 years, I have also written a vile prophe- 
 sying 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 an- 
 nually 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 Ma- 
 thematics 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 Ger- 
 man principles, and bound by such fa- 
 mily ties, that even if the emperor should 
 consent, 1 could not, without the greatest 
 difficulty, remove my dwelling-place from 
 Germany into Italy. And although the 
 glory of holding so distinguished a situa- 
 tion among the venerable professors of 
 Bologna stimulates me, and there ap- 
 pears great likelihood of notably in- 
 creasing 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 an- 
 swer, I have yet hopes that your most 
 honourable invitation will be of service 
 to me, and may make the imperial trea- 
 surer more ready than he has hitherto 
 been to fulfil his master's intentions to- 
 wards 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 fruit- 
 less." 
 
 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. Kiistner, in his " His- 
 tory 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. 
 
KEPLER. 39 
 
 CHAPTER VII. tion of great importance, for on this 
 
 account is it that the heptagon, and other 
 figures of this kind, have not been em- 
 ployed 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 accu- 
 rately found, may yet be found within 
 any degree of approximation by an ex- 
 pert calculator. In conclusion he again 
 remarks that " the side of the heptagon 
 has no place among scientific existences, 
 since its formal description is impos- 
 sible, 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 pro- 
 portions." 
 
 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 our- 
 selves with merely citing his own words, 
 without any attempt to explain the dif- 
 ference between the astrology which he 
 believed, and that which he con- 
 temptuously 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 rea- 
 soning powers, it is not of much conse- 
 quence 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 contem- 
 porary philosophers as a reason for 
 embodying them in a regular form. 
 " Since many very celebrated professors 
 of philosophy and medicine are of opinion 
 
 Kepler publishes his ' Harmonics 
 Account of his Astrological Opinions 
 and Discovery of the Law of the Pe- 
 riods 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 con- 
 sidered as due merely to the vivacity of 
 a young man ; but as if purposely to 
 shew that his maturer age did not re- 
 nounce the creations of his youthful 
 fancy, he reprinted the " Mystery" in 
 1619, nearly at the same time when he 
 published his celebrated work on Har- 
 monics ; 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, Geo- 
 metrical, on the origin and demonstration 
 of the laws of t'ne 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 na- 
 ture 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 hea- 
 venly bodies, and on their effect in na- 
 ture, and on the sublunary and human 
 soul ; the fifth, Astronomical and Me- 
 taphysical, on the very exquisite harmo- 
 nies 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 inscrip- 
 tion of regular polygons in a circle. 
 The following passage is curious, pre- 
 senting an analogous idea to that con- 
 tained in one of the extracts already 
 given fropi 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 ques- 
 
KEPLER. 
 
 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 Kep- 
 ler'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 configura- 
 tions 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 astrolo- 
 gical superstitions of that vulgar and 
 childish race of dreamers, the prognos- 
 ticators." 
 
 The real manner in which the con- 
 figurations of the stars operate, accord- 
 ing 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 attunted 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, espe- 
 cially at those times when the rays of 
 the planets form harmonious configura- 
 tions on the earth." " I have been con- 
 firmed 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 configu- 
 Yations ; but the earth sometimes ap- 
 pears lazy and obstinate, and at another 
 time (after important and long-continued 
 configurations) she becomes exas- 
 perated, 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 be- 
 come 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 particula- 
 rity of details into which we forbear 
 to follow him, the analogies he re- 
 cognized 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 men- 
 tioned 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 accord- 
 ing to the motion of the sun and moon, 
 as animals have daily and nightly alter- 
 nations of sleep and waking, I shall not 
 think his philqsophy 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. 
 
KEPLER. 
 
 how much Kepler did, and how much he 
 didnotbelieveonthe 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 configu- 
 ration 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, as- 
 saults, attacks, and panic fears, gene- 
 rally happen at the time of ihe aspects 
 of Mars and Mercury, Mars and Ju- 
 piter, 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 prin- 
 cipal agent in this so-called influence of 
 the heavens. Indeed this word influ- 
 ence has so fascinated some philosophers 
 that they prefer raving with the sense- 
 less vulgar, to learning the truth with 
 me. This essential property is the prin- 
 cipal foundation of that admirable ge- 
 nethliac 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 child- 
 hood 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 na- 
 tivity. I am not checked by the re- 
 proach of boastfulness, notwithstanding 
 those who, by speech or conduct, con- 
 demn 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 ple- 
 beian 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 quadra- 
 tures 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 wea- 
 ther; for, after a frost of some days, 
 that very day became warmer, there 
 was a thaw and a fall of rain.*" 
 
 " 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 obser- 
 vations from that folly or madness as it 
 should rather be called. For, following 
 up this example, I knew a ladyt, 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 fa- 
 mily,, and is the cause to herself of de- 
 plorable 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 
 
 * Tliis mode of verifying configurations, though 
 something of the boldest, was by no means un- 
 usual. ,Ona former occasion Kepler, wishing to 
 cast the nativity of his friend Zehentmaier, and 
 being unable to procure more accurate informa- 
 tion than that he was born about three o'clock in 
 the afternoon of the 21st of October, 1751, sup- 
 plied the deficiency by a record of fevers and acci- 
 dents at known periods of his life, from which he 
 deduced a more exact horoscope. 
 
 f Kepler probably meant his own mother, whose 
 horoscope he in many places declared to be nearly 
 the same as his own, 
 
 L2 
 
KEPLER. 
 
 was born a male, and not a female, for 
 astrologers have sought in vain to dis- 
 tinguish sexes in the sky ; thirdly, I de- 
 rive 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 pro- 
 perty to which I might succeed and be- 
 come attached ; fifthly, there were the 
 schools, and the liberality of the magis- 
 tracy 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 re- 
 motely alluding to it. The learned con- 
 fess that several not despicable branches 
 of philosophy have been newly extri- 
 cated or amended or brought to per- 
 fection by me : but here my constella- 
 tions 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 re- 
 mained 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 Em- 
 peror, 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 Har- 
 monies, and the other matters on which 
 I am engaged." 
 
 " However, it may be owing to Ju- 
 piter'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 fan- 
 tastic 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 mathe- 
 matical language, by saying that the 
 squares of the times vary as the cubes 
 of the distances*. Kepler's rapture on 
 detecting it was unbounded, as may be 
 
 * See Preliminary Treatise, p. 13. 
 
 seen from the exulting rhapsody with 
 which he announced it. "What Ipro- 
 phecied 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 astro 
 nomical contemplations, at 'length I 
 have brought to light, and have recog- 
 nized its truth beyond my most san- 
 guine 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 mo- 
 tions, not indeed in the manner which 
 I imagined, (that is not the least part of 
 my delight,) but in another very differ- 
 ent, 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*, 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 particu- 
 larity, the manner and precise moment 
 of the discovery. " Another part of my 
 1 Cosmographical Mystery,' suspended 
 twenty-two years ago, because it was 
 then undetermined, is completed and in- 
 troduced 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 in- 
 vestigating the true proportion of the 
 periodic times to the orbits, 
 
 Sera quidem respexit inertcm, 
 
 Respexit tamen, et longo post tempore venit. 
 
 If you would know the precise moment, 
 the first idea came across me on Hie 8th 
 March of this year, 1G18 ; but chancing 
 
 * Jn allusion to the Harmonics of Ptolemy. 
 
KEPLER. 
 
 43 
 
 to make a mistake in the calculation, I 
 rejected it as false. I returned again to 
 it with new force on the 1 5th 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 sesquipli- 
 cate proportion of the mean distances of 
 the orbits." 
 
 There is high authority for not attempt- 
 ing over anxiously to understand the 
 rest of the work. Delambre sums it up 
 as follows: "In the music of the ce- 
 lestial 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 mysti- 
 cism, 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 astronomi- 
 cal opinions, drawn up in a popular 
 style in the form of question and an- 
 swer. We find there a singular argu- 
 ment 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 be- 
 tween 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 fol- 
 lowing 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 mate* 
 
 riality, a naturaHnability to move from 
 place to place : they have a natural in- 
 ertness 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 re- 
 volves 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 re- 
 taining 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 at- 
 traction takes place only on one side, re- 
 pulsion on the other. 
 
 " P. Whence, then, arises that differ- 
 ence 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 fa- 
 culty of attracting, repelling, or retain- 
 ing the planet. So that it is probable 
 that the centre of the solar body corre- 
 sponds to one extremity or pole of the 
 magnet, and its whole surface to the 
 other pole, 
 " P. If this were so, all the planets 
 
44 
 
 KEPLER. 
 
 would be restored* 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 r 
 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 vio- 
 lence First, because the virtue emana- 
 ting from the sun has the same degree of 
 weakness at different distances, as the 
 distances or the width of the circles de- 
 scribed on these distancest. 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 ema- 
 nating 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 Sa- 
 turn as is collected in the very narrow 
 one of Mercury, it is very rare and there- 
 fore 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 quan- 
 tity 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. 
 
 * 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. 
 
 > f In other parts of -his works,.Kepler assumes 
 The diminution to be proportional to the circles 
 themselves, not to the diameters. 
 
 The circular paths of the planets are in 
 the simple ratio of the distances ; the 
 weights or quantities of matter in diffe- 
 rent planets are in the subduplicate ratio 
 of the same distances, as has been 
 already proved; so that with every in- 
 crease 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 com- 
 pensate each other in a comparison of 
 different planets: the simple and sub- 
 duplicate proportion compound the ses- 
 quiplicate 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 indisputa- 
 bly 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 never- 
 theless 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 sup- 
 positions. 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 observa- 
 tions we are able to collect. His reason 
 for asserting that the sizes of the dif- 
 ferent planets are proportional to their 
 distances from the sun, was simply be- 
 cause he chose to take for granted that 
 either their solidities, surfaces, or dia- 
 meters, 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 rea- 
 soning 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 in- 
 disputable 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 
 
KEPLER, 
 
 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 densi- 
 ties, 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 dia- 
 metrically 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 sup- 
 posing 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 devia- 
 tions from this manner of moving, as 
 exceptions and disturbances occasioned 
 by some external cause. To this sup- 
 posed cause is generally given the name 
 pf 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 pro- 
 ceeds 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. 
 
 A second law of motion, founded upon 
 experiment, is this : if a body have mo- 
 tion 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 B C' 
 in one second, and by the other alone 
 through any other space Be in the same- 
 time, it will, when both are 
 given to it at the same in 
 stant, pass in the same 
 time (in the present in- 
 stance in one second) through B C the 
 
 diagonal of the parallelogram of which 
 B C' and B c are sides. 
 
 Let a body, acted upon by no force, 
 be moving along the line AE ; that 
 
 15 
 
 means, according to what has been said, 
 let it pass over the equal straight lines 
 A B, B C, C D, D E, Sec., in equal times. 
 If we take any point S not in the line 
 A E, and join A S, B S, &c., the triangles 
 A S B, B S C, &c. are also equal, having 
 a common altitude and standing on 
 equal bases, so that if a string were con- 
 ceived reaching from S to the moving 
 body (being lengthened or shortened in 
 each posit ion to suit its distance from 
 S), this string, as the body moved along 
 A E, would sweep over equal trian- 
 gular areas in equal times. 
 
 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 A B. If left to itself it would, 
 in an equal time (say 1") go through 
 B C' in the same straight line with and 
 equal to AB. But just as it reaches 
 B, and is beginning to move along B C', 
 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. Ac- 
 cording to the second law of motion, its 
 direction during this I", in consequence 
 of the two motions combined, will be 
 along B C, the diagonal of the parallelo- 
 gram of which B C', B c, are sides. In- 
 
46 
 
 KEPLER. 
 
 this case, as this figure is drawn, B C, 
 though passed in the same time, is longer 
 than A B ; 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 C C' is parallel to B c, the tri- 
 angles SCB, SC'B are equal, being 
 on the same base S B, arid between 
 the same parallels S B, C C', and S C'B 
 is equal to S B A as before, therefore 
 S C B, S B A are equal. The body is 
 now moving uniformly (though quicker 
 than along A B) along B C. As before, 
 it would in a time equal to the time of 
 passing along B C, go through an equal 
 space C D' 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 C D, the diagonal of the 
 parallelogram, whose sides are C D', 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, some- 
 times 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 por- 
 tion, 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 
 H A', 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 A B 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 re- 
 mark, that the same equality which sub- 
 sists 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, B C, CD, D E, cor- 
 
 responding to the four areas A S B, 
 B S C, C S D, D S E, that is, to the area 
 ABODES, are passed in the same 
 time as the four E F, F G, GH, H A, cor- 
 responding to the equal area E F G H A S. 
 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 pe- 
 riods. 
 
 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 ex- 
 erted 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 con- 
 tented to observe, that the law holds, 
 however close the pulls are brought to- 
 gether, 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 dis- 
 tances 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 be- 
 tween 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 de- 
 
KEPLER. 
 
 scribe, in very general terms, the manner 
 in which Newton, who was the first who 
 systematically extended the laws of mo- 
 tion 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 sup- 
 posed 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 com- 
 paring the motion of the moon with that 
 of heavy bodies at the surface of the 
 earth. Taking L P* 
 to represent part of 
 the moon's orbit de- 
 scribed in one minute, 
 the line P M 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 dis- 
 tance and motion of the moon, this line 
 P M is found to be about sixteen feet. 
 The distance of the moon is about sixty 
 times the radius of the earth, and there- 
 fore 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. Ga- 
 lileo 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 pro- 
 portional to the squares of the times du- 
 ring 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 1 6 feet in one second, which 
 was precisely the space previously esta- 
 blished by numerous experiments. 
 
 With this confirmation of the suppo- 
 sition, Newton proceeded to the purely 
 geometrical calculation of the law of 
 centripetal* force necessary to make a 
 * In many curves, as in the circle and ellipse, 
 
 moving body describe an ellipse round 
 its foci>s, which Kepler's observations 
 had established to be the form of the or- 
 bits 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 re- 
 ceived additional confirmation. His me- 
 thod of doing this may, perhaps, be un- 
 derstood 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 C S D being pro 
 portional 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 va- 
 rying directly as C d, and inversely in the 
 duplicate proportion of the triangular 
 area C S D, that is to say, proportional to 
 
 perpendicular on S C. If this polygon 
 represent an ellipse, so that C D repre- 
 sents a small arc of the curve, of which 
 S is the focus, it is found by the nature 
 
 of that curve, that _ , , is the same at 
 
 (D liy 
 
 all points of the curve, so that the law of 
 variation of the force in the same ellipse 
 
 is represented solely by p 2 . If C d, 
 
 Sec. are drawn so that 
 
 Cd 
 
 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 
 
 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 im- 
 mediate consequence of this determina- 
 tion ; for, according to what has been 
 already shown, the time of revolution 
 round the whole ellipse, or, as it is corn- 
 
 there is a point to which the name of centre is 
 given, on uccount of peculiar properties belonging 
 to it : but the term " centripetal force" always re- 
 fers to the place towards which the force is di- 
 rected, whether or not situated in the centre of the 
 curve. 
 
48 
 
 KEPLER. 
 
 monly 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 de- 
 scribed in an unit of time is proportional 
 to S C x DA, that is to say, is in the sub- 
 
 D A- 
 
 duplicate ratio of S C 2 x DA 9 , or 77-71 
 
 L> a 
 
 when the force varies inversely as the 
 square of the distance S C ; and in the 
 ellipse, as we have said already, this is 
 equal to a third proportional to the 
 principal axes; consequently the pe- 
 riodic times in different ellipses, which 
 are proportional to the whole areas of 
 the ellipses directly, and the areas de- 
 scribed in the 'unit of time inversely, 
 are in the compound ratio of the rec- 
 tangle of the axes directly, and subdu- 
 plicatly as a third proportional to the 
 axes inversely ; that is to say, the squares 
 of these times are proportional to the 
 cubes t of the longest axes, which is 
 Kepler's law. 
 
 CHAPTER VIII. 
 
 The Epitome prohibited at Rome Lo- 
 garithmic Tables Trial of Catha- 
 rine Kepler Kepler invited to Eng- 
 land Rudolphine Tables Death 
 Conclusion. 
 
 KEPLER'S " Epitome," almost immedi- 
 ately on its appearance, enjoyed the ho- 
 nour 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 diffi- 
 culties in publishing his future writings. 
 His words to Remus, who had communi- 
 cated 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 cen- 
 sure, and that you will inform me whe- 
 ther 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 rne to know whether there is any 
 chance of the same censure being ex- 
 tended 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 de- 
 sire 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 gainsay ed by no 
 one, and, in short, I must give up Aus- 
 tria 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 conse- 
 quences and opinions : and besides, Ga- 
 lileo 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. 11 
 
 We shall not dwell upon Kepler's dif- 
 ferent works on comets, beyond men- 
 tioning 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 theo- 
 ries have shewn that they obey the same 
 laws of motion as the planets, differing 
 from them only in the extreme excen- 
 tricity 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 
 ifrom the depth of the sea; and the sug- 
 gestion is thrown out that perhaps 
 comets are something of the nature of 
 silkworms, and are wasted and con- 
 sumed in spinning their own tails. 
 
 Among his other laborious employ- 
 ments, Kepler yet found time to cal- 
 culate tables of logarithms, he having 
 been one of the first in Germany to appre- 
 ciate the full importance of the facilities 
 they afford to the numerical calculator. 
 In 1618 he wrote to his friend Schick- 
 hard : " There is a Scottish Baron (whose 
 name has escaped my memory), who has 
 made a famous contrivance, by which 
 
KEPLER. 
 
 49 
 
 all need of multiplication and division is 
 supplied by mere addition and subtrac- 
 tion ; and he does it without sines. But 
 even he wants a table of tangents *, and 
 the variety, frequency, and difficulty of 
 the additions and subtractions, in some 
 cases, is greater than the labour of mul- 
 
 tiplying and dividing." 
 K( 
 
 lepler dedicated his " Ephemeris" for 
 1620 to the author of this celebrated in- 
 vention, 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 num- 
 bers, then proceeding by the quotients of 
 every ten to 100, and by hundreds to 
 1 00,000. 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 cal- 
 culation, 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 demon- 
 stration rested on a fiction of geometri- 
 cal motion, too loose and slippery for a 
 sound method of reasonable demonstra- 
 tion to be founded on itt. " This led 
 
 * 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." 
 
 f This was the objection originally made to 
 Newton's " Fluxions," and in fact, Napier's idea of 
 logarithms is identical with that method of con- 
 ceiving 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 propor- 
 tional 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 mo- 
 tions. (Mirifici logarithmorum cauonis 
 descriptio, Edinburgi 1614.) 
 
 - This last definition contains what we should now 
 
 call the differential equation between a number 
 
 and the logarithm of its reciprocal, 
 
 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 arith- 
 metic, 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 num- 
 ber corresponding to this sum or differ- 
 ence, as the case may be, will be the 
 required product or quotient. This, 
 1 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 arith- 
 metical 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 precepti- 
 cles." 
 
 The year 1622 was marked by the ca- 
 tastrophe of a singular adventure which 
 befell Kepler's mother, Catharine, then 
 nearly seventy years old, and by which 
 he had been greatly harassed and an- 
 noyed 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 diffi- 
 culties. One of her female acquaint- 
 ance, whose manner of life had been by 
 no means unblemished, was attacked 
 after a miscarriage by violent head- 
 aches, and Catharine, who had often 
 taken occasion to sneer at her noto- 
 rious reputation, was accused with hav- 
 ing 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 termina- 
 tion during five years, until the judge 
 before whom it was tried was displaced. 
 He was succeeded by another, already in- 
 disposed 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 ta- 
 
50 
 
 KEPLER. 
 
 hies on her, and in her turn became the 
 accuser. The end of the matter was, 
 that in July, 1620, Catharine was im- 
 prisoned, and condemned to the torture. 
 Kepler was then at Linz, but as soon 
 as he learned his mother's danger, hur- 
 ried 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 con- 
 duct 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 pri- 
 son 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 un- 
 expected turn in the course of her liti- 
 gation. 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 diffi- 
 culties, 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 neigh- 
 bourhood seems abandoned to flame and 
 destruction. Shall I then cross the sea, 
 whither Wotton invites me ? I, a Ger- 
 man ? a lover of firm land ? who dread 
 the confinement of an island ? who pre- 
 sage its dangers, and must drag along 
 with me my little wife and flock of chil- 
 dren? Besides my son Louis, now 
 thirteen years old, 1 have a marriage- 
 able 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 Rudol- 
 phine 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 ade- 
 quate 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 prece- 
 dence 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 Wirlembenr, 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 Mat- 
 thias had been succeeded by Ferdi- 
 nand III., who still continued to Kepler 
 his barren title of imperial mathema- 
 tician. 
 
 In 1624 Kepler went to Vienna, in 
 the hopes of getting money to complete 
 theRudolphineTables,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 em- 
 peror. On his return he revisited the 
 University of Tubingen, where he found 
 his old preceptor, Mastlin, still alive, 
 but almost worn out with old age. 
 Mastlin had well deserved the' regard 
 Kepler always appears to have enter- 
 tained for him ; he had treated him with 
 great liberality whilst at the University, 
 where he refused to receive any remune- 
 ration for his instruction. Kepler took 
 every opportunity of shewing his grati- 
 tude ; even whilst he was struggling with 
 poverty he contrived to send his old 
 master a handsome silver cup, in ac- 
 knowledging the receipt of which Mast- 
 lin 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, not- 
 withstanding the recent grant, by the 
 disturbances arising out of the two par- 
 ties 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 fol- 
 lowed a popular insurrection, and the 
 
KEPLER. 
 
 51 
 
 peasantry blockaded Linz, so that it was 
 not until 1627 that these celebrated tables 
 finally made their appearance, the ear- 
 liest calculated on the supposition that 
 the planets move in elliptic orbits. 
 Ptolemy's tables had been succeeded by 
 the " Alphonsine," so called from Al- 
 phonso, King of Castile, who, in the 
 thirteenth century, was an enlightened 
 patron of astronomy. After the disco- 
 veries 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 TychoBrahe 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 cal- 
 culations. In the second are tables of 
 the elements of the sun, moon, and 
 planets. The fourth gives the places of 
 1000 stars as determined byTycho, 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 in- 
 sensible above 45 of altitude, and 
 even at half that altitude in the case of 
 the fixed stars. A more detailed ac- 
 count 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 con- 
 struct these, he would have well earned 
 the title of a most useful and indefati- 
 gable calculator. 
 
 Some copies of these tables have pre- 
 fixed 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 clear- 
 ing it of parallax ; and if the hour at 
 Uraniburg be computed by the Rudol- 
 phine 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 net, 
 
 for by this means it may come to be 
 corrected." 
 
 This is probably one pf the earliest 
 announcements of the method of deter- 
 mining longitudes by occultations ; the 
 imperfect theory of the moon long re- 
 mained a principal obstacle to its intro- 
 duction in practice. Another interesting 
 passage connected with the same object 
 may be introduced here. In a letter to 
 his friend Cruger, 'dated in 1616, Kep- 
 ler says : " You propose a method of 
 observing the distances of places by sun- 
 dials 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 fbr their astrological predictions. 
 Everything in his hands became an 
 allegory ; and on this occasion he says, 
 "Astronomy is the daughter of As- 
 trology, and this modern Astrology, 
 again, is the daughter of Astronomy, 
 bearing something of the lineaments of 
 her grandmother; and, as 1 have al- 
 ready said, this foolish daughter, Astro- 
 logy, supports her wise but needy mother, 
 Astronomy, from the profits of a profes- 
 sion not generally considered credit- 
 able." 
 
 Soon after the publication of these 
 tables, the Grand Duke of Tuscany sent 
 him a golden chain ; and if we remem- 
 ber 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 remark- 
 able men in the history of that time. 
 
52 
 
 KEPLER. 
 
 Wallenstein was a firm believer in as- 
 trology, and the reception Kepler ex- 
 perienced 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 pa- 
 tron than any one of his three em- 
 perors ; 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 address- 
 ed, by the missionary Terrentio, from 
 China, to the Jesuits at Ingolstadt. The 
 object of this communication was to ob- 
 tain from Europe means for carrying 
 into effect a projected scheme for im- 
 proving the Chinese calendar. In this 
 essay Kepler maintains the opinion, 
 which has been discussed with soiimich 
 warmth in more modern times, that the 
 pretended ancient observations of the 
 Chinese were obtained by computing 
 them backwards from a much more re- 
 cent date. Wallenstein furnished him 
 with an assistant for his calculations, and 
 with a printing press ; and through his 
 influence nominated him to the profes- 
 sorship 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 vvhich Ferdinand would gladly have 
 transferred to the charge of "Wallenstein, 
 still remained unsatisfied. Kepler made 
 a last attempt to obtain them at Ratis- 
 bon, where the imperial meeting was 
 held, but without success. The fatigue 
 and vexation occasioned by his fruitless 
 journey brought on a fever, which un- 
 expectedly put an end to his life, in the 
 early part of November, 1630, in his 
 fifty-ninth year. His old master, Mast- 
 lin, survived him for* about a year, dy- 
 ing 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 mar- 
 ried, 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 Fried- 
 land 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 em- 
 peror. 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 chil- 
 dren were left in very straightened cir- 
 cumstances, which induced Louis, Kep- 
 ler'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 conse- 
 quence 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 prepar- 
 ing it for publication at the time of 
 their respective deaths ; and Louis con- 
 fessed that he did not approach the task 
 without apprehension that he was in- 
 curring some risk of a similar fate. 
 This little rhapsody is entitled a " Dream 
 on Lunar Astronomy;" and was in- 
 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 Du- 
 racoto, the son of an Icelandic enchan- 
 tress, of the name of Fiolxhildis. Kep- 
 ler tells us that he chose the last name 
 from an old map of Europe in his house, 
 in which Iceland was called Fiolx : Du- 
 racoto seemed to him analogous to the 
 names he found in the history of Scot- 
 land, the neighbouring country. Fiolx- 
 hildis 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. Duracotb 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 be- 
 came acquainted with Tycho Brahe. 
 On his return to Iceland, Fiolxhildis 
 received him kindly, and was delighted 
 with the progress he had made in astro- 
 nomy. She then informed him of the 
 existence of certain spirits, or demons, 
 from whom, although no traveller her- 
 self, she acquired a knowledge of other 
 countries, and especially of a very re- 
 markable country, called Livania. Du- 
 racoto 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 
 
KEPLER. 
 
 53 
 
 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 con- 
 tinual use of post-horses, or who sail 
 frequently to the Indies ; who are ac- 
 customed 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 petti- 
 coats. 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 ac- 
 count given of the various pheno- 
 mena 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 A&tronomia 
 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 termi- 
 nated by a storm, in which, says Kep- 
 ler, " 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 17 14, Hantsch 
 issued a prospectus for publishing them 
 by subscription, in twenty -two folio 
 
 volumes. The plan met no encourage- 
 ment, 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 un- 
 availing 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. Pe- 
 ter'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 deso- 
 lated the country. In 1786, a proposal 
 was made to erect a marble monument 
 to his memory, but nothing was done. 
 Kastner, on whose authority it is men- 
 tioned, says upon this, rather bitterly, 
 that it matters little whether or not Ger- 
 many, 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 Con- 
 stance, and that a monument has been 
 erected in the Botanical Garden at Ra- 
 tisbon, near the place of his interment. 
 It is built in, the form of a temple, sur- 
 mounted 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 frontis- 
 piece 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 com- 
 mon pedestal is apian of the observatory 
 at Uraniburg ; in another, a printing 
 press ; in a third is the figure of a man, 
 meant for Kepler, sealed 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 pre- 
 sented it'toBernegger; 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 
 
KEPLER. 
 
 completed. A portrait of Kepler is en- 
 graved 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 Kiistner, " 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 maybe 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 me- 
 thod in the pursuit of truth, by the judg- 
 ment pronounced by Delambre, as well 
 
 sidering 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 at- 
 tempts 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 ob- 
 stinate perseverance that must triumph 
 over all difficulties but those which are 
 insurmountable*." 
 
 On his failures as On his SUCCeSS. "Con- * HUtoiredel'AstronomieModerne, Paris, 1821. 
 
 List of Kepler's published Works. 
 
 Ein Calender 
 
 Prodromus Dissertat. Cosmograph. 
 
 De fundamentis Astrologiae 
 
 Paralipomena ad Vitellionem . , 
 
 Epistola de Solis deliquio 
 
 De Stella nova . 
 
 Vom Kometen . . . 
 
 Antwort an Rb'slin . 
 
 Astronomia Nova 
 
 Tertius interveniens ... 
 
 Dissertatio cum Nuncio Sidereo 
 
 Strena, seu De nive sexangula . 
 
 Dioptrica .... 
 
 Vom Geburts Jahre des Heylandes 
 
 Respons. ad e'pist S. Calvisiii 
 
 Eclogae Chronicae . . . 
 
 Nova Stereometria . . . 
 
 Ephemerides 16171620 
 
 Epitomes Astron. Copern. Libri i. ii. iii. 
 
 De Cometis .... 
 
 Harm on ice Mundi . , 
 
 Kanones Pueriles . . . 
 
 Epitomes Astron. Copern. Liber iv. 
 
 Epitomes Astron. Copern. Libri v. vi. vii. 
 
 Discurs von der grossen Conjunction 
 
 Chilias Logarithmorum . 
 
 Supplementum . . 
 
 Hyperaspistes 
 
 Tabulae liudolphinae . . . 
 
 Resp. ad epist. J. Bartschii 
 
 De anni 1631 phaenomenis 
 
 Terrentii epistolium cum conimentatiuncu]& 
 
 Ephemerides .... 
 
 Gratz, 
 
 Tubingce, 
 
 Pragce, 
 
 Francofurli, 
 
 . Pragce, 
 
 Halle, 
 
 Pragce, 
 
 Pragce. 
 
 Frankfurt', 
 
 Francofurti, 
 
 Frankfurt, 
 
 Francofurti, 
 
 Strasburg, 
 
 Francofurti, 
 
 Frankfurt, 
 
 Lincii, 
 
 . Lincii, 
 
 Lentiis, 
 
 Aug. Vindelic. 
 Lincii. 
 
 . UlmcK, 
 
 Lentiis, 
 
 Francofurti, 
 
 iMZ. 
 
 Marpurgi, 
 
 Lentiis, 
 
 Francofurti, 
 
 U/mce, 
 
 Sagani, 
 
 Lipsa, 
 
 , Sagani, 
 
 Sagani, 
 
 1594 
 
 1596, 4 to. 
 1602, 4to. 
 1604, 4to. 
 1605 
 1606, 4 to. 
 
 1608, 4to. 
 
 1609, 4to. 
 
 1609, fol. 
 
 1610, 4to. 
 
 1610, 4to. 
 
 1611, 4to. 
 1611, 4to. 
 
 1613, 4to. 
 
 1614, 4 to. 
 1615,4(o. 
 1615,4to. 
 1616, 4to. 
 
 1618, 8vo. 
 1619,4lo. 
 
 1619, fol. 
 1620 
 
 1622, 8vo. 
 1622, 8vo. 
 Ifi23, 4to. 
 
 1624, fol. 
 
 1625, 4to. 
 1625, 8vo. 
 1627, fol. 
 1629, 4to. 
 
 1629, 4to. 
 
 1630, 4to. 
 1630, 4to. 
 
 Somnium . 
 Tabulae mannales 
 
 Francofurti, 1634, 4 to. 
 Arycnlorati, 1700, 12mo. 
 
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