THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 PRESENTED BY 
 
 PROF. CHARLES A. KOFOID AND 
 MRS. PRUDENCE W. KOFOID 
 
HISTORY 
 
 OF THE 
 
 INDUCTIVE SCIENCES. 
 
 VOL. I. 
 
y/.l 
 
 TO 
 
 SIR JOHN FREDERICK WILLIAM HERSCHEL, 
 
 K. G. H. 
 
 MY DEAR HERSCHEL, 
 
 IT is with no common pleasure that I take 
 up my pen to dedicate these volumes to you. They are 
 the result of trains of thought which have often been 
 the subject of our conversation, and of which the origin 
 goes back to the period of our early companionship at 
 the University. And if I had ever wavered in my pur- 
 pose of combining such reflections and researches into 
 a whole, I should have derived a renewed impulse and 
 increased animation from your delightful Discourse on a 
 kindred subject. For I could not have read it without 
 finding this portion of philosophy invested with a fresh 
 charm; and though I might be well aware that I could 
 not aspire to that large share of popularity which your 
 work so justly gained, I should still have reflected, that 
 something was due to the subject itself, and should have 
 hoped that my own aim was so far similar to yours, 
 that the present work might have a chance of exciting 
 an interest in some of your readers. That it will interest 
 you, I do not at all hesitate to believe. 
 
 If you were now in England I should stop here : but 
 when a friend is removed for years to a far distant land, 
 
 a 2 
 
iv DEDICATION. 
 
 we seem to acquire a right to speak openly of his good 
 qualities. I cannot, therefore, prevail upon myself to 
 lay down my pen without alluding to the affectionate 
 admiration of your moral and social, as well as intel- 
 lectual excellencies, which springs up in the hearts of 
 your friends, whenever you are thought of. They are 
 much delighted to look upon the halo of deserved fame 
 which plays round your head; but still more, to recol- 
 lect, as one of them said, that your head is far from 
 being the best part about you. 
 
 May your sojourn in the southern hemisphere be as 
 happy and successful as its object is noble and worthy of 
 you ; and may your return home be speedy and prosperous, 
 as soon as your purpose is attained. 
 
 Ever, my dear Herschel, Yours, 
 
 22 March, 1837. W. WflEWELL. 
 
 P. S. So I wrote nearly ten years ago, when you 
 were at the Cape of Good Hope, employed in your great 
 task of making a complete standard survey of the nebulae 
 and double stars visible to man. Now that you are, as I 
 trust, in a few weeks about to put the crowning stone 
 upon your edifice by the publication of your " Obser- 
 vations in the Southern Hemisphere," I cannot refrain 
 from congratulating you upon having had your life ennobled 
 by the conception and happy execution of so great a de- 
 sign, and once more offering you my wishes that you may 
 long enjoy the glory you have so well won. 
 
 TRINITY COLLEGE, W. W. 
 
 Nov. 22, 1846. 
 
PREFACE 
 
 TO THE SECOND EDITION. 
 
 THE demand for a new edition of my History of the 
 Inductive Sciences imposes upon me the welcome 
 duty of correcting the mistakes and supplying some 
 of the deficiencies of the former edition. In doing 
 this, I have for the most part made only slight 
 changes in the text, and such as were required to 
 rectify absolutely erroneous assertions. I have not 
 even altered the references to the time and circum- 
 stances which were present when I formerly wrote, 
 but have reserved for Notes the notices of subse- 
 quent events, and the other additions which I 
 thought necessary. I have followed this plan, as 
 the best, both for the reader and the subject. 
 
 Those who already know the work, if they wish 
 again to refer to it, will naturally think of it such 
 as it is, and not such as I might make it by writing- 
 it afresh. To attempt to incorporate with the 
 former narrative of the progress of each science, a 
 view of its most recent advance, would really be 
 to write each portion of the history from a new 
 
vi PREFACE TO THE 
 
 point of view, and thus, to write a new work, not 
 to publish a new edition. 
 
 I have, however, in Notes at the end of each 
 Book, given an account of some of the most impor- 
 tant recent advances in each subject, considered as 
 an Inductive Science. I introduce this limitation, 
 because it is my justification, as well in the present 
 as in the former edition, for the omission of many 
 topics which are of great interest, both in a prac- 
 tical and in a scientific view, but which are applica- 
 tions of discoveries already made, not steps towards 
 discovery ; deductive results of laws of nature, not 
 inductions of such laws from observation. This was 
 my reason for passing over such inventions as 
 printing and porcelain, glass and gunpowder, steam- 
 boats and rail -roads, gas -lighting and chemical 
 bleaching, in the former edition ; this is my excuse 
 for saying nothing now of photography, the electric 
 telegraph, and other striking recent inventions. I 
 have omitted, for like reasons, many remarkable 
 inventions, still more directly bearing upon the 
 progress of science, as Daniel's galvanic battery, 
 and the very ingenious battery of Mr. Grove. Even 
 implements of scientific research, if we are not able 
 to bring into view the points to which they lead, 
 cannot be put in their place in the history of 
 
SECOND EDITION. Vll 
 
 science ; just as in a history of a present war, those 
 military operations of which the aim and effect are 
 yet unknown, cannot be rightly narrated. 
 
 From this cause, it can hardly happen but 
 that such a work as this must fail to give to some 
 distinguished contemporary labourers in the field 
 of science the pre-eminence and lustre which their 
 activity and intelligence merit ; because their labour 
 is not yet crowned by its result. For such cases, 
 my office is like writing the story of Columbus while 
 he was still sailing westwards. So far as I have 
 ventured to deal with lines of scientific research at 
 present incomplete, what I have to offer is rather a 
 discussion of principles than a narrative of facts ; 
 and accordingly, such discussions, on several points 
 now in question, will be found in the Philosophy of 
 the Inductive Sciences ; sufficient, I hope, to show 
 that I have stopped where I have, out of no want 
 of sympathy with the ulterior progress of know- 
 ledge. 
 
 In correcting the errours of the work, I have 
 availed myself of all the critiques of the former 
 edition which have come under my notice, without 
 regard to the spirit in which they were written, 
 whether hostile or friendly. I have not noticed 
 such criticism in any other way than by thus using 
 
vni PREFACE TO THE 
 
 it. A series of controversial Notes would have been 
 of little value to the reader ; and I trust my critics 
 will be content without further acknowledgment of 
 the assistance which I have derived from them. 
 Those who wrote kindly will, I am sure, willingly 
 bestow upon me this additional kindness; and if 
 any have criticized me in another temper, I hope 
 they will not be sorry to see that I have no wish to 
 perpetuate our hostilities. 
 
 But it is only justice to the work to say that 
 the errours which required correction were neither 
 numerous (considering its extent,) nor fundamental. 
 And there is one circumstance which gives me a 
 hope that this essay may have some permanent 
 value. The attempt to throw the histories of all the 
 Sciences into Inductive Epochs, each Epoch having 
 its Prelude and its Sequel, and thus to combine the 
 persons and the events which fill these histories into 
 intelligible groups, was, so far as I know, new. To 
 these Epochs, as they are selected and presented in 
 this work, I have seen no objection made; and it 
 would seem, therefore, to be generally allowed that 
 the Epochs here marked out, are the cardinal points 
 of scientific history. Nor have I seen any complaint 
 (with one exception, of slight importance, but fully 
 noticed in this edition,) that the principal figures 
 
SECOND EDITION. JX 
 
 in each Epoch are not properly chosen. I have 
 had, therefore, little to alter, either in the general 
 outline or in the detail of the work. 
 
 The German translator of this History, the late 
 Director of the Imperial Observatory at Vienna, 
 M. Littrow, has added to his translation, besides 
 other valuable notes, a biographical notice of each 
 of the persons mentioned in the work. But though 
 these additions are very interesting, they did not 
 belong to the plan of the work as I had conceived 
 it, and would have greatly augmented its bulk. I 
 have, therefore, with a few exceptions, omitted them. 
 
 I have not introduced any new branches of 
 science into this edition, and on this account, among 
 others, I have said nothing of the recent progress 
 of Organic Chemistry. The discoveries which are 
 alleged to have been made in that department will 
 require to have many intermediate steps clearly 
 marked and fairly established, before they can stand 
 by the side of Historical Chemistry as examples of 
 Inductive Science. Still less have I attempted to 
 introduce any notice of recent steps in the sciences 
 which I have more especially termed Organic, as 
 Zoology and Physiology. I am aware that the study 
 of the nervous system, for instance, has been prose- 
 cuted with highly interesting results. But I never 
 
X PREFACE TO THE 
 
 pretended to do more than give some examples of 
 the historical progress of this subject, and shall not 
 presume to carry the account further than I have 
 already done. 
 
 I do not deviate from my original plan in thus 
 limiting my narrative. For, as was formerly stated, 
 the main object of the work was to present such a 
 survey of the advances already made in physical 
 knowledge, and of the mode in which they have 
 been made, as might serve as a real and firm basis 
 for our speculations concerning the progress of 
 human knowledge, and the processes by which 
 sciences are formed. And an attempt to frame 
 such speculations on this basis was made in the 
 Philosophy of the Inductive Sciences, which was 
 published shortly after this History. To that work 
 I must refer, for a further explanation of any views 
 respecting the nature and progress of science which 
 may here appear defective or obscure. It is my 
 intention to prepare for the press a new edition of 
 the work, as soon as I shall have finished the pre- 
 paration of the present publication. 
 
 I add a Postscript, containing a notice of a few 
 points in the history of science which have come 
 into view during the printing of the following 
 pages. 
 
SECOND EDITION. xi 
 
 POSTSCRIPT TO THE SECOND EDITION. 
 
 (1). The planet exterior to Uranus, of which 
 the existence was interred by M. Le Verrier and Mr. 
 Adams from the motions of Uranus (vol. n. Note 
 (L) ), has since been discovered. This confirmation of 
 calculations founded upon the doctrine of universal 
 gravitation, may be looked upon as the most re- 
 markable event of the kind since the return of 
 Halley's comet in 1757 ; and in some respects, as a 
 more striking event even than that; inasmuch as 
 the new planet had never been seen at all, and 
 was discovered by mathematicians entirely by their 
 feeling of its influence, which they perceived through 
 the organ of mathematical calculation. 
 
 There can be no doubt that to M. Le Verrier 
 belongs the glory of having first published a pre- 
 diction of the place and appearance of the new 
 planet, and of having thus occasioned its discovery 
 by astronomical observers. M. Le Verrier's first 
 prediction was published in the Comptes Rendus de 
 I'Acad. des Sciences, for June 1, 1846, (not Jan. 1, 
 as erroneously printed in my Note.) A subsequent 
 paper on the subject was read Aug. 31. The planet 
 was seen by M. Le Galle, at the Observatory of Berlin, 
 on September 23, on which day he had received an 
 
xii PREFACE TO THE 
 
 express application from M. Le Verrier, recommend- 
 ing him to endeavour to recognize the stranger by 
 its having a visible disk. Professor Challis, at the 
 Observatory of Cambridge, was looking out for the 
 new planet from July 29, and saw it on Aug. 4, and 
 again on Aug. 12, but without recognizing it, in 
 consequence of his plan of not comparing his obser- 
 vations till he had accumulated a greater number 
 of them. On Sept. 29, having read for the first time 
 M. Le Verrier's second paper, he altered his plan, 
 and paid attention to the physical appearance rather 
 than the position of the star. On that very evening, 
 not having then heard of M. Le Galle's discovery, he 
 singled out the star by its seeming to have a disk. 
 
 M. Le Verrier's mode of discussing the circum- 
 stances of Uranus's motion, and inferring the new 
 planet from these circumstances, is in the highest 
 degree sagacious and masterly. Justice to him 
 cannot require that the contemporaneous, though 
 unpublished, labours of Mr. Adams of St. John's 
 College, Cambridge, should not also be recorded. 
 Mr. Adams made his first calculations to account 
 for the anomalies in the motion of Uranus, on the 
 hypothesis of a more distant planet, in 1843 1 . At 
 
 1 Mr. Adams informs me that as early as 1841 he conjectured 
 the existence of a planet exterior to Uranus, and recorded in a 
 
SECOND EDITION. xiii 
 
 first he had not taken into account the earlier 
 Greenwich observations; but these were supplied 
 to him by the Astronomer Royal, in 1844. In Sep- 
 tember, 1845, Mr. Adams communicated to Prof. 
 Challis values of the elements of the supposed 
 disturbing body ; namely, its mean distance, mean 
 longitude at a given epoch, longitude of perihelion, 
 eccentricity of orbit, and mass. In the next month, 
 he communicated to the Astronomer Royal values 
 of the same elements, somewhat corrected. The 
 note, p. 306, vol. n., of the present work, in which 
 the names of MM. Le Verrier and Adams are men- 
 tioned in conjunction, was in the press in August, 
 1846, a month before the planet* was seen. As I 
 have stated in the text, Mr. Adams and M. Le Ver- 
 rier assigned to the unseen planet nearly the same 
 position; they also assigned to it nearly the same 
 mass ; namely, 2^ times the mass of Uranus. And 
 hence, supposing the density to be not greater than 
 that of Uranus, it followed that the visible diameter 
 
 memorandum his design of examining its effect : but deferred the 
 calculation till he had completed his preparation for his exami- 
 ntion in January 1843. He was the Senior Wrangler on that 
 occasion. The conjecture of an exterior planet was not quite 
 new. It had occurred to Mr. Hussey, M. Alexis Bouvard, and 
 and M. Hansen, as early as 1834. See Mr. Airy's Account read 
 to the Royal Astronomical Society, Nov. 13, 1846. 
 
xiv PREFACE TO THE 
 
 would be about 3", an apparent magnitude not 
 much smaller than Uranus himself. 
 
 M. Le Verrier has mentioned for the new planet 
 the name Neptunus; and probably, deference to his 
 authority as its discoverer will obtain general cur- 
 rency for this name. 
 
 (2). To the account of Tables of the Sun, Moon, 
 and Planets, given vol. n. p. 304, I may add a 
 notice of an important volume recently published ; 
 Reductions of the Observations of Planets made at 
 the Royal Observatory, Greenwich, from 1750 to 
 1830, (1845). These Reductions were made under 
 the superintendence of the Astronomer Royal, the 
 computations being executed by order of the Lords 
 of the Treasury, and published by order of the 
 Lords of the Admiralty. The volume contains the 
 observations reduced and compared with Lindenau's 
 Tables of Mercury, Venus, and Mars, and with 
 Bouvard's Tables of Jupiter, Saturn, and Uranus. 
 The object of the work is stated to be (Introd. 
 p. xxx.) "the comparison of a long series of observed 
 places with theoretical places, computed by means 
 of the same fundamental elements (duly corrected 
 for perturbation) throughout." The ultimate end 
 contemplated by such a work is the correction of 
 the fundamental elements of the planetary motions. 
 
SECOND EDITION. xv 
 
 (3). Upon a reconsideration of Mr. Airy's Trea- 
 tise On Tides and Waves, I am no longer disposed 
 to say, as I have said vol. n. p. 311, that for the 
 actual case of the distribution of land and water, 
 nothing has been done to bring the hydrody- 
 namical theory of oceanic tides into agreement 
 with observation. In this admirable work, Mr. Airy 
 has, by peculiar artifices, solved problems which 
 come so near the actual cases that they may repre- 
 sent them. He has, in this way, deduced the laws of 
 the semi-diurnal and the diurnal tide, and the other 
 features of the tides which the equilibrium theory 
 in some degree imitates ; but he has also, taking into 
 account the effect of friction, shown that the actual 
 tide may be represented as the tide of an earlier 
 epoch ; that the relative mass of the moon and sun, 
 as inferred from the tides, would depend upon the 
 depth of the ocean (Art. 455) ; with many other 
 results remarkably explaining the observed pheno- 
 mena. He has also shown that the relation of the 
 cotidal lines to the tide waves really propagated is, 
 in complex cases, very obscure, because different 
 waves of different magnitudes, travelling in differ- 
 ent directions, may coexist, and the cotidal line is 
 the compound result of all these. 
 
xvi PREFACE TO THE SECOND EDITION. 
 
 (4). Page 509. Mr. Airy's explanation of the 
 phenomena termed by Sir D. Brewster a new pro- 
 perty of light, is completed in the Philosophical 
 Magazine for Nov. 1846. It is there shown that 
 a dependence of the breadth of the bands upon the 
 aperture of the pupil, which had been supposed to 
 result from the theory, and which does not appear 
 in the experiment, did really result from certain 
 limited conditions of the hypothesis, which condi- 
 tions do not belong to the experiment; and that 
 when the problem is solved without those limita- 
 tions, the discrepance of theory and observation 
 vanishes : so that, as Mr. Airy says, " this very 
 remarkable experiment, which long appeared inex- 
 plicable, seems destined to give one of the strongest 
 confirmations to the Undulatory Theory." 
 
 TRINITY COLLEGE, CAMBRIDGE, 
 
 November 7, 1846. 
 
 
PREFACE TO THE FIRST EDITION. 
 
 AT the present day, any endeavour to improve and 
 extend the Philosophy of Science may hope to excite 
 some interest. All persons of cultivated minds will 
 agree, that a very important advantage would be 
 gained, if any light could be thrown upon the modes 
 of discovering truth, the powers that we possess for 
 this end, and the points to which these may most 
 profitably be applied. Most men, too, will allow, that 
 in these respects much remains to be done. The 
 attempts of this kind, made from time to time, 
 are far from rendering future efforts superfluous. 
 For example, the Great Reform of Philosophy and 
 Method, in which Bacon so eloquently called upon 
 men to unite their exertions in his day, has, even in 
 ours, been very imperfectly carried into effect. And, 
 even if his plan had been fully executed, it would 
 now require to be pursued and extended. If Bacon 
 had weighed well all that Science had achieved in 
 his time, and had laid down a complete scheme of 
 rules for scientific research, so far as they could be 
 collected from the lights of that age, it would still 
 be incumbent upon the philosophical world to aug- 
 ment as well as preserve the inheritance which he 
 left ; by combining with his doctrines such new views 
 as the advances of later times cannot fail to produce 
 or suggest ; and by endeavouring to provide, for 
 every kind of truth, methods of research as effective 
 VOL. I. b 
 
xvin PREFACE TO THE 
 
 as those to which we owe the clearest and surest 
 portions of our knowledge. Such a renovation and 
 extension of the reform of philosophy appears to 
 belong peculiarly to our own time. We may discern 
 no few or doubtful presages of its approach ; and an 
 attempt to give form and connexion to the elements 
 of such a scheme cannot now be considered pre- 
 mature. 
 
 The Novum Organon of Bacon was suitably 
 ushered into the world by his Advancement of Learn- 
 ing ; and any attempt to continue and extend his 
 Keform of the Methods and Philosophy of Science 
 may, like his, be most fitly preceded by, and founded 
 upon, a comprehensive Survey of the existing state 
 of human knowledge. The wish to contribute some- 
 thing, however little it may be, to such a Eeform, 
 gave rise to that study of the History of Science of 
 which the present Work is the fruit. And the effect 
 of these researches has been, a persuasion, that we 
 need not despair of seeing, even in our own time, 
 a renovation of sound philosophy, directed by the 
 light which the History of Science sheds. Such a 
 reform, when its Epoch shall arrive, will not be the 
 work of any single writer, but the result of the intel- 
 lectual tendencies of the age. He who is most for- 
 ward in the work will wisely repeat the confession 
 of his sagacious predecessor : Ipse certe (ut ingenue 
 fatear) soleo sBstimare hoc opus magis pro partu Tem- 
 poris quam Ingenii. 
 
 To such a work, whensoever and by whomsoever 
 executed, I venture to hope that the present Volumes 
 may be usefully subservient. But I trust, also, that 
 
FIRST EDITION. XIX 
 
 in its independent character, as a History, this book 
 may be found not altogether unworthy of the aim 
 which its title implies. 
 
 It is impossible not to see that the writer of such 
 a history imposes upon himself a task of no ordinary 
 difficulty and delicacy ; since it is necessary for him 
 to pronounce a judgment upon the characters and 
 achievements of all the great physical philosophers of 
 all ages, and in all sciences. But the assumption 
 of this judicial position is so inevitably involved in 
 the functions of the historian (whatever be his sub- 
 ject), that he cannot justly be deemed presumptuous 
 on that account. It is true, that the historian of the 
 progress of science is required by his undertaking 
 to judge of the merits of men, in reference to subjects 
 which demand a far intenser and more methodical 
 study than the historian of practical, life gives to the 
 actions of which he treats ; and the general voice of 
 mankind, which may often serve as a guide, because 
 it rarely errs widely or permanently in its estimate 
 of those who are prominent in public life, is of little 
 value when it speaks of things belonging to the region 
 of exact science. But to balance these disadvan- 
 tages, and to enable us to judge of the characters who 
 must figure in our history, we may recollect that 
 we have before us, not the record only of their 
 actions, but the actions themselves ; for ,the acts of 
 a philosopher are his writings. We do not receive 
 his exploits on tradition, but by sight ; we do not 
 read of him, we read him. And if I may speak of 
 my own grounds of trust and encouragement in 
 venturing on such a task, I knew that my life had 
 
XX PREFACE TO THE 
 
 been principally 'spent in those studies which were 
 most requisite to enable me to understand what had 
 thus been done ; and I had been in habits of inter- 
 course with several of the most eminent men of science 
 of our time, both in our own and in other countries. 
 Having thus lived with some of the great intellects of 
 the past and the present, I had found myself capable 
 of rejoicing in their beauties, of admiring their endow- 
 ments, and, I trusted, also, of understanding their 
 discoveries and views, their hopes and aims. I did 
 not, therefore, turn aside from the responsibility 
 which the character of the Historian of Science im- 
 posed upon me. I have not even shrunk from it 
 when it led me into the circle of those who are now 
 alive, and among whom we move. For it seemed to 
 me that to omit such portions of the history as I 
 must have omitted to avoid thus speaking of my 
 contemporaries, would have left my work mutilated 
 and incomplete ; and would have prevented its form- 
 ing a platform on which we might stand and look 
 forward into the future. I trusted, moreover, that 
 my study of the philosophers of former times had 
 enabled me to appreciate the discoveries of the pre- 
 sent, and that I should be able to speak of persons 
 now alive, with the same impartiality and in the same 
 spirit as if they were already numbered with the great 
 men of the past. Seeking encouragement in these 
 reflections, and in the labour and thought which I was 
 conscious of having bestowed upon my task, I have 
 conducted my history from the earliest ages of the 
 speculative world up to our own days. 
 
 To some persons it may appear that I am not 
 
FIRST EDITION. XXI 
 
 justified in calling that a History of the Inductive 
 Sciences, which contains an account of the progress 
 of the physical sciences only. But it would have 
 conveyed a false impression of my purpose, had I 
 described my history in any manner which implied 
 that the sciences which it embraces are partially 
 selected or arbitrarily limited. Those of which the 
 progress is exhibited in the present volumes, appear 
 to me to form a connected and systematic body 
 of knowledge. And if there be branches of know- 
 ledge which regard Morals, or Politics, or the Fine 
 Arts, and which may properly be called Inductive 
 (an opinion which I by no means gainsay) ; still it 
 must be allowed, I think, that the processes of col- 
 lecting general truths from assemblages of special 
 facts, and of ascending from propositions of a limited 
 to those of a larger generality, which the term Induc- 
 tion peculiarly implies, have hitherto been far more 
 clearly exhibited in the physical sciences which form 
 the subject of the present work, than in those hyper- 
 physical sciences to which I have not extended my 
 history. I will further add, that if I should be ena- 
 bled hereafter to lay before the world a view of 
 the Philosophy of Inductive Science in its general 
 bearings, it will be requisite, in order to exhibit, in 
 its due light the state of the philosophy of morals, or 
 art, or any similar subject, to give a view of the steps 
 by which it has reached its present position ; and 
 thus such a work will supply that which some may 
 judge wanting to fill up the outline of this historical 
 undertaking. 
 
 As will easily be supposed, I have borrowed. 
 
xxn PREFACE TO THE 
 
 largely from other writers, both of the histories of 
 special sciences and of philosophy in general*. I 
 have done this without scruple, since the novelty of 
 my work was intended to consist, not in its supe- 
 riority as a collection of facts, but in the point of 
 view in which the facts were placed I have, how- 
 ever, in all cases, given references to my authorities, 
 and there are very few instances in which I have 
 not verified the references of previous historians, and 
 studied the original authors. According to the plan 
 which I have pursued, the history of each science 
 forms a whole in itself, divided into distinct but 
 connected members, by the Epochs of its successive 
 advances. If I have satisfied the competent judges 
 in each science by my selection of such epochs, the 
 scheme of the work must be of permanent value, 
 however imperfect may be the execution of any of its 
 portions. 
 
 With all these grounds of hope, it is still impos- 
 sible not to see that such an undertaking is, in no 
 small degree, arduous, and its event obscure. But 
 all who venture upon such tasks must gather trust 
 
 1 Among these, I may mention as works to which I have peculiar 
 obligations, Tennemann's Geschiohte der Philosophic, Degerando's 
 Histoire Comparee des Systemes de Philosophic, Montucla's Histoire 
 des Mathematiques, with Delalande's continuation of it, Delambre's 
 Astronomic Ancienne, Astronomic du Moyen Age, Astronomic 
 Moderne, and Astronomic du Dixhuitieme Siecle ; Bailly's Histoire 
 d' Astronomic Ancienne, and Histoire d'Astronomie Moderne, Voiron's 
 Histoire d'Astronomie (published as a continuation of Bailly), Fischer s 
 Geschichte der Physik, Gmelin's Geschichte der Chemie, Thomson's 
 History of Chemistry, Sprengel's History of Medicine, his History of 
 Botany, and in all branches of Natural History and Physiology, 
 Cuvier's works, in their historical, as in all other portions, most 
 admirable and instructive. 
 
FIRST EDITION. xxin 
 
 and encouragement from reflections like those by 
 which their great forerunner prepared himself for his 
 endeavours ; by recollecting that they are aiming 
 to advance the best interests and privileges of man ; 
 and that they may expect all the best and wisest of 
 men to join them in their aspirations and to aid them 
 in their labours. 
 
 " Concerning ourselves we speak not ; but as 
 touching the matter which we have in hand, this we 
 ask ; that men deem it not to be the setting up of 
 an Opinion, but the performing of a Work ; and 
 that they receive this as a certainty ; that we are 
 not laying the foundations of any sect or doctrine, 
 but of the profit and dignity of mankind : Further- 
 more, that being well disposed to what shall advan- 
 tage themselves, and putting off factions and preju- 
 dices, they take common counsel with us, to the end 
 that being by these our aids and appliances freed and 
 defended from wanderings and impediments, they 
 may lend their hands also to the labours which 
 remain to be performed : And yet, further, that 
 they be of good hope ; neither feign and imagine 
 to themselves this our Eeform as something of infi- 
 nite dimension and beyond the grasp of mortal man, 
 when, in truth, it is, of infinite errour, the end and 
 true limit ; and is by no means unmindful of the 
 condition of mortality and humanity, not confiding 
 that such a thing can be carried to its perfect close 
 in the space of one single age, but assigning it as a 
 task to a succession of generations." 
 
 Instaur. Mag. Prcef. ad fin. 
 
CONTENTS 
 
 THE FIRST VOLUME. 
 
 INTRODUCTION . . 3 
 
 BOOK I. 
 
 HISTORY OF THE GREEK SCHOOL PHILOSOPHY, WITH 
 REFERENCE TO PHYSICAL SCIENCE. 
 
 CHAPTER I. PRELUDE TO THE GREEK SCHOOL PHILOSOPHY. 
 
 Sect. 1. First Attempts of the Speculative Faculty in Phy- 
 sical Inquiries ...... 25 
 
 Sect, 2. Primitive Mistake in Greek Physical Philosophy . 34 
 
 CHAPTER II. THE GREEK SCHOOL PHILOSOPHY. 
 
 Sect. 1. The general Foundation of the Greek School Phi- 
 losophy . ... 39 
 Sect. 2. The Aristotelian Physical Philosophy . . 43 
 Sect. 3. Technical Forms of the Greek Schools . . 57 
 
 1 . of the Aristotelian Philosophy . 57 
 
 2. of the Platonists ... 61 
 
 3. of the Pythagoreans . . 64 
 
 4. of the Atomists and others . . 66 
 
 CHAPTER III. FAILURE OP THE GREEK SCHOOL PHILOSOPHY. 
 
 Sect. 1. Result of the Greek School Philosophy . . 69 
 Sect. 2. Cause of the Failure of the Greek Physical Phi- 
 losophy ....... 74 
 

 xxvi CONTENTS OF THE FIRST VOLUME. 
 
 BOOK II. 
 
 HISTORY OF THE PHYSICAL SCIENCES IN ANCIENT 
 GREECE. 
 
 PAGE 
 
 Introduction ......... 95 
 
 CHAPTER I. EARLIEST STAGES OF MECHANICS AND 
 HYDROSTATICS. 
 
 Sect. 1. Mechanics ....... 97 
 
 Sect. 2. Hydrostatics 101 
 
 CHAPTER II. EARLIEST STAGES OF OPTICS . .105 
 CHAPTER III. EARLIEST STAGES OF HARMONICS . 109 
 
 BOOK III. 
 
 HISTORY OF GREEK ASTRONOMY. 
 Introduction . . . . . . .121 
 
 CHAPTER I. EARLIEST STAGES of ASTRONOMY. 
 
 Sect. 1. Formation of the Notion of a Year . . .123 
 Sect. 2. Fixation of the Civil Year . . .126 
 
 Sect. 3. Correction of the Civil Year. (Julian Calendar) . 132 
 Sect. 4. Attempts at the Fixation of the Month . . 135 
 Sect. 5. Invention of Lunisolar Years . . . .138 
 
 Sect. 6. The Constellations 145 
 
 Sect. 7. The Planets 149 
 
 Sect. 8. The Circles of the Sphere . . . . 153 
 Sect. 9. The Globular Form of the Earth . . .159 
 
 Sect. 10. The Phases of the Moon .... 163 
 
 Sect. 11. Eclipses 164 
 
 Sect. 12. Sequel to the Early Stages of Astronomy . 167 
 
 CHAPTER II. PRELUDE TO THE INDUCTIVE EPOCH OF 
 
 HIPPARCHUS. . . . .170 
 CHAPTER III. INDUCTIVE EPOCH OF HIPPARCHUS. 
 
 Sect. 1. Establishment of the Theory of Epicycles and 
 
 Eccentrics . ..... 182 
 
CONTENTS OF THE FIRST VOLUME. xxvii 
 
 PAOK 
 
 Sect. 2. Estimate of the Value of the Theory of Eccentrics 
 
 and Epicycles . . . . . . 102 
 
 Sect 3. Discovery of the Precession of the Equinoxes . 199 
 
 CHAPTER IV. SEQUEL TO THE INDUCTIVE EPOCH OF 
 HIPPARCHUS. 
 
 Sect. 1. Researches which verified the Theory . . 203 
 
 Sect. 2. Researches which did not verify the Theory . 207 
 
 Sect. 3. Methods of Observation of the Greek Astronomers 210 
 
 Sect. 4. Period from Hipparchus to Ptolemy . .219 
 
 Sect. 5. Measures of the Earth .... 224 
 
 Sect. 6. Ptolemy's Discovery of Evection .... 22(5 
 
 Sect. 7. Conclusion of the History of Greek Astronomy . 234 
 
 Sect. 8. Arabian Astronomy 236 
 
 BOOK IV. 
 
 \ 
 
 HISTORY OF PHYSICAL SCIENCE IN THE 
 MIDDLE AGES. 
 
 Introduction . . . . . .' .251 
 
 CHAPTER I. ON THE INDISTINCTNESS OF IDEAS OF THE 
 
 MIDDLE AGES. . 251 
 
 1 . Collections of Opinions ..... 255 
 
 2. Indistinctness of Ideas in Mechanics . .257 
 
 3. shewn in Architecture . . 263 
 
 4. in Astronomy .... 264 
 
 5. shewn by Skeptics . . 265 
 
 6. Neglect of Physical Reasoning in Christendom . . 268 
 
 7- Question of Antipodes .... 269 
 
 8. Intellectual Condition of the Religious Orders . . 273 
 
 9. Popular Opinions ....... 276 
 
 CHAPTER II. THE COMMENTATORIAL SPIRIT OF THE 
 
 MIDDLE AGES 280 
 
 1. Natural Bias to Authority 282 
 
 2. Character of Commentators ..... 284 
 
 3. Greek Commentators of Aristotle .... 287 
 
xxvm CONTENTS OF THE FIRST VOLUME. 
 
 4. Greek Commentators of Plato and others . . . 291 
 
 5. Arabian Commentators of Aristotle . . . 292 
 
 CHAPTER III. OF THE MYSTICISM OF THE MIDDLE 
 
 AGES 297 
 
 1. Neoplatonic Theosophy ...... 299 
 
 2. Mystical Arithmetic . . . . . . . 305 
 
 3. Astrology 309 
 
 4. Alchemy 320 
 
 5. Magic 323 
 
 CHAPTER IV. OF THE DOGMATISM OF THE MIDDLE 
 AGES. 
 
 1. Origin of the Scholastic Philosophy .... 328 
 
 2. Scholastic Dogmas .... . 333 
 
 3. Scholastic Physics .... . 341 
 
 4. Authority of Aristotle among the Schoolmen . . 342 
 
 5. Subjects omitted. Civil Law. Medicine . . . 346 
 
 CHAPTER V. PROGRESS OF THE ARTS IN THE MIDDLE 
 AGES. 
 
 1. Art and Science ... ... 349 
 
 2. Arabian Science ....... 355 
 
 3. Experimental Philosophy of the Arabians . . 356 
 
 4. Roger Bacon ........ 359 
 
 5. Architecture of the Middle Ages . . . .361 
 
 6. Treatises on Architecture . 365 
 
 BOOK Y. 
 
 HISTORY OF FORMAL ASTRONOMY AFFER THE 
 STATIONARY PERIOD. 
 
 Introduction ........ 375 
 
 CHAPTER I. PRELUDE TO THE INDUCTIVE EPOCH OF 
 
 COPERNICUS .... 379 
 
 CHAPTER II. INDUCTION OF COPERNICUS. THE HELIO- 
 CENTRIC THEORY ASSERTED ON FORMAL GROUNDS . 388 
 
CONTENTS OF THE FIRST VOLUME. xxix 
 
 PAGE 
 
 CHAPTER III. SEQUEL TO COPERNICUS. THE RECEPTION 
 AND DEVELOPEMENT OF THE COPERNICAN THEORY. 
 
 Sect. 1. First Reception of the Copernican Theory . . 401 
 Sect. 2. Diffusion of the Copernican Theory . . 404 
 
 Sect. 3. The Heliocentric Theory confirmed by Facts. 
 
 Galibo's Astronomical Discoveries . .412 
 Sect. 4. The Copernican System opposed on Theological 
 
 Grounds . . .418 
 
 Sect. 5. The Heliocentric Theory confirmed on Physical 
 Considerations. (Prelude to Kepler's Astro- 
 nomical Discoveries.) .... 426 
 
 CHAPTER IV. INDUCTIVE EPOCH OP KEPLER. 
 
 Sect. 1. Intellectual Character of Kepler . . . 432 
 
 Sect. 2. Kepler's Discovery of his Third Law . . 437 
 Sect. 3. Kepler's Discovery of his First and Second Laws. 
 
 Elliptical Theory of the Planets . . 443 
 
 CHAPTER V. SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, 
 VERIFICATION, AND EXTENSION OF THE ELLIPTICAL THEORY. 
 
 Sect. 1. Application of the Elliptical Theory to the Planets 453 
 Sect. 2. Application of the Elliptical Theory to the Moon . 455 
 Sect. 3. Causes of further Progress of Astronomy . . 458 
 
CORRECTIONS. 
 
 Vol. I. p. 158, note 45 , for Acronical read Acronycal (ctKpoi/uao<?, 
 
 happening at the extremity of the night), 
 p. 315, line 24, add, the late Mr. Henderson of the 
 Edinburgh Observatory, also determined the parallax 
 of this star to be 1". 
 Vol. II. p. 319, line 16, for 1835, read 1833. 
 
 p. 500, line 17, for Lobeck read Seebeck. 
 
INDEX OF PROPER NAMES. 
 
 The letters , 6, c, indicate vol. i., vol. n., vol. in., respectively. 
 
 ABDOLLATIF, c. 391 
 
 Aboazen, a. 317 
 
 AboulWefa, a. 242 
 
 Achard, b. 573 
 
 Achillini, c. 434 
 
 Adam Marsh, a. 274 
 
 Adanson, c. 307 
 
 Adelbold, a. 274 
 
 Adelhard Goth, a. 274 
 
 Adet, c. 151 
 
 Achilles Tatius, a. 151 
 
 ^Epinus, c. 17, 24, 35 
 
 Agassiz, c. 409, 561, 593 
 
 Agatharchus, b. 342 
 
 Airy, b. 109, 230, 283, 398, 484 
 
 Albategnius, a. 237 
 
 Albertus Magnus, a. 325, 343 ; 
 
 c. 302 
 
 Albumazar, a. 317 
 Alexander Aphrodisiensis, a. 288 
 Alexander the Great, a. 181 
 Alfarabi, a. 295 
 Alfred, a. 273 
 Algazel, . 267 
 Alhazen, a. 357; b. 377 
 Alis-ben-Isa, a. 226 
 Alkindi, a. 295 
 Almansor, a. 237 
 Almeric, a. 343 
 Alpetragius, a. 239 
 Alphonzo X., a. 193, 239 
 Amauri, a. 343 
 
 Ammonius Saccas, a. 289, 300 
 Ampere, b. 586 ; c. 89, 92, 95, 159 
 Anaxagoras, a. 66; b. 375 
 Anaximander, a. 156, 160, 164 
 Anaximenes, a. 28 
 Anderson, 6. 57 
 Anna Comnena, a. 290 
 Anselm, a. 331 
 
 Arago, b 405, 420, 453, 472; c. 105 
 Aratus, a. 222 
 
 Archimedes, a. 97, 101 ; b. 376 
 Arduino, c. 552 
 Aristarchus, a. 169, 382 
 Aristillus, a. 181 
 
 Aristophanes, a. 137 
 
 Aristotle, a. 43; 6. 45, 325, 382; c. 
 
 293, 379, 387, 392, 423, 433, 
 
 453, 651 
 
 Arnold de Villa Nova, a. 325 
 Arriaga, b. 46 
 Artedi, c. 397 
 Artephius, a. 325 
 Aryabatta, a. 384 
 Arzachel, a. 238 
 Asclepiades, c. 424 
 Asclepigenia, a. 304 
 Aselli, c. 448 
 Avecibron, a. 336 
 Averroes, a. 268, 296 
 Avicenna, a. 295 
 Avienus, a. 222 
 Aubriet, c. 336 
 Audouin, c. 501 
 Augustine, a. 272, 312, 335 
 Autolycus, a. 155, 158 
 Auzout, 6. 279 
 
 Babbage, Mr., c. 106, 610 
 
 Bachman, c. 334 
 
 Bacon, Francis, a. 406 ; 6. 135, 182, 
 
 326, 340, 558 
 Bacon, Roger, b. 377 
 Bailly, . 275 ; b. 236 
 Baliani, 6. 31, 66 
 Banister, c. 323 
 Barlow, b. 398 ; c. 60, 94, 106 
 Bartholin, b. 400 
 Barton, b. 491 
 Bauhin, John, c. 324 
 Bauhin, Gaspard, c. 326 
 Beaumont, Elie de, c. 574, 582, 
 
 590, 650 
 Beccaria, c. 18 
 Beccher, c. 133 
 Bede, a. 273, 335 
 Bell, Sir Charles, c. 467 
 Belon, c. 394, 489 
 Benedetti, b. 10, 21, 27, 48 
 Bentley, b. 198, 202 
 Berard, b. 547 
 
XXX11 
 
 INDEX OF PROPER NAMES. 
 
 Bergman, c. 130, 155, 224 
 Bernard of Chartres, a. 331 
 Bernoulli, Daniel, b. 112, 116, 118, 
 
 121, 208, 339, 349, 353 
 Bernoulli, James, b. 84 
 Bernoulli, James, the younger, b. 
 
 359 
 Bernoulli, John, b. 86, 89, 94, 99, 
 
 111, 149, 208, 339 
 Bernoulli, John, the younger, b. 340 
 Berthollet, c. 132, 149, 155 
 Berzelius, c. 1 59, 169, 195, 247, 267 
 Bessel, b. 108 
 Betancourt, b. 573 
 Beudant, c. 269 
 Bichat, c. 467 
 Bidone, 6. 71 
 Biela, b. 245 
 Biker, b. 574 
 Biot, b. 410, 412, 421, 528 ; c. 59, 
 
 60, 101 
 
 Black, b. 555; c. 141, 155 
 Blair, b. 398 
 Bloch, c. 403 
 Blondel, b. 57 
 Bock, c. 308 
 Boethius, a. 273, 289 
 Boileau, b. 145 
 Bonaparte, c. 85, 180 
 Bonaventura, a. 338 
 Bontius, c. 343 
 
 Borelli, b. 24, 140, 150, 170, 172 
 Bossut, b. 71 
 Boue, Ami, c. 567 
 Bouguer, b. 114 
 Bouillet, b. 560 
 Bourdon, c. 463 
 Bournon, c. 233 
 Bouvard, b. 231 
 Boyle, b. 153, 419, 557; c. 125 
 Boze, c. 14 
 
 Bradley, b. 221, 227, 250, 262, 264 
 Brander, c. 541, 555 
 Brassavola, c. 304 
 Brewster, Sir David, b. 394, 410, 
 
 421,471, 481, 488; c. 242 
 Briggs, a. 411 
 
 Brisbane, Sir Thomas, &. 284 
 Brocchi, c. 560, 661 
 Brochant de Villiers, c. 573, 582 
 Broderip, c. 622 
 
 Brongniart, Alexandre, c. 554, 579 
 Brongniart, Adolphe, c. 592 
 Brook Taylor, b. 86, 111, 337 
 
 Brooke, Mr. c. 232 
 
 Brougham, Lord, b. 418, 468 
 
 Brown, Robert, c. 373, 485 
 
 Brunfels, e. 305 ' 
 
 Bruno, Giordano, a. 405 
 
 Buat, b. 71 
 
 Buch, Leopold von, c. 567, 572, 
 
 591, 613 
 
 Buckland, Dr., c. 585 
 Budaeus, a. 59 
 Buflfon, c. 216, 460, 488 
 Bullfinger, b. 89 
 Bullialdus, a. 229; b. 157 
 Burckhardt, b. 229, 240 
 Burg, b. 231 
 Burkard, c. 459 
 Burnet, c. 613, 652 
 
 Cabanis, e. 510 
 Csesalpinus, c. 216, 309, 312 
 Calceolarius, c. 541 
 Calippus, a. 142, 175 
 Callisthenes, a. 181 
 Camerarius, Joachim, c. 310 
 Camerarius, Rudolph Jacob, c. 457, 
 
 459 
 
 Campanella, a. 320, 344 
 Campani, b. 279 
 Camper, c. 488 
 Canton, c. 1 7, 53 
 Capelli, b. 217 
 Cappeller, c. 218 
 Cardan, b. 10, 18, 38, 46 
 Carlini, b. 252 
 Carne, c. 589 
 Caroline, Queen, 6. 199 
 Carpa, c. 434 
 Casraeus, b. 31 
 Cassini, Dominic, b. 248, 261, 287, 
 
 341 
 
 Cassini, J., b. 223, 261 
 Castelli, 6. 53, 56, 63, 69 
 Catelan, b. 83 
 Cavallieri, b. 209 
 
 Cavendish, b. 252; c. 26, 142, 150 
 Cauchy, 6. 118, 360,494 
 Caus, Solomon de, b. 41 
 Cesare Cesariano, a. 367 
 Chalid ben Abdplmalic, a. 226 
 Chatelet, Marquise du, b. 90 
 Chaussier, c. 467 
 Chladni, b. 355, 358 
 Christie, c. 106 
 Christina, b. 144 
 
INDEX OF PROPER NAMES. 
 
 xxxm 
 
 Chrompre, c. 190 
 
 Cicero, a. 136 
 
 Cigna, b. 113; c. 22 
 
 Clairaut, b. 100, 114, 179, 220, 245, 
 
 249, 397 
 
 Clarke, b. 89, 202 
 Cleomedes, a. 211, 220 
 Clusius, c. 320 
 Cobo, c. 333 
 
 Colombe, Ludovico delle, b. 63 
 Columbus, Realdus, c. 436, 443 
 Columna, Fabius, c. 334 
 Commandinus, b. 15 
 Comparetti, b. 418 
 Condamine, b. 248 
 Constantine of Africa, c. 302 
 Conti, Abbe de, b. 88 
 Conybeare, c. 560, 570 
 Copernicus, a, 379 
 Cosmas Indicopleustes, a. 271 
 Cotes, b. 98, 203 
 Coulomb, c. 25, 30, 34, 57 
 Crabtree, a. 411, 454; b. 154 
 Cramer, b. 345 
 Cronstedt, c. 255 
 Cruickshanks, c. 82 
 Gumming, Prof., c. 94 
 Cunaeus, c. 14 
 Cuvier, c. 391, 471, 491, 496, 508, 
 
 515, 556, 564, 658 
 
 D'Alembert, b, 90, 97, 101, 109, 
 110, 117, 235, 339, 349 
 
 D'Alibard, c. 18 
 
 Dalton, Dr. John, b. 550, 566, 574 ; 
 c. 164, 170 
 
 Daniell, b. 578; c. 609 
 
 Dante, a. 277 
 
 D'Arcy, b. 121 
 
 Davy, c. 162, 175, 179, 189 
 
 Daubenton, c. 488 
 
 Daubeny, Dr., c. 605 
 
 Daussy, b. 258 
 
 De Candolle, Prof., c. 373, 483 
 
 Dechen, M. von, c. 583 
 
 Defrance, c. 554, 559 
 
 Degerando, a. 268, 328 
 
 De la Beche, Sir H., c. 560 
 
 Delambre, b. 229, 238 
 
 De la Rive, Prof., b. 592 
 
 Le Lisle, b. 209 
 
 De Luc, b. 563, 578 
 
 Demeste, c. 221 
 
 Democritus, a. 66 ; c. 270 
 
 VOL. I. 
 
 Derham, b. 559 
 
 Desaguliers, c. 1 1 
 
 Descartes, b. 25, 33, 52, 58, 67, 77, 
 
 140, 200, 379, 383 ; c. 55 
 Des Hayes, c. 561 
 Desmarest, c. 548, 550 
 Dexippus, a. 291 
 Digges, b. 38 
 Dillemus, c. 363 
 Diogenes Laertius, a. 255 
 Dioscorides, c. 297, 302 
 Dollond, b. 280, 397 
 Dominis, Antonio de, b. 382 
 Dubois, c. 434 
 Dufay, c. 10, 13, 21 
 Du Four, b. 418 
 Dufrenoy, c. 573, 582 
 Dulong, b. 538, 592 
 Duns Scotus, a. 338, 344 
 Dunthorne, 6. 216 
 Dupuis, a. 147 
 Durret, a. 428 
 Dutens, a. 73 
 Duvernay, c. 487 
 
 Ebn lounis, a. 238 
 
 Encke, b. 245, 269, 292 
 
 Eratosthenes, a. 206 
 
 Ericsen, 6. 562 
 
 Eristratus, c. 448 
 
 Etienne, c. 434 
 
 Evelyn, 6. 198 
 
 Euclid, . 106, 158 
 
 Eudoxus, a. 174, 179 
 
 Euler, 6. 94, 101, 105, 114, 121, 221, 
 
 339, 354 
 Eusebius, a. 269 
 Eustachius, c. 435, 449 
 Eustratus, a. 290 
 
 Fabricius, a. 291 
 
 Fabricius of Acquapendente, c. 453 
 
 Fabricius, David, a. 449 
 
 Fallopius, c. 435 
 
 Faraday, Dr., c. 94, 105, 172, 174, 
 
 181, 192 
 
 Fermat, b. 56, 74 
 Fitton, Dr., c. 568 
 Flacourt, c. 323 
 Flamsteed, a. 457; 6. 178, 187, 205, 
 
 217 
 
 Fleischer, b. 380 
 Fontaine, b. 109 
 Fontenelle, b. 224; c. 128, 543 
 
XXXIV 
 
 INDEX OF PROPER NAMES. 
 
 Forbes, Prof. James, b. 547 
 Forster, Rev. Charles, a. 357 
 Fourcroy, c. 149, 155 
 Fourier, b. 523, 535, 542, 580 
 Fowler, c. 86 
 Fracastoro, c. 540 
 Francis I. (king of France), a. 344 
 Franklin, c. 12, 15, 22, 33 
 Fraunhofer, b. 280, 314, 399,448,495 
 Frederic II., Emperor, a. 343 
 Fresnel, b. 405, 438, 444, 455, 472, 
 
 579 
 
 Fries, c. 389 
 Frontinus, a. 369 
 Fuchs, c. 246, 306 
 Fuchsel, c. 549 
 
 Gsertner, c. 367 
 
 Galen, c. 425, 431, 433, 465, 468 
 
 Galileo, a. 412; b. 17, 23, 26, 28, 
 
 47, 57, 63 
 Gall, c. 467, 469 
 Galvani, c. 80, 86 
 Gambart, b. 308 
 Gascoigne, b. 273 
 Gassendi, a. 428 ; b. 56, 145, 148, 
 
 341 
 
 Gauss, 6. 108, 240 
 Gay-Lussac, 551, 565, 579; c. 158, 
 
 170 
 
 Geber, a. 239, 320 
 Gellibrand, c. 52 
 Geminus, a. 134, 178, 220 
 Generelli, Cirillo, c. 657 
 Geoffrey (botanist), c. 458 
 Geoffrey (chemist), c. 128 
 Geoffrey Saint-Hilaire, c. 491, 495, 
 
 500 
 
 George Pachymerus, a. 290 
 Gerbert, a. 274 
 Germain, Mile. Sophie, b. 360 
 Germanicus, . 222 
 Gesner, c. 216, 310, 541 
 Ghini, c. 318 
 Gibbon, a. 355 
 Gilbert, a. 409; b. 151; c. 7, 49, 
 
 53,62 
 
 Giordano Bruno, a. 405 
 Girard, 6. 72 
 Girtanner, b. 565 
 Giseke, c. 355 
 Glisson, c. 469 
 Gmelin, c. 269 
 Godefroy of St. Victor, a. 333 
 
 Goldfuss, c. 561 
 
 Goppert, c. 642 
 
 Gothe, b. 390; c. 476, 483 
 
 Gough, b. 569 
 
 Graham, 6. 274; c. 53 
 
 Grammatici, 6. 217 
 
 Grazia, Vincenzio de, 6. 63 
 
 Greenough, c. 573 
 
 Gregory, David, b. 203, 216 
 
 Gregory VII., Pope, a. 325 
 
 Gregory IX., Pope, a. 343 
 
 Gren, b. 573 
 
 Grew, c. 455, 487 
 
 Grey, c. 10 
 
 Grignon, c. 220 
 
 Grimaldi, b. 56, 385, 417 
 
 Grotthus, c. 196 
 
 Guericke, Otto, 6. 341 ; c. 9 
 
 Guettard, c. 544 
 
 Gulielmini, c. 218 
 
 Guyton de Morveau, c. 149, 155 
 
 Hachette, 6. 71 
 
 Hadley, b. 278 
 
 Haidinger, c. 241 
 
 Halicon, a. 191 
 
 Haller, c. 361, 471 
 
 Halley, b. 78, 155, 158, 197, 203, 
 
 217,232,243, 250,288; c. 47 
 Haly, a. 317 
 Hamilton, Sir W. (mathem.), b. 489, 
 
 499 
 
 Hampden, Dr., a. 328 
 Hansen, b. 108, 131 
 Hansteen, c. 52 
 Harding, b. 240 
 Harris, Mr. Snow, c. 35 
 Harrison, b. 277 
 Hartsoecker, 6. 279 
 Harvey, c. 437, 441, 453 
 Hausmann, c. 239 
 Hauy, c. 223, 230, 259 
 Hawkesbee, c. 9, 12 
 Hegel, b. 188 
 Helmont, c. 123 
 Henckel, c. 218 
 Henslow, Professor, c. 486 
 Heraclitus, a. 28 
 Herman, Paul, c. 322 
 Hermann, Contractus, a. 274 
 Hermann, James, 6. 86, 91, 94 ; 
 
 c. 334 
 
 Hermolaus Barbaras, a. 59 
 Hernandez, c. 322 
 
INDEX OF PROPER NAMES. 
 
 XXXV 
 
 Herodotus, a. 29 ; c. 292, 537 
 Herophilus, c. 427 
 Herrenschneider, b. 531 
 Herschel, Sir John, b. 269, 398, 
 
 422; c. 106, 243, 611, 616 
 Herschel, Sir William, b. 236, 419 
 Hevelius, b. 243, 273, 287 
 Higgins, c. 155 
 Hill, c. 220, 364 
 Hipparchus, a. 181 
 Hippasus, a. 1 1 1 
 Hippocrates, c. 423 
 Hoff, K. E. A. von, c. 600 
 Hoffmann, c. 573 
 Home, c. 560 
 Homer, c. 423 
 Hooke, b. 26, 74, 77, 140, 153, 158, 
 
 163, 172, 334, 358, 388, 413, 
 
 417, 427; c. 657 
 Hopkins, b. 355 ; c. 614 
 Horrox, a. 411, 454 ; b. 154 
 Hoskins, b. 78 
 Howard, Mr. Luke, b. 579 
 Hudson, c. 364 
 Hugo of St. Victor, . 333 
 Humboldt, Alexander von, c. 52, 
 
 567, 590, 604 
 
 Humboldt, Wilhelm von, c. 85 
 Hunter, John, c. 488 
 Hutton (fossilist), c. 561 
 Hutton(geologist),6. 252 ; c. 552, 653 
 Huyghens, b. 49, 58, 75, 82, 114, 
 
 140, 182, 341, 388, 401, 428 
 Hyginus, a 222 
 
 lamblichus, a. 303 
 
 Ideler, a. 125 
 
 Ivory, b. 108 
 
 Jacob of Edessa, a. 294 
 
 Jameson, Professor, c. 252, 551 
 
 Job, a. 145 
 
 John of Damascus, a. 290 
 
 John Philoponus, a. 289 
 
 John of Salisbury, a. 336, 339 
 
 John Scot Erigena, a. 331 
 
 Jordanus Nemorarius, b. 11, 40 
 
 Joseph, a. 325 
 
 Julian, a. 304 
 
 Jung, Joachim, c. 330 
 
 Jussieu, Adrien de, c. 370 
 
 Jussieu, Antoine Laurent de, c. 369 
 
 Jussieu, Bernard de, c. 3<W 
 
 Kaempfer, c. 323 
 
 Kant, c. 512 
 
 Kazwiri, c. 650 
 
 Keckerman, a. 341 
 
 Keill, b. 100, 204; c. 126 
 
 Kelland, Mr. Philip, b. 495, 499 
 
 Kempelen, b. 368 
 
 Kepler, a. 391, 403, 432 ; 6. 74, 
 
 136, 184, 262, 379 
 Key, c. 147 
 Kircher, . 309 
 Kirwan, c. 144, 150 
 Klaproth, c. 151 
 Klingenstierna, b. 279, 397 
 Knaut, Christopher, c. 334 
 Knaut, Christian, c. 334 
 Konig, c. 559 
 Krafft, b. 525 ; c. 63 
 Kratzenstein, b. 560 
 Kriege, c. 323 
 
 Lacaille, b. 229, 248 
 
 Lactantius, a. 269 
 
 Lagrange, b. 101, 104, 111, 121, 
 
 233, 345, 349, 353 
 Lame, b. 499 
 La Hire, b. 223, 261 
 Lalande, b. 225, 237 
 Lamarck, c. 339, 448, 512 
 Lambert, b. 854, 526 ; c. 57 
 Landen, b. 1 1 1 
 Lansberg, a. 428, 454 
 Laplace, b. 105, &c., 233, 253, 346, 
 
 523, 534, 588 
 Lasus, a. 1 1 1 
 Latreille, c. 503 
 Lavoisier, c. 145, 153 
 Laughton, 6. 202 
 Launoy, a. 343 
 Laurencet, c. 502 
 Lawrence, c. 625 
 Lecchi, 6. 71 
 
 Leeuwenhoek, c. 453, 459 
 Legendre, c. 59 
 L'Hopital, b. 85 
 Leibnitz, b. 87, 147 
 Le Monnier, b. 217, 220, 262 
 Leonardo da Vinci, a. 369 ; b. 125 ; 
 
 c. 539, 656 
 Leonicenus, c. 304 
 Le Roi, b. 561, 578 
 Leslie, 6. 530, 542, 583 
 Levy, c. 217 
 Leucippus, a. 66, 77 
 Lexell, b. 237, 246 
 
XXXVI 
 
 INDEX OF 
 
 PROPER 
 
 NAMES. 
 
 Lhwyd, c. 242 
 
 Libn, b. 540 
 
 Lindenau, &. 226 
 
 Lindley, c. 485, 561 
 
 Linnaeus, c. 219, 337, 399 
 
 Linus, b. 387 
 
 Lister, c. 543, 546 
 
 Littrow, 6. 283 
 
 Lloyd, Professor, 6. 490, 499 
 
 Lobel, c. 324, 372 
 
 Locke, b. 198 
 
 Longomontanus, a. 444, 454 
 
 LouvUle, b. 210, 224 
 
 Lubbock, 6. 108, 131, 256 
 
 Lucan, a. 261 
 
 Lucas, b. 388 
 
 LyeU, c. 529, 578, 601, 617, 620, 
 
 662 
 
 Macleay, c. 388 
 Msestlin, a. 403, 427 
 Magin, a. 402 
 Mairan, b. 89 
 Malpighi, c. 454 
 Malus, b. 403, 408 
 Manilius, a. 222 
 Maraldi, b. 223, 418 
 Marcet, b. 592 
 Margrave, c. 395 
 Marinus (anatomist), c. 465 
 Marinus (Neoplatonist), a. 304 
 Mariotte, 6. 60 
 Marsilius Ficinus, a. 345 
 Martianus Capella, a. 383 
 Martyn, T. c. 363 
 Matthioli, c. 326 
 Maupertuis, b. 101, 210, 248 
 Mayer Tobias, &. 221, 532; c. 29, 57 
 Mayo, Herbert, c. 467 
 Mayow, c. 147 
 Mazeas, b. 419 ; c. 19 
 MacCullagh, Professor, b. 487, 499 
 Meckel, c. 506 
 Melloni, b. 547 
 Menelaus, . 220 
 
 Mersenne,6. 33,56,66,144,332,348 
 Messa, c. 434 
 Meton, a. 140 
 Meyranx, c. 602 
 Michael Scot, a. 325 
 Michell, c. 547 
 Michelotti, b. 71 
 Miller, Professor, c. 242 
 Milton, a. 278, 409 ; b. 54 
 Mitscherlich, c. 245 
 
 Mohs, c. 232, 238, 203 
 
 Mondino, c. 434 
 
 Monge, c. 144 
 
 Monnet, c. 544 
 
 Monnier, c. 16 
 
 Monteiro, c. 242 
 
 Montfauon, a. 271 
 
 Morin, a. 428 
 
 Morison, c. 327 
 
 Moro, Lazzaro, c. 657 
 
 Morveau, Guyton de, c. 149, 155 
 
 Mosotti, c. 39 
 
 Munro, c. 488 
 
 Murchison, Sir Roderic, c. 578 
 
 Muschenbroek, &. 560 
 
 Napier, . 411, 460 
 
 Naudseus, a. 324 
 
 Naumann, c. 249 
 
 Newton, b. 60, 69, 74, 78, 93, 160, 
 &C., 196, 210, 262, 341, 352, 
 384, 401, 407, 414, 431, 525 ; 
 c. 445 
 
 Nicephorus Blemmydes, a. 290 
 
 Nicholas de Cusa, a, 387 
 
 Nicomachus, a. 109 
 
 Nigidius Figulus, . 312 
 
 Nobili, b. 547 
 
 NoUet, c. 13 
 
 Nordenskiold, c. 272 
 
 Norman, c. 51 
 
 Norton, b. 38 
 
 Numa, a. 134, 386 
 
 Odoardi, c. 549, 551 
 Oersted, Professor, c. 91 
 (Eyenhausen, c. 583 
 Oken, Professor, c. 490 
 Olbers, b. 239 
 Orpheus, a. 303 
 Osiander, . 398 
 Ott, b. 531 
 
 Otto Guericke, c. 9, 13 
 Ovid, c. 537 
 
 Pabst von Ohain, c. 257 
 
 Packe, c. 544 
 
 Pallas, c. 488, 549 
 
 Papin, &. 572 
 
 Pappus, a. 258 
 
 Paracelsus, . 325; c. 123 
 
 Pardies, 6. 387 
 
 Pascal, b. 64 
 
 Paulus III., Pope, a. 397 
 
INDEX OF PROPER NAMES. 
 
 xxxvn 
 
 Pecquet, c. 44'.) 
 
 Pepys, b. 198 
 
 Perrier, 6. 68 
 
 Peter of Apono, a. 325 
 
 Peter Bungo, a. 309 
 
 Peter Damien, a. 333 
 
 Peter the Lombard, a. 334 
 
 Peter de Vineis, a. 343 
 
 Petit, b. 538, 592 
 
 Petrarch, a. 345 
 
 Philip, Dr. Wilson, c. 451 
 
 Phillips, William, c. 232, 260, 570 
 
 Philolaus, a. 382 
 
 Photius, a. 292 
 
 Piazzi, b. 239, 316 
 
 Picard, b. 161), 263, 273, 341 
 
 Piccolomini, b. 47 
 
 Pictet, b. 564 
 
 Picus of Mirandula, a. 325, 345 
 
 Plana, b. 108 
 
 Playfair, b. 199 
 
 Pliny, a. 190, 255, 312 ; c. 215, 290, 
 
 296 
 
 Plotinus, a. 291, 300 
 Plumier, c. 523 
 Plutarch, a. 64, 255, 383 
 Poisson, b. 108, 115, 354, 360, 585 ; 
 
 c. 32, 59, 612 
 Polemarchus, a. 1 75 
 Poncelet, b. 72 
 Pond, 6. 283 
 
 Pontanus, Jovianus, c. 457 
 Ponte'coulant, b. 108 
 Pope, b. 204 
 Porphyry, a. 288, 291 
 Posidomus, a. 225 
 Potter, Mr. Richard, 6. 491, 499 
 Powell, Prof., b. 494, 499, 546 
 Prevost, Pierre, b. 526 
 Prevost, Constant, c. 661 
 Pochard, Dr., c. 529, 625 
 Priestley, c. 140, 143, 151 
 Proclus, a. 285, 291, 304, 307, 316 
 Prony, b. 72, 573 
 Proust, c. 132 
 Prout, Dr., c. 170, 451 
 Psellus, a. 291 
 Ptolemy, a. 190, &c.; b. 329 
 Ptolemy Euergetes, a. 200 
 Purbach, a. 426 
 Pythagoras, a. 26, 65, 149, 307 
 Pytheas, a. 212 
 
 Quctelet, M., 6. 499 
 
 Raleigh, c. 322 
 
 Ramsden, b. 274 
 
 llamus, a. 344, 451 
 
 Raspe, c. 552, 555 
 
 Ray, c. 330, 395 
 
 Raymund Lully, a. 325 
 
 Reaumur, c. 543 
 
 Recchi, c. 323 
 
 Redi, c. 487 
 
 Reichenbach, 6. 314 
 
 Reinhold, a. 401 
 
 Rennie, Mr. George, b. 72 
 
 Rheede, c. 323 
 
 Rheticus, a. 395, 400 
 
 Riccioli, a. 428 ; b. 56 
 
 Richman, b. 525 ; c. 19 
 
 Richter, c. 163 
 
 Riffault, c. 196 
 
 Riolan, c. 439 
 
 Rivinus, c. 334 
 
 Rivius, a. 368 ; b. 29 
 
 Robert Grostete, a. 274, 325 
 
 Robert of Lorraine, a 274 
 
 Robert Marsh, a. 274 
 
 Roberval, b. 341 
 
 Robins, 6. 57 
 
 Robinson, Dr., b. 283 
 
 Robison, b. 565, 572; c. 29 
 
 Roger Bacon, a. 274, 325, 357 
 
 Rohault, 6. 147, 200 
 
 Rome, de Lisle, c. 195, 108, 205 
 
 Romer, b. 263, 287, 341 
 
 Rondelet, c. 394 
 
 Roscoe, c. 374 
 
 Ross, Sir John, c. 52 
 
 Rothman, a. 392 
 
 Rouelle, c. 548, 553 
 
 Rousseau, c. 362 
 
 Rudberg, 6. 495 
 
 Ruellius, c. 304 
 
 Rufus, c. 427 
 
 Rumphe, c. 323 
 
 Saluces, b. 112 
 Salusbury, a. 411 
 Salviani, c. 394 
 Santbach, 6. 28 
 Santorini, c. 466 
 Saron, b. 237 
 Savart, 6. 355, 362 ; c. 94 
 Savile, a. 287 
 Saussure, 6. 578; c. 549 
 Sauveur, 6. 334, 348 
 Scheele, c. 140 
 
XXXV111 
 
 INDEX OF PROPER NAMES. 
 
 Schelling, b. 391 
 
 Schlottheim, c. 551, 561 
 
 Schmidt, c. 563, 614 
 
 Schomberg, Cardinal, a. 397 
 
 Schweigger, c. 103 
 
 Schwerd, b. 490 
 
 Scffla, c. 540 
 
 Scot, Michael, c. 302 
 
 Scrope, Mr. Poulett, c. 604 
 
 Sedgwick, Professor, c. 583, 589 
 
 Sediliot, M., a. 241 
 
 Seebeck,Dr., 6. 410,422, 500; c. 103 
 
 Segner, 6. 110 
 
 Seneca, a. 223, 383 ; b, 64, 67 
 
 Sergius, a. 294 
 
 Servetus, c. 435 
 
 Sextus Empiricus, a. 266 
 
 S'Gravesande, b. 89 
 
 Sharpe, b. 574 
 
 Sherard, c. 324 
 
 Simon of Genoa, c. 302, 363 
 
 Simplicius, a. 285, 289 
 
 Sloane, c. 324 
 
 Smith, Mr. Archibald, b. 499 
 
 Smith, Sir James Edward, c. 364 
 
 Smith, William, c. 553, 563 
 
 Snell, 6. 379 
 
 Socrates, c. 430 
 
 Solomon, a. 325 ; c. 292 
 
 Sorge, &. 350 
 
 Sosigenes, a. 135, 224 
 
 Southern, b. 574 
 
 Sowerby, c. 561 
 
 Spallanzani, c. 451 
 
 Spix, c. 490 
 
 Sprengel, c. 482 
 
 Stahl, c. 133 
 
 Stancari, b. 334 
 
 Steno, c. 217, 540, 548 
 
 Stephanus, c. 434 
 
 Stevinus, b. 16, 48, 62, 124 
 
 Stillingfleet, c. 364 
 
 Stobseus, a. 292 
 
 Stokes, Mr. C., c. 642 
 
 Strabo, a. 284 ; c. 295, 657 
 
 Strachey, c. 547 
 
 Stukeley, c. 547 
 
 Svanberg, 6. 537 
 
 Surian, c. 324 
 
 Sylvester, II. (Pope), . 274, 325 
 
 Sylvius, c. 124,434, 436 
 
 Symmer, c. 22 
 
 Syncellus, a. 133 
 
 Synesius, a. 219 
 
 Tacitus, a. 313 
 
 Tartalea, b. 13, 20, 29 
 
 Tartini, b. 350 
 
 Taylor, Brook, b. 86, 111, 337 
 
 Tcnong-Kang, a. 165,212 
 
 Telauge, a. 307 
 
 Tennemann, a. 328 
 
 Thales, a. 26, 28, 39, 155 
 
 Thebit, a. 325 
 
 Thenard, c. 158 
 
 Theodore Metochytes, a. 291 
 
 Theodosius, a. 220 
 
 Theophrastus, a. 287; c. 290, 293, 
 
 307 
 
 Thomas Aquinas, a. 325, 335, 344 
 Thomson, Dr., c. 166, 170 
 Tiberius, a. 313 
 Timocharis, a. 131 
 Torricelli, b. 49, 53, 66, 69 
 Touraefort, c. 333, 458 
 Tostatus, a. 272 
 Totaril, Cardinal, a. 344 
 Tragus, c. 308 
 Trithemius, a. 325 
 Troughton, b. 274 
 Turner, c. 170 
 Tycho Brahe, a. 444, 454 ; b. 378 
 
 Vaillant, Sebastian, c. 458 
 
 Vallisneri, c. 540 
 
 Van Helmont, c. 123 
 
 Varignon, b. 60 ; c. 450 
 
 Varolius, c. 466 
 
 Varro, Michael, 6. 10, 17, 31, 40 
 
 Vesalius, c. 432, 434, 465 
 
 Vicq d'Azyr, c. 467, 488 
 
 Vieussens, c. 467 
 
 Vincent, b. 78 
 
 Vincent of Beauvais, c. 302 
 
 Vinci, Leonardo da, a. 369 ; b. 125 ; 
 
 c. 539, 656 
 
 Virgil (bishop of Salzburg), a. 272 
 Virgil (a necromancer), a. 325 
 Vitello, &. 378 
 
 Vitruvius, a. 367, 369 ; b. 327 
 Viviani, 6. 50, 54 
 Voet, 6. 144 
 Voigt, c. 484 
 Volta, c. 82, 86 
 Voltaire, 6. 90, 209 
 Voltz, c. 588 
 Von Kleist, c. 14 
 
 Ubaldi, b. 10 
 
INDEX OF PROPER NAMES. 
 
 xxxix 
 
 Ulugh Beigh, a. 238 
 Ungern-Sternberg, Count, c. (503 
 Uranus, a. 294 
 Ure, Dr., b. 574 
 listen, c. 483 
 
 Wallerius, c. 221 
 
 Wallis, . 411 ; b. 54, 58, 140, 153, 
 
 348 
 
 Walmesley, 6. 225 
 Warburton, b. 204 
 Ward, Seth, 0. 411; 6. 154 
 Wargentin, 6. 227 
 Watson, c. 12, 15,22 
 Weber, Ernest and William, b. 361 
 Weiss, Prof., c. 234, 237 
 Wells, b. 567, 577; c. 87 
 Wenzel, c. 163 
 Werner, c. 221, 249, 257, 550, 562, 
 
 566, 653 
 
 Wheatstone, b. 361 
 Wheler, c. 324 
 WTiewell, b. 257; c. 241 
 Whiston, 6. 202 
 Wilcke, b. 596; c. 18, 25 
 
 Wilkins (Bishop), a. 410; b. 41, 153 
 William of Hirsaugen, a. 274 
 Willis, Rev. Robert, a. 362 ; b. 355, 
 
 368 
 
 Willis, Thomas, c. 465, 469 
 Willoughby, c. 395, 397 
 Wolf, Caspar Frederick, c. 481 
 Wolff, 6. 89, 559 
 Wollaston, b. 399, 401, 403, 422; 
 
 c. 166, 232 
 
 Woodward, c. 542, 546, 652 
 Wren, a. 411; b. 58, 153, 197 
 Wright, 6. 217 
 
 Xanthus, c. 290 
 
 Yates, c. 52 
 
 Young, Thomas, 6. 72, 361, 438, 
 &c., 467 
 
 Zabarella, a. 341 
 Zach, b. 239 
 Ziegler, 6. 573 
 Zimmerman, c. 614 
 
INDEX OF TECHNICAL TERMS. 
 
 ABERRATION, b. 264 
 
 Absolute and relative, a. 50 
 
 Accelerating force, b. 30 
 
 Achromatism, 6. 397 
 
 Acid, c. 125 
 
 Acoustics, b. 323 
 
 Acronycal rising and setting, . 158 
 
 Action and reaction, b. 59 
 
 Acuation, c. 123 
 
 Acumination, c. 221 
 
 Acute harmonics, b. 348 
 
 /Etiology, c. 528 
 
 Affinity (in Chemistry), c. 129 
 
 Affinity (in Natural History), c. 388 
 
 Agitation, center of, b. 82 
 
 Alidad, a. 245 
 
 Alineations, a. 205, 211 
 
 Alkali, c. 125 
 
 Almacantars, a. 245 
 
 Almagest, a. 227 
 
 Almanac, a. 245 
 
 Alphonsine tables, a. 239 
 
 Alternation (of formations), c. 590 
 
 Amphoteric silicides, c. 281 
 
 Analogy (in Natural History), c. 
 
 388, 390 
 Analysis (chemical), c. 123 
 
 (polar, of light), b. 420 
 
 Angle of cleavage, c. 227 
 
 incidence, b. 374 
 
 reflection, 6. 374 
 
 Animal electricity, c. 80 
 Ani'on, c. 185 
 
 Annus, a. 125 
 Anode, c. 185 
 Anomaly, a. 172, 176 
 Antarctic circle, a. 157 
 Antichthon, a. 72 
 Anticlinal line, c. 588 
 Antipodes, a. 253 
 Apogee, a. 184 
 
 Apotelesmatic astrology, a. 317 
 Apothecse, c. 300 
 Appropriate ideas, a. 81 
 Arctic circle, a. 157 
 Armed magnets, c. 53 
 
 Armil, a. 214 
 
 Art and science, a. 358 
 
 Articulata, c. 492 
 
 Artificial magnets, c. 54 
 
 Ascendant, a. 316 
 
 Astrolabe, a. 216 
 
 Atmology, b. 518, 556 
 
 Atom, a. 64 
 
 Atomic theory, c. 1 62 
 
 Axes of symmetry (of crystals), c. 
 
 236 
 
 Axis (of a mountain chain), c. 588 
 Azimuth, a. 245 
 Azot, c. 146 
 
 Ballistics, 6. 98 
 Bases (of salts), c. 127 
 Basset (of strata), c. 548 
 Beats, b. 335 
 
 Calippic period, a. 143 
 
 Caloric, b, 526 
 
 Canicular period, a. 134 
 
 Canon, a. 185 
 
 Capillary action, b. 115 
 
 Carbonic acid gas, c. 146 
 
 Carolinian tables, a. 457 
 
 Catasterisms, a. 206 
 
 Categories, a. 288 
 
 Cathion, c. 185 
 
 Cathode, c. 185 
 
 Cation, c. 185 
 
 Causes, material, formal, efficient, 
 
 final, a. 57 
 
 Centrifugal forces, b. 37 
 Cerebral system, c. 467 
 Chemical attraction, c. 127 
 Chyle, c. 448 
 Chyme, c. 450 
 Circles of the sphere, a. 153 
 Circular polarization, b. 423, 482 
 Circular progression (in Natural 
 
 History), c. 388 
 Civil year, a. 132 
 Climate, b. 531 
 Coexistence of vibrations, b. 349 
 
INDEX OF TECHNICAL TEKM8. 
 
 xli 
 
 Coexistent vibrations, b. 112 
 
 Colures, a. 157 
 
 Conditions of existence (of animals), 
 
 c. 500, 515 
 Conducibility, b. 527 
 Conductibility, 6. 527 
 Conduction, b. 468 
 Conductivity, b. 527 
 Conductors, c. 1 1 
 Conical refraction, b. 489 
 Conservation of areas, b. 120 
 Consistence (in Thermotics), b. 554 
 Constellations, a. 145 
 Constituent temperature, b. 567 
 Contact-theory of the Voltaic pile, 
 
 c. 178 
 
 Cor (of plants), c. 315 
 Cosmical rising and setting, a. 158 
 Cotidal lines, b. 259 
 Craters of elevation, c. 613 
 
 Da?mon, a. 303 
 
 D'Alembert's principle, b. 97 
 
 Day, a. 123 
 
 Decussation of nerves, c. 4G6 
 
 Deduction, a. 16 
 
 Deferent, a. 235 
 
 Definite proportions (in Chemistry), 
 
 c. 162 
 
 Delta, c. 603 
 
 Dephlogisticated air, c. 143 
 Depolarization, 5. 420 
 Depolarization of heat, b. 548 
 Depolarizing axes, b. 421 
 Descriptive phrase (in Botany), 
 
 c. 346 
 
 Dew, b. 576 
 Dichotomized, a. 169 
 Diffraction, b. 417 
 Dimorphism, c. 248 
 Dioptra, a. 217 
 Dipolarization, 6. 420, 424 
 Direct motion of planets, a. 1 7 1 
 Discontinuous functions, b. 346 
 Dispensatoria, c. 300 
 Dispersion (of light), b. 492 
 Doctrine of the sphere, a. 156 
 Dogmatic school (of medicine), c. 424 
 Double refraction, b. 400 
 
 Eccentric, a. 183 
 Echineis, a. 261 
 Eclipses, . 164 
 Effective forces, b. 86 
 
 Elective attraction, c. 128 
 
 Electrical current, c. 88 
 
 Electricity, c. 7 
 
 Electrics, c. 1 1 
 
 Electric tension, c. 88 
 
 Electro-dynamical, c. 95 
 
 Electrodes, c. 185 
 
 Electrolytes, c. 184 
 
 Electro-magnetism, c. 91 
 
 Electro-magnetic induction, c. 109 
 
 Elements (chemical), c. 204 
 
 Elliptical polarization, b. 485, 488 
 
 Empiric school (of medicine), c. 424 
 
 Empyrean, a. 72 
 
 Enneads, a. 301 
 
 Entelechy, a. 59 
 
 Eocene, c. 577 
 
 Epicycles, a. 173, 182 
 
 Epochs, a. 12 
 
 Equant, a. 235 
 
 Equation of time, a. 206 
 
 Equator, a. 157 
 
 Equinoctial points, a. 157 
 
 Escarpment, c. 588 
 
 Evection, a. 228 
 
 Exchanges of heat, theory of, b. 527 
 
 Facts and ideas, a. 6 
 
 Faults (in strata), c. 588 
 
 Final causes, c. 429, 515 
 
 Finite intervals, (hypothesis of), 
 
 b. 493 
 
 First law of motion, b. 23 
 Fits of easy transmission, b. 414, 433 
 Fixed air, c. 142 
 Fixity of the stars, a. 214 
 Formal optics, b. 372 
 Franklinism, c. 22 
 Fresnel's rhomb, b. 424 
 Fringes of shadows, b. 417, 490 
 Fuga vacui, b. 65 
 Full months, a. 140 
 Function (in Physiology), c. 417 
 
 Galvanism, c. 83 
 Galvanometer, c. 103 
 Ganglionic system, c. 467 
 Ganglions, c. 466 
 Generalization, a. 11 
 Geocentric theory, a. 380 
 Gnomon, a. 131 
 Gnomonick, a. 168 
 Golden number, a. 142 
 Grave harmonics, b. 350 
 
xlii 
 
 INDEX OF TECHNICAL TERMS. 
 
 Gravitate, b. 171 
 
 Habitations (of plants), e. 621 
 Haecceity, a. 338 
 Hakemite tables, a. 239 
 Halogenes, c. 204 
 Haloide, c. 375 
 Harmonics, acute, b. 348 
 
 grave, b. 350 
 
 Heat, b. 520 
 
 latent, b. 554 
 
 Heccaedecaeteris, a. 139 
 Height of a homogenous atmo- 
 sphere, b. 344 
 
 Heliacal rising and setting, a. 158 
 Heliocentric theory, a. 380 
 Hemisphere of Berosus, a. 213 
 Hollow months, . 140 
 Homoiomeria, . 66 
 Horizon, a. 158 
 Horoscope, . 316 
 Horrour of a vacuum, b. 65 
 Houses (in Astrology), a. 316 
 Hydracids, c. 159 
 Hygrometer, b. 577 
 Hygrometry, b. 519 
 Hypostatical principles, c. 123 
 
 latro-chemists, c. 1 24 
 Ideas of the Platonists, a. 61 
 Ilchanic tables, a. 238 
 Impressed forces, b. 86 
 Inclined plane, b. 9 
 Induction (electric), c. 1 7 
 Induction (logical), a. 6 
 Inductive, . 6 
 Inductive charts, a. 13 
 Inductive epochs, a. 12 
 Inflammable air, c. 142 
 Influences, a. 294 
 Intercalation, a. 121 
 Interferences, b. 427, 439 
 Ionic school, a. 24 
 Isomorphism, c. 245 
 Isothermal lines, b. 533 ; c. 590 
 Italic school, a. 24 
 
 Joints (in rocks), c. 589 
 Judicial astrology, a. 317 
 Julian calendar, a. 135 
 
 Lacteals, c. 448 
 
 Latent heat, b. 499 
 
 Laws of motion, first, b. 23 
 
 Laws of motion, second, b. 37 
 
 third, b. 43 
 
 Leap year, a. 133 
 Ley den phial, c. 14 
 Librations (of planets), a. 443 
 Libration of Jupiter^ Satellites, 
 
 b. 227 
 
 Limb of an instrument, a. 213 
 Longitudinal vibrations, c. 364 
 Lunisolar year, a. 138 
 Lymphatics, c. 449 
 
 Magnetic elements, c. 58 
 
 equator, c. 52 
 
 Magnetism, c. 49 
 Matter and form, a. 57 
 Mean temperature, b. 532 
 Mechanical mixture of gases, b. 569 
 Mechanico-chemical sciences, c. 5 
 Meiocene, c. 577 
 Meridian line, a. 215 
 Metals, c. 201 
 Meteorology, b. 518 
 Meteors, a. 80 
 
 Methodic school (of medicine), c. 425 
 Metonic cycle, a. 142 
 Mineral alkali, c. 126 
 Mineralogical axis, c. 588 
 Minutes, a. 215 
 Miocene, c. 577 
 Mollusca, c. 492 
 Moment of inertia, b. 81 
 Momentum, b. 50 
 Moon's libration, b. Ill 
 Morphology, c. 475, 478 
 Moveable polarization, b. 462 
 Multiple proportions (in Chemis- 
 try), c. 162 
 
 Music of the spheres, a. 71 
 Mysticism, a. 281 
 
 Nadir, a. 245 
 
 Nebular hypothesis, c. 531 
 
 Neoplatomsts, a. 291 
 
 Neutral axes, b. 418 
 
 Neutralization (in Chemistry), c. 125 
 
 Newton's rings, b. 414, 488 
 
 scale of colour, b. 414 
 
 Nitrous air, c. 143 
 Nomenclature, c. 340 
 Nominalists, a. 347 
 Non-electrics, c. 11 
 Numbers of the Pythagoreans, c. 64 
 Nutation, b. 266 
 
INDEX OF TECHNICAL TERMS. 
 
 xliii 
 
 Nycthemer, a. 207 
 
 Octaeteris, a. 139 
 Octants, a. 235 
 Oolite, c. 578 
 Optics, ft. 372 
 Organical sciences, c. 417 
 Organic molecules, c. 460 
 Organization, c. 417 
 Oscillation, center of, b. 80 
 Outcrop (of strata), c. 548 
 Oxide, c. 155 
 Oxyd, c. 155 
 Oxygen, c. 146 
 
 Palaeontology, c. 560 
 Palaetiological sciences, c. 527 
 Parallactic instrument, a. 217 
 Parallax, a. 203 
 Percussion, center of, b. 82 
 Perfectihabia, a. 60 
 Perigee, a. 182 
 Perijove, ft. 235 
 Periodical colours, b. 439 
 Phases of the moon, a. 162 
 Philolaic tables, . 457 
 Phlogisticated air, c. 143 
 Phlogiston, c. 135 
 Phthongometer, b. 368 
 Physical optics, 6. 372 
 Piston, b. 64 
 Plagihedral faces, b. 424 
 Plane of maximum areas, b. 1 20 
 Pleiocene, c. 577 
 Plesiomorphous, c. 248 
 Pliocene, c. 577 
 Plumb line, a. 216 
 Pneumatic trough, c. 142 
 Poikilite, c. 578 _ 
 Polar decompositions, c. 176 
 Polarization, b. 406, 409 
 
 circular, 6. 423. 482 
 
 elliptical, b. 485, 488 
 
 moveable, 6. 462 
 
 plane, ft. 483 
 
 of heat, 6. 545 
 
 Poles (voltaic), c. 185 
 
 of maximum cold, b. 533 
 
 Potential levers, 6. 125 
 Power and act, a. 58 
 Precession of the equinoxes, fl. 1 99 
 Predicables, a. 288 
 Predicaments, a. 288 
 
 Preludes of epochs, a. 12 
 
 Primary rocks, c. 549 
 
 Primitive rocks, c. 549 
 
 Primum calidum, a. 64 
 
 Principal plane (of a rhomb), 6. 407 
 
 Principle of least action, b. 121 
 
 Prosthaphaeresis, a. 184 
 
 Provinces (of plants and animals), 
 
 c. 621 
 
 Prutenic tables, a. 402 
 Pulses, b. 343 
 Pyrites, c. 275 
 
 Quadrant, a. 215 
 Quadrivium, a. 276 
 Quiddity, a. 338 
 
 Quinary division (in Natural His- 
 tory), c. 388 
 Quintessence, a. 54 
 
 Radiata, c. 492 
 Radiation, 6. 520 
 Rays, 6. 375 
 Realists, a. 347 
 Refraction, b. 376 
 
 of heat, b. 548 
 
 Remora, a. 261 
 
 Resinous electricity, c. 12 
 
 Rete mirabile, c. 466 
 
 Retrograde motion of planets, a. 172 
 
 Roman calendar, a. 143 
 
 Rotatory vibrations, b. 362 
 
 Rudolphine tables, a. 402, 454 
 
 Saros, a. 166 
 
 Scholastic philosophy, a. 332 
 
 School philosophy, a. 18 
 
 Science, a. 6 
 
 Secondary rocks, c. 549 
 
 mechanical sciences, b. 3 2 3 
 
 Second law of motion, b. 37 
 Seconds, a. 215 
 Secular inequalities, b. 106 
 Segregation, c. 615 
 Seminal contagion, c. 457 
 
 proportions, a. 67 
 
 Sequels of epochs, a. 13 
 Silicides, c. 276 
 Silurian rocks, c. 578 
 Simples, c. 301 
 Sine, a. 244 
 Solar heat, b. 530 
 Solstitial points, a. 157 
 Solution of water in air, b. 561 
 Sothic period, a. 134 
 
xliv 
 
 INDEX OF TECHNICAL TERMS. 
 
 Spagiric ait, c. 123 
 Specific heat, b. 553 
 Sphere, a. 156 
 
 Spontaneous generation, c. 455 
 Statical electricity, c. 33 
 Stationary periods, a. 15 
 
 pknets, a. 172 
 
 Stations (of plants), c. 621 
 Sympathetic sounds, b. 348 
 Systematic Botany, c. 286 
 
 Systems of crystallization, c. 237 
 
 Tables, Solar (of Ptolemy), a. 184 
 
 Hakemite, . 238 
 
 Toletan, a. 238 
 
 Ilchanic, a. 238 
 
 Alphonsine, a. 238 
 
 Prutenic, a. 402 
 
 Rudolphine, a. 454 
 
 Perpetual (of Lansberg) 
 
 a. 454 
 
 Philolaic, a. 457 
 
 Carolinian, a. 457 
 
 Tangential vibrations, b. 362 
 
 Tautochronous curves, b. 109 
 
 Technical terms, c. 340 
 
 Temperament, b. 367 
 
 Temperature, b. 521 
 
 Terminology, c. 340 
 
 Tertiary rocks, c. 549 
 
 Tetractys, a. 65 
 
 Theory of analogues, c. 500 
 
 Thermomultiplier, 6. 547 
 
 Thermotics, b. 517 
 
 Thick plates, colours of, 6. 419 
 
 Thin plates, colours of, b. 413 
 
 Third law of motion, b. 45 
 
 Three principles (in Chemistry), c. 
 
 122 
 
 Toletan tables, a. 238 
 Transition rocks, c. 578 
 
 Transverse vibrations, b. 362, 440, 
 
 453 
 
 Travertin, c. 603 
 
 Trepidation of the fixed stars, a. 241 
 Trigonometry, a. 221 
 Trivial names, c. 345 
 Trivium, a. 276 
 Tropics, a. 157 
 
 Truncation (of crystals), c. 220 
 Type (in Comparative Anatomy), 
 
 c. 489 
 
 Variation of the moon, a. 241, 456 
 Vegetable alkali, c. 126 
 Vertebrata, c. 492 
 Vibrations, b. 362 
 Vicarious elements, c. 246 
 
 solicitations, b. 86 
 
 Virtual velocities, b. 42 
 Vitreous electricity, c. 12 
 Volatile alkali, c. 126 
 Volta-electrometer, c. 186 
 Voltaic electricity, c. 83 
 
 pile, c. 84 
 
 Volumes, theory of, c. 171 
 Voluntary, violent, and natural mo- 
 tion, b. 18 
 Vortices, b. 141 
 
 Uniform force, b. 32 
 
 Unity of composition (in Compara- 
 tive Anatomy), c. 600 
 
 Unity of plan (in Comparative Ana- 
 tomy), c. 600 
 
 Week, a. 151 
 Year, a. 123 
 
 Zenith, a. 245 
 Zodiac, a. 157 
 Zones, a. 167 
 
HISTORY 
 
 OF THK 
 
 INDUCTIVE SCIENCES 
 
 INTRODUCTION. 
 
 VOL. I. B 
 
" A JUST story of learning, containing the antiquities and originals 
 of KNOWLEDGES, and their sects; their inventions, their diverse 
 administrations and managings ; their flourishings, their oppo- 
 sitions, decays, depressions, oblivions, removes; with the causes 
 and occasions of them, and all other events concerning learn- 
 ing, throughout all ages of the world ; I may truly affirm to he 
 wanting. 
 
 " The use and end of which work I do not so much design for 
 curiosity, or satisfaction of those that are the lovers of learning : 
 but chiefly for a more serious and grave purpose ; which is this, 
 in few words, that it will make learned men more wise in the use 
 and administration of learning." 
 
 BACON, Advancement of Learning, book ii. 
 
INTRODUCTION. 
 
 IT is my purpose to write the History of some 
 of the most important of the Physical Sciences, 
 from the earliest to the most recent periods. I shall 
 thus have to trace some of the most remarkable 
 branches of human knowledge, from their first germ 
 to their growth into a vast and varied assemblage 
 of undisputed truths ; from the acute, but fruitless, 
 essays of the early Greek Philosophy, to the com- 
 prehensive systems, and demonstrated generaliza- 
 tions, which compose such sciences as the Me- 
 chanics, Astronomy, and Chemistry, of modern 
 times. 
 
 The completeness of historical view which be- 
 longs to such a design, consists, not in accumulating 
 all the details of the cultivation of each science, but 
 in marking clearly the larger features of its forma- 
 tion. The historian must endeavour to point out 
 how each of the important advances was made, by 
 which the sciences have reached their present posi- 
 tion ; and when and by whom each of the valuable 
 truths was obtained, of which the aggregate now 
 constitutes a costly treasure. 
 
 B 2 
 
4 HISTORY OF INDUCTIVE SCIENCES. 
 
 Such a task, if fitly executed, must have a well- 
 founded interest for all those who look at the 
 existing condition of human knowledge with com- 
 placency and admiration. The present generation 
 finds itself the heir of a vast patrimony of science ; 
 and it must needs concern us to know the steps by 
 which these possessions were acquired, and the 
 documents by which they are secured to us and our 
 heirs for ever. Our species, from the time of its 
 creation, has been travelling onwards in pursuit of 
 truth ; and now that we have reached a lofty and 
 commanding position, with the broad light of day 
 around us, it must be grateful to look back on the 
 line of our past progress ; to review the journey, 
 begun in early twilight amid primeval wilds ; for a 
 long time continued with slow advance and obscure 
 prospects ; and gradually and in later days followed 
 along more open and lightsome paths, in a wide 
 and fertile region. The historian of science, from 
 early periods to the present times, may hope for 
 favour on the score of the mere subject of his nar- 
 rative, and in virtue of the curiosity which the men 
 of the present day may naturally feel respecting the 
 events and persons of his story. 
 
 But such a survey may possess also an interest 
 of another kind ; it may be instructive as well as 
 agreeable ; it may bring before the reader the pre- 
 sent form and extent, the future hopes and pro- 
 spects of science, as well as its past progress. The 
 eminence on which we stand may enable us to see 
 
INTRODUCTION. 5 
 
 the land of promise, as well as the wilderness 
 through which we have passed. The examination 
 of the steps by which our ancestors acquired our 
 intellectual estate, may make us acquainted with 
 our expectations as well as our possessions; may 
 not only remind us of what we have, but may teach 
 us how to improve and increase our store. It will 
 be universally expected that a History of Inductive 
 Science should point out to us a philosophical dis- 
 tribution of the existing body of knowledge, and 
 afford us some indication of the most promising 
 mode of directing our future efforts to add to its 
 extent and completeness. 
 
 To deduce such lessons from the past history of 
 human knowledge, was the intention which origin- 
 ally gave rise to the present work. Nor is this 
 portion of the design in any measure* abandoned ; 
 but its execution, if it take place, must be attempted 
 in a separate and future treatise, On ike Philosophy 
 of the Inductive Sciences. An essay of this kind 
 may, I trust, from the progress already made in it, 
 be laid before the public at no long interval after 
 the present history. 
 
 Though, therefore, many of the principles and 
 maxims of such a work will disclose themselves 
 with more or less of distinctness in the course of 
 the history on which we are about to enter, the 
 systematic and complete exposition of such prin- 
 ciples must be reserved for this other treatise. My 
 attempts and reflections have led me to the opinion 
 
6 HISTORY OF INDUCTIVE SCIENCES. 
 
 that justice cannot be done to the subject without 
 such a division of it. 
 
 To this future work, then, I must refer the 
 reader who is disposed to require, at the outset, a 
 precise explanation of the terms which occur in my 
 title. It is not possible, without entering into this 
 philosophy, to explain adequately how science which 
 is INDUCTIVE differs from that which is not so ; or 
 why some portions of knowledge may properly be 
 selected from the general mass and termed SCIENCE. 
 It will be sufficient at present to say, that the sci- 
 ences of which we have here to treat, are those 
 which are commonly known as the Physical Sci- 
 ences ; and that by Induction is to be understood 
 that process of collecting general truths from the 
 examination of particular facts, by which such sci- 
 ences have been formed. 
 
 There are, however, two or three remarks, of 
 which the application will occur so frequently, and 
 will tend so much to give us a clearer view of some 
 of the subjects which occur in our history, that 
 I will state them now in a brief and general 
 manner (A). 
 
 Facts and Ideas. In the first place, then, I 
 remark, that, to the formation of science, two things 
 are requisite; Facts and Ideas; observation of 
 Things without, and an inward effort of Thought; 
 or, in other words, Sense and Reason. Neither of 
 these elements, by itself, can constitute substantial 
 general knowledge. The impressions of sense, un- 
 
INTRODUCTION. 7 
 
 connected by some rational and speculative prin- 
 ciple, can only end in a practical acquaintance with 
 individual objects; the operations of the rational 
 faculties, on the other hand, if allowed to go on 
 without a constant reference to external things, can 
 lead only to empty abstraction and barren inge- 
 nuity. Real speculative knowledge demands the 
 combination of the two ingredients ; right reason, 
 and facts to reason upon. It has been well said, 
 that true knowledge is the interpretation of nature ; 
 and thus it requires both the interpreting mind, and 
 nature for its subject ; both the document, and the 
 ingenuity to read it aright. Thus invention, acute- 
 ness, and connexion of thought, are necessary on the 
 one hand, for the progress of philosophical know- 
 ledge ; and on the other hand, the precise and 
 steady application of these faculties -to facts well 
 known and clearly conceived. It is easy to point 
 out instances in which science has failed to advance, 
 in consequence of the absence of one or other of 
 these requisites ; indeed, by far the greater part of 
 the course of the world, the history of most times 
 and most countries, exhibits a condition thus sta- 
 tionary with respect to knowledge. The facts, the 
 impressions on the senses, on which the first suc- 
 cessful attempts at physical knowledge proceeded, 
 were as well known long before the time when they 
 were thus turned to account, as at that period. The 
 motions of the stars, and the effects of weight, were 
 familiar to man before the rise of the Greek astro- 
 
8 HISTORY OF INDUCTIVE SCIENCES. 
 
 nomy and mechanics: but the "diviner mind" was 
 still absent ; the act of thought had not been ex- 
 erted, by which these facts were bound together 
 under the form of laws and principles. And even 
 at this day, the tribes of uncivilized and half-civilized 
 man over the whole face of the earth, have before 
 their eyes a vast body of facts, of exactly the same 
 nature as those with which Europe has built the 
 stately fabric of her physical philosophy; but, in 
 almost every other part of the earth, the process of 
 the intellect by which these facts become science, is 
 unknown. The scientific faculty does not work. 
 The scattered stones are there, but the builder's 
 hand is wanting. And again, we have no lack of 
 proof that mere activity of thought is equally ineffi- 
 cient in producing real knowledge. Almost the 
 whole of the career of the Greek schools of philo- 
 sophy ; of the schoolmen of Europe in the middle 
 ages ; of the Arabian and Indian philosophers ; 
 shows us that we may have extreme ingenuity and 
 subtlety, invention and connexion, demonstration 
 and method ; and yet that out of these germs, no 
 physical science may be developed. "We may ob- 
 tain, by such means, logic and metaphysics, and 
 even geometry and algebra ; but out of such mate- 
 rials we shall never form mechanics and optics, 
 chemistry and physiology. How impossible the 
 formation of these sciences is without a constant 
 and careful reference to observation and experi- 
 ment; how rapid and prosperous their progress 
 
INTRODUCTION. 
 
 may be when they draw from such sources the 
 materials on which the mind of the philosopher 
 employs itself; the history of those branches of 
 knowledge for the last three hundred years abun- 
 dantly teaches us. 
 
 Accordingly, the existence of clear Ideas applied 
 to distinct Facts will be discernible in the History 
 of Science, whenever any marked advance takes 
 place. And, in tracing the progress of the various 
 provinces of knowledge which come under our 
 survey, it will be important for us to see, that, at 
 all such epochs, such a combination has occurred ; 
 that whenever any material step in general know- 
 ledge has been made, whenever any philosophical 
 discovery arrests our attention; some man or 
 men come before us, who have possessed, in an 
 eminent degree, a clearness of the ideas which be- 
 long to the subject in question, and who have 
 applied such ideas in a vigorous and distinct man- 
 ner to ascertained facts and exact observations. We 
 shall never proceed through any considerable range 
 of our narrative, without having occasion to remind 
 the reader of this reflection. 
 
 Successive Steps in Science. But there is an- 
 other remark which we must also make. Such 
 sciences as we have here to do with, are, com- 
 monly, not formed by a single act ; they are not 
 completed by the discovery of one great prin- 
 ciple. On the contrary, they consist in a long-con- 
 tinued advance; a series of changes; a repeated 
 
 
10 HISTORY OF INDUCTIVE SCIENCES. 
 
 progress from one principle to another, different 
 and often apparently contradictory. Now, it is im- 
 portant to remember that this contradiction is ap- 
 parent only. The principles which constituted the 
 triumph of the preceding stages of the science, may 
 appear to be subverted and ejected by the later 
 discoveries, but in fact they are, (so far as they 
 were true,) taken up into the subsequent doctrines 
 and included in them. They continue to be an 
 essential part of the science. The earlier truths 
 are not expelled but absorbed, not contradicted but 
 extended ; and the history of each science, which 
 may thus appear like a succession of revolutions, is, 
 in reality, a series of developements. In the intel- 
 lectual, as in the material world, 
 
 Omnia mutantur nil interit 
 
 Nee manet ut fuerat nee form as servat easdem, 
 Sed tamen ipsa eadem est. 
 
 All changes, nought is lost; the forms are changed, 
 And that which has been is not what it was, 
 Yet that which has been is. 
 
 Nothing which was done was useless or unessential, 
 though it ceases to be conspicuous and primary. 
 
 Thus the final form of each science contains the 
 substance of each of its preceding modifications; 
 and all that was at any antecedent period dis- 
 covered and established, ministers to the ultimate 
 developement of its proper branch of knowledge. 
 Such previous doctrines may require to be made 
 precise and definite, to have their superfluous and 
 
INTRODUCTION. 1 1 
 
 arbitrary portions expunged, to be expressed in new 
 language, to be taken up into the body of science 
 by various processes; but they do not on such 
 accounts cease to be true doctrines, or to form a 
 portion of the essential constituents of our know- 
 ledge. 
 
 Terms record Discoveries. The modes in which 
 the earlier truths of science are preserved in its 
 later forms, are indeed various. From being as- 
 serted at first as strange discoveries, such truths 
 come at last to be implied as almost self-evident 
 axioms. They are recorded by some familiar maxim, 
 or perhaps by some new word or phrase, which 
 becomes part of the current language of the philoso- 
 phical world ; and thus asserts a principle, while it 
 appears merely to indicate a transient notion; 
 preserves as well as expresses a truth ;- and, like a 
 medal of gold, is a treasure as well as a token. 
 We shall frequently have to notice the manner in 
 which great discoveries thus stamp their impress 
 upon the terms of a science ; and, like great poli- 
 tical revolutions, are recorded by the change of the 
 current coin which has accompanied them. 
 
 Generalization. The great changes which thus 
 take place in the history of science, the revolutions 
 of the intellectual world, have, as a usual and lead- 
 ing character, this, that they are steps of generali- 
 zation; transitions from particular truths to others 
 of a wider extent, in which the former are included. 
 This progress of knowledge, from individual facts 
 
12 HISTORY OF INDUCTIVE SCIENCES. 
 
 to universal laws, from particular propositions to 
 general ones, and from these to others still more 
 general, with reference to which the former general- 
 izations are particular, is so far familiar to men's 
 minds, that without here entering into further ex- 
 planation, its nature will be understood sufficiently 
 to prepare the reader to recognise the exemplifi- 
 cations of such a process, which he will find at 
 every step of our advance. 
 
 Inductive Epochs; Preludes; Sequels. In our 
 history, it is the progress of knowledge only which 
 we have to attend to. This is the main action of 
 our drama ; and all the events which do not bear 
 upon this, though they may relate to the cultiva- 
 tion and the cultivators of philosophy, are not a 
 necessary part of our theme. Our narrative will 
 therefore consist mainly of successive steps of gene- 
 ralization, such as have just been mentioned. But 
 among these, we shall find some of eminent and 
 decisive importance, which have more peculiarly 
 influenced the fortunes of physical philosophy, and 
 to which we may consider the rest as subordinate 
 and auxiliary. These primary movements, when 
 the Inductive process, by which science is formed, 
 has been exercised in a more energetic and power- 
 ful manner, may be distinguished as the Inductive 
 Epochs of scientific history; and they deserve our 
 more express and pointed notice. They are, for the 
 most part, marked by the great discoveries and the 
 great philosophical names which all civilized na- 
 
INTRODUCTION. 1 3 
 
 tions have agreed in admiring. But, when we 
 examine more clearly the history of such disco- 
 veries, we find that these epochs have not occurred 
 suddenly and without preparation. They have been 
 preceded by a period, which we may call their 
 Prelude, during which the ideas and facts on which 
 they turned were called into action; were gra- 
 dually evolved into clearness and connexion, per- 
 manency and certainty; till at last the discovery 
 which marks the Epoch, seized and fixed for ever 
 the truth which had till then been obscurely and 
 doubtfully discerned. And again, when this step 
 has been made by the principal discoverers, there 
 may generally be observed another period, which 
 we may call the Sequel of the Epoch, during which 
 the discovery has acquired a more perfect certainty 
 and a more complete developement among the 
 leaders of the advance; has been diffused to the 
 wider throng of the secondary cultivators of such 
 knowledge, and traced into its distant consequences. 
 This is a work, always of time and labour, often of 
 difficulty and conflict. To distribute the History of 
 science into such Epochs, with their Preludes and 
 Sequels, if successfully attempted, must needs make 
 the series and connexion of its occurrences more 
 distinct and intelligible. Such periods form rest- 
 ing-places, where we pause till the dust of the con- 
 fused march is laid, and the prospect of the path 
 is clear. 
 
 Inductive Charts. Since the advance of science 
 
14 HISTORY OF INDUCTIVE SCIENCES. 
 
 consists in collecting by induction true general laws 
 from particular facts, and in combining several such 
 laws into one higher generalization, in which they 
 still retain their truth ; we might form a Chart, or 
 Table, of the progress of each science, by setting 
 down the particular facts which have thus been com- 
 bined, so as to form general truths, and by marking 
 the further union of these general truths into others 
 more comprehensive. The Table of the progress of 
 any science would thus resemble the Map of a River, 
 in which the waters from separate sources unite 
 and make rivulets, which again meet with rivulets 
 from other fountains, and thus go on forming by 
 their junction trunks of a higher and higher order. 
 The representation of the state of a science in this 
 form, would necessarily exhibit all the principal 
 doctrines of the science; for each general truth con- 
 tains the particular truths from which it was de- 
 rived, and may be followed backwards till we have 
 these before us in their separate state. And the 
 last and most advanced generalization would have, 
 in such a scheme, its proper place and the evidence 
 of its validity. Hence such an Inductive Table of 
 each science would afford a criterion of the correct- 
 ness of our distribution of the inductive Epochs, by 
 its coincidence with the views of the best judges, as 
 to the substantial contents of the science in ques- 
 tion. By forming, therefore, such Inductive Tables 
 of the principal sciences of which I have here to 
 speak, and by regulating by these tables, my views 
 
INTRODUCTION. 15 
 
 of the history of the sciences, 1 conceive that I 
 have secured the distribution of my history from 
 material error ; for no merely arbitrary division of 
 the events could satisfy such conditions. But though 
 I have constructed such charts to direct the course 
 of the present history, I shall not insert them in 
 the work, reserving them for the illustration of the 
 philosophy of the subject; for to this they more pro- 
 perly belong, being a part of the Logic of Induction. 
 
 Stationary Periods. By the lines of such maps 
 the real advance of science is depicted, and nothing 
 else. But there are several occurrences of other 
 kinds, too interesting and too instructive to be alto- 
 gether omitted. In order to understand the condi- 
 tions of the progress of knowledge, we must attend, 
 in some measure, to the failures as well as the suc- 
 cesses by which such attempts have been attended. 
 When we reflect during how small a portion of the 
 whole history of human speculations, science has 
 really been, in any marked degree, progressive, we 
 must needs feel some curiosity to know what was 
 doing in these stationary periods ; what field could 
 be found which admitted of so wide a deviation, or 
 at least so protracted a wandering. It is highly 
 necessary to our purpose, to describe the baffled 
 enterprises as well as the achievements of human 
 speculation. 
 
 Deduction. During a great part of such sta- 
 tionary periods, we shall find that the process which 
 we have spoken of as essential to the formation of 
 
16 HISTORY OF INDUCTIVE SCIENCES. 
 
 real science, the conjunction of clear ideas with dis- 
 tinct facts, was interrupted; and, in such cases, men 
 dealt with ideas alone. They employed themselves 
 in reasoning from principles, and they arranged, 
 and classified, and analyzed their ideas, so as to 
 make their reasonings satisfy the requisitions of 
 our rational faculties. This process of drawing 
 conclusions from our principles, by rigorous and 
 unimpeachable trains of demonstration, is termed 
 Deduction. In its due place, it is a highly import- 
 ant part of every science ; but it has no value when 
 the fundamental principles, on which the whole of 
 the demonstration rests, have not first been obtain- 
 ed by the induction of facts, so as to supply the 
 materials of substantial truth. Without such ma- 
 terials, a series of demonstrations resembles physi- 
 cal science only as a shadow resembles a real object. 
 To give a real significance to our propositions, In- 
 duction must provide what Deduction cannot sup- 
 ply. From a pictured hook we can hang only a 
 pictured chain. 
 
 Distinction of common Notions and Scientific 
 Ideas. When the notions with which men are 
 conversant in the common course of practical life, 
 which give meaning to their familiar language, and 
 employment to their hourly thoughts, are compared 
 with the Ideas on which exact science is founded, 
 we find that the two classes of intellectual opera- 
 tions have much that is common and much that is 
 different. Without here attempting fully to explain 
 

 INTRODUCTION. 17 
 
 this relation, (which, indeed, is one of the hardest 
 problems of our philosophy,) we may observe that 
 they have this in common, that both are acquired 
 by acts of the mind exercised in connecting ex- 
 ternal impressions, and may be employed in con- 
 ducting a train of reasoning ; or, speaking loosely, 
 (for we cannot here pursue the subject so as to 
 arrive at philosophical exactness,) we may say, that 
 all notions and ideas are obtained by an inductive, 
 and may be used in a deductive process. But sci- 
 entific Ideas and common Notions differ in this, that 
 the former are precise and stable, the latter vague 
 and variable; the former are possessed with clear 
 insight, and employed in a sense rigorously limited, 
 and always identically the same; the latter have 
 grown up in the mind from a thousand dim and 
 diverse suggestions, and the obscurity and incon- 
 gruity which belongs to their origin hangs about 
 all their applications. Scientific Ideas can often be 
 adequately exhibited for all the purposes of rea- 
 soning, by means of Definitions and Axioms ; all 
 attempts to reason by means of Definitions from 
 common Notions, lead to empty forms or entire con- 
 fusion. 
 
 Such common Notions are sufficient for the com- 
 mon practical conduct of human life; but man is 
 not a practical creature merely ; he has within him 
 a speculative tendency, a pleasure in the contem- 
 plation of ideal relations, a love of knowledge as 
 knowledge. It is this speculative tendency which 
 VOL. i. C 
 
18 HISTORY OF INDUCTIVE SCIENCES. 
 
 brings to light the difference of common Notions 
 and scientific Ideas, of which we have spoken. The 
 mind analyzes such Notions, reasons upon them, 
 combines and connects them; for it feels assured 
 that intellectual things ought to be able to bear 
 such handling. Even practical knowledge, we see 
 clearly, is not possible without the use of the reason ; 
 and the speculative reason is only the reason satis- 
 fying itself of its own consistency. This speculative 
 faculty cannot be controlled from acting. The mind 
 cannot but claim a right to speculate concerning 
 all its own acts and creations ; yet, when it exercises 
 this right upon its common practical notions, we 
 find that it runs into barren abstractions and ever- 
 recurring cycles of subtlety. Such Notions are like 
 waters naturally stagnant; however much we urge 
 and agitate them, they only revolve in stationary 
 whirlpools. But the mind is capable of acquiring 
 scientific Ideas, which are fitted to undergo this 
 discussion and impulsion. When our speculations 
 are duly fed from the spring-heads of observation, 
 and frequently drawn off into the region of applied 
 science, we may have a living stream of consistent 
 and progressive knowledge. That science may be 
 both real as to its import, and logical as to its 
 form, the examples of many existing sciences suffi- 
 ciently prove. 
 
 School Philosophy. So long, however, as at- 
 tempts are made to form sciences, without such 
 a verification and realization of their fundamental 
 
INTRODUCTION. 19 
 
 ideas, there is, in the natural series of speculation, 
 no self-correcting principle. A philosophy con- 
 structed on notions obscure, vague, and unsub- 
 stantial, and held in spite of the want of corre- 
 spondence between its doctrines and the actual train 
 of physical events, may long subsist, and occupy 
 men's minds. Such a philosophy must depend for 
 its permanence upon the pleasure which men feel 
 in tracing the operations of their own and other 
 men's minds, and in reducing them to logical con- 
 sistency and systematical arrangement. 
 
 In these cases the main subjects of attention are 
 not external objects, but speculations previously 
 delivered ; the object is not to interpret nature, but 
 man's mind. The opinions of the masters are the 
 facts which the disciples endeavour to reduce to 
 unity, or to follow into consequences. A series of 
 speculators who pursue such a course, may properly 
 be termed a School, and their philosophy & School 
 Philosophy; whether their agreement in such a 
 mode of seeking knowledge arise from personal 
 communication and tradition, or be merely the 
 result of a community of intellectual character and 
 propensity. The two great periods of School Phi- 
 losophy (it will be recollected that we are here 
 directing our attention mainly to physical science), 
 were that of the Greeks and that of the Middle 
 Ages; the period of the first waking of science, and 
 that of its mid-day slumber. 
 
20 HISTORY OF INDUCTIVE SCIENCES. 
 
 What has been said thus briefly and imperfectly, 
 would require great detail and much explanation, 
 to give it its full significance and authority. But it 
 seemed proper to state so much in this place, in 
 order to render more intelligible and more instruc- 
 tive at the first aspect, the view of the attempted 
 or effected progress of science. 
 
 It is, perhaps, a disadvantage inevitably attend- 
 ing an undertaking like the present, that it must set 
 out with statements so abstract; and must present 
 them without their adequate developement and proof. 
 Such an Introduction, both in its character and its 
 scale of execution, may be compared to the geogra- 
 phical sketch of a country, with which the historian 
 of its fortunes often begins his narration. So much 
 of Metaphysics is as necessary to us as such a por- 
 tion of Geography is to the Historian of an Empire ; 
 and what has hitherto been said, is intended as a 
 slight outline of the Geography of that Intellectual 
 World, of which we have here to study the History. 
 
 To that History we now proceed. 
 
NOTES TO THE INTRODUCTION. 
 
 A HISTORY OF THE INDUCTIVE SCIENCES. This title has 
 the fault of seeming to exclude from the rank of Inductive 
 Sciences those which are not included in the History ; as 
 Ethnology and Glossology, Political Economy, Psychology. 
 This exclusion I by no means wish to imply ; but I could 
 find no other way of compendiously describing my sub- 
 ject, which was intended to comprehend those Sciences in 
 which, by the observation of facts and the use of reason, 
 systems of doctrine have been established which are uni- 
 versally received as truths among thoughtful men ; and 
 which may therefore be studied as examples of the manner 
 in which truth is to be discovered. Perhaps a more exact 
 description of the work would have been, A History of the 
 principal Sciences hitherto established by Induction. I may 
 add that I do not include in the phrase " Inductive Sci- 
 ences," the branches of Pure Mathematics, (Geometry, 
 Arithmetic, Algebra, and the like,) because, as I have 
 elsewhere stated (Phil. Ind. Sc., B. n. c. 1), these are 
 not Inductive but Deductive Sciences : they do not infer 
 true theories from observed facts, and more general from 
 more limited laws : but they trace the conditions of all 
 theory, the properties of space and number; and deduce 
 results from ideas without the aid of experience. The 
 History of these Sciences is briefly given in Chapter 13 of 
 the Book just referred to. 
 
 (A.) p. 7- The points belonging to the Philosophy of 
 the Sciences, which are briefly noticed in this Introduction, 
 
22 NOTES TO THE INTRODUCTION. 
 
 are considered more fully in my work on that subject. 
 The Antithesis of Facts and Ideas is treated of in Book i., 
 chapter 2, 3, 4 of that work : Successive Generalizations in 
 chap. 7 : Technical Terms in chap. 8 : Inductive Charts, 
 such as are here referred to in p. 13, are given with re- 
 ference to the History of Astronomy and of Optics, in 
 Book XL, chap. 6, of the Philosophy. Scientific Ideas, such 
 as are here spoken of in p. 16, are discussed in the Philo- 
 sophy, from Book n. to Book x. ; and the principal con- 
 troversies are there noticed by which this discussion has 
 been historically carried on. 
 
BOOK I. 
 
 HISTORY 
 
 OF THE 
 
 GREEK SCHOOL PHILOSOPHY, 
 
 WITH REFERENCE TO 
 
 PHYSICAL SCIENCE. 
 
Tis yap apx" &UTO vavriXias ; 
 Tis 8e KLvdvvos Kparcpols da/iai/- 
 TOS ftfjcrcv aXois ; 
 
 'ETTC! 8' e/ij3($Xot> 
 
 Kpe/jacrav aynvpas vnepBev 
 Xpva-eav xeipeo-0-i Xa/3toj/ (piaXav 
 'Ap%os cv 7rpvp.vq Trarep 
 'Eyx fLK *P avvov Z^a, Kai 
 
 arcay pinas, dvcpav T' e/caXei, 
 , Kal TTOVTOV KeXtvBovs, 
 "Ap.aTa T evfppova, KOI 
 VWTOI.O fioipav. 
 
 PINDAR. Pyth. iv. 124, 349. 
 
 Whence came their voyage ? them what peril held 
 With adamantine rivets firmly bound? 
 
 But soon as on the vessel's how 
 
 The anchor was hung up, 
 Then took the Leader on the prow 
 
 In hands a golden cup, 
 And on great Father Jove did call, 
 And on the Winds and Waters all, 
 
 Swept by the hurrying blast; 
 And on the Nights, and Ocean Ways, 
 And on the fair auspicious Days, 
 
 And loved return at last. 
 
BOOK I. 
 
 HISTORY OF THE GREEK SCHOOL PHILOSOPHY, 
 WITH REFERENCE TO PHYSICAL SCIENCE. 
 
 CHAPTER I. 
 PRELUDE TO THE GREEK. SCHOOL PHILOSOPHY. 
 
 Sect. 1. First Attempts of the Speculative Faculty 
 in Physical Inquiries. 
 
 AT an early period of history there appeared in 
 men a propensity to pursue speculative inqui- 
 ries concerning the various parts and properties of 
 the material world. What they saw excited them to 
 meditate, to conjecture, and to reason : they endea- 
 voured to account for natural events, to trace their 
 causes, to reduce them to their principles. This habit 
 of mind, or, at least that modification of it which we 
 have here to consider, seems to have been first un- 
 folded among the Greeks. And during that obscure 
 introductory interval which elapsed while the specu- 
 lative tendencies of men were as yet hardly disentan- 
 gled from the practical, those who were most eminent 
 in such inquiries were distinguished by the same 
 term of praise which is applied to sagacity in matters 
 of action, and were called wise men vo<pol. But 
 
26 THE GREEK SCHOOL PHILOSOPHY. 
 
 when it came to be clearly felt by such persons that 
 their endeavours were suggested by the love of 
 knowledge, a motive different from those which lead 
 to the wisdom of active life, a name was adopted of 
 a more appropriate, as well as of a more modest 
 signification, and they were termed philosophers, or 
 lovers of wisdom. This appellation is said 1 to have 
 been first assumed by Pythagoras. Yet he, in 
 Herodotus, instead of having this title, is called a 
 
 powerful Sophist 'EXX^iwi' ou TW da-OevecrTaTw ao- 
 
 <ncrTri TlvOayoprj 2 ', the historian using this word, as 
 it would seem, without intending to imply that 
 misuse of reason which the term afterwards came 
 to denote. The historians of literature place Pytha- 
 goras at the origin of the Italic School, one of the 
 two main lines of succession of the early Greek 
 philosophers: but the other, the Ionic School, which 
 more peculiarly demands our attention, in conse- 
 quence of its character and subsequent progress, is 
 deduced from Thales, who preceded the age of Phi- 
 losophy, and was one of the sophi, or "wise men 
 of Greece." 
 
 The Ionic School was succeeded in Greece by 
 several others ; and the subjects which occupied the 
 attention of these schools became very extensive. 
 In fact, the first attempts were, to form systems 
 which should explain ,the laws and causes of the 
 material universe; and to these were soon added all 
 the great questions which our moral condition and 
 
 1 ,Cic. Tusc. v. 3. 2 Herod, iv. 95. 
 
PRELUDE. 27 
 
 faculties suggest. The physical philosophy of these 
 schools is especially deserving of our study, as 
 exhibiting the character and fortunes of the most 
 memorable attempt at universal knowledge which 
 has ever been made. It is highly instructive to 
 trace the principles of this undertaking; for the 
 course pursued was certainly one of the most 
 natural and tempting which can be imagined; the 
 essay was made by a nation unequalled in fine 
 mental endowments, at the period of its greatest 
 activity and vigour; and yet it must be allowed, 
 (for, at least so far as physical science is concerned, 
 none will contest this,) to have been entirely unsuc- 
 cessful. We cannot consider otherwise than as an 
 utter failure, an endeavour to discover the causes 
 of things, of which the most complete results are 
 the Aristotelian physical treatises ; and which, after 
 reaching the point which these treatises mark, left 
 the human mind to remain stationary, at any rate 
 on all such subjects, for nearly two thousand years. 
 The early philosophers of Greece entered upon 
 the work of physical speculation in a manner which 
 showed the vigour and confidence of the question- 
 ing spirit, as yet untamed by labours and reverses. 
 It was for later ages to learn that man must 
 acquire, slowly and patiently, letter by letter, the 
 alphabet in which nature writes her answers to such 
 inquiries : the first students wished to divine, at a 
 single glance, the whole import, of her book. They 
 endeavoured to discover the origin and principle of 
 
28 THE GREEK SCHOOL PHILOSOPHY. 
 
 the universe; according to Thales, water was the 
 origin of all things, according to Anaximenes, air ; 
 and Heraclitus considered fire as the essential prin- 
 ciple of the universe. It has been conjectured, 
 with great plausibility, that this tendency to give 
 to their philosophy the form of a cosmogony, was 
 owing to the influence of the poetical cosmogonies 
 and theogonies which had been produced and ad- 
 mired at a still earlier age. Indeed, such wide and 
 ambitious doctrines as those which have been men- 
 tioned, were better suited to the dim magnificence 
 of poetry, than to the purpose of a philosophy which 
 was to bear the sharp scrutiny of reason. When 
 we speak of the principles of things, the term, even 
 now, is very ambiguous and indefinite in, its import, 
 but how much more was that the case in the first 
 attempts to use such abstractions ! The term which 
 is commonly used in this sense (apxn)> signified at 
 first the beginning ; and in its early philosophical 
 applications implied some obscure mixed reference 
 to the mechanical, chemical, organic, and historical 
 causes of the visible state of things, besides the 
 theological views which at this period were only just 
 beginning to be separated from the physical. Hence 
 we are not to be surprised if the sources from which 
 the opinions of this period appear to be derived are 
 rather vague suggestions and casual analogies, than 
 any reasons which will bear examination. Aristotle 
 conjectures, with considerable probability, that the 
 doctrine of Thales, according to which water was 
 
PRELUDE. 29 
 
 the universal element, resulted from the manifest 
 importance of moisture in the support of animal 
 and vegetable life 3 . But such precarious analyses 
 of these obscure and loose dogmas of early antiquity 
 are of small consequence to our object. 
 
 In more limited and more definite examples of 
 inquiry concerning the causes of natural appear- 
 ances, and in the attempts made to satisfy men's 
 curiosity in such cases, we appear to discern a more 
 genuine prelude to the true spirit of physical in- 
 quiry. One of the most remarkable instances of 
 this kind is to be found in the speculations which 
 Herodotus records, relative to the cause of the floods 
 of the Nile. " Concerning the nature of this river," 
 says the father of history 4 , " I was not able to learn 
 anything, either from the priests or from any one 
 besides, though I questioned them very pressingly. 
 For the Nile is flooded for a hundred days, be- 
 ginning with the summer solstice; and after this 
 time it diminishes, and is, during the whole winter, 
 very small. And on this head I was not able to 
 obtain anything satisfactory from any one of the 
 Egyptians, when I asked what is the power by 
 which the Nile is in its nature the reverse of other 
 rivers." 
 
 We may see, I think, in the historian's account, 
 
 that the Grecian mind felt a craving to discover the 
 
 reasons of things which other nations did not feel. 
 
 The Egyptians, it appears, had no theory, and felt 
 
 3 Metaph. i. 3. 4 Herod, ii. 19. 
 
30 THE GREEK SCHOOL PHILOSOPHY. 
 
 no want of a theory. Not so the Greeks ; they had 
 their reasons to render, though they were not such 
 as satisfied Herodotus. " Some of the Greeks," he 
 says, "who wish to be considered great philosophers, 
 
 ('EAA>/Vft)i/ Tive$ eTTicriiiJiOi /3ov\o/jLvoi yeveaOai cro(pir)v) 
 
 have propounded three ways of accounting for these 
 floods. Two of them," he adds, "I do not think 
 worthy of record, except just so far as to mention 
 them." But as these are some of the earliest Greek 
 essays in physical philosophy, it will be worth while, 
 even at this day, to preserve the brief notice he has 
 given of them, and his own reasonings upon the 
 same subject. 
 
 " One of these opinions holds that the Etesian 
 winds [which blew from the north] are the cause of 
 these floods, by preventing the Nile from flowing 
 into the sea." Against this the historian reasons 
 very simply and sensibly. "Very often when the 
 Etesian winds do not blow, the Nile is flooded 
 nevertheless. And moreover, if the Etesian winds 
 were the cause, all other rivers, which have their 
 course opposite to these winds, ought to undergo 
 the same changes as the Nile ; which the rivers of 
 Syria and Libya so circumstanced do not." 
 
 "The next opinion is still more unscientific, 
 (av7ri(TTritJiov6crTpr)) and is, in truth, marvellous for 
 its folly. This holds that the ocean flows all round 
 the earth, and that the Nile comes out of the ocean, 
 and by that means produces its effects." "Now," 
 says the historian, "the man who talks about this 
 
PRELUDE. 31 
 
 ocean-river, goes into the region of fable, where it 
 is not easy to demonstrate that he is wrong. I 
 know of no such river. But I suppose that Homer 
 or some of the earlier poets invented this fiction 
 and introduced it into their poetry." 
 
 He then proceeds to a third account, which to a 
 modern reasoner would appear not at all unphilo- 
 sophical in itself, but which he, nevertheless, rejects 
 in a manner no less decided than the others. " The 
 third opinion, though much the most plausible, is 
 still more wrong than the others ; for it asserts an 
 impossibility, namely, that the Nile proceeds from 
 the melting of the snow. Now the Nile flows out 
 of Libya, and through Ethiopia, which are very hot 
 countries, and thus comes into Egypt, which is a 
 colder region. How then can it proceed from 
 snow ?" He then offers several other reasons " to 
 show," as he says, " to any one capable of reasoning 
 
 on such subjects" (avSpi ye XoyifyaOai TOIOVTWI/ Trepi 
 
 dtp Te eovTi), that the assertion cannot be true. The 
 winds which blow from the southern regions are 
 hot ; the inhabitants are black ; the swallows and 
 kites (iKrlvoi) stay in the country the whole year; 
 the cranes fly the colds of Scythia, and seek their 
 warm winter-quarters there; which would not be 
 if it snowed ever so little." He adds another reason, 
 founded apparently upon some limited empirical 
 maxim of weather-wisdom taken from the climate 
 of Greece. " Libya," he says, " has neither rain nor 
 ice, and therefore no snow ; for, in five days after ;i 
 
32 THE GREEK SCHOOL PHILOSOPHY. 
 
 fall of snow there must be a fall of rain ; so that if 
 it snowed in those regions it must rain too." I need 
 not observe that Herodotus was not aware of the 
 difference between the climate of high mountains 
 and plains in a torrid region; but it is impossible 
 not to be struck both with the activity and the co- 
 herency of thought displayed by the Greek mind in 
 this primitive physical inquiry. 
 
 But I must not omit the hypothesis which Hero- 
 dotus himself proposes, after rejecting those which 
 have been already given. It does not appear to me 
 easy to catch his exact meaning, but the statement 
 will still be curious. "If," he says, "one who has 
 condemned opinions previously promulgated may 
 put forwards his own opinion concerning so obscure 
 a matter, I will state why it seems to me that the 
 Nile is flooded in summer." This opinion he pro- 
 pounds at first with an oracular brevity, which it is 
 difficult to suppose that he did not intend to be 
 impressive. " In winter the sun is carried by the 
 seasons away from his former course, and goes to 
 the upper parts of Libya. And there, in shoi% is 
 the whole account; for that region to which this 
 divinity (the sun) is nearest, must naturally be most 
 scant of water, and the river-sources of that country 
 must be dried up." 
 
 But the lively and garrulous Ionian immediately, 
 relaxes from this apparent reserve. "To explain 
 the matter more at length," he proceeds, " it is thus. 
 The sun, when he traverses the upper parts of Libya, 
 
PRELUDE. 33 
 
 does what he commonly does in summer; he draws 
 
 the water to him (e\/cet evr' ewi/rov TO vSwp), and 
 
 having thus drawn it, he pushes it to the upper 
 regions (of the air probably,) and then the winds 
 take it and disperse it till they dissolve in moisture. 
 And thus the winds which blow from those coun- 
 tries, Libs and Notus, are the most moist of all 
 winds. Now when the winter relaxes and the sun 
 returns to the north, he still draws water from all 
 the rivers, but they are increased by showers and 
 rain-torrents, so that they are in flood till the 
 summer comes ; and then, the rain failing and the 
 sun still drawing them, they become small. But 
 the Nile, not being fed by rains, yet being drawn 
 by the sun, is, alone of all rivers, much more scanty 
 in the winter than in the summer. For in summer 
 it is drawn like all other rivers, but in winter it 
 alone has its supplies shut up. And in this way, I 
 have been led to think the sun is the cause of the 
 occurrence in question." We may remark that the 
 historian here appears to ascribe the inequality of 
 the Nile at different seasons to the influence of the 
 sun upon its springs alone, the other cause of change, 
 the rains, being here excluded: and that, on this 
 supposition, the same relative effects would be pro- 
 duced whether the sun increase the sources in winter 
 by melting the snows, or diminish them in summer 
 by what he calls drawing them upwards. 
 
 This specimen of the early efforts of the Greeks 
 in physical speculations, appears to me to speak 
 VOL. i. D 
 
34 THE GREEK SCHOOL PHILOSOPHY. 
 
 strongly for the opinion that their philosophy on 
 such subjects was the native growth of the Greek 
 mind, and owed nothing to the supposed lore of 
 Egypt and the East; an opinion which has been 
 adopted with regard to the Greek philosophy in 
 general by the most competent judges on a full 
 survey of the evidence 5 . Indeed, we have no evi- 
 dence whatever that, at any period, the African or 
 Asiatic nations, (with the exception perhaps of the 
 Indians,) ever felt this importunate curiosity with 
 regard to the definite application of the idea of 
 cause and effect to visible phenomena ; or drew so 
 strong a line between a fabulous legend and a reason 
 rendered; or attempted to ascend to a natural cause 
 by classing together phenomena of the same kind. 
 We may be well excused, therefore, for believing 
 that they could not impart to the Greeks what they 
 themselves did not possess ; and so far as our survey 
 goes, physical philosophy has its origin, apparently 
 spontaneous and independent, in the active and 
 acute intellect of Greece. 
 
 Sect. 2. Primitive Mistake in Greek Physical 
 Philosophy. 
 
 WE now proceed to examine with what success the 
 Greeks followed the track into which they had thus 
 struck. And here we are obliged to confess that 
 
 5 Thirlwall, Hist. Gr., ii. 130; and, as there quoted, Ritter, 
 Geschichteder Philosophic^ i. 159173. 
 
PRELUDE. 35 
 
 they very soon turned aside from the right road 
 to truth, and deviated into a vast field of error, 
 in which they and their successors have wandered 
 almost to the present time. It is not necessary 
 here to inquire why those faculties which appear to 
 be bestowed upon us for the discovery of truth, 
 were permitted by Providence to fail so signally in 
 answering that purpose ; whether, like the powers 
 by which we seek our happiness, they involve a 
 responsibility on our part, and may be defeated by 
 rejecting the guidance of a higher faculty ; or 
 whether these endowments, though they did not 
 immediately lead man to profound physical know- 
 ledge, answered some nobler and better purpose in 
 his constitution and government. The fact un- 
 doubtedly was, that the physical philosophy of the 
 Greeks soon became trifling and worthless; and it 
 is proper to point out, as precisely as we can, in 
 what the fundamental mistake consisted. 
 
 To explain this, we may in the first place return 
 for a moment to Herodotus's account of the cause 
 of the floods of the Nile. 
 
 The reader will probably have observed a re- 
 markable phrase used by Herodotus, in his own 
 explanation of these inundations. He says that the 
 sun draws, or attracts, the water; a metaphorical 
 term, obviously intended to denote some more gene- 
 ral and abstract conception than that of the visible 
 operation which the word primarily signifies. This 
 abstract notion of ' drawing' is, in the historian, as 
 
 D2 
 
36 THE GREEK SCHOOL PHILOSOPHY. 
 
 we see, very vague and loose ; it might, with equal 
 propriety, be explained to mean what we now un- 
 derstand by mechanical or by chemical attraction, 
 or pressure, or evaporation. And in like manner, 
 all the first attempts to comprehend the operations 
 of nature, led to the introduction of abstract con- 
 ceptions, often vague, indeed, but not, therefore, 
 unmeaning ; such as motion and velocity, force and 
 pressure, impetus and momentum (/WJ). And the 
 next step in philosophizing, necessarily was to en- 
 deavour to make these vague abstractions more clear 
 and fixed, so that the logical faculty should be able 
 to employ them securely and coherently. But there 
 were two ways of making this attempt ; the one, by 
 examining the words only, and the thoughts which 
 they call up; the other, by attending to the facts 
 and things which bring these abstract terms into 
 use. The latter, the method of real inquiry, was 
 the way to success; but the Greeks followed the 
 former, the verbal or notional course, and failed. 
 
 If Herodotus, when the notion of the sun's at- 
 tracting the waters of rivers had entered into his 
 mind, had gone on to instruct himself, by attention 
 to facts, in what manner this notion could be made 
 more definite, while it still remained applicable to 
 all the knowledge which could be obtained, he would 
 have made some progress towards a true solution of 
 his problem. If, for instance, he had tried to ascer- 
 tain whether this Attraction which the sun exerted 
 upon the waters of rivers, depended on his influence 
 
PRELUDE. 37 
 
 at their fountains only, or was exerted over their 
 whole course, and over waters which were not parts 
 of rivers, he would have been led to reject his 
 hypothesis; for he would have found, by observa- 
 tions sufficiently obvious, that the sun's Attraction, 
 as shown in such cases, is a tendency to lessen all 
 expanded and open collections of moisture, whether 
 flowing from a spring or not ; and it would then be 
 seen that this influence, operating on the whole 
 surface of the Nile, must diminish it as well as 
 other rivers, in summer, and therefore could not 
 be the cause of its overflow. He would thus have 
 corrected his first loose conjecture by a real study 
 of nature, and might, in the course of his medita- 
 tions, have been led to available notions of Evapora- 
 tion, or other natural actions. And, in like manner, 
 in other cases, the rude attempts at explanation, 
 which the first exercise of the speculative faculty 
 produced, might have been gradually concentrated 
 and refined, so as to fall in, both with the requisi- 
 tions of reason and the testimony of sense. 
 
 But this was not the direction which the Greek 
 speculators took. On the contrary ; as soon as they 
 had introduced into their philosophy any abstract 
 and general conceptions, they proceeded to scrutinize 
 these by the internal light of the mind alone, with- 
 out any longer looking abroad into the world of 
 sense. They took for granted that philosophy must 
 result from the relations of those notions which are 
 involved in the common use of language, and they 
 
38 THE GREEK SCHOOL PHILOSOPHY. 
 
 proceeded to seek their philosophical doctrines by 
 studying such notions. They ought to have reformed 
 and fixed their usual conceptions by Observation; 
 they only analyzed and expanded them by Reflec- 
 tion: they ought to have sought by trial, among the 
 Notions which passed through their minds, some 
 one which admitted of exact application to Facts ; 
 they selected arbitrarily, and, consequently, erro- 
 neously, the Notions according to which Facts 
 should be assembled and arranged : they ought to 
 have collected clear Fundamental Ideas from the 
 world of things by inductive acts of thought ; they 
 only derived results by Deduction from one or 
 other of their familiar Conceptions (B). 
 
 When this false direction had been extensively 
 adopted by the Greek philosophers, we may treat 
 of it as the method of their Schools. Under that 
 title we must give a further account of it. 
 
39 
 
 CHAPTER II. 
 THE GREEK SCHOOL PHILOSOPHY. 
 
 Sect. 1. The general Foundation of the Greek 
 School Philosophy. 
 
 THE physical philosophy of the Greek Schools 
 was formed by looking at the material world 
 through the medium of that common language which 
 men employ to answer the common occasions of life; 
 and by adopting, arbitrarily, as the grounds of com- 
 parison of facts, and of inference from them, notions 
 more abstract and large than those with which 
 men are practically familiar, but not less vague and 
 obscure. Such a philosophy, however much it might 
 be systematized, by classifying and analyzing the 
 conceptions which it involves, could not overcome 
 the vices of its fundamental principle. But before 
 speaking of these defects, we must give some indi- 
 cations of its character. 
 
 The propensity to seek for principles in the com- 
 mon usages of language may be discerned at a very 
 early period. Thus we have an example of it in a 
 saying which is reported of Thales, the founder of 
 Greek philosophy 1 . When he was asked "What is 
 the greatest thing?" he replied, " Place; for all other 
 
 1 Pint. Conv. Sept. Sap. Diog. Laert. i. 35. 
 
40 THE GREEK SCHOOL PHILOSOPHY. 
 
 things are in the world, but the world is in it." In 
 Aristotle we have the consummation of this mode 
 of speculation. The usual point from which he 
 starts in his inquiries is, that tee say thus or thus in 
 common language. Thus, when he has to discuss 
 the question, whether there be, in any part of the 
 universe, a Void, or space in which there is nothing, 
 he inquires first in how many senses we say that 
 one thing is in another. He enumerates many of 
 these 2 ; we say the part is in the whole, as the finger 
 is in the hand ; again we say, the species is in the 
 genus, as man is included in animal; again, the 
 government of Greece is in the king; and various 
 other senses are described or exemplified, but of all 
 these the most proper is when we say a thing is in a 
 vessel, and generally, in place. He next examines 
 what place is, and comes to this conclusion, that 
 "if about a body there be another body including* 
 it, it is in place, and if not, not." A body moves 
 when it changes its place; but he adds, that if 
 water be in a vessel, the vessel being at rest, the 
 parts of the water may still move, for they are in- 
 cluded by each other ; so that while the whole does 
 not change its place, the parts may change their 
 places in a circular order. Proceeding then to the 
 question of a void, he, as usual, examines the dif- 
 ferent senses in which the term is used, and adopts, 
 as the most proper, place without matter ; with no 
 useful result, as we shall soon see. 
 2 Pbvsic. Ausc. iv. 3. 
 
ITS FOUNDATION. 41 
 
 Again 3 , in a question concerning mechanical 
 action, he says, "When a man moves a stone by 
 pushing it with a stick, we say both that the man 
 moves the stone, and that the stick moves the stone, 
 but the latter more properly." 
 
 Again, we find the Greek philosophers applying 
 themselves to extract their dogmas from the most 
 general and abstract notions which they could detect; 
 for example, from the conception of the Universe 
 as One or as Many things. They tried to determine 
 how far we may, or must, combine with these con- 
 ceptions that of a whole, of parts, of number, of 
 limits, of place, of beginning or end, of full or void, 
 of rest or motion, of cause and effect, and the like. 
 The analysis of such conceptions with such a view, 
 occupies, for instance, almost the whole of Aristo- 
 tle's Treatise on the Heavens. 
 
 The Dialogue of Plato, which is entitled Par^ 
 menides, appears at first as if its object were to show 
 the futility of this method of philosophizing; for 
 the philosopher whose name it bears, is represented 
 as arguing with an Athenian named Aristotle, (c) 
 and, by a process of metaphysical analysis, reduc- 
 ing him at least to this conclusion, "that whether 
 One exist, or do not exist, it follows that both it 
 and other things, with reference to themselves and 
 to each other, all and in all respects, both are and 
 are not, both appear and appear not." Yet the 
 method of Plato, so far as concerns truth of that 
 
 3 Phvsic. Ausc. viii. 5. 
 
42 THE GREEK SCHOOL PHILOSOPHY. 
 
 kind with which we are here concerned, was little 
 more efficacious than that of his rival. It consists 
 mainly, as may be seen in several of the dialogues, 
 and especially in the Timwus, in the application of 
 notions as loose as those of the Peripatetics; for 
 example, the conceptions of the Good, the Beau- 
 tiful, the Perfect ; and these are rendered still more 
 arbitrary, by assuming an acquaintance with the 
 views of the Creator of the universe. The philo- 
 sopher is thus led to maxims which agree with 
 those of the Aristotelians, that there can be no 
 void, that things seek their own place, and the 
 like 4 . 
 
 Another mode of reasoning, very widely applied 
 in these attempts, was the doctrine of contrarieties, 
 in which it was assumed, that adjectives or sub- 
 stantives which are in common language, or in some 
 abstract mode of conception, opposed to each other, 
 must point at some fundamental antithesis in nature, 
 which it is important to study. Thus Aristotle 5 
 says, that the Pythagoreans, from the contrasts 
 which number suggests, collected ten principles, 
 Limited and Unlimited, Odd and Even, One and 
 Many, Right and Left, Male and Female, Rest and 
 Motion, Straight and Curved, Light and Darkness, 
 Good and Evil, Square and Oblong. We shall see 
 hereafter, that Aristotle himself deduced the doc- 
 trine of Four Elements, and other dogmas, by oppo- 
 sitions of the same kind. 
 
 4 Timaeus, p. 80. 5 Metaph. 1. 5. 
 
ARISTOTELIAN PHYSICS. 43 
 
 The physical speculator of the present day will 
 learn without surprise, that such a mode of discus- 
 sion as this, led to no truths of real or permanent 
 value. The whole mass of the Greek philosophy, 
 therefore, shrinks into an almost imperceptible com- 
 pass, when viewed with reference to the progress of 
 physical knowledge. Still the general character of 
 this system, and its fortunes from the time of its 
 founders to the overthrow of their authority, are not 
 without their instruction, and, it may be hoped, not 
 without their interest. I proceed, therefore, to give 
 some account of these doctrines in their most fully 
 developed and permanently received form, that in 
 which they were presented by Aristotle. 
 
 Sect. 2. The Aristotelian Physical Philosophy. 
 
 THE principal physical treatises of Aristotle are, 
 the eight Books of " Physical Lectures," the four 
 Books "Of the Heavens," the two Books "Of Pro- 
 duction and Destruction:" for the Book "Of the 
 World" is now universally acknowledged to be 
 spurious ; and the " Meteorologies," though full of 
 physical explanations of natural phenomena, does 
 not exhibit the doctrines and reasonings of the 
 school in so general a form ; the same may be said 
 of the "Mechanical Problems." The treatises on 
 the various subjects of Natural History, " On Ani- 
 mals," "On the Parts of Animals," "On Plants," 
 "On Physiognomonics," "On Colours," "On Sound," 
 
44 THE GREEK SCHOOL PHILOSOPHY. 
 
 contain an extraordinary accumulation of facts, and 
 manifest a wonderful power of systematizing ; but 
 are not works which expound principles, and there- 
 fore do not require to be here considered. 
 
 The Physical Lectures are possibly the work 
 concerning which a well-known anecdote is related 
 by Simplicius, a Greek commentator of the sixth 
 century, as well as by Plutarch. It is said, that 
 Alexander the Great wrote to his former tutor to 
 this effect ; " You have not done well in publishing 
 these lectures ; for how shall we, your pupils, excel 
 other men, if you make that public to all, which we 
 learnt from you." To this Aristotle is said to have 
 replied ; " My Lectures are published and not pub- 
 lished ; they will be intelligible to those who heard 
 them, and to none beside." This may very easily 
 be a story invented and circulated among those who 
 found the work beyond their comprehension; and 
 it cannot be denied, that to make out the meaning 
 and reasoning of every part, would be a task very 
 laborious and difficult, if not impossible. But we 
 may follow the import of a large portion of the 
 Physical Lectures with sufficient clearness to appre- 
 hend the character and principles of the reasoning ; 
 and this is what I shall endeavour to do. 
 
 The author's introductory statement of his view 
 of the nature of philosophy falls in very closely with 
 what has been said, that he takes his facts and 
 generalizations as they are implied in the structure 
 of language. " We must in all cases proceed," he 
 
ARISTOTELIAN PHYSICS -15 
 
 says, "from what is known to what is unknown." 
 This will not be denied ; but we can hardly follow 
 him in his inference. He adds, " we must proceed, 
 therefore, from universal to particular. And some- 
 thing of this," he pursues, "may be seen in lan- 
 guage ; for names signify things in a general and 
 indefinite manner, as circle, and by defining we un- 
 fold them into particulars." He illustrates this by 
 saying, " thus children at first call all men father, 
 and all women mother, but afterwards distinguish." 
 In accordance with this view, he endeavours to 
 settle several of the great questions concerning the 
 universe, which had been started among subtle and 
 speculative men, by unfolding the meaning of the 
 words and phrases which are applied to the most 
 general notions of things and relations. We have 
 already noticed this method. A few examples will 
 ' illustrate it further : Whether there was or was 
 not a void, or place without matter, had already been 
 debated among rival sects of philosophers. The an- 
 tagonist arguments were briefly these: There must 
 be a void, because a body cannot move into a space 
 except it is empty, and therefore without a void 
 there could be no motion : and, on the other hand, 
 there is no void, for the intervals between bodies 
 are filled with air, and air is something. These 
 opinions had even been supported by reference to 
 experiment. On the one hand, Anaxagoras and 
 his school had shown, that air when confined, re- 
 sisted compression, by squeezing a blown bladder, 
 
46 THE GREEK SCHOOL PHILOSOPHY. 
 
 and pressing down an inverted vessel in the water ; 
 on the other hand, it was alleged that a vessel full 
 of fine ashes held as much water as if the ashes 
 were not there, which could only be explained by 
 supposing void spaces among the ashes. Aristotle 
 decides that there is no void, on such arguments as 
 this 6 : In a void there could be no difference of up 
 and down; for as in nothing there are no differences, 
 so there are none in a privation or negation ; but a 
 void is merely a privation or negation of matter; 
 therefore, in a void, bodies could not move up and 
 down, which it is in their nature to do. It is easily 
 seen that such a mode of reasoning elevates the 
 familiar forms of language and the intellectual con- 
 nexions of terms, to a supremacy over facts ; making 
 truth depend upon whether terms are or are not 
 privative, and whether we say that bodies fall na- 
 turally. In such a philosophy every new result of 
 observation would be compelled to conform to the 
 usual combinations of phrases, as these had become 
 associated by the modes of apprehension previously 
 familiar. 
 
 It is not intended here to intimate that the com- 
 mon modes of apprehension, which are the basis of 
 common language, are limited and casual. They 
 imply, on the contrary, universal and necessary con- 
 ditions of our perceptions and conceptions : thus all 
 things are necessarily apprehended as existing in 
 Time and Space, and as connected by relations of 
 
 6 Physic. Ausc. iv. 7- P- 215. 
 
ARISTOTELIAN PHYSICS. 47 
 
 Cause and Effect ; and so far as the Aristotelian phi- 
 losophy reasons from these assumptions, it has a 
 real foundation, though even in this case the con- 
 clusions are often insecure. We have an example 
 of this reasoning in the eighth Book 7 , where he 
 proves that there never was a time in which change 
 and motion did not exist ; " For if all things were 
 at rest, the first motion must have been produced 
 by some change in some of these things; that is, 
 there must have been a change before the first 
 change ;" and again, " How can before and after 
 apply when time is not ? or how can time be when 
 motion is not ? If," he adds, " time is a numeration 
 of motion, and if time be eternal, motion must be 
 eternal." But he sometimes introduces principles of 
 a more arbitrary character ; and besides the general 
 relations of thought, takes for granted the inven- 
 tions of previous speculators ; such, for instance, as 
 the then commonly received opinions concerning 
 the frame of the world. From the assertion that 
 motion is eternal, proved in the manner just stated, 
 Aristotle proceeds by a curious train of reasoning, 
 to identify this eternal motion with the diurnal 
 motion of the heavens. " There must," he says, " be 
 something which is the First Mover 8 :" this follows 
 from the relation of causes and effects. Again, 
 "motion must go on constantly, and, therefore, 
 must be either continuous or successive. Now what 
 
 7 Physic. Ausc. viii. 1. p. 251. 
 3 Physic. Ausc. viii. 6. p. 258. 
 
48 THE GREEK SCHOOL PHILOSOPHY. 
 
 is continuous is more properly said to take place 
 constantly, than what is successive. Also the con- 
 tinuous is better ; but we always suppose that which 
 is better to take place in nature, if it be possible.. 
 The motion of the First Mover will, therefore, be 
 continuous, if such an eternal motion be possible." 
 We here see the vague judgment of better and worse 
 introduced, as that of natural and unnatural was 
 before, into physical reasonings. 
 
 I proceed with Aristotle's argument 9 . "We 
 have now, therefore, to show that there may be an 
 infinite, single, continuous motion, and that this is 
 circular." This is, in fact, proved, as may readily 
 be conceived, from the consideration that a body 
 may go on perpetually revolving uniformly in a 
 circle. And thus we have a demonstration, on the 
 principles of this philosophy, that there is and must 
 be a First Mover, revolving eternally with a uni- 
 form circular motion. 
 
 Though this kind of philosophy may appear too 
 trifling to deserve being dwelt upon, it is important 
 for our purpose so far as to exemplify it, that we 
 may afterwards advance, confident that we have 
 done it no injustice. 
 
 I will now pass from the doctrines relating to 
 the motions of the heavens, to those which concern 
 the material elements of the universe. And here it 
 may be remarked that the tendency (of which we 
 are here tracing the developement) to extract specu- 
 9 viii. 8. 
 
ARISTOTELIAN PHYSICS. 49 
 
 lative opinions from the relations of words, must be 
 very natural to man ; for the very widely accepted 
 doctrine of the Four Elements which appears to be 
 founded on the opposition of the adjectives hot and 
 cold, wet and dry, is much older than Aristotle, and 
 was probably one of the earliest of philosophical 
 dogmas. The great master of this philosophy, how- 
 ever, puts the opinion in a more systematic manner 
 than his predecessors. 
 
 " We seek," he says 10 , " the principles of sensible 
 things, that is, of tangible bodies. We must take, 
 therefore, not all the contrarieties of quality, but 
 those only which have reference to the touch. Thus 
 black and white, sweet and bitter, do not differ as 
 tangible qualities, and therefore must be rejected 
 from our consideration. 
 
 "Now the contrarieties of quality which refer 
 to the touch are these : hot, cold ; dry, wet ; heavy, 
 light; hard, soft; unctuous, meagre; rough, smooth; 
 dense, rare." He then proceeds to reject all but the 
 four first of these, for various reasons ; heavy and 
 light, because they are not active and passive quali- 
 ties; the others, because they are combinations of 
 the four first, which therefore he infers to be the 
 four elementary qualities. 
 
 ""Now in four things there are six combina- 
 tions of two ; but the combinations of two opposites, 
 as hot and cold, must be rejected ; we have, there- 
 fore, four elementary combinations, which agree 
 
 10 De Gen. et Corrupt ii. 2. " iii. 3. 
 
 VOL. I. E 
 
50 THE GREEK SCHOOL PHILOSOPHY. 
 
 with the four apparently elementary bodies. Fire 
 is hot and dry; air is hot and wet (for steam is air); 
 water is cold and wet, earth is cold and dry." 
 
 It may be remarked that this disposition to as- 
 sume that some common elementary quality must 
 exist in the cases in which we habitually apply a 
 common adjective, as it began before the reign of 
 the Aristotelian philosophy, so also survived its 
 influence. Not to mention other cases, it would be 
 difficult to free Bacon's Inquisitio in naturam 
 calidi, "Examination of the nature of heat," from 
 the charge of confounding together very different 
 classes of phenomena under the cover of the word 
 hot. 
 
 The correction of these opinions concerning the 
 elementary composition of bodies belongs to an ad- 
 vanced period in the history of physical knowledge, 
 even after the revival of its progress. But there 
 are some of the Aristotelian doctrines which parti- 
 cularly deserve our attention, from the prominent 
 share they had in the very first beginnings of that 
 revival, I mean the doctrines concerning motion. 
 
 These are still founded upon the same mode of 
 reasoning from adjectives ; but in this case, the re- 
 sult follows, not only from the opposition of the 
 words, but also from the distinction of their being 
 absolutely or relatively true. "Former writers," 
 says Aristotle, "have considered heavy and light 
 relatively only, taking cases, where both things have 
 weight, but one is lighter than the other ; and they 
 
ARISTOTELIAN PHYSICS. 51 
 
 imagined that, in this way, they defined what was 
 absolutely (aTrAoJs) heavy and light." We now know 
 that things which rise by their lightness do so only 
 because they are pressed upwards by heavier sur- 
 rounding bodies; and this assumption of absolute 
 levity, which is evidently gratuitous, or rather 
 merely nominal, entirely vitiated the whole of the 
 succeeding reasoning. The inference was, that fire 
 must be absolutely light, since it tends to take its 
 place above the other three elements ; earth abso- 
 lutely heavy, since it tends to take its place below 
 fire, air, and water. The philosopher argued also, 
 with great acuteness, that air, which tends to take 
 its place below fire and above water, must do so by 
 its nature, and not in virtue of any combination of 
 heavy and light elements. " For if air were com- 
 posed of the parts which give fire its levity, joined 
 with other parts which produce gravity, we might 
 assume a quantity of air so large, that it should be 
 lighter than a small quantity of fire, having more 
 of the light parts." It thus follows that each of the 
 four elements tends to its own place, fire being the 
 highest, air the next, water the next, and earth tile 
 lowest. 
 
 The whole of this train of errors arises from 
 fallacies which have a verbal origin; from consi- 
 dering light as opposite to heavy; and from con- 
 sidering levity as a quality of a body, instead of 
 regarding it as the effect of surrounding bodies. 
 
 It is worth while to notice that a difficulty which 
 
 E2 
 
52 THE GREEK SCHOOL PHILOSOPHY. 
 
 often embarrasses persons on their entrance upon 
 physical speculations, the difficulty of conceiving 
 that up and down are different directions in dif- 
 ferent places, had been completely got over by 
 Aristotle and the Greek philosophers. They were 
 steadily convinced of the roundness of the earth, 
 and saw that this truth led to the conclusion that 
 all heavy bodies tend in converging directions to 
 the centre. And, they added, as the heavy tends 
 to the centre, the light tends to the exterior, 
 " for Exterior is opposite to Centre as heavy is to 
 light 12 ." 
 
 The tendencies of bodies downwards and up- 
 wards, their weight, their fall, their floating or sink- 
 ing, were thus accounted for in a manner which, 
 however unsound, satisfied the greater part of the 
 speculative world till the time of Galileo and Ste- 
 vinus, though Archimedes in the mean time pub- 
 lished the true theory of floating bodies, which is 
 very different from that above stated. Other parts 
 of the doctrines of motion were delivered by the 
 Stagirite in the same spirit and with the same suc- 
 cess. The motion of a body which is thrown along 
 the ground diminishes and finally ceases; the motion 
 of a body which falls from a height goes on becom- 
 ing quicker and quicker ; this was accounted for on 
 the usual principle of opposition, by saying that the 
 former is a violent, the latter a natural motion. 
 And the later writers of this school expressed the 
 12 De Coelo, iv. 4, 
 
ARISTOTELIAN PHYSICS. 53 
 
 characters of such motions in verse. The rule of 
 natural motion was 13 
 
 Principium tepeat, medium cum fine calebit. 
 Cool at the first, it warm and warmer glows. 
 
 And of violent motion, the law was 
 
 Principium fervet, medium calet, ultima friget. 
 Hot at the first, then barely warm, then cold. 
 
 It appears to have been considered by Aristotle 
 a difficult problem to explain why a stone thrown 
 from the hand continues to move for some time, and 
 then stops. If the hand was the cause of the mo- 
 tion, how could the stone move at all when left 
 to itself? if not, why does it ever stop? And he 
 answers this difficulty by saying 14 , "that there is a 
 motion communicated to the air, the successive parts 
 of which urge the stone onwards;, and that each 
 part of this medium continues to act for some while 
 after it has been acted on, and the motion ceases 
 when it comes to a particle which cannot act after 
 it has ceased to be acted on." It will be readily 
 seen that the whole of this difficulty, concerning a 
 body which moves forwards and is retarded till it 
 stops, arises from ascribing the retardation, not to 
 the real cause, the surrounding resistances, but to 
 the body itself. 
 
 One of the doctrines which was the subject of 
 the warmest discussion between the defenders and 
 opposers of Aristotle, at the revival of physical 
 
 13 Alsted. Encyc. torn i. p. 687- M Phys. Ausc. viii. 10. 
 
54 THE GREEK SCHOOL PHILOSOPHY. 
 
 knowledge, was that in which he asserts 15 "That 
 body is heavier than another which in an equal bulk 
 moves downward quicker." The opinion maintained 
 by the Aristotelians at the time of Galileo was, that 
 bodies fall quicker exactly in proportion to their 
 weight. The master himself asserts this in express 
 terms, and reasons upon it 16 . Yet in another passage 
 he appears to distinguish between weight and actual 
 motion downwards 17 . "In physics, we call bodies 
 heavy and light from their power of motion ; but 
 these names are not applied to their actual opera- 
 tions (evepyeiais) except any one thinks momentum 
 (poTrrj) to be a word of both applications. But 
 heavy and light are, as it were, the embers or sparks 
 of motion, and therefore proper to be treated of 
 here." 
 
 The distinction just alluded to between Power or 
 Faculty of Action, and actual Operation or Energy, 
 is one very frequently referred to by Aristotle ; and 
 though not by any means useless, may easily be so 
 used as to lead to mere verbal refinements instead 
 of substantial knowledge. 
 
 The Aristotelian distinction of Causes has not 
 any very immediate bearing upon the parts of phy- 
 sics of which we have here mainly spoken ; but it 
 was so extensively accepted, and so long retained, 
 that it may be proper to notice it 18 . " One kind of 
 
 15 De Coelo, iv. 1, p. 308. 16 De Ccelo, iii. 2. 
 
 17 De Coelo, iv. 1, p. 307- 18 Phys. ii. 3. 
 
ARISTOTELIAN PHYSICS. 55 
 
 Cause is the matter of which any thing is made, as 
 bronze of a statue, and silver of a phial ; another is 
 the form and pattern, as the Cause of an octave is 
 the ratio of two to one ; again, there is the Cause 
 which is the origin of the production, as the father 
 of the child ; and again, there is the End, or that 
 for the sake of which anything is done, as health 
 is the cause of walking." These four kinds of Cause, 
 the material, informal, the efficient, and the final, 
 were long leading points in all speculative inquiries; 
 and our familiar forms of speech still retain traces 
 of the influence of this division. 
 
 It is my object here to present to the reader in 
 an intelligible shape, the principles and mode of 
 reasoning of the Aristotelian philosophy, not its 
 results. If this were not the case, it would be easy 
 to excite a smile by insulating some of the passages 
 which are most remote from modern notions. I 
 will only mention, as specimens, two such passages, 
 both very remarkable. 
 
 In the beginning of the book " On the Heavens,'' 
 he proves 19 the world to be perfect, by reasoning of 
 the following kind : " The bodies of which the world 
 is composed are solids, and therefore have three 
 dimensions ; now three is the most perfect number ; 
 it is the first of numbers, for of one we do not speak 
 as a number ; of two we say both ; but three is the 
 first number of which we say all; moreover, it has 
 a beginning, a middle, and an end." 
 
 19 De Coelo, i. 1. 
 
56 THE GREEK SCHOOL PHILOSOPHY. 
 
 The reader will still perceive the verbal founda- 
 tions of opinions thus supported. 
 
 " The simple elements must have simple motions, 
 and thus fire and air have their natural motions 
 upwards, and water and earth have their natural 
 motions downdards; but besides these motions, there 
 is motion in a circle, which is unnatural to these 
 elements, but which is a more perfect motion than 
 the other, because a circle is a perfect line, and a 
 straight line is not; and there must be something 
 to which this motion is natural. From this it is 
 evident," he adds, with obvious animation, "that 
 there is some essence of body different from those 
 of the four elements, more divine than those, and 
 superior to them. If things which move in a circle 
 move contrary to nature, it is marvellous, or rather 
 absurd, that this, the unnatural motion, should alone 
 be continuous and eternal; for unnatural motions 
 decay speedily. And so, from all this, we must col- 
 lect, that besides the four elements which we have 
 here and about us, there is another removed far 
 off, and the more excellent in proportion as it is 
 more distant from us." This fifth element was the 
 " quinta essentia" of after writers, of which we have 
 a trace in our modern literature, in the word quint- 
 essence. 
 
ITS TECHNICAL FORMS. 57 
 
 Sect. 3. Technical Forms of the Greek Schools. 
 
 WE have hitherto considered only the principle of 
 the Greek Physics ; which was, as we have seen, to 
 deduce its doctrines by an analysis of the notions 
 which common language involves. But though the 
 Grecian philosopher began by studying words in 
 their common meanings, he soon found himself led 
 to fix upon some special shades or applications of 
 these meanings as the permanent and standard 
 notion, which they were to express; that is, he made 
 his language technical. The invention and esta- 
 blishment of technical terms is an important step 
 in any philosophy, true or false ; we must, there- 
 fore, say a few words on this process, as exemplified 
 in the ancient systems. 
 
 1. Technical Forms of the Aristotelian Philo- 
 sophy. We have already had occasion to cite some 
 of the distinctions introduced by Aristotle, which 
 may be considered as technical; for instance, the 
 classification of Causes as material, formal, efficient, 
 and final; and the opposition of Qualities as absolute 
 and relative. A few more of the most important 
 examples may suffice. An analysis of objects into 
 Matter and Form, when metaphorically extended 
 from visible objects to things conceived in the most 
 general manner, became an habitual hypothesis of 
 the Aristotelian school. Indeed this metaphor is 
 even yet one of the most significant of those which 
 we can employ, to suggest one of the most compre- 
 
58 THE GREEK SCHOOL PHILOSOPHY. 
 
 hensive and fundamental antitheses with which phi- 
 losophy has to do; the opposition of sense and 
 reason, of impressions and laws. In this application, 
 the German philosophers have, up to the present 
 time, rested upon this distinction a great part of the 
 weight of their systems ; as when Kant says, that 
 Space and Time are the Forms of Sensation. Even 
 in our own language, we retain a trace of the in- 
 fluence of this Aristotelian notion, in the word 
 Information, when used for that knowledge, which 
 may be conceived as moulding the mind into a 
 definite shape, instead of leaving it a mere mass of 
 unimpressed susceptibility. * <; 
 
 Another favourite Aristotelian antithesis is that 
 of Power and Act (3i/Va/xis, evepyeia). This distinc- 
 tion is made the basis of most of the physical phi- 
 losophy of the school; being, however, generally 
 introduced with a peculiar limitation. Thus, Light 
 is defined to be " the Act of what is lucid, as being 
 lucid. And if," it is added, "the lucid be so in 
 power but not in act, we have darkness." The 
 reason of the limitation, " as being lucid," is, that a 
 lucid body may act in other ways ; thus a torch may 
 move as well as shine, but its moving is not its act 
 as being a lucid body. 
 
 Aristotle appears to be well satisfied with this 
 explanation, for he goes on to say, " Thus Light is 
 not Fire, nor any body whatever, or the emanation 
 of any body, (for that would be a kind of body,) but 
 it is the presence of something like Fire in the 
 
ITS TECHNICAL FORMS. f>9 
 
 body; it is, however, impossible that two bodies 
 should exist in the same place, so that it is not a 
 body;" and this reasoning appears to leave him 
 more satisfied with his doctrine, that Light is an 
 Energy or Act. 
 
 But we have a more distinctly technical form 
 given to this notion. Aristotle introduced a word 
 formed by himself, to express the act which is thus 
 opposed to inactive power: this is the celebrated 
 word tWeXe'^eia. Thus the noted definition of Mo- 
 tion in the third book of the Physics 20 , is that it is 
 "the Entelechy, or Act, of a moveable body in 
 respect of being moveable;" and the definition of 
 the Soul is 21 that it is " the Entelecliy of a natural 
 body which has life by reason of its power." This 
 word has been variously translated by the followers 
 of Aristotle, and some of them have declared it 
 untranslateable. Act and Action are held to be 
 inadequate substitutes; the very act, ipse cursus 
 actionis is employed by some; primus actus is 
 employed by many, but another school use pri- 
 mus actus of a non-operating form. Budseus uses 
 efficacia. Cicero 22 translates it "quasi quandam 
 continuatam motionem, et perennem ;" but this pa- 
 raphrase, though it may fall in with the description 
 of the soul, which is the subject with which Cicero 
 is concerned, does not appear to agree with the 
 general applications of the term. Hermolaus Bar- 
 barus is said to have been so much oppressed with 
 
 20 Phys. in. 1. 2 ' De Anima. ii. 1. 22 Tusc. i. 10. 
 
60 THE GREEK SCHOOL PHILOSOPHY. 
 
 this difficulty of translation, that he consulted the 
 evil spirit by night, entreating to be supplied with 
 a more common and familiar substitute for this 
 word : the mocking fiend, however, suggested only 
 a word equally obscure, and the translator, discon- 
 tented with this, invented for himself the word per- 
 fectihabia. 
 
 We need not here notice the endless apparatus 
 of technicalities which was, in later days, introduced 
 into the Aristotelian philosophy; but we may re- 
 mark, that their long continuance and extensive use 
 show us how powerful technial phraseology is, for 
 the perpetuation either of truth or error. The Aris- 
 totelian terms, and the metaphysical views which 
 they tend to preserve, are not yet extinct among us. 
 In a very recent age of our literature it was thought 
 a worthy employment by some of the greatest 
 writers of the day, to attempt to expel this system 
 of technicalities by ridicule. 
 
 "Crambe regretted extremely that substantial 
 forms, a race of harmless beings, which had lasted 
 for many years, and afforded a comfortable subsist- 
 ence to many poor philosophers, should now be 
 hunted down like so many wolves, without a possi- 
 bility of retreat. He considered that it had gone 
 much harder with them than with essences, which 
 had retired from the schools into the apothecaries* 
 shops, where some of them had been advanced to 
 the degree of quintessences. 
 
 23 Martinus Scriblerus, cap. vii. 
 
ITS TECHNICAL FORMS. 61 
 
 We must now say a few words on the technical 
 terms which others of the Greek philosophical sects 
 introduced. 
 
 2. Technical Forms of the Platonists. The 
 other sects of the Greek philosophy, as well as the 
 Aristotelians, invented and adopted technical terms, 
 and thus gave fixity to their tenets and consist- 
 ency to their traditionary systems ; of these I will 
 mention a few. 
 
 A technical expression of a contemporary school 
 has acquired perhaps greater celebrity than any of 
 the terms of Aristotle. I mean the Ideas of Plato. 
 The account which Aristotle gives of the origin of 
 these will serve to explain their nature 21 . " Plato," 
 says he, " who, in his youth, was in habits of com- 
 munication first with Cratylus and the Heraclitean 
 opinions, which represent all the objects of sense 
 as being in a perpetual flux, so that concerning 
 these no science nor certain knowledge can exist, 
 entertained the same opinions at a later period also. 
 When, afterwards, Socrates treated of moral sub- 
 jects, and gave no attention to physics, but in the 
 subjects which he did discuss, arrived at univer- 
 sal truths, and before any other man, turned his 
 thoughts to definitions, Plato adopted similar doc- 
 trines on this subject also ; and construed them in 
 this way, that these truths and definitions must be 
 applicable to something else, and not to sensible 
 
 24 Arist. Metaph. i. 6. The same account is repeated, and 
 the subject discussed, Metaph. xii. 4. 
 
62 THE GREEK SCHOOL PHILOSOPHY. 
 
 things : for it was impossible, he conceived, that 
 there should be a general common definition of any 
 sensible object, since such were always in a state of 
 change. The things, then, which were the subjects 
 of universal truths he called Ideas ; and held that 
 objects of sense had their names according to Ideas 
 and after them ; so that things participated in that 
 Idea which had the same name as was applied to 
 them." 
 
 In agreement with this, we find the opinions 
 suggested in the Parmenides of Plato, the dialogue 
 which is considered by many to contain the most 
 decided exposition of the doctrine of Ideas. In this 
 dialogue, Parmenides is made to say to Socrates, 
 then a young man 25 , " Socrates, philosophy has 
 not yet claimed you for her own, as, in my judg- 
 ment, she will claim you, and you will not dishonour 
 her. As yet, like a young man as you are, you look 
 to the opinions of men. But tell me this : it ap- 
 pears to you, as you say, that there are certain 
 Kinds or Ideas (ei^) of which things partake and 
 receive applications according to that of which they 
 partake : thus those things which partake of Like- 
 ness are called like ; those things which partake of 
 Greatness are called great ; those things which par- 
 take of Beauty and Justice are called beautiful and 
 just" To this Socrates assents. And in another part 
 of the dialogue he shows that these Ideas are not 
 included in our common knowledge, from whence 
 
 26 Parmenid. p. 131. 
 
ITS TECHNICAL FORMS. 63 
 
 he infers that they are objects of the Divine 
 mind. 
 
 In the Phsedo the same opinion is maintained, 
 and is summed up in this way, by a reporter of the 
 last conversation of Socrates 26 elvai TL eVaa-roi/ ru>v 
 
 , Kal TOVTWV -r'aXAa /uLeTaXanfidvovTa avTwv TOVTWV 
 
 yew \ " that each Kind has an exist- 
 ence, and that other things partake of these Kinds, 
 and are called according to the Kind of which they 
 partake." 
 
 The inference drawn from this view was, that 
 in order to obtain true and certain knowledge, men 
 must elevate themselves, as much as possible, to 
 these Ideas of the qualities which they have to 
 consider : and as things were thus called after the 
 Ideas, the Ideas had a priority and pre-eminence 
 assigned them. The Idea of Good, Beautiful, and 
 Wise, was the " First Good," the " First Beautiful," 
 the "First Wise." This dignity and distinction 
 were ultimately carried to a large extent. Those 
 Ideas were described as eternal and self-subsisting, 
 forming an " Intelligible World," full of the models 
 or archetypes of created things. But it is not to 
 our purpose here to consider the Platonic Ideas in 
 their theological bearings. In physics they were 
 applied in the same form as in morals. The primum 
 calidum, primum frigidum, were those Ideas or 
 fundamental Principles by participation of which, all 
 things were hot or cold. 
 
 28 Pheedo, p. 102. 
 
04 THE GREEK SCHOOL PHILOSOPHY. 
 
 This school did not much employ itself in the 
 developement of its principles as applied to physical 
 inquiries : but we are not without examples of such 
 speculations. Plutarch's Treatise Uept TOV Tipwrov 
 ^v^pov 9 " On the First Cold," may be cited as one. 
 It is in reality a discussion of a question which has 
 been agitated in modern times also ; whether cold 
 be a positive quality or a mere privation. " Is there, 
 O Favorinus," he begins, " a First Power and Essence 
 of the Cold, as Fire is of the Hot ; by a certain pre- 
 sence and participation of which all other things are 
 cold : or is rather coldness a privation of heat, as 
 darkness is of light, and rest of motion ?" 
 
 3. Technical Forms of the Pythagoreans. The 
 Numbers of the Pythagoreans, when propounded 
 as the explanation of physical phenomena, as they 
 were, are still more obscure than the ideas of the 
 Platonists. There were, indeed, considerable re- 
 semblances in the way in which these two kinds of 
 notions were spoken of. Plato called his Ideas 
 unities, monads ; and as, according to him, Ideas, so, 
 according to the Pythagoreans, Numbers, were the 
 causes of things being what they are 87 . But there 
 was this difference, that things shared the nature of 
 the Platonic Ideas "by participation," while they 
 shared the nature of Pythagorean Numbers "by 
 imitation." Moreover, the Pythagoreans followed 
 their notion out into much greater developement 
 than any other school, investing particular numbers 
 
 27 Arist. Metapb. i. 6. 
 
ARISTOTELIAN PHYSICS. 65 
 
 with extraordinary attributes, and applying them 
 by very strange and forced analogies. Thus the 
 number Four, to which they gave the name of 
 Tetractys, was held to be the most perfect number, 
 and was conceived to correspond to the human 
 soul, in some way which appears to be very imper- 
 fectly understood by the commentators of this phi- 
 losophy. 
 
 It has been observed by a distinguished modern 
 scholar 28 , that the place which Pythagoras ascribed 
 to his numbers is intelligible only by supposing that 
 he confounded, first a numerical unit with a geo- 
 metrical point, and then this with a material atom. 
 But this criticism appears to place systems of phy- 
 sical philosophy under requisitions too severe. If 
 all the essential properties and attributes of things 
 were fully represented by the relations of number, 
 the philosophy which supplied such an explanation 
 of the universe, might well be excused from ex- 
 plaining also that existence of objects which is dis- 
 tinct from the existence of all their qualities and 
 properties. The Pythagorean love of numerical 
 speculations might have been combined with the 
 doctrine of atoms, and the combination might have 
 led to results well worth notice. But so far as we 
 are aware, no such combination was attempted in 
 the ancient schools of philosophy; and perhaps 
 we of the present day are only just beginning to 
 perceive, through the disclosures of chemistry and 
 
 28 Thirl wall's Hist. Gr. ii. 142. 
 VOL. I. F 
 
66 THE GREEK SCHOOL PHILOSOPHY. 
 
 crystallography, the importance of such a line of 
 inquiry. 
 
 4. Technical Forms of the Atomists and Others. 
 The atomic doctrine, of which we have just 
 spoken, was one of the most definite of the physical 
 doctrines of the ancients, and was applied with 
 most perseverance and knowledge to the expla- 
 nation of phenomena. Though, therefore, it led to 
 no success of any consequence in ancient times, it 
 served to transmit, through a long series of ages, 
 a habit of really physical inquiry; and on this 
 account, has been thought worthy of an historical 
 disquisition by Bacon 29 . 
 
 The technical term, Atom, marks sufficiently the 
 nature of the opinion. According to this theory, 
 the world consists of a collection of simple particles, 
 of one kind of matter, and of indivisible smallness, 
 (as the name indicates,) and by the various confi- 
 gurations and motions of these particles, all kinds of 
 matter and all material phenomena are produced. 
 
 To this, the Atomic Doctrine of Leucippus and 
 Democritus, was opposed the Homoiomeria of Anax- 
 agoras; that is, the opinion that material things 
 consist of particles which are homogeneous in each 
 kind of body, but various in different kinds : thus 
 for example, since by food the flesh and blood and 
 bones of man increase, the author of this doc- 
 trine held that there are in food particles of flesh, 
 
 w Parmenidis et Telesii et praecipue Democriti Philosophia, 
 c., Works, vol. ix. 317. 
 

 ITS TECHNICAL FORMS. (17 
 
 and blood, and bone. As the former tenet points 
 to the corpuscular theories of modern times, so the 
 latter may be considered as a dim glimpse of the 
 idea of chemical analysis. The Stoics also, who 
 were, especially at a later period, inclined to ma- 
 terialist views, had their technical modes of speak- 
 ing on such subjects. They asserted that matter 
 contained in itself tendencies or dispositions to 
 certain forms, which dispositions they called \oyoi 
 cnrepiuLariKol, seminal proportions, or seminal rea- 
 sons. 
 
 Whatever of sound view, or right direction, 
 there might be in the notions which suggested these 
 and other technical expressions, was, in all the 
 schools of philosophy (so far as physics was con- 
 cerned), quenched and overlaid by the predominance 
 of trifling and barren speculations ; and by the love 
 of subtilizing and commenting upon the works of 
 earlier writers, instead of attempting to interpret 
 the book of nature. Hence these technical terms 
 served to give fixity and permanence to the tradi- 
 tional dogmas of the sect, but led to no progress of 
 knowledge. 
 
 The advances which were made in physical 
 science proceeded, not from these schools of philo- 
 sophy, (if we except, perhaps, the obligations of the 
 science of Harmonics to the Pythagoreans,) but from 
 reasoners who followed an independent path. The 
 sequel of the ambitious hopes, the vast schemes, 
 the confident undertakings of the philosophers of 
 
68 THE GREEK SCHOOL PHILOSOPHY. 
 
 ancient Greece, was an entire failure in the phy- 
 sical knowledge of which it is our business to trace 
 the history. Yet we are not, on that account, to 
 think slightingly of these early speculators. They 
 were men of extraordinary acuteness, invention, and 
 range of thought; and above all, they had the 
 merit of first completely unfolding the speculative 
 faculty; of starting in that keen and vigorous 
 chase of knowledge, out of which all the subsequent 
 culture and improvement of man's intellectual stores 
 have arisen. The sages of early Greece form the 
 heroic age of science. Like the first navigators in 
 their own mythology, they boldly ventured their 
 untried bark in a distant and arduous voyage, urged 
 on by the hopes of a supernatural success ; and 
 though they missed the imaginary golden prize 
 which they sought, they unlocked the gates of dis- 
 tant regions, and opened the seas to the keels of 
 the thousands of adventurers, who, in succeeding 
 times, sailed to and fro, to the indefinite increase of 
 the mental treasures of mankind. 
 
 But inasmuch as their attempts, in one sense, 
 and at first, failed, we must proceed to offer some 
 account of this failure, and of its nature and causes. 
 
CHAPTER IIL 
 
 FAILURE OF THE PHYSICAL PHILOSOPHY OF THE 
 GREEK SCHOOLS. 
 
 Sect. 1. Result of the Greek School Philosophy. 
 
 THE methods and forms of philosophizing which 
 we have described as employed by the Greek 
 Schools, failed altogether in their application to 
 physics. No discovery of general laws, no explana- 
 tion of special phenomena, rewarded the acuteness 
 and boldness of these early students of nature. As- 
 tronomy, which made considerable progress during 
 the existence of the sects of Greek philosophers, 
 gained perhaps something by the authority with 
 which Plato taught the supremacy and universality 
 of mathematical rule and order ; and the truths of 
 Harmonics, which had probably given rise to the 
 Pythagorean passion for numbers, were cultivated 
 with much care by that school. But after these 
 first impulses, the sciences owed nothing to the phi- 
 losophical sects ; and the vast and complex accumu- 
 lations and apparatus of the Stagirite do not appear 
 to have led to any theoretical physical truths. 
 
 This assertion hardly requires proof, since in the 
 existing body of science there are no doctrines for 
 
70 THE GREEK SCHOOL PHILOSOPHY. 
 
 which we are indebted to the Aristotelian School. 
 Real truths, when once established, remain to the 
 end of time a part of the mental treasure of man, 
 and may be discerned through all the additions of 
 later days. But we can point out no physical doc- 
 trine now received, of which we trace the anticipa- 
 tion in Aristotle, in the way in which we see the 
 Copernican system anticipated by Aristarchus, the 
 resolution of the heavenly appearances into circular 
 motions suggested by Plato, and the numerical rela- 
 tions of musical intervals ascribed to Pythagoras. 
 But it may be worth while to look at this matter 
 more closely. 
 
 Among the works of Aristotle, are thirty-eight 
 chapters of " Problems," which may serve to exem- 
 plify the progress he had really made in the reduc- 
 tion of phenomena to laws and causes. Of these 
 Problems, a large proportion are physiological, and 
 these I here pass by, as not illustrative of the state of 
 physical knowledge. But those which are properly 
 physical are, for the most part, questions concerning 
 such facts and difficulties as it is the peculiar busi- 
 ness of theory to explain. Now it may be truly said, 
 that in scarcely any one instance are the answers, 
 which Aristotle gives to his questions, of any value. 
 For the most part, indeed, he propounds his answer 
 with a degree of hesitation or vacillation, which of 
 itself shows the absence of all scientific distinctness 
 of thought ; and the opinions so offered never appear 
 to involve any settled or general principle. 
 
ITS FAILURE. 71 
 
 We may take, as examples of this, the problems 
 of the simplest kind, where the principles lay nearest 
 at hand, the mechanical ones. "Why," he asks 1 , 
 " do small forces move great weights by means of a 
 lever, when they have thus to move the lever added 
 to the weight? Is it," he suggests, "because a greater 
 radius moves faster ?" " Why does a small wedge 
 split great weights 2 ? Is it because the wedge is 
 composed of two opposite levers ?" " Why 3 , when 
 a man rises from a chair, does he bend his leg and 
 his body to acute angles with his thigh ? Is it be- 
 cause a right angle is connected with equality and 
 rest?" "Why 4 can a man throw a stone further 
 with a sling than with his hand ? Is it that when he 
 throws with his hand he moves the stone from rest, 
 but when he uses the sling he throws it already in 
 motion ?" " Why 5 , if a circle be thrown on the 
 ground, does it first describe a straight line and then 
 a spiral, as it falls ? Is it that the air first presses 
 equally on the two sides and supports it, and after- 
 wards presses on one side more?" " Why 6 is it dif- 
 ficult to distinguish a musical note from the octave 
 above ? Is it that proportion stands in the place of 
 equality ?" It must be allowed that these are very 
 vague and worthless surmises ; for even if we were, 
 as some commentators have done, to interpret some 
 of them so as to agree with sound philosophy, we 
 should still be unable to point out, in this author's 
 
 1 Mech. Prob. 4. 2 Ib. 18. 3 Ib. 31. * Ib. 13. 
 6 Uepi 'A^xct. 11. 6 Uepi 'Ap^ov. 14. 
 
72 THE GREEK SCHOOL PHILOSOPHY. 
 
 works, any clear or permanent apprehension of the 
 general principles which such an interpretation 
 implies. 
 
 Thus the Aristotelian physics cannot be con- 
 sidered as otherwise than a complete failure. It 
 collected no general laws from facts ; and conse- 
 quently, when it tried to explain facts, it had no 
 principles which were of any avail. 
 
 The same may be said of the physical specula- 
 tions of the other schools of philosophy. They 
 arrived at no doctrines from which they could de- 
 duce, by sound reasoning, such facts as they saw; 
 though they often venture so far to trust their prin- 
 ciples as to infer from them propositions beyond 
 the domain of sense. Thus, the principle that each 
 element seeks its own place, led to the doctrine, 
 that, the place of fire being the highest, there is, 
 above the air, a Sphere of Fire; of which doctrine 
 the word Empyrean, used by our poets, still con- 
 veys a reminiscence. The Pythagorean tenet that 
 ten is a perfect number 7 , led some persons to as- 
 sume that the heavenly bodies are in number ten ; 
 and as nine only were known to them, they asserted 
 that there was an antichthon, or counter-earth, on 
 the other side of the sun, invisible to us. Their 
 opinions respecting numerical ratios, led to various 
 other speculations concerning the distances and 
 positions of the heavenly bodies : and as they had, 
 in other cases, found a connexion between propor- 
 7 Arist. Metaph. i. 5. 
 
ITS FAILURE. 73 
 
 tions of distance and musical notes, they assumed, 
 on this suggestion, the music of the spheres. 
 
 Although we shall look in vain in the physical 
 philosophy of the Greek Schools, for any results 
 more valuable than those just mentioned, we shall 
 not be surprised to find, recollecting how much an 
 admiration for classical antiquity has possessed the 
 minds of men, that some writers estimate their 
 claims much more highly than they are stated here. 
 Among such writers we may notice Dutens, who, 
 in 1766, published his "Origin of the Discoveries 
 attributed to the Moderns; in which it is shown that 
 our most celebrated Philosophers have received the 
 greatest part of their knowledge from the Works 
 of the Ancients." The thesis of this work is at- 
 tempted to be proved, as we might expect, by very 
 large interpretations of the general phrases used 
 by the ancients. Thus, when Timseus, in Plato's 
 dialogue, says of the Creator of the world 8 , " that 
 he infused into it two powers, the origins of motions, 
 both of that of the same thing, and of that of dif- 
 ferent things ;" Dutens 9 finds in this a clear indica- 
 tion of the projectile and attractive forces of modern 
 science. And in some of the common declamation 
 of the Pythagoreans and Platonists, concerning the 
 general prevalence of numerical relations in the. 
 universe, he discovers their acquaintance with the 
 law of the inverse square of the distance by which 
 gravitation is regulated, though he allows 10 that it 
 
 8 Tim. 96. a 3d ed. p. 83. 10 Ib. p. 88, 
 
74 THE GREEK SCHOOL PHILOSOPHY. 
 
 required all the penetration of Newton and his fol- 
 lowers to detect this law in the scanty fragments 
 by which it is transmitted. 
 
 Argument of this kind is palpably insufficient to 
 cover the failure of the Greek attempts at a general 
 physical philosophy; or rather we may say, that 
 such arguments, since they are as good as can be 
 brought in favour of such an opinion, show more 
 clearly how entire the failure was. I proceed now 
 to endeavour to point out its causes. 
 
 Sect. 2. Cause of the Failure of the Greek Phy- 
 sical Philosophy. 
 
 THE cause of the failure of so many of the at- 
 tempts of the Greeks to construct physical science 
 is so important, that we must endeavour to bring it 
 into view here; though the full developement of 
 such subjects belongs rather to the philosophy of in- 
 duction. The subject must, at present, be treated 
 very briefly. 
 
 I will first notice some errors which may na- 
 turally occur to the reader's mind, as possible causes 
 of failure, but which, we shall be able to show, 
 were not the real reasons in this case. 
 
 The cause of failure was not the neglect of facts. 
 It is often said that the Greeks disregarded experi- 
 ence, and spun their philosophy out of their own 
 thoughts alone ; and this is supposed by many to be 
 their essential error. It is, no doubt, true, that the 
 disregard of experience is a phrase which may be 
 
CAUSE OF ITS FAILURE. 75 
 
 so interpreted as to express almost any defect of 
 philosophical method; since coincidence with ex- 
 perience is requisite to the truth of all theory. But 
 ff we fix a more precise sense on our terms, I con- 
 ceive it may be shown that the Greek philosophy 
 did, in its opinions, recognize the necessity and para- 
 mount value of observations ; did, in its origin, pro- 
 ceed upon observed facts; and did employ itself 
 to no small extent in classifying and arranging 
 phenomena. We must endeavour to illustrate these 
 assertions, because it is important to show that these 
 steps alone do not necessarily lead to science. 
 
 1. The acknowledgment of experience as the 
 main ground of physical knowledge is so generally 
 understood to be a distinguishing feature of later 
 times, that it may excite surprise to find that 
 Aristotle, and other ancient philosophers, not only 
 asserted in the most pointed manner that all our 
 knowledge must begin from experience, but also 
 stated in language much resembling the habitual 
 phraseology of the most modern schools of philoso- 
 phising, that particular facts must be collected; that 
 from these, general principles must be obtained by 
 induction ; and that these principles, when of the 
 most general kind, are axioms. A few passages will 
 show this. 
 
 "The way 11 must be the same," says Aristotle, 
 in speaking of the rules of reasoning, " with respect 
 to philosophy, as it is with respect to any art or 
 
 11 Anal. Prior, i. 30. 
 
76 THE GREEK SCHOOL PHILOSOPHY. 
 
 science whatever ; we must collect the facts, and the 
 things to which the facts happen, in each subject, 
 and provide as large a supply of these as possible." 
 He then proceeds to say that " we are not to look 
 at once at all this collected mass, but to consider 
 small and definite portions"..." And thus it is the 
 office of observation to supply principles in each 
 subject ; for instance, astronomical observation sup- 
 plies the principles of astronomical science. For 
 the phenomena being properly assumed, the astro- 
 nomical demonstrations were from these discovered. 
 And the same applies to every art and science. So 
 that if we take the facts (rd vTrap^ovra) belonging 
 to each subject, it is our task to mark out clearly 
 the course of the demonstrations. For if in our 
 natural history (/cara Triv \aTopiav) we have omitted 
 nothing of the facts and properties which belong to 
 the subject, we shall learn what we can demonstrate 
 and what we cannot." 
 
 These facts, TO. vira^ovra^ he, at other times, in- 
 cludes in the term sensation. Thus he says 12 , " It is 
 obvious that if any sensation is wanting, there must 
 be also some knowledge wanting which we are thus 
 prevented from having, since we arrive at know- 
 ledge either by induction or by demonstration. 
 Demonstration proceeds from universal proposi- 
 tions, induction from particulars. But we cannot 
 have universal theoretical propositions except from 
 induction ; and we cannot make inductions without 
 
 12 Anal. Post. i. 18. 
 
CAUSE OF ITS FAILURE. 77 
 
 having sensation ; for sensation has to do with par- 
 ticulars." 
 
 In another place 13 , after stating that principles 
 must be prior to, and better known than conclu- 
 sions, he distinguishes such principles into absolutely 
 prior, and prior relative to us ; " The prior princi- 
 ples, relative to us, are those which are nearer to 
 the sensation; but the principles absolutely prior 
 are those which are more remote from the sensa- 
 tion. The most general principles are the more 
 remote, the more particular are nearer. The ge- 
 neral principles which are necessary to knowledge 
 
 are axioms." 
 
 We may add to these passages, that in which he 
 gives an account of the way in which Leucippus was 
 led to the doctrine of atoms. After describing the 
 opinions of some earlier philosophers, he says 14 , 
 "Thus, proceeding in violation of sensation, and 
 disregarding it, because, as they held, they must 
 follow reason, some came to the conclusion that the 
 universe was one, and infinite, and at rest. As it 
 appeared, however, that though this ought to be by 
 reasoning, it would go near to madness to hold such 
 opinions in practice, (for no one was ever so mad as 
 to think fire and ice to be one,) Leucippus, therefore, 
 pursued a line of reasoning which was in accordance 
 with sensation, and which was not irreconcileable 
 with the production and decay, the motion and mul- 
 titude of things." It is obvious that the school to 
 13 Anal. Post. i. 2. u De Gen. et Cor. i. 8. 
 
78 THE GREEK SCHOOL PHILOSOPHY. 
 
 which Leucippus belonged (the Eclectic) must have 
 been, at least in its origin, strongly impressed with 
 the necessity of bringing its theories into harmony 
 with the observed course of nature. 
 
 2. Nor was this recognition of the fundamental 
 value of experience a mere profession. The Greek 
 philosophy did, in its beginning, proceed upon ob- 
 servation. Indeed it is obvious that the principles 
 which it adopted were, in the first place, assumed in 
 order to account for some classes of facts, however 
 imperfectly they might answer their purpose. The 
 principle of things seeking their own places, was in- 
 vented in order to account for the falling and float- 
 ing of bodies. Again, Aristotle says, that heat is 
 that which brings together things of the same kind, 
 cold is that which brings together things whether of 
 the same or of different kinds : it is plain that in 
 this instance he intended by his principle to explain 
 some obvious facts, as the freezing of moist sub- 
 stances, and the separation of heterogeneous things 
 by fusion ; for, as he adds, if fire brings together 
 things which are akin, it will separate those which 
 are not akin. It would be easy to illustrate the 
 remark further, but its truth is evident from the na- 
 ture of the case ; for no principles could be accepted 
 for a moment, which were the result of an arbi- 
 trary caprice of the mind, and which were not in 
 some measure plausible, and apparently confirmed 
 by facts. 
 
 But the works of Aristotle show, in another way, 
 
CAUSE OF ITS FAILURE. 79 
 
 how unjust it would be to accuse him of disregarding 
 facts. Many large treatises of his consist almost 
 entirely of collections of facts, as for instance, those 
 "On Colours," "On Sounds," and the collection of 
 Problems to which we have already referred; to say 
 nothing of the numerous collection of facts bearing 
 on natural history and physiology, which form a great 
 portion of his works, and are even now treasuries 
 of information. A moment's reflection will convince 
 us that the physical sciences of our own times, for 
 example, mechanics and hydrostatics, are founded 
 almost entirely upon facts with which the ancients 
 were as familiar as we are. The defect of their phi- 
 losophy, therefore, wherever it may lie, exists neither 
 in the speculative depreciation of the value of facts, 
 nor in the practical neglect of their use. 
 
 3. Nor again, should we hit upon the truth, if 
 we were to say that Aristotle and other ancient 
 philosophers, did indeed collect facts ; but that they 
 took no steps in classifying and comparing them; 
 and that thus they failed to obtain from them any 
 general knowledge. For, in reality, the treatises of 
 Aristotle which we have mentioned, are as remark- 
 able for the power of classifying and systematizing 
 which they exhibit, as for the industry shown in the 
 accumulation. But it is not classification of facts 
 merely which can lead us to knowledge, except we 1 
 adopt that special arrangement, which, in each case, 
 brings into view the principles of the subject. We 
 may easily show how unprofitable an arbitrary or 
 
80 THE GREEK SCHOOL PHILOSOPHY. 
 
 random classification is, however orderly and syste- 
 matic it may be. 
 
 For instance, for a long period all unusual fiery 
 appearances in the sky were classed together as 
 meteors. Comets, shooting-stars, and globes of fire, 
 and the aurora borealis in all its forms, were thus 
 grouped together, and classifications of considerable 
 extent and minuteness were proposed with reference 
 to these objects. But this classification was of a 
 mixed and arbitrary kind. Figure, colour, motion, 
 duration, were all combined as characters, and the 
 imagination lent its aid, transforming these striking 
 appearances into fiery swords and spears, bears and 
 dragons, armies and chariots. The facts so classified 
 were, notwithstanding, worthless; and would not 
 have been one jot the less so, had they and their 
 classes been ten times as numerous as they were. 
 No rule or law that would stand the test of obser* 
 vation was or could be thus discovered. Such clas- 
 sifications have, therefore, long been neglected and 
 forgotten. Even the ancient descriptions of these 
 objects of curiosity are unintelligible, or unworthy 
 of trust, because the spectators had no steady con- 
 ception of the usual order of such phenomena. For, 
 however much we may fear to be misled by precon- 
 ceived opinions, the caprices of imagination distort 
 our impressions far more than the anticipations of 
 reason. In this case men had, indeed we may say 
 with regard to many of these meteors, they still 
 have, no science : not for want of facts, nor even foi; 
 
CAUSE OF ITS FAILURE. 81 
 
 want of classification of facts ; but because the clas- 
 sification was one in which no real principle was 
 contained. 
 
 4. Since, as we have said before, two things are 
 requisite to science, Facts and Ideas; and since, as 
 we have seen, Facts were not wanting in the physical 
 speculations of the ancients, we are naturally led to 
 ask, Were they then deficient in Ideas ? Was there 
 a want among them of mental activity, and logical 
 connexion of thought? But it is so obvious that 
 the answer to this inquiry must be in the negative, 
 that we need not dwell upon it. No one who 
 knows anything of the history of the ancient Greek 
 mind, can question, that in acuteness, in ingenuity, 
 in the power of close and distinct reasoning, they 
 have never been surpassed. The common opinion, 
 which considers the defect of their philosophical 
 character to reside rather in the exclusive activity 
 of such qualities, than in the absence of them, is at 
 least so far just. 
 
 5. We come back again, therefore, to the ques- 
 tion, What was the radical and fatal defect in the 
 physical speculations of the Greek philosophical 
 schools ? 
 
 To this I answer : The defect was, that though 
 they had in their possession Facts and Ideas, the 
 Ideas were not distinct and appropriate to the 
 Facts (D). 
 
 The peculiar characteristics of scientific ideas, 
 which I have endeavoured to express by speaking 
 VOL. i. G 
 
82 THE GREEK SCHOOL PHILOSOPHY. 
 
 of them as distinct and appropriate to the facts, must 
 be more fully and formally set forth, when we come 
 to the philosophy of the subject. In the mean 
 time, the reader will probably have no difficulty in 
 conceiving that, for each class of Facts, there is some 
 special set of Ideas, by means of which the facts 
 can be included in general scientific truths; and that 
 these Ideas, which may thus be termed appropriate, 
 must be possessed with entire distinctness and clear- 
 ness, in order that they may be successfully applied. 
 It was the want of Ideas having this reference to 
 material phenomena, which rendered the ancient 
 philosophers, with very few exceptions, helpless and 
 unsuccessful speculators on physical subjects. 
 
 This must be illustrated by one or two examples. 
 One of the facts which Aristotle endeavours to 
 explain is this ; that when the sun's light passes 
 through a hole, whatever be the form of the hole, 
 the bright image, if formed at any considerable dis- 
 tance from the hole, is round, instead of imitating 
 the figure of the hole, as shadows resemble their 
 objects in form. We shall easily perceive this 
 appearance to be a necessary consequence of the 
 circular figure of the sun, if we conceive light to be 
 diffused from the luminary by means of straight rays 
 proceeding from every point of the sun's disk and 
 passing through every point within the boundary of 
 the hole. By attending to the consequences of this 
 mode of conception, it will be seen that each point 
 of the hole will be the vertex of a double cone of 
 
CAUSE OF ITS FAILURE. 83 
 
 rays which has the sun's disk for its base on one 
 side and an image of the sun on the other ; and the 
 figure of the image of the hole will be determined 
 by supposing a series of equal bright circles, images 
 of the sun, to be placed along the boundary of an 
 image equal to the hole itself. The figure of the 
 image thus determined will partake of the form of 
 the hole, and of the circular form of the sun's image: 
 let these circular images become larger and larger 
 as they are farther from the hole, while the central 
 image of the hole remains always of the original 
 size ; and thus at a considerable distance from the 
 hole, the trace of the hole's form is nearly obli- 
 terated, and the image is nearly a perfect circle. 
 Instead of this distinct conception of a cone of rays 
 which has the sun's disk for its basis, Aristotle has 
 the following loose conjecture 15 . "Is it because 
 light is emitted in a conical form ; and of a cone, 
 the base is a circle ; so that on whatever the rays 
 of the sun fall, they appear more circular?" And 
 thus though he applies the notion of rays to this 
 problem, he possesses this notion so indistinctly 
 that his explanation is of no value. He does not 
 introduce into his explanation the consideration of 
 the sun's circular figure, and is thus prevented from 
 giving a true account of this very simple optical 
 phenomenon. 
 
 Again, to pass to a more extensive failure : why 
 was it that Aristotle, knowing the property of the 
 
 Problem. 15. oo-a /jia^^/uaTtx^?, &o. 
 
 G2 
 
84 THE GREEK SCHOOL PHILOSOPHY. 
 
 lever, and many other mechanical truths, was unable 
 to form them into a science of mechanics, as Archi- 
 medes afterwards did ? 
 
 The reason was, that, instead of considering rest 
 and motion directly, and distinctly, with reference 
 to the Idea of Cause, that is Force, he wandered in 
 search of reasons among other ideas and notions, 
 which could not be brought into steady connexion 
 with the facts; the ideas of properties of circles, 
 of proportions of velocities, -the notions of "strange" 
 and "common," of "natural" and "unnatural." 
 Thus, in the Proem to his Mechanical Problems, 
 after stating some of the difficulties which he has 
 to attack, he says, " Of all such cases, the circle 
 contains the principle of the cause. And this is 
 what might be looked for ; for it is nothing absurd, 
 if something wonderful is derived from some- 
 thing more wonderful still. Now the most won- 
 derful thing is, that opposites should be combined; 
 and the circle is constituted of such combinations 
 of opposites. For it is constructed by a stationary 
 point and a moving line, which are contrary to 
 each other in nature; and hence we may the less 
 be surprised at the resulting contrarieties. And 
 in the first place, the circumference of the circle, 
 though a line without breadth, has opposite qua- 
 lities; for it is both convex and concave. In the 
 next place, it has, at the same time, opposite mo- 
 tions, for it moves forward and backward at the 
 same time. For the circumference, setting out from 
 
CAUSE OF ITS FAILURE. 85 
 
 any point, comes to the same point again, so that 
 by a continuous progression, the last point becomes 
 the first. So that, as was before stated, it is not 
 surprising that the circle should be the principle of 
 all wonderful properties." 
 
 Aristotle afterwards proceeds to explain more 
 specially how he applies the properties of the circle 
 in this case. " The reason," he says, in his fourth 
 Problem, " why a force, acting at a greater distance 
 from the fulcrum, moves a weight more easily, is, 
 that it describes a greater circle." He had already 
 asserted that when a body at the end of a lever is 
 put in motion, it may be considered as having two 
 motions ; one in the direction of the tangent, and 
 one in the direction of the radius; the former motion 
 is, he says, according to nature, the latter, contrary 
 to nature. Now in the smaller circle, the motion, 
 contrary to nature, is more considerable than it is 
 in the larger circle. "Therefore," he adds, "the 
 mover or weight at the larger arm will be trans- 
 ferred further by the same force than the weight 
 moved, which is at the extremity of the shorter arm." 
 
 These loose and inappropriate notions of " na- 
 tural" and " unnatural" motions, were unfit to lead 
 to any scientific truths ; and, with the habits of 
 thought which dictated these speculations, a per- 
 ception of the true grounds of mechanical proper- 
 ties was impossible. 
 
 Thus, in this instance, the error of Aristotle was 
 the neglect of the Idea appropriate to the facts, 
 
86 THE GREEK SCHOOL PHILOSOPHY. 
 
 namely, the Idea of Mechanical Cause, which is 
 Force; and the substitution of vague or inappli- 
 cable notions involving only relations of space, or 
 emotions of wonder. The errors of those who failed 
 similarly in other instances, were of the same kind. 
 To detail or classify these would lead us too far into 
 the philosophy of science ; since we should have to 
 enumerate the Ideas which are appropriate, and the 
 various class of Facts on which the different sciences 
 are founded, a task not to be now lightly under- 
 taken. But it will be perceived, without further 
 explanation, that it is necessary, in order to obtain 
 from facts any general truth, that we should apply 
 to them that appropriate Idea, by which permanent 
 and definite relations are established among them. 
 
 In such ideas the ancients were very poor, and 
 the stunted and deformed growth of their physical 
 science was the result of this penury. The Ideas of 
 Space and Time, Number and Motion, they did in- 
 deed possess distinctly ; and so far as these went, 
 their science was tolerably healthy. They also 
 caught a glimpse of the Idea of a Medium by which 
 the qualities of bodies, as colours and sounds, are 
 perceived. But the idea of Substance remained 
 barren in their hands; in speculating about elements 
 and qualities, they went the wrong way, assuming 
 that the properties of the Compounds must resemble 
 those of the Elements which determine them ; and 
 their loose notions of Contrariety never approached 
 the form of those ideas of Polarity, which, in mo- 
 
CAUSE OF ITS FAILURE. 87 
 
 dern times, regulate many parts of physics and 
 chemistry. 
 
 If this statement should seem to any one to be 
 technical or arbitrary, we must refer, for the justi- 
 fication of it, to the Philosophy of Science, of which 
 we hope hereafter to treat. But it will appear, even 
 from what has been here said, that there are certain 
 Ideas or Forms of mental apprehension, which may 
 be applied to Facts in such a manner as to bring into 
 view fundamental principles of science ; while the 
 same Facts, however arrayed or reasoned about, so 
 long as these appropriate Ideas are not employed, 
 cannot give rise to any exact or substantial know- 
 ledge. 
 
 We shall, in the next Book, see the influence of 
 the appropriate general Ideas, in the formation of 
 various sciences. It need only be observed, before 
 we proceed, that, in order to do full justice to the 
 physical knowledge of the Greek Schools of philo- 
 sophy, it is not necessary to study their course after 
 the time of their founders. Their fortunes, in respect 
 of such acquisitions as we are now considering, were 
 not progressive. The later chiefs of the Schools fol- 
 lowed the earlier masters; and though they varied 
 much, they added little. The Romans adopted the 
 philosophy of their Greek subjects ; but they were 
 always, and, indeed, acknowledged themselves to be, 
 inferior to their teachers. They were as arbitrary 
 and loose in their ideas as the Greeks, without 
 
88 THE GREEK SCHOOL PHILOSOPHY. 
 
 possessing their invention, acuteness, and spirit of 
 system. 
 
 In addition to the vagueness which was com- 
 bined with the more elevated trains of philoso- 
 phical speculation among the Greeks, the Romans, 
 introduced into their treatises a kind of declamatory 
 rhetoric, which arose probably from their forensic 
 and political habits, and which still further ob- 
 scured the waning gleams of truth. Yet we may 
 also trace, in the Roman philosophers to whom this 
 charge mostly applies (Lucretius, Pliny, Seneca), the 
 national vigour and ambition. There is something 
 Roman in the public spirit and anticipation of uni- 
 versal empire which they display, as citizens of the 
 intellectual republic. Though they speak sadly or 
 slightingly of the achievements of their own gene- 
 ration, they betray a more abiding and vivid belief 
 in the dignity and destined advance of human know- 
 ledge as a whole, than is obvious among the Greeks. 
 
 We must, however, turn back, in order to de- 
 scribe steps of more definite value to the progress 
 of science than those which we have hitherto no- 
 ticed. 
 
89 
 
 NOTES TO BOOK I. 
 
 (B.) p. 38. THE course by which the Sciences were 
 formed, and which is here referred to as that which the 
 Greeks did not follow, is described in detail in the Philo- 
 sophy, Book XL, Of the Construction of Science. 
 
 (c.) p. 41. This Aristotle is not the Stagirite, who 
 was forty-five years younger than Plato, but one of the 
 " thirty tyrants," as they were called. 
 
 (D.) p. 81. This account of the cause of failure in 
 the physical speculations of the ancient Greek philoso- 
 phers has been objected to as unsatisfactory. I will offer 
 a few words in explanation of it. 
 
 The mode of accounting for the failure of the Greeks 
 in physics is, in substance ; that the Greeks in their phy- 
 sical speculations fixed their attention upon the wrong 
 aspects and relations of the phenomena ; and that the 
 aspects and relations in which phenomena are to be viewed 
 in order to arrive at scientific truths may be arranged 
 under certain heads, which I have termed Ideas ; such as 
 Space, Time, Number, Cause, Likeness. In every case, 
 there is an Idea to which the phenomena may be referred 
 so as to bring into view the Laws by which they are 
 governed ; this Idea I term the appropriate Idea in such 
 case ; and in order that the reference of the phenomena 
 to the Law may be clearly seen, the Idea must be dis- 
 tinctly possessed. 
 
 Thus the reason of Aristotle's failure in his attempts 
 at Mechanical Science is, that he did not refer the facts 
 
90 NOTES TO BOOK I. 
 
 to the appropriate Idea, namely Force, the Cause of 
 Motion, but to relations of Space and the like ; that is, 
 he introduces Geometrical instead of Mechanical Ideas. 
 It may be said that we learn little by being told that 
 Aristotle's failure in this and the like cases arose from his 
 referring to the wrong class of Ideas; or, as I have 
 otherwise expressed it, fixing his attention upon the wrong 
 aspects and relations of the facts ; since, it may be said, 
 this is only to state in other words that he did fail. But 
 this criticism is, I think, ill-founded, The account which 
 I have given is not only a statement that Aristotle, and 
 others who took a like course, did fail ; but also, that 
 they failed in one certain point out of several which are 
 enumerated. They did not fail because they neglected to 
 observe facts ; they did not fail because they omitted to 
 class facts ; they did not fail because they had not ideas 
 to reason from ; but they failed because they did not 
 take the right ideas in each case. And so long as they 
 were in the wrong in this point, no industry in collect- 
 ing facts, or ingenuity in classing them and reasoning 
 about them, could lead them to solid truth. Nor is this 
 account of the nature of their mistake without its in- 
 struction for us ; although we are not to expect to derive 
 from the study of their failure any technical rule which 
 shall necessarily guide us to scientific discovery. For 
 their failure teaches us that, in the formation of science, 
 an Errour in the Ideas is as fatal to the discovery of 
 Truth as an Errour in the Facts ; and may as completely 
 impede the progress of knowledge. I have in Books ir. 
 to x. of the Philosophy, shown historically how large a 
 portion of the progress of Science consists in the esta- 
 blishment of Appropriate Ideas as the basis of each science. 
 
NOTES TO BOOK I. 91 
 
 Of the two main processes by which science is con- 
 structed, as stated in Book xi. of that work, namely the 
 Explication of Conceptions and the Colligation of Facts, the 
 former must precede the latter. In Book xn. chap. 5, of 
 the Philosophy, I have stated the maxim concerning ap- 
 propriate Ideas in this form, that the Idea and the Facts 
 must be homogeneous. 
 
 When I say that the failure of the Greeks in physical 
 science arose from their not employing appropriate Ideas 
 to connect the facts, I do not use the term "appropriate" 
 in a loose popular sense ; but I employ it as a somewhat 
 technical term, to denote the appropriate Idea, out of that 
 series of Ideas which have been made (as I have shown 
 in the Philosophy) the foundation of sciences; namely 
 Space, Time, Number, Cause, Likeness, Substance, and 
 the rest. It appears to me just to say that Aristotle^s 
 failure in his attempts to deal with problems of equili- 
 brium, arose from his referring to circles, velocities, no- 
 tions of natural and unnatural, and the like, conceptions 
 
 depending upon Ideas of Space, of Nature, &c which are 
 
 not appropriate to these problems, and from his missing 
 the Idea of Mechanical Force or Pressure, which is the 
 appropriate Idea. 
 
 I give this, not as an account of all failures in attempts 
 at science, but only as the account of such radical and 
 fundamental failures as this of Aristotle ; who, with a 
 knowledge of the facts, failed to connect them into a 
 really scientific view. If I had to compare rival theories 
 of a more complex kind, I should not necessarily say that 
 one involved an appropriate Idea and the other did not, 
 though I might judge one to be true and the other to be 
 false. For instance, in comparing the emissive and the 
 
92 NOTES TO BOOK I. 
 
 undulatory theory of light, we see that both involve the 
 same Idea ; the Idea of a Medium acting by certain 
 mechanical properties. The question there is, what is 
 the true view of the mechanism of the Medium I 
 
 The other example of Aristotle's failure in physics, 
 given in p. 82, namely, his attempted explanation of the 
 round image of a square hole, is a specimen rather of in- 
 distinct than of inappropriate ideas. In the first edition 
 I had not accurately represented Aristotle's statement. 
 
 The geometrical explanation of this phenomena, which 
 I have inserted in the text, was given by Maurolycus, and 
 before him, by Leonardo da Vinci. 
 
BOOK II. 
 
 HISTORY 
 
 OF THE 
 
 PHYSICAL SCIENCES 
 
 IN 
 
 ANCIENT GREECE. 
 
de Orjpapai Trvpos 
 ^v K\oiraiav, rj did<rKa\os re^v^s 
 
 7T(pf)ve KOI p.cyas iropos. 
 
 Prom. Vinct. 109. 
 
 I brought to earth the spark of heavenly fire, 
 Concealed at first, and small, but spreading soon 
 Among the sons of men, and burning on, 
 Teacher of art and use, and fount of power. 
 
 
BOOK II. 
 
 HISTORY OF PHYSICAL SCIENCE IN ANCIENT 
 GREECE. 
 
 
 INTRODUCTION. 
 
 IN order to the acquisition of any such exact and 
 real knowledge of nature as that which we pro- 
 perly call Physical Science, it is requisite, as has 
 already been said, that men should possess Ideas 
 both distinct and appropriate, and should apply 
 them to ascertained Facts. They are thus led to 
 propositions of a general character, which are ob- 
 tained by Induction, as will elsewhere be more fully 
 explained. We proceed now to trace the forma- 
 tion of Sciences among the Greeks by such pro- 
 cesses. The provinces of knowledge which thus 
 demand our attention are, Astronomy, Mechanics 
 and Hydrostatics, Optics and Harmonics ; of which 
 I must relate, first, the earliest stages, and next, 
 the subsequent progress. 
 
 Of these portions of human knowledge, Astro- 
 nomy is, beyond doubt or comparison, much the 
 most ancient and the most remarkable; and pro- 
 bably existed, in somewhat of a scientific form, in 
 Chaldea and Egypt, and other countries, before the 
 
96 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 period of the intellectual activity of the Greeks. 
 But I will give a brief account of some of the other 
 Sciences before I proceed to Astronomy, for two 
 reasons ; first, because the origin of Astronomy is 
 lost in the obscurity of a remote antiquity; and 
 therefore we cannot exemplify the conditions of the 
 first rise of science so well in that subject as we can 
 in others which assumed their scientific form at 
 known periods ; and next, in order that I may not 
 have to interrupt, after I have once begun it, the 
 history of the only progressive Science which the 
 ancient world produced (E). 
 
97 
 
 CHAPTER I. 
 
 EARLIEST STAGES OF MECHANICS AND HYDRO- 
 STATICS. 
 
 Sect. 1. Mechanics. 
 
 A STRONOMY is a science so ancient that we 
 _L\_ can hardly ascend to a period when it did not 
 exist ; Mechanics, on the other hand, is a science 
 which did not begin to be till after the time of 
 Aristotle ; for Archimedes must be looked upon as 
 the author of the first sound knowledge on this 
 subject. What is still more curious, and shows 
 remarkably how little the continued progress of 
 science follows inevitably from the nature of man, 
 this department of knowledge, after the right road 
 had been fairly entered upon, remained absolutely 
 stationary for nearly two thousand years ; no single 
 step was made, in addition to the propositions esta- 
 blished by Archimedes, till the time of Galileo 
 and Stevinus. This extraordinary halt will be a 
 subject of attention hereafter; at present we must 
 consider the original advance. 
 
 The great step made by Archimedes in Mecha- 
 nics was the establishing, upon true grounds, the 
 general proposition concerning a straight lever, 
 loaded with two heavy bodies, and resting upon a 
 
 VOL. i. H 
 
98 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 fulcrum. The proposition is, that two bodies so 
 circumstanced will balance each other, when the 
 distance of the smaller body from the fulcrum is 
 greater than the distance of the other, in exactly 
 the same proportion in which the weight of the 
 body is less. 
 
 This proposition is proved by Archimedes in a 
 work which is still extant ; and the proof holds its 
 place in our treatises to this day, as the simplest 
 which can be given. The demonstration is made 
 to rest on assumptions which amount in effect to 
 such Definitions and Axioms as these : That those 
 bodies are of equal weight which balance each 
 other at equal arms of a straight lever; and that 
 in every heavy body there is a definite point called 
 a Centre of Gravity, in which point we may sup- 
 pose the weight of the body collected. 
 
 The principle, which is really the foundation 
 of the validity of the demonstration thus given, and 
 which is the condition of all experimental know- 
 ledge on the subject, is this ; that when two equal 
 weights are supported on a lever, they act on the 
 fulcrum of the lever with the same effect as if they 
 were both together supported immediately at that 
 point. Or more generally, we may state the prin- 
 ciple to be this ; that the pressure by which a 
 heavy body is supported continues the same, how- 
 ever we alter the form or position of the body, so 
 long as the magnitude and material continue the 
 same. 
 
MECHANICS AND HYDROSTATICS. 99 
 
 The experimental truth of this principle is a 
 matter of obvious and universal experience. The 
 weight of a basket of stones is not altered by shak- 
 ing the stones into new positions. We cannot 
 make the direct burden of a stone less by altering 
 its position in our hands ; and if we try the effect 
 on a balance or a machine of any kind, we shall 
 see still more clearly and exactly that the altered 
 position of one weight, or the altered arrangement 
 of several, produces no change in their effect, so 
 long as their point of support remains unchanged. 
 
 This general fact is obvious, when we possess in 
 our minds the ideas which are requisite to appre- 
 hend it clearly. But when we are so prepared, the 
 truth appears to be manifest, even independent of 
 experience, and is seen to be a rule to which expe- 
 rience must conform. What then is the leading Idea 
 which thus enables us to reason effectively upon 
 mechanical subjects? By attention to the course 
 of such reasonings, we perceive that it is the Idea 
 of Pressure ; Pressure being conceived as a mea- 
 surable effect of heavy bodies at rest, distinguish- 
 able from all other effects, such as motion, change 
 of figure, and the like. It is not here necessary to 
 attempt to trace the history of this Idea in our 
 minds ; but it is certain that such an Idea may be 
 distinctly formed, and that upon it the whole 
 science of statics may be built. Pressure, load, 
 weight, are names by which this Idea is denoted 
 when the effect tends directly downwards; but we 
 
 H2 
 
100 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 may have pressure without motion, or dead pull, in 
 other cases, as at the critical instant when two 
 nicely-matched wrestlers are balanced by the exer- 
 tion of the utmost strength of each. 
 
 Pressure in any direction may thus exist with- 
 out any motion whatever. But the causes which 
 produce such pressure are capable of producing 
 motion, and are generally seen producing motion, 
 as in the above instance of the wrestlers, or in a 
 pair of scales employed in weighing ; and thus men 
 come to consider pressure as the exception, and 
 motion as the rule; or perhaps they image to them- 
 selves the motion which might or would take place; 
 for instance, the motion which the arms of a lever 
 would have if they did move. They turn away 
 from the case really before them, which is that of 
 bodies at rest, and balancing each other, and pass 
 to another case, which is arbitrarily assumed to re- 
 present the first. Now this arbitrary and capricious 
 evasion of the question we consider as opposed to 
 the introduction of the distinct and proper Idea of 
 Pressure, by means of which the true principles of 
 this subject can be apprehended. 
 
 We have already seen that Aristotle was in the 
 number of those who thus evaded the difficulties 
 of the problem of the lever, and consequently lost 
 the reward of success. He failed, as has before 
 been stated, in consequence of his seeking his prin- 
 ciples in notions, either vague and loose, as the 
 distinction of natural and unnatural motions, or 
 
MECHANICS AND HYDROSTATICS. .101 
 
 else inappropriate, as the circle which the weight 
 mould describe, the velocity which it would have 
 if it moved ; circumstances which are not part of 
 the fact under consideration. The influence of such 
 modes of speculation was the main hinderance to 
 the prosecution of the true Archimedean form of 
 the science of Mechanics. 
 
 The mechanical doctrine of Equilibrium, is 
 Statics. It is to be distinguished from the mecha- 
 nical doctrine of Motion which is termed Dyna- 
 mics, and which was not successfully treated till the 
 time of Galileo. 
 
 Sect. 2. Hydrostatics. 
 
 ARCHIMEDES not only laid the foundations of the 
 Statics of solid bodies, but also solved the principal 
 problem of Hydrostatics, or the Statics of Fluids ; 
 namely, the conditions of the floating of bodies. 
 This is the more remarkable, since not only did 
 the principles which Archimedes established on this 
 subject remain unpursued till the revival of science 
 in modern times, but, when they were again put 
 forward, the main proposition was so far from ob- 
 vious that it was termed, and is to this day called, 
 the hydrostatic paradox. The true doctrine of 
 Hydrostatics, however, assuming the Idea of Pres- 
 sure, which it involves, in common with the Mecha- 
 nics of solid bodies, requires also a distinct Idea 
 
102 PHYSICAL SCIENCES JN ANCIENT GREECE. 
 
 of a Fluid, as a body of which the parts are per- 
 fectly moveable among each other by the slightest 
 partial pressure, and in which all pressure exerted 
 on one part is transferred to all other parts. From 
 this idea of Fluidity, necessarily follows that mul- 
 tiplication of pressure which constitutes the hydro- 
 static paradox; and the notion being seen to be 
 verified in nature, the consequences were also rea- 
 lized as facts. This notion of Fluidity is expressed 
 in the postulate which stands at the head of Archi- 
 medes's " Treatise on Floating Bodies." And from 
 this principle are deduced the solutions, not only 
 of the simple problems of the science, but of some 
 problems of considerable complexity. 
 
 The difficulty of holding fast this Idea of Flu- 
 idity so as to trace its consequences with infallible 
 strictness of demonstration, may be judged of from 
 the circumstance that, even at the present day, 
 men of great talents, not unfamiliar with the sub- 
 ject, sometimes admit into their reasonings an over- 
 sight or fallacy with regard to this very point. 
 The importance of the Idea when clearly appre- 
 hended and securely held, may be judged of from 
 this, that the whole science of Hydrostatics in its 
 most modern form is only the developement of the 
 Idea. And what kind of attempts at science would 
 be made by persons destitute of this Idea, we may 
 see in the speculations of Aristotle concerning light 
 and heavy bodies, which we have already quoted ; 
 
MECHANICS AND HYDROSTATICS. 103 
 
 where, by considering* light and heavy as opposite 
 qualities, residing in things themselves, and by an 
 inability to apprehend the effect of surrounding 
 fluids in supporting bodies, the subject was made 
 a mass of false or frivolous assertions, which the 
 utmost ingenuity could not reconcile with facts, and 
 could still less deduce from the asserted doctrines 
 any new practical truths. 
 
 In the case of Statics and Hydrostatics, the 
 most important condition of their advance was un- 
 doubtedly the distinct apprehension of these two 
 appropriate Ideas, Statical Pressure, and Hydrosta- 
 tical Pressure as included in the idea of Fluidity. 
 For the Ideas being once clearly possessed, the 
 experimental laws which they served to express 
 (that the whole pressure of a body downwards was 
 always the same ; and that water, and the like, 
 were fluids according to the above idea of fluidity) 
 were so obvious, that there was no doubt nor dif- 
 ficulty about them, These two ideas lie at the 
 root of all mechanical science ; and the firm pos- 
 session of them is, to this day, the first requisite 
 for a student of the subject. After being clearly 
 awakened in the mind of Archimedes, these ideas 
 slept for many centuries, till they were again called 
 up in Galileo, and more remarkably in Stevinus. 
 This time, they were not destined again to slum- 
 ber; and the results of their activity have been 
 the formation of two Sciences, which are as certain 
 
104 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 and severe in their demonstrations as geometry 
 itself, and as copious and interesting in their con- 
 clusions; but which, besides this recommendation, 
 possess one of a different order ; that they exhibit 
 the exact impress of the laws of the physical world; 
 and unfold a portion of the rules according to 
 which the phenomena of nature take place, and 
 must take place, till nature herself shall alter. 
 
105 
 
 CHAPTER II. 
 EARLIEST STAGES OF OPTICS. 
 
 THE progress made by the ancients in Optics 
 was nearly proportional to that which they 
 made in Statics. As they discovered the true 
 grounds of the doctrine of Equilibrium, without 
 obtaining any sound principles concerning Motion, 
 so they discovered the law of the Reflection of 
 light, but had none but the most indistinct notions 
 concerning Refraction. 
 
 The extent of the principles which they really 
 possessed is easily stated. They knew that vision 
 is performed by rays which proceed in straight 
 lines, and that these rays are reflected by certain 
 surfaces (mirrors) in such manner that the angles 
 which they make with the surface on each side are 
 equal. They drew various conclusions from these 
 premises by the aid of geometry ; as, for instance, 
 the convergence of rays which fall on a concave 
 speculum. 
 
 It may be observed that the Idea which is here 
 introduced, is that of visual rays, or lines along 
 which vision is produced and light carried. This 
 idea once clearly apprehended, it was not difficult 
 to show that these lines are straight lines, both in 
 the case of light and of sight. In the beginning 
 
106 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 of Euclid's " Treatise on Optics," some of the argu- 
 ments are mentioned by which this was established. 
 We are told in the Proem, "In explaining what 
 concerns the sight, he adduced certain arguments 
 from which he inferred that all light is carried 
 in straight lines. The greatest proof of this is 
 shadows, and the bright spots which are produced 
 by light coming through windows and cracks, and 
 which could not be, except the rays of the sun 
 were carried in straight lines. So in fires, the 
 shadows are greater than the bodies if the fire be 
 small, but less than the bodies if the fire be greater." 
 A clear comprehension of the principle would lead 
 to the perception of innumerable proofs of its truth 
 on every side. 
 
 The Law of Equality of Angles of Incidence and 
 Reflection was not quite so easy to verify ; but the 
 exact resemblance of the object and its image in a 
 plane mirror, (as the surface of still water, for in- 
 stance,) which is a consequence of this law, would 
 afford convincing evidence of its truth in that case, 
 and would be confirmed by the examination of 
 other cases. 
 
 With these true principles was mixed much 
 error and indistinctness, even in the best writers. 
 Euclid, and the Platonists, maintained that vision 
 is exercised by rays proceeding from the eye, not 
 to it ; so that when we see objects, we learn their 
 form as a blind man would do, by feeling it out 
 with his staff. This mistake, however, though Mon- 
 
OPTICS. 107 
 
 tucla speaks severely of it, was neither very dis- 
 creditable nor very injurious ; for the mathematical 
 conclusions on each supposition are necessarily the 
 same. Another curious, and false assumption is, 
 that these visual rays are not close together, but 
 separated by intervals, like the fingers when the 
 hand is spread. The motive for this invention was 
 the wish to account for the fact, that in looking 
 for a small object, as a needle, we often cannot 
 see it when it is under our nose ; which it was 
 conceived would be impossible if the visual rays 
 reached to all points of the surface before us. 
 
 These errours would not have prevented the pro- 
 gress of the science. But the Aristotelian physics, 
 as usual, contained speculations more essentially 
 faulty. Aristotle's views led him to try to de- 
 scribe the kind of causation by which vision is pro- 
 duced, instead of the laws by which it is exercised ; 
 and the attempt consisted, as in other subjects, of 
 indistinct principles, and ill-combined facts. Ac- 
 cording to him, vision must be produced by a 
 Medium, by something between the object and the 
 eye, for if we press the object on the eye, we 
 do not see it ; this Medium is Light, or " the trans- 
 parent in action ;" darkness occurs when the trans- 
 parency is potential not actual ; colour is not the 
 " absolute visible," but something which is on the 
 absolute visible ; colour has the power of setting 
 the transparent in action; it is not, however, all 
 colours that are seen by means of light, but only 
 
108 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 the proper colour of each object ; for some things, 
 as the heads, and scales, and eyes of fish, are seen 
 in the dark ; but then they are not seen with their 
 proper colour 1 . 
 
 In all this there is no steady adherence either 
 to one notion, or to one class of facts. The dis- 
 tinction of Power and Act is introduced to modify 
 the Idea of Transparency, according to the formula 
 of the school; then Colour is made to be some- 
 thing unknown in addition to Visibility ; and the 
 distinction of " proper" and " improper" colours is 
 assumed, as sufficient to account for a phenomenon. 
 Such classifications have in them nothing of which 
 the mind can take steady hold; nor is it difficult 
 to see that they do not come under those condi- 
 tions of successful physical speculation, which we 
 have laid down (F). 
 
 1 De Anim. ii. 6. 
 
109 
 
 CHAPTER III. 
 EARLIEST STAGES OF HARMONICS. 
 
 AMONG the ancients, the science of Music was 
 an application of Arithmetic, as Optics and 
 Mechanics were of Geometry. The story which is 
 told concerning the origin of their arithmetical 
 music, is the following, as it stands in the Arith- 
 metical Treatise of Nicomachus. 
 
 Pythagoras, walking one day, meditating on the 
 means of measuring musical notes, happened to 
 pass near a blacksmith's shop, and had his atten- 
 tion arrested by hearing the hammers, as they 
 struck the anvil, produce sounds which had a mu- 
 sical relation to each other. On listening further, 
 he found that the intervals were a Fourth, a Fifth, 
 and an Octave; and on weighing the hammers, it 
 appeared that the one which gave the Octave was 
 one-half the heaviest, the one which gave the Fifth 
 was two-thirds, and the one which gave the Fourth 
 was three-quarters. He returned home, reflected 
 upon this phenomenon, made trials, and finally dis- 
 covered, that if he stretched musical strings of 
 equal length, by weights which have the proportion 
 of one-half, two-thirds, and three-fourths, they pro- 
 duced intervals which were an Octave, a Fifth, and 
 
110 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 a Fourth. This observation gave an arithmetical 
 measure of the principal musical intervals, and 
 made Music an arithmetical subject of specula- 
 tion. 
 
 This story, if not entirely a philosophical fable, 
 is undoubtedly inaccurate; for the musical inter- 
 vals thus spoken of, would not be produced by 
 striking with hammers of the weights there stated. 
 But it is true that the notes of strings have a 
 definite relation to the forces which stretch them ; 
 and this truth is still the groundwork of the theory 
 of musical concords and discords (G). 
 
 It may at first appear that the truth, or even 
 the possibility of this history, by referring the dis- 
 covery to accident, disproves our doctrine, that this, 
 like all other fundamental discoveries, required a 
 distinct and well-pondered Idea as its condition. In 
 this, however, as in all cases of supposed accidental 
 discoveries in science, it will be found, that it was 
 exactly the possession of such an Idea which made 
 the accident possible. 
 
 Pythagoras, assuming the truth of the tradition, 
 must have had an exact and ready apprehension 
 of those relations of musical sounds, which are 
 called respectively an Octave, a Fifth, and a Fourth. 
 If he had not been able to conceive distinctly this 
 relation, the sounds of the anvil would have struck 
 his ears to no more purpose than they did those 
 of the smiths themselves. He must have had, too, 
 a ready familiarity with numerical ratios; and* 
 
HARMONICS. Ill 
 
 moreover, (that in which, probably, his superiority 
 most consisted,) a disposition to connect one notion 
 with the other the musical relation with the arith- 
 metical, if it were found possible. When the con- 
 nexion was once suggested, it was easy to devise 
 experiments by which it might be confirmed. 
 
 "The philosophers of the Pythagorean School 1 , 
 and in particular, Lasus of Hermione, and Hip- 
 pasus of Metapontum, made many such experi- 
 ments upon strings ; varying both their lengths and 
 the weights which stretched them; and also upon 
 vessels filled with water, in a greater or less de- 
 gree." And thus was established that connexion 
 of the Idea with the Fact, which this science, like 
 all others, requires. 
 
 I shall quit the Physical Sciences of Ancient 
 Greece, with the above brief statement of the dis- 
 covery of the fundamental principles which they 
 involved ; not only because such initial steps must 
 always be the most important in the progress of 
 science, but because, in reality, the Greeks made 
 no advances beyond these. There took place among 
 them no additional inductive processes, by which 
 new facts were brought under the dominion of 
 principles, or by which principles were presented 
 in a more comprehensive shape than before. Their 
 
 1 Montucla, iii. 10. 
 
112 PHYSICAL SCIENCES IN ANCIENT GREECE. 
 
 advance terminated in a single stride. Archimedes 
 had stirred the intellectual world, but had not put 
 it in progressive motion : the science of mechanics 
 stopped where he left it. And though, in some 
 subjects, as in Harmonics, much was written, the 
 works thus produced consisted of deductions from 
 the fundamental principles, by means of arithme- 
 tical calculations ; occasionally modified, indeed, by 
 reference to the pleasures which music, as an art, 
 affords, but not enriched by any new scientific 
 truths. 
 
113 
 
 NOTES TO BOOK II. 
 
 (E.) p. 96. IT has been objected to the arrangement 
 here employed that it is not symmetrical ; and that 
 Astronomy, as being one of the Physical Sciences, ought 
 to have occupied a chapter in this Second Book, instead 
 of having a whole Book to itself (BooK in). I do not 
 pretend that the arrangement is symmetrical, and have 
 employed it only on the ground of convenience. The 
 importance and extent of the history of Astronomy are 
 such that this science could not, with a view to our 
 purposes, be made co-ordinate with Mechanics or Optics. 
 (F.) p. 108. It is proper to notice more distinctly 
 the nature of the Geometrical Propositions contained in 
 Euclid's work. The Optica contains Propositions con- 
 cerning Vision and Shadows, derived from the principle 
 that the rays of light are rectilinear : as, that the shadow 
 is greater than the object if the illuminating body be less, 
 and vice versa. The Gatoptrica contains Propositions con- 
 cerning the effects of Reflection, derived from the prin- 
 ciple that the Angles of Incidence and Reflection are 
 equal : as, that in a convex mirror the object appears con- 
 vex, and smaller than the object. We see here an exam- 
 ple of the promptitude of the Greeks in deduction. When 
 they had once obtained a knowledge of a principle, they 
 followed it to its mathematical consequences with great 
 acuteness. The subject of concave mirrors is pursued 
 further in Ptolemy's Optics. 
 
 VOL. I. I 
 
114 NOTES TO BOOK II. 
 
 The Greek writers also cultivated the subject of Per- 
 spective speculatively, in mathematical treatises, as well as 
 practically, in pictures. The whole of this theory is a 
 consequence of the principle that vision takes place in 
 straight lines drawn from the object to the eye. 
 
 The ancients were in some measure acquainted with 
 the Refraction as well as the Reflection of Light, as 
 I have noticed in Book ix. Chap. 2. The current know- 
 ledge on this subject must have been very slight and 
 confused; for it does not appear to have enabled them 
 to account for one of the simplest results of Refraction, 
 the magnifying effect of convex transparent bodies. I 
 have noticed in the passage just referred to, Seneca's 
 crude notions on this subject ; and in like manner Pto- 
 lemy in his Optics asserts that an object placed in water 
 must always appear larger than when taken out. Aristotle 
 uses the term di/a/fAacris, (Meteorol. iii. 2), but apparently 
 in a very vague manner. It is not evident that he dis- 
 tinguished Refraction from Reflection. His Commen- 
 tators however do distinguish these as Sia&acris and 
 ai>a/cXacns. See Olympiodorus in Schneider's Eclogce Phy- 
 sicce, vol. i. p. 397. And Refraction had been the sub- 
 ject of special attention among the Greek Mathematicians. 
 Archimedes had noticed (as we learn from the same 
 writer) that in certain cases, a ring which cannot be seen 
 over the edge of the empty vessel in which it is placed, 
 becomes visible when the vessel is filled with water. The 
 same fact is stated in the Optics of Euclid. We do not 
 find this fact explained in that work as we now have it : 
 but in Ptolemy's Optics the fact is explained by a flexure 
 of the visual ray : it is noticed that this flexure is dif- 
 ferent at different angles from the perpendicular, and 
 
NOTES TO BOOK II. 115 
 
 there is an elaborate collection of measures of the flexure 
 at different angles, made by means of an instrument 
 devised for the purpose. There is also a collection of 
 similar measures of the refraction when the ray passes 
 from air to glass, and when it passes from glass to water. 
 This part of Ptolemy's work is, I think, the oldest 
 extant example of a collection of experimental measures, 
 in any other subject than astronomy ; and in astronomy, 
 our measures are the result of observation, rather than 
 of experiment. As Delambre says (Astron. Anc. vol. ii. 
 p. 427.) " On y voit des experiences de physique bien 
 faites, ce qui est sans example chez les anciens." 
 
 Ptolemy's Optical work was known only by Roger 
 Bacon's references to it (Opus Majus, p. 286, &c.) till 
 1816: but copies of Latin translations of it were known 
 to exist in the Royal Library at Paris, and in the 
 Bodleian at Oxford. Delambre has given an account of 
 the contents of the Paris copy in his Astron. Anc. ii. 414. 
 and in the Connoissance des Temps for 1816; and Prof. 
 Rigaud's account of the Oxford copy is given in the 
 article Optics, in the Encyclopaedia Britannica. Ptolemy 
 shews great sagacity in applying the notion of Refraction 
 to the explanation of the displacement of astronomical ob- 
 jects which is produced by the atmosphere, Astronomical 
 Refraction, as it is commonly called. He represents the 
 visual ray as refracted in passing from the ether, which is 
 above the air, into the air ; the air being bounded by a 
 spherical surface which has for its center " the center of all 
 the elements, the center of the earth;" and the refraction 
 being a flexure towards the line drawn perpendicular to 
 this surface. He thus constructs, says Delambre, the 
 same figure on which Cassini afterwards founded the 
 
 12 
 
116 NOTES TO BOOK II. 
 
 whole of his theory ; and gives a theory more complete 
 than that of any astronomer previous to him. Tycho 
 for : instance believed that astronomical refraction was 
 caused only by the vapours of the atmosphere, and did 
 not exist above the altitude of 45. 
 
 Cleomedes, about the time of Augustus, had guessed 
 at Refraction as an explanation of an eclipse in which the 
 sun and moon are both seen at the same time. " Is it not 
 possible, 1 ' he says, " that the ray which proceeds from the 
 eye and traverses moist and cloudy air may bend down- 
 wards to the sun, even when he is below the horizon 2" 
 And Sextus Empiricus, a century later, says, " The air 
 being dense, by the refraction of the visual ray, a constel- 
 lation may be seen above the horizon when it is yet below 
 the horizon." But from what follows, it appears doubtful 
 whether he clearly distinguished Refraction and Reflec- 
 tion. 
 
 In order that we may not attach too much value 
 to the vague expressions of Cleomedes and Sextus Empi- 
 ricus, we may remark that Cleomedes conceives such an 
 eclipse as he describes not to be possible, though he 
 offers an explanation of it if it be : (the fact must occur 
 whenever the moon is seen in the horizon in the middle 
 of an eclipse) : and that Sextus Empiricus gives his sug- 
 gestion of the effect of refraction as an argument why 
 the Chaldean astrology cannot be true, since the con- 
 stellation which appears to be rising at the moment of 
 a birth is not the one which is truly rising. The Chal- 
 deans might have answered, says Delambre, that the star 
 begins to shed its influence, not when it is really in the 
 horizon, but when its light is seen. (Ast. Anc. vol. i. 
 p. 281, and vol. ii. p. 548.) 
 
NOTES TO BOOK If. 117 
 
 It has been said that Vitellio, or Vitello, whom we 
 shall have hereafter have to speak of in the history of 
 Optics, took his Tables of Refractions from Ptolemy. 
 This is contrary to what Delambre states. He says that 
 Vitello may be accused of plagiarism from Alhazen, and 
 that Alhazen did not borrow his Tables from Ptolemy. 
 Roger Bacon had said (Opus Majus, p. 288), " Ptolemeus 
 in libro de Opticis, id est, de Aspectibus, seu in Perspec- 
 tive, sua, qui prius quam Alhazen dedit hanc sententiam, 
 quam a Ptolemaeo acceptam Alhazen exposuit." This re- 
 fers only to the opinion that visual rays proceed from the 
 eye. But this also is erroneous; for Alhazen maintains 
 the contrary: "Visio fit radiis a visibili extrinsecus ad 
 visum manantibus." (Opt. Lib. i. cap. 5.) Vitello says of 
 his Table of Refractions, " acceptis instrumentaliter, prout 
 potuimus propinquius, angulis omnium refractionum . . . 
 invenimus quod semper iidem sunt anguli refractionum: 
 ...secundum hoc fecimus has tabulas." 
 
 (G.) p. 110. Nicomachus says that Pythagoras found 
 the weights to be, as I have mentioned, in the pro- 
 portion of J 2, 6, 8, 9 ; and the intervals, an Octave, 
 corresponding to the proportion 12 to 6, or 2 to 1 ; a 
 Fifth, corresponding to the proportion 12 to 8, or 3 to 2; 
 and a Fourth, corresponding to the proportion 12 to 9, or 
 4 to 3. There is no doubt that this statement of ; the 
 ancient writer is inexact as to the physical fact, for 
 the rate of vibration of a string, on which its note de- 
 pends, is, other things being equal, not as the weight, but 
 as the square root of the weight. But he is right as 
 to the essential point, that those ratios of 2 to 1, 3 to 2, 
 and 4 to 3, are the characteristic ratios of the Octave, 
 Fifth and Fourth. In order to produce these intervals, 
 
118 NOTES TO BOOK II. 
 
 the appended weights must be, not as 12, 9, 8, and 6, 
 but as 12, 6|, 51, and 3. 
 
 The numerical relations of the other intervals of the 
 musical scale, as well as of the Octave, Fifth and Fourth, 
 were discovered by the Greeks. Thus they found that 
 the proportion in a Major Third was 5 to 4 ; in a Minor 
 Third 6 to 5 ; in a Major Tone 9 to 8 ; in a Semitone or 
 Diesis 16 to 15. They even went so far as to deter- 
 mine the Comma, in which the interval of two notes is so 
 small that they are in the proportion of 81 to 80. This 
 is the interval between two notes each of which may be 
 called the Seventeenth above the key-note ; the one note 
 being obtained by ascending a Fifth four times over ; the 
 other being obtained by ascending through two Octaves 
 and a Major Third. The want of coincidence between 
 these two notes is an inherent arithmetical imperfection 
 in the musical scale, of which the consequences are very 
 extensive. 
 
 The numerical properties of the musical scale were 
 worked out to a very great extent by the Greeks, and 
 many of their Treatises on this subject remain to us. 
 The principal ones are the seven authors published by 
 Meibomius*. These arithmetical elements of Music are 
 to the present day important and fundamental portions 
 of the Science of Harmonics. 
 
 * Antiques Musicce Scriptores septem, 1652. 
 
BOOK III. 
 
 HISTORY 
 
 OF 
 
 GREEK ASTRONOMY. 
 
ToSe 8e fjLrjbeis ITOTC (frofirjQfi TOOI/ 'EXX^'i/coi;, cos ov xP'n 7rf P l r " 
 6ela TTOTe TrpayparevccrBai BVTJTOVS omas' Trav Se TOVTOV diavorjdfjvai 
 
 0)S O0T6 a<ppOV (TTl 7TOT6 TO ^6tOJ/, OVT6 ayj/Ol 7TOU TJ^V 
 
 (frv(riv' aXX' oifiej/ ort, SiSao-Koj/ros avrou, ^vz/aicaXov^crei 
 /cai p.adi](j-Tai TO. Sidd(TKop,eva. 
 
 PLATO, Epinomis, p. 988. 
 
 Nor should any Greek have any misgiving of this kind ; that it is 
 not fitting for us to inquire narrowly into the operations of superior 
 Powers, such as those by which the motions of the heavenly bodies 
 are produced: but, on the contrary, men should consider that the 
 Divine Powers never act without purpose, and that they know the 
 nature of man : they know that by their guidance and aid, man may 
 follow and comprehend the lessons which are vouchsafed him on such 
 subjects. 
 
INTRODUCTION. 
 
 THE earliest and fundamental conceptions of 
 men respecting the objects with which Astro- 
 nomy is concerned, are formed by familiar pro- 
 cesses of thought, without appearing to have in 
 them anything technical or scientific. Days, Years, 
 Months, the Sky, the Constellations, are notions 
 which the most uncultured and incurious minds 
 possess. Yet these are elements of the Science of 
 Astronomy. The reasons why, in this case alone, 
 of all the provinces of human knowledge, men 
 were able, at an early and unenlightened period, 
 to construct a science out of the obvious facts of 
 observation, with the help of the common furniture 
 of their minds, will be more apparent in the course 
 of the philosophy of science ; but I may here barely 
 mention two of these reasons. They are, first, that 
 the familiar act of thought, exercised for the com- 
 mon purposes of life, by which we give to an 
 assemblage of our impressions such a unity as is 
 implied in the above notions and terms, a Month, 
 a Year, the Sky, and the like, is, in reality, an 
 inductive act, and shares the nature of the pro- 
 cesses by which all sciences are formed; and, in 
 the next place, that the ideas appropriate to the 
 induction in this case, are those which, even in 
 
122 THE GREEK ASTRONOMY. 
 
 the least cultivated minds, are very clear and de- 
 finite ; namely, the ideas of Space and Figure, 
 Time and Number, Motion and Recurrence. Hence, 
 from their first origin, the modifications of those 
 ideas assume a scientific form. 
 
 We must now trace in detail the peculiar course 
 which, in consequence of these causes, the know- 
 ledge of man respecting the heavenly bodies took, 
 from the earliest period of his history. 
 
123 
 
 CHAPTER I. 
 EARLIEST STAGES OF ASTRONOMY 
 
 Sect. 1. Formation of the Notion of a Year. 
 
 THE notion of a Day is early and obviously 
 impressed upon man in almost any condition 
 in which we can imagine him. The recurrence of 
 light and darkness, of comparative warmth and 
 cold, of noise and silence, of the activity and repose 
 of animals ; the rising, mounting, descending, and 
 setting of the sun; the varying colours of the 
 clouds, generally, notwithstanding their variety, 
 marked by a daily progression of appearances ; 
 the calls of the desire of food and of sleep in man 
 himself, either exactly adjusted to the period of this 
 change, or at least readily capable of being accom- 
 modated to it ; the recurrence of these circum- 
 stances at intervals, equal, so far as our obvious 
 judgment of the passage of time can decide ; and 
 these intervals so short that the repetition is noticed 
 with no effort of attention or memory; this as- 
 semblage of suggestions makes the notion of a day 
 necessarily occur to man, if we suppose him to 
 
124 THE GREEK ASTRONOMY. 
 
 have the conception of Time, and of Recurrence. 
 He naturally marks by a term such a portion of 
 time, and such a cycle of recurrence ; he calls each 
 portion of time, in which this series of appearances 
 and occurrences come round, a Day : and such a 
 group of particulars are considered as appearing 
 or happening in the same day. 
 
 A Year is a notion formed in the same man- 
 ner ; implying in the same way the notion of 
 recurring facts ; and also the faculty of arranging 
 facts in time, and of appreciating their recurrence. 
 But the notion of a Year, though undoubtedly 
 very obvious, is, on many accounts, less so than 
 that of a Day. The repetition of similar circum- 
 stances, at equal intervals, is less manifest in this 
 case, and the intervals being much longer, some 
 exertion of memory becomes requisite in order that 
 the recurrence may be perceived. A child might 
 easily be persuaded that successive years were of 
 unequal length ; or, if the summer were cold, and 
 the spring and autumn warm, might be made to 
 believe, if all who spoke in its hearing agreed to 
 support the delusion, that one year was two. It 
 would be impossible to practise such a deception 
 with regard to the day, without the use of some 
 artifice beyond mere words. 
 
 Still, the recurrence of the appearances which 
 suggest the notion of a Year is so obvious, that we 
 can hardly conceive man without it. But though, 
 in all climes and times, there would be a recur- 
 
EARLIEST STAGES OF ASTRONOMY. 125 
 
 rence, and at the same interval in all, the recur- 
 ring appearances would be extremely different in 
 different countries ; and the contrasts and resem- 
 blances of the seasons would be widely varied. In 
 some places the winter utterly alters the face of 
 the country, converting grassy hills, deep, leafy 
 woods of various hues of green, and running waters, 
 into snowy and icy wastes, and bare snow-laden 
 branches; while in others, the field retains its 
 herbage, and the tree its leaves, all the year ; and 
 the rains and the sunshine alone, or various agricul- 
 tural employments quite different from ours, mark 
 the passing seasons. Yet in all parts of the world 
 the yearly cycle of changes has been singled out 
 from all others, and designated by a peculiar name. 
 The inhabitant of the equatorial regions has the 
 sun vertically over him at the end of every period 
 of six months, and similar trains of celestial pheno- 
 mena fill up each of these intervals, yet we do not 
 find years of six months among such nations. The 
 Arabs alone 1 , who practise neither agriculture nor 
 navigation, have a year depending upon the moon 
 only ; and borrow the word from other languages, 
 when they speak of the solar year. 
 
 In general nations have marked this portion 
 of time by some word which has a reference to the 
 returning circle of seasons and employments. Thus 
 the Latin annus signified a ring, as we see in the 
 derivative annulus: the Greek term eviavTos implies 
 
 1 Ideler, Berl Trans. 1813. p. 51. 
 
126 THE GREEK ASTRONOMY. 
 
 something which returns into Itself: and the word 
 as it exists in Teutonic languages, of which our 
 word year is an example, is said to have its 
 origin in the word yra, which means a ring in 
 Swedish, and is perhaps connected with the Latin 
 gyrus. 
 
 Sect. 2. Fixation of the Civil Year. 
 
 THE year, considered as a recurring cycle of sea- 
 sons and of general appearances, must attract the 
 notice of man as soon as his attention and memory 
 suffice to bind together the parts of a succession 
 of the length of several years. But to make the 
 same term imply a certain fixed number of days, 
 we must know how many days the cycle of the sea- 
 sons occupies; a knowledge which requires faculties 
 and artifices beyond what we have already men- 
 tioned. For instance, men cannot reckon as far as 
 any number at all approaching the number of days 
 in the year, without possessing a system of numeral 
 terms, and methods of practical numeration on 
 which such a system of terms is always founded 2 . 
 The South American Indians, the Koussa Caffres 
 and Hottentots, and the natives of New Holland, 
 all of whom are said to be unable to reckon further 
 than the fingers of their hands and feet 3 , cannot 
 as we do, include, in their notion of a year, the 
 fact of its consisting of 365 days. This fact is not 
 
 2 Arithm. in Encyc. Metrop. (by Dr. Peacock,) Art. 8. 
 
 3 Ibid. Art. 32. 
 
ITS EARLIEST STAGES. 127 
 
 likely to be known to any nation except those 
 which have advanced far beyond that which may 
 be considered as the earliest scientific process which 
 we can trace in the history of the human race, 
 the formation of a method of designating the suc- 
 cessive numbers to an indefinite extent, by means 
 of names, framed according to the decimal, quinary, 
 or vigenary scale. 
 
 But even if we suppose men to have the habit 
 of recording the passage of each day, and of count- 
 ing the score thus recorded, it would be by no 
 means easy for them to determine the exact num- 
 ber of days in which the cycle of the seasons 
 recurs; for the indefiniteness of the appearances 
 which mark the same season of the year, arid the 
 changes to which they are subject as the seasons 
 are early or late, would leave much uncertainty 
 respecting the duration of the year. They would 
 not obtain any accuracy on this head, till they had 
 attended for a considerable time to the motions 
 and places of the sun ; circumstances which require 
 more precision of notice than the general facts of 
 the degrees of heat and light. The motions of the 
 sun, the succession of the places of his rising and 
 setting at different times of the year, the greatest 
 heights which he reaches, the proportion of the 
 length of day and night, would all exhibit several 
 cycles. The turning back of the sun, when he had 
 reached his greatest distance to the south or to 
 the north, as shown either by his rising or by his 
 
128 THE GREEK ASTRONOMY. 
 
 height at noon, would perhaps be the most observ- 
 able of such circumstances. Accordingly the -rpo-rrai 
 rieXioio, the turnings of the sun, are used repeatedly 
 by Hesiod as a mark from which he reckons the 
 seasons of various employments. " Fifty days," he 
 says, " after the turning of the sun, is a seasonable 
 time for beginning a voyage 4 ." 
 
 The phenomena would be different in different 
 climates, but the recurrence would be common to 
 all. Any one of these kinds of phenomena, noted 
 with moderate care for a year, would show what 
 was the number of days of which a year consisted ; 
 and if several years were included in the interval 
 through which the scrutiny extended, the know- 
 ledge of the length of the year so acquired would 
 be proportionally more exact. 
 
 Besides those notices of the sun, which offered 
 exact indications of the seasons, other more inde- 
 finite natural occurrences were used ; as the arrival 
 of the swallow (xe\Mv) and the kite (IKTIV). The 
 birds, in Aristophanes's play of that name, mention 
 it, as one of their offices, to mark the seasons; 
 Hesiod similarly notices the cry of the crane as an 
 indication of the departure of winter 5 . 
 
 Among the Greeks the seasons were at first 
 only summer and winter (Oepos and ^etjuwV), the 
 
 4 "HjUCtTa irevTiiKovTa pera T^OTTC?? r}e\ioto 
 Es T6\o<? eXdovTos Qepeos. 
 
 Op. et Dies, 661. 
 6 Ideler, i. 240. 
 
ITS EARLIEST STAGES. 129 
 
 latter including all the rainy and cold portion of 
 the year. The winter was then subdivided into the 
 Xeinwv and cap, and the summer, less definitely, into 
 06/oos and oTrwpa. Tacitus says that the Germans 
 knew neither the blessings nor the name of autumn, 
 "Autumni perinde nomen ac bona ignorantur." Yet 
 harvest, herbst, is certainly an old German word 6 . 
 
 In the same period in which the sun goes 
 through his cycle of positions, the stars also go 
 through a cycle of appearances belonging to them ; 
 and these appearances were perhaps employed at 
 as early a period as those of the sun in determin- 
 ing the exact length of the year. Many of the 
 groups of fixed stars are readily recognized, as 
 exhibiting always the same configuration ; and par- 
 ticular bright stars are singled out as objects of 
 attention. These are observed, at particular sea- 
 sons, to appear in the west after sunset ; but it is 
 noted that when they do this, they are found nearer 
 and nearer to the sun every successive evening, 
 and at last disappear in his light. It is observed 
 also, that at a certain interval after this, they rise 
 visibly before the dawn of day renders the stars 
 invisible ; and after they are seen to do this, they 
 rise every day at a longer interval before the sun. 
 The risings and settings of the stars under these 
 circumstances, or under others which are easily re- 
 cognized, were, in countries where the sky is usually 
 clear, employed at an early period, to mark the 
 
 ' Ideler, i. 243. 
 VOL. I. K 
 
130 THE GREEK ASTRONOMY. 
 
 seasons of the year. Eschylus 7 makes Prometheus 
 mention this among the benefits of which he, the 
 teacher of arts to the earliest race of men, was the 
 communicator. 
 
 Thus, for instance, the rising 8 of the Pleiades in 
 the evening was a mark of the approach of winter. 
 The rising of the waters of the Nile in Egypt coin- 
 cided with the heliacal rising of Sirius, which star 
 the Egyptians called Sothis. Even without any 
 artificial measure of time or position, it was not 
 difficult to carry observations of this kind to such 
 a degree of accuracy as to learn from them the 
 number of days which compose the year ; and to 
 fix the precise season from the appearance of the 
 stars. 
 
 7 OUK v\v yap auTo?? OVTG ^et/uaro? T6K/j.ap, 
 "OuT* ai/0e/x<oBoue qpos, ow'Se itapTrifjLOv 
 
 fiefiaiov' d\\' arep yvto/jiijs TO rrav 
 o-oi/, co-re ? afyiv a'i/aToA.ccs e<yft> 
 i; e3eta, rets -re 3i'<rKp<Tou? SuVeis. 
 
 Prom. Y. 454. 
 
 8 Ideler (Chronol. i. 242) says that this rising of the Pleiades 
 took place at a time of the year which corresponds to our llth 
 May, and the setting to the 20th October; hut this does not 
 agree with the forty days of their being " concealed/' which, 
 from the context, must mean, I conceive, the interval between 
 their setting and rising. Pliny, however, says, "Yergiliarum 
 exortu sestas incipit, occasu hiems; semestri spatio intra se 
 messes vindemiasque et omnium maturitatem complexse. (H. N. 
 xviii. 69.) 
 
 The autumn of the Greeks, oVwpot, was earlier than our 
 autumn, for Homer calls Sirius da-Trip oirupivds, which rose at 
 the end of July. 
 
ITS EARLIEST STAGES. 131 
 
 A knowledge concerning the stars appears to 
 have been first cultivated with the last-mentioned 
 view, and makes its first appearance in literature 
 with this for its object. Thus Hesiod directs the 
 husbandman when to reap by the rising, and when 
 to plough by the setting of the Pleiades 9 . In like 
 manner Sirius 10 , Arcturus 11 , the Hyades and Orion 12 , 
 are noticed. 
 
 By such means it was determined that the year 
 consisted, at least, nearly, of 365 days. The Egyp- 
 tians, as we learn from Herodotus 13 , claimed the 
 
 'ATAayei/ewi/ e 
 d/jLr}TOV' dpoTOio Be, 
 
 ''At B; TOl VVKTO.S T KCLt YJjJiCLTa. T<T(T6pdKOVTa 
 
 KeKpu(aTi, ai/Ti? Be -rrepnrXo/jievov evtavrov 
 Qdivovrat. 
 
 Op. et Dies, 1. 381. 
 
 10 1. 413. 
 
 11 EVT' aV B' e^ijKovra /uera T^OTra? rjeXioio 
 
 ea-y Zeu<? ^/xara, S/ pa TOT da-Ttjp 
 irpoXfiroav tepov poov 'fiiceai/o?o 
 TlpcaTov TrajOK^ati/wi/ eTTireAXerat dtcpoKvetyaios. 
 
 Ib. 562. 
 
 'EuT aV 3' Qpiu)i> Kai 2etpto? e? jj.e<rov e\6y 
 
 oi/, ApKTovpov B* eo-iBt; ^oBoBctKruXo? ;(o?. 
 
 Ib. 607. 
 
 . avTap Girrjv 
 'Ya'Be? TC TO TC a-devos ' 
 
 Ib. 612. 
 
 These methods were employed to a late period, because the 
 .Greek months, being lunar, did not correspond to the seasons. 
 Tables of such motions were called TrapaTr^Y/waTa. Ideler, Hist. 
 Untersuchungen, p. 209. 
 
 13 ii. 4. 
 
 K2 
 
132 THE GREEK ASTRONOMY. 
 
 honour of this discovery. The priests informed 
 him, he says, "that the Egyptians were the first 
 men who discovered the year, dividing it into 
 twelve equal parts; and this they asserted that they 
 discovered from the stars." Each of these parts 
 or months consisted of 30 days, and they added 5 
 days more at the end of the year, " and thus the 
 circle of the seasons comes round." It seems, also, 
 that the Jews, at an early period, had a similar 
 reckoning of time, for the Deluge which continued 
 150 days (Gen. vii. 24,) is stated to have lasted 
 from the 17th day of the second month (Gen. vii. 11) 
 to the 17th day of the seventh month (Gen. viii. 4,) 
 that is, 5 months of 30 days. 
 
 A year thus settled as a period of a certain 
 number of days is called a Civil Year. It is one 
 of the earliest discoverable institutions of states 
 possessing any germ of civilization; and one of the 
 earliest portions of human systematic knowledge 
 is the discovery of the length of the civil year, 
 so that it should agree with the natural year, or 
 year of the seasons. 
 
 Sect. 3. Correction of the Civil Year. (Julian 
 Calendar.) 
 
 IN reality, by such a mode of reckoning as we 
 have described, the circle of the seasons would not 
 come round exactly. The real length of the year 
 is very nearly 365 days and a quarter. If a year 
 of 365 days were used, in four years the year 
 
ITS EARLIEST STAGES. 133 
 
 would begin a day too soon, when considered with 
 reference to the sun and stars ; and in 60 years it 
 would begin 15 days too soon, a quantity percep- 
 tible to the loosest degree of attention. The civil 
 year would be found not to coincide with the year 
 of the seasons ; the beginning of the former would 
 take place at different periods of the latter; it 
 would wander into various seasons, instead of re- 
 maining fixed to the same season; the term year, 
 and any number of years, would become ambi- 
 guous ; some correction, at least some comparison, 
 would be requisite. 
 
 We do not know by whom the insufficiency of 
 the year of 365 days was first discovered 14 ; we 
 find this knowledge diffused among all civilized 
 nations, and various artifices used in making the 
 correction. The method which we employ, and 
 which consists in reckoning an additional day at 
 the end of February every fourth or leap year, is 
 an example of the principle of intercalation, by 
 which the correction was most commonly made. 
 Methods of intercalation for the same purpose were 
 found to exist in the new world. The Mexicans 
 added 13 days at the end of every 52 years. The 
 method of the Greeks was more complex; (by 
 means of the octaeteris or cycle of 8 years ;) but 
 it had the additional object of accommodating itself 
 
 14 Syncellus (Chronographia, p. 123), says, that according to 
 the legend, it was King Aseth who first added the 5 additional 
 days to 360, for the year, in the eighteenth century B. c. 
 
134 THE GREEK ASTRONOMY. 
 
 to the motions of the moon, and therefore must 
 be treated of hereafter. The Egyptians, on the 
 other hand, knowingly permitted their civil year 
 to wander, at least so far as their religious observ- 
 ances were concerned. "They do not wish," says 
 Geminus 15 , "the same sacrifices of the gods to be 
 made perpetually at the same time of the year, 
 but that they should go through all the seasons, 
 so that the same feast may happen in summer and 
 winter, in spring and autumn." The period in, 
 which any festival would thus pass through all the 
 seasons of the year is 1461 years ; for 1460 years 
 of 365^ days are equal to 1461 years of 365 days. 
 This period of 1461 years is called the Sothic 
 period, from Sothis, the name of the dog-star, by 
 which their fixed year was determined; and for the 
 same reason it is called the canicular period 16 . 
 
 Other nations did not regulate their civil year 
 by intercalation at short intervals, but rectified it 
 by a reform when this became necessary. The 
 Persians are said to have added a month of 30 
 days every 120 years. The Roman calendar, at 
 first very rude in its structure, was reformed by 
 Numa, and was directed to be kept in order by the 
 perpetual interposition of the augurs. This, how- 
 ever, was, from various causes, not properly done ; 
 and the consequence was, that the reckoning fell 
 into utter disorder, in which state it was found by 
 
 15 Uranol. p. 33. 
 
 16 Censorinus de Die Natali, c. 18. 
 
ITS EARLIEST STAGES. 135 
 
 Julius Caesar, when he became dictator. By the 
 advice of Sosigenes, he adopted the mode of inter- 
 calation of one day in 4 years, which we still retain; 
 and in order to correct the derangement which had 
 already been produced, he added 90 days to a year 
 of the usual length, which thus became what was 
 called the year of confusion. The Julian Calen- 
 dar, thus reformed, came into use, January 1, 
 B. c. 45. 
 
 Sect. 4. Attempts at the Fixation of the Month. 
 
 THE circle of changes through which the moon 
 passes in about thirty days, is marked, in the 
 earliest stages of language, by a word which implies 
 the space of time which one such circle occupies ; 
 just as the circle of changes of the seasons is desig- 
 nated by the word year. The lunar changes are, 
 indeed, more obvious to the sense, and strike a 
 more careless person, than the annual ; the moon, 
 when the sun is absent, is almost the sole natural 
 object which attracts our notice ; and we look at 
 her with a far more tranquil and agreeable atten- 
 tion than we bestow on any other celestial object. 
 Her changes of form and place are definite and 
 striking to all eyes; they are uninterrupted, and 
 the duration of their cycle is so short as to require 
 no effort of memory to embrace it. Hence it ap- 
 pears to be more easy, and in earlier stages of 
 civilization more common, to count time by moons 
 than by years. 
 
136 THE GREEK ASTRONOMY. 
 
 The words by which this period of time is desig- 
 nated in various languages, seem to refer us to the 
 early history of language. Our word month is con- 
 nected with the word moon, and a similar con- 
 nexion is noticeable in the other branches of the 
 Teutonic. The Greek word u.v\v in like manner is 
 related to wvy, which, though not the common 
 word for the moon, is found in Homer with that 
 signification. The Latin word mensis is probably 
 connected with the same group 17 . 
 
 The month is not any exact number of days, 
 being more than 29 and less than 30. The latter 
 number was first tried, for men more readily select 
 numbers possessing some distinction of regularity. 
 It existed for a long period in many countries. A 
 very few months of 30 days, however, would suffice 
 to derange the agreement between the days of the 
 months and the moon's appearance. A little fur- 
 ther trial would show that months of 29 and 30 
 days alternately, would preserve, for a consider- 
 able period, this agreement. 
 
 17 Cicero derives this word from the verb to measure ; " quia 
 mensa spatia conficiunt menses nominantur :" and other etymolo- 
 gists, with similar views, connect the above-mentioned words 
 with the Hebrew manah, to measure, (with which the Arabic 
 work almanack is connected.) Such a derivation would have 
 some analogy with that of annus, &c., noticed above : but if we 
 are to attempt to ascend to the earliest condition of language, 
 we must conceive it probable that men would have a name for 
 a most conspicuous visible object, the moon, before they would 
 have a verb denoting the very abstract and general notion, to 
 measure. 
 
ITS EARLIEST STAGES. 137 
 
 The Greeks adopted this calendar, and, in con- 
 sequence, considered the days of their month as 
 representing the changes of the moon : the last day 
 of the month was called evrj Kal vea, "the old and 
 new," as belonging to both the waning and the 
 reappearing moon 18 : and their festivals and sacri- 
 fices, as determined by the calendar, were con- 
 ceived to be necessarily connected with the same 
 periods of the cycles of the sun and moon. " The 
 laws and the oracles," says Geminus, "which di- 
 rected that they should in sacrifices observe three 
 things, months, days, years, were so understood." 
 With this persuasion, a correct system of intercala- 
 tion became a religious duty. 
 
 The above rule of alternate months of 29 and 
 30 days, supposes the length of the months 29 days 
 and a half, which is not exactly the length of a 
 lunar month. Accordingly the Months and the 
 Moon were soon at variance. Aristophanes, in 
 " The Clouds," makes the Moon complain of the 
 disorder when the calendar was deranged. 
 
 OVK ayeiv rd? yimepas 
 
 /~v ' ^ * '/"I"" '\"\'' ' ' ^ ^ ** 
 
 (Jvcev opuws, aX\ avw re /ecu KCITO) KvooicoTrav 
 ''Q<jT ctTretXelv <pri<j\v ctvrfi TOVS Oeovs e/ca<rroTe 
 
 18 Aratus says of the moon, in a passage quoted by Geminus,, 
 p. 33: 
 
 "Aiei B' u\\odev a\\a TrapctKXivovo-a 
 7repiT\\ r rai 
 
 As still her shifting visage changing turns 
 By her we count the monthly round of morns. 
 
138 THE GREEK ASTRONOMY. 
 
 'Hi/<V av -^/evorOcoo-i SC/OTOV KCLTTLWUIV 
 
 TJ/S eoprrjs ju.tj TV^OVTCS Kara \oyov TWV '/}/u.pa)v. 
 
 Nubes, 61519. 
 
 CHORUS OF CLOUDS. 
 
 The Moon by us to you her greeting sends, 
 
 But bids us say that she's an ill-used moon, 
 
 And takes it much amiss that you should still 
 
 Shuffle her days, and turn them topsy-turvy; 
 
 And that the gods (who know their feast-days well,) 
 
 By your false count are sent home supperless, 
 
 And scold and storm at her for your neglect 19 . 
 
 The correction of this inaccuracy, however, was 
 not pursued separately, but was combined with 
 another object, the securing a correspondence be- 
 tween the lunar and solar years, the main purpose 
 of all early cycles. 
 
 Sect. 5. Invention of Lunisolar Years. 
 
 THERE are 12 complete lunations in a year ; which 
 according to the above rule, would make 354 days, 
 leaving 12 J days of difference between such a lunar 
 year and a solar year. It is said, that at an early 
 period, this was attempted to be corrected by inter- 
 polating a month of 30 days every alternate year ; 
 and Herodotus 20 relates a conversation of Solon, 
 implying a still ruder mode of intercalation. This 
 
 19 This passage is supposed by the commentators to be 
 intended as a satire upon those who had introduced the cycle of 
 Meton (spoken of in Sect. 5), which had been done at Athens a 
 few years before " The Clouds" was acted. 
 
 20 B. i. c. 15. 
 
ITS EARLIEST STAGES. 139 
 
 can hardly be considered as an improvement in the 
 Greek calendar already described. 
 
 The first cycle which produced any near corre- 
 spondence of the reckoning of the moon and the 
 sun, was the Octaeteris, or period of 8 years: 8 
 years of 354 days, together with 3 months of 30 
 days each, making up (in 99 lunations,) 2922 days ; 
 which is exactly the amount of 8 years of 365^ 
 days each. Hence this period would answer its 
 purpose so far as the above lengths of the lunar 
 and solar cycles are exact; and it might assume 
 various forms, according to the manner in which 
 the three intercalary months were distributed. The 
 customary method was to add a thirteenth month 
 at the end of the third, fifth, and eighth year of 
 the cycle. This period is ascribed to various per- 
 sons and times; probably different persons pro- 
 posed different forms of it. Dodwell places its 
 introduction in the 59th Olympiad, or in the 6th 
 century, B. c. : but Ideler thinks the astronomical 
 knowledge of the Greeks of that age was too 
 limited to allow of such a discovery. 
 
 This cycle, however, was imperfect. The dura- 
 tion of 99 lunations is something more than 2922 
 days; it is more nearly 29231; hence in 16 years 
 there was a deficiency of 3 days, with regard to 
 the motions of the moon. This cycle of 16 years 
 (Hecccedecaeteris), with 3 interpolated days at the 
 end, was used, it is said, to bring the calculation 
 right with regard to the moon; but in this way 
 
140 THE GREEK ASTRONOMY. 
 
 the origin of the year was displaced with regard to* 
 the sun. After 10 revolutions of this cycle, or 
 160 years, the interpolated days would amount to 
 30, and hence the end of the lunar year would be 
 a month in advance of the end of the solar. By 
 terminating the lunar year at the end of the pre- 
 ceding month, the two years would again be 
 brought into agreement : and we have thus a cycle 
 of 160 years 21 . 
 
 This cycle of 160 years, however, was calcu- 
 lated from the cyle of 16 years; and was probably 
 never used in civil reckoning ; which the others, or 
 at least that of 8 years, appear to have been. 
 
 The cycles of 16 and 160 years, were correc- 
 tions of the cycle of 8 years; and were readily 
 suggested, when the length of the solar and lunar 
 periods became known with accuracy. But a much 
 more exact cycle, independent of these, was dis- 
 covered and introduced by Meton 22 , 432 years B. c. 
 This cycle consisted of 19 years, and is so correct 
 and convenient, that it is in use among ourselves 
 to this day. The time occupied by 19 years, and 
 by 235 lunations, is very nearly the same; (the 
 former time is less than 6940 days by 9^ hours, 
 the latter, by 7^ hours.) Hence, if the 19 years 
 be divided into 235 months, so as to agree with the 
 changes of the moon, at the end of that period 
 the same succession may begin again with great 
 exactness. 
 
 sl Geminus. Ideler. sa Ideler, Hist. Unters. p. 208. 
 
ITS EARLIEST STAGES. 141 
 
 In order that 235 months, of 30 and 29 days, 
 may make up 6940 days, we must have 125 of the 
 former, which were called full months, and 110 
 of the latter, which were termed hollow. An 
 artifice was used in order to distribute 110 hollow 
 months among 6940 days. It will be found that 
 there is a hollow month for each 63 days nearly. 
 Hence if we reckon 30 days to every month, but at 
 every 63d day leap over a day in the reckoning, 
 we shall, in the 19 years, omit 110 days ; and this 
 accordingly was done. Thus the 3d day of the 
 3d month, the 6th day of the 5th month, the 9th 
 day of the 7th, must be omitted, so as to make 
 these months ' hollow.' Of the 19 years, seven 
 must consist of 13 months; and it does not appear 
 to be known according to what order these seven 
 years were selected. Some say they were the 3d, 
 6th, 8th, llth, 14th, 17th, and 19th; others, the 
 3d, 5th, 8th, llth, 13th, 16th, and 19th. 
 
 The near coincidence of the solar and lunar 
 periods in this cycle of 19 years, was undoubtedly 
 a considerable discovery at the time when it was 
 first accomplished. It is not easy to trace the way 
 in which such a discovery was made at that time ; 
 for we do not even know the manner in which 
 men then recorded the agreement or difference 
 between the calendar day and the celestial pheno- 
 menon which ought to correspond to it. It is 
 most probable, that the length of the month was 
 obtained with some exactness, by the observation 
 
142 THE GREEK ASTRONOMY. 
 
 of eclipses, at considerable intervals of time from 
 each other; for eclipses are very noticeable phe- 
 nomena, and must have been very soon observed 
 to occur only at new and full moon 23 . 
 
 The exact length of a certain number of months 
 being thus known, the discovery of a cycle which 
 should regulate the calendar with sufficient accu- 
 racy, would be a business of arithmetical skill, and 
 would depend, in part, on the existing knowledge 
 of arithmetical methods ; but in making the dis- 
 covery, a natural arithmetical sagacity was pro- 
 bably more efficacious than method. It is very 
 possible that the Cycle of Melon is correct more 
 nearly than its author was aware, and more nearly 
 than he could ascertain from any evidence and 
 calculation known to him. It is so exact that it 
 is still used in calculating the new moon for the 
 time of Easter; and the Golden Number, which 
 is spoken of in stating such rules, is the number 
 of this Cycle corresponding to the current year 24 . 
 
 Meton's Cycle was corrected a hundred years 
 later (330 B. c.), by Calippus, who discovered the 
 
 23 Thucyd. vii. 50. *H o-eAtji/f? efcAetTrer ervy^ave yap irav<re- 
 Xrjvos ov<ra. iv. 52. Tov q\iov 6K&HT ri eyevero irep\ vov- 
 jj.r]victv. ii. 28. Nou/A7i//a K.O.TO. treXtjvrjv (Jatrirep K.O.I fjiovov oo/ce? 
 ctvai yiyvecrOat Sui/aroi/) o qXios e^eXnre /xera ae<rt//u/?|0<ai/ KCU TraAti/ 
 av 67r \/0co 0f/, yei/ojmei/os /nrjvoeicri'i KOI dcrTeptav Tivtov eKfyavewrutv. 
 
 * 4 The same cycle of 19 years has been used by the Chinese 
 for a very great length of time ; their civil year consisting, like 
 that of the Greeks, of months of 29 and 30 days. 
 
 The Siamese also have this period. (Astron. Lib. U. K.) 
 
ITS EARLIEST STAGES. 143 
 
 error of it by observing an eclipse of the moon 
 six years before the death of Alexander 25 . In this 
 corrected period, four cycles of 19 years were 
 taken, and a day left out at the end of the 76 
 years, in order to make allowance for the hours 
 by which, as already observed, 6940 days are 
 greater than 19 years, and than 235 lunations : 
 and this Calippic period is used in Ptolemy's Al- 
 magest, in stating observations of eclipses. 
 
 The Metonic and Calippic periods undoubtedly 
 imply a very considerable degree of accuracy in the 
 knowledge which the astronomers, to whom they 
 are due, had of the length of the month ; and the 
 first is a very happy invention for bringing the 
 solar and lunar calendars into agreement. 
 
 The Roman Calendar, from which our own is 
 derived, appears to have been a much less skilful 
 contrivance than the Greek; though scholars are 
 not agreed on the subject of its construction, we 
 can hardly doubt that months, in this as in other 
 cases, were intended originally to have a reference 
 to the moon. In whatever manner the solar and 
 lunar motions were intended to be reconciled, the 
 attempt seems altogether to have failed, and to 
 have been soon abandoned. The Roman months, 
 both before and after the Julian correction, were 
 portions of the year, having no reference to full 
 and new moons ; and we, having adopted this divi- 
 sion of the year, have thus, in our common calen- 
 15 Delamb. A. A. p. 17- 
 
144 THE GREEK ASTRONOMY. 
 
 dar, the traces of one of the early attempts of 
 mankind to seize the law of the succession of 
 celestial phenomena, in a case where the attempt 
 was a complete failure. 
 
 Considered as a part of the progress of our 
 astronomical knowledge, improvements in the calen- 
 dar do not offer many points to our observation, 
 but they exhibit a few very important steps. Ca- 
 lendars which, belonging apparently to unscientific 
 ages and nations, possess a great degree of accord- 
 ance with the true motions of the sun and moon, 
 like the solar calendar of the Mexicans, and the 
 lunar calendar of the Greeks, contain the only 
 record now extant of discoveries which must have 
 required a great deal of observation, of thought, 
 and probably of time. The later improvements in 
 calendars, which take place when astronomical ob- 
 servation has been attentively pursued, are of little 
 consequence to the history of science; for they 
 are generally founded on astronomical determina- 
 tions, and are posterior in time, and inferior in 
 accuracy, to the knowledge on which they depend. 
 But cycles of correction, which are both short and 
 close to exactness, like that of Meton, may perhaps 
 be the original form of the knowledge which they 
 imply; and certainly require both accurate facts 
 and sagacious arithmetical reasonings. The dis- 
 covery of such a cycle must always have the ap- 
 pearance of a happy guess, like other discoveries 
 of laws of nature. Beyond this point, the interest 
 
ITS EARLIEST STAGES. 145 
 
 of the study of calendars, as bearing on our sub- 
 ject, ceases: they may be considered as belonging 
 rather to art than to science ; rather as an appli- 
 cation of a part of our knowledge to the uses of 
 life, than a means or an evidence of its extension. 
 
 Sect. 6. The Constellations. 
 
 SOME tendency to consider the stars as formed into 
 groups, is inevitable when men begin to attend to 
 them ; but how men were led to the fanciful system 
 of names of Stars and of Constellations, which we 
 find to have prevailed in early times, it is very 
 difficult to determine. Single stars, and very close 
 groups, as the Pleiades, were named in the time 
 of Homer and Hesiod, and at a still earlier period, 
 as we find in the book of Job 26 . 
 
 Two remarkable circumstances with respect to 
 the Constellations are, first, that they appear in most 
 cases to be arbitrary combinations; the artificial 
 figures which are made to include the stars, not 
 having any resemblance to their obvious configura- 
 tions ; and, second, that these figures, in different 
 
 26 Job xxxviii. 31. " Canst thou bind the sweet influences of 
 Chima (the Pleiades), or loose the bands of Kesil (Orion) ? Canst 
 thou bring forth Mazzaroth (Sirius) in his season? or canst 
 thou guide Ash (or Aisch) ( Arcturus) with his sons ?" 
 
 And ix. 9. " Which maketh Arcturus, Orion, and Pleiades, 
 and the chambers of the south." 
 
 Dupuis, vi. 545, thinks that Aisch was cuf , the goat and kids. 
 See Hyde, Ulughbeigh. 
 
 VOL. I. L 
 
146 THE GREEK ASTRONOMY. 
 
 countries, are so far similar, as to imply some com- 
 munication. The arbitrary nature of these figures 
 shows that they were rather the work of the ima- 
 ginative and mythological tendencies of man, than 
 of mere convenience and love of arrangement. 
 " The constellations," says an astronomer of our 
 own time 27 , "seem to have been almost purposely 
 named and delineated to cause as much confusion 
 and inconvenience as possible. Innumerable snakes 
 twine through long and contorted areas of the 
 heavens, where no memory can follow them : bears, 
 lions, and fishes, large and small, northern and 
 southern, confuse all nomenclature. A better system 
 of constellations might have been a material help 
 as an artificial memory." When men indicate the 
 stars by figures, borrowed from obvious resem- 
 blances, they are led to combinations quite dif- 
 ferent from the received constellations. Thus the 
 common people in our own country find a wain 
 or waggon, or a plough, in a portion of the great 
 bear 28 . 
 
 The similarity of the constellations recognized 
 in different countries is very remarkable. The Chal- 
 dean, the Egyptian, and the Grecian skies have a 
 resemblance which cannot be overlooked. Some 
 
 27 Sir J. Herschel. 
 
 28 So also the Greeks, Homer. 77. xvm. 487. 
 
 The northern bear which oft the wain they call. 
 
 was the traditional name, a'^afa, that suggested by the 
 form. 
 
ITS EARLIEST STAGES. 147 
 
 have conceived that this resemblance may be traced 
 also in the Indian and Arabic constellations, at 
 least in those of the zodiac 29 . But while the 
 figures are the same, the names and traditions con- 
 nected with them are different, according to the 
 histories and localities of each country 30 ; the river 
 among the stars which the Greeks called the Eri- 
 danus, the Egyptians asserted to be the Nile. Some 
 conceive that the signs of the zodiac, or path along 
 which the sun and moon pass, had its divisions 
 marked by signs which had a reference to the 
 course of the seasons, to the motion of the sun, or 
 the employments of the husbandman. If we take 
 the position of the heavens, which, from the know- 
 ledge we now possess, we are sure they must have 
 had 15000 years ago, the significance of the signs 
 of the zodiac, in which the sun was, as referred 
 to the Egyptian year, becomes very marked 31 , and 
 has led some to suppose that the zodiac was in- 
 vented at such a period. Others have rejected this 
 as an improbably great antiquity, and have thought 
 it more likely that the constellation assigned to 
 each season was that which at that season rose 
 at the beginning of the night : thus the balance 
 (which is conceived to designate the equality of 
 days and nights) was placed among the stars which 
 
 29 Dupuis, vi. 548. The Indian zodiac contains, in the place 
 of our Capricorn, a ram and a fish, which proves the resem- 
 blance without chance of mistake. Bailly, i. p. 157- 
 
 30 Dupuis, vi. 549. 31 Laplace, Hist. Astron. p. 8. 
 
 L2 
 
148 THE GREEK ASTRONOMY. 
 
 rose in the evening : when the spring began: this 
 would fix the origin of these signs 2500 years 
 before our era. . 
 
 It is clear, as has already been said, that fancy, 
 and probably superstition, had a share in forming 
 the collection of constellations. It is certain that, 
 at an early period, superstitious notions were asso- 
 ciated with the stars 32 . Astrology is of very high 
 antiquity in the East. The stars were supposed to 
 influence the character and destiny of man, and 
 to be in some way connected with superior natures 
 and powers. 
 
 We may, . I conceive, look upon the formation 
 of the constellations, and the notions thus con- 
 nected with them, as a very early attempt to find 
 a meaning in the relations of the stars ; and as an 
 utter failure. The first effort to associate the ap- 
 pearances and motions of the skies by conceptions 
 implying unity and connexion, was made in a 
 wrong direction, as may very easily be supposed. 
 Instead of considering the appearances only with 
 reference to space, time, number, in a manner 
 purely rational, a number of other elements, ima- 
 gination, tradition, hope, fear, awe of the super- 
 natural, belief in destiny, were called into action. 
 Man, still young, as a philosopher at least, had yet 
 to learn what notions his successful guesses on these 
 subjects must involve, and what they must exclude. 
 At that period, nothing could be more natural or 
 
 32 Dupuis, vi. 546. 
 
ITS EARLIEST STAGES. 140 
 
 excusable than this ignorance ; but it is curious to 
 see how long obstinately the belief lingered (if 
 indeed it be yet extinct) that the motions of the 
 stars, and the dispositions and fortunes of men, 
 may come under some common conceptions and 
 laws, by which a connexion between the one and 
 the other may be established. 
 
 We cannot, therefore, agree with those who 
 consider astrology in the early ages as "only a 
 degraded astronomy, the abuse of a more ancient 
 science 33 ." It was the first step to astronomy, by 
 leading to habits and means of grouping pheno- 
 mena ; and, after a while, by showing that pictorial 
 and mythological relations among the stars had 
 no value, or at least no very obvious value. From 
 that time, the inductive process went on steadily 
 in the true road, under the guidance of ideas of 
 space, time, and number. 
 
 Sect. 7. The Planets. 
 
 WHILE men were becoming familiar with the fixed 
 stars, the planets must have attracted their notice. 
 Venus, from her brightness, and from her accom- 
 panying the sun at no great distance, and thus 
 appearing as the morning and evening star, was 
 very conspicuous. Pythagoras is said to have main- 
 tained that the evening and morning star are the 
 same body; which certainly must have been one 
 13 Dupuis, vi. 546. 
 
150 THE GREEK ASTRONOMY. 
 
 of the earliest discoveries on this subject ; and 
 indeed, we can hardly conceive men noticing the 
 stars for a year or two without coming to this 
 conclusion. 
 
 Jupiter and Mars, sometimes still brighter than 
 Venus, were also very noticeable. Saturn and Mer- 
 cury were less so, but in fine climates they and 
 their motion would soon be detected by persons 
 observant of the heavens. To reduce to any rule 
 the movements of these luminaries must have taken 
 time and thought; probably before this was done, 
 certainly very early, these heavenly bodies were 
 brought more peculiarly under those views which 
 we have noticed as leading to astrology. 
 
 At a time beyond the reach of certain history, 
 the planets, along with the sun and moon, had 
 been arranged in a certain recognized order by the 
 Egyptians or some other ancient nation. Probably 
 this arrangement had been made according to the 
 slowness of their motions among the stars; for 
 though the motion of each is very variable, the 
 gradation of their velocities is, on the whole, very 
 manifest ; and the different rate of travelling of 
 the different planets, and probably other circum* 
 stances of difference, led, in the ready fancy of early 
 times, to the attribution of a peculiar character to 
 each luminary. Thus Saturn was held to be of 
 a cold and gelid nature; Jupiter, who, from his 
 more rapid motion, was supposed to be lower in 
 
ITS EARLIEST STAGES. 151 
 
 place, was temperate ; Mars, fiery, and the 
 like 34 . 
 
 It is not necessary to dwell on the details of 
 these speculations, but we may notice a very re- 
 markable evidence of their antiquity and generality 
 in the structure of one of the most familiar of our 
 measures of time, the Week. This distribution 
 of time according to periods of seven days, comes 
 down to us, as we learn from the Jewish scrip- 
 tures, from the beginning of man's existence on 
 the earth. The same usage is found over all the 
 East; it existed among the Arabians, Assyrians, 
 Egyptians 35 . The same week is found in India 
 among the Bramins; it has, there also, its days 
 marked by those of the heavenly bodies; and it 
 has been ascertained that the same day has, in 
 that country, the name corresponding with its de- 
 signation in other nations. 
 
 The notion which led to the usual designations 
 of the days of the week is not easily unravelled. 
 The days each correspond to one of the heavenly 
 bodies, which were, in the earliest systems of the 
 world, conceived to be the following, enumerating 
 
 34 Achilles Tatius (Uranol pp. 135, 136,) gives the Grecian 
 and Egyptian names of the planets. 
 
 Egyptian. Greek. 
 
 Saturn . . Ne^eo-e'ws Kpoi/ou da-Trjp tpaivcov 
 
 Jupiter . . 'Ocr/|oi3o9 Alb? 
 Mars . . 'HjOctKAeoi/s 
 Venus . . A(f)po%iTt]<; 
 
 Mercury . 'ATroAAwi/o? 'Ep^ou 
 
 35 Laplace, Hist. Aslron. p. 16. 
 
152 THE GREEK ASTRONOMY. 
 
 them in the order of their remoteness from the 
 earth 36 ; Saturn, Jupiter, Mars, the Sun, Venus, 
 Mercury, the Moon. At a later period, the received 
 systems placed the seven luminaries in the seven 
 spheres. The knowledge which was implied in this 
 view, and the time when it was obtained, we must 
 consider hereafter. The order in which the names 
 are assigned to the days of the week (beginning 
 with Saturday,) is, Saturn, the Sun, the Moon, 
 Mars, Mercury, Jupiter, Venus; and various ac- 
 counts are given of the manner in which one of 
 these orders is obtained from the other; all the 
 methods proceeding upon certain arbitrary arith- 
 metical processes, connected in some way with 
 astrological views. It is perhaps not worth our 
 while here- to examine further the steps of this 
 process; it would be difficult to determine with 
 certainty why the former order of the planets was 
 adopted, and how and why the latter was deduced 
 from it. But there is something very remarkable 
 in the universality of the notions, apparently so 
 fantastic, which have produced this result; and we 
 may probably consider the Week, with Laplace 37 , 
 as "the most ancient monument of astronomical 
 knowledge." This period has gone on without in- 
 terruption or irregularity from the earliest recorded 
 times to our own days, traversing the extent of 
 ages and the revolutions of empires ; the names of 
 the ancient deities which were associated with the 
 38 Pkilol. Mus. No. 1. 37 Hist. Ast. p. 17- 
 
. ITS EARLIEST STAGES. 153 
 
 stars have been replaced by those of the objects of 
 the worship of our Teutonic ancestors; according 
 to their views of the correspondence of the two 
 mythologies ; and the Quakers, in rejecting these 
 names of days, have cast aside the most ancient 
 existing relic of astrological as well as idolatrous 
 superstition. 
 
 Sect. 8. The Circles of the Sphere. 
 
 THE inventions hitherto noticed, though undoubt- 
 edly they were steps in astronomical knowledge, 
 can hardly be considered as purely abstract and 
 scientific speculations; for the exact reckoning of 
 time is one of the wants, even of the least civilized 
 nations. But the distribution of the places and 
 motions of the heavenly bodies by means of a 
 celestial sphere with imaginary lines drawn upon 
 it, is a step in speculative astronomy, and was occa- 
 sioned and rendered important by the scientific 
 propensities of man. 
 
 It is not easy to say with whom this notion 
 originated. Some parts of it are obvious. The 
 appearance of the sky naturally suggests the idea 
 of a concave Sphere, with the stars fixed on its 
 surface. Their motions during any one night, it 
 would be readily seen, might be represented by 
 supposing this Sphere to turn round a Pole or 
 Axis ; for there is a conspicuous star in the heavens 
 which apparently stands still (the Pole-star); all the 
 others travel round this in circles, and keep the 
 
154 THE GREEK ASTRONOMY. 
 
 same positions with respect to each other. This 
 stationary star is every night the same, and in the 
 same place ; the other stars also have the same 
 relative position ; but their general position at the 
 same time of night varies gradually from night to 
 night, so as to go through its cycle of appearances 
 once a year. All this would obviously agree with 
 the supposition that the sky is a concave sphere 
 or dome, that the stars have fixed places on this 
 sphere, and that it revolves perpetually and uni- 
 formly about the Pole or fixed point. 
 
 But this supposition does not at all explain the 
 way in which the appearances of different nights 
 succeed each other. This, however, may be ex- 
 plained, it appears, by supposing the sun also to 
 move among the stars on the surface of the con- 
 cave sphere. The sun by his brightness makes the 
 stars invisible which are on his side of the heavens; 
 this we can easily believe; for the moon, when 
 bright, also puts out all but the largest stars ; and 
 we see the stars appearing in the evening, each 
 in its place, according to their degree of splendour, 
 as fast as the declining light of day allows them 
 to become visible. And as the sun brings day, and 
 his absence night, if he move through the circuit 
 of the stars in a year, we shall have, in the course 
 of that time, every part of the starry sphere in 
 succession presented to us as our nocturnal sky. 
 
 This notion, that the sun moves round among 
 the stars in a year, is the basis of astronomy, 
 
ITS EARLIEST STAGES. 155 
 
 and a considerable part of the science is only the 
 developement and particularization of this general 
 conception. It is not easy to ascertain either the 
 exact method by which the path of the sun among 
 the stars was determined, or the author and date 
 of the discovery. That there is some difficulty in 
 tracing the course of the sun among the stars will 
 be clearly seen, when it is considered that no star 
 can ever be seen at the same time with the sun. 
 If the whole circuit of the sky be divided into 
 twelve parts or signs, it is estimated by Autolycus, 
 the oldest writer on these subjects whose works 
 remain to us 38 , that the stars which occupy one of 
 these parts are obsorbed by the solar rays, so that 
 they cannot be seen. Hence the stars which are 
 seen nearest to the place of the setting and the 
 rising sun in the evening and in the morning, are 
 distant from him by the half of a sign ; the evening 
 stars being to the west, and the morning stars to 
 the east of him. If the observer had previously 
 obtained a knowledge of the places of all the prin- 
 cipal stars, he might in this way determine the 
 position of the sun each night, and thus trace his 
 path in a year. 
 
 In this, or some such way, the sun's path was 
 determined by the early astronomers of Egypt. 
 Thales, who is mentioned as the father of Greek 
 astronomy, probably learnt among the Egyptians 
 the results of such speculations, and introduced 
 
 18 Delamb. A. A. p. xiii. 
 
156 THE GREEK ASTRONOMY. 
 
 them into his own country. His knowledge, indeed, 
 must have been a great deal more advanced than 
 that which we are now describing, if it be true, 
 as is asserted, that he predicted an eclipse. But 
 his having done so is not very consistent with what 
 we are told of the steps which his successors had 
 still to make. 
 
 The Circle of the Signs, in which the sun moves 
 among the stars, is obliquely situated with regard 
 to the circles in which the stars move about the 
 poles. Pliny 39 states that Anaximander 40 , a scholar 
 of Thales, was the first person who pointed out 
 this obliquity, and thus, as he says, "opened the 
 gate of nature." Certainly the person who first 
 had a clear view of the nature of the sun's path in 
 the celestial sphere, made that step which led to 
 all the rest ; but it is difficult to conceive that the 
 Egyptians and Chaldeans had not already advanced 
 so far. 
 
 The diurnal motion of the celestial sphere, and 
 the motion of the moon in the circle of the signs, 
 gave rise to a mathematical science, the Doctrine 
 of the Sphere, which was one of the earliest 
 branches of applied mathematics. A number of 
 technical conceptions and terms were soon intro- 
 duced. The Sphere of the heavens was conceived 
 to be complete, though we see but a part of it ; it 
 
 39 Lib. ii. c. (viii.) 
 
 40 Plutarch, De Plac. Phil. lib. ii. cap. xii. says Pythagoras 
 was the author of this discovery. 
 
ITS EARLIEST STAGES. 157 
 
 was supposed to turn about the visible pole and 
 another pole opposite to this, and these poles were 
 connected by an imaginary Axis. The circle which 
 divided the sphere exactly midway between these 
 poles was called the Equator (to-^e pivos) . The 
 two circles parallel to this which bounded the 
 sun's path among the stars were called Tropics 
 (rpoTTiKai), because the sun turns back again towards 
 the equator when he reaches them. The stars 
 which never set are bounded by a circle called 
 the Arctic Circle (ap/cn/co?, and apKTos, the Bear, 
 the constellation to which some of the principal 
 stars within that circle belong). A circle about 
 the opposite pole is called Antarctic, and the stars 
 which are within it can never rise to us 41 . The 
 sun's path or circle of the signs is called the 
 Zodiac, or circle of animals ; the points where this 
 circle meets the equator are the Equinoctial Points, 
 the days and nights being equal when the sun is 
 in them ; the Solstitial Points are those where the 
 sun's path touches the tropics; his motion to the 
 south or to the north ceases when he is there, 
 and he appears in that respect to stand still. The 
 Colures (KoXovpoi, mutilated) are circles which pass 
 
 t through the poles and through the equinoctial 
 and solstitial points; they have their name because 
 they are only visible in part, a portion of them 
 being below the horizon. 
 
 41 The Arctic and Antarctic Circles of modern astronomers 
 are different from these. 
 
158 THE GREEK ASTRONOMY. 
 
 The Horizon (optfyv) is commonly understood 
 as the boundary of the visible earth and heaven. 
 In the doctrine of the sphere, this boundary is a, 
 great circle, that is, a circle of which the plane 
 passes through the centre of the sphere ; and, there- 
 fore, an entire hemisphere is always above the 
 horizon. The term occurs for the first time in the 
 work of Euclid, called Phenomena (<bau>6neva). We 
 possess two treatises written by Autolycus 42 (who 
 lived about 300 B.C.) which trace deductively the 
 results of the doctrine of the sphere. Supposing its 
 diurnal motion to be uniform, in a work entitled 
 Uepl Kivovpevrjs S^cujoa?, "On the Moving Sphere," 
 he demonstrates various properties of the diurnal 
 risings, settings, and motions of the stars. In another 
 work, Uepl 'E7m-oAdw KCU AJo-eow, "On Risings and 
 Settings 43 ," tacitly assuming the sun's motion in his 
 circle to be uniform, he proves certain propositions, 
 with regard to the risings and settings of the stars, 
 at the same time when the sun rises and sets 44 , 
 or vice versa* 5 ; and also their apparent risings and 
 settings when they cease to be visible after sun-set, 
 or begin to be visible after sun-rise 46 . Several of 
 the propositions contained in the former of these 
 treatises are still necessary to be understood, as 
 fundamental parts of astronomy. 
 
 The work of Euclid, just mentioned, is of the 
 
 42 Delambre, Astron. Ancienne, p. 19. 4S Ib. p. 25. 
 
 44 Cosmical setting and rising. 45 Acronical. 
 
 46 Heliacal. 
 
ITS EARLIEST STAGES. 159 
 
 same kind. Delambre 47 finds in it evidence that 
 Euclid was merely a book-astronomer, who had 
 never observed the heavens. 
 
 We may here remark the first instance of that 
 which we shall find abundantly illustrated in every 
 part of the history of science ; that man is prone 
 to become a deductive reasoner ; that as soon as 
 he obtains principles which can be traced to details 
 by logical consequence, he sets about forming a 
 body of science, by making a system of such rea- 
 sonings. Geometry has always been a favourite 
 mode of exercising this propensity: and that science, 
 along with Trigonometry, Plane and Spherical, to 
 which the early problems of astronomy gave rise, 
 have, up to the present day, been a constant field 
 for the exercise of mathematical ingenuity ; a feAv 
 simple astronomical truths being assumed as the 
 basis of the reasoning. 
 
 Sect. 9. The Globular Form of the Earth. 
 
 THE establishment of the globular form of the 
 earth is an important step in astronomy, for it is 
 the first of those convictions, directly opposed to 
 the apparent evidence of the senses, which astro- 
 nomy irresistibly proves. To make men believe 
 that up and down are different directions in dif- 
 ferent places; that the sea, which seems so level, 
 is, in fact, convex; that the earth, which appears 
 to rest on a solid foundation, is, in fact, not sup- 
 
 47 A. A. p. 53. 
 
160 THE GREEK ASTRONOMY. 
 
 ported at all ; are great triumphs both of the 
 power of discovering and the power of convincing. 
 We may readily allow this, when we recollect how 
 recently the doctrine of the antipodes, or the 
 existence of inhabitants of the earth, who stand 
 on the opposite side of it, with their feet turned 
 towards ours, was considered both monstrous and 
 heretical. 
 
 Yet the different positions of the horizon at 
 different places, necessarily led the student of sphe- 
 rical astronomy toward this notion of the earth 
 as a round body. Anaximander 48 is said by some 
 to have held the earth to be globular, and to be 
 detached or suspended ; he is also stated to have 
 constructed a sphere, on which were shown the 
 extent of land and water. As, however, we do 
 not know the arguments upon which he maintained 
 the earth's globular form, we cannot judge of the 
 value of his opinion ; it may have been no better 
 founded than a different opinion ascribed to him 
 by Laertius, that the earth had the shape of a 
 pillar. Probably, the authors of the doctrine of 
 the globular form of the earth were led to it, as 
 we have said, by observing the different height of 
 the pole at different places. They would find that 
 the space which they passed over from north to 
 south on the earth, was proportional to the change 
 of place of the horizon in the celestial sphere ; and 
 as the horizon is, at every place, in the direction 
 48 See Brucker, Hist. Phil vol. i. p. 486. 
 
ITS EARLIEST STAGES. 1G1 
 
 of the earth's apparently level surface, this obser- 
 vation would naturally suggest to them the opinion 
 that the earth is placed within the celestial sphere, 
 as a small globe in the middle of a much larger 
 one. 
 
 We find this doctrine so distinctly insisted on 
 by Aristotle, that we may almost look on him as 
 the establisher of it 49 . "As to the figure of the 
 earth, it must necessarily be spherical." This he 
 proves, first by the tendency of things, in all places, 
 downwards. He then adds 50 , " And, moreover, from 
 the phenomena according to the sense : for if it 
 were not so, the eclipses of the moon would not 
 have such sections as they have. For in the con- 
 figurations in the course of a month, the deficient 
 part takes all different shapes; it is straight, and 
 concave, and convex ; but in eclipses it always has 
 the line of division convex; wherefore, since the 
 moon is eclipsed in consequence of the interposi- 
 tion of the earth, the periphery of the earth must 
 be the cause of this by having a spherical form. 
 And again, from the appearances of the stars, it 
 is clear, not only that the earth is round, but that 
 its size is not very large: for when we make a 
 small removal to the south or the north, the circle 
 of the horizon becomes palpably different, so that 
 the stars overhead undergo a great change, and 
 are not the same to those that travel to the north 
 
 19 Arist. de Coelo. Lib. ii. cap. xiv. ed. Casaub. p. 290. 
 50 p. 291 C. 
 
 VOL. I. M 
 
162 THE GREEK ASTRONOMY. 
 
 and to the south. For some stars are seen in 
 Egypt or at Cyprus, but are not seen in the 
 countries to the north of these ; and the stars that 
 in the north are visible while they make a com- 
 plete circuit, there undergo a setting. So that 
 from this it is manifest, not only that the form of 
 the earth is round, but also that it is a part of 
 not a very large sphere : for otherwise the dif- 
 ference would not be so obvious to persons making 
 so small a change of place. Wherefore we may 
 judge that those persons who connect the region 
 in the neighbourhood of the pillars of Hercules 
 with that towards India, and mho assert that in 
 this way the sea is ONE, do not assert things very 
 improbable. They confirm this conjecture more- 
 over by the elephants, which are said to be of 
 the same species (761/0?) towards each extreme ; as 
 if this circumstance was a consequence of the con- 
 junction of the extremes. The mathematicians, 
 who try to calculate the measure of the circum- 
 ference, make it amount to 400,000 stadia ; whence 
 we collect that the earth is not only spherical, but 
 is not large compared with the magnitude of the 
 other stars." 
 
 When this notion was once suggested, it was 
 defended and confirmed by such arguments as we 
 find in later writers: for instance 51 , that the ten- 
 dency of all things was to fall to the place of heavy 
 bodies, and that this place being the center of the 
 
 51 Pliny, Nat. Hist. ii. LXV. 
 
ITS EARLIEST STAGES. 163 
 
 earth, the whole earth had no such tendency ; that 
 the inequalities on the surface were so small as 
 not materially to affect the shape of so vast a 
 mass; that drops of water naturally form them- 
 selves into figures with a convex surface ; that the 
 end of the ocean would fall if it were not rounded 
 off; that we see ships, when they go out to sea, 
 disappearing downwards, which shows the surface 
 to be convex. These are the arguments still em- 
 ployed in impressing the doctrines of astronomy 
 upon the student of our own days ; and thus we 
 find that, even at the early period of which we 
 are now speaking, truths had begun to accumulate 
 which form a part of our present treasures. 
 
 Sect. 10. The Phases of the Moon. 
 
 WHEN men had formed a steady notion of the 
 moon as a solid body, revolving about the earth, 
 they had only further to conceive it spherical, and 
 to suppose the sun to be beyond the region of the 
 moon, and they would find that they had obtained 
 an explanation of the varying forms which the 
 bright part of the moon assumes in the course of 
 a month. For the convex side of the crescent- 
 moon, and her full edge when she is gibbous, are 
 always turned towards the sun. And this expla- 
 nation, once suggested, would be confirmed, the 
 more it was examined. For instance, if there be 
 near us a spherical stone, on which the sun is 
 
 M2 
 
164 THE GREEK ASTRONOMY. 
 
 shining, and if we place ourselves so that this stone 
 and the moon are seen in the same direction, (the 
 moon appearing just over the top of the stone,) 
 we shall find that the visible part of the stone, 
 which is then illuminated by the sun, is exactly 
 similar in form to the moon, at whatever period 
 of her changes she may be. The stone and the 
 moon being in the same position with respect to 
 us, and both being enlightened by the sun, the 
 bright parts are the same in figure ; the only dif- 
 ference is, that the dark part of the moon is usually 
 not visible at all. 
 
 This doctrine is ascribed to Anaximander. Aris- 
 totle was fully aware of it 52 . It could not well 
 escape the Chaldeans and Egyptians, if they spe- 
 culated at all about the causes of the appearances 
 in the heavens. 
 
 Sect. 11. Eclipses. 
 
 ECLIPSES of the sun and moon were from the 
 earliest times regarded with a peculiar interest. 
 The notions of superhuman influences and relations, 
 which, as we have seen, were associated with the 
 luminaries of the sky, made men look with alarm 
 at any sudden and striking change in those objects; 
 and as the constant and steady course of the 
 celestial revolutions was contemplated with a feel- 
 ing of admiration and awe, any marked interrup- 
 
 52 Probl. Cap. xv. Art. 7- 
 
ITS EARLIEST STAGES. 165 
 
 tion and deviation in this course, was regarded 
 with surprize and terror. This appears to be the 
 case with all nations at an early stage of their 
 civilization. 
 
 This impression would cause Eclipses to be 
 noted and remembered ; and accordingly we find 
 that the records of Eclipses are the earliest astro- 
 nomical information which we possess. When men 
 had discovered some of the laws of succession of 
 other astronomical phenomena, for instance, of the 
 usual appearances of the moon and sun, it might 
 then occur to them that these unusual appearances 
 also might probably be governed by some rule. 
 
 The search after this rule was successful at an 
 early period. The Chaldeans were able to predict 
 Eclipses of the Moon. This they did, probably, by 
 means of their cycle of 223 months, or about 18 
 years ; for at the end of this time, the eclipses of 
 the moon begin to return, at the same intervals 
 and in the same order as at the beginning 53 . Pro- 
 bably this was the first instance of the prediction 
 of peculiar astronomical phenomena. The Chinese 
 have, indeed, a legend, in which it is related that 
 a solar eclipse happened in the reign of Tchong- 
 kang, above 2000 years before Christ, and that the 
 emperor was so much irritated against two great 
 officers of state, who had neglected to predict this 
 eclipse, that he put them to death. But this can- 
 
 ' 3 The eclipses of the sun are more difficult to calculate ; since 
 they depend upon the place of the spectator on the earth. 
 
166 THE GREEK ASTRONOMY. 
 
 not be accepted as a real event: for during the 
 next ten centuries, we find no single observation, 
 or fact, connected with astronomy, in the Chinese 
 histories ; and their astronomy has never advanced 
 beyond a very rude and imperfect condition. 
 
 We can only conjecture the mode in which the 
 Chaldeans discovered their period of 18 years; and 
 we may make very different suppositions with re- 
 gard to the degree of science by which they were 
 led to it. We may suppose, with Delambre 54 , that 
 they carefully recorded the eclipses which hap- 
 pened, and then, by the inspection of their registers, 
 discovered that those of the moon recurred after 
 a certain period. Or we may suppose, with other 
 authors, that they sedulously determined the mo- 
 tions of the moon, and having obtained these with 
 considerable accuracy, sought and found a period 
 which should include cycles of these motions. This 
 latter mode of proceeding would imply a consider- 
 able degree of knowledge. 
 
 It appears probable rather that such a period 
 was discovered by noticing the recurrence of 
 eclipses, than by studying the moon's motions. 
 After 6585J days, or 223 lunations, the same 
 eclipses nearly will recur. It is not contested that 
 the Chaldeans were acquainted with this period, 
 which they called Saros ; or that they calculated 
 eclipses by means of it. 
 
 54 A. A.; P . 212. 
 
ITS EARLIEST STAGES. 167 
 
 Sect. 12. Sequel to the Early Stages of Astronomy. 
 
 EVERY stage of science has its train of practical 
 applications and systematic inferences, arising both 
 from the demands of convenience and curiosity, 
 and from the pleasure, which, as we have already 
 said, ingenious and active-minded men feel in exer- 
 cising the process of deduction. The earliest con- 
 dition of astronomy in which it can be looked 
 upon as a science, exhibits several examples of 
 such applications and inferences, of which we may 
 mention a few. 
 
 Prediction of Eclipses. The cycles which served 
 to keep in order the calendar of the early nations 
 of antiquity, in some instances enabled them also, 
 as has just been stated, to predict eclipses ; and 
 this application of knowledge necessarily excited 
 great notice. Cleomedes, in the time of Augustus, 
 says, "we never see an eclipse happen which has 
 not been predicted by those who make use of the 
 
 Tables." (VTTO TU)V KCIVOVIKWV.) 
 
 Terrestrial Zones. The globular form of the 
 earth being assented to, the doctrine of the sphere 
 was appplied to the earth as well as the heavens ; 
 and its surface was divided by various imaginary 
 circles; among the rest, the equator, the tropics, 
 and circles at the same distance from the poles as 
 the tropics are from the equator. One of the curious 
 consequences of this division was the assumption, 
 that there must be some marked difference in the 
 
168 THE GREEK ASTRONOMY. 
 
 stripes or zones into which the earth's surface was 
 thus divided. In going to the south, Europeans 
 found countries hotter and hotter, in going to the 
 north, colder and colder; and it was supposed 
 that the space between the tropical circles must 
 be uninhabitable from heat, and that within the 
 polar circles, again, uninhabitable from cold. This 
 fancy was, as we now know, entirely unfounded. 
 But the principle of the globular form of the earth, 
 when dealt with by means of spherical geometry, 
 led to many true and important propositions con- 
 cerning the lengths of days and nights at different 
 places. These propositions still form a part of our 
 Elementary Astronomy. 
 
 Gnomonick. Another important result of the 
 doctrine of the sphere was Gnomonick or Dialling. 
 Anaximenes is said by Pliny to have first taught 
 this art in Greece ; and both he and Anaximander 
 are reported to have erected the first dial at Lace- 
 demon. Many of the ancient dials remain to us; 
 some of these are of complex forms, and must 
 have required great ingenuity and considerable 
 geometrical knowledge in their construction. 
 
 Measure of the Suns Distance. The explana- 
 tion of the phases of the moon led to no result so 
 remarkable as the attempt of Aristarchus of Samos 
 to obtain from this doctrine a measure of the dis- 
 tance of the sun as compared with that of the 
 moon. If the moon was a perfectly smooth sphere, 
 when she was exactly midway between the new 
 
ITS EARLIEST STAGES. 169 
 
 and full in position (that is a quadrant from the 
 sun) she would be somewhat more than a half 
 moon ; and the place when she was dichotomized, 
 that is, was an exact semicircle, the bright part 
 being bounded by a straight line, would depend 
 upon the sun's distance from the earth. Aristar- 
 chus endeavoured to fix the exact place of this 
 Dichotomy ; but the irregularity of the edge which 
 bounds the bright part of the moon, and the dif- 
 ficulty of measuring with accuracy, by means then 
 in use, either the precise time, when the boundary 
 was most nearly a straight line or the exact dis- 
 tance of the moon from the sun at that time, 
 rendered his conclusion false and valueless. He 
 collected that the sun is at 18 times the distance 
 of the moon from us ; we now know that he is 
 at 400 times the moon's distance. 
 
 It would be easy to dwell longer on subjects of 
 this kind ; but we have already perhaps entered 
 too much in detail. We have been tempted to 
 do this by the interest which the mathematical 
 spirit of the Greeks gave to the earliest astrono- 
 mical discoveries, when these were the subjects of 
 their reasonings : but we must now proceed to con- 
 template them engaged in a worthier employment, 
 namely, in adding to these discoveries. 
 
CHAPTER II. 
 
 PRELUDE TO THE INDUCTIVE EPOCH OF 
 HIPPARCHUS. 
 
 WITHOUT pretending that we have exhausted 
 the consequences of the elementary disco- 
 veries which we have enumerated, we now proceed 
 to consider the nature and circumstances of the 
 next great discovery which makes an Epoch in the 
 history of astronomy ; and this we shall find to be 
 the Theory of Epicycles and Eccentrics. Before, 
 however, we relate the establishment of this theory, 
 we must, according to the general plan we have 
 marked out, notice some of the conjectures and 
 attempts by which it was preceded, and the grow- 
 ing acquaintance with facts, which made the want 
 of such an explanation felt. 
 
 In the steps previously made in astronomical 
 knowledge, no ingenuity had been required, to 
 devise the view which was adopted. The motions 
 of the stars and sun were most naturally and 
 almost irresistibly conceived as the results of mo- 
 tion in a revolving sphere ; the indications of posi- 
 tion which we obtain from different places on the 
 earth's surface, when clearly combined, obviously 
 imply a globular shape. In these cases, the first 
 conjectures, the supposition of the simplest form, 
 
PRELUDE TO THE EPOCH OF HIPPARCHUS. 171 
 
 of the most uniform motion, required no after-cor- 
 rection. But this manifest simplicity, this easy and 
 obvious explanation, did not apply to the move- 
 ment of all the heavenly bodies. The planets, the 
 "wandering stars," could not be so easily under- 
 stood ; the motion of each, as Cicero says, " under- 
 going very remarkable changes in its course, going 
 before and behind, quicker and slower, appear- 
 ing in the evening, but gradually lost there, and 
 emerging again in the morning 1 ." A continued 
 attention to these stars would, however detect 
 a kind of intricate regularity in their motions, 
 which might naturally be described as " a dance." 
 The Chaldeans are stated by Diodorus 2 , to have 
 observed assiduously the risings and settings of 
 the planets, from the top of the temple of Belus. 
 By doing this, they would find the times in which 
 the forwards and backwards movements of Saturn, 
 Jupiter, and Mars recur; and also the time in 
 which they come round to the same part of the 
 heavens 3 . Venus and Mercury never recede far 
 from the sun, and the intervals which elapse while 
 either of them leaves its greatest distance from 
 
 1 Cic. de Nat. D. lib. ii. p. 450. " Ea qua; Saturni stella 
 dicitur, ^cuWque a Grascis nominatur, quas a terra abest pluri- 
 mum, xxx fere annis cursum suum conficit ; in quo cursu multa 
 mirabiliter efficiens, turn antecedendo, turn retardando, turn ves- 
 pertinis temporibus delitescendo, turn matutinis se rursum ape- 
 riendo, nihil immutat sempiternis sseculorum aetatibus, quin 
 eadem iisdem temporibus efficiat." And so of the other planets. 
 
 2 Del. A. A.; i. p. 4. 3 Plin. H. N. ii. p. 204. 
 
172 THE GREEK ASTRONOMY. 
 
 the sun and returns again to the greatest distance 
 on the same side, would easily be observed. 
 
 Probably the manner in which the motions of 
 the planets were originally reduced to rule was 
 something like the following : In about 30 of our 
 years, Saturn goes 29 times through his Anomaly, 
 that is, the succession of varied motions by which 
 he sometimes goes forwards and sometimes back- 
 wards among the stars. During this time, he goes 
 once round the heavens, and returns nearly to the 
 same place. This is the cycle of his apparent 
 motions. 
 
 Perhaps the eastern nations contented them- 
 selves with thus referring these motions to cycles 
 of time, so as to determine their recurrence. Some- 
 thing of this kind was done at an early period, 
 as we have seen. 
 
 But the Greeks soon attempted to frame to 
 themselves a sensible image of the mechanism by 
 which these complex motions were produced : nor 
 did they find this difficult. Venus, for instance, 
 who, upon the whole, moves from west to east 
 among the stars, is seen, at certain intervals, to 
 return or move retrograde a short way back from 
 east to west, then to become for a short time 
 stationary, then to turn again and resume her 
 direct motion westward, and so on. Now this can 
 be explained by supposing that she is placed in the 
 rim of a wheel, which is turned edgeways to us, 
 and of which the center turns round in the heavens 
 
PRELUDE TO THE EPOCH OF HIPPARCHUS. 173 
 
 from west to east, while the wheel, carrying the 
 planet in its motion, moves round its own center. 
 In this way the motion of the wheel about its 
 center, would, in some situations, counterbalance 
 the general motion of the center, and make the 
 planet retrograde, while, on the whole, the wes- 
 terly motion would prevail. Just as if we suppose 
 that a person, holding a lamp in his hand in the 
 dark, and at a distance, so that the lamp alone 
 is visible, should run on turning himself round; 
 we should see the light sometimes stationary, some- 
 times retrograde, but on the whole progressive. 
 
 A mechanism of this kind was imagined for 
 each of the planets, and the wheels of which we 
 have spoken were, in the end, called Epicycles. 
 
 The application of such mechanism to the 
 planets appears to have arisen in Greece about 
 the time of Aristotle. In the works of Plato we 
 find a strong taste for this kind of mechanical 
 speculation. In the tenth book of the " Polity," 
 we have the apologue of Alcinus the Pamphylian, 
 who, being supposed to be killed in battle, revived 
 when he was placed on the funeral pyre, and re- 
 lated what he had seen during his trance. Among 
 other revelations, he beheld the machinery by 
 which all the celestial bodies revolve. The axis 
 of these revolutions is the adamantine distaff which 
 Destiny holds between her knees ; on this are 
 fixed, by means of different sockets, flat rings, by 
 which the planets are carried. The order and 
 
174 THE GREEK ASTRONOMY. 
 
 magnitude of these spindles are minutely detailed. 
 Also, in the "Epilogue to the Laws" (Epinomis), 
 he again describes the various movements of the 
 sky, so as to show a distinct acquaintance with 
 the general character of the planetary motions : 
 and, after speaking of the Egyptians and Syrians 
 as the original cultivators of such knowledge, he 
 adds some very remarkable exhortations to his 
 countrymen to prosecute the subject. " Whatever 
 we Greeks," he says, " receive from the barbarians, 
 we improve and perfect; there is good hope and 
 promise, therefore, that Greeks will carry this know- 
 ledge far beyond that which was introduced from 
 abroad." To this task, however, he looks with a 
 due appreciation of the qualities and preparation 
 which it requires. "An astronomer must be," he 
 says, " the wisest of men ; his mind must be duly 
 disciplined in youth ; especially is mathematical 
 study necessary; both an acquaintance with the 
 doctrine of number, and also with that other branch 
 of mathematics, which, closely connected as it is 
 with the science of the heavens, we very absurdly 
 call geometry, the measurement of the earth 4 1 ." 
 
 These anticipations were very remarkably veri- 
 fied in the subsequent career of the Greek astro- 
 nomy. 
 
 The theory, once suggested, probably made 
 rapid progress. Simplicius 5 relates, that Eudoxus 
 
 4 Epinomis, pp. 988, 990. 
 
 5 Lib. ii. de Ccelo. Bullialdus, p. 18. 
 
PRELUDE TO THE EPOCH OF HIPPARCHUS. 175 
 
 of C nidus introduced the hypothesis of revolving 
 circles or spheres. Calippus of Cyzicus, having 
 visited Polemarchus, an intimate friend of Eudoxus, 
 they went together to Athens, and communicated 
 to Aristotle the invention of Eudoxus, and with his 
 help improved and corrected it. 
 
 Probably at first this hypothesis was applied 
 only to account for the general phenomena of the 
 progressions, retrogradations, and stations of the 
 planet ; but it was soon found that the motions of 
 the sun and moon, and the circular motions of 
 the planets, which the hypothesis supposed, had 
 other anomalies or irregularities, which made a 
 further extension of the hypothesis necessary. 
 
 The defect of uniformity in these motions of the 
 sun and moon, though less apparent than in the 
 planets, is easily detected, as soon as men endea- 
 vour to obtain any accuracy in their observations. 
 We have already stated (Chap. I.) that the Chal- 
 deans were in possession of a period of about 18 
 years, which they used in the calculation of eclipses, 
 and which might have been discovered by close 
 observation of the moon's motions; although it 
 was probably rather hit upon by noting the recur- 
 rence of eclipses. The moon moves in a manner 
 which is not reducible to regularity without con- 
 siderable care and time. If we trace her path 
 among the stars, we find that, like the path of the 
 sun, it is oblique to the equator, but it does not, 
 like that of the sun, pass over the same stars in 
 
176 THE GREEK ASTRONOMY. 
 
 successive revolutions. Thus its latitude, or dis- 
 tance from the equator, has a cycle different from 
 its revolution among the stars ; and its Nodes, or 
 the points where it cuts the equator, are perpe- 
 tually changing their position. In addition to this, 
 the moon's motion in her own path is not uniform ; 
 in the course of each lunation, she moves alter- 
 nately slower and quicker, passing gradually through 
 the intermediate degrees of velocity ; and goes 
 through the cycle of these changes in something 
 less than a month : this is called a revolution of 
 Anomaly. When the moon has gone through a 
 complete number of revolutions of Anomaly, and 
 has, in the same time, returned to the same posi- 
 tion with regard to the Sun, and also with regard 
 to her Nodes, her motions with respect to the sun 
 will thenceforth be the same as at the first, and 
 all the circumstances on which lunar eclipses de- 
 pend being the same, the eclipses will occur in 
 the same order. In 6585J days there are 239 
 revolutions of anomaly, 241 revolutions with regard 
 to one of the nodes, and, as we have said, 223 
 lunations or revolutions with regard to the sun. 
 Hence this period will bring about a succession of 
 the same lunar eclipses. 
 
 If the Chaldeans observed the moon's motion 
 among the stars with any considerable accuracy, 
 so as to detect this period by that means, they 
 could hardly avoid discovering the anomaly or un- 
 equal motion of the moon ; for in every revolution, 
 
PRELUDE TO THE EPOCH OF HIPPARCHUS. 177 
 
 her daily progression in the heavens varies from 
 about 22 to 26 times her own diameter. But there 
 is not, in the existence of this period, any evidence 
 that they had measured the amount of this varia- 
 tion ; and Delambre 6 is probably right in attribut- 
 ing all such observations to the Greeks. 
 
 The sun's motion would also be seen to be 
 irregular as soon as men had any exact mode 
 of determining the lengths of the four seasons, by 
 means of the passage of the sun through the equi- 
 noctial and solstitial points. For spring, summer, 
 autumn, and winter, which would each consist of 
 an equal number of days if the motions were 
 uniform, are, in fact, found to be unequal in 
 length. 
 
 It was not very difficult to see that the mecha- 
 nism of epicycles might be applied so as to explain 
 irregularities of this kind. A wheel travelling 
 round the earth, while it revolved upon its center, 
 might produce the effect of making the sun or 
 moon fixed in its rim go sometimes faster and 
 sometimes slower in appearance, just in the same 
 way as the same suppositions would account for a 
 planet going sometimes forwards and sometimes 
 backwards: the epicycles of the sun and moon 
 would, for this purpose, be less than those of the 
 planets. Accordingly, it is probable that, at the 
 time of Plato and Aristotle, philosophers were 
 already endeavouring to apply the hypothesis to 
 
 6 Astronomic Ancienne, i. 212. 
 VOL. I. N 
 
178 THE GREEK ASTRONOMY. 
 
 these cases, though it does not appear that any 
 one fully succeeded before Hipparchus. 
 
 The problem which was thus present to the 
 minds of astronomers, and which Plato is said to 
 have proposed to them in a distinct form, was, 
 " To reconcile the celestial phenomena by the com- 
 bination of equable circular motions." That the 
 circular motions should likewise be equable, was 
 a condition, which, if it had been merely tried 
 at first, as the most simple and definite conjecture, 
 would have deserved praise. But this condition, 
 which is, in reality, inconsistent with nature, was, 
 in the sequel, adhered to with a pertinacity which 
 introduced endless complexity into the system. The 
 history of this assumption is one of the most 
 marked instances of that love of simplicity and 
 symmetry, which is the source of all general truths, 
 though it so often produces and perpetuates errour. 
 At present we can easily see how fancifully the 
 notion of simplicity and perfection was interpreted, 
 in the arguments by which the opinion was de- 
 fended, that the real motions of the heavenly bodies 
 must be circular and uniform. The Pythagoreans, 
 as well as the Platonists, maintained this dogma. 
 According to Geminus, "They supposed the mo- 
 tions of the sun, and the moon, and the five planets, 
 to be circular and equable: for they would not allow 
 of such disorder among divine and eternal things, 
 as that they should sometimes move quicker, and 
 sometimes slower, and sometimes stand still; for 
 
PRELUDE TO THE EPOCH OF HIPPARCHUS. 170 
 
 no one would tolerate such anomaly in the move- 
 ments, even of a man, who was decent and orderly. 
 The occasions of life, however, are often reasons 
 for men going quicker or slower, but in the incor- 
 ruptible nature of the stars, it is not possible that 
 any cause can be alleged of quickness and slow- 
 ness. Whereupon they propounded this question, 
 how the phenomena might be represented by 
 equable and circular motions." 
 
 These conjectures and assumptions led natu- 
 rally to the establishment of the various parts of 
 the Theory of Epicycles. It is probable that this 
 theory was adopted with respect to the planets 
 at or before the time of Plato. And Aristotle 
 gives us an account of the system thus devised 7 . 
 "Eudoxus," he says," "attributed four spheres to 
 each Planet : the first revolved with the fixed stars 
 (and this produced the diurnal motion) ; the second 
 gave the planet a motion along the ecliptic (the 
 mean motion in longitude) ; the third had its axis 
 perpendicular 8 to the ecliptic (and this gave the 
 inequality of each planetary motion) ; the fourth 
 produced the oblique motion transverse to this 
 (the motion in latitude)." He is also said to have 
 attributed a motion in latitude and a correspond- 
 
 7 Metaph. xi. 8. 
 
 a Aristotle says " has its poles in the ecliptic," but this must 
 be a mistake of his. He professes merely to receive these opinions 
 from the professed astronomers "e'/c T^ olK.eioTa.Tris <pt\o(ro(f)ia<; 
 
180 THE GREEK ASTRONOMY. 
 
 ing sphere to the Sun as well as to the Moon, 
 of which it is difficult to understand the meaning, 
 if Aristotle has reported rightly of the theory ; for 
 it would be absurd to ascribe to Eudoxus a know- 
 of the motions by which the sun deviates from 
 the ecliptic. Calippus conceived that two addi- 
 tional spheres must be given to the sun and to 
 the moon, in order to explain the phenomena: 
 probably he was aware of the inequalities of the 
 motions of these luminaries. He also proposed an 
 additional sphere for each planet, to account, we 
 may suppose, for the results of the eccentricity of 
 the orbits. 
 
 The hypothesis, in this form, does not appear 
 to have been reduced to measure, and was, more- 
 over, unnecessarily complex. The resolution of the 
 oblique motion of the moon into two separate mo- 
 tions, by Eudoxus, was not the simplest way of 
 conceiving it; and Calippus imagined the con- 
 nexion of these spheres in some way which made 
 it necessary nearly to double their number ; in this 
 manner his system had no less than 55 spheres. 
 
 Such was the progress which the Idea of the 
 hypothesis of epicycles had made in men's minds, 
 previously to the establishment of the theory by 
 Hipparchus. There had also been a preparation 
 for this step, on the other side, by the collection of 
 Facts. We know that observations of the eclipses 
 of the moon were made by the Chaldeans 367 B.C. 
 at Babylon, and were known to the Greeks; for 
 
PRELUDE TO THE EPOCH OF HIPPARCHUS. 181 
 
 Hipparchus and Ptolemy founded their theory of 
 the moon on these observations. Perhaps we can- 
 not consider, as equally certain, the story that, at 
 the time of Alexander's conquest, the Chaldeans 
 possessed a series of observations, which went back 
 1903 years, and which Aristotle caused Callisthenes 
 to bring to him in Greece. All the Greek observa- 
 tions which are of any value, begin with the school 
 of Alexandria. Aristyllus and Timocharis appear, 
 by the citations of Hipparchus, to have observed 
 the places of stars and planets, and the times of the 
 solstices, at various periods from B.C. 295 to B.C. 
 269. Without their observations, indeed, it would 
 not have been easy for Hipparchus to establish 
 either the theory of the sun or the precession of the 
 equinoxes. 
 
 In order that observations at distant intervals 
 may be compared with each other, they must be 
 referred to some common era. The Chaldeans 
 dated by the era of Nabonassar, which commenced 
 749 B.C. The Greek observations were referred to 
 the Calippic periods of 76 years, of which the first 
 began 331 B.C. These are the dates used by Hip- 
 parchus and Ptolemy. 
 
CHAPTER III. 
 INDUCTIVE EPOCH OF HIPPARCHUS. 
 
 Sect. 1. Establishment of the Theory of Epicycles 
 and Eccentrics. 
 
 A LTHOUGH, as we have already seen, at the 
 _/jL time of Plato, the Idea of Epicycles had been 
 suggested, and the problem of its general applica- 
 tion proposed, and solutions of this problem offered 
 by his followers; we still consider Hipparchus as 
 the real discoverer and founder of that theory; 
 inasmuch as he not only guessed that it might, but 
 showed that it must, account for the phenomena, 
 both as to their nature and as to their quantity. 
 The assertion that " he only discovers who proves," 
 is just ; not only because, until a theory is proved 
 to be the true one, it has no pre-eminence over the 
 numerous other guesses among which it circulates, 
 and above which the proof alone elevates it; but 
 also because he who takes hold of the theory so 
 as to apply calculation to it, possesses it with a 
 distinctness of conception which makes it pecu- 
 liarly his. 
 
 In order to establish the Theory of Epicycles, it 
 was necessary to assign the magnitudes, distances, 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 183 
 
 and positions of the circles or spheres in which the 
 heavenly bodies were moved, in such a manner as to 
 account for their apparently irregular motions. We 
 may best understand what was the problem to be 
 solved, by calling to mind what we now know to be 
 the real motions of the heavens. The true motion 
 of the earth round the sun, and therefore the appa- 
 rent annual motion of the sun, is performed, not in 
 a circle of which the earth is the center, but in an 
 ellipse or oval, the earth being nearer to one end 
 than to the other; and the motion is most rapid 
 when the sun is at the nearer end of this oval. But 
 instead of an oval, we may suppose the sun to move 
 uniformly in a circle, the earth being now, not in 
 the center, but nearer to one side ; for on this sup- 
 position, the sun will appear to move most quickly 
 when he is nearest to the earth, or in his Perigee, 
 as that point is called. Such an orbit is called an 
 Eccentric, and the distance of the earth from the 
 center of the circle is called the Eccentricity. It 
 may easily be shown by geometrical reasoning, that 
 the inequality of apparent motion so produced, is 
 exactly the same in detail, as the inequality which 
 follows from the hypothesis of a small Epicycle, 
 turning uniformly on its axis, and carrying the sun 
 in its circumference, while the center of this epicycle 
 moves uniformly in a circle of which the earth is 
 the center. This identity of the results of the hypo- 
 thesis of the Eccentric and the Epicyle is proved by 
 Ptolemy in the third book of the "Almagest." 
 
184 THE GREEK ASTRONOMY. 
 
 The Suns Eccentric. When Hipparchus had 
 clearly conceived these hypotheses, as possible ways 
 of accounting for the sun's motion, the task which he 
 had to perform, in order to show that they deserved 
 to be adopted, was to assign a place to the Perigee, 
 a magnitude to the Eccentricity, and an Epoch at 
 which the sun was at the perigee ; and to show that, 
 in this way, he had produced a true representation 
 of the motions of the sun. This, accordingly, he did ; 
 and having thus determined, with considerable ex- 
 actness, both the law of the solar irregularities, and 
 the numbers on which their amount depends, he 
 was able to assign the motions and places of the 
 sun for any moment of future time with correspond- 
 ing exactness ; he was able, in short, to construct 
 Solar Tables, by means of which the sun's place 
 with respect to the stars could be correctly found 
 at any time. These tables (as they are given by 
 Ptolemy 1 ,) give the Anomaly, or inequality of the 
 sun's motion; and this they exhibit by means of the 
 Prosthapheresis, the quantity which, at any distance 
 of the sun from the Apogee, it is requisite to add 
 to or subtract from the arc, which he would have 
 described if his motion had been equable. 
 
 The reader might perhaps expect that the calcu- 
 lations which thus exhibited the motions of the sun 
 for an indefinite future period must depend upon 
 a considerable number of observations made at all 
 seasons of the year. That, however, was not the 
 1 Syntax. 1. iii. 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 185 
 
 case ; and the genius of the discoverer appeared, as 
 such genius usually does appear, in his perceiving 
 how small a number of facts, rightly considered, 
 were sufficient to form a foundation for the theory. 
 The number of days contained in two seasons of 
 the year sufficed for this purpose to Hipparchus. 
 " Having ascertained," says Ptolemy, " that the time 
 from the vernal equinox to the summer tropic is 
 941 days, and the time from the summer tropic to 
 the autumnal equinox 92^ days, from these phenor- 
 mena alone he demonstrates that the straight line 
 joining the centre of the sun's eccentric path with 
 the centre of the zodiac (the spectator's eye) is 
 nearly the 24th part of the radius of the eccentric 
 path ; and that its apogee precedes the summer 
 solstice by 241 degrees nearly, the zodiac con- 
 taining 360." 
 
 The exactness of the Solar Tables, or Canon, 
 which was founded on these data, was manifested, 
 not only by the coincidence of the sun's calculated 
 place with such observations as the Greek astrono- 
 mers of this period were able to make, (which were 
 indeed very rude,) but by its enabling them to cal- 
 culate solar and lunar eclipses; phenomena which 
 are a very precise and severe trial of the accuracy 
 of such tables, inasmuch as a very minute change 
 in the apparent place of the sun or moon would 
 completely alter the obvious features of the eclipse. 
 Though the tables of this period were by no means 
 perfect, they bore with tolerable credit this trying 
 
186 THE GREEK ASTRONOMY. 
 
 and perpetually recurring test; and thus proved the 
 soundness of the theory on which the tables were 
 calculated. 
 
 The Moon's Eccentric. The moon's motions 
 have many irregularities ; but when the hypothesis 
 of an Eccentric or an Epicycle had sufficed in the 
 case of the sun, it was natural to try to explain, in 
 the same way, the motions of the moon ; and it was 
 shown by Hipparchus that such hypotheses would 
 account for the more obvious anomalies. It is not 
 very easy to describe the several ways in which 
 these hypotheses were applied, for it is, in truth, 
 very difficult to explain in words even the mere 
 facts of the moon's motion. If she were to leave a 
 visible bright line behind her in the heavens wher- 
 ever she moved, the path thus exhibited would be 
 of an entremely complex nature ; the circle of each 
 revolution slipping away from the preceding, and 
 the traces of successive revolutions forming a sort 
 of band of net-work running round the middle of 
 the sky 2 . In each revolution, the motion in longi- 
 tude is affected by an anomaly of the same nature 
 as the sun's anomaly already spoken of; but besides 
 this, the path of the moon deviates from the ecliptic 
 to the north and to the south of the ecliptic, and 
 thus she has a motion in latitude. This motion in 
 latitude would be sufficiently known if we knew the 
 
 2 The reader will find an attempt to make the nature of this 
 path generally intelligible in the Companion to the British 
 Almanack for 1834. 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 187 
 
 period of its restoration, that is, the time which the 
 moon occupies in moving from any latitude till she 
 is restored to the same latitude ; as, for instance, 
 from the ecliptic on one side of the heavens to the 
 ecliptic on the same side of the heavens again. But 
 it is found that the period of the restoration of the 
 latitude is not the same as the period of the restora- 
 tion of the longitude, that is, as the period of the 
 moon's revolution among the stars; and thus the 
 moon describes a different path among the stars in 
 every successive revolution, and her path, as well as 
 her velocity, is constantly variable. 
 
 Hipparchus, however, reduced the motions of 
 the moon to rule and to Tables, as he did those of 
 the sun, and in the same manner. He determined, 
 with much greater accuracy than any preceding 
 astronomer, the mean or average equable motions 
 of the moon in longitude and in latitude ; and he 
 then represented the anomaly of the motion in 
 longitude by means of an eccentric, in the same 
 manner as he had done for the sun. 
 
 But here there occurred still an additional 
 change, besides those of which we have spoken. 
 The Apogee of the Sun was always in the same 
 place in the heavens ; or at least so nearly so, that 
 Ptolemy could detect no error in the place assigned 
 to it by Hipparchus 250 years before. But the 
 Apogee of the Moon was found to have a motion 
 among the stars. It had been observed before the 
 time of Hipparchus, that in 6585*- days, there are 
 
188 THE GREEK ASTRONOMY. 
 
 241 revolutions of the moon with regard to the 
 stars, but only 239 revolutions with regard to the 
 anomaly. This difference could be suitably repre- 
 sented by supposing the eccentric, in which the 
 moon moves, to have itself an angular motion, per- 
 petually carrying its apogee in the same direction in 
 which the moon travels; but this supposition being 
 made, it was necessary to determine, not only the 
 eccentricity of the orbit, and place of the apogee at 
 a certain time, but also the rate of motion of the 
 apogee itself, in order to form tables of the moon. 
 
 This task, as we have said, Hipparchus executed ; 
 and in this instance, as in the problem of the reduc- 
 tion of the sun's motion to tables, the data which 
 he found it necessary to employ were very few. He 
 deduced all his conclusions from six eclipses of the 
 moon 3 . Three of these, the records of which were 
 brought from Babylon, where a register of such 
 occurrences was kept, happened in the 366th and 
 367th years from the era of Nabonassar, and ena- 
 bled Hipparchus to determine the eccentricity and 
 apogee of the moon's orbit at that time. The three 
 others were observed at Alexandria, in the 547th 
 year of Nabonassar, which gave him another posi- 
 tion of the orbit at an interval of 180 years; and 
 he thus became acquainted with the motion of the 
 orbit itself, as well as its form 4 . 
 
 3 Ptol. Syn. iv. 10. 
 
 4 Ptolemy uses the hypothesis of an epicycle for the moon's 
 first inequality : but Hipparchus employs an eccentric. 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 189 
 
 The moon's motions are really affected by seve- 
 ral other inequalities, of very considerable amount, 
 besides those which were thus considered by Hip- 
 parchus; but the lunar paths, constructed on the 
 above data, possessed a considerable degree of cor- 
 rectness, and especially when applied, as they were 
 principally, to the calculation of eclipses ; for the 
 greatest of the additional irregularities which we 
 have mentioned disappear at new and full moon, 
 which are the only times when eclipses take place. 
 
 The numerical explanation of the motions of the 
 sun and moon, by means of the hypothesis of ec- 
 centrics, and the consequent construction of Tables, 
 was one of the great achievements of Hipparchus. 
 The general explanation of the motions of the pla- 
 nets, by means of the hypothesis of epicycles, was 
 in circulation previously, as we have seen. But the 
 special motions of the planets, in their epicycles, 
 are, in reality, affected by anomalies of the same 
 kind as those which render it necessary to introduce 
 eccentrics in the cases of the sun and moon. 
 
 Hipparchus determined, with great exactness, 
 the mean motions of the Planets ; but he was not 
 able, from want of data, to explain the planetary 
 irregularities by means of eccentrics. The whole 
 mass of good observations of the planets which he 
 received from preceding ages, did not contain so 
 many, says Ptolemy, as those which he has trans- 
 mitted to us of his own. " Hence 5 it was," he adds, 
 
 5 Synt. ix. 2. 
 
190 THE GREEK ASTRONOMY. 
 
 "that while he laboured, in the most assiduous 
 manner, to represent the motions of the sun and 
 moon by means of equable circular motions ; with 
 respect to the planets, so far as his works show, he 
 did not even make the attempt, but merely put the 
 extant observations in order, added to them himself 
 more than the whole of what he received from pre- 
 ceding ages, and showed the insufficiency of the 
 hypothesis current among astronomers to explain 
 the phenomena." It appears, that preceding mathe- 
 maticians had already pretended to construct "a 
 Perpetual Canon," that is, Tables which should give 
 the places of the planets at any future time ; but 
 these, being constructed without .regard to the 
 eccentricity of the orbits, must have been very 
 erroneous. 
 
 Ptolemy declares, with great reason, that Hip- 
 parchus showed his usual love of truth, and his 
 right sense of the responsibility of his task, in leav- 
 ing this part of it to future ages. The Theories of 
 the Sun and Moon, which we have already described, 
 constitute him a great astronomical discoverer, and 
 justify the reputation he has always possessed. 
 There is, indeed, no philosopher who is so uni- 
 formly spoken of in terms of admiration. Ptolemy, 
 to whom we owe our principal knowledge of him, 
 perpetually couples with his name epithets of praise : 
 he is not only an excellent and careful observer, but 
 "a 6 most truth-loving and labour-loving person," 
 6 Synt. ix. 2. 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 191 
 
 one who had shown extraordinary sagacity and re- 
 markable desire of truth in every part of science. 
 Pliny, after mentioning him and Thales, breaks out 
 into one of his passages of declamatory vehemence ; 
 " Great men ! elevated above the common standard 
 of human nature, by discovering the laws which 
 celestial occurrences obey, and by freeing the 
 wretched mind of man from the fears which 
 eclipses inspired. Hail to you and to your genius, 
 interpreters of heaven, worthy recipients of the 
 laws of the universe, authors of principles which 
 connect gods and men ! " Modern writers have 
 spoken of Hipparchus with the same admiration ; 
 and even the exact but severe historian of astrono- 
 my, Delambre, who bestows his praise so sparingly, 
 and his sarcasm so generally ; who says 7 that it is 
 unfortunate for the memory of Aristarchus that his 
 work has come to us entire, and who cannot refer 8 
 to the statement of an eclipse rightly predicted by 
 Halicon of Cyzicus without adding, that if the story 
 be true, Halicon was more lucky than prudent; 
 loses all his bitterness when he comes to Hippar- 
 chus 9 . " In Hipparchus," says he, " we find one of 
 the most extraordinary men of antiquity ; the very 
 greatest, in the sciences which require a combina- 
 tion of observation with geometry." Delambre adds, 
 apparently in the wish to reconcile this eulogium 
 with the depreciating manner in which he habitu- 
 ally speaks of all astronomers whose observations 
 
 7 Astronomic Ancienne, i. 75. 8 i. 17- 9 i. 186. 
 
192 THE GREEK ASTRONOMY. 
 
 are inexact, "a long period and the continued 
 efforts of many industrious men are requisite to 
 produce good instruments, but energy and assiduity 
 depend on the man himself." 
 
 Hipparchus was the author of other great dis- 
 coveries and improvements in astronomy, besides 
 the establishment of the Doctrine of Eccentrics and 
 Epicycles; but this, being the greatest advance in 
 the theory of the celestial motions which was made 
 by the ancients, must be the leading subject of our 
 attention in the present work ; our object being to 
 discover in what the progress of real theoretical 
 knowledge consists, and under what circumstances 
 it has gone on. 
 
 Sect . 2. Estimate of the Value of the Theory of 
 Eccentrics and Epicycles. 
 
 IT may be useful here to explain the value of the 
 theoretical step which Hipparchus thus made ; and 
 the more so, as there are, perhaps, opinions in 
 popular circulation, which might lead men to think 
 lightly of the merit of introducing or establishing 
 the Doctrine of Epicycles. For, in the first place, 
 this doctrine is now acknowledged to be false ; and 
 some of the greatest men in the more modern his^ 
 tory of astronomy owe the brightest part of their, 
 fame to their having been instrumental in over- 
 turning this hypothesis. And, moreover, in the 
 next place, the theory is not only false, but ex- 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 193 
 
 tremely perplexed and entangled, so that it is 
 usually looked upon as a mass of arbitrary and 
 absurd complication. Most persons are familiar 
 with passages in which it is thus spoken of 10 . 
 
 He his fabric of the heavens 
 
 Hath left to their disputes, perhaps to move 
 His laughter at their quaint opinions wide; 
 Hereafter when they come to model heaven 
 And calculate the stars, how will they wield 
 The mighty frame ! how build, unbuild, contrive, 
 To save appearances ! how gird the sphere 
 With centric and eccentric scribbled o'er, 
 Cycle in epicycle, orb in orb ! 
 
 And every one will recollect the celebrated saying 
 of Alphonso X., king of Castile 11 , when this com- 
 plex system was explained to him ; that " if God 
 had consulted him at the creation, the universe 
 should have been on a better and simpler plan." 
 In addition to this, the system is represented as 
 involving an extravagant conception of the nature 
 of the orbs which it introduces; that they are 
 crystalline spheres, and that the vast spaces which 
 intervene between the celestial luminaries are a solid 
 mass, formed by the fitting together of many masses 
 perpetually in motion; an imagination which is 
 presumed to be incredible and monstrous. 
 
 We must endeavour to correct or remove these 
 prejudices, not only in order that we may do justice 
 to the Hipparchian, or, as it is usually called, Ptole- 
 maic system of astronomy, and to its founder ; but 
 
 10 Paradise Lost, viii. A. D. 1252. 
 
 VOL. I. 
 
194 THE GREEK ASTRONOMY. 
 
 for another reason, much more important to the 
 purpose of this work; namely, that we may see how 
 theories may be highly estimable, though they con- 
 tain false representations of the real state of things, 
 and may be extremely useful, though they involve 
 unnecessary complexity. In the advance of know- 
 ledge, the value of the true part of a theory may 
 much outweigh the accompanying errour, and the 
 use of a rule may be little impaired by its want 
 of simplicity. The first steps of our progress do not 
 lose their importance because they are not the last; 
 and the outset of the journey may require no less 
 vigour and activity than its close. 
 
 That which is true in the Hipparchian theory, 
 and which no succeeding discoveries have deprived 
 of its value, is the Resolution of the apparent 
 motions of the heavenly bodies into an assemblage 
 of circular motions. The test of the truth and rea- 
 lity of this Resolution is, that it leads to the con- 
 struction of theoretical Tables of the motions of the 
 luminaries, by which their places are given at any 
 time, agreeing nearly with their places as actually 
 observed. The assumption that these circular mo- 
 tions, thus introduced, are all exactly uniform, is the 
 fundamental principle of the whole process. Thi& 
 assumption is, it may.be said, false; and we have 
 seen how fantastic some of the arguments were, 
 which were originally urged in its favour. But 
 some assumption is necessary, in order that the 
 motions, at different points of a revolution, may be 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 195 
 
 somehow connected, that is, in order that we may 
 have any theory of the motions ; and no assumption 
 more simple than the one now mentioned can be 
 selected. The merit of the theory is this; that 
 obtaining the amount of the eccentricity, the place 
 of the apogee, and, it may be, other elements, from 
 a fere observations, it deduces from these, results 
 agreeing with all observations, however numerous 
 and distant. To express an inequality by means of 
 an epicycle, implies, not only that there is an in- 
 equality, but further, that the inequality is at its 
 greatest value at a certain known place, diminishes 
 in proceeding from that place by a known law, 
 continues its diminution for a known portion of the 
 revolution of the luminary, then increases again ; 
 and so on: that is, the introduction of the epi- 
 cycle represents the inequality of motion, as com- 
 pletely as it can be represented with respect to 
 its quantity. 
 
 We may further illustrate this, by remarking 
 that such a Resolution of the unequal motions of 
 the heavenly bodies into equable circular motions, 
 is, in fact, equivalent to the most recent and im- 
 proved processes by which modern astronomers 
 deal with such motions. Their universal method is 
 to resolve all unequal motions into a series of 
 terms, or expressions of partial motions ; and these 
 terms involve sines and cosines, that is, certain 
 technical modes of measuring circular motion, the 
 circular motion having some constant relation to 
 
 02 
 
196 THE GREEK ASTRONOMY. 
 
 the time. And thus the problem of the resolution 
 of the celestial motions into equable circular ones, 
 which was propounded above two thousand years 
 ago in the school of Plato, is still the great object 
 of the study of modern astronomers, whether ob- 
 servers or calculators. 
 
 That Hipparchus should have succeeded in the 
 first great steps of this resolution for the sun and 
 moon, and should have seen its applicability in 
 other cases, is a circumstance which gives him one 
 of the most distinguished places in the roll of great 
 astronomers. As to the charges or the sneers 
 against the complexity of his system, to which we 
 have referred, it is easy to see that they are of no 
 force. As a system of calculation, his is not only 
 good, but, as we have just said, in many cases no 
 better has yet been discovered. If, when the actual 
 motions of the heavens are calculated in the best 
 possible way, the process is complex and difficult, 
 and if we are discontented at this, nature, and not 
 the astronomer, must be the object of our dis- 
 pleasure. This plea of the astronomers must be 
 allowed to be reasonable. " We must not be re- 
 pelled," says Ptolemy 12 , "by the complexity of the 
 hypotheses, but explain the phenomena as well as 
 we can. If the hypotheses satisfy each apparent 
 inequality separately, the combination of them will 
 represent the truth; and why should it appear 
 wonderful to any that such a complexity should 
 12 Synt. xiii. 2. 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 197 
 
 exist in the heavens, when we know nothing of 
 their nature which entitles us to suppose that any 
 inconsistency will result?" 
 
 But it may be said, we now know that the 
 motions are more simple than they were thus 
 represented, and that the theory of epicycles was 
 false, as a conception of the real construction of the 
 heavens. And to this we may reply, that it does 
 not appear that the best astronomers of antiquity 
 conceived the cycles and epicycles to have a mate- 
 rial existence. Though the dogmatic philosophers, 
 as the Aristotelians, appear to have taught that the 
 celestial spheres were real solid bodies, they are 
 spoken of by Ptolemy as imaginary 13 ; and it is clear, 
 from his proof of the identity of the results of the 
 hypothesis of an eccentric and an epicycle, that they 
 are intended to pass for no more than geometrical 
 conceptions, in which view they are true represen- 
 tations of the apparent motions. 
 
 It is true, that the real motions of the heavenly 
 bodies are simpler than the apparent motions ; and 
 that we, who are in the habit of representing to our 
 minds their real arrangement, become impatient of 
 the seeming confusion and disorder of the ancient 
 hypotheses. But this real arrangement never could 
 have been detected by philosophers, if the apparent 
 motions had not been strictly examined and suc- 
 cessfully analyzed. How far the connexion between 
 the facts and the true theory is from being obvious 
 
 13 Synt. iii. 3. 
 
19B THE GREEK ASTRONOMY. 
 
 or easily traced, any one may satisfy himself by 
 endeavouring, from a general conception of the 
 moon's real motions, to discover the rules which 
 regulate the occurrences of eclipses; or even to 
 explain to a learner, of what nature the apparent 
 motions of the moon among the stars will be. 
 
 The unquestionable evidence of the merit and 
 value of the theory of epicycles is to be found in 
 this circumstance; that it served to embody all 
 the most exact knowledge then extant, to direct 
 astronomers to the proper methods of making it 
 more exact and complete, to point out new objects 
 of attention and research ; and that, after doing this 
 at first, it was also able to take in, and preserve, all 
 the new results of the active and persevering la- 
 bours of a long series of Greek, Latin, Arabian, and 
 modern European astronomers, till a new theory 
 arose which could discharge this office. It may> 
 perhaps, surprise some readers to be told, that the 
 author of this next great step in astronomical 
 theory, Copernicus, adopted the theory of epicycles; 
 that is, he employed that which we have spoken of 
 as its really valuable characteristic. "We 14 must 
 confess," he says, "that the celestial motions are 
 circular, or compounded of several circles, since 
 their inequalities observe a fixed law and recur in 
 value at certain intervals, which could not be, exr 
 cept they were circular ; for a circle alone can make 
 that which has been, recur again." 
 
 14 Copernicus. De Rev. I. i. c. 4. 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 199 
 
 In this sense, therefore, the Hipparchian theory 
 was a real and indestructible truth, which was not 
 rejected, and replaced by different truths, but was 
 adopted and incorporated into every succeeding 
 astronomical theory ; and which can never cease to 
 be one of the most important and fundamental 
 parts of our astronomical knowledge. 
 
 A moment's reflection will show that, in the 
 events just spoken of, the introduction and esta- 
 blishment of the theory of epicycles, those charac- 
 teristics were strictly exemplified, which we have 
 asserted to be the conditions of every real advance 
 in progressive science; namely, the application of 
 distinct and appropriate Ideas to a real series of 
 Facts. The distinctness of the geometrical concep- 
 tions which enabled Hipparchus to assign the orbits 
 of the sun and moon, requires no illustration ; and 
 we have just explained how these ideas combined 
 into a connected whole the various motions and 
 places of those luminaries. To make this step in 
 astronomy, required diligence and care exerted in 
 collecting observations, and mathematical clearness 
 and steadiness of view exercised in seeing and 
 showing that the theory was a successful analysis 
 of them. 
 
 Sect. 3. Discovery of the Precession of the 
 Equinoxes. 
 
 THE same qualities which we trace in the researches 
 of Hipparchus already examined, diligence in col- 
 lecting observations, and clearness of idea in repre- 
 
200 THE GREEK ASTRONOMY. 
 
 senting them, appear also in other discoveries of 
 his, which we must not pass unnoticed. The Pre- 
 cession of the Equinoxes, in particular, is one of the 
 most important of these discoveries. 
 
 The circumstance here brought into notice was 
 a Change of Longitude of the Fixed Stars. The 
 longitudes of the heavenly bodies, being measured 
 from the point where the sun's annual path cuts the 
 equator, will change if that path changes. Whether 
 this happens, however, is not very easy to decide ; 
 for the sun's path among the stars is made out, not 
 by merely looking at the heavens, but by a series 
 of inferences from other observable facts. Hippar- 
 chus used for this purpose eclipses of the moon ; for 
 these, being exactly opposite to the sun, afford data 
 in marking out his path. By comparing the eclipses 
 of his own time with those observed at an earlier 
 period by Timocharis, he found that the bright star, 
 Spica Virginis, was six degrees behind the equi- 
 noctial point in his own time, and had been eight 
 degrees behind the same point at an earlier epoch. 
 The suspicion was thus suggested, that the longi- 
 tudes of all the stars increase perpetually ; but Hip- 
 parchus had too truly philosophical a spirit to take 
 this for granted. He examined the places of Re- 
 gulus, and those of other stars, as he had done those 
 of Spica; and he found, in all these instances, a 
 change of place which could be explained by a cer- 
 tain alteration of position in the circles to which 
 the stars are referred, which alteration is described 
 as the Precession of the Equinoxes. 
 
INDUCTIVE EPOCH OF HIPPARCHUS. 201 
 
 The distinctness with which Hipparchus con- 
 ceived this change of relation of the heavens, is 
 manifested by the question which, as we are told by 
 Ptolemy, he examined and decided ; that this mo- 
 tion of the heavens takes place about the poles of the 
 ecliptic, and not about those of the equator. The 
 care with which he collected this motion from the 
 stars themselves, may be judged of from this, that 
 having made his first observations for this purpose 
 on Spica and Regulus, zodiacal stars, his first suspi- 
 cion was that the stars of the zodiac alone changed 
 their longitude, which suspicion he disproved by the 
 examination of other stars. By his processes, the 
 idea of the nature of the motion, and the evidence 
 of its existence, the two conditions of a discovery, 
 were fully brought into view. The scale of the 
 facts which Hipparchus was thus able to reduce to 
 law, may be in some measure judged of, by recol- 
 lecting that the precession, from his time to ours, 
 has only carried the stars through one sign of the 
 zodiac ; and that, to complete one revolution of the 
 sky by the motion thus discovered, would require a 
 period of 25,000 years. Thus this discovery con- 
 nected the various aspects of the heavens at the 
 most remote periods of human history; and, ac- 
 cordingly, the novel and ingenious views which 
 Newton published in his chronology, are founded 
 on this single astronomical fact, of the Precession of 
 the Equinoxes. 
 
 The two discoveries which have been described, 
 
202 , THE GREEK ASTRONOMY. 
 
 the mode of constructing Solar and Lunar Tables, 
 and the Precession, were advances of the greatest 
 importance in astronomy, not only in themselves, 
 but in the new objects and undertakings which 
 they suggested to astronomers. The one detected 
 a constant law and order in the midst of perpetual 
 change and apparent disorder; the other disclosed 
 mutation and movement perpetually operating 
 where everything had been supposed fixed and 
 stationary. Such discoveries were well adapted to 
 call up many questionings in the minds of specu- 
 lative men; for, after this, nothing could be sup- 
 posed constant till it had been ascertained to be so 
 by close examination ; and no apparent complexity 
 or confusion could justify the philosopher in turnr 
 ing away in despair from the task of simplification. 
 To answer the inquiries thus suggested, new me- 
 thods of observing the facts were requisite, more 
 exact and uniform than those hitherto employed. 
 Moreover the discoveries which were made, and 
 others which could not fail to follow in their train, 
 led to many consequences, required to be reasoned 
 upon, systematized, completed, enlarged. In short, 
 the Epoch of Induction led, as we have stated that 
 such epochs must always lead, to a Period of 
 Developement, of Verification, Application, and 
 Extension. 
 
203 
 
 CHAPTER IV. 
 SEQUEL TO THE INDUCTIVE EPOCH OF HIPPARCHUS. 
 
 Sect. 1. Researches which verified the Theory. 
 
 THE discovery of the leading Laws of the Solar 
 and Lunar Motions, and the detection of the 
 Precession, may be considered as the great positive 
 steps in the Hipparchian astronomy; the parent 
 discoveries, from which many minor improvements 
 proceeded. The task of pursuing the collateral 
 and consequent researches which now offered them- 
 selves, of bringing the other parts of astronomy 
 up to the level of its most improved portions, was 
 prosecuted by a succession of zealous observers and 
 calculators, first, in the school of Alexandria, and 
 afterwards in other parts of the world. We must 
 notice the various labours of this series of astro- 
 nomers ; but we shall do so very briefly ; for the 
 ulterior developement of doctrines once established, 
 is not so important an object of contemplation for 
 our present purpose, as the first conception and 
 proof of those fundamental truths on which sys- 
 tematic doctrines are founded. Yet Periods of 
 Verification, as well as Epochs of Induction, de- 
 serve to be attended to ; and they can nowhere be 
 
204 THE GREEK ASTRONOMY. 
 
 studied with so much advantage as in the history of 
 astronomy. 
 
 In truth, however, Hipparchus did not leave to 
 his successors the task of pursuing into detail those 
 views of the heavens to which his discoveries led 
 him. He examined with scrupulous care almost 
 every part of the subject. We must briefly mention 
 some of the principal points which were thus set- 
 tled by him. 
 
 The verification of the laws of the changes 
 which he assigned to the skies, implied that the 
 condition of the heavens was constant, except so far 
 as it was affected by those changes. Thus, the doc- 
 trine that the changes of position of the stars were 
 rightly represented by the precession of the equi- 
 noxes, supposed that the stars were fixed with 
 regard to each other; and the doctrine that the 
 unequal number of days, in certain subdivisions of 
 months and years, was adequately explained by the 
 theory of epicycles, assumed that years and days 
 were always of constant lengths. But Hipparchus 
 was not content with assuming these bases of his 
 theory, he endeavoured to prove them. 
 
 1. Fixity of the Stars. The question neces- 
 sarily arose after the discovery of the precession, 
 even if such a question had never suggested itself 
 before, whether the stars which were called fixed, 
 and to which the motions of the other luminaries 
 are referred, do really retain constantly the same 
 relative position. In order to determine this funda- 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 205 
 
 mental question, Hipparchus undertook to construct 
 a Map of the heavens ; for though the result of his 
 survey was expressed in words, we may give this 
 name to his Catalogue of the positions of the most 
 conspicuous stars. These positions are described by 
 means of alineations ; that is, three or more such 
 stars are selected as can be touched by an apparent 
 straight line drawn in the heavens. Thus Hippar- 
 chus observed that the southern claw of Cancer, 
 the bright star in the same constellation which pre- 
 cedes the head of the Hydra, and the bright star 
 Procyon, were nearly in the same line. Ptolemy 
 quotes this and many other of the configurations 
 which Hipparchus had noted, in order to show that 
 the positions of the stars had not changed in the 
 intermediate time ; a truth which the catalogue of 
 Hipparchus thus gave astronomers the means of 
 ascertaining. It contained 1080 stars. 
 
 The construction of this catalogue of the stars 
 by Hipparchus is an event of great celebrity in the 
 history of astronomy. Pliny 1 , who speaks of it with 
 admiration as a wonderful and superhuman task 
 (" ausus rem etiam Deo improbam, annumerare pos- 
 teris stellas") asserts the undertaking to have been 
 suggested by a remarkable astronomical event, the 
 appearance of a new star ; " novam stellam et aliam 
 in sevo suo genitam deprehendit ; ej usque motu, 
 qua die fulsit, ad dubitationem est adductus anne 
 hoc ssepius fieret, moverenturque et eae quas puta- 
 1 Hist. Nat. Lib. ii. (xxvi.) 
 
206 THE GREEK ASTRONOMY. 
 
 mus affixas." There is nothing inherently impro- 
 bable in this tradition, but we may observe, with 
 Delambre 2 , that we are not informed whether this 
 new star remained in the sky, or soon disappeared 
 again. Ptolemy makes no mention of the star or' 
 the story; and his catalogue contains no bright star 
 which is not found in the " Catasterisms" of Eratos- 
 thenes. These Catasterisms were an enumeration 
 of 475 of the principal stars, according to the con- 
 stellations in which they are ; and were published 
 about sixty years before Hipparchus. 
 
 2. Constant Length of Years. Hipparchus 
 also attempted to ascertain whether successive 
 years are all of the same length ; and though, with 
 his scrupulous love of accuracy 3 , he does not ap- 
 pear to have thought himself justified in asserting 
 that the years were always exactly equal, he showed, 
 both by observations of the time when the sun; 
 passed the equinoxes, and by eclipses, that the 
 difference of successive years, if there were any 
 difference, must be extremely slight. The obser- 
 vations of succeeding astronomers, and especially 
 of Ptolemy, confirmed this opinion, and proved, 
 with certainty, that there is no progressive increase 
 or diminution in the duration of the year. 
 
 3. Constant Length of Days. Equation of 
 Time. The equality of days was more difficult to 
 ascertain than that of years ; for the year is mea- 
 sured, as on a natural scale, by the number of 
 
 2 A. A. i. 290. 3 Ptolem. Synt. iii. 2. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 207 
 
 days which it contains; but the day can be sub- 
 divided into hours only by artificial means; and 
 the mechanical skill of the ancients did not enable 
 them to attain any considerable accuracy in the 
 measure of such portions of time; though clep- 
 sydras and similar instruments were used by astro- 
 nomers. The equality of days could only be proved, 
 therefore, by the consequences of such a suppo- 
 sition ; and in this manner it appears to have been 
 assumed, as the fact really is, that the apparent 
 revolution of the stars is accurately uniform, never 
 becoming either quicker or slower. It followed as 
 a consequence of this, that the solar days (or rather 
 the nycthemers, compounded of a night and a day,) 
 would be unequal, in consequence of the sun's 
 unequal motion, thus giving rise to what we now 
 call the Equation of Time, the interval by which 
 the time, as marked on a dial, is before or after 
 the time, as indicated by the accurate time-pieces 
 which modern skill can produce. This inequality 
 was fully taken account of by the ancient astro- 
 nomers ; and they thus in fact assumed the equality 
 of the sidereal days. 
 
 Sect. 2. Researches which did not verify the 
 Theory. 
 
 SOME of the researches of Hipparchus and his fol- 
 lowers fell upon the weak parts of his theory; 
 and if the observations had been sufficiently exact, 
 must have led to its being corrected or rejected. 
 
208 THE GREEK ASTRONOMY. 
 
 Among these we may notice the researches 
 which were made concerning the Parallax of the 
 heavenly bodies, that is, their apparent displace- 
 ment by the alteration of position of the observer 
 from one part of the earth's surface to the other. 
 This subject is treated of at length by Ptolemy; and 
 there can be no doubt that it was well examined 
 by Hipparchus, who invented a parallatic instru- 
 ment for that purpose. The idea of parallax, as 
 a geometrical possibility, was indeed too obvious 
 to be overlooked by geometers at any time; and 
 when the doctrine of the sphere was established, 
 it must have appeared strange to the student, that 
 every place on the earth's surface might alike be 
 considered as the center of the celestial motions. 
 But if this was true with respect to the motions 
 of the fixed stars, was it also true with regard to 
 those of the sun and moon? The displacement 
 of the sun by parallax is so small that the best 
 observers among the ancients could never be sure 
 of its existence ; but with respect to the moon, the 
 ease is different. She may be displaced by this 
 cause to the amount of twice her own breadth, a 
 quantity easily noticed by the rudest process of in- 
 strumental observation. The law of the displace- 
 ment thus produced is easily obtained by theory, 
 the globular form of the earth being supposed 
 known; but the amount of the displacement de- 
 pends upon the distance of the moon from the 
 earth, and requires at least one good observation 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 209 
 
 to determine it. Ptolemy has given a table of the 
 effects of parallax, calculated according to the 
 apparent altitude of the moon, assuming certain 
 supposed distances ; these distances, however, do 
 not follow the real law of the moon's distances, in 
 consequence of their being founded upon the Hypo-. 
 thesis of the Eccentric and Epicycle. 
 
 In fact this Hypothesis, though a very close 
 representation of the truth, so far as the positions 
 of the luminaries are concerned, fails altogether 
 when we apply it to their distances. The radius 
 of the epicycle, or the eccentricity of the eccentric, 
 are determined so as to satisfy the observations of 
 the apparent motions of the bodies : but, inasmuch 
 as the hypothetical motions are different altogether 
 from the real motions, the Hypothesis does not, at 
 the same time, satisfy the observations of the dis- 
 tances of the bodies, if we are able to make any 
 such observations. 
 
 Parallax is one method by which the distances 
 of the moon, at different times, may be compared ; 
 her Apparent Diameters afford another method. 
 Neither of these modes, however, is easily capable 
 of such accuracy as to overturn at once the Hypo- 
 thesis of epicycles; and, accordingly, the Hypothesis 
 continued to be entertained in spite of such mea- 
 sures; the measures being, indeed, in some degree 
 falsified in consequence of the reigning opinion. 
 In fact, however, the imperfection of the methods 
 of measuring parallax and magnitude, which were 
 VOL. i. P 
 
210 THE GREEK ASTRONOMY. 
 
 in use at this period, was such, their results could 
 not lead to any degree of conviction deserving to 
 be set in opposition to a theory which was so 
 satisfactory with regard to the more certain obser- 
 vations. 
 
 The Eccentricity, or the Radius of the Epicycle, 
 which would satisfy the inequality of the motions 
 of the moon, would, in fact, double the inequality 
 of the distances. The Eccentricity of the moon's 
 orbit is determined by Ptolemy as T ^ of the radius 
 of the orbit ; but its real amount is only half as 
 great; this difference is a necessary consequence 
 of the supposition of uniform circular motions, on 
 which the Epicyclic Hypothesis proceeds. 
 
 We see, therefore, that this part of the Hippar- 
 chian theory carries in itself the germ of its own 
 destruction. As soon as the art of celestial mea- 
 surement was so far perfected, that astronomers 
 could be sure of the apparent diameter of the moon 
 within sV or 5^ of the whole, the inconsistency 
 of the theory with itself would become manifest. 
 We shall see, hereafter, the way in which this 
 inconsistency operated; in reality, a very long 
 period elapsed before the methods of observing 
 were sufficiently good to bring it clearly into view. 
 
 Sect. 3. Methods of Observation of the Greek 
 Astronomers. 
 
 WE must now say a word concerning the Methods 
 above spoken of. Since one of the most important 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 211 
 
 tasks of a period of verification is to ascertain with 
 accuracy the magnitude of the quantities which 
 enter, as elements, into the theory which occupies 
 men during the period ; the improvement of instru- 
 ments, and the methods of observing and experi- 
 menting, are principal features in such periods. We 
 shall, therefore, mention some of the facts which 
 bear upon this point. 
 
 The estimation of distances among the stars by 
 the eye, is an extremely inexact process. In some 
 of the ancient observations, however, this appears 
 to have been the method employed : and stars are 
 described as being a cubit or two cubits from other 
 stars. We may form some notion of the scale of 
 this kind of measurement, from what Cleomedes 
 remarks 4 , that the sun appears to be about a foot 
 broad ; an opinion which he confutes at length. 
 
 A method of determining the positions of the 
 stars, susceptible of a little more exactness than 
 the former, is the use of alineations, already noticed 
 in speaking of Hipparchus's catalogue. Thus, a 
 straight line passing through two stars of the Great 
 Bear passes also through the pole-star: this is, 
 indeed, even now a method usually employed to 
 enable us readily to fix on the pole-star ; and the 
 two stars, j3 and a of Ursa Major, are hence often 
 called " the pointers." 
 
 But nothing like accurate measurements of any 
 portions of the sky were obtained, till astronomers 
 
 4 Del. A. A. i. 222. 
 
 P2 
 
212 THE GREEK ASTRONOMY. 
 
 adopted the method of making visual coincidences 
 of the objects with the instruments, either by means 
 of shadows or of sights. 
 
 Probably the oldest and most obvious measure- 
 ments of the positions of the heavenly bodies were 
 those in which the elevation of the sun was deter- 
 mined by comparing the length of the shadow of 
 an upright staff or gnomon, with the length of the 
 staff itself. It appears 5 , from a memoir of Gautil, 
 first printed in the Connaissance des Temps for 
 1809, that, at the lower town of Loyang, now called 
 Hon-anfou, Tchon-kong found the length of the 
 shadow of the gnomon, at the summer solstice, 
 equal to one foot and a half, the gnomon itself 
 being eight feet in length. This was about 1100 
 B.C. The Greeks, at an early period, used the 
 same method. Strabo says 6 that " Byzantium and 
 Marseilles are on the same parallel of latitude, 
 because the shadows at those places have the same 
 proportion to the gnomon, according to the state- 
 ment of Hipparchus, who follows Pytheas." 
 
 But the relations of position which astronomy 
 considers, are, for the most part, angular distances ; 
 and these are most simply expressed by the inter- 
 cepted portion of a circumference described about 
 the angular point. The use of the gnomon might 
 lead to the determination of the angle by the 
 graphical methods of geometry ; but the numerical 
 expression of the circumference required some pro- 
 
 5 Lib. U. K. Hist. Ast. p. 5. Del. A. A. i. 257. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 213 
 
 gress in trigonometry ; for instance, a table of the 
 tangents of angles. 
 
 Instruments were soon invented for measuring 
 angles, by means of circles, which had a border, 
 or limb, divided into equal parts. The whole cir- 
 cumference was divided into 360 degrees : perhaps 
 because the circles, first so divided, were those 
 which represented the sun's annual path; one such 
 degree would be the sun's daily advance, more 
 nearly than any other convenient aliquot part which 
 could be taken. The position of the sun was de- 
 termined by means of the shadow of one part of 
 the instrument upon the other. The most ancient 
 instrument of this kind appears to be the Hemi- 
 sphere of Berosus. A hollow hemisphere was placed 
 with its rim horizontal, and a style was erected 
 in such a manner that the extremity of the style 
 was exactly at the center of the sphere. The 
 shadow of this extremity, on the concave surface, 
 had the same position with regard to the lowest 
 point of the sphere which the sun had with regard 
 to the highest point of the heavens. But this 
 instrument was in fact used rather for dividing 
 the day into portions of time than for determining 
 position. 
 
 Eratosthenes 7 observed the amount of the obli- 
 quity of the sun's path to the equator; we are 
 not informed what instruments he used for this 
 purpose : but he is said to have obtained, from the 
 7 Delambre, A. A. i. 86. 
 
214 THE GREEK ASTRONOMY. 
 
 munificence of Ptolemy Euergetes, two Armils, or 
 instruments composed of circles, which were placed 
 in the portico at Alexandria, and long used for 
 observations. If a circular rim were placed so 
 as to coincide with the plane of the equator, the 
 inner concave edge would be enlightened by the 
 sun's rays which came under the front edge, when 
 the sun was south of the equator, and by the rays 
 which came over the front edge, when the sun was 
 north of the equator : the moment of the transi- 
 tion would be the time of the equinox. Such an 
 instrument appears to be referred to by Hippar- 
 chus, as quoted by Ptolemy 8 . " The circle of cop- 
 per, which stands at Alexandria in what is called 
 the Square Porch, appears to mark, as the day of 
 the equinox, that on which the concave surface 
 begins to be enlightened from the other side." Such 
 an instrument was called an equinoctial armil. 
 
 A solstitial armil is described by Ptolemy, con- 
 sisting of two circular rims, one sliding round 
 within the other, and the inner one furnished with 
 two pegs standing out from its surface at right 
 angles, and diametrically opposite to each other. 
 These circles being fixed in the plane of the meri- 
 dian, and the inner one turned, till, at noon, the 
 shadow of the peg in front falls upon the peg 
 behind, the position of the sun at noon would be 
 determined by the degrees on the outer circle. 
 
 In calculation, the degree was conceived to 
 8 Ptol. Synt. iii. 2. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 215 
 
 be divided into 60 minutes, the minute into 60 
 seconds, and so on. But in practice it was impos- 
 sible to divide the limb of the instrument into 
 parts so small. The armils of Alexandria were 
 divided into no parts smaller than sixths of degrees, 
 or divisions of 10 minutes. 
 
 The angles, observed by means of these divi- 
 sions, were expressed as a fraction of the circum- 
 ference. Thus Eratosthenes stated the interval 
 between the tropics to be ^J of the circumference 9 . 
 
 It was soon remarked that the whole circum- 
 ference of the circle was not wanted for such 
 observations. Ptolemy 10 says, that he found it more 
 convenient to observe altitudes by means of a 
 square flat piece of stone or wood, with a quadrant 
 of a circle described on one of its flat faces, about 
 a center near one of the angles. A peg was 
 placed at the center, and one of the extreme radii 
 of the quadrant being perpendicular to the horizon, 
 the elevation of the sun above the horizon was 
 determined by observing the point of the arc of 
 the quadrant on which the shadow of the peg fell. 
 
 As the necessity of accuracy in the observations 
 was more and more felt, various adjustments of 
 such instruments were practised. The instruments 
 were placed in the meridian by means of a meridian 
 
 9 Delambre, A. A. i. 87- It is probable that his observation 
 
 , . A * 9 , r - ,. 47$ 143 11-13 11 
 
 gave him 47| degrees. The fraction m 
 
 jl 
 which is very nearly ^ . 
 
 10 Synt. i. 1. 
 
216 THE GREEK ASTRONOMY. 
 
 line drawn by astronomical methods on the floor on 
 which they stood. The plane of the instrument 
 was made vertical by means of a plumb-line : the 
 bounding radius, from which angles were measured, 
 was also adjusted by the plumb-line 11 . 
 
 In this manner, the places of the sun and of the 
 moon could be observed by means of the shadows 
 which they cast. In order to observe the stars' 2 , 
 the observer looked along the face of the circle 
 of the armil, so as to see its two edges apparently 
 brought together, and the star apparently touch- 
 ing them 13 . 
 
 It was afterwards found important to ascertain 
 the position of the sun with regard to the ecliptic : 
 and, for this purpose, an instrument, called an 
 astrolabe, was invented, of which we have a de- 
 scription in Ptolemy 14 . This also consisted of cir- 
 cular rims, moveable within one another, or about 
 poles; and contained circles which were to be 
 brought into the position of the ecliptic, and of 
 a plane passing through the sun and the poles of 
 the ecliptic. The position of the moon with regard 
 to the ecliptic, and its position in longitude with 
 
 11 The curvature of the plane of the circle, by warping, was 
 noticed. Ptol. iii. 2. p. 155, observes that his equatorial circle 
 was illuminated on the hollow side twice in the same day. (He 
 did not know that this might arise from refraction.) 
 
 12 Delamb. A. A. i. 185. 
 
 13 Ptol. Synt. i. 1. 'Qa-irep KeKoAAf/jme'i/o? 
 TCUS eTTKpaveiais o da-Ttjp ev T(O Bt' auTtoi/ eirnre 
 
 14 Synt. v. 1. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 217 
 
 regard to the sun or a star, were thus deter- 
 mined. 
 
 The astrolabe continued long in use, but not so 
 long as the quadrant described by Ptolemy ; this 
 in a larger form, is the mural quadrant, which 
 has been used up to the most recent times. 
 
 It may be considered surprising 15 , that Hip- 
 parchus, after having observed, for some time, 
 right ascensions and declinations, quitted equatorial 
 armils for the astrolabe, which immediately refers 
 the stars to the ecliptic. He probably did this 
 because, after the discovery of precession, he found 
 the latitudes of the stars constant, and wanted to 
 ascertain their motion in longitude. 
 
 To the above instruments, may be added the 
 dioptra and the parallactic instrument of Hippar- 
 chus, and Ptolemy. In the latter, the distance of 
 a star from the zenith was observed by looking 
 through two sights fixed in a rule, this being an- 
 nexed to another rule, which was kept in a vertical 
 position by a plumb-line; and the angle between 
 the two rules was measured. 
 
 The following example of an observation, taken 
 from Ptolemy, may serve to show the form in 
 which the results of the instruments, just described, 
 were usually stated 16 . 
 
 " In the 2nd year of Antoninus, the 9th day of 
 Pharmouthi, the sun being near setting, the last 
 division of Taurus being on the meridian (that is, 
 14 Del. A. A. 181. " Del. A. A. ii. 248. 
 
218 THE GREEK ASTRONOMY. 
 
 5^ equinoctial hours after noon), the moon was in 
 3 degrees of Pisces, by her distance from the sun 
 (which was 92 degrees, 8 minutes) ; and half an 
 hour after, the sun being set, and the quarter of 
 Gemini on the meridian, Regulus appeared, by the 
 other circle of the astrolabe, 57^ degrees more 
 forwards than the moon in longitude." From these 
 data the longitude of Regulus is calculated. 
 
 From what has been said respecting the obser- 
 vations of the Alexandrian astronomers, it will 
 have been seen that their instrumental observations 
 could not be depended on for any close accuracy. 
 This defect, after the general reception of the Hip- 
 parchian theory, operated very unfavourably on the 
 progress of the science. If they could have traced 
 the moon's place distinctly from day to day, they 
 must soon have discovered all the inequalities 
 which were known to Tycho Brahe ; and if they 
 could have measured her parallax or her diameter 
 with any considerable accuracy, they must have 
 obtained a confutation of the epicycloidal form of 
 her orbit. By the badness of their observations, 
 and the imperfect agreement of these with calcu- 
 lation, they not only were prevented making such 
 steps, but were led to receive the theory with 
 a servile assent and an indistinct apprehension, 
 instead of that rational conviction and intuitive 
 clearness which would have given a progressive 
 impulse to their knowledge. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 219 
 
 Sect. 4. Period from Hipparchus to Ptolemy. 
 
 WE have now to speak of the cultivators of astro- 
 nomy from the time of Hipparchus to that of 
 Ptolemy, the next great name which occurs in the 
 history of this science ; though even he holds place 
 only among those who verified, developed, and 
 extended the theory of Hipparchus. The astro- 
 nomers who lived in the intermediate time, indeed, 
 did little, even in this way ; though it might have 
 been supposed that their studies were carried on 
 under considerable advantages, inasmuch as they 
 all enjoyed the liberal patronage of the kings of 
 Egypt 17 . The " divine school of Alexandria," as it 
 is called by Synesius, in the fourth century, appears 
 to have produced few persons capable of carrying 
 forwards, or even of verifying, the labours of its 
 great astronomical teacher. The mathematicians 
 of the school wrote much, and apparently they ob- 
 served sometimes; but their observations are of 
 little value : and their books are expositions of the 
 theory and its geometrical consequences, without 
 any attempt to compare it with observation. For 
 instance, it does not appear that any one verified 
 the remarkable discovery of the precession, till the 
 time of Ptolemy, 250 years after; nor does the 
 statement of this motion of the heavens appear in 
 the treatises of the intermediate writers ; nor does 
 Ptolemy quote a single observation of any person 
 
 17 Delamb. A. A. ii. 240. 
 
220 THE GREEK ASTRONOMY. 
 
 made in this long interval of time ; while his refer- 
 ences to those of Hipparchus are perpetual ; and 
 to those of Aristyllus and Timocharis, and of others, 
 as Conon, who preceded Hipparchus, are not un- 
 frequent. 
 
 This Alexandrian period, so inactive and barren 
 in the history of science, was prosperous, civilized, 
 and literary ; and many of the works which belong 
 to it are come down to us, though those of Hip- 
 parchus are lost. We have the " Uranologion" of 
 Geminus 18 , a systematic treatise on Astronomy, ex- 
 pounding correctly the Hipparchian Theories and 
 their consequences, and containing a good account 
 of the use of the various cycles, which ended in 
 the adoption of the Calippic period. We have 
 likewise "The Circular Theory of the Celestial 
 Bodies" of Cleomedes 19 , of which the principal part 
 is a developement of the doctrine of the sphere, 
 including the consequences of the globular form 
 of the earth. We have also another work on 
 "Spherics" by Theodosius of Bithynia 20 , which con- 
 tains some of the most important propositions of 
 the subject, and has been used as a book of in- 
 struction even in modern times. Another writer 
 on the same subject is Menelaus, who lived some- 
 what later, and whose Three Books on Spherics 
 still remain. 
 
 One of the most important kinds of deduction 
 from a geometrical theory, such as that of the 
 
 18 B. c. 70. 19 B. c. 60. 20 B. c. 50. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 221 
 
 doctrine of the sphere, or that of epicycles, is the 
 calculation of its numerical results in particular 
 cases. With regard to the latter theory, this was 
 done in the construction of Solar and Lunar Tables, 
 as we have already seen ; and this process required 
 the formation of a Trigonometry, or system of 
 rules for calculating the relations between the sides 
 and angles of triangles. Such a science had been 
 formed by Hipparchus, who appears to be the 
 author of every great step in ancient astronomy 21 . 
 He wrote a work in twelve books, "On the Con- 
 struction of the Tables of Chords of Arcs ;" such 
 a table being the means by which the Greeks 
 solved their triangles. The Doctrine of the Sphere 
 required, in like manner, a Spherical Trigono- 
 metry, in order to enable mathematicians to cal- 
 culate its results ; and this branch of science also 
 appears to have been formed by Hipparchus 22 , who 
 gives results that imply the possession of such a 
 method. Hypsicles, who was a contemporary of 
 Ptolemy, also made some attempts at the solution 
 of such problems : but it is extraordinary that the 
 writers whom we have mentioned as coming after 
 Hipparchus, namely, Theodosius, Cleomedes, and 
 Menelaus, do not even mention the calculation of 
 triangles 23 , either plane or spherical; though the 
 latter writer 24 is said to have written on "the 
 Table of Chords," a work which is now lost. 
 
 21 Delamb. A. A. ii. 37. 22 A. A. i. 117. 
 
 83 A. A. i. 249. a4 A. A. ii. 37. 
 
222 THE GREEK ASTRONOMY. 
 
 We shall see, hereafter, how prevalent a dis- 
 position in literary ages is that which induces 
 authors to become commentators. This tendency 
 showed itself at an early period in the school of 
 Alexandria. Aratus 25 , who lived 270 B.C. at the 
 court of Antigonus, king of Macedonia, described 
 the celestial constellations in two poems, entitled 
 " Phenomena," and "Prognostics." These poems 
 were little more than a versification of the treatise 
 of Eudoxus on the acronycal and heliacal risings 
 and settings of the stars. The work was the subject 
 of a comment by Hipparchus, who perhaps found 
 this the easiest way of giving connexion and cir- 
 culation to his knowledge. Three Latin translations 
 of this poem gave the Romans the means of be- 
 coming acquainted with it : the first is by Cicero, 
 of which we have numerous fragments extant 26 ; 
 Germanicus Caesar, one of the sons-in-law of Au- 
 gustus, also translated the poem, and this transla- 
 tion remains almost entire. Finally, we have a 
 complete translation by Avienus 27 . The "Astro- 
 nomica" of Manilius, the "Poeticon Astronomicon" 
 of Hyginus, both belonging to the time of Au- 
 gustus, are, like the work of Aratus, poems which 
 combine mythological ornament with elementary 
 astronomical exposition ; but have no value in the 
 
 26 A. A. i. 74. 
 
 26 Two copies of this translation, illustrated by drawings of 
 different ages, one set Roman, and the other Saxon, according 
 to Mr. Ottley, are described in the Archceologta, vol. xviii. 
 
 27 Mont. i. 221. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 223 
 
 history of science. We may pass nearly the same 
 judgment upon the explanations and declamations 
 of Cicero, Seneca, and Pliny, for they do not apprize 
 us of any additions to astronomical knowledge; 
 and they do not always indicate a very clear ap- 
 prehension of the doctrines which the writers 
 adopt. 
 
 Perhaps the most remarkable feature in the 
 two last-named writers, is the declamatory expres- 
 sion of their admiration for the discoverers of 
 physical knowledge ; and in one of them, Seneca, 
 the persuasion of a boundless progress in science 
 to which man was destined. Though this belief 
 was no more than a vague and arbitrary conjec- 
 ture, it suggested other conjectures in detail, some 
 of which, having been verified, have attracted much 
 notice. For instance, in speaking of comets 28 , 
 Seneca says, "The time will come when those 
 things which are now hidden shall be brought 
 to light by time and persevering diligence. Our 
 posterity will wonder that we should be ignorant of 
 what is so obvious." " The motions of the planets," 
 he adds, "complex and seemingly confused, have 
 been reduced to rule; and some one will come 
 hereafter, who will reveal to us the paths of 
 comets." Such convictions and conjectures are not 
 to be admired for their wisdom; for Seneca was 
 led rather by enthusiasm, than by any solid rea- 
 sons, to entertain this opinion ; nor, again, are they 
 to be considered as merely lucky guesses, implying 
 
 28 Seneca. Qu. N. vii. 25. 
 
224 THE GREEK ASTRONOMY. 
 
 no merit : they are remarkable as showing how 
 the persuasion of the universality of law, and the 
 belief of the probability of its discovery by man, 
 grow up in men's minds, when speculative know- 
 ledge becomes a prominent object of attention. 
 
 An important practical application of astrono- 
 mical knowledge was made by Julius Caesar, in his 
 correction of the calendar, which we have already 
 noticed: and this was strictly due to the Alexan- 
 drian School : Sosigenes, an astronomer belonging 
 to that school, came from Egypt to Rome for the 
 purpose. 
 
 Sect. 5. Measures of the Earth. 
 
 THERE were, as we have said, few attempts made, 
 at the period of which we are speaking, to improve 
 the accuracy of any of the determinations of the 
 early Alexandrian astronomers. One question na- 
 turally excited much attention at all times, the 
 magnitude of the earth, its figure being universally 
 acknowledged to be a globe. The Chaldeans, at 
 an earlier period, had asserted that a man, walking 
 without stopping, might go round the circuit of 
 the earth in a year; but this might be a mere 
 fancy, or a mere guess. The attempt of Eratos- 
 thenes to decide this question went upon principles 
 entirely correct. Syene was situated on the tropic ; 
 for there, on the day of the solstice, at noon, ob- 
 jects cast no shadow ; and a well was enlightened 
 to the bottom by the sun's rays. At Alexandria, 
 on the same day, the sun was, at noon, distant 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 225 
 
 from the zenith by a fiftieth part of the circum- 
 ference. These two cities were north and south 
 from each other : and the distance had been deter- 
 mined, by the royal overseers of the roads, to be 
 5000 stadia. This gave a circumference of 250,000 
 stadia to the earth, and a radius of about 40,000. 
 Aristotle 21 says that the mathematicians make the 
 circumference 400,000 stadia. Hipparchus con- 
 ceived that the measure of Eratosthenes ought to 
 be increased by about one tenth 30 . Posidonius, the 
 friend of Cicero, made another attempt of the 
 same kind. At Rhodes, the star Canopus but just 
 appeared above the horizon: at Alexandria, the 
 same star rose to an altitude of ^ th of the cir- 
 cumference ; the direct distance on the meridian 
 was 5000 stadia, which gave 240,000 for the whole 
 circuit. We cannot look upon these measures as 
 very precise ; the stadium employed is not certainly 
 known ; and no peculiar care appears to have been 
 bestowed on the measure of the direct distance. 
 
 When the Arabians, in the ninth century, came 
 to be the principal cultivators of astronomy, they 
 repeated this observation in a manner more suited 
 to its real importance and capacity of exactness. 
 Under the Caliph Almamon 31 , the vast plain of 
 Singiar, in Mesopotamia, was the scene of this un- 
 dertaking. The Arabian astronomers there divided 
 themselves into two bands, one under the direction 
 
 29 De Ccelo. ii. ad fin. 30 Plin. ii. (cviii.) 
 
 31 Montu. i. 357. 
 
 VOL. I. Q 
 
226 THE GREEK ASTRONOMY. 
 
 of Chalid ben Abdolmalic, and the other having 
 at its head Alis ben Isa. These two parties pro- 
 ceeded, the one north, the other south, determining 
 the distance by the actual application of their mea- 
 suring-rods to the ground, till each was found, 
 by astronomical observation, to be a degree from 
 the place at which they started. It then appeared 
 that these terrestrial degrees were respectively 
 56 miles, and 56 miles and two thirds, the mile 
 being 4000 cubits. In order to remove all doubt 
 concerning the scale of this measure, we are in- 
 formed that the cubit is that called the black 
 cubit, which consists of 27 inches, each inch being 
 the thickness of six grains of barley. 
 
 Sect. 6. Ptolemy s Discovery of Evection. 
 
 BY referring, in this place, to the last-mentioned 
 measure of the earth, we include the labours of 
 the Arabian as well as the Alexandrian astrono- 
 mers, in the period of mere detail, which forms 
 the sequel to the great astronomical revolution 
 of the Hipparchian epoch. And this period of 
 verification is rightly extended to those later times; 
 not merely because astronomers were then still 
 employed in determining the magnitude of the 
 earth, and the amount of other elements of the 
 theory; for these are some of their employments 
 to the present day; but because no great inter- 
 vening discovery marks a new epoch, and begins 
 a new period; because no great revolution in 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 9 
 
 the theory added to the objects of investigation, 
 or presented them in a new point of view. This 
 being the case, it will be more instructive for 
 our purpose to consider the general character and 
 broad intellectual features of this period, than 
 to offer a useless catalogue of obscure and worth- 
 less writers, and of opinions either borrowed or 
 unsound. But before we do this, there is one 
 writer whom we cannot leave undistinguished in 
 the crowd ; since his name is more celebrated 
 even than that of Hipparchus ; his works contain 
 ninety-nine hundredths of what we know of the 
 Greek astronomy; and though he was not the 
 author of a new theory, he made some very re- 
 markable steps in the verification, correction, and 
 extension of the theory which he received. I speak 
 of Ptolemy, whose work, " The Mathematical Con- 
 struction" (of the heavens), contains a complete 
 exposition of the state of astronomy in his time, 
 the reigns of Adrian and Antonine. This book 
 is familiarly known to us by a term which contains 
 the record of our having received our first know- 
 ledge of it from the Arabic writers. The " Me- 
 giste Syntaxis," or Great Construction, gave rise, 
 among them, to the title A I Magisti, or Almagest, 
 by which the work is commonly described. As 
 a mathematical exposition of the Theory of Epi- 
 cycles and Eccentrics, of the observations and 
 calculations which were employed in order to ap- 
 ply this theory to the sun, moon, and planets, and 
 
 Q2 
 
228 THE GREEK ASTRONOMY. 
 
 of the other calculations which are requisite, in 
 order to deduce the consequences of this theory, 
 the work is a splendid and lasting monument of 
 diligence, skill and judgment. Indeed, all the other 
 astronomical works of the ancients hardly add any- 
 thing whatever to the information we obtain from 
 the Almagest ; and the knowledge which the 
 student possesses of the ancient astronomy must 
 depend mainly upon his acquaintance with Pto- 
 lemy. Among other merits, Ptolemy has that of 
 giving us a very copious account of the manner in 
 which Hipparchus established the main points of 
 his theories; an account the more agreeable, in 
 consequence of the admiration and enthusiasm with 
 which this author everywhere speaks of the great 
 master of the astronomical school. 
 
 In our present survey of the writings of Pto- 
 lemy, we are concerned less with his exposition 
 of what had been done before him, than with 
 his own original labours. In most of the branches 
 of the subject, he gave additional exactness to 
 what Hipparchus had done ; but our main business, 
 at present, is with those parts of the Almagest 
 which contain new steps in the application of the 
 Hipparchian hypothesis. There are two such cases, 
 both very remarkable, that of the moon's Elec- 
 tion, and that of the Planetary Motions. 
 
 The law of the moon's anomaly, that is, of the 
 leading and obvious inequality of her motion, could 
 be represented, as we have seen, either by an 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 229 
 
 eccentric or an epicycle ; and the amount of this 
 inequality had been collected by observations of 
 eclipses. But though the hypothesis of an epicycle, 
 for instance, would bring the moon to her proper 
 place, so far as eclipses could show it, that is, 
 at new and full moon, this hypothesis did not 
 rightly represent her motions at other points of 
 her course. This appeared, when Ptolemy set 
 about measuring her distances from the sun at dif- 
 ferent times. " These," he 32 says, sometimes agreed, 
 and sometimes disagreed." But by further atten- 
 tion to the facts, a rule was detected in these dif- 
 ferences. "As my knowledge became more complete 
 and more connected, so as to show the order of 
 this new inequality, I perceived that this difference 
 was small, or nothing, at new and full moon ; and 
 that at both the dichotomies (when the moon is 
 half illuminated,) it was small, or nothing, if the 
 moon was at the apogee or perigee of the epicycle, 
 and was greatest when she was in the middle of 
 the interval, and therefore when the first inequality 
 was greatest also." He then adds some further 
 remarks on the circumstances according to which 
 the moon's place, as affected by this new inequality, 
 is before or behind the place, as given by the 
 epicyclical hypothesis. 
 
 Such is the announcement of the celebrated 
 discovery of the moon's second inequality, after- 
 wards called (by Bullialdus) the Ejection. Ptolemy 
 
 M Synt. v. 2. 
 
230 THE GREEK ASTRONOMY. 
 
 soon proceeded to represent this inequality by a 
 combination of circular motions, uniting, for this 
 purpose, the hypothesis of an epicycle, already 
 employed to explain the first inequality, with the 
 hypothesis of an eccentric, in the circumference of 
 which the center of the epicycle was supposed to 
 move. The mode of combining these was some- 
 what complex; more complex we may, perhaps, 
 say, than was absolutely requisite 33 ; the apogee of 
 the eccentric moved backwards, or contrary to the 
 order of the signs, and the center of the epicycle 
 moved forwards nearly twice as fast upon the cir- 
 cumference of the eccentric, so as to reach a place 
 nearly, but not exactly, the same, as if it had 
 moved in a concentric instead of an eccentric path. 
 Thus the center of the epicycle went twice round 
 the eccentric in the course of one month : and in 
 this manner it satisfied the condition that it should 
 vanish at new and full moon, and be greatest 
 when the moon was in the quarters of her monthly 
 course (G). 
 
 The discovery of the Evection, and the reduction 
 of it to the epicyclical theory, was, for several 
 reasons, an important step in astronomy; some 
 of these reasons may be stated. 
 
 1. It obviously suggested, or confirmed, the 
 
 33 If Ptolemy had used the hypothesis of an eccentric instead 
 of an epicycle for the first inequality of the moon, an epicycle 
 would have represented the second inequality more simply than 
 his method did. 
 
SEQUEL TO THE EPOCH OF H1PPARCHUS. 237 
 
 suspicion that the motions of the heavenly bodies 
 might be subject to many inequalities ; that when 
 one set of anomalies had been discovered and re- 
 duced to rule, another set might come into view ; 
 that the discovery of a rule was a step to the 
 discovery of deviations from the rule, which would 
 require to be expressed in other rules ; that in the 
 application of theory to observation, we find, not 
 only the stated phenomena, for which the theory 
 does account, but also residual phenomena, which 
 remain unaccounted for, and stand out beyond 
 the calculation; that thus nature is not simple 
 and regular, by conforming to the simplicity and 
 regularity of our hypotheses, but leads us forwards 
 to apparent complexity, and to an accumulation 
 of rules and relations. A fact like the Evection, 
 explained by an Hypothesis like Ptolemy's, tended 
 altogether to discourage any disposition to guess 
 at the laws of nature from mere ideal views, or 
 from a few phenomena. 
 
 2. The discovery of Evection had an import- 
 ance which did not come into view till long 
 afterwards, in being the first of a numerous series 
 of inequalities of the moon, which result from 
 the Disturbing Force of the sun. These inequal- 
 ities were successively discovered; and led finally 
 to the establishment of the law of universal gravi- 
 tation. The moon's first inequality arises from a 
 different cause; from the same cause as the 
 inequality of the sun's motion ; from the motion 
 
232 THE GREEK ASTRONOMY. 
 
 in an ellipse, so far as the central attraction is 
 undisturbed by any other. This first inequality 
 is called the Elliptic Inequality, or, more usually 
 the Equation of the Center (H). All the planets 
 have such inequalities, but the Evection is peculiar 
 to the moon. The discovery of other inequalities 
 of the moon's motion, the Variation and Annual 
 Equation, made an immediate sequel in the order 
 of the subject to the discoveries of Ptolemy, al- 
 though separated by a long interval of time ; for 
 these discoveries were only made by Tycho Brahe 
 in the sixteenth century. The imperfection of 
 astronomical instruments was the great cause of 
 this long delay. 
 
 3. The Epicyclical Hypothesis was found 
 capable of accommodating itself to such new dis- 
 coveries. These new inequalities could be repre- 
 sented by new combinations of eccentrics and 
 epicycles: all the real and imaginary discoveries 
 of astronomers, up to Copernicus, were actually 
 embodied in these hypotheses; Copernicus, as we 
 have said, did not reject such hypotheses; the 
 lunar inequalities which Tycho detected might 
 have been similarly exhibited ; and even Newton 34 
 represents the motion of the moon's apogee by 
 means of an epicycle. As a mode of expressing 
 the law of the irregularity, and of calculating 
 its results in particular cases, the epicyclical 
 theory was capable of continuing to render great 
 
 34 Principia , lib. iii. prop. xxxv. 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 233 
 
 service to astronomy, however extensive the pro- 
 gress of the science might be. It was, in fact, 
 as we have already said, the modern process of 
 representing the motion by means of a series of 
 circular functions. 
 
 4. But though the doctrine of eccentrics and 
 epicycles was thus admissible as an Hypothesis, 
 and convenient as a means of expressing the laws 
 of the heavenly motions, the successive occasions 
 on which it was called into use, gave no countenance 
 to it as a Theory ; that is, as a true view of the 
 nature of these motions, and their causes. By 
 the steps of the progress of this Hypothesis, it 
 became more and more complex, instead of be- 
 coming more simple, which, as we shall see, was 
 the course of the true Theory. The notions con- 
 cerning the position and connexion of the heavenly 
 bodies, which were suggested by one set of phe- 
 nomena, were not confirmed by the indications of 
 another set of phenomena; for instance, those 
 relations of the epicycles which were adopted to 
 account for the Motions of the heavenly bodies, were 
 not found to fall in with the consequences of their 
 apparent Diameters and Parallaxes. In reality, as 
 we have said, if the relative distances of the sun 
 and moon at different times could have been accu- 
 rately determined, the Theory of Epicycles must 
 have been forthwith overturned. The insecurity of 
 such measurements alone maintained the theory to 
 later times (i). 
 
234 THE GREEK ASTRONOMY. 
 
 Sect. 7. Conclusion of the History of Greek 
 Astronomy. 
 
 I MIGHT now proceed to give an account of 
 Ptolemy's other great step, the determination of 
 the Planetary Orbits ; but as this, though in itself 
 very curious, would not illustrate any point beyond 
 those already noticed, I shall refer to it very 
 briefly. The planets all move in ellipses about 
 the sun, as the moon moves about the earth ; 
 and as the sun apparently moves about the earth. 
 They will therefore each have an Elliptic Inequality 
 or Equation of the center, for the same reason 
 that the sun and moon have such inequalities. 
 And this inequality may be represented, in the 
 cases of the planets, just as in the other two, by 
 means of an eccentric ; the epicycle, it will be re- 
 collected, had already been used in order to repre- 
 sent the more obvious changes of the planetary 
 motions. To determine the amount of the Eccen- 
 tricities and the places of the Apogees of the 
 planetary orbits, was the task which Ptolemy un- 
 dertook; Hipparchus, as we have seen, having 
 been destitute of the observations which such 
 a process required. The determination of the 
 Eccentricities in these cases involved some pecu- 
 liarities which might not at first sight occur to the 
 reader. The elliptical motion of the planets takes 
 place about the sun ; but Ptolemy considered their 
 movements as altogether independent of the sun, 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 235 
 
 and referred them to the earth alone; and thus 
 the apparent eccentricities which he had to account 
 for, were the compound result of the Eccentricity 
 of the Earth's orbit, and of the proper Eccentricity 
 of the orbit of the Planet. He explained this 
 result by the received mechanism of an eccentric 
 Deferent, carrying an Epicycle; but the motion 
 in the Deferent is uniform, not about the center 
 of the circle, but about another point, the Equant. 
 Without going further into detail, it may be 
 sufficient to state that, by a combination of 
 Eccentrics and Epicycles, he did account for the 
 leading features of these motions; and by using 
 his own observations, compared with more ancient 
 ones, (for instance, those of Timocharis for Venus,) 
 he was able to determine the Dimensions and 
 Positions of the Orbits (j). 
 
 I shall here close my account of the astrono- 
 mical progress of the Greek School. My purpose 
 is only to illustrate the principles on which the 
 progress of science depends, and therefore I have 
 not at all pretended to touch upon every part 
 of the subject! Some portions of the ancient the- 
 ories, as for instance, the mode of accounting for 
 the motions of the moon and planets in latitude, 
 are sufficiently analogous to what has been ex- 
 plained, not to require any more especial notice. 
 Other parts of the Greek astronomical knowledge, 
 as, for instance, their acquaintance with refraction, 
 did not assume any clear or definite form, and can 
 
236 THE GREEK ASTRONOMY. 
 
 only be considered as the prelude to modern 
 discoveries on the same subject. And before we 
 can with propriety pass on to these, there is a 
 long and remarkable, though unproductive inter- 
 val, of which some account must be given. 
 
 Sect. 8. Arabian Astronomy. 
 
 THE interval to which I have just alluded may be 
 considered as extending from Ptolemy to Coper- 
 nicus; we have no advance in Greek astronomy 
 after the former; no signs of a revival of the 
 power of discovery till the latter. During this 
 interval of 1350 years 35 , the principal cultivators 
 of astronomy were the Arabians, who adopted this 
 science from the Greeks whom they conquered, 
 and from whom the conquerors of western Europe 
 again received back their treasure, when the love 
 of science and the capacity for it had been 
 awakened in their minds. In the intervening time, 
 the precious deposit had undergone little change. 
 The Arab astronomer had been the scrupulous 
 but unprofitable servant, who kept his talent 
 without apparent danger of loss, but also without 
 prospect of increase. There is little in Arabic 
 literature which bears upon the progress of astro- 
 nomy; but as the little that there' is must be 
 considered as a sequel to the Greek science, I shall 
 
 35 Ptolemy died about A. D. 150. Copernicus was living A. D. 
 1500 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 237 
 
 notice one or two points before I treat of the 
 stationary period in general. 
 
 When the sceptre of western Asia had passed 
 into the hands of the Abasside caliphs 36 , Bagdad, 
 " the city of peace," rose to splendour and refine- 
 ment, and became the metropolis of science under 
 the successors of Almansor the Victorious, as Alex- 
 andria had been under the successors of Alexander 
 the Great. Astronomy attracted peculiarly the 
 favour of the powerful as well as the learned ; and 
 almost all the culture which was bestowed upon 
 the science, appears to have had its source in the 
 patronage, often also in the personal studies, of 
 Saracen princes. Under such encouragement, much 
 was done, in those scientific labours which money 
 and rank can command. Translations of Greek 
 works were made, large instruments were erected, 
 observers were maintained; and accordingly as 
 observation showed the defects and imperfection 
 of the extant tables of the celestial motions, new 
 ones were constructed. Thus under Almansor, the 
 Grecian works of science were collected from all 
 quarters, and many of them translated into Arabic 37 . 
 The translation of the "Megiste Syntaxis" of Pto- 
 lemy, which thus became the Almagest, is ascribed 
 to Isaac ben Homain in this reign. 
 
 The greatest of the Arabian astronomers comes 
 half a century later. This is Albategnius, as he 
 is commonly called; or more exactly, Muhammed 
 46 Gibbon, x. 31 37 Id. x. 36. 
 
238 THE GREEK ASTRONOMY. 
 
 ben Geber Albatani, the last appellation indicat- 
 ing that he was born at Batan, a city of Mesopo- 
 tamia 38 . He was a Syrian prince, whose residence 
 was at Aracte or Racha in Mesopotamia ; a part 
 of his observations were made at Antioch. His 
 work still remains to us in Latin. " After having 
 read," he says, "the Syntaxis of Ptolemy, and 
 learnt the methods of calculation employed by the 
 Greeks, his observations led him to conceive that 
 some improvements might be made in their re- 
 sults. He found it necessary to add to Ptolemy's 
 observations, as Ptolemy had added to those of 
 Abrachis" (Hipparchus). He then published Tables 
 of the motions of the sun, moon, and planets, 
 which long maintained a high reputation. 
 
 These, however, did not prevent the publication 
 of others. Under the Caliph Hakem (about A.D. 
 1000,) Ebon lounis published Tables of the Sun, 
 Moon, and Planets, which were hence called the 
 Hakemite Tables. Not long after, Arzachel of 
 Toledo published the Tdetan Tables. In the 13th 
 century, Nasir Eddin published Tables of the Stars, 
 dedicated to Ilchan, a Tartar prince, and hence 
 termed the Mckanic Tables. Two centuries later, 
 Ulugh Beigh, the grandson of Tamerlane, and prince 
 of the countries beyond the Oxus, was a zealous 
 practical astronomer; and his Tables, which were 
 published in Europe by Hyde in 1665, are referred 
 to as important authority by modern astronomers. 
 
 38 Del., Astronomic du Moyen Age, 4. 
 
SEQEUL TO THE EPOCH OF HIPPARCHUS. 239 
 
 The series of Astronomical Tables which we have 
 thus noticed, in which, however, many are omitted, 
 leads us to the Alphonsine tables, which were put 
 forth in 1488, and in succeeding years, under the 
 auspices of Alphonso, king of Castile ; and thus 
 brings us to the verge of modern astronomy. 
 
 For all these Tables, the Ptolemaic hypotheses 
 were employed; and, for the most part, without 
 alteration. The Arabs sometimes felt the extreme 
 complexity and difficulty of the doctrine which 
 they studied ; but their minds did not possess that 
 kind of invention and energy by which the phi- 
 losophers of Europe, at a later period, won their 
 way into a simpler and better system. 
 
 Thus Alpetragius states, in the outset of his 
 "Planetarum Theorica," that he was at first asto- 
 nished and stupified with this complexity, but that 
 afterwards " God was pleased to open to him the 
 occult secret in the theory of his orbs, and to 
 make known to him the truth of their essence, and 
 the rectitude of the quality of their motion." His 
 system consists, according to Delambre 39 , in attri- 
 buting to the planets a spiral motion from east 
 to west, an idea already refuted by Ptolemy. Geber 
 of Seville criticizes Ptolemy very severely 40 , but 
 without introducing any essential alteration into 
 his system. The Arabian observations are in many 
 cases valuable ; both because they were made with 
 more skill and with better instruments than those 
 
 39 Delambre, M. A. p. 7- 40 M. A. p. 180, &c. 
 
240 THE GREEK ASTRONOMY. 
 
 of the Greeks ; and also because they illustrate 
 the permanence or variability of important ele- 
 ments, such as the obliquity of the ecliptic and the 
 inclination of the moon's orbit. 
 
 We must, however, notice one or two peculiar 
 Arabian doctrines. The most important of these 
 is the discovery of the Motion of the Sun's Apogee 
 by Albategnius. He found the Apogee to be in 
 longitude 82 degrees; Ptolemy had placed it in 
 longitude 65 degrees. The difference of 17 degrees 
 was beyond all limit of probable errour of calcu- 
 lation, though the process is not capable of great 
 precision ; and the inference of the Motion of the 
 Apogee was so obvious, that we cannot agree with 
 Delambre, in doubting or extenuating the claim 
 of Albategnius to this discovery, on the ground 
 of his not having expressly stated it. 
 
 In detecting this motion, the Arabian astrono- 
 mers reasoned rightly from facts well observed ; 
 they were not always so fortunate. Arzachel, in 
 the llth century, found the apogee of the sun to 
 be less advanced than Albategnius had found it, 
 by some degrees; he inferred that it had receded in 
 the intermediate time ; but we now know, from an 
 acquaintance with its real rate of moving, that the 
 true inference would have been, that Albategnius, 
 whose method was less trustworthy than that of 
 Arzachel, had made an errour to the amount of the 
 difference thus arising. A curious, but utterly false 
 hypothesis was founded on observations thus erro- 
 
SEQUEL TO THE EPOCH OF H1PPARCHUS. 241 
 
 neously appreciated; namely, the Trepidation of 
 the fixed stars. Arzachel conceived that a uniform 
 Precession of the equinoctial points would not ac- 
 count for the apparent changes of position of the 
 stars, and that for this purpose, it was necessary 
 to conceive two circles of about 8 degrees radius 
 described round the equinoctial points of the im- 
 moveable sphere, and to suppose the first points of 
 Aries and Libra to describe the circumferences of 
 these circles in about 800 years. This would pro- 
 duce, at one time a progression, and at another 
 a regression, of the apparent equinoxes, and would 
 moreover change the latitudes of the stars. Such 
 a motion is entirely visionary ; but the doctrine 
 made a sect among astronomers, and was adopted 
 in the first edition of the Alphonsine Tables, though 
 afterwards rejected. 
 
 An important exception to the general unpro- 
 gressive character of Arabian science has been 
 pointed out recently by M. Sedillot 11 . It appears 
 that Mohammed- Aboul Wefa-al-Bouzdjani, an Ara- 
 bian astronomer of the tenth century, who resided 
 at Cairo, and observed at Bagdad in 975, dis- 
 covered a third inequality of the moon, in addition 
 to the two expounded by Ptolemy, the Equation 
 of the Center, and the Evection. This third inequa- 
 lity, the Variation, is usually supposed to have 
 been discovered by Tycho Brahe, six centuries 
 
 41 Sedillot, Nouvelles Rech. sur 1'Hist. de 1'Astron. chez les 
 Arabes. Nouvean Journal Asialif/ue. 1836. 
 
 VOL. I. R 
 
242 THE GREEK ASTRONOMY. 
 
 later. It is an inequality of the moon's motion, 
 in virtue of which she moves quickest when she 
 is at new or full, and slowest at the first and 
 third quarter ; in consequence of this, from the 
 first quarter to the full, she is behind her mean 
 place ; at the full, she does not differ from her 
 mean place ; from the full to the third quarter, 
 she is before her true place ; and so on ; and the 
 greatest eifect of the inequality is in the octants, 
 or points half-way between the four quarters. In 
 an Almagest of Aboul Wefa, a part of which exists 
 in the Royal Library at Paris, after describing the 
 two inequalities of the moon, he has a Section ix., 
 " Of the Third Anomaly of the Moon called Mu- 
 hazal or Prosneusis." He there says, that taking 
 cases when the moon was in apogee or perigee, 
 and when, consequently, the effect of the two first 
 inequalities vanishes, he found, by observation of 
 the moon, when she was nearly in trine and in 
 sextile with the sun, that she was a degree and 
 a quarter from her calculated place. " And hence," 
 he adds, "I perceived that this anomaly exists 
 independently of the two first : and this can only 
 take place by a declination of the diameter of 
 the epicycle with respect to the center of the 
 zodiac." 
 
 We may remark that we have here this in- 
 equality of the moon made out in a really philoso- 
 phical manner; a residual quantity in the moon's 
 longitude being detected by observation, and the 
 
SEQUEL TO THE EPOCH OF HIPPARCHUS. 243 
 
 cases in which it occurs selected and grouped by 
 an inductive effort of the mind. The advance is 
 not great; for Aboul Wefa appears only to have 
 detected the existence, and not to have fixed the 
 law or the exact quantity of the inequality ; but 
 still it places the scientific capacity of the Arabs 
 in a more favourable point of view than any cir- 
 cumstance with which we were previously ac- 
 quainted. 
 
 But this discovery of Aboul Wefa appears to 
 have excited no notice among his contemporaries 
 and followers ; at least it had been long quite for- 
 gotten when Tycho Brahe rediscovered the same 
 lunar inequality. We can hardly help looking upon 
 this circumstance as an evidence of a servility 
 of intellect belonging to the Arabian period. The 
 learned Arabians were so little in the habit of 
 considering science as progressive, and looking with 
 pride and confidence at examples of its progress, 
 that they had not the courage to believe in a 
 discovery which they themselves had made, and 
 were dragged back by the chain of authority, even 
 when they had advanced beyond their Greek mas- 
 ters. 
 
 As the Arabians took the whole of their theory 
 (with such slight exceptions as we have been 
 noticing) from the Greeks, they took from them 
 also the mathematical processes by which the con- 
 sequences of the theory were obtained. Arithmetic 
 and Trigonometry, two main branches of these 
 
 R2 
 
244 THE GREEK ASTRONOMY. 
 
 processes, received considerable improvements at 
 their hands. In the former, especially, they ren- 
 dered a service to the world which it is difficult 
 to estimate too highly, in abolishing the cumbrous 
 Sexagesimal Arithmetic of the Greeks, and intro- 
 ducing the notation by means of the digits 1, 2, 3, 
 4, 5, 6, 7, 8, 9, 0, which we now employ 42 . These 
 numerals appear to be of Indian origin, as is 
 acknowledged by the Arabs themselves ; and thus 
 form no exception to the sterility of the Arabian 
 genius as to great scientific inventions. Another 
 improvement, of a subordinate kind, but of great 
 utility, was Arabian, being made by Albategnius. 
 He introduced into calculation the sine, or half- 
 chord of the double arc, instead of the chord of 
 the arc itself, which had been employed by the 
 Greek astronomers. There have been various con- 
 jectures concerning the origin of the word sine; 
 the most probable appears to be that sinus is the 
 Latin translation of the Arabic word gib, which 
 signifies a fold, the two halves of the chord being 
 conceived to be folded together. 
 
 The great obligation which Science owes to the 
 Arabians, is to have preserved it during a period 
 of darkness and desolation, so that Europe might 
 receive it back again when the evil days were 
 past. We shall see hereafter how differently the 
 European intellect dealt with this hereditary trea- 
 sure when once recovered. 
 
 42 Mont. i. 376. 
 
SEQUEL TO THE EPOCH OF H1PPARCHUS. 245 
 
 Before quitting the subject, we may observe 
 that Astronomy brought back, from her sojourn 
 among the Arabs, a few terms which may still be 
 perceived in her phraseology. Such are the zenith, 
 and the opposite imaginary point, the nadir; 
 the circles of the sphere termed almacantars and 
 azimuth circles. The alidad of an instrument is 
 its index, which possesses an angular motion. Some 
 of the stars still retain their Arabic names; Aide- 
 bar an, Rig el, Fomalhaut; many others were known 
 by such appellations a little while ago. Perhaps 
 the word almanac is the most familiar vestige of 
 the Arabian period of astronomy 43 . 
 
 13 It is foreign to my purpose to note any efforts of the intel- 
 lectual faculties among other nations, which may have taken 
 place independently of the great system of progressive European 
 culture, from which all our existing science is derived. Other- 
 wise I might speak of the astronomy of some of the Orientals, 
 for example, the Chinese, who are said, by Montucla (i. 465) 
 to have discovered the first equation of the moon, and the proper 
 motion of the fixed stars (the Precession), in the third century of 
 our era. The Greeks had made these discoveries 500 years 
 earlier. 
 
246 
 
 NOTES TO BOOK HI. 
 
 (G.) p. 230. I WILL insert here the explanation which 
 my German translator, the late distinguished astronomer 
 Littrow, has given of this point. The Rule of this In- 
 equality, the Evection, may be most simply expressed 
 thus. If a denote the excess of the Moon's Longitude 
 over the Sun's, and b the Anomaly of the moon reckoned 
 from her Perigee, the Evection is equal to l.3.sin (2a -b). 
 At New and Full Moon, a is or 180, and thus the 
 Evection is - l.3.sin&. At both quarters, or dicho- 
 tomies, a is 90 or 270, and consequently the Evection is 
 + l.3.sin b. The Moon's Elliptical Equation of the 
 center is at all points of her orbit equal to 6. 3 . sin b. 
 The Greek Astronomers before Ptolemy observed the 
 moon only at the time of eclipses ; and hence they neces- 
 sarily found for the sum of these two greatest inequalities 
 of the moon's motion the quantity 6. 3 . sin 5 - l.3.sin&, 
 or 5. sin b : and as they took this for the moon's equation 
 of the center, which depends upon the excentricity of the 
 moon's orbit, we obtain from this too small equation of 
 the center, an excentricity also smaller than the truth. 
 Ptolemy, who first observed the moon in her quarters, 
 found for the sum of those Inequalities at those points the 
 quantity 6 . 3 . sin b + 1 . 3 . sin b, or 7 . 6 . sin b ; and 
 thus made the excentricity of the moon as much too 
 great at the quarters as the observers of eclipses had made 
 it too small. He hence concluded that the excentricity of 
 the Moon's orbit is variable, which is not the case. 
 
NOTES TO BOOK III. 
 
 (H.) p. 232. The Equation of the Center is the 
 difference between the place of the Planet in its elliptical 
 orbit, and that place which a Planet would have, which 
 revolved uniformly round the Sun as a center in a circular 
 orbit in the same time. An imaginary Planet moving in 
 the manner last described, is called the mean Planet, 
 while the actual Planet which moves in the ellipse is 
 called the true Planet. The Longitude of the mean 
 Planet at a given time is easily found, because its motion 
 is uniform. By adding to it the Equation of the Center, 
 we find the Longitude of the true Planet, and thus, its 
 place in its orbit. Littrow's Note. 
 
 I may add that the word Equation, used in such cases, 
 denotes in general a quantity which must be added to or 
 subtracted from a mean quantity, to make it equal to the 
 true quantity : or rather, a quantity which must be added 
 to or subtracted from a variably increasing quantity, to 
 make it increase equably. 
 
 (i.) p. 233. The alteration of the apparent diameter 
 of the moon is so great that it cannot escape us, even 
 with very moderate instruments. This apparent diameter 
 contains, when the moon is nearest the earth, 2010 
 seconds, when she is farthest off, 1762 seconds; that is, 
 248 seconds; or 4 minutes 8 seconds, less than in the 
 former case. [The two quantities are in the proportion of 
 8 to 7, nearly]. Littrow's Note. 
 
 (j.) p. 235. Ptolemy determined the Radius and the 
 Periodic Time of his two circles for each Planet in the 
 following manner : For the inferior Planets, that is, 
 Mercury and Venus, he took the Radius of the Deferent 
 equal to the Radius of the Earth's orbit, and the Radius 
 of the Epicycle equal to that of the Planet's orbit. For 
 
248 NOTES TO BOOK III. 
 
 these Planets, according to his assumption, the Periodic 
 Time of the Planet in its Epicycle was to the Periodic 
 Time of the Epicyclical Center on the Deferent, as the 
 synodical Revolution of the Planet to the tropical Revo- 
 lution of the Earth above the Sun. For the three supe- 
 rior Planets, Mars, Jupiter, and Saturn, the Radius of 
 the Deferent was equal to the Radius of the Planet's 
 orbit, and the Radius of the Epicycle was equal to the 
 Radius of the Earth's orbit ; the Periodic Time of the 
 Planet in its Epicycle was to the Periodic Time of the 
 Epicyclical Center on the Deferent, as the synodical 
 Revolution of the Planet to the tropical Revolution of the 
 same Planet. 
 
 Ptolemy might obviously have made the geometrical 
 motions of all the Planets correspond with the observa- 
 tions by one of these two modes of construction ; but he 
 appears to have adopted this double form of the theory, 
 in order that in the inferior, as well as in the superior 
 Planets, he might give the smaller of the two Radii to 
 the Epicycle : that is, in order that he might make the 
 smaller circle move round the larger, not vice versa. 
 Littrovfs Note. 
 
BOOK IV. 
 
 HISTORY 
 
 OF 
 
 PHYSICAL SCIENCE IN THE MIDDLE AGES; 
 
 OR, 
 
 VIEW OF THE STATIONARY PERIOD OF 
 INDUCTIVE SCIENCE. 
 
In vain, in vain! the all-composing hour 
 Resistless falls , 
 
 As one by one, at dread Medea's strain, 
 
 The sickening stars fade off th' ethereal plain ; 
 
 As Argus' eyes, by Hermes' wand opprest, 
 
 Closed one by one to everlasting rest; 
 
 Thus at her felt approach and secret might, 
 
 Art after art goes out, and all is night. 
 
 See skulking Truth to her old cavern fled, 
 
 Mountains of casuistiy heaped on her head; 
 
 Philosophy, that reached the heavens before, 
 
 Shrinks to her hidden cause, and is no more. 
 
 Physic of Metaphysic begs defence, 
 
 And Metaphysic calls for aid to Sense: 
 
 See Mystery to Mathematics fly! 
 
 In vain! they gaze, turn giddy, rave, and die. 
 
 Dunciad, B. iv. 
 
INTRODUCTION. 
 
 WE have now to consider more especially a 
 long and barren period, which intervened 
 between the scientific activity of ancient Greece, 
 and that of modern Europe ; and which we may, 
 therefore, call the Stationary Period of Science. It 
 would be to no purpose to enumerate the vari- 
 ous forms in which, during these times, men repro- 
 duced the discoveries of the inventive ages : or to 
 trace in them the small successes of Art, void 
 of any principle of genuine Philosophy. Our ob- 
 ject requires rather that we should point out the 
 general and distinguishing features of the intellect 
 and habits of those times. We must endeavour 
 to delineate the character of the Stationary Period, 
 and, as far as possible, to analyze its defects and 
 errours ; and thus obtain some knowledge of the 
 causes of its barrenness and darkness. 
 
 A^e have already stated, that real scientific pro- 
 gress requires distinct general Ideas, applied to 
 many special and certain Facts. In the period of 
 which we now have to speak, men's Ideas were ob- 
 scured, their disposition to bring their general views 
 into accordance with Facts was enfeebled. They 
 were thus led to employ themselves unprofitably, 
 among indistinct and unreal notions. And the evil 
 
252 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 of these tendencies was further inflamed, by moral 
 peculiarities in the character of those times ; by 
 an abjectness of thought on the one hand, which 
 could not help looking towards some intellectual 
 superior, and by an impatience of dissent on the 
 other. To this must be added an enthusiastic tem- 
 per, which, when introduced into speculation, tends 
 to subject the mind's operations to ideas altogether 
 distorted and delusive. 
 
 These characteristics of the stationary period, 
 its obscurity of thought, its servility, its intolerant 
 disposition, and its enthusiastic temper, will be 
 treated of in the four following chapters, on the 
 Indistinctness of Ideas, the Commentatorial Spirit, 
 the Dogmatism, and the Mysticism of the Middle 
 Ages. 
 
253 
 
 CHAPTER I. 
 
 ON THE INDISTINCTNESS OF IDEAS OF THE 
 MIDDLE AGES. 
 
 THAT firm and entire possession of certain clear 
 and distinct general ideas which is necessary to 
 sound science^ was the character of the minds of 
 those among the ancients who created the several 
 sciences which arose among them. It was indis- 
 pensable, that such inventors should have a 
 luminous and steadfast apprehension of certain 
 general relations, such as those of space and num- 
 ber, order and cause ; and should be able to apply 
 these notions with perfect readiness and precision 
 to special facts and cases. It is necessary that 
 such scientific notions should be more definite 
 and precise than those which common language 
 conveys; and in this state of unusual clearness, 
 they must be so familiar to the philosopher, that 
 they are the language in which he thinks. The 
 discoverer is thus led to doctrines which other 
 men adopt and follow out, in proportion as they 
 seize the fundamental ideas, and become acquainted 
 with the leading facts. Thus Hipparchus, con- 
 ceiving clearly the motions and combinations of 
 motion which enter into his theory, saw that the 
 
254 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 relative lengths of the seasons were sufficient data 
 for determining the form of the sun's orbit; thus 
 Archimedes, possessing a steady notion of mechani- 
 cal pressure, was able, not only to deduce the pro- 
 perties of the lever and of the center of gravity, 
 but also to see the truth of those principles respect- 
 ing the distribution of pressure in fluids, on which 
 the science of hydrostatics depends. 
 
 With the progress of such distinct ideas, the in- 
 ductive sciences rise and flourish ; with the decay 
 and loss of such distinct ideas, these sciences become 
 stationary, languid, and retrograde. When men 
 merely repeat the terms of science, without attaching 
 to them any clear conceptions ; when their appre- 
 hensions become vague and dim; when they assent 
 to scientific doctrines as a matter of tradition, rather 
 than of conviction, on trust rather than on sight; 
 when science is considered as a collection of 
 opinions, rather than a record of laws by which 
 the universe is really governed ; it must inevitably 
 happen, that men will lose their hold on the know- 
 ledge which the great discoverers who preceded them 
 have brought to light. They are not able to push 
 forwards the truths on which they lay so feeble 
 and irresolute a hand ; probably they cannot even 
 prevent their sliding back towards the obscurity 
 from which they had been drawn, or from being 
 lost altogether. Such indistinctness and vacillation 
 of thought appear to have prevailed in the station- 
 ary period, and to be, in fact, intimately connected 
 
INDISTINCTNESS OF IDEAS. 255 
 
 with its stationary character. I shall point out 
 some indications of the intellectual peculiarity of 
 which I speak. 
 
 1 . Collections of Opinions. The fact, that mere 
 Collections of the opinions of physical philosophers 
 came to hold a prominent place in literature, already 
 indicated a tendency to an indistinct and wandering 
 apprehension of such opinions. I speak of such works 
 as Plutarch's five Books " on the Opinions of Philo- 
 sophers," or the physical opinions which Diogenes 
 Laertius gives in his "Lives of the Philosophers." 
 At an earlier period still, books of this kind appear ; 
 as for instance, a large portion of Pliny's Natural 
 History, a work which has very appropriately been 
 called the Encyclopaedia of Antiquity ; even Aris- 
 totle himself is much in the habit of enumerating 
 the opinions of those who had preceded him. To 
 present such statements as an important part of 
 physical philosophy, shows an erroneous and loose 
 apprehension of its nature. For the only proof 
 of which its doctrines admit, is the possibility of 
 applying the general theory to each particular 
 case : the authority of great men, which in moral 
 and practical matters may or must have its weight, 
 is here of no force; and the technical precision 
 of ideas which the terms of a sound physical theory 
 usually demand, renders a mere statement of the 
 doctrines very imperfectly intelligible to readers 
 familiar with common notions only. To dwell 
 upon such collections of opinions, therefore, both 
 
256 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 implies, and produces, in writers and readers, an 
 obscure and inadequate apprehension of the full 
 meaning of the doctrines thus collected ; supposing 
 there be among them any which really possess 
 such a clearness, solidity, and reality, as to make 
 them important in the history of science. Such 
 diversities of opinion convey no truth; such a 
 multiplicity of statements of what has been said, 
 in no degree teaches us what is ; such accumula- 
 tions of indistinct notions, however vast and varied, 
 do not make up one distinct idea. On the contrary, 
 the habit of dwelling upon the verbal expressions 
 of the views of other persons, and of being content 
 with such an apprehension of doctrines as a tran- 
 sient notice can give us, is fatal to firm and clear 
 thought : it indicates wavering and feeble concep- 
 tions, which are inconsistent with sound physical 
 speculation. 
 
 We may, therefore, consider the prevalence of 
 Collections of the kind just referred to, as indicating 
 a deficiency of philosophical talent in the ages now 
 under review. As evidence of the same character, 
 we may add the long train of publishers of Abstracts, 
 Epitomes, Bibliographical Notices, and similar wri- 
 ters. All such writers are worthless for all purposes 
 of science, and their labours may be considered as 
 dead works; they have in them no principle of 
 philosophical vitality; they draw their origin and 
 nutriment from the death of true physical know- 
 ledge ; and resemble the swarms of insects that are 
 
INDISTINCTNESS OF IDEAS. 
 
 born from the perishing carcass of some nobler 
 animal. 
 
 2. Indistinctness of Ideas in Mechanics. But 
 the indistinctness of thought which is so fatal a 
 feature in the intellect of the stationary period, 
 may be traced more directly in the works, even of 
 the best authors, of those times. We find that they 
 did not retain steadily the ideas on which the 
 scientific success of the previous period had de- 
 pended. For instance, it is a remarkable circum- 
 stance in the history of the science of Mechanics, 
 that it did not make any advance from the time of 
 Archimedes to that of Stevinus and Galileo. Archi- 
 medes had established the doctrine of the lever; 
 several persons tried, in the intermediate time, to 
 prove the property of the inclined plane, and none 
 of them succeeded. But let us look to the attempts ; 
 for example, that of Pappus, in the eighth Book of 
 his Mathematical Collections, and we may see the 
 reason of the failure. His Problem shows, in the 
 very terms in which it is propounded, the want of 
 a clear apprehension of the subject. " Having given 
 the power which will draw a given weight along 
 a horizontal plane, to find the additional power 
 which will draw the same weight along a given 
 inclined plane." This is proposed without previ- 
 ously defining how Powers, producing such effects, 
 are to be measured ; and as if the speed with 
 which the body were drawn, and the nature of 
 the surface of the plane, were of no consequence. 
 VOL. i. S 
 
258 PHYSICAL SCIENCE IN THE MIDDLE AGES 
 
 The proper elementary Problem is, To find the 
 force which will support a body on a smooth inclined 
 plane; and no doubt the solution of Pappus has 
 more reference to this problem than to his own. 
 His reasoning is, however, totally at variance with 
 mechanical ideas on any view of the problem. He 
 supposes the weight to be formed into a sphere ; 
 and this sphere being placed in contact with the 
 inclined plane, he assumes that the effect will be 
 the same as if the weight were supported on a 
 horizontal lever, the fulcrum being the point of 
 contact of the sphere with the plane, and the power 
 acting at the circumference of the sphere. Such 
 an assumption implies an entire absence of those 
 distinct ideas of force and mechanical pressure, on 
 which our perception of the identity or difference of 
 different modes of action must depend; of those 
 ideas by the help of which Archimedes had been able 
 to demonstrate the properties of the lever, and Ste- 
 vinus afterwards discovered the true solution of the 
 problem of the inclined plane. The motive to Pap- 
 pus's assumption was probably no more than this ; 
 he perceived that the additional power, which he 
 thus obtained, vanished when the plane became 
 horizontal, and increased as the inclination became 
 greater. Thus his views were vague; he had no 
 clear conception of mechanical action, and he tried 
 a geometrical conjecture. This is not the way 
 to real knowledge. 
 
 Pappus (who lived about A.D. 400) was one 
 
INDISTINCTNESS OF IDEAS. 259 
 
 of the best mathematicians of the Alexandrian 
 school; and, on subjects where his ideas were so 
 indistinct, it is not likely that any much clearer 
 were to be found in the minds of his contempo- 
 raries. Accordingly, on all subjects of speculative 
 mechanics, there appears to have been an entire 
 confusion and obscurity of thought till modern 
 times. Men's minds were busy in endeavouring 
 to systematize the distinctions and subtleties of 
 the Aristotelian school, concerning Motion and 
 Power ; and, being, thus employed among doctrines 
 in which there was involved no definite meaning 
 capable of real exemplification, they, of course, 
 could not acquire sound physical knowledge. We 
 have already seen that the physical opinions of 
 Aristotle, even as they came from him, had no 
 proper scientific precision. His followers, in their 
 endeavours to perfect and develop his statements, 
 never attempted to introduce clearer ideas than 
 those of their master ; and as they never referred, 
 in any steady manner, to facts, the vagueness of 
 their notions was not corrected by any collision 
 with observation. The physical doctrines which 
 they extracted from Aristotle were, in the course 
 of time, built up into a regular system ; and though 
 these doctrines could not be followed into a prac- 
 tical application without introducing distinctions 
 and changes, such as deprived the terms of all 
 steady signification, the dogmas continued to be 
 repeated, till the world was persuaded that they 
 
 S2 
 
260 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 were self-evident ; and when, at a later period, ex- 
 perimental philosophers, such as Galileo and Boyle, 
 ventured to contradict these current maxims, their 
 new principles sounded in men's ears as strange 
 as they now sound familiar. Thus Boyle promul- 
 gated his opinions on the mechanics of fluids, as 
 " Hydrostatical Paradoxes, proved and illustrated 
 by experiments." And the opinions which he there 
 opposes, are those which the Aristotelian philo- 
 sophers habitually propounded as certain and indis- 
 putable ; such, for instance, as that " in fluids the 
 upper parts do not gravitate on the lower;" that 
 "a lighter fluid will not gravitate on a heavier;" 
 that " levity is a positive quality of bodies as well 
 as gravity." So long as these assertions were left 
 uncontested and untried, men heard and repeated 
 them, without perceiving the incongruities which 
 they involved : and thus they long evaded refu- 
 tation, amid the vague notions and undoubting 
 habits of the stationary period. But when the 
 controversies of Galileo's time had made men think 
 with more acuteness and steadiness, it was dis- 
 covered that many of these doctrines were incon- 
 sistent with themselves, as well as with experiment. 
 We have an example of the confusion of thought 
 to which the Aristotelians were liable, in their 
 doctrine concerning falling bodies. "Heavy bodies," 
 said they, " must fall quicker than light ones ; for 
 weight is the cause of their fall, and the weight 
 of the greater bodies is greater." They did not 
 
hN DISTINCTNESS OF IDEAS. 261 
 
 perceive that, if they considered the weight of the 
 body as a power acting to produce motion, they 
 must consider the body itself as offering a resist- 
 ance to motion ; and that the effect must depend 
 on the proportion of the power to the resistance ; 
 in short, they had no clear idea of accelerating 
 force. This defect runs through all their mecha- 
 nical speculations, and renders them entirely value- 
 less. 
 
 We may exemplify the same confusion of 
 thought on mechanical subjects in writers of a less 
 technical character. Thus, if men had any distinct 
 idea of mechanical action, they could not have 
 accepted for a moment the fable of the Echineis 
 or Remora, a little fish which was said to be able 
 to stop a large ship merely by sticking to it. 
 Lucan 1 refers to this legend in a poetical manner, 
 and notices this creature only in bringing together 
 a collection of monstrosities ; but Pliny relates the 
 tale gravely, and moralizes upon it after his man- 
 ner. " What," he cries 2 , " is more violent than 
 the sea and the winds? what, a greater work of 
 art than a ship ? Yet one little fish (the Echineis) 
 
 1 Lucan is describing one of the poetical compounds intro- 
 duced in incantations. 
 
 Hue quicquid fbetu genuit Natura sinistro 
 Miscetur: non spuma canum quibus unda timori est, 
 Viscera non lyncis, non durae nodus hyaenas 
 Defuit, et cervi pasti serpente medulla; 
 Non puppes retinens, Euro tendente rudentes 
 In mediis Echineis aquis, oculique draconum. 
 
 Etc. Pharsalia, iv. 670. 
 
 3 Plin. Hist. N. xxxii. 1. 
 
262 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 can hold back all these when they all strain the 
 same way. The winds may blow, the waves may 
 rage ; but this small creature controls their fury, 
 and stops a vessel, when chains and anchors would 
 not hold it : and this it does, not by hard labour, 
 but merely by adhering to it. Alas, for human 
 vanity ! when the turretted ships which man has 
 built, that he may fight from castle-walls, at sea 
 as well as at land, are held captive and motionless 
 by a fish a foot and a half long. Such a fish is 
 said to have stopt the admiral's ship at the bat- 
 tle of Actium, and compelled Antony to go into 
 another. Airtl in our own memory, one of these 
 animals held fast the ship of Caius, the emperor, 
 when he was sailing from Astura to Antium. The 
 stopping of this ship, when all the rest of the fleet 
 went on, caused surprize; but this did not last 
 long, for some of the men jumped into the water 
 to look for the fish, and found it sticking to the 
 rudder; they showed it to Caius, who was indig- 
 nant that this animal should interpose its prohi- 
 bition to his progress, when impelled by four 
 hundred rowers. It was like a slug; and had no 
 power, after it was taken into the ship." 
 
 A very little advance in the power of thinking 
 clearly on the force which is exerted in pulling, 
 would have enabled the Romans to see, that the 
 ship and its rowers must pull the adhering fish 
 by the hold the oars had upon the water; and 
 that, except the fish had a hold equally strong on 
 some external body, it could not resist this force, 
 
INDISTINCTNESS OF IDEAS. 
 
 3. Indistinctness of Ideas shown in Architec- 
 ture. Perhaps it may serve to illustrate still fur- 
 ther the extent to which, under the Roman empire, 
 men's notions of mechanical relations became faint, 
 wavered, and disappeared, if we observe the change 
 which took place in architecture. All architec- 
 ture, to possess genuine beauty, must be mecha- 
 nically consistent. The decorative members m ust 
 represent a structure which has in it a principal of 
 support and stability. Thus the Grecian colonnade 
 was a straight horizontal beam, resting on vertical 
 props; and the pediment imitated a frame like a 
 roof, where oppositely-inclined beams support each 
 other. These forms of building were, therefore, 
 proper models of art, because they implied sup- 
 porting forces. But to be content with colonnades 
 and pediments, which, though they imitated the 
 forms of the Grecian ones, were destitute of their 
 mechanical truth, belonged to the decline of art ; 
 and showed that men had lost the idea of force, 
 and retained only that of shape. Yet this was what 
 the architects of the empire did. Under their 
 hands, the pediment was severed at its vertex, and 
 divided into separate halves, so that it was no 
 longer a mechanical possibility. The entablature 
 no longer lay straight from pillar to pillar, but, 
 projecting over each column, turned back to the 
 wall, and adhered to it in the intervening space. 
 The splendid remains of Palmyra, Balbec, Petra, 
 exhibit endless examples of this kind of perverse 
 
264 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 inventiveness ; and show us, very instructively, how 
 the decay of art and of science alike accompany 
 this indistinctness of ideas which we are endea- 
 vouring to illustrate. 
 
 4. Indistinctness of Ideas in Astronomy. 
 Returning to the sciences, it may be supposed, at 
 first sight, that, with regard to astronomy, we have 
 not the same ground for charging the stationary 
 period with indistinctness of ideas on that subject, 
 since they were able to acquire and verify, and, 
 in some measure, to apply, the doctrines previously 
 established. And, undoubtedly, it must be con- 
 fessed that men's notions of the relations of space 
 and number are never very indistinct. It appears 
 to be impossible for these chains of elementary 
 perception ever to be much entangled. The later 
 Greeks, the Arabians, and the earliest modern 
 astronomers, must have conceived the hypotheses 
 of the Ptolemaic system with tolerable complete- 
 ness. And yet, we may assert, that, during the 
 stationary period, men did not possess the notions, 
 even of space and number, in that vivid and vigor- 
 ous manner which enables them to discover new 
 truths. If they had perceived distinctly that the 
 astronomical theorist had merely to do with rela- 
 tive motions, they must have been led to see the 
 possibility, at least, of the Copernican system ; as 
 the Greeks, at an earlier period, had already per- 
 ceived it. We find no trace of this. Indeed the 
 mode in which the Arabian mathematicians pre- 
 
INDISTINCTNESS OF IDEAS. 265 
 
 sent the solutions of their problems, does not indi- 
 cate that clear apprehension of the relations of 
 space, and that delight in the contemplation of 
 them, which the Greek geometrical speculations 
 imply. The Arabs are in the habit of giving con- 
 clusions without demonstrations, precepts without 
 the investigations by which they are obtained; as 
 if their main object were practical rather than 
 speculative, the calculation of results rather than 
 the exposition of theory. Delambre* has been ob- 
 liged to exercise great ingenuity, in order to dis- 
 cover the method by which Ibn lounis proved his 
 solution of certain difficult problems. 
 
 5. Indistinctness of Ideas shown by Skeptics. 
 The same unsteadiness of ideas which prevents 
 men from obtaining clear views, and steady and 
 just convictions, on special subjects, may lead them 
 to despair of or deny the possibility of acquiring 
 certainty at all, and may thus make them skeptics 
 with regard to all knowledge. Such skeptics are 
 themselves men of indistinct views, for they could 
 not otherwise avoid assenting to the demonstrated 
 truths of science; and, so far as they may be 
 taken as specimens of their contemporaries, they 
 prove that indistinct ideas prevail in the age in 
 which they appear. In the stationary period, more- 
 over, the indefinite speculations and unprofitable 
 subtleties of the schools might further impel a 
 man of bold and acute mind to this universal skep- 
 3 Dfclamb. M. A. p. 125-8. 
 
266 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 ticism, because they offered nothing which could 
 fix or satisfy him. And thus the skeptical spirit 
 may deserve our notice as indicative of the defects 
 of a system of doctrine too feeble in demonstra- 
 tion to control such resistance. 
 
 The most remarkable of these philosophical 
 skeptics is Sextus Empiricus; so called, from his 
 belonging to that medical sect which was termed 
 the empirical, in contradistinction to the rational 
 and methodical sects. His works contain a series 
 of treatises, directed against all the divisions of 
 the science of his time. He has chapters against 
 the Geometers, against the Arithmeticians, against 
 the Astrologers, against the Musicians, as well as 
 against Grammarians, Rhetoricians and Logicians ; 
 and, in short, as a modern writer has said, his skep- 
 ticism is employed as a sort of frame-work which 
 embraces an encyclopedical view of human know- 
 ledge. It must be stated, however, that his objec- 
 tions are rather to the metaphysical grounds, than to 
 the details of the sciences; he rather denies the 
 possibility of speculative truth in general, than the 
 experimental truths which had been then obtained. 
 Thus his objections to geometry and arithmetic 
 are founded on abstract cavils concerning the na- 
 ture of points, letters, unities, &c. And when he 
 comes to speak against astrology, he says, " I am 
 not going to consider that perfect science which 
 rests upon geometry and arithmetic; for I have 
 already shown the weakness of those sciences ; nor 
 
INDISTINCTNESS OF IDEAS. 267 
 
 that faculty of prediction (of the motions of the 
 heavens) which belongs to the pupils of Eudoxus, 
 and Hipparchus, and the rest, which some call 
 Astronomy; for that is an observation of pheno- 
 mena, like agriculture or navigation; but against 
 the Art of Prediction from the time of birth, 
 which the Chaldeans exercise." Sextus, therefore, 
 though a skeptic by profession, was not insensible 
 to the difference between experimental knowledge 
 and mystical dogmas, though the former had no- 
 thing which excited his admiration. 
 
 The skepticism which denies the evidence of the 
 truths of which the best established physical sciences 
 consist, must necessarily involve a very indistinct 
 apprehension of those truths ; for such truths, pro- 
 perly exhibited, contain their own evidence, and 
 are the best antidote to this skepticism. But an 
 incredulity or contempt towards the asserted truths 
 of physical science may arise also from the attention 
 being mainly directed to the certainty and import- 
 ance of religious truths. A veneration for revealed 
 religion may thus assume the aspect of a skepticism 
 with regard to natural knowledge. Such appears to 
 be the case with Algazel or Algezeli, who is adduced 
 by Degerando 4 as an example of an Arabian skeptic. 
 He was a celebrated teacher at Bagdad in the ele- 
 venth century, and he declared himself the enemy, 
 not only of the mixed Peripatetic and Platonic 
 philosophy of the time, but of Aristotle himself. 
 
 4 Degerando, Hist. Comp. des Systemes, iv. 224. 
 
268 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 His work entitled The Destructions of the Philo- 
 sophers, is known to us by the refutation of it 
 which Averrhoes published, under the title of 
 Destruction of AlgazeTs Destructions of the Phi- 
 losophers. It appears that he contested the fun- 
 damental principles both of the Platonic and of the 
 Aristotelian schools, and denied the possibility of a 
 known connexion between cause and effect; thus 
 making a prelude, says Degerando, to the celebrated 
 argumentation of Hume (K). 
 
 6. Neglect of Physical Reasoning in Christen- 
 dom. If the Arabians, who, during the ages of 
 which we are speaking, were the most eminent 
 cultivators of science, entertained only such com- 
 paratively feeble and servile notions of its doctrines, 
 it will easily be supposed, that in the Christendom 
 of that period, where physical knowledge was com- 
 paratively neglected, there was still less distinctness 
 and vividness in the prevalent ideas on such subjects. 
 Indeed, during a considerable period of the history 
 of the Christian church, and by many of its principal 
 authorities, the study of natural philosophy was not 
 only disregarded but discommended. The great 
 practical doctrines which were presented to men's 
 minds, and the serious tasks, of the regulation of 
 the will and affections, which religion impressed 
 upon them, made inquiries of mere curiosity seem 
 to be a reprehensible misapplication of human 
 powers; and many of the fathers of the church 
 revived, in a still more peremptory form, the opi- 
 
INDISTINCTNESS OF IDEAS. 269 
 
 nion of Socrates, that the only valuable philosophy 
 is that which teaches us our moral duties and 
 religious hopes 5 . Thus Eusebius says 6 , " It is not 
 through ignorance of the things admired by them, 
 but through contempt of their useless labour, that 
 we think little of these matters, turning our souls 
 to the exercise of better things." When the thoughts 
 were thus intentionally averted from those ideas 
 which natural philosophy involves, the ideas inevit- 
 ably became very indistinct in their minds ; and 
 they could not conceive that any other persons 
 could find, on such subjects, grounds of clear con- 
 viction and certainty. They held the whole of their 
 philosophy to be, as Lactantius : asserts it to be 
 " empty and false." " To search," says he, " for the 
 causes of natural things ; to inquire whether the 
 sun be as large as he seems, whether the moon is 
 convex or concave, whether the stars are fixed 
 in the sky or float freely in the air ; of what size 
 and of what material are the heavens ; whether they 
 be at rest or in motion ; what is the magnitude of 
 the earth ; on what foundations it is suspended and 
 balanced ; to dispute and conjecture on such mat- 
 ters, is just as if we chose to discuss what we think 
 of a city in a remote country, of which we never 
 heard but the name." It is impossible to express 
 more forcibly that absence of any definite notions on 
 physical subjects which led to this tone of thought. 
 7. Question of Antipodes. With such habits 
 
 3 Bnifker, iii. 317- Pra>p. Ev. xv. (51 ' Inst. 1. iii. init. 
 
270 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 of thought, we are not to be surprized if the relations 
 resulting from the best established theories were 
 apprehended in an imperfect and incongruous man- 
 ner. We have some remarkable examples of this ; 
 and a very notable one is the celebrated question of 
 the existence of Antipodes, or persons inhabiting 
 the opposite side of the globe of the earth, and con- 
 sequently having the soles of their feet directly 
 opposed to ours. The doctrine of the globular form 
 of the earth results, as we have seen, by a geometrical 
 necessity, from a clear conception of the various 
 points of knowledge which we obtain, bearing upon 
 that subject. This doctrine was held distinctly by 
 the Greeks ; it was adopted by all astronomers, 
 Arabian and European, who followed them; and 
 was, in fact, an inevitable part of every system of 
 astronomy which gave a consistent and intelligible 
 representation of phenomena. But those who did 
 not call before their minds any distinct representa- 
 tion at all, and who referred the whole question to 
 other relations than those of space, might still deny 
 this doctrine ; and they did so. The existence of 
 inhabitants on the opposite side of the terraqueous 
 globe, was a fact of which experience alone could 
 teach the truth or falsehood ; but the religious re- 
 lations, which extend alike to all mankind, were 
 supposed to give the Christian philosopher grounds 
 for deciding against the possibility of such a race of 
 men. Lactantius 8 in the fourth century, argues this 
 
 8 Inst. 1. iii. 23. 
 
INDISTINCTNESS OF IDEAS. L>71 
 
 matter, in a way very illustrative of that impatience 
 of such speculations, and consequent confusion of 
 thought which we have mentioned. " Is it possible," 
 he says, " that men can be so absurd as to believe 
 that the crops and trees on the other side of the 
 earth hang downwards, and that men there have 
 their feet higher than their heads? If you ask 
 of them how they defend these monstrosities ? how 
 things do not fall away from the earth on that side? 
 they reply, that the nature of things is such that 
 heavy bodies tend towards the center, like the 
 spokes of a wheel, while light bodies, as clouds, 
 smoke, fire, tend from the center towards the hea- 
 vens on all sides. Now I am really at a loss what 
 to say of those who, when they have once gone 
 wrong, steadily persevere in their folly, and defend 
 one absurd opinion by another." It is obvious that 
 so long as the writer refused to admit into his 
 thoughts the fundamental conception of their theory, 
 he must needs be at a loss what to say to their 
 arguments, without being on that account in any 
 degree convinced of their doctrines. 
 
 In the sixth century, indeed, in the reign of 
 Justinian, we find a writer (Cosmas Indicopleustes 9 ) 
 who does not rest in this obscurity of representa- 
 tion ; but in this case, the distinctness of his pictures 
 only serves to show his want of 'any clear conception 
 
 9 Montfaucon, Collectio Nova Pat rum, t. ii. p. 113. Cosmas 
 Indicopleustes. Christianorum Opiniones de Mundo, sive Tb- 
 pographia Christiana. 
 
272 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 as to what suppositions would explain the pheno- 
 mena. He describes the earth as an oblong floor, 
 surrounded by upright walls, and covered by a vault, 
 below which the heavenly bodies perform their re- 
 volutions, going round a certain high mountain, 
 which occupies the northern parts of the earth, and 
 makes night by intercepting the light of the sun. 
 In Augustin 10 (who flourished A.D. 400) the opinion 
 is treated on other grounds ; and without denying 
 the globular form of the earth, it is asserted that 
 there are no inhabitants on the opposite side, be- 
 cause no such race is recorded by Scripture among 
 the descendants of Adam (L). Considerations of the 
 same kind operated in the well-known instance of 
 Virgil, bishop of Salzburg, in the eighth century. 
 When he was reported to Boniface, archbishop of 
 Mentz, as holding the existence of Antipodes, the 
 prelate was shocked at the assumption, as it seemed 
 to him, of a world of human beings, out of the reach 
 of the conditions of salvation ; and application was 
 made to Pope Zachary for a censure of the holder 
 of this dangerous doctrine. It does not however 
 appear that this led to any severity ; and the story 
 of the deposition of Virgil from his bishopric, which 
 is circulated by Kepler and by more modern writers, 
 is undoubtedly altogether false. The same scruples 
 continued to prevail among Christian writers to 
 a later period; and Tostatus 1 ' notes the opinion of 
 the rotundity of the earth as an "unsafe" doctrine, 
 
 10 Civ. D. xvi. 9. " Montfauc. Pair. t. ii. 
 
INDISTINCTNESS OF IDEAS. 273 
 
 only a few years before Columbus visited the other 
 hemisphere. 
 
 8. Intellectual Condition of the Religious Or- 
 ders. It must be recollected, however, that though 
 these were the views and tenets of many religious 
 writers, and though they may be taken as indi- 
 cations of the prevalent and characteristic temper 
 of the times of which we speak, they never were 
 universal. Such a confusion of thought affects the 
 minds of many persons, even in the most enlight- 
 ened times ; and in what we call the Dark Ages, 
 though clear views on such subjects might be more 
 rare, those who gave their minds to science, enter- 
 tained the true opinion of the figure of the earth. 
 Thus Boethius 12 (in the sixth century) urges the 
 smallness of the globe of the earth, compared with 
 the heavens, as a reason to repress our love of 
 glory. This work, it will be recollected, was trans- 
 lated into the Anglo-Saxon by our own Alfred. 
 It was also commented on by Bede, who, in what 
 he says on this passage, assents to the doctrine, 
 and shows an acquaintance with Ptolemy and his 
 commentators, both Arabian and Greek. Gerbert, 
 in the tenth century, went from France to Spain 
 to study astronomy with the Arabians, and soon 
 surpassed his masters. He is reported to have 
 fabricated clocks, and an astrolabe of peculiar con- 
 struction. Gerbert afterwards, (in the last year 
 of the first thousand from the birth of Christ,) 
 
 12 Boethius, Cons. ii. pr. 7- 
 VOL. I. T 
 
274 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 became pope, by the name of Sylvester II. Among 
 other cultivators of the sciences, some of whom, 
 from their proficiency, must have possessed with 
 considerable clearness and steadiness the elemen- 
 tary ideas on which it depends, we may here men- 
 tion, after Montucla 13 , Adelbold, whose work On 
 the Sphere was addressed to Pope Sylvester, and 
 whose geometrical reasonings are, according to 
 Montucla 11 , vague and chimerical; Hermann Con- 
 tractus, a monk of St. Gall, who, in 1050, published 
 astronomical works; William of Hirsaugen, who 
 followed this example in 1080 ; Robert of Lorraine, 
 who was made Bishop of Hereford by William 
 the Conqueror, in consequence of his astronomical 
 knowledge. In the next century, Adelhard Goth, 
 an Englishman, travelled among the Arabs for 
 purposes of study, as Gerbert had done in the 
 preceding age; and on his return, translated the 
 Elements of Euclid, which he had brought from 
 Spain or Egypt. Robert Grostete, Bishop of Lin- 
 coln, was the author of an Epitome on the Sphere ; 
 Roger Bacon, in his youth the contemporary of 
 Robert, and of his brother Adam Marsh, praises 
 very highly their knowledge in mathematics. 
 
 " And here," says the French historian of mathe- 
 matics, whom I have followed in the preceding 
 relation, "it is impossible not to reflect that all 
 those men who, if they did not augment the trea- 
 sure of the sciences, at least served to transmit it, 
 13 Mont. i. 502. " Mont. i. 503. 
 
INDISTINCTNESS OF IDEAS. 275 
 
 were monks, or had been such originally. Con- 
 vents were, during these stormy ages, the asylum 
 of sciences and letters. Without these religious 
 men, who, in the silence of their monasteries, oc- 
 cupied themselves in transcribing, in studying, and 
 in imitating the works of the ancients, well or ill, 
 those works would have perished ; perhaps not one 
 of them would have come down to us. The thread 
 which connects us with the Greeks and Romans 
 would have been snapt asunder; the precious 
 productions of ancient literature would no more 
 exist for us, than the works, if any there were, 
 published before the catastrophe that annihilated 
 that highly scientific nation, which, according to 
 Bailly, existed in remote ages in the center of 
 Tartary, or at the roots of Caucasus. In the 
 sciences we should have had all to create ; and at 
 the moment when the human mind should have 
 emerged from its stupor and shaken off its slum- 
 bers, we should have been no more advanced than 
 the Greeks were after the taking of Troy." He 
 adds, that this consideration inspires feelings to- 
 wards the religious orders very different from those 
 which, when he wrote, were prevalent among his 
 countrymen. 
 
 Except so far as their religious opinions inter- 
 fered, it was natural that men who lived a life of 
 quiet and study, and were necessarily in a great 
 measure removed from the absorbing and blind- 
 ing interests with which practical life occupies the 
 
 T2 
 
276 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 thoughts, should cultivate science more successfully 
 than others, precisely because their ideas on specu- 
 lative subjects had time and opportunity to become 
 clear and steady. The studies which were culti- 
 vated under the name of the Seven Liberal Arts 
 necessarily tended to favour this effect. The 
 Trivium, indeed, which consisted of Grammar, 
 Logic, and Rhetoric, had no direct bearing upon 
 those ideas with which physical science is con- 
 cerned; but the Quadrivium, Music, Arithmetic, 
 Geometry, Astronomy, could not be pursued with 
 any attention, without a corresponding improve- 
 ment of the mind for purposes of sound know- 
 ledge 16 . 
 
 9. Popular Opinions. That, even in the best 
 intellects, something was wanting to fit them for 
 scientific progress and discovery, is obvious from the 
 fact that science was so long absolutely stationary. 
 And I have endeavoured to show that one part of 
 this deficiency was the want of the requisite clear- 
 ness and vigour of the fundamental scientific ideas. 
 If these were wanting, even in the most powerful and 
 most cultivated minds, we may easily conceive that 
 still greater confusion and obscurity prevailed in 
 
 15 Bruck. iii. 597- 
 
 1(5 Roger Bacon, in his Specula Mathematica, cap. i., says, 
 " Harum scientiarum porta et clavis est mathematica, quam 
 sancti a principio mundi invenerunt, etc. Cujus negligentia 
 jam per triginla vel quadraginta annos destruxit totum studium 
 Latinorum " I do not know on what occasion this neglect took 
 place. 
 
INDISTINCTNESS OF IDEAS. 277 
 
 the common class of mankind. They actually 
 adopted the belief, however crude and inconsistent, 
 that the form of the earth and heavens really is 
 what at any place it appears to be ; that the earth 
 is flat, and the waters of the sky sustained above 
 a material floor, through which in showers they 
 descend. Yet the true doctrines of astronomy ap- 
 pear to have had some popular circulation. For 
 instance, a French poem of the time of Edward 
 the Second, called Ymage du Monde, contains 
 a metrical account of the earth and heavens, ac- 
 cording to the Ptolemaic views; and in a manu- 
 script of this poem, preserved in the library of 
 the University of Cambridge, there are represen- 
 tations, in accordance with the text, of a spherical 
 earth, with men standing upright upon it on every 
 side : and by way of illustrating the tendency of 
 all things to the center, perforations of the earth, 
 entirely through its mass, are described and de- 
 picted; and figures are exhibited dropping balls 
 down each of these holes, so as to meet in the 
 interior. And, as bearing upon the perplexity 
 which attends the motions of up and down, when 
 applied to the globular earth, and the change of 
 the direction of gravity which would occur in pass- 
 ing the center, the readers of Dante will recollect 
 the extraordinary manner in which the poet and 
 his guide emerge from the bottom of the abyss; 
 and the explanation which Virgil imparts to him of 
 what he there sees. After they have crept through 
 
278 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 the aperture in which Lucifer is placed, the poet 
 
 says, 
 
 "Io levai gli occhi e credetti vedere 
 Lucifero com' io 1' avea lasciato, 
 E vidile le gambe in su tenere." 
 
 " Quest! come e fitto 
 
 Si sottasopra?" .... 
 
 " Quando mi volsi, tu passast' il punto 
 Al qual si traggon d' ogni parte i pesi." 
 
 Inferno, xxxiv. 
 
 "I raised mine eyes, 
 
 Believing that I Lucifer should see 
 
 Where he was lately left, but saw him now 
 
 With legs held upward." .... 
 
 "How standeth he in posture thus reversed?" 
 
 "Thou wast on the other side so long as I 
 Descended; when I turned, thou didst o'erpass 
 That point to which from every part is dragged 
 All heavy substance." 
 
 CARY. 
 
 This is more philosophical than Milton's repre- 
 sentation, in a more scientific age, of Uriel sliding 
 to the earth on a sun-beam, and sliding back again, 
 when the sun had sunk below the horizon. 
 
 " Uriel to his charge 
 
 Returned on that bright beam whose point now raised, 
 Bore him slope downward to the sun, now fallen 
 Beneath the Azores." 
 
 Par. Lost, B. iv. 
 
 The philosophical notions of up and down are 
 too much at variance with the obvious suggestions 
 of our senses, to be held steadily and justly by 
 
INDISTINCTNESS OF IDEAS. 279 
 
 minds undisciplined in science. Perhaps it was 
 some misunderstood statement of the curved sur- 
 face of the ocean, which gave rise to the tradition 
 of there being a part of the sea directly over the 
 earth, from which at times an object has been 
 known to fall, or an anchor to be let down. Even 
 such whimsical fancies are not without instruction, 
 and may serve to show the reader what that vague- 
 ness and obscurity of ideas is, of which I have 
 been endeavouring to trace the prevalence in the 
 dark ages. 
 
 We now proceed to another of the features 
 which appears to me to mark, in a very prominent 
 manner, the character of the stationary period. 
 
280 
 
 CHAPTER II. 
 
 THE COMMENTATORIAL SPIRIT OF THE 
 
 MIDDLE AGES. 
 
 WE have already noticed, that, after the first 
 great achievements of the founders of sound 
 speculation, in the different departments of human 
 knowledge, had attracted the interest and admira- 
 tion which those who became acquainted with them 
 could not but give to them, there appeared a dispo- 
 sition among men to lean on the authority of some 
 of these teachers ; to study the opinions of others 
 as the only mode of forming their own ; to read 
 nature through books; to attend to what had 
 been already thought and said, rather than to what 
 really is and happens. This tendency of men's 
 minds requires our particular consideration. Its 
 manifestations were very important, and highly 
 characteristic of the stationary period ; it gave, in 
 a great degree, a peculiar bias and direction to the 
 intellectual activity of many centuries; and the 
 kind of labour with which speculative men were 
 occupied in consequence of this bias, took the 
 place of that examination of realities which must 
 be their employment, in order that real knowledge 
 may make any decided progress. 
 
 In some subjects, indeed, as, for instance, in 
 
THE COMMENTATORIAL SPIRIT. 281 
 
 the domains of morals, poetry, and the arts whose 
 aim is the production of beauty, this opposition 
 between the study of former opinion and present 
 reality, may not be so distinct ; inasmuch as it may 
 be said by some, that, in these subjects, opinions 
 are realities ; that the thoughts and feelings which 
 prevail in men's minds are the material upon which 
 we must work, the particulars from which we are 
 to generalize, the instruments which we are to use ; 
 and that, therefore, to reject the study of antiquity, 
 or even its authority, would be to show ourselves 
 ignorant of the extent and mutual bearing of the 
 elements with which we have to deal; would be 
 to cut asunder that which we ought to unite into 
 a vital whole. Yet even in the provinces of his- 
 tory and poetry, the poverty and servility of men's 
 minds during the middle ages, are shown by indi- 
 cations so strong as to be truly remarkable ; for 
 instance, in the efforts of the antiquarians of almost 
 every European country to assimilate the early 
 history of their own state to the poet's account of 
 the foundation of Rome, by bringing from the sack 
 of Troy, Brutus to England, Bavo to Flanders, and 
 so on. But however this may be, our business 
 at present is, to trace the varying spirit of the 
 physical philosophy of different ages; trusting that, 
 hereafter, this prefatory study will enable us to 
 throw some light upon the other parts of philo- 
 sophy. And in physics the case undoubtedly was, 
 that the labour of observation, which is one of 
 
282 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 the two great elements of the progress of know- 
 ledge, was in a great measure superseded by the 
 collection, the analysis, the explanation, of previous 
 authors and opinions ; experimenters were replaced 
 by commentators ; criticism took the place of in- 
 duction; and instead of great discoverers we had 
 learned men. 
 
 1. Natural Bias to Authority. It is very evi- 
 dent that, in such a bias of men's studies, there is 
 something very natural ; however strained and tech- 
 nical this erudition may have been, the propensities 
 on which it depends are very general, and are easily 
 seen. Deference to the authority of thoughtful and 
 sagacious men, a disposition which men in general 
 neither reject nor think they ought to reject in 
 practical matters, naturally clings to them, even in 
 speculation. It is a satisfaction to us to suppose 
 that there are, or have been, minds of transcendent 
 powers, of wide and wise views, superior to the 
 common errors and blindnesses of our nature. The 
 pleasure of admiration, and the repose of confi- 
 dence, are inducements to such a belief. There are 
 also other reasons why we willingly believe that 
 there are in philosophy great teachers, so profound 
 and sagacious, that, in order to arrive at truth, 
 we have only to learn their thoughts, to under- 
 stand their writings. There is a peculiar interest 
 which men feel in dealing with the thoughts of 
 their fellow-men, rather than with brute matter. 
 Matter feels and excites no sympathies ; in seeking 
 
THE COMMENTATORIAL SPIRIT. 283 
 
 for mere laws of nature, there is nothing of mental 
 intercourse with the great spirits of the past, as 
 there is in studying Aristotle or Plato. More- 
 over, a large portion of this employment is of 
 a kind the most agreeable to most speculative 
 minds; it consists in tracing the consequences of 
 assumed principles : it is deductive like geometry ; 
 and the principles of the teachers being known, 
 and being undisputed, the deduction and applica- 
 tion of their results is an obvious, self-satisfying, 
 and inexhaustible exercise of ingenuity. 
 
 These causes, and probably others, make cri- 
 ticism and commentation flourish, when invention 
 begins to fail, oppressed and bewildered by the 
 acquisitions it has already made ; and when the 
 vigour and hope of men's minds are enfeebled by 
 civil and political changes. Accordingly 1 , the Alex- 
 andrian school was eminently characterized by a 
 spirit of erudition, of literary criticism, of inter- 
 pretation, of imitation. These practices, which 
 reigned first in their full vigour in the Museum, 
 are likely to be, at all times, the leading propen- 
 sities of similar academical institutions. 
 
 How natural it is to select a great writer as 
 a paramount authority, and to ascribe to him ex- 
 traordinary profundity and sagacity, we may see, 
 in the manner in which the Greeks looked upon 
 Homer ; and the fancy which detected in his poems 
 traces of the origin of all arts and sciences, has, 
 
 1 Degerando, Hist, des Syst. de Philos. iii. p. 134. 
 
284 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 as we know, found favour even in modern times. 
 To pass over earlier instances of this feeling, we 
 may observe, that Strabo begins his Geography by 
 saying that he agrees with Hipparchus, who had 
 declared Homer to be the first author of our geo- 
 graphical knowledge : and he does not confine the 
 application of this assertion to the various and 
 curious topographical information which the Iliad 
 and Odyssey contain, concerning the countries sur- 
 rounding the Mediterranean ; but in phrases which, 
 to most persons, might appear the mere play of 
 a poetical fancy, or a casual selection of circum- 
 stances, he finds unquestionable evidence of a 
 correct knowledge of general geographical truths. 
 Thus', when Homer speaks of the sun " rising from 
 the soft and deep-flowing ocean," of his " splendid 
 blaze plunging in the ocean ;" of the northern con- 
 stellation 
 
 "Alone unwashen by the ocean wave;" 
 
 and of Jupiter " who goes to the ocean to feast 
 with the blameless Ethiopians ;" Strabo is satisfied 
 from these passages that Homer knew the dry land 
 to be surrounded with water: and he reasons in 
 like manner with respect to other points of geo- 
 graphy. 
 
 2. Character of Commentators. The spirit of 
 commentation, as has already been suggested, turns 
 to questions of taste, of metaphysics, of morals, 
 
 3 Strabo, i. p. 5. 
 
THE COMMENTATORIAL SPIRIT. 285 
 
 with far more avidity than to physics. Accord- 
 ingly, critics and grammarians were peculiarly the 
 growth of this school ; and, though the commen- 
 tators sometimes chose works of mathematical or 
 physical science for their subject (as Proclus, who 
 commented on Euclid's Geometry, and Simplicius, 
 on Aristotle's Physics,) these commentaries were, 
 in fact, rather metaphysical than mathematical. It 
 does not appear that the commentators have, in 
 any instance, illustrated the author by bringing his 
 assertions of facts to the test of experiment. Thus, 
 when Simplicius comments on the passage concern- 
 ing a vacuum, which we formerly adduced, he 
 notices the argument which went upon the asser- 
 tion, that a vessel full of ashes would contain as 
 much water as an empty vessel ; and he mentions 
 various opinions of different authors, but no trial 
 of the fact. Eudemus had said, that the ashes 
 contained something hot, as quicklime does, and 
 that by means of this, a part of the water was 
 evaporated ; others supposed the water to be con- 
 densed, and so on 3 . 
 
 The commentator's professed object is to explain, 
 to enforce, to illustrate doctrines assumed as true. 
 He endeavours to adapt the work on which he 
 employs himself to the state of information and of 
 opinion in his own time; to elucidate obscurities and 
 technicalities; to supply steps omitted in the reason- 
 ing ; but he does not seek to obtain additional truths 
 
 3 Simplicius, p. 170. 
 
286 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 or new generalizations. He undertakes only to give 
 what is virtually contained in his author ; to deve- 
 lope, but not to create. He is a cultivator of the 
 thoughts of others: his labour is not spent on a 
 field of his own; he ploughs but to enrich the 
 granary of another man. Thus he does not work 
 as a freeman, but as one in a servile condition ; 
 or rather, his is a menial, and not a productive 
 service : his office is to adorn the appearance of 
 his master, not to increase his wealth. 
 
 Yet though the commentator's employment is 
 thus subordinate and dependent, he is easily led 
 to attribute to it the greatest importance and dig- 
 nity. To elucidate good books is, indeed, a useful 
 task ; and when those who undertake this work 
 execute it well, it would be most unreasonable to 
 find fault with them for not doing more. But the 
 critic, long and earnestly employed on one author, 
 may easily underrate the relative value of other 
 kinds of mental exertion. He may ascribe too 
 large dimensions to that which occupies the whole 
 of his own field of vision. Thus he may come to 
 consider such study as the highest aim, and best 
 evidence of human genius. To understand Aris- 
 totle, or Plato, may appear to him to comprise all 
 that is possible of profundity and acuteness. And 
 when he has travelled over a portion of their 
 domain, and satisfied himself that of this he too 
 is master, he may look with complacency at the 
 circuit he has made, and speak of it as a labour 
 
THE COMMENTATOR1AL SPIRIT. 287 
 
 of vast effort and difficulty. We may quote, as an 
 expression of this temper, the language of Sir 
 Henry Savile, in concluding a course of lectures 
 on Euclid, delivered at Oxford 4 . "By the grace 
 of God, gentlemen hearers, I have performed my 
 promise ; I have redeemed my pledge. I have ex- 
 plained, according to my ability, the definitions, 
 postulates, axioms, and first eight propositions of 
 the Elements of Euclid. Here, sinking under the 
 weight of years, I lay down my art and my instru- 
 ments." 
 
 We here speak of the peculiar province of the 
 commentator ; for undoubtedly, in many instances, 
 a commentary on a received author has been made 
 the vehicle of conveying systems and doctrines en- 
 tirely different from those of the author himself; 
 as, for instance, when the New Platonists wrote, 
 taking Plato for their text. The labours of learned 
 men in the stationary period, which came under 
 this description, belong to another class. 
 
 3. Greek Commentators on Aristotle. The com- 
 mentators or disciples of the great philosophers did 
 not assume at once their servile character. At first 
 their object was to supply and correct, as well as to 
 explain their teacher. Thus among the earlier com- 
 mentators of Aristotle, Theophrastus invented five 
 moods of syllogism in the first figure, in addition to 
 
 4 Exolvi per Dei gratiam, Domini auditores, promissum ; 
 liberavi fidem meam; explicavi pro meo modulo, definitiones, 
 petitiones, communes sententias, et octo priores propositiones 
 Elementorum Euclidis. Hie, annis fessus, cyclos artemque repono. 
 
288 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 the four invented by Aristotle, and stated with 
 additional accuracy the rules of hypothetical syllo- 
 gisms. He also, not only collected much informa- 
 tion concerning animals, and natural events, which 
 Aristotle had omitted, but often differed with his 
 master; as, for instance, concerning the saltness 
 of the sea : this, which the Stagirite attributed to 
 the effect of the evaporation produced by the sun's 
 rays, was ascribed by Theophrastus to beds of salt 
 at the bottom. Porphyry 5 , who flourished in the 
 third century, wrote a book on the Predicables, 
 which was found to be so suitable a complement to 
 the Predicaments or Categories of Aristotle, that it 
 was usually prefixed to that treatise ; and the two 
 have been used as an elementary work together, up 
 to modern times. The Predicables are the five steps 
 which the gradations of generality and particularity 
 introduce; genus, species, difference, individual, 
 accident ; the Categories are the ten heads under 
 which assertions or predications may be arranged ; 
 substance, quantity, relation, quality, place, time, 
 position, habit, action, passion. 
 
 At a later period, the Aristotelian commentators 
 became more servile, and followed the author step 
 by step, explaining, according to their views, his 
 expressions and doctrines ; often, indeed, with ex- 
 treme prolixity, expanding his clauses into sentences, 
 and his sentences into paragraphs. Alexander 
 Aphrodisiensis, who lived at the end of the second 
 
 6 Buhle, Arist. i. 284. 
 
THE COMMENTATORIAL SPIRIT. 289 
 
 century, is of this class ; " sometimes useful," as one 
 of the recent editors of Aristotle says 6 ; " but by the 
 prolixity of his interpretation, by his perverse itch 
 for himself discussing the argument expounded by 
 Aristotle, for defending his opinions, and for refuting 
 or reconciling those of others, he rather obscures 
 than enlightens." At various times, also, some of 
 the commentators, and especially those of the Alex- 
 andrian school, endeavoured to reconcile, or com- 
 bined without reconciling, opposing doctrines of the 
 great philosophers of the earlier times. Simplicius, 
 for instance, and, indeed, a great number of the 
 Alexandrian philosophers 7 , as Alexander, Ammo- 
 nius, and others, employed themselves in the futile 
 task of reconciling the doctrines of the Pythagoreans, 
 of the Eleatics, of Plato, and of the Stoics, with 
 those of Aristotle. Boethius 8 entertained the design 
 of translating into Latin the whole of Aristotle's 
 and Plato's works, and of showing their agreement ; 
 a gigantic plan, which he never executed. Others 
 employed themselves in disentangling the confusion 
 which such attempts produced, as John the Gram- 
 marian, surnamed Philoponus, "the Labour-loving ;" 
 who, towards the end of the seventh century, main- 
 tained that Aristotle was entirely misunderstood by 
 Porphyry and Proclus 9 , who had pretended to in- 
 corporate his doctrines into those of the New Pla- 
 tonic school, or even to reconcile him with Plato 
 
 9 Buhle, i. 288. 7 Buhle, i. 311. 
 
 * Degerando, Hist, des Syst. iv. 100. 9 Ib. iv. 155. 
 
 VOL. I. U 
 
290 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 himself on the subject of ideas. Others, again, 
 wrote Epitomes, Compounds, Abstracts ; and endea- 
 voured to throw the works of the philosopher into 
 some simpler and more obviously regular form, as 
 John of Damascus, in the middle of the eighth 
 century, who made abstracts of some of Aristotle's 
 works, and introduced the study of the author into 
 theological education. These two writers lived 
 under the patronage of the Arabs ; the former was 
 favoured by Amrou, the conqueror of Egypt ; the 
 latter was at first secretary to the Caliph, but after- 
 wards withdrew to a monastery 10 . 
 
 At this period the Arabians became the fosterers 
 and patrons of philosophy, rather than the Greeks. 
 Justinian had, by an edict, closed the school of 
 Athens, the last of the schools of heathen philo- 
 sophy. Leo, the Isaurian, who was a zealous Ico- 
 noclast, abolished also the schools where general 
 knowledge had been taught, in combination with 
 Christianity 11 ; yet the line of the Aristotelian com- 
 mentators was continued, though feebly, to the later 
 ages of the Greek empire. Anna Comnena 12 men- 
 tions a Eustratus who employed himself upon the 
 dialectic and moral treatises, and whom she does 
 not hesitate to elevate above the Stoics and Pla- 
 tonists, for his talent in philosophical discussions. 
 Nicephorus Blemmydes wrote logical and physical 
 epitomes for the use of John Ducas ; George Pachy- 
 meus composed an epitome of the philosophy of 
 
 10 Deg. iv. 150. ll Ib. iv. 163, 12 Ib. 167. 
 
THE COMMENTATORIAL SPIRIT. 291 
 
 Aristotle, and a compend of his logic : Theodore 
 Metochytes, who was famous in his time alike for 
 his eloquence and his learning, has left a paraphrase 
 of the books of Aristotle on Physics, on the Soul, 
 the Heavens 13 , &c. Fabricius states that this writer 
 has a chapter, the object of which is to prove, that 
 all philosophers, and Aristotle and Plato in par- 
 ticular, have disdained the authority of their prede- 
 cessors. He could hardly help remarking in how 
 different a spirit philosophy had been pursued since 
 their time. 
 
 3. Greek Commentators of Plato and others. 
 I have spoken principally of the commentators of 
 Aristotle, for he was the great subject of the com- 
 mentators proper; and though the name of his 
 rival, Plato, was graced by a list of attendants hardly 
 less numerous, these, the Neoplatonists, as they are 
 called, had introduced new elements into the doc- 
 trines of their nominal master, to such an extent 
 that they must be placed in a different class. We 
 may observe here however, how, in this school as in 
 the Peripatetic, the race of commentators multiplied 
 itself. Porphyry, who commented on Aristotle, was 
 commented on by Ammonius; Plotiiius's Enneads 
 were commented on by Proclus and Dexippus. 
 Psellus 14 the elder was a paraphrast of Aristotle; 
 Psellus the younger, in the eleventh century, at- 
 tempted to restore the New Platonic school. The 
 former of these two writers had for his pupils two 
 
 13 Deg. iv. 168. M Ib. iv. 169. 
 
 U2 
 
292 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 men, the emperor Leo, surnamed the Philosopher, 
 and Photius the patriarch, who exerted themselves 
 to restore the study of literature at Constantinople. 
 We still possess the Collection of Extracts of Pho- 
 tius, which, like that of Stobseus and others, shows 
 the tendency of the age to compilations, abstracts, 
 and epitomes, the extinction of philosophical vi- 
 tality. 
 
 4. Arabian Commentators of Aristotle. The 
 reader might perhaps have expected, that when the 
 philosophy of the Greeks was carried among a new 
 race of intellects, of a different national character 
 and ' condition, the chain of this servile tradition 
 would have been broken ; that some new thoughts 
 would have started forth ; that some new direction, 
 some new impulse, would have been given to the 
 search for truth. It might have been anticipated 
 that we should have had schools among the Arabians 
 which should rival the Peripatetic, Academic and 
 Stoic among the Greeks; that they would pre- 
 occupy the ground on which Copernicus and Galileo, 
 Lavoisier and Linnaeus, won their fame ; that they 
 would make the next great steps in the progressive 
 sciences. Nothing of this, however, happened. The 
 Arabians cannot claim, in science or philosophy, 
 any really great names ; they produced no men and 
 no discoveries which have materially influenced the 
 course and destinies of human knowledge; they 
 tamely adopted the intellectual servitude of the 
 nation which they conquered by their arms; they 
 
THE COMMENTATORIAL SPIRIT. 293 
 
 joined themselves at once to the string of slaves 
 who were dragging the car of Aristotle and Plotinus. 
 Nor, perhaps, on a little further reflection, shall we 
 be suprized at this want of vigour and productive 
 power, in this period of apparent national youth. 
 The Arabians had not been duly prepared rightly 
 to enjoy and use the treasures of which they 
 became possessed. They had, like most uncivilized 
 nations, been passionately fond of their indigenous 
 poetry ; their imagination had been awakened, but 
 their rational powers and speculative tendencies 
 were still torpid. They received the Greek philo- 
 sophy without having passed through those grada- 
 tions of ardent curiosity and keen research, of ob- 
 scurity brightening into clearness, of doubt succeeded 
 by the joy of discovery, by which the Greek mind 
 had been enlarged and exercised. Nor had the 
 Arabians ever enjoyed, as the Greeks had, the indi- 
 vidual consciousness, the independent volition, the 
 intellectual freedom, arising from the freedom of 
 political institutions. They had not felt the con- 
 tagious mental activity of a small city ; the elation 
 arising from the general sympathy in speculative 
 pursuits diffused through an intelligent and acute 
 audience; in short, they had not had a national 
 education such as fitted the Greeks to be disciples 
 of Plato and Hipparchus. Hence, their new literary 
 wealth rather encumbered and enslaved, than en- 
 riched and strengthened them : in their want of 
 taste for intellectual freedom, they were glad to 
 
294 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 give themselves up to the guidance of Aristotle and 
 other dogmatists. Their military habits had accus- 
 tomed them to look to a leader ; their reverence for 
 the book of their law had prepared them to accept 
 a philosophical Koran also. Thus the Arabians, 
 though they never translated the Greek poetry, 
 translated, and merely translated, the Greek philo- 
 sophy ; they followed the Greek philosophers with- 
 out deviation, or, at least, without any philosophical 
 deviations. They became for the most part Aristo- 
 telians ; studied not only Aristotle, but the com- 
 mentators of Aristotle ; and themselves swelled the 
 vast and unprofitable herd. 
 
 The philosophical works of Aristotle had, in 
 some measure, made their way in the east, before 
 the growth of the Saracen power. In the sixth 
 century, a Syrian, Uranus 15 , encouraged by the love 
 of philosophy manifested by Cosroes, had translated 
 some of the writings of the Stagirite; about the 
 same time, Sergius had given some translations in 
 Syriac. In the seventh century, Jacob of Edessa 
 translated into this language the Dialectics, and 
 added Notes to the work. Such labours became 
 numerous ; and the first Arabic translations of Aris- 
 totle were formed upon these Persian or Syriac 
 texts. In this succession of transfusions, some mis- 
 takes must inevitably have been introduced. 
 
 The Arabian interpreters of Aristotle, like a 
 large portion of the Alexandrian ones, gave to the 
 16 Deg. iv. 196. 
 
THE COMMENTATORIAL SPIRIT. 295 
 
 philosopher a tinge of opinions borrowed from 
 another source, of which I shall have to speak 
 under the head of Mysticism. But they are, for 
 the most part, sufficiently strong examples of the 
 peculiar spirit of commentation, to make it fitting 
 to notice them here. At the head of them stands 16 
 Alkindi, who appears to have lived at the court 
 of Almamon, and who wrote commentaries on the 
 Organon of Aristotle. But Alfarabi was the glory 
 of the school of Bagdad ; his knowledge included 
 mathematics, astronomy, medicine and philosophy. 
 Born in an elevated rank, and possessed of a rich 
 patrimony, he led an austere life, and devoted him- 
 self altogether to study and meditation. He em- 
 ployed himself particularly in unfolding the import 
 of Aristotle's treatise On the Soul 17 . Avicenna (Ebn 
 Sina) was at once the Hippocrates and the Aristotle 
 of the Arabians ; and certainly the most extraordi- 
 nary man that the nation produced. In the course 
 of an unfortunate and stormy life, occupied by 
 politics and by pleasures, he produced works which 
 were long revered as a sort of code of science. In 
 particular, his writings on medicine, though they 
 contain little besides a compilation of Hippocrates 
 and Galen, took the place of both, even in the 
 universities of Europe ; and were studied as models 
 at Paris and Montpellier, till the end of the seven- 
 teenth century, at which period they fell into an 
 almost complete oblivion. Avicenna is conceived, 
 
 18 Deg. iv.187. 17 Ib. iv. 205. 
 
296 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 by some modern writers 18 , to have shown some 
 power of original thinking in his representations 
 of the Aristotelian Logic and Metaphysics. Aver- 
 roes (Ebn Roshd) of Cordova, was the most illus- 
 trious of the Spanish Aristotelians, and became 
 the guide of the schoolmen 19 , being placed by them 
 on a level with Aristotle himself, or above him. 
 He translated Aristotle from the first Syriac ver- 
 sion, not being able to read the Greek text. He 
 aspired to, and retained for centuries, the title of 
 the Commentator; and he deserves this title by 
 the servility with which he maintains that Aris- 
 totle 20 carried the sciences to the highest possible 
 degree, measured their whole extent, and fixed 
 their ultimate and permanent boundaries ; although 
 his works are conceived to exhibit a trace of the 
 New Platonism. Some of his writings are directed 
 against an Arabian skeptic, of the name of Al- 
 gazel, whom we have already noticed. 
 
 When the schoolmen had adopted the supre- 
 macy of Aristotle to the extent in which Averroes 
 maintained it, their philosphy went further than 
 a system of mere commentation, and became a 
 system of dogmatism; we must, therefore, in another 
 chapter, say a few words more of the Aristotelians 
 in this point of view, before we proceed to the 
 revival of science; but we must previously con- 
 sider some other features in the character of the 
 Stationary Period. 
 
 18 Deg. iv. 206. 19 Ib. iv. 247- Averroes died A. D. 1206. 
 
 20 Deg. iv. 248. 
 
297 
 
 CHAPTER III. 
 OF THE MYSTICISM OF THE MIDDLE AGES. 
 
 IT has been already several times hinted, that 
 a new and peculiar element was introduced 
 into the Greek philosophy which occupied the at- 
 tention of the Alexandrian school ; and that this 
 element tinged a large portion of 'the speculations 
 of succeeding ages. We may speak of this peculiar 
 element as Mysticism ; for, from the notion usually 
 conveyed by this term, the reader will easily ap- 
 prehend the general character of the tendency 
 now spoken of; and especially when he sees its 
 effect pointed out in various subjects. Thus, instead 
 of referring the events of the external world to 
 space and time, to sensible connexion and causa- 
 tion> men attempted to reduce such occurrences 
 under spiritual and supersensual relations and de- 
 pendencies; they referred them to superior intel- 
 ligences, to theological conditions, to past and 
 future events in the moral world, to states of mind 
 and feelings, to the creatures of an imaginary my- 
 thology or demonology. And thus their physical 
 Science became Magic, their Astronomy became 
 Astrology, the study of the Composition of bodies 
 became Alchemy, Mathematics became the contem- 
 
298 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 plation of the Spiritual Relations of number and 
 figure, and Philosophy became Theosophy. 
 
 The examination of this feature in the history 
 of the human mind is important for us, in conse- 
 quence of its influence upon the employments and 
 the thoughts of the times now under our notice. 
 This tendency materially affected both men's spe- 
 culations and their labours in the pursuit of know- 
 ledge. By its direct operation, it gave rise to the 
 newer Platonic philosophy among the Greeks, and 
 to corresponding doctrines among the Arabians; 
 and by calling into a prominent place astrology, 
 alchemy, and magic, it long occupied most of the 
 real observers of the material world. In this man- 
 ner it delayed and impeded the progress of true 
 science ; for we shall see reason to believe that 
 human knowledge lost more by the perversion of 
 men's minds and the misdirection of their efforts, 
 than it gained by any increase of zeal arising from 
 the peculiar hopes and objects of the mystics. 
 
 It is not to our purpose to attempt any general 
 view of the progress and fortunes of the various 
 forms of Mystical Philosophy ; but only to exhibit 
 some of its characters, in so far as they illustrate 
 those tendencies of thought which accompanied 
 the retrogradation of inductive science. And of 
 these, the leading feature which demands our notice 
 is that already alluded to ; namely, the practice of 
 referring things and events, not to clear and dis- 
 tinct relations, obviously applicable to such cases ; 
 
THEIR MYSTICISM. 299 
 
 not to general rules capable of direct verifica- 
 tion ; but to notions vague, distant, and vast, which 
 we cannot bring into contact with facts, because 
 they belong to a different region from the facts ; 
 as when we connect natural events with moral 
 or historical causes, or seek spiritual meanings in 
 the properties of number and figure. Thus the 
 character of Mysticism is, that it refers particulars, 
 not to generalizations homogeneous and immediate, 
 but to such as are heterogeneous and remote; to 
 which we must add, that the process of this re- 
 ference is not a calm act of the intellect, but is 
 accompanied with a glow of enthusiastic feeling. 
 
 1. Neoplatonic Theosophy. The Newer Pla- 
 tonism is the first example of this Mystical Philo- 
 sophy which I shall consider. The main points 
 which here require our notice are, the doctrine of 
 an Intellectual World resulting from the act of the 
 Divine Mind, as the only reality; and the aspira- 
 tion after the union of the human soul with this 
 Divine Mind, as the object of human existence. 
 The " Ideas" of Plato were forms of our knowledge ; 
 but among the Neoplatonists they became really 
 existing, indeed the only really existing, objects ; 
 and the inaccessible scheme of the universe which 
 these ideas constitute, was offered as the great sub- 
 ject of philosophical contemplation. The desire of 
 the human mind to approach towards its Creator 
 and Preserver, and to obtain a spiritual access to 
 Him, leads to an employment of the thoughts which 
 
300 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 is well worth the notice of the religious philoso- 
 pher; but such an effort, even when founded on 
 revelation and well regulated, is not a means of 
 advance in physics : and when it is the mere result 
 of natural enthusiasm, it may easily obtain such a 
 place in men's minds as to unfit them for the 
 successful prosecution of natural philosophy. The 
 temper, therefore, which introduces such super- 
 natural communion into the general course of its 
 speculations, may be properly treated as mystical, 
 and as one of the causes of the decline of science 
 in the Stationary Period. The Neoplatonic philo- 
 sophy requires our notice as one of the most re- 
 markable forms of this Mysticism. 
 
 Though Ammonius Saccas, who flourished at the 
 end of the second century, is looked upon as the 
 beginner of the Neoplatonists, his disciple Plo- 
 tinus is, in reality, the great founder of the school, 
 both by his works, which still remain to us, and by 
 the enthusiasm which his character and manners 
 inspired among his followers. He lived a life of 
 meditation, gentleness, and self-denial, and died in 
 the second year of the reign of Claudius (A.D. 270). 
 His disciple, Porphyry, has given us a Life of him, 
 from which we may see how well his habitual 
 manners were suited to make his doctrines im- 
 pressive. " Plotinus, the philosopher of our time," 
 Porphyry thus begins his biography, "appeared 
 like a person ashamed that he was in the body. 
 In consequence of this disposition, he could not 
 
THEIR MYSTICISM. 301 
 
 bear to talk concerning his family, or his parents, 
 or his country. He would not allow himself to be 
 represented by a painter or statuary; and once, 
 when Aurelius entreated him to permit a likeness 
 of him to be taken, he said, ' Is it not enough for 
 us to carry this image in which nature has en- 
 closed us, but we must also try to leave a more 
 durable image of this image, as if it were so great 
 a sight ?' And he retained the same temper to the 
 last. When he was dying, he said, ' I am trying 
 to bring the divinity which is in us to the divinity 
 which is in the universe.'" He was looked upon 
 by his successors with extraordinary admiration 
 and reverence ; and his disciple Porphyry collected 
 from his lips, or from fragmental notes, the six 
 Enneads of his doctrines (that is, parts each con- 
 sisting of nine Books,) which he arranged and 
 annotated. 
 
 We have no difficulty in finding in this remark- 
 able work examples of mystical speculation. The 
 Intelligible World of realities or essences corre- 
 sponds to the world of sense 1 in the classes of 
 things which it includes. To the Intelligible World, 
 man's mind ascends, by a triple road which Plo- 
 tinus figuratively calls that of the Musician, the 
 Lover, the Philosopher 2 . The activity of the human 
 soul is identified by analogy with the motion of 
 the heavens. "This activity is about a middle 
 point, and thus it is circular; but a middle point 
 
 1 vi. Ennead, iii. 1. Mi. E. ii. 2. 
 
302 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 is not the same in body and in the soul ; in that, 
 the middle point is local, in this, it is that on 
 which the rest depends. There is, however, an 
 analogy ; for as in one case, so in the other, there 
 must be a middle point, and as the sphere revolves 
 about its center, the soul revolves about God 
 through its affections." 
 
 The conclusion of the work is 3 , as might be 
 supposed, upon the approach to, union with, and 
 fruition of God. The author refers again to the 
 analogy between the movements of the soul and 
 those of the heavens. " We move round him like 
 a choral dance ; even when we look from him we 
 revolve about him ; we do not always look at him, 
 but when we do, we have satisfaction and rest, and 
 the harmony which belongs to that divine move- 
 ment. In this movement, the mind beholds the 
 fountain of life, the fountain of mind, the origin 
 of being, the cause of good, the root of the soul 4 ." 
 " There will be a time when this vision shall be 
 continual; the mind being no more interrupted, 
 nor suffering any perturbation from the body. Yet 
 that which beholds is not that which is disturbed ; 
 and when this vision becomes dim, it does not 
 obscure the knowledge which resides in demon- 
 stration, and faith, and reasoning; but the vision 
 itself is not reason, but greater than reason, and 
 before reason 5 .'* 
 
 The fifth book of the third Ennead, has for its 
 
 3 vi. Eim. ix. 8. 4 Ib. 9. Ib. 10. 
 
THEIR MYSTICISM. 303 
 
 subject the Daemon which belongs to each man. 
 It is entitled "Concerning Love;" and the doc- 
 trine appears to be, that the Love, or common 
 source of the passions which is in each man's mind, 
 is "the Daemon which they say accompanies each 
 man 6 ." These daemons were, however, (at least 
 by later writers,) invested with a visible aspect and 
 with a personal character, including a resemblance 
 of human passions and motives. It is curious thus 
 to see an untenable and visionary generalization 
 falling back into the domain of the senses and the 
 fancy, after a vain attempt to support itself in the 
 region of the reason. This imagination soon pro- 
 duced pretensions to the power of making these 
 daemons or genii visible; and the Treatise on the 
 Mysteries of the Egyptians, which is attributed to 
 lamblichus, gives an account of the secret cere- 
 monies, the mysterious words, the sacrifices and 
 expiations, by which this was to be done. 
 
 It is unnecessary for us to dwell on the progress 
 of this school ; to point out the growth of the The- 
 urgy which thus arose ; or to describe the attempts 
 to claim a high antiquity for this system, and to 
 make Orpheus, the poet, the first promulgator of 
 its doctrines. The system, like all mystical systems, 
 assumed the character rather of a religion than 
 of a theory. The opinions of its disciples materially 
 influenced their lives. It gave the world the spec- 
 tacle of an austere morality, a devotional exaltation, 
 
 6 Ficinus, Comm. in v. Enn. iii. 
 
304 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 combined with the grossest superstitions of Pagan- 
 ism. The successors of lamblichus appeared rather 
 to hold a priesthood, than the chair of a philoso- 
 phical school 7 . They were persecuted by Constan- 
 tine and Constantius, as opponents of Christianity. 
 Sopater, a Syrian philosopher of this school, was 
 beheaded by the former emperor, on a charge that 
 he had bound the winds by the power of magic 8 . 
 But Julian, who shortly after succeeded to the 
 purple, embraced with ardour the opinions of lam- 
 blichus. Proclus (who died A.D. 487,) was one of 
 the greatest of the teachers of this school 9 ; and 
 was, both in his life and doctrines, a worthy suc- 
 cessor of Plotinus, Porphyry, and lamblichus. We 
 possess a biography, or rather a panegyric of him, 
 by his disciple Marinus, in which he is exhibited 
 as a representation of the ideal perfection of the 
 philosophic character, according to the views of 
 the Neoplatonists. His virtues are arranged as 
 physical, moral, purificatory, theoretic, and theurgic. 
 Even in his boyhood, Apollo and Minerva visited 
 him in his dreams: he studied oratory at Alex- 
 andria, but it was at Athens that Plutarch and 
 Lysianus initiated him in the mysteries of the New 
 Platonists. He received a kind of consecration at 
 the hands of the daughter of Plutarch, the cele- 
 brated Asclepigenia, who introduced him to the 
 traditions of the Chaldeans, and the practices of 
 theurgy; he was also admitted to the mysteries 
 7 Deg. iii. 407- * Gibbon, iii. 352. 9 Deg. iii 419. 
 
THEIR MYSTICISM. 305 
 
 of Eleusis. He became celebrated for his knowledge 
 and eloquence; but especially for his skill in the 
 supernatural arts which were connected with the 
 doctrines of his sect. He appears before us rather 
 as a hierophant than a philosopher. A large por- 
 tion of his life was spent in evocations, purifications, 
 fastings, prayers, hymns, intercourse with appari- 
 tions, and with the gods, and in the celebration 
 of the festivals of Paganism, especially those which 
 were held in honour of the Mother of the Gods. 
 His religious admiration extended to all forms of 
 mythology. The philosopher, said he, is not the 
 priest of a single religion, but of all the religions 
 in the world. Accordingly, he composed hymns in 
 honour of all the divinities of Greece, Rome, Egypt, 
 Arabia ; Christianity alone was excluded from his 
 favour (M). 
 
 2. Mystical Arithmetic. It is unnecessary 
 further to exemplify, from Proclus, the general 
 mystical character of the school and time to which 
 he belonged; but we may notice more specially 
 one of the forms of this mysticism, which very 
 frequently offers itself to our notice, especially in 
 him ; and which we may call Mystical Arithmetic. 
 Like all the kinds of Mysticism, this consists in 
 the attempt to connect our conceptions of external 
 objects by general and inappropriate notions of 
 goodness, perfection, and relation to the divine 
 essence and government ; instead of referring such 
 conceptions to those appropriate ideas, which, by 
 VOL. i. X 
 
306 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 due attention, become perfectly distinct, and capa- 
 ble of being positively applied and verified. The 
 subject which is thus dealt with, in the doctrines 
 of which we now speak, is Number; a notion 
 which tempts men into these visionary specula- 
 tions more naturally than any other. For num- 
 ber is really applicable to moral notions, to 
 emotions and feelings, and to their objects, as 
 well as to the things of the material world. More- 
 over, by the discovery of the principle of musical 
 concords, it had been found, probably most unex- 
 pectedly, that numerical relations were closely 
 connected with sounds which could hardly be dis- 
 tinguished from the expression of thought and 
 feeling; and a suspicion might easily arise, that 
 the universe, both of matter and of thought, might 
 contain many general and abstract truths of some 
 analogous kind. The relations of number have so 
 wide a bearing, that the ramifications of such a sus- 
 picion could not easily be exhausted, supposing men 
 willing to follow them into darkness and vague- 
 ness; which it is precisely the mystical tendency 
 to do. Accordingly, this kind of speculation ap- 
 peared very early, and showed itself first among 
 the Pythagoreans, as we might have expected, from 
 the attention which they gave to the theory of har- 
 mony : and this, as well as some other of the doc- 
 trines of the Pythagorean philosophy, was adopted 
 by the later Platonists, and, indeed, by Plato him- 
 self, whose speculations concerning number have 
 
THEIR MYSTICISM. 307 
 
 decidedly a mystical character. The mere mathe- 
 matical relations of numbers, as odd and even, 
 perfect and imperfect, abundant and defective, 
 were, by a willing submission to an enthusiastic 
 bias, connected with the notions of good and beauty, 
 which were suggested by the terms expressing 
 their relations ; and principles resulting from such 
 a connexion were woven into a wide and complex 
 system. It is not necessary to dwell long on this 
 subject ; the mere titles of the works which treated 
 of it show its nature. Archytas 10 is said to have 
 written a treatise on the number ten : Telauge, 
 the daughter of Pythagoras, wrote on the number 
 four. This number, indeed, which was known by 
 the name of the Tetractys, was very celebrated 
 in the school of Pythagoras. It is mentioned in 
 the "Golden Verses," which are ascribed to him: 
 the pupil is conjured to be virtuous, 
 
 Ncu fj.d TOV dpcTepa ^"X? Trapa<)ovTa TCTpaKTuv 
 Ylaydv devvctov (pv(jew<$ 
 
 By him who stampt The Four upon the mind, 
 The .Fowr, the fount of nature's endless stream. 
 
 In Plato's works, we have evidence of a similar 
 belief in religious relations of Number ; and in 
 the New Platonists, this doctrine was established 
 as a system. Proclus, of whom we have been 
 speaking, founds his philosophy, in a great mea- 
 sure, on the relation of Unity and Multiple ; from 
 this, he is led to represent the causality of the 
 10 Mont. ii. 123. 
 
 X2 
 
308 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 Divine Mind by three Triads of abstractions; and 
 in the developement of one part of this system, 
 the number seven is introduced 11 . "The intelli- 
 gible and intellectual gods produce all things tria- 
 dically ; for the monads in these latter are divided 
 according to number ; and what the monad was in 
 the former, the number is in these latter. And the 
 intellectual gods produce all things hebdomically ; 
 for they evolve the intelligible, and at the same 
 time intellectual triads, into intellectual hebdo- 
 mads, and expand their contracted powers into 
 intellectual variety." Seven is what is called by 
 arithmeticians a prime number, that is, it cannot 
 be produced by the multiplication of other num- 
 bers. In the language of the New Platonists, the 
 number seven is said to be a virgin, and without 
 a mother, and it is therefore sacred to Minerva. 
 The number six is a perfect number, and is con- 
 secrated to Venus. 
 
 The relations of space were dealt with in like 
 manner, the geometrical properties being associated 
 with such physical and metaphysical notions as 
 vague thought and lively feeling could anyhow 
 connect with them. We may consider, as an ex- 
 ample of this 1G , Plato's opinion concerning the par- 
 ticles of the four elements. He gave to each kind 
 of particle one of the five regular solids, about 
 which the geometrical speculations of himself and 
 his pupils had been employed. The particles of 
 
 n Procl. v. 3, Taylor's Translation. 12 Stanley, Hist. Phil. 
 
THEIR MYSTICISM. 309 
 
 fire were pyramids, because they are sharp, and 
 tend upwards; those of earth are cubes, because 
 they are stable, and fill space ; the particles of air 
 are octahedral, as most nearly resembling those of 
 fire ; those of water are icositetrahedron, as most 
 nearly spherical. The dodecahedron is the figure 
 of the element of the heavens, and shows its in- 
 fluence in other things, as in the twelve signs of 
 the zodiac. In such examples we see how loosely 
 space and number are combined or confounded by 
 these mystical visionaries. 
 
 These numerical dreams of ancient philosphers 
 have been imitated by modern writers; for instance, 
 by Peter Bungo and Kircher, who have written 
 De Mysteriis Numerorum. Bungo treats of the 
 mystical properties of each of the numbers in 
 order, at great length. And such speculations 
 have influenced astronomical theories. In the first 
 edition of the Alphonsine tables 13 , the precession 
 was represented by making the first point of Aries 
 move, in a period of 7000 years, through a circle 
 of which the radius was 18 degrees, while the circle 
 moved round the ecliptic in 49,000 years; and 
 these numbers, 7000 and 49,000, were chosen pro- 
 bably by Jewish calculators, or with reference to 
 Judaical Sabbatarian notions. 
 
 3. Astrology. Of all the forms which mysticism 
 assumed, none was cultivated more assiduously 
 than astrology. Although this art prevailed most 
 13 Montucla, i. 511. 
 
310 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 universally and powerfully during the stationary 
 period, its existence, even as a detailed technical 
 system, goes back to a very early age. It pro- 
 bably had its origin in the East; it is universally 
 ascribed to the Babylonians and Chaldeans; the 
 name Chaldean was, at Rome, synonymous with 
 mathematicus, or astrologer ; and we read repeat- 
 edly that this class of persons were expelled from 
 Italy by a decree of the senate, both during the 
 times of the republic and of the empire 14 . The 
 recurrence of this act of legislation shows that it 
 was not effectual ; " It is a class of men," says 
 Tacitus, "which, in our city, will always be pro- 
 hibited, and will always exist." In Greece, it does 
 not appear that the state showed any hostility to 
 the professors of this art. They undertook, it 
 would seem, then, as at a later period, to determine 
 the course of a man's character and life from the 
 configuration of the stars at the moment of his 
 birth. We do not possess any of the speculations 
 of the earlier astrologers ; and we cannot therefore 
 be certain that the notions which operated in men's 
 minds when the art had its birth, agreed with the 
 views on which it was afterwards defended, when 
 it became a matter of controversy. But it ap- 
 pears probable, that, though it was at later periods 
 supported by physical analogies, it was originally 
 suggested by mythological belief. The Greeks 
 spoke of the influences or effluxes (airoppotas) which 
 
 14 Tacit. Ann. ii. 32. xii. 52. Hist. I. 22, II. 62. 
 
THEIR MYSTICISM. 311 
 
 proceeded from the stars ; but the Chaldeans had 
 probably thought rather of the powers which they 
 exercised as deities. In whatever manner the 
 sun, moon, and planets came to be identified with 
 gods and goddesses, it is clear that the characters 
 ascribed to these gods and goddesses regulate the 
 virtues and powers of the stars which bear their 
 names. This association, so manifestly visionary, 
 was retained, amplified, and pursued, in an enthu- 
 siastic spirit, instead of being rejected for more 
 distinct and substantial connexions; and a pre- 
 tended science was thus formed, which bears the 
 obvious stamp of mysticism. 
 
 That common sense of mankind which teaches 
 them that theoretical opinions are to be calmly 
 tried by their consequences and their accordance 
 with facts, appears to have counteracted the pre- 
 valence of astrology in the better times of the 
 human mind. Eudoxus, as we are informed by 
 Cicero 15 , rejected the pretensions of the Chaldeans; 
 and Cicero himself reasons against them with ar- 
 guments as sensible and intelligent as could be 
 adduced by a writer of the present day; such as 
 the different fortunes and characters of persons 
 born at the same time ; and the failure of the pre- 
 dictions, in the case of Pompey, Crassus, Csesar, to 
 whom the astrologers had foretold glorious old age 
 and peaceful death. He also employs an argument 
 which the reader would perhaps not expect from 
 15 Cic. de Div. ii. 42. 
 
312 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 him, the very great remoteness of the planets as 
 compared with the distance of the moon. " What 
 contagion can reach us," he asks, " from a distance 
 almost infinite ?" 
 
 Pliny argues on the same side, and with some 
 of the same arguments 16 . "Homer," he says, "tells 
 us that Hector and Polydamas were born the 
 same night ; men of such different fortune. And 
 every hour, in every part of the world, are born 
 lords and slaves, kings and beggars." 
 
 The impression made by these arguments is 
 marked in an anecdote told concerning Publius 
 Nigidius Figulus, a Roman of the time of Julius 
 Ca?sar, whom Lucan mentions as a celebrated astro- 
 loger. It is said, that when an opponent of the 
 art urged as an objection the different fates of 
 persons born in two successive instants, Nigidius 
 bade him make two contiguous marks on a potter's 
 wheel, which was revolving rapidly near them. On 
 stopping the wheel, the two marks were found to 
 be really far removed from each other; and Ni- 
 gidius is said to have received the name of Figulus 
 (the potter), in remembrance of this story. His 
 argument, says St. Augustine, who gives us the 
 narrative, was as fragile as the ware which the 
 wheel manufactured. 
 
 As the darkening times of the Roman empire 
 advanced, even the stronger minds seem to have 
 lost the clear energy which was requisite to throw 
 16 Hist. Nat. vii. 49. 
 
THEIR MYSTICISM. 313 
 
 off this delusion. Seneca appears to take the 
 influence of the planets for granted; and even 
 Tacitus 17 seems to hesitate. "For my own part," 
 says he, " I doubt ; but certainly the majority of 
 mankind cannot be weaned from the opinion, that, 
 at the birth of each man, his future destiny is 
 fixed ; though some things may fall out differently 
 from the predictions, by the ignorance of those 
 who profess the art ; and that thus the art is un- 
 justly blamed, confirmed as it is by noted examples 
 in all ages." The occasion which gives rise to 
 these reflections of the historian is the mention of 
 Thrasyllus, the favourite astrologer of the Emperor 
 Tiberius, whose skill is exemplified in the follow- 
 ing narrative. Those who were brought to Tiberius 
 on any important matter, were admitted to an 
 interview in an apartment situated on a lofty cliff 
 in the island of Capreae. They reached this place 
 by a narrow path, accompanied by a single freed- 
 man of great bodily strength ; and on their return, 
 if the emperor had conceived any doubts of their 
 trustworthiness, a single blow buried the secret 
 and its victim in the ocean below. After Thra- 
 syllus had, in this retreat, stated the results of his 
 art as they concerned the emperor, Tiberius asked 
 him whether he had calculated how long he him- 
 self had to live. The astrologer examined the 
 aspect of the stars, and while he did this, as the 
 narrative states, showed hesitation, alarm, increas- 
 17 Ann. vi. 22. 
 
314 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 ing terrour, and at last declared that, " the present 
 hour was for him critical, perhaps fatal." Tiberius 
 embraced him, and told him " he was right in 
 supposing he had been in danger, but that he 
 should escape it ;" and made him thenceforth his 
 confidential counsellor. 
 
 The belief in the power of astrological predic- 
 tion which thus obtained dominion over the minds 
 of men of literary cultivation and practical energy, 
 naturally had a more complete sway among the 
 speculative but unstable minds of the later philo- 
 sophical schools of Alexandria, Athens, and Rome. 
 We have a treatise on astrology by Proclus, which 
 will serve to exemplify the mystical principle in 
 this form. It appears as a commentary on a work 
 on the same subject called " Tetrabiblos," ascribed 
 to Ptolemy; though we may reasonably doubt whe- 
 ther the author of the " Megale Syntaxis" was also 
 the writer of the astrological work. A few notices 
 of the commentary of Proclus will suffice 18 . The 
 science is defended by urging how powerful we 
 know the physical effects of the heavenly bodies to 
 be. " The sun regulates all things on earth ; the 
 birth of animals, the growth of fruits, the flowing 
 of waters, the change of health, according to the 
 seasons ; he produces heat, moisture, dryness, cold, 
 according to his approach to our zenith. The moon, 
 which is the nearest of all bodies to the earth, gives 
 out much influence ; and all things, animate and 
 
 18 I. 2. 
 
THEIR MYSTICISM. 315 
 
 inanimate, sympathize with her; rivers increase 
 and diminish according to her light; the advance of 
 the sea, and its recess, are regulated by her rising 
 and setting ; and along with her, fruits and animals 
 wax and wane, either wholly or in part." It is easy 
 to see that by pursuing this train of associations 
 (some real and some imaginary) very vaguely and 
 very enthusiastically, the connexions which astro- 
 logy supposes would receive a kind of countenance. 
 Proclus then proceeds to state 19 the doctrines of 
 the science. "The Sun," he says, "is productive 
 of heat and dryness ; this power is moderate in its 
 nature, but is more perceived than that of the 
 other luminaries, from his magnitude, and from the 
 change of seasons. The nature of the Moon is for 
 the most part moist ; for being the nearest to the 
 earth, she receives the vapours which rise from 
 moist bodies, and thus she causes bodies to soften 
 and rot. But by the illumination she receives from 
 the sun, she partakes in a moderate degree of heat. 
 Saturn is cold and dry, being most distant both 
 from the heating power of the sun, and the moist 
 vapours of the earth. His cold, however, is most 
 prevalent, his dryness is more moderate. Both he 
 and the rest receive additional powers from the 
 configurations which they make with respect to the 
 sun and moon." In the same manner it is remarked 
 that Mars is dry and caustic, from his fiery nature, 
 which, indeed, his colour shows. Jupiter is well 
 
 19 I. 4, 
 
316 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 compounded of warm and moist, as is Venus. Mer- 
 cury is variable in his character. From these no- 
 tions were derived others concerning the beneficial 
 or hurtful effect of these stars. Heat and moisture 
 are generative and creative elements ; hence the 
 ancients, says Proclus, deemed Jupiter, and Venus, 
 and the Moon, to have a good power; Saturn and 
 Mercury, on the other hand, had an evil nature. 
 
 Other distinctions of the character of the stars 
 are enumerated, equally visionary, and suggested by 
 the most fanciful connexions. Some are masculine, 
 and some feminine : the Moon and Venus are of 
 the latter kind. This appears to be merely a my- 
 thological or etymological association. Some are 
 diurnal, some nocturnal ; the Moon and Venus are 
 of the latter kind, the Sun and Jupiter of the for- 
 mer ; Saturn and Mars are both. 
 
 The fixed stars, also, and especially those of the 
 zodiac, had especial influences and subjects assigned 
 to them. In particular, each sign was supposed to 
 preside over a particular part of the body; thus 
 Aries had the head assigned to it, Taurus the neck, 
 and so on. 
 
 The most important part of the sky in the 
 astrologer's consideration, was that sign of the zo- 
 diac which rose at the moment of the child's birth ; 
 this was, properly speaking, the horoscope, the as- 
 cendant, or the first house ; the whole circuit of the 
 heavens being divided into twelve houses, in which 
 
THEIR MYSTICISM. 317 
 
 life and death, marriage and children, riches and 
 honours, friends and enemies, were distributed. 
 
 We need not attempt to trace the progress of 
 this science. It prevailed extensively among the 
 Arabians, as we might expect from the character 
 of that nation. Albumasar, of Balkh in Khorasan, 
 who flourished in the ninth century, who was one 
 of their greatest astronomers, was also a great as- 
 trologer; and his work on the latter subject, "De 
 Magnis Conjunctionibus, Annorum Revolutionibus 
 ac eorum Perfectionibus," was long celebrated in 
 Europe. Aboazen Haly (the writer of a treatise 
 "De Judiciis Astrorum,") who lived in Spain in 
 the thirteenth century, was one of the classical 
 authors on this subject. 
 
 It will easily be supposed that when this apo- 
 telesmatic or judicial astrology obtained firm pos- 
 session of men's minds, it would be pursued into 
 innumerable subtle distinctions and extravagant 
 conceits; and the more so, as experience could 
 offer little or no check to such exercises of fancy 
 and subtlety. For the correction of rules of astro- 
 logical divination by comparison with known events, 
 though pretended to by many professors of the 
 art, was far too vague and fallible a guidance to 
 be of any real advantage. Even in what has been 
 called Natural Astrology, the dependence of the 
 weather on the heavenly bodies, it is easy to see 
 what a vast accumulation of well-observed facts is 
 requisite to establish any true rule ; and it is well 
 
318 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 known how long, in spite of facts, false and ground- 
 less rules (as the dependence of the weather on the 
 moon) may keep their hold on men's minds. When 
 the facts are such loose and many-sided things as 
 human characters, passions, and happiness, it was 
 hardly to be expected that even the most powerful 
 minds should be able to find a footing sufficiently 
 firm, to enable them to resist the impression of a 
 theory constructed of sweeping and bold assertions, 
 and filled out into a complete system of details. 
 Accordingly, the connexion of the stars with human 
 persons and actions was, for a long period, un- 
 disputed. The vague, obscure, and heterogeneous 
 character of such a connexion, and its unfitness 
 for any really scientific reasoning, could, of course, 
 never be got rid of: and the bewildering feeling 
 of earnestness and solemnity, with which the con- 
 nexion of the heavens with man was contemplated, 
 never died away. In other respects, however, the 
 astrologers fell into a servile commentatorial spirit; 
 and employed themselves in annotating and illus- 
 trating the works of their predecessors to a con- 
 siderable extent, before the revival of true science. 
 It may be mentioned, that astrology has long 
 been, and probably is, an art held in great esteem 
 and admiration among other eastern nations besides 
 the Mohammedans : for instance, the Jews, the 
 Indians, the Siamese, and the Chinese. The pre- 
 valence of vague, visionary, and barren notions 
 among these nations, cannot surprize us; for with 
 
THEIR MYSTICISM. 319 
 
 regard to them wo have no evidence, as with re- 
 gard to Europeans we have, that they are capable, 
 on subjects of physical speculation, of originating 
 sound and rational general principles. The Arts 
 may have had their birth in all parts of the globe ; 
 but it is only Europe, at particular favoured 
 periods of its history, which has ever produced 
 Sciences. 
 
 We are, however, now speaking of a long 
 period, during which this productive energy was 
 interrupted and suspended. During this period 
 Europe descended, in intellectual character, to the 
 level at which the other parts of the world have 
 always stood. Her Science was then a mixture 
 of Art and Mysticism ; we have considered several 
 forms of this Mysticism, but there are two others 
 which must not pass unnoticed, Alchemy and Magic. 
 
 We may observe, before we proceed, that the 
 deep and settled influence which Astrology had ob- 
 tained among men, appears perhaps most strongly 
 in the circumstance, that the most vigorous and 
 clear-sighted minds which were concerned in the 
 revival of science, did not, for a long period, shake 
 off the persuasion, that there was, in this art, some 
 element of truth. Roger Bacon, Cardan, Kepler, 
 Tycho Brahe, Francis Bacon, are examples of this. 
 These, or most of them, rejected all the more ob- 
 vious and extravagant absurdities with which the 
 subject had been loaded; but still conceived that 
 some real and valuable truth remained when all 
 
320 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 these were removed. Thus Campanella 50 , whom 
 we shall have to speak of as one of the first op- 
 ponents of Aristotle, wrote an " Astrology purified 
 from all the Superstitions of the Jews and Ara- 
 bians, and treated physiologically." 
 
 4. Alchemy. Like other kinds of Mysticism, 
 Alchemy seems to have grown out of the notions of 
 moral, personal, and mythological qualities, which 
 men associated with terms, of which the primary 
 application was to physical properties. This is 
 the form in which the subject is presented to us 
 in the earliest writings which we possess on the 
 subject of chemistry ; those of Geber 21 of Seville, 
 who is supposed to have lived in the eighth or 
 ninth century. The very titles of Geber's works 
 show the notions on which this pretended science 
 proceeds. They are, "Of the Search of Perfec- 
 tion ;" " Of the Sum of Perfection, or of the Perfect 
 Magistery ;" " Of the Invention of Verity, or Per- 
 fection." The basis of this phraseology is the dis- 
 tinction of metals into more or less perfect ; gold 
 being the most perfect, as being the most valuable, 
 most beautiful, most pure, most durable; silver 
 the next ; and so on. The " Search of Perfection," 
 was, therefore, the attempt to convert other metals 
 into gold ; and doctrines were adopted which re- 
 presented the metals as all compounded of the 
 same elements, so that this was theoretically pos- 
 
 20 Bacon, De Aug. Hi. 4. 
 
 2J Thomson's Hist, of Chem. i. 117. 
 
THEIR MYSTICISM. 321 
 
 sible. But the mystical trains of association were 
 pursued much further than this; gold and silver 
 were held to be the most noble of metals; gold 
 was their King, and silver their Queen. Mytho- 
 logical associations were called in aid of these 
 fancies, as had been done in astrology. Gold was 
 Sol, the sun ; silver was Luna, the moon ; copper, 
 iron, tin, lead, were assigned to Venus, Mars, Ju- 
 piter, Saturn. The processes of mixture and heat 
 were spoken of as personal actions and relations, 
 struggles and victories. Some elements were con- 
 querors, some conquered ; there existed prepara- 
 tions which possessed the power of changing the 
 whole of a body into a substance of another kind : 
 these were called magisteries 22 . When gold and 
 quicksilver are combined, the king and the queen 
 are married, to produce children of their own 
 kind. It will easily be conceived, that when che- 
 mical operations were described in phraseology of 
 this sort, the enthusiasm of the fancy would be 
 added to that of the hopes, and observation would 
 not be permitted to correct the delusion, or to 
 suggest sounder and more rational views. 
 
 The exaggeration of the vague notion of per- 
 fection and power in the object of the alchemist's 
 search, was carried further still. The same prepa- 
 ration which possessed the faculty of turning baser 
 metals into gold, was imagined to be also a uni- 
 versal medicine, to have the gift of curing or pre- 
 
 28 Boyle, Thomson's Hist. Ch. i. 25. Carolus Musitanus. 
 VOL. I. Y 
 
322 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 venting diseases, prolonging life, producing bodily 
 strength and beauty : the philosophers' stone was 
 finally invested with every desirable efficacy which 
 the fancy of the " philosophers" could devise. 
 
 It has been usual to say that Alchemy was the 
 mother of Chemistry; and that men would never 
 have made the experiments on which the real sci- 
 ence is founded, if they had not been animated 
 by the hopes and the energy which the delusive 
 art inspired. To judge whether this is truly said, 
 we must be able to estimate the degree of interest 
 which men feel in purely speculative truth, and 
 in the real and substantial improvement of art to 
 which it leads. Since the fall of Alchemy, and 
 the progress of real Chemistry, these motives have 
 been powerful enough to engage in the study of 
 the science, a body far larger than the Alchemists 
 ever were, and no less zealous. There is no ap- 
 parent reason why the result should not have been 
 the same, if the progress of true science had begun 
 sooner. Astronomy was long cultivated without 
 the bribe of Astrology. But, perhaps, we may 
 justly say this; that, in the stationary period, 
 men's minds were so far enfeebled and degraded, 
 that pure speculative truth had not its full effect 
 upon them; and the mystical pursuits in which 
 some dim and disfigured images of truth were 
 sought with avidity, were among the provisions by 
 which the human soul, even when sunk below its 
 best condition, is perpetually directed to something 
 
THEIR MYSTICISM. 323 
 
 above the mere objects of sense and appetite; 
 a contrivance of compensation, as it were, in the 
 intellectual and spiritual constitution of man. 
 
 5. Magic. Magical Arts, so far as they were 
 believed in by those who professed to practise 
 them, and so far as they have a bearing in science, 
 stand on the same footing as astrology; and, in- 
 deed, a close alliance has generally been main- 
 tained between the two pursuits. Incapacity and 
 indisposition to perceive natural and philosophical 
 causation, an enthusiastic imagination, and such a 
 faith as can devise and maintain supernatural and 
 spiritual connexions, are the elements of this, as 
 of other forms of Mysticism. And thus that temper 
 which led men to aim at the magician's supposed 
 authority over the elements, is an additional ex- 
 emplification of those habits of thought which 
 prevented the progress of real science, and the 
 acquisition of that command over nature which is 
 founded on science, during the interval now before 
 us. 
 
 But there is another aspect under which the 
 opinions connected with this pursuit may serve to 
 illustrate the mental character of the stationary 
 period. 
 
 The tendency, during the middle ages, to at- 
 tribute the character of Magician to almost all 
 persons eminent for great speculative or practical 
 knowledge, is a feature of those times, which shows 
 how extensive and complete was the inability to 
 
 Y2 
 
324 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 apprehend the nature of real science. In cultivated 
 and enlightened periods, such as those of ancient 
 Greece, or modern Europe, knowledge is wished 
 for and admired, even by those who least possess 
 it: but in dark and degraded periods, superior 
 knowledge is a butt for hatred and fear. In the 
 one case, men's eyes are open; their thoughts are 
 clear ; and, however high the philosopher may be 
 raised above the multitude, they can catch glimpses 
 of the intervening path, and see that it is free 
 to all, and that elevation is the reward of energy 
 and labour. In the other case, the crowd are 
 not only ignorant, but spiritless ; they have lost 
 the pleasure in knowledge, the appetite for it, 
 and the feeling of dignity which it gives : there is 
 no sympathy which connects them with the learned 
 man : they see him above them, but know not how 
 he is raised or supported: he becomes an object 
 of aversion and envy, of vague suspicion and terror; 
 and these emotions are embodied and confirmed 
 by association with the fancies and dogmas of 
 superstition. To consider superior knowledge as 
 Magic, and Magic as a detestable and criminal em- 
 ployment, was the form which these feelings of 
 dislike assumed ; and at one period in the history 
 of Europe, almost every one who had gained any 
 eminent literary fame, was spoken of as a magician. 
 Naudseus, a learned Frenchman, in the seventeenth 
 century, wrote " An Apology for all the Wise Men 
 who have been unjustly reported Magicians, from 
 
THEIR MYSTICISM. 325 
 
 the Creation to the present Age." The list of per- 
 sons whom he thus thinks it necessary to protect, 
 are of various classes and ages. Alkindi, Geber, 
 Artephius, Thebit, Raymund Lully, Arnold de Villa 
 Nova, Peter of Apono, and Paracelsus, had in- 
 curred the black suspicion as physicians or alche- 
 mists. Thomas Aquinas, Roger Bacon, Michael 
 Scot, Picus of Mirandula, and Trithemius, had not 
 escaped it, though ministers of religion. Even 
 dignitaries, such as Robert Grosteste, bishop of Lin- 
 coln, Albertus Magnus, bishop of Ratisbon, Popes 
 Sylvester the Second, and Gregory the Seventh, 
 had been involved in the wide calumny. In the 
 same way in which the vulgar confounded the 
 eminent learning and knowledge which had ap- 
 peared in recent times, with skill in dark and 
 supernatural arts, they converted into wizards all 
 the best-known names in the rolls of fame ; as 
 Aristotle, Solomon, Joseph, Pythagoras; and, finally, 
 the poet Virgil was a powerful and skilful necro- 
 mancer, and this fancy was exemplified by many 
 strange stories of his achievements and prac- 
 tices. 
 
 The various results of the tendency of the human 
 mind to mysticism, which we have here noticed, 
 form prominent features in the intellectual charac- 
 ter of the world, for a long course of centuries. 
 The theosophy and theurgy of the Neoplatonists, 
 the mystical arithmetic of the Pythagoreans and 
 
326 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 their successors, the predictions of the astrologers, 
 the pretences of alchemy and magic, represent, not 
 unfairly, the general character and disposition of 
 men's thoughts, with reference to philosophy and 
 science. That there were stronger minds, which 
 threw off in a greater or less degree this train of 
 delusive and unsubstantial ideas, is true ; as, on the 
 other hand, Mysticism, among the vulgar or the 
 foolish, often went to an extent of extravagance 
 and superstition, of which I have not attempted to 
 convey any conception. The lesson which the pre- 
 ceding survey teaches us is, that during the sta- 
 tionary period, Mysticism, in its various forms, was 
 a leading character, both of the common mind, and 
 of the speculations of the most intelligent and pro- 
 found reasoners; and that this Mysticism was the 
 opposite of that habit of thought which we have 
 stated Science to require ; namely, clear Ideas, dis- 
 tinctly employed to connect well-ascertained Facts ; 
 inasmuch as the Ideas in which it dealt were vague 
 and unstable, and the temper in which they were 
 contemplated was an urgent and aspiring enthu- 
 siasm, which could not submit to a calm conference 
 with experience upon even terms. The fervour of 
 thought in some degree supplied the place of reason 
 in producing belief; but opinions so obtained had 
 no enduring value ; they did not exhibit a per- 
 manent record of old truths, nor a firm foundation 
 for new. Experience collected her stores in vain, 
 
THEIR MYSTICISM. 327 
 
 or ceased to collect them, when she had only to 
 pour them into the flimsy folds of the lap of Mys- 
 ticism ; who was, in truth, so much absorbed in 
 looking for the treasures which were to fall from 
 the skies, that she heeded little how scantily she 
 obtained, or how loosely she held, such riches as 
 might be found near her. 
 
328 
 
 CHAPTER IV. 
 OF THE DOGMATISM OF THE STATIONARY PERIOD. 
 
 IN speaking of the character of the age of com- 
 mentators, we noticed principally the ingenious 
 servility which it displays; the acuteness with 
 which it finds ground for speculation in the ex- 
 pression of other men's thoughts ; the want of all 
 vigour and fertility in acquiring any real and new 
 truths. Such was the character of the reasoners of 
 the stationary period from the first ; but, at a later 
 day, this character, from various causes, was modi- 
 fied by new features. The servility which had 
 yielded itself to the yoke, insisted upon forcing it 
 on the necks of others ; the subtlety which found all 
 the truth it needed in certain accredited writings, 
 resolved that no one should find there, or in any 
 other region, any other truths; speculative men 
 became tyrants without ceasing to be slaves; to 
 their character of commentators they added that of 
 dogmatists. 
 
 1. Origin of the Scholastic Philosophy. The 
 causes of this change have been very happily ana- 
 lyzed and described by several modern writers 1 . 
 
 1 Dr. Hampden, in the Life of Thomas Aquinas, in the Encyc. 
 Metrop. Degerando, Hist. Comparee, vol. iv. Also Tennemann, 
 Hist, of Phil. vol. viii. Introduction. 
 
DOGMATISM OF THE STATIONARY PERIOD. 329 
 
 The general nature of the process may be briefly 
 stated to have been the following. 
 
 The tendencies of the later times of the Roman 
 empire to a commenting literature, and a second- 
 hand philosophy, have already been noticed. The 
 loss of the dignity of political freedom, the want of 
 the cheerfulness of advancing prosperity, and the 
 substitution of the less philosophical structure of 
 the Latin language for the delicate intellectual me- 
 chanism of the Greek ; fixed and augmented the pre- 
 valent feebleness and barrenness of intellect. Men 
 forgot, or feared, to consult nature, to seek for new 
 truths, to do what the great discoverers of other 
 times had done ; they were content to consult li- 
 braries, to study and defend old opinions, to talk of 
 what great geniuses had said. They sought their 
 philosophy in accredited treatises, and dared not 
 question such doctrines as they there found. 
 
 The character of the philosophy to which they 
 were thus led, was determined by this want of cou- 
 rage and originality. There are various antagonist 
 principles of opinion, which seem alike to have their 
 root in the intellectual constitution of man, and 
 which 'are maintained and developed by opposing 
 sects, when the intellect is in vigorous action. Such 
 principles are, for instance, the claims of Autho- 
 rity and of Reason to our assent; the source of 
 our knowledge in Experience or in Ideas; the 
 superiority of a Mystical or of a Skeptical turn of 
 thought. Such oppositions of doctrine were found 
 
330 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 in writers of the greatest fame ; and two of those, 
 who most occupied the attention of students, Plato 
 and Aristotle, were, on several points of this nature, 
 very diverse from each other in their tendency. The 
 attempt to reconcile these philosophers by Boethius 
 and others, we have already noticed; and the at- 
 tempt was so far successful, that it left on men's 
 minds the belief in the possibility of a great philo- 
 sophical system which should be based on both 
 these writers, and have a claim to the assent of all 
 sober speculators. 
 
 But, in the mean time, the Christian Religion 
 had become the leading subject of men's thoughts ; 
 and divines had put forward its claims to be, not 
 merely the guide of men's lives, and the means of 
 reconciling them to their heavenly Master; but also 
 to be a Philosophy in the widest sense in which the 
 term had been used ; a consistent speculative view 
 of man's condition and nature, and of the world in 
 which he is placed. 
 
 These claims had been acknowledged ; and, un- 
 fortunately, from the intellectual condition of the 
 times, with no due apprehension of the necessary 
 ministry of Observation, and Reason dealing with 
 observation, by which alone such a system can be 
 embodied. It was held, without any regulating 
 principle, that the Philosophy which had been 
 bequeathed to the world by the great geniuses of 
 heathen antiquity, and the Philosophy which was 
 deduced from, and implied by, the Revelations made 
 
DOGMATISM OF THE STATIONARY PERIOD. 331 
 
 by God to man, must be identical ; and therefore, 
 that Theology is the only true Philosophy. Indeed, 
 the Neoplatonists had already arrived, by other 
 roads, at the same conviction. John Scot Erigena, 
 in the reign of Alfred, and consequently before the 
 existence of the Scholastic Philosophy, properly so 
 called, had reasserted this doctrine 2 . Anselm, in 
 the eleventh century, again brought it forward 3 ; 
 and Bernard de Chartres, in the thirteenth 4 . 
 
 This view was confirmed by the opinion which 
 prevailed, concerning the nature of philosophical 
 truth ; a view supported by the theory of Plato, the 
 practice of Aristotle, and the general propensities 
 of the human mind : I mean the opinion that all 
 science may be obtained by the use of reasoning 
 alone ; that by analyzing and combining the no- 
 tions which common language brings before us, we 
 may learn all that we can know. Thus Logic came 
 to include the whole of Science ; and accordingly 
 this Abelard expressly maintained 5 . I have already 
 explained, in some measure, the fallacy of this be- 
 lief, which consists, as has been well said 6 , " in mis- 
 taking the universality of the theory of language 
 for the generalization of facts." But on all accounts 
 this opinion is readily accepted ; and it led at once 
 to the conclusion, that the Theological Philosophy 
 which we have described, is complete as well as 
 true. 
 
 8 Deg. iv. 351. 3 Ib. iv. 388. 4 Ib. iv. 418. 
 
 6 Ib. iv. 407. " Enc. Met. 807- 
 
332 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 Thus a Universal Science was established, with 
 the authority of a Religious Creed. Its universality 
 rested on erroneous views of the relation of words 
 and truths; its pretensions as a science were ad- 
 mitted by the servile temper of men's intellects ; 
 and its religious authority was assigned it, by 
 making all truth part of religion. And as Religion 
 claimed assent within her own jurisdiction under 
 the most solemn and imperative sanctions, Phi- 
 losophy shared in her imperial power, and dissent 
 from their doctrines was no longer blameless or 
 allowable. Errour became wicked, dissent became 
 heresy; to reject the received human doctrines, was 
 nearly the same as to doubt the Divine declarations. 
 The Scholastic Philosophy claimed the assent of all 
 believers. 
 
 The external form, the details, and the text 
 of this philosophy, were taken,* in a great measure, 
 from Aristotle ; though, in the spirit, the general 
 notions, and the style of interpretation, Plato and 
 the Platonists had no inconsiderable share. Various 
 causes contributed to the elevation of Aristotle to 
 this distinction. His Logic had early been adopted 
 as an instrument of theological disputation; and 
 his spirit of systematization, of subtle distinction, 
 and of analysis of words, as well as his disposition 
 to argumentation, afforded the most natural and 
 grateful employment to the commentating pro- 
 pensities. Those principles which we before noted 
 as the leading points of his physical philosophy, 
 
DOGMATISM OF THE STATIONARY PERIOD. 333 
 
 were selected and adopted ; and these, presented in 
 a most technical form, and applied in a systematic 
 manner, constitute a large portion of the philosophy 
 of which we now speak, so far as it pretends to deal 
 with physics. 
 
 2. Scholastic Dogmas. But before the com- 
 plete ascendancy of Aristotle was thus established, 
 when something of an intellectual waking took 
 place after the darkness and sleep of the ninth and 
 tenth centuries, the Platonic doctrines seem to have 
 had, at first, a strong attraction for men's minds, as 
 better falling in with the mystical speculations and 
 contemplative piety which belonged to the times. 
 John Scot Erigena 7 may be looked upon as the 
 reviver of the New Platonism in the tenth century. 
 Towards the end of the eleventh, Peter Damien 8 , in 
 Italy, reproduced, involved in a theological discus- 
 sion, some Neoplatonic ideas. Godefroy 9 also, cen- 
 sor of St. Victor, has left a treatise*, entitled Micro- 
 cosmus ; this is founded on a mystical analogy, 
 often afterwards again brought forward, between 
 Man and the Universe. " Philosophers and theolo- 
 gians," says the writer, " agree in considering man 
 as a little world ; and as the world is composed of 
 four elements, man is endowed with four faculties, 
 the senses, the imagination, reason, and understand- 
 ing." Bernard of Chartres 10 , in his Megascosmus 
 and Microcosmus took up the same notions. Hugo, 
 
 7 Deg. iv. 35. 8 Ib. iv. 367. 9 Ib. iv. 413. 
 
 10 Ib. iv. 419. 
 
334 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 abbot of St. Victor, made a contemplative life the 
 main point and crown of his philosophy; and is 
 said to have been the first of the scholastic writers 
 who made psychology his special study 11 . He says 
 the faculties of the mind are "the senses, the 
 imagination, the reason, the memory, the under- 
 standing, and the intelligence." 
 
 Physics does not originally and properly form 
 any prominent part of the Scholastic Philosophy, 
 which consists mainly of a series of questions and 
 determinations upon the various points of a certain 
 technical divinity. Of this kind is the Book of 
 Sentences of Peter the Lombard (bishop of Paris), 
 who is, on that account, usually called "Magister 
 Sententiarum ;" a work which was published in the 
 twelfth century, and was long the text and standard 
 of such discussions. The questions are decided by 
 the authority of Scripture and of the Fathers of the 
 Church ; and are divided into four Books, of which 
 the first contains questions concerning God and the 
 doctrine of the Trinity in particular ; the second is 
 concerning the Creation; the third, concerning 
 Christ and the Christian Religion ; and the fourth 
 treats of Religious and Moral Duties. In the second 
 Book, as in many of the writers of this time, the 
 nature of Angels is considered in detail, and the 
 Orders of their Hierarchy, of which there were held 
 to be nine. The physical discussions enter only 
 as bearing upon the scriptural history of the crea- 
 11 Deg. iv. 4J5. 
 

 DOGMATISM OF THE STATIONARY PERIOD. 335 
 
 tion, and cannot be taken as a specimen of the 
 work ; but I may observe, that in speaking of the 
 division of the waters above the firmament, from 
 the waters under the firmament, he gives one opinion, 
 that of Bede, that the former waters are the solid 
 crystalline heavens in which the stars are fixed 12 , 
 "for crystal, which is so hard and transparent, is 
 made of water." But he mentions also the opi- 
 nion of St. Augustine, that the waters above the 
 heavens are there in a state of vapour (vapora- 
 liter) and in minute drops; "if, then, water can, 
 as we see in clouds, be so minutely divided that 
 it may be thus supported as vapour on air, which is 
 naturally lighter than water; why may we not 
 believe that it floats above that lighter celestial 
 element in still minuter drops and still lighter 
 vapours ? But in whatever manner the waters are 
 there, we do not doubt that they are there." 
 
 The celebrated Summa Theologice of Thomas 
 Aquinas is a work of the same kind ; and anything 
 which has a physical bearing forms an equally small 
 part of it. Thus, of the 512 Questions of the 
 Summa, there is only one (Part I., Quest. 115) "on 
 Corporeal Action," or on any part of the material 
 world; though there are several concerning the 
 celestial Hierarchies, as "on the Act of Angels," 
 "on the Speaking of Angels," "on the Subordi- 
 nation of Angels," " on Guardian Angels," and the 
 like. This, of course, would not be remarkable in a 
 
 12 Lib. ii. Distinct, xiv. De opere secundce diei. 
 
336 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 treatise on Theology, except this Theology were 
 intended to constitute the whole of Philosophy. 
 
 We may observe, that in this work, though 
 Plato, Avecibron, and many other heathen as well 
 as Christian philosophers, are adduced as authority, 
 Aristotle is referred to in a peculiar manner as 
 "the philosopher." This is nbticed by John of 
 Salisbury, as attracting attention in his time; (he 
 died A.D. 1182.) "The various masters of Dia- 
 lectic," says he 13 , "shine, each with his peculiar 
 merit; but all are proud to worship the footsteps 
 of Aristotle ; so much so, indeed, that the name 
 of philosopher, which belongs to them all, has been 
 pre-eminently appropriated to him. He is called 
 the philosopher autonomatice, that is, by excel- 
 lence." 
 
 The Question concerning Corporeal Action, in 
 Aquinas, is divided into six Articles ; and the con- 
 clusion delivered upon the first, is 14 , that "Body 
 being compounded of power and act, is active as 
 well as passive." Against this it is urged, that 
 quantity is an attribute of body, and that quantity 
 prevents action; that this appears in fact, since a 
 larger body is more difficult to move. The author 
 replies, that "quantity does not prevent corporeal 
 form from action altogether, but prevents it from 
 being a universal agent inasmuch as the form is 
 individualized, which, in matter subject to quantity, 
 it is. Moreover, the illustration deduced from the 
 
 13 Metalogicus, lib. ii. cap. 16. M Summce, P. i. Q. 115. Art. 1. 
 
DOGMATISM OF THE STATIONARY PERIOD. 337 
 
 ponderousness of bodies is not to the purpose ; first, 
 because the addition of quantity is not the cause of 
 gravity, as is proved in the fourth book, De Coelo 
 and De Mundo" (we see that he quotes familiarly 
 the physical treatises of Aristotle) ; " second, be- 
 cause it is false that ponderousness makes motion 
 slower ; on the contrary, in proportion as anything 
 is heavier, the more does it move with its proper 
 motion ; thirdly, because action does not take place 
 by local motion, as Democritus asserted ; but by 
 this, that something is drawn from power into act." 
 It does not belong to our purpose to consider 
 either the theological or the metaphysical doctrines 
 which form so large a portion of the treatises of the 
 schoolmen. Perhaps it may hereafter appear, that 
 some light is thrown on some of the questions 
 which have occupied metaphysicians in all ages, by 
 that examination of the history of the Progressive 
 Sciences in which we are now engaged ; but till we 
 are able to analyze the leading controversies of this 
 kind, it would be of little service to speak of them 
 in detail. It may be noticed, however, that many 
 of the most prominent of them refer to the great 
 question, "What is the relation between actual 
 things and general terms?" Perhaps in modern 
 times, the actual things would be more commonly 
 taken as the point to start from ; and men would 
 begin by considering how classes and universals are 
 obtained from individuals. But the schoolmen, 
 founding their speculations on the received modes 
 VOL. i. Z 
 
338 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 of considering such subjects, to which both Aristotle 
 and Plato had contributed, travelled in the opposite 
 direction, and endeavoured to discover how indi- 
 viduals were deduced from genera and species; 
 what was "the Principle of Individuation." This 
 was variously stated by different reasoners. Thus 
 Bonaventura 15 solves the difficulty by the aid of the 
 Aristotelian distinction of Matter and Form. The 
 individual derives from the Form the property of 
 being something, and from the Matter the property 
 of being that particular thing. Duns Scotus 16 , the 
 great adversary of Thomas Aquinas in theology, 
 placed the Principle of Individuation in " a certain 
 positive determining entity," which his school called 
 Hcecceity, or thisness. " Thus an individual man is 
 Peter, because his humanity is combined with Pe- 
 treityT The force of abstract terms is a curious 
 question, and some remarkable experiments in their 
 use had been made by the Latin Aristotelians before 
 this time. In the same way in which we talk of 
 the quantity and quality of a thing, they spoke of 
 its quiddity' 1 . 
 
 We may consider the reign of mere disputation 
 as fully established at the time of which we are now 
 speaking ; and the only kind of philosophy hence- 
 forth studied was one in which no sound physical 
 science had or could have a place. The wavering 
 abstractions, indistinct generalizations, and loose 
 classifications of common language, which we have 
 15 Deg. iv. 573. 16 Ib. iv. 523. 17 Ib. iv. 494. 
 
DOGMATISM OF THE STATIONARY PERIOD. 339 
 
 already noted as the fountain of the physics of the 
 Greek schools of philosophy, were also the only 
 source from which the schoolmen of the middle 
 ages drew their views, or rather their arguments : 
 and though these notional and verbal relations 
 were invested with a most complex and pedantic 
 technicality, they did not, on that account, become 
 at all more precise as notions, or most likely to lead 
 to a single real truth. Instead of acquiring dis- 
 tinct ideas, they multiplied abstract terms ; instead 
 of real generalizations, they had recourse to verbal 
 distinctions. The whole course of their employ- 
 ments tended to make them, not only ignorant 
 of physical truth, but incapable of conceiving its 
 nature. 
 
 Having thus taken upon themselves the task of 
 raising and discussing questions by means of ab- 
 stract terms, verbal distinctions, and logical rules 
 alone, there was no tendency in their activity to 
 come to an end, as there was no progress. The 
 same questions, the same answers, the same diffi- 
 culties, the same solutions, the same verbal subtle- 
 ties, sought for, admired, cavilled at, abandoned, 
 reproduced, and again admired, might recur with- 
 out limit. John of Salisbury 18 observes of the Pa- 
 
 18 He studied logic at Paris, at St. Gene vie ve, and then left 
 them. " Duodecennium mihi elapsum est diversis studiis oc- 
 cupatum. Jucundum itaque visum est veteres quos reliqueram, 
 et quos adhuc Dialectica detinebat in monte, (Sanctse Genovefae) 
 revisere socios, conferre cum eis super ambiguitatibus pristinis ; 
 ut nostrum invicem collatione mutua commetiremur profectum. 
 
 Z 2 Inventi 
 
340 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 risian teachers, that, after several years' absence he 
 found them not a step advanced, and still employed 
 in urging and parrying the same arguments; and 
 this, as Mr. Hallam remarks 19 , " was equally appli- 
 cable to the period of centuries." The same knots 
 were tied and untied ; the same clouds were formed 
 and dissipated. The poet's censure of " the Sons of 
 Aristotle," is as just as happily expressed : 
 
 They stand 
 
 Locked up together hand in hand; 
 Every one leads as he is led, 
 The same bare path they tread, 
 And dance like Fairies a fantastic round, 
 But neither change their motion nor their ground. 
 
 It will, therefore, be unnecessary to go into any 
 detail respecting the history of the school philo- 
 sophy of the thirteenth, fourteenth, and fifteenth 
 centuries. We may suppose it to have been, during 
 the intermediate time, such as it was at first and at 
 last. An occasion to consider its later days will be 
 brought before us by the course of our subject. 
 But, even during the most entire ascendency of the 
 scholastic doctrines, the elements of change were 
 at work. % While the doctors and the philosophers 
 received all the ostensible homage of men, a doc- 
 trine and a philosophy of another kind were gradu- 
 
 Inventi sunt, qui fuerant, et ubi ; neque enim ad palmam visi 
 sunt processisse ad quasstiones pristinas dirimendas, neque pro- 
 positiunculam unam adjecerant. Quibus urgebant stimulis eisdem 
 et ipsi urgebantur." &c. Metalogicus, lib. ii. cap. 10. 
 19 Middle Ages, iii. 537. 
 
DOGMATISM OF THE STATIONARY PERIOD. 341 
 
 ally forming: the practical instincts of man, their 
 impatience of tyranny, the progress of the useful 
 arts, the promises of alchemy, were all disposing 
 men to reject the authority and deny the preten- 
 sions of the received philosophical creed. Two an- 
 tagonist forms of opinion were in existence, which 
 for some time went on detached, and almost inde- 
 pendent of each other ; but, finally, these came into 
 conflict, at the time of Galileo ; and the war speedily 
 extended to every part of civilized Europe. 
 
 3. Scholastic Physics. It is difficult to give 
 briefly any appropriate examples of the nature of 
 the Aristotelian physics which are to be found in 
 the works of this time. As the gravity of bodies 
 was one of the first subjects of dispute when the 
 struggle of the rival methods began, we may notice 
 the mode in which it was treated 20 . "Zabarella 
 maintains that the proximate cause of the motion 
 of elements is the form, in the Aristotelian sense of 
 the term : but to this sentence we," says Keeker- 
 man, "cannot agree; for in all other things the 
 form is the proximate cause, not of the act, but 
 of the power or faculty from which the act flows. 
 Thus in man, the rational soul is not the cause of 
 the act of laughing, but of the risible faculty or 
 power." Keckerman's system was at one time a 
 work of considerable authority : it was published 
 in 1 614. By comparing and systematizing what he 
 finds in Aristotle, he is led to state his results in the 
 
 20 Keckerman, p. 1428. 
 
342 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 form of definitions and theorems. Thus, "gravity 
 is a motive quality, arising from cold, density, and 
 bulk, by which the elements are carried down- 
 wards." " Water is the lower intermediate element, 
 cold and moist." The first theorem concerning 
 water is, " The moistness of water is controlled by 
 its coldness, so that it is less than the moistness of 
 the air; though, according to the sense of the 
 vulgar, water appears to moisten more than air." 
 It is obvious that the two properties of fluids, to 
 have their parts easily moved, and to wet other 
 bodies, are here confounded. I may, as a con- 
 cluding specimen of this kind, mention those pro- 
 positions or maxims concerning fluids, which were 
 so firmly established, that, when Boyle propounded 
 the true mechanical principles of fluid action, he 
 was obliged to state his opinions as " hydrostatical 
 paradoxes." These were, that fluids do not gravi- 
 tate in proprio loco; that is, that water has no 
 gravity in or on water, since it is in its own place ; 
 that air has no gravity on water, since it is above 
 water, which is its proper place; that earth in 
 water tends to descend, since its place is below 
 water; that the water rises in a pump or siphon, 
 because nature abhors a vacuum ; that some bo- 
 dies have a positive levity in others, as oil in water ; 
 and the like. 
 
 4. Authority of Aristotle among the School- 
 men. The authority of Aristotle, and the practice 
 of making him the text and basis of the system. 
 
DOGMATISM OF THE STATIONARY PERIOD. 343 
 
 especially as it regarded physics, prevailed during 
 the period of which we speak. This authority was 
 not, however, without its fluctuations. Launoy has 
 traced one part of its history in a book On the 
 ntrious Fortune of Aristotle in the University of 
 Paris. The most material turns of this fortune de- 
 pend on the bearing which the works of Aristotle 
 were supposed to have upon theology. Several of 
 Aristotle's works, and more especially his metaphy- 
 sical writings, had been translated into Latin, and 
 were explained in the schools of the University of 
 Paris, as early as the beginning of the thirteenth 
 century 21 . At a council held at Paris in 1209, they 
 were prohibited, as having given occasion to the 
 heresy of Almeric (or Amauri), and because " they 
 might give occasion to other heresies not yet in- 
 vented." The Logic of Aristotle recovered its credit 
 some years after this, and was publicly taught in 
 the University of Paris, in the year 1215; but the 
 Natural Philosophy and Metaphysics were prohi- 
 bited by a decree of Gregory the Ninth, in 1231. 
 The emperor, Frederic the Second, employed a 
 number of learned men to translate into Latin, from 
 the Greek and Arabic, certain books of Aristotle, 
 and of other ancient sages ; and we have a letter of 
 Peter de Vineis, in which they are recommended to 
 the attention of the University of Bologna : pro- 
 bably the same recommendation was addressed to 
 other Universities. Both Albertus Magnus and 
 " Mosheim, iii. 157- 
 
344 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 Thomas Aquinas wrote commentaries on Aristotle's 
 works ; and as this was done soon after the decree 
 of Gregory the Ninth, Launoy is much perplexed to 
 reconcile the fact with the orthodoxy of the two 
 doctors. Campanella, who was one of the first to 
 cast off the authority of Aristotle, says, " We are by 
 no means to think that St. Thomas aristotelized ; 
 he only expounded Aristotle, that he might correct 
 his errours ; and I should conceive he did this with 
 the license of the Pope." This statement, however, 
 by no means gives a just view of the nature of 
 Albertus's and Aquinas's commentaries. Both have 
 followed their author with profound deference 22 . 
 For instance, Aquinas 3 attempts to defend Aris- 
 totle's assertion, that if there were no resistance, a 
 body would move through a space in no time ; and 
 the same defence is given by Scotus. 
 
 We may imagine the extent of authority and 
 admiration which Aristotle would attain, when 
 thus countenanced, both by the powerful and the 
 learned. In universities, no degree could be taken 
 without a knowledge of the philosopher. In 1452, 
 Cardinal Totaril established this rule in the Uni- 
 versity of Paris 24 . When Ramus, in 1543, pub- 
 lished an attack upon Aristotle, it was repelled by 
 the power of the court, and the severity of the 
 law. Francis the First published an edict, in which 
 he states that he had appointed certain judges, 
 
 22 Deg. N. 475. 23 F. Piccolomini, ii. 835. 
 
 a * Launoy, pp. 108, 128. 
 
DOGMATISM OF THE STATIONARY PERIOD. 345 
 
 who had been of opinion 25 , "que le dit Ramus 
 avoit te te'meraire arrogant et impudent; et que 
 parcequ'en son livre des animadversions il reprenait 
 Aristotle, estait evidemment connue et manifeste 
 son ignorance." The books are then declared to 
 be suppressed. It was often a complaint of pious 
 men, that theology was corrupted by the influence 
 of Aristotle and his commentators. Petrarch says* 6 , 
 that one of the Italian learned men conversing 
 with him, after expressing much contempt for the 
 apostles and fathers, exclaimed, " Utinam tu Aver- 
 roen pati posses, ut videres quanto ille tuis his 
 nugatoribus major sit!" 
 
 When the revival of letters began to take place, 
 and a number of men of ardent and elegant minds, 
 susceptible to the impressions of beauty of style 
 and dignity of thought, were brought in contact 
 with Greek literature, Plato had naturally greater 
 charms for them. A powerful school of Platonists 
 (not Neoplatonists) was formed in Italy, including 
 some of the principal scholars and men of genius 
 of the time ; as Picus of Mirandula in the middle, 
 Marsilius Ficinus at the end, of the fifteenth cen- 
 tury. At one time, it appeared as if the ascen- 
 dancy of Aristotle was about to be overturned; 
 but, in physics at least, his authority passed un- 
 shaken through this trial. It was not by disputa- 
 tion that Aristotle could be overthrown; and the 
 Platonists were not persons whose doctrines led 
 
 23 Launoy, p. 132. 2 < Hallam, M. A., iii. 536. 
 
346 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 them to use the only decisive method in such cases, 
 the observation and unfettered interpretation of 
 facts. 
 
 The history of their controversies, therefore, 
 does not belong to our design. For like reasons 
 we do not here speak of other authors, who op- 
 posed the scholastic philosophy on general theore- 
 tical grounds of various kinds. Such examples of 
 insurrection against the dogmatism which we have 
 been reviewing, , are extremely interesting events 
 in the history of the philosophy of science. But, in 
 the present work, we are to confine ourselves to 
 the history of science itself; in the hope that we 
 may thus be able hereafter, to throw a steadier 
 light upon that philosophy by which the succession 
 of stationary and progressive periods which we are 
 here tracing, may be in some measure explained, 
 We are now to close our account of the stationary 
 period, and to enter upon the great subject of the 
 progress of physical science in modern times. 
 
 5. Subjects omitted. Civil Law. Medicine. 
 My object has been to make my way, as rapidly 
 as possible, to this period of progress ; and in doing 
 this, I have had to pass over a long and barren 
 tract, where almost all traces of the right road 
 disappear. In exploring this region, it is not with- 
 out some difficulty that he who is travelling with 
 objects such as mine, continues a steady progress 
 in the proper direction ; for many curious and 
 attractive subjects of research come in his way: 
 
DOGMATISM OF THE STATIONARY PERIOD. 347 
 
 he crosses the track of many a controversy, which 
 in its time divided the world of speculators, and 
 of which the results may be traced, even now, in 
 the conduct of moral, or political, or metaphy- 
 sical discussions ; or in the common associations of 
 thought, and forms of language. The wars of the 
 Nominalists and Realists; the disputes concerning 
 the foundations of morals, and the motives of 
 human actions; the controversies concerning pre- 
 destination, free will, grace, and the many other 
 points of metaphysical divinity; the influence of 
 theology and metaphysics upon each other, and 
 upon other subjects of human curiosity ; the effects 
 of opinion upon politics, and of political condition 
 upon opinion ; the influence of literature and phi- 
 losophy upon, each other, and upon society; and 
 many other subjects ; might be well worth exami- 
 nation, if our hopes of success did not reside in 
 pursuing, steadily and directly, those inquiries in 
 which we can look for a definite and certain reply. 
 We must even neglect two of the leading studies 
 of those times, which occupied much of men's time 
 and thoughts, and had a very great influence on 
 society; the one dealing with Notions, the other 
 with Things ; the one employed about moral rules, 
 the other about material causes, but both for prac- 
 tical ends; I mean, the study of the Civil Law, 
 and of Medicine. The second of these studies will 
 hereafter come before us, as one of the principal 
 occasions which led to the cultivation of chemistry ; 
 
348 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 but, in itself, its progress is of too complex and 
 indefinite a nature to be advantageously compared 
 with that of the more exact sciences. The Roman 
 Law is held, by its admirers, to be a system of 
 deductive science, as exact as the mathematical 
 sciences themselves ; and it may, therefore, be use- 
 ful to consider it, if we should, in the sequel, have 
 to examine how far there can exist an analogy 
 between moral and physical science. But, after 
 a few more words on the middle ages, we must 
 return to our task of tracing the progress of the 
 latter. 
 
349 
 
 CHAPTER V. 
 PROGRESS OF THE ARTS IN THE MIDDLE AGES. 
 
 1. /4RT an d Science. I shall, before I resume 
 ^LjL the history of science, say a few words on 
 the subject described in the title of this chapter, 
 both because I might otherwise be accused of doing 
 injustice to the period now treated of; and also, 
 because we shall by this means bring under our 
 notice, some circumstances which were important 
 as being the harbingers of the revival of progres- 
 sive knowledge. 
 
 The accusation of injustice towards the state 
 of science in the middle ages, 'if we were to ter- 
 minate our survey of them with what has hitherto 
 been said, might be urged from obvious topics. 
 How do we recognize, it might be asked, in a pic- 
 ture of mere confusion and mysticism of thought, 
 of servility and dogmatism of character, the powers 
 and acquirements to which we owe so many of the 
 most important inventions which we now enjoy? 
 Parchment and paper, printing and engraving, 
 improved glass and steel, gunpowder, clocks, tele- 
 scopes, the mariner's compass, the reformed calen- 
 dar, the decimal notation, algebra, trigonometry, 
 chemistry, counterpoint, an invention equivalent to 
 a new creation of music ; these are all possessions 
 
350 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 which we inherit from that which has been so dis- 
 paragingly termed the Stationary Period. Above 
 all, let us look at the monuments of architecture 
 of this period ; the admiration and the despair 
 of modern architects, not only for their beauty, 
 but for the skill disclosed in their construction. 
 With all these evidences before us, how can we 
 avoid allowing that the masters of the middle ages 
 not only made some small progress in Astronomy, 
 which has, grudgingly as it would seem, been ad- 
 mitted in a former Book ; but also that they were 
 no small proficients in other sciences, in Optics, 
 in Harmonics, in Physics, and, above all, in Me- 
 chanics ? 
 
 If, it may be added, we are allowed in the pre- 
 sent day, to refer to the perfection of our Arts 
 as evidence of the advanced state of our physical 
 philosophy; if our steam-engines, our gas-illumi- 
 nation, our buildings, our navigation, our manu- 
 factures, are cited as triumphs of science; shall 
 not prior inventions, made under far heavier dis- 
 advantages, shall not greater works, produced in 
 an earlier state of knowledge, also be admitted as 
 witnesses that the middle ages had their share, 
 and that not a small or doubtful one, of science ? 
 
 To these questions I answer, by distinguishing 
 between Art, and Science in that sense of general 
 Inductive Systematic Truth, which it bears in this 
 work. To separate and compare, with precision, 
 these two processes, belongs to the Philosophy of 
 
PROGRESS OF THE ARTS. 351 
 
 Induction ; and the attempt must be reserved for 
 another place : but the leading differences are suf- 
 ficiently obvious. Art is practical, Science is spe- 
 culative : the former is seen in doing ; the latter 
 rests in the contemplation of what is known. The 
 Art of the builder appears in his edifice, though 
 he may never have meditated on the abstract pro- 
 positions on which its stability and strength de- 
 pends. The Science of the mathematical mechani- 
 cian consists in his seeing that, under certain con- 
 ditions, bodies must sustain each other's pressure, 
 though he may never have applied his knowledge 
 in a single case. 
 
 Now the remark which I have to make is this : 
 in all cases the Arts are prior to the related 
 Sciences. Art is the parent, not the progeny, of 
 Science ; the realization of principles in practice 
 forms part of the prelude, as well as of the sequel, 
 of theoretical discovery. And thus the inventions 
 of the middle ages, which have been above enu- 
 merated, though at the present day they may be 
 portions of our sciences, are no evidence that the 
 sciences then existed ; but only that those powers 
 of practical observation and practical skill were 
 at work, which prepare the way for theoretical 
 views and scientific discoveries. 
 
 It may be urged, that the great works of art 
 do virtually take for granted principles of science ; 
 and that, therefore, it is unreasonable to deny 
 science to great artists. It may be said, that the 
 
352 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 grand structures of Cologne, or Amiens, or Can- 
 terbury, could not have been erected without a 
 profound knowledge of mechanical principles. 
 
 To this we reply, that such knowledge is mani- 
 festly not of the nature of that which we call 
 science. If the beautiful and skilful structures of 
 the middle ages prove that mechanics then existed 
 as a science, mechanics must have existed as a 
 science also among the builders of the Cyclopean 
 walls of Greece and Italy, or of our own Stone- 
 henge; for the masses which are there piled on 
 each other, could not be raised without consider- 
 able mechanical skill. But we may go much fur- 
 ther. The actions of every man who raises and 
 balances weights, or walks along a pole, take for 
 granted the laws of equilibrium ; and even animals 
 constantly avail themselves of such principles. Are 
 these, then, acquainted with mechanics as a science? 
 Again, if actions which are performed by taking 
 advantage of mechanical properties prove a know- 
 ledge of the science of mechanics, they must also 
 be allowed to prove a knowledge of the science of 
 geometry, when they proceed on geometrical pro- 
 perties. But the most familiar actions of men and 
 animals do this. The Epicureans held, as Proclus 
 informs us, that even asses knew that two sides 
 of a triangle are greater than the third. And they 
 may truly be said to have a practical knowledge 
 of this ; but they have not, therefore, a science of 
 geometry. And in like manner among men, if we 
 
PROGRESS OF THE ARTS. 353 
 
 consider the matter strictly, a practical assumption 
 of a principle does not imply a speculative know- 
 ledge of it. 
 
 We may, in another way also, show how in- 
 admissible are the works of the master Artists of 
 the middle ages into the series of events which 
 mark the advance of Science. The following maxim 
 is applicable to a history, such as we are here 
 endeavouring to write. We are employed in trac- 
 ing the progress of such general principles as 
 constitute each of the sciences which we are re- 
 viewing ; and no facts or subordinate truths belong 
 to our scheme, except so far as they lead to or 
 are included in these higher principles; nor are 
 they important to us, any further than as they 
 prove such principles. Now with regard to pro- 
 cesses of art like those which we have referred 
 to, as the inventions of the middle ages, let us ask, 
 what principle each of them illustrates? What 
 chemical doctrine rests for its support on the phe- 
 nomena of gunpowder, or glass, or steel? What 
 new harmonical truth was illustrated in the Gre- 
 gorian chant? What mechanical principle unknown 
 to Archimedes was displayed in the printing-press? 
 The practical value and use, the ingenuity and skill 
 of these inventions is not questioned; but what 
 is their place in the history of speculative know- 
 ledge? Even in those cases in which they enter 
 into such a history, how minute a figure do they 
 make ! how great is the contrast between their 
 VOL. i. A A 
 
354 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 practical and theoretical importance ! They may 
 in their operation have changed the face of the 
 world ; but in the history of the principles of the 
 sciences to which they belong, they may be omitted 
 without being missed. 
 
 As to that part of the objection which was 
 stated by asking, why, if the arts of our age prove 
 its scientific eminence, the arts of the middle ages 
 should not be received as proof of theirs ; we must 
 reply to it, by giving up some of the pretensions 
 which are often put forwards on behalf of the sci- 
 ence of our times. The perfection of the mechani- 
 cal and other arts among us proves the advanced 
 condition of our sciences, only in so far as these 
 arts have been perfected by the application of some 
 great scientific truth, with a clear insight into its 
 nature. The greatest improvement of the steam- 
 engine was due to the steady apprehension of an 
 atmological doctrine by Watt; but what distinct 
 theoretical principle is illustrated by the beautiful 
 manufactures of porcelain, or steel, or glass? A 
 chemical view of these compounds, which would 
 explain the conditions of success and failure in their 
 manufacture, would be of great value in art ; and 
 it would also be a novelty in chemical theory ; so 
 little is the present condition of those processes a 
 triumph of science, shedding intellectual glory on 
 our age. And the same might be said of many, 
 or of most, of the processes of the arts as now 
 practised. 
 

 PROGRESS OF THE ARTS. 355 
 
 2. Arabian Science. Having, I trust, estab- 
 lished the view I have stated, respecting the relation 
 of Art and Science, we shall be able very rapidly to 
 dispose of a number of subjects which otherwise 
 might seem to require a detailed notice. Though 
 this distinction has been recognized by others, it 
 has hardly been rigorously adhered to, in conse- 
 quence of the indistinct notion of science which has 
 commonly prevailed. Thus Gibbon, in speaking 
 of the knowledge of the period now under our 
 notice, says 1 , "Much useful experience had been 
 acquired in the practice of arts and manufactures ; 
 but the science of chemistry owes its origin and 
 improvement to the industry of the Saracens. 
 They," he adds, "first invented and named the 
 alembic for the purposes of distillation, analyzed 
 the substances of the three kingdoms of nature, 
 tried the distinction and affinities of alcalis and 
 acids, and converted the poisonous minerals into 
 soft and salutary medicines." The formation and 
 realization of the notions of analysis and of affinity, 
 were important steps in chemical science, which, as 
 I shall hereafter endeavour to show, it remained 
 for the chemists of Europe to make at a much later 
 period. If the Arabians had done this, they might 
 with justice have been called the authors of the 
 science of chemistry ; but no doctrines can be ad- 
 duced from their works which give them any title 
 to this eminent distinction. Their claims are dis- 
 
 1 Decline and Fall, vol. x. p. 43. 
 
 AA2 
 
356 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 sipated at once by the application of the maxim 
 above stated. What analysis of theirs tended 
 to establish any received principle of chemistry? 
 What true doctrine concerning the differences and 
 affinities of acids and alkalis did they teach ? We 
 need not wonder if Gibbon, whose views of the 
 boundaries of scientific chemistry were probably 
 very wide and indistinct, could include the arts of 
 the Arabians within its domain; but they cannot 
 pass the frontier of science if philosophically defined, 
 and steadily guarded. 
 
 The judgment which we are thus led to form 
 respecting the chemical knowledge of the middle 
 ages, and of the Arabians in particular, may serve 
 to measure the condition of science in other depart- 
 ments; for chemistry has justly been considered 
 one of their strongest points. In botany, anatomy, 
 zoology, optics, acoustics, we have still the same 
 observation to make, that the steps in science 
 which, in the order of progress, next followed what 
 the Greeks had done, were left for the Europeans 
 of the sixteenth and seventeenth centuries. The 
 merits and advances of the Arabian philosophers in 
 astronomy and pure mathematics, we have already 
 described. 
 
 3. Experimental Philosophy of the Arabians. 
 The estimate to which we have thus been led, of 
 the scientific merits of the learned men of the 
 middle ages, is much less exalted than that which 
 has been formed by many writers ; and, among the 
 
PROGRESS OF THE ARTS. 357 
 
 rest, by some of our own time. But I am persuaded 
 that any attempt to answer the questions just asked, 
 will expose the untenable nature of the higher 
 claims which have been advanced in favour of the 
 Arabians. We can deliver no just decision, except 
 we will consent to use the terms of science in a 
 strict and precise sense 2 : and if we do this, we 
 shall find little, either in the particular discove- 
 ries or general methods of the Arabians, which 
 is important in the history of the Inductive Sci- 
 ences. 
 
 The credit due to the Arabians for improve- 
 ments in the general methods of philosophizing, is 
 a more difficult question ; and cannot be discussed 
 at length by us, till we examine the history of such 
 methods in the abstract, which, in the present work, 
 it is not our intention to do. But we may observe, 
 that we cannot agree with those who rank their 
 
 2 If I might take the liberty of criticizing an author who has 
 given a very interesting view of the period in question (Maho- 
 metanism Unveiled, by the Rev. Charles Forster, 1829), I would 
 remark, that in his work this caution is perhaps too little ob- 
 served. Thus, he says, in speaking of Alhazen (vol. ii. p. 270), 
 "the theory of the telescope may be found in the work of this 
 astronomer ;" and of another, " the uses of magnifying glasses 
 and telescopes, and the principle of their construction, are ex- 
 plained in the Great Work of (Roger) Bacon, with a truth and 
 clearness which have commanded universal admiration." Such 
 phrases would be much too strong, even if used respecting the 
 optical doctrines of Kepler, which were yet incomparably more 
 true and clear than those of Bacon. To employ such language, 
 in such cases, is to deprive such terms as theory and principle* 
 of all meaning 
 
358 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 merits high in this respect. We have already seen, 
 that their minds were completely devoured by the 
 worst habits of the stationary period, mysticism 
 and commentation. They followed their Greek 
 leaders, for the most part, with abject servility, and 
 with only that kind of acuteness and independent 
 speculation which the commentator's vocation im- 
 plies. And in their choice of the standard subjects 
 of their studies, they fixed upon those works, the 
 Physics of Aristotle, which have never promoted 
 the progress of science, except so far as they incited 
 men to refute them ; an effect which they never 
 produced on the Arabians. That the Arabian 
 astronomers made some advances beyond the 
 Greeks, we have already stated : the two great in- 
 stances are, the discovery of the Motion of the Sun's 
 Apogee by Albategnius, and the discovery (recently 
 brought to light) of the existence of the Moon's 
 Second Inequality, by Aboul Wefa. But we cannot 
 but observe in how different a manner they treated 
 these discoveries, from that with which Hipparchus 
 or Ptolemy would have done. The Variation of the 
 moon, in particular, instead of being incorporated 
 into the system by means of an Epicycle, as Ptolemy 
 had done with the Evection, was allowed, almost 
 immediately, so far as we can judge, to fall into 
 neglect and oblivion : so little were the learned 
 Arabians prepared to take their lessons from obser- 
 vation as well as books. That in many subjects 
 they made experiments, may easily be allowed: 
 
PROGRESS OF THE ARTS. 359 
 
 there never was a period of the earth's history, and 
 least of all a period of commerce and manufactures, 
 luxury and art, medicine and engineering, in which 
 were not going on innumerable processes, which 
 may be termed experiments; and, in addition to 
 these, the Arabians adopted the pursuit of alchemy, 
 and the love of exotic plants and animals. But so 
 far from their being, as has been maintained 3 , a 
 people whose " experimental intellect " fitted them 
 to form sciences which the " abstract intellect " of 
 the Greeks failed in producing, it rather appears, 
 that several of the sciences which the Greeks had 
 founded, were never even comprehended by the 
 Arabians. I do not know any evidence that these 
 pupils ever attained to understand the real prin- 
 ciples of mechanics, hydrostatics, and harmonics, 
 which their masters had established. At any rate, 
 when these sciences again came progressive, Europe 
 had to start where Europe had stopped. There 
 is no Arabian name which any one has thought of 
 interposing between Archimedes the ancient, and 
 Stevinus and Galileo the moderns. 
 
 4. Roger Bacon. There is one writer of the 
 middle ages, on whom much stress has been laid, 
 and who was certainly a most remarkable person. 
 Roger Bacon's works are not only so far beyond his 
 age in the knowledge which they contain, but so 
 different from the temper of the times, in his asser- 
 tion of the supremacy of experiment, and in his 
 
 3 Mahometanism Unveiled, ii. 271- 
 
360 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 contemplation of the future progress of knowledge, 
 that it is difficult to conceive how such a character 
 could then exist. That he received much of his 
 knowledge from Arabic writers, there can be no 
 doubt ; for they were in his time the repositories of 
 all traditionary knowledge. But that he derived 
 from them his disposition to shake off the authority 
 of Aristotle, to maintain the importance of experi- 
 ment, and to look upon knowledge as in its infancy, 
 I cannot believe, because I have not myself hit upon, 
 nor seen quoted by others, any passages in which 
 Arabian writers express such a disposition. On the 
 other hand, we do find in European writers, in the 
 authors of Greece and Rome, the solid sense, the 
 bold and hopeful spirit, which suggest such tenden- 
 cies. We have already seen that Aristotle asserts, 
 as distinctly as words can express, that all know- 
 ledge must depend on observation, and that science 
 must be collected from facts by induction. We 
 have seen, too, that the Roman writers, and Seneca 
 in particular, speak with an enthusiastic confidence 
 of the progress which science must make in the 
 course of ages. When Roger Bacon holds similar 
 language in the thirteenth century, the resemblance 
 is probably rather a sympathy of character, than a 
 matter of direct derivation ; but I know 7 of nothing 
 which proves even so much as this sympathy with 
 regard to Arabian philosophers. 
 
 A good deal has been said of late of the coin- 
 cidences between his views, and those of his great 
 
PROGRESS OF THE ARTS. 361 
 
 namesake in later times, Francis Bacon 4 . The re- 
 semblances consist mainly in such points as I have 
 just noticed ; and we cannot but acknowledge, that 
 many of the expressions of the Franciscan friar 
 remind us of the large thoughts and lofty phrases 
 of the philosophical chancellor. How far the one 
 can be considered as having anticipated the me- 
 thod of the other, we shall examine more advan- 
 tageously, when we come to consider what the 
 character and effect of Francis Bacon's works really 
 are (N). 
 
 5. Architecture of the Middle Ages. But though 
 we are thus compelled to disallow several of the 
 claims which have been put forwards in support of 
 the scientific character of the middle ages, there are 
 two points in which we may, I conceive, really trace 
 the progress of scientific ideas among them ; and 
 which, therefore, may be considered as the prelude 
 to the period of discovery. I mean their practical 
 architecture, and their architectural treatises. 
 
 In a previous chapter of this book, we have 
 endeavoured to explain how the indistinctness of 
 ideas, which attended the decline of the Roman em- 
 pire, appears in the forms of their architecture ; 
 in the disregard, which the decorative construction 
 exhibits, of the necessary mechanical conditions of 
 support. The original scheme of Greek ornamental 
 architecture, had been horizontal masses resting on 
 
 4 Hallam's Middle Ages, iii. 549. Forster's Mahom. U. ii. 
 313. 
 
362 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 vertical columns : when the arch was introduced by 
 the Romans, it was concealed, or kept in state of 
 subordination: and the lateral support which it 
 required was supplied latently, masked by some 
 artifice. But the struggle between the mechanical 
 and the decorative construction^, ended in the com- 
 plete disorganization of the classical style. The in- 
 consistencies and extravagancies, of which we have 
 noticed the occurrence, were results and indications 
 of the fall of good architecture. The elements of 
 the ancient system had lost all principle of con- 
 nexion and regard to rule. Building became not 
 only a mere art, but an art exercised by masters 
 without skill, and without feeling for real beauty (o). 
 When, after this deep decline, architecture rose 
 again, as it did in the twelfth and succeeding cen- 
 turies, in the exquisitely beautiful and skilful forms 
 of the Gothic style, what was the nature of the 
 change which had taken place, so far as it bears 
 upon the progress of science? It was this: the 
 idea of true mechanical relations in an edifice had 
 been revived in men's minds, as far as was requisite 
 for the purposes of art and beauty: and this, though 
 a very different thing from the possession of the 
 idea as an element of speculative science, was the 
 proper preparation for that acquisition. The notion 
 of support and stability again became conspicuous 
 in the decorative construction, and universal in the 
 
 5 See Mr. Willis's admirable Remarks on the Architecture of 
 the Middle Ages, chap. ii. 
 
PROGRESS OF THE ARTS. 363 
 
 forms of building. The eye which, looking for 
 beauty in definite and significant relations of parts, 
 is never satisfied except the weights appear to be 
 duly supported", was again gratified. Architecture 
 threw off its barbarous characters : a new decorative 
 construction was matured, not thwarting and con- 
 trolling, but assisting and harmonizing with the 
 mechanical construction. All the ornamental parts 
 were made to enter into the apparent construction. 
 Every member, almost every moulding, became a 
 sustainer of weight; and by the multiplicity of 
 props assisting each other, and the consequent sub- 
 division of weight, the eye was satisfied of the stabi- 
 lity of the structure, notwithstanding the curiously- 
 slender forms of the separate parts. The arch and 
 the vault, no longer trammelled by an incompatible 
 system of decoration, but favoured by more tract- 
 able forms, were only limited by the skill of the 
 builders. Everything showed that, practically at 
 least, men possessed and applied, with steadiness 
 and pleasure, the idea of mechanical pressure and 
 support. 
 
 The possession of this idea, as a principle of art, 
 led, in the course of time, to its speculative deve- 
 lopement as the foundation of a science ; and thus 
 architecture prepared the way for mechanics. But 
 this advance required several centuries. The inter- 
 
 6 Willis, pp. 15 21. I have throughout this description of 
 the formation of the Gothic style availed myself of Mr. Willis'* 
 well-chosen expressions. 
 
364 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 val between the admirable cathedrals of Salisbury, 
 Amiens, Cologne, and the mechanical treatises of 
 Stevinus, is not less than three hundred years. 
 During this time, men were advancing towards 
 science, but in the meantime, and perhaps from 
 the very beginning of the time, art had begun to 
 decline. The buildings of the fifteenth century, 
 erected when the principles of mechanical support 
 were just on the verge of being enunciated in 
 general terms, exhibit those principles with a far 
 less impressive simplicity and elegance than those 
 of the thirteenth. We may hereafter inquire whe- 
 ther we find any other examples to countenance the 
 belief, that the formation of Science is commonly 
 accompanied by the decline of Art. 
 
 The leading principle of the style of the Gothic 
 edifices was, not merely that the weights were sup- 
 ported, but that they were seen to be so ; and that 
 not only the mechanical relations of the larger 
 masses, but of the smaller members also, were dis- 
 played. Hence we cannot admit as an origin or 
 anticipation of the Gothic, a style in which this 
 principle is not manifested. I do not see, in any of 
 the representations of the early Arabic buildings, 
 that distribution of weights to supports, and that 
 mechanical consistency of parts, which elevates 
 them above the character of barbarous architecture. 
 Their masses are broken into innumerable members, 
 without subordination or meaning, in a manner 
 suggested apparently by caprice and the love of 
 
PROGRESS OF THE ARTS. 365 
 
 the marvellous. " In the construction of their 
 mosques, it was a favourite artifice of the Arabs to 
 sustain immense and ponderous masses of stone by 
 the support of pillars so slender, that the incum- 
 bent weight seemed, as it were, suspended in the 
 air by an invisible hand 7 ." This pleasure in the 
 contemplation of apparent impossibilities is a very 
 general disposition among mankind ; but it appears 
 to belong to the infancy, rather than the maturity 
 of intellect. On the other hand, the pleasure in 
 the contemplation of what is clear, the craving for 
 a thorough insight into the reasons of things, which 
 marks the European mind, is the temper which 
 leads to science. 
 
 6. Treatises on Architecture. No one who has 
 attended to the architecture which prevailed in 
 England, France, and Germany, from the twelfth to 
 the fifteenth century, so far as to comprehend its 
 beauty, harmony, consistency, and uniformity, even 
 in the minutest parts and most obscure relations, 
 can look upon it otherwise than as a remarkably 
 connected and definite artificial system. Nor can 
 we doubt that it was exercised by a class of artists 
 who formed themselves by laborious study and 
 practice, and by communication with each other. 
 There must have been bodies of masters and of 
 scholars, discipline, traditions, precepts of art. How 
 these associated artists diffused themselves over 
 Europe, and whether history enables us to trace 
 them in a distinct form, I shall not here discuss. 
 
 7 Mahometanism Unveiled, ii. 255. 
 
366 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 But the existence of a course of instruction, and of 
 a body of rules of practice, is proved beyond dis- 
 pute by the great series of European cathedrals 
 and churches, so nearly identical in their general 
 arrangements, and in their particular details. The 
 question then occurs, have these rules and this 
 system of instruction anywhere been committed to 
 writing ? Can we, by such evidence, trace the pro- 
 gress of the scientific idea, of which we see the 
 working in these buildings? 
 
 We are not to be surprized, if, during the most 
 flourishing and vigorous period of the art of the 
 middle ages, we find none of its precepts in books. 
 Art has, in all ages and countries, been taught and 
 transmitted by practice and verbal tradition, not by 
 writing. It is only in our own times, that the 
 thought occurs as familiar, of committing to books 
 all that we wish to preserve and convey. And, 
 even in our own times, most of the Arts are learned 
 far more by practice, and by intercourse with prac- 
 titioners, than by reading. Such is the case, not 
 only with Manufactures and Handicrafts, but with 
 the Fine Arts, with Engineering, and even yet, with 
 that art, Building, of which we are now speaking. 
 
 We are not, therefore, to wonder, if we have 
 no treatises on Architecture belonging to the great 
 period of the Gothic masters ; or if it appears to 
 have required some other incitement and some 
 other help, besides their own possession of their 
 practical skill, to lead them to shape into a literary 
 form the precepts of the art which they knew so 
 
PROGRESS OF THE ARTS. 3G7 
 
 well how to exercise : or if, when they did write on 
 such subjects, they seem, instead of delivering their 
 own sound practical principles, to satisfy themselves 
 with pursuing some of the frivolous notions and 
 speculations which were then current in the world 
 of letters. 
 
 Such appears to be the case. The earliest trea- 
 tises on Architecture come before us under the 
 form which the commentatorial spirit of the middle 
 ages inspired. They are translations of Vitruvius, 
 with annotations. In some of these, particularly 
 that of Cesare Cesariano, published at Como, in 
 1521, we see, in a very curious manner, how the 
 habit of assuming that, in every department of 
 literature, the ancients must needs be their mas- 
 ters, led these writers to subordinate the members 
 of their own architecture to the precepts of the 
 Roman author. We have Gothic shafts, mouldings, 
 and arrangements, given as parallelisms to others, 
 which profess to represent the Roman style, but 
 which are, in fact, examples of that mixed manner 
 which is called the style of the cinque cento by 
 the Italians, of the renaissance by the French, and 
 which is commonly included in our Elizabethan. 
 But in the early architectural works, besides the 
 superstitions and mistaken erudition which thus 
 choked the growth of real architectural doctrines, 
 another of the peculiar elements of the middle 
 ages comes into view ; its mysticism. The dimen- 
 sions and positions of the various parts of edifices 
 
368 PHYSICAL SCIENCE IN THE MIDDLE AGES. 
 
 and of their members, are determined by drawing 
 triangles, squares, circles, and other figures, in 
 such a manner as to bound them: and to these 
 geometrical figures were assigned many abstruse 
 significations. The plan and the front of the Cathe- 
 dral at Milan -are thus represented in Cesariano's 
 work, bounded and subdivided by various equi- 
 lateral triangles ; and it is easy to see, in the ear- 
 nestness with which he points out these relations, the 
 evidence of a fanciful and mystical turn of thought 8 . 
 We thus find erudition and mysticism take the 
 place of much of that developement of the archi- 
 tectural principles of the middle ages which would 
 be so interesting to us. Still, however, these works 
 are by no means without their value. Indeed 
 many of the arts appear to flourish not at all the 
 worse, for being treated in a manner somewhat 
 mystical ; and it may easily be, that the relations 
 of geometrical figures, for which fantastical rea- 
 sons are given, may really involve principles of 
 beauty or stability. But independently of this, we 
 
 8 The plan which he has given, fol. 14, he has entitled 
 " Ichnographia Fundamenti sacras JEdis baricephake, Germanico 
 more, a Trigono ac Pariquadrato perstructa, uti etiam ea quse 
 nunc Milani videtur." 
 
 The work of Cesariano was translated into German by 
 Gualter Rivius, and published at Nuremberg, in 1548, under 
 the title of Fitruvius Teutsch, with copies of the Italian dia- 
 grams. A few years ago, in an article in the Wiener Jahr- 
 biichir, (Oct. Dec., 1821), the reviewer maintained, on the 
 authority of the diagrams in Rivius's book, that Gothic archi- 
 tecture had its origin in Germany, and not in England. 
 
PROGRESS OF THE ARTS. 369 
 
 find, in the best works of the architects of all ages 
 (including engineers), evidence that the true idea 
 of mechanical pressure exists among them more 
 distinctly than among men in general, although it 
 may not be developed in a scientific form. This 
 is true up to our own time, and the arts which 
 such persons cultivate could not be successfully 
 exercised if it were not so. Hence the writings 
 of architects and engineers during the middle ages 
 do really form a prelude to the works on scientific 
 mechanics. Vitruvius, in his Architecture, and 
 Julius Frontinus, who, under Vespasian, wrote On 
 Aqueducts, of which he was superintendent, have 
 transmitted to us the principal part of what we 
 know respecting the practical mechanics and hy- 
 draulics of the Romans. In modern times the 
 series is resumed. The early writers on architec- 
 ture are also writers on engineering, and often on 
 hydrostatics: for example, Leonardo da Vinci wrote 
 on the equilibrium of water. And thus we are 
 led up to Stevinus of Bruges, who was engineer 
 to Prince Maurice of Nassau, and inspector of the 
 dykes in Holland; and in whose work, on the 
 processes of his art, is contained the first clear 
 modern statement of the scientific principles of 
 hydrostatics. 
 
 Having thus explained both the obstacles and 
 the prospects which the middle ages offered to the 
 progress of science, I now proceed to the history of 
 the progress, when it was once again resumed. 
 VOL. i. BB 
 
370 
 
 NOTES TO BOOK IV. 
 
 (K.) p. 268. SINCE the publication of my first edition, 
 an account of Algazel or Algazzali and his works has been 
 published under the title of Essai sur les Ecoles Philoso- 
 phiques chez les Arabes, et notamment sur la Doctrine cfAl- 
 gazzali, par August Schmolders. Paris. 1842. From this 
 book it appears that Degerando's account of Algazzali is 
 correct, when he says T that " his skepticism seems to have 
 essentially for its object to destroy all systems of merely 
 rational theology, in order to open an indefinite career, 
 not only to faith guided by revelation, but also to the 
 free exaltation of a mystical enthusiasm." It is remarked 
 by Dr. Schmolders, following M. de Hammer-Purgstall, 
 that the title of the work referred to in the text ought 
 rather to be Mutual Refutation of the Philosophers : and 
 that its object is to shew that Philosophy consists of a 
 mass of systems, each of which overturns the others. 
 The work of Algazzali which Dr. Schmolders has published, 
 On the Err ours of Sects, #c., contains a kind of autographi- 
 cal account of the way in which the author was led to his 
 views. He does not reject the truths of science, but he 
 condemns the mental habits which are caused by laying 
 too much stress upon science. Religious men, he says, 
 are, by such a course, led to reject all science, even what 
 relates to eclipses of the moon and sun ; and men of 
 science are led to hate religion 2 . 
 
 1 Hist. Comp. iv. p. 227. 2 Essai, p. 33. 
 
NOTES TO BOOK IV. 371 
 
 (L.) p. 272. It appears however that scriptural argu- 
 ments were found on the other side. St. Jerome says 8 , 
 speaking of the two cherubims with four faces, seen by 
 the prophet, and the interpretation of the vision ; " Alii 
 vero qui philosophorum stultam sequunter sapientiam, duo 
 hemispheria in duobus templi cherubim, nos et antipodes, 
 quasi supinos et cadentes homines suspicantur." 
 
 (M.) p. 305. The reader will find an interesting view 
 of the School of Alexandria^ in M. Barthelemy Saint- 
 Hilaire^s Rapport on the Memoires sent to the Academy 
 of Moral and Political Sciences at Paris, in consequence 
 of its having, in 1841, proposed this as the subject of 
 a prize, which was awarded in 1844. M. Saint-Hilaire 
 has prefixed to this Rapport a dissertation on the Mys- 
 ticism of that school. He, however, uses the term 
 Mysticism in a wider sense than my purpose, which re- 
 garded mainly the bearing of the doctrines of this school 
 upon the progress of the Inductive Sciences, led me to 
 do. Although he finds much to admire in the Alexan- 
 drian philosophy, he declares that they were incapable 
 of treating scientific questions. The extent to which this 
 is true is well illustrated by the extract which he gives 
 from Plotinus, on the question, "Why objects appear 
 smaller in proportion as they are more distant." Plo- 
 tinus denies that the reason of this is that the angles 
 of vision become smaller. His reason for this denial is 
 curious enough. If it were so, he says, how could the 
 heaven appear smaller than it is, since it occupies the 
 whole of the visual angle? 
 
 (N.) p. 361. In the Philosophy of the Inductive 
 Sciences, I have given an account at considerable length 
 
 3 Comm. in Ezech., i. 6. 
 
 BB2 
 
372 NOTES TO BOOK IV, 
 
 of Roger Bacon's mode of treating Arts and Sciences ; 
 and have also compared more fully his philosophy with 
 that of Francis Bacon ; and I have given a view of the 
 bearing of this latter upon the progress of Science in 
 modern times. See Phil. Ind. Sc. B. xn. chaps. 7 and 1 1 . 
 
 (o.) p. 362. Since the publication of my first edition, 
 Mr. Willis has shown that much of the " mason-craft " 
 of the middle ages consisted in the geometrical methods 
 by which the artists wrought out of the blocks the complex 
 forms of their decorative system. 
 
 To the general indistinctness of speculative no- 
 tions on mechanical subjects prevalent in the middle 
 ages, there may have been some exceptions, and espe- 
 cially so long as there were readers of Archimedes. 
 Boetius had translated the niechanical works of Archi- 
 medes into Latin, as we learn from the enumeration of 
 his works by his friend Cassiodorus (Variar. lib. i. 
 cap. 45), " Mechanicum etiam Archimedem latialem 
 siculis reddidisti." But Mechanicus was used in those 
 times rather for one skilled in the art of constructing 
 wonderful machines than in the speculative theory of 
 them. The letter from which the quotation is taken 
 is sent by King Theodoric to Boetius, to urge him to send 
 the king a water-clock. 
 
BOOK V. 
 
 HISTORY 
 
 OP 
 
 FORMAL ASTRONOMY 
 
 AFTER THE STATIONARY PERIOD. 
 
. . . Cyclopum educta caminis 
 
 Maenia conspicio, atque adverso fornice portas. 
 
 His demum exactis, perfecto munere Divse, 
 Devenere locos laetos et amsena vireta 
 Fortunatorum nemorum sedesque beatas. 
 Largior hie campos aether et lumine vestit 
 Purpureo: solemque suum, sua sidera norunt. 
 
 VIRGIL, Mn. vi. 630. 
 
 They leave at length the nether gloom, and stand 
 
 Before the portals of a hetter land : 
 
 To happier plains they come, and fairer groves, 
 
 The seats of those whom heaven, benignant, loves; 
 
 A brighter day, a bluer ether, spreads 
 
 Its lucid depths above their favoured heads; 
 
 And, purged from mists that veil our earthly skies, 
 
 Shine suns and stars unseen by mortal eyes. 
 
INTRODUCTION. 
 Of Formal and Physical Astronomy. 
 
 WE have thus rapidly traced the causes of the 
 almost complete blank which the history 
 of physical science offers, from the decline of the 
 Roman empire, for a thousand years. Along with 
 the breaking up of the ancient forms of society, 
 were broken up the ancient energy of thinking, the 
 clearness of idea, and steadiness of intellectual 
 action. This mental declension produced a servile 
 admiration for the genius of the better periods, and 
 thus, the spirit of Commentation: Christianity esta- 
 blished the claim of truth to govern the world; and 
 this principle, misinterpreted and combined with 
 the ignorance and servility of the times, gave rise 
 to the Dogmatic System : and the love of specula- 
 tion, finding no secure and permitted path on solid 
 ground, went off into the regions of Mysticism. 
 
 The causes which produced the inertness and 
 blindness of the stationary period of human know- 
 ledge, began at last to yield to the influence of 
 the principles which tended to progression. The 
 indistinctness of thought, which was the original 
 feature in the decline of sound knowledge, was in 
 a measure remedied by the steady cultivation of 
 pure mathematics and astronomy, and by the pro- 
 
376 INTRODUCTION. 
 
 gress of inventions in the arts, which call out and 
 fix the distinctness of our conceptions of the re- 
 lations of natural phenomena. As men's minds 
 became clear, they became less servile : the per- 
 ception of the nature of truth drew men away from 
 controversies about mere opinion; when they saw 
 distinctly the relations of things, they ceased to 
 give their whole attention to what had been said 
 concerning them; and thus, as science rose into 
 view, the spirit of commentation lost its sway. 
 And when men came to feel what it was to think 
 for themselves on subjects of science, they soon 
 rebelled against the right of others to impose 
 opinions upon them. When they threw off their 
 blind admiration for the ancients, they were dis- 
 posed to cast away also their passive obedience to 
 the ancient system of doctrines. When they were 
 no longer inspired by the spirit of commentation, 
 they were no longer submissive to the dogmatism 
 of the schools. When they began to feel that they 
 could discover truths, they felt also a persuasion 
 of a right and a growing will so to do. 
 
 Thus the revived clearness of ideas, which made 
 its appearance at the revival of letters, brought on 
 a struggle with the authority, intellectual and civil, 
 of the established schools of philosophy. This clear- 
 ness of idea showed itself, in the first instance, 
 in Astronomy, and was embodied in the system of 
 Copernicus; but the contest did not come to a 
 crisis till a century later, in the time of Galileo 
 
INTRODUCTION. 377 
 
 and other disciples of the new doctrine. It is our 
 present business to trace the principles of this 
 series of events in the history of philosophy. 
 
 I do not profess to write a history of Astro- 
 nomy, any further than is necessary in order to 
 exhibit the principles on which the progression of 
 science proceeds; and, therefore, I neglect subor- 
 dinate persons and occurrences, in order to bring 
 into view the leading features of great changes. 
 Now in the introduction of the Copernican system 
 into general acceptation, two leading views operated 
 upon men's minds ; the consideration of the system 
 as exhibiting the apparent motions of the uni- 
 verse, and the consideration of this system with 
 reference to its causes ; the formal and the phy- 
 sical aspect of the Theory ; the relations of Space 
 and Time, and the relations of Force and Matter. 
 These two divisions of the subject were at first 
 not clearly separated ; the second was long mixed, 
 in a manner very dim and obscure, with the first, 
 without appearing as a distinct subject of atten- 
 tion; but at last it was extricated and treated in 
 a manner suitable to its nature. The views of 
 Copernicus rested mainly on the formal condition 
 of the universe, the relations of space and time ; 
 but Kepler, Galileo, and others, were led, by con- 
 troversies and other causes, to give a gradually 
 increasing attention to the physical relations of 
 the heavenly bodies; an impulse was given to the 
 study of Mechanics (the Doctrine of Motion,) which 
 
378 INTRODUCTION. 
 
 became very soon an important and extensive 
 science ; and in no long period, the discoveries of 
 Kepler, suggested by a vague but intense belief 
 in the physical connexion of the parts of the uni- 
 verse, led to the decisive and sublime generali- 
 zations of Newton. 
 
 The distinction of formal and physical Astro- 
 nomy thus becomes necessary, in order to treat 
 clearly of the discussions which the propounding 
 of the Copernican theory occasioned. But it may 
 be observed that, besides this great change, Astro- 
 nomy made very great advances in the same path 
 which we have already been tracing, namely, the 
 determination of the quantities and laws of the 
 celestial motions, in so far as they were exhibited 
 by the ancient theories, or might be represented 
 by obvious modifications of those theories. I speak 
 of new Inequalities, new Phenomena, such as Co- 
 pernicus, Galileo, and Tycho Brahe discovered. As, 
 however, these were very soon referred to the 
 Copernican rather than the Ptolemaic hypothesis, 
 they may be considered as developements rather 
 of the new than of the old Theory ; and I shall, 
 therefore, treat of them, agreeably to the plan of 
 the former part, as the sequel of the Copernican 
 Induction. 
 
370 
 
 CHAPTER I. 
 
 PRELUDE TO THE INDUCTIVE EPOCH OF 
 COPERNICUS. 
 
 THE Doctrine of Copernicus, that the Sun is 
 the true center of the celestial motions, de- 
 pends primarily upon the consideration that such 
 a supposition explains very simply and completely 
 all the obvious appearances of the heavens. In 
 order to see that it does this, nothing more is 
 requisite than a distinct conception of the nature 
 of Relative Motion, and a knowledge of the prin- 
 cipal Astronomical Phenomena. There was, there- 
 fore, no reason why such a doctrine might not be 
 discovered, that is, suggested as a theory plausible 
 at first sight, long before the time of Copernicus; 
 or rather, it was impossible that this guess, among 
 others, should not be propounded as a solution 
 of the appearances of the heavens. We are not, 
 therefore, to be surprized if we find, in the earliest 
 times of astronomy, and at various succeeding 
 periods, such a system spoken of by astronomers, 
 and maintained by some as true, though rejected 
 by the majority, and by the principal writers. 
 
 When we look back at such a difference of 
 opinion, having in our minds, as we unavoidably 
 have, the clear and irresistible considerations by 
 
380 HISTORY OF FORMAL ASTRONOMY. 
 
 which the Copernican Doctrine is established for 
 us, it is difficult for us not to attribute superior 
 sagacity and candour to those who held that side 
 of the question, and to imagine those who clung 
 to the Ptolemaic Hypothesis to have been blind 
 and prejudiced; incapable of seeing the beauty 
 of simplicity and symmetry, or indisposed to resign 
 established errours, and to accept novel and com- 
 prehensive truths. Yet in judging thus, we are 
 probably ourselves influenced by prejudices arising 
 from the knowledge and received opinions of our 
 own times. For is it, in reality, clear that, before 
 the time of Copernicus, the Heliocentric Theory 
 (that which places the center of the celestial mo- 
 tions in the Sun,) had a claim to assent so decidedly 
 superior to the Geocentric Theory, which places 
 the Earth in the center? What is the basis of 
 the heliocentric theory? That the relative mo- 
 tions are the same, on that and on the other sup- 
 position. So far, therefore, the two hypotheses are 
 exactly on the same footing. But, it is urged, on 
 the heliocentric side we have the advantage of sim- 
 plicity : true ; but we have, on the other side, the 
 testimony of our senses ; that is, the geocentric 
 doctrine is the obvious and spontaneous interpre- 
 tation of the appearances. Both these arguments, 
 simplicity on the one side, and obviousness on the 
 other, are vague, and we may venture to say, both 
 indecisive. We cannot establish any strong pre- 
 ponderance of probability in favour of the former 
 
PRELUDE TO THE EPOCH OF COPERNICUS. 381 
 
 doctrine, without going much further into the ar- 
 guments of the question. 
 
 Nor, when we speak of the superior simplicity 
 of the Copernican theory, must we forget, that 
 though this theory has undoubtedly, in this respect, 
 a great advantage over the Ptolemaic, yet that the 
 Copernican system itself is very complex, when it 
 undertakes to account, as the Ptolemaic did, for 
 the inequalities of the motions of the sun, moon, 
 and planets ; and that, in the hands of Copernicus, 
 it retained a large share of the eccentrics and 
 epicycles of its predecessor, and, in some parts, with 
 increased machinery. The heliocentric theory, with- 
 out these appendages, would not approach the 
 Ptolemaic, in the accurate explanation of facts; 
 and as those who had placed the sun in the center 
 had never, till the time of Copernicus, shown how 
 the inequalities were to be explained on that sup- 
 position, we may assert that after the promulga- 
 tion of the theory of eccentrics and epicycles on 
 the geocentric hypothesis, there was no published 
 heliocentric theory which could bear a comparison 
 with that hypothesis. 
 
 It is true, that all the contrivances of epicycles, 
 and the like, by which the geocentric hypothesis 
 was made to represent the phenomena, were sus- 
 ceptible of an easy adaptation to a heliocentric 
 method, when a good mathematician had once pro- 
 posed to himself the problem ; and this was pre- 
 cisely what Copernicus undertook and executed. 
 
382 HISTORY OF FORMAL ASTRONOMY. 
 
 But, till the appearance of his work, the helio- 
 centric system had never come before the world 
 except as a hasty and imperfect hypothesis ; which 
 bore a favourable comparison with the phenomena, 
 so long as their general features only were known ; 
 but which had been completely thrown into the 
 shade by the labour and intelligence bestowed upon 
 the Hipparchian or Ptolemaic theories by a long 
 series of great astronomers of all civilized countries. 
 
 But, though the astronomers who, before Co- 
 pernicus, held the heliocentric opinion, cannot, on 
 any good grounds, be considered as much more 
 enlightened than their opponents, it is curious to 
 trace the early and repeated manifestations of this 
 view of the universe. The distinct assertion of the 
 heliocentric theory among the Greeks is an evidence 
 of the clearness of their thoughts, and the vigour of 
 their minds; and it is a proof of the feebleness 
 and servility of intellect in the stationary period, 
 that, till the period of Copernicus, no one was found 
 to try the fortune of this hypothesis, modified 
 according to the improved astronomical knowledge 
 of the time. 
 
 The most ancient of the Greek philosophers to 
 whom the ancients ascribe the heliocentric doc- 
 trine, is Pythagoras ; but Diogenes Laertius makes 
 Philolaus, one of the followers of Pythagoras, the 
 first author of this doctrine. We learn from Ar- 
 chimedes, that it was held by his contempo- 
 rary, Aristarchus. " Aristarchus of Samos," says 
 
PRELUDE TO THE EPOCH OF COPERNICUS. 383 
 
 he 1 , makes this supposition, that the fixed stars and 
 the sun remain at rest, and that the earth revolves 
 round the sun in a circle." Plutarch 2 asserts that 
 this, which was only a hypothesis in the hands of 
 Aristarchus, was proved by Seleucus ; but we may 
 venture to say that, at that time, no such proof was 
 possible. Aristotle had recognized the existence of 
 this doctrine by arguing against it. " All things," 
 says he 3 , " tend to the center of the earth, and rest 
 there, and therefore the whole mass of the earth can- 
 not rest except there." Ptolemy had in like manner 
 argued against the diurnal motion of the earth : 
 such a revolution would, he urged, disperse into 
 surrounding space all the loose parts of the earth. 
 Yet he allowed that such a supposition would 
 facilitate the explanation of some phenomena. 
 Cicero appears to make Mercury and Venus revolve 
 about the sun, as does Martianus Capella at a later 
 period; and kSsneca says 4 , it is a worthy subject of 
 contemplation, whether the earth be at rest or in 
 motion: but at this period, as we may see from 
 Seneca himself, that habit of intellect which was 
 requisite for the solution of such a question, had 
 been succeeded by indistinct views, and rhetorical 
 forms of speech. If there were any good mathe- 
 maticians and good observers at this period, they 
 were employed in cultivating and verifying the Hip- 
 parchian theory. 
 
 1 Archim. Arenarius. 2 Quest. Plat. Delamb. A. A. vi. 
 3 Copernic. i. 7- 4 Quest. Nat. vii. 2. 
 
384 HISTORY OF FORMAL ASTRONOMY. 
 
 Next to the Greeks, the Indians appear to have 
 possessed that original vigour and clearness of 
 thought, from which true science springs. It is 
 remarkable that the Indians, also, had their helio- 
 centric theorists. Aryabatta 5 , (AD. 1322), and other 
 astronomers of that country, are said to have advo- 
 cated the doctrine of the earth's revolution on its 
 axis ; which opinion, however, was rejected by sub- 
 sequent philosophers among the Hindoos. 
 
 Some writers have thought that the heliocentric 
 doctrine was derived by Pythagoras and other 
 European philosophers, from some of the oriental 
 nations. This opinion, however, will appear to have 
 little weight, if we consider that the heliocentric 
 hypothesis, in the only shape in which the ancients 
 knew it, was too obvious to require much teaching; 
 that it did not and could not, so far as we know, 
 receive any additional strength from anything which 
 the oriental nations could teach; and that each 
 astronomer was induced to adopt or reject.it, not 
 by any information which a master could give him, 
 but by his love of geometrical simplicity on the 
 one hand, or the prejudices of sense on the other. 
 Real science, depending on a clear view of the 
 relation of phenomena to general theoretical ideas, 
 cannot be communicated in the way of secret and 
 exclusive traditions, like the mysteries of certain 
 arts and crafts. If the philosopher do not see 
 that the theory is true, he is little the better for 
 5 Lib. U. K. Hist. Ast. p. 11. 
 
PRELUDE TO THE EPOCH OF COPERNICUS. 385 
 
 having heard or read the words which assert its 
 truth. 
 
 It is impossible, therefore, for us to assent to 
 those views which would discover in the heliocentric 
 doctrines of the ancients, traces of a more profound 
 astronomy than any which they have transmitted 
 to us. Those doctrines were merely the plausible 
 conjectures of men with sound geometrical notions; 
 but they were never extended so as to embrace the 
 details of the existing astronomical knowledge ; and 
 perhaps we may say, that the analysis of the pheno- 
 mena into the arrangements of the Ptolemaic sys- 
 tem, was so much more obvious than any other, 
 that it must necessarily come first, in order to form 
 an introduction to the Copernican. 
 
 The true foundation of the heliocentric theory 
 for the ancients, was, as we have intimated, its per- 
 fect geometrical consistency with the general fea- 
 tures of the phenomena, and its simplicity. But 
 it was unlikely that the human mind would be con- 
 tent to consider the subject under this strict and 
 limited aspect alone. In its eagerness for wide 
 speculative views, it naturally looked out for other 
 and vaguer principles of connexion and relation. 
 Thus, as it had been urged in favour of the geo- 
 centric doctrine, that the heaviest body must be 
 in the center, it was maintained, as a leading recom- 
 mendation of the opposite opinion, that it placed 
 the Fire, the noblest element, in the Center of the 
 Universe. The authority of mythological ideas was 
 
 VOL. i. C c 
 
386 HISTORY OF FORMAL ASTRONOMY. 
 
 called in on both sides to support these views. 
 Numa, as Plutarch 6 informs us, built a circular 
 temple over the ever-burning Fire of Vesta ; typi- 
 fying, not the earth, but the Universe, which, 
 according to the Pythagoreans, has the Fire seated 
 at its Center. The same writer, in another of his 
 works, makes one of his interlocutors say, "Only, 
 my friend, do not bring me before a court of law 
 on a charge of impiety; as Cleanthes said, that 
 Aristarchus the Samian ought to be tried for im- 
 piety, because he removed that homestead of the 
 universe." This, however, seems to have been in- 
 tended as a pleasantry. 
 
 The prevalent physical views, and the opinions 
 concerning the causes of the motions of the parts 
 of the universe, were scarcely more definite than 
 those concerning the relations of the four elements, 
 till Galileo had founded the true doctrine of motion. 
 Though, therefore, arguments on this part of the 
 subject were the most important part of the contro- 
 versy after Copernicus, the force of such arguments 
 was at his time almost balanced. Even if more had 
 been known on such subjects, the arguments would 
 not have been conclusive : for instance, the vast mass 
 of the heavens, which is commonly urged as a reason 
 why the heavens do not move round the earth, 
 would not make such a motion impossible ; and, on 
 the other hand, the motions of bodies at the earth's 
 surface, which were alleged as inconsistent with its 
 
 6 De Facie in Orbe Lnnce, 6. 
 
PRELUDE TO THE EPOCH OP COPERNICUS. 387 
 
 motion, did not really disprove such an opinion. 
 But according to the state of the science of motion 
 before Copernicus, all reasonings from such prin- 
 ciples were utterly vague and obscure. 
 
 We must not omit to mention a modern who 
 preceded Copernicus, in the assertion at least of the 
 heliocentric doctrine. This was Nicholas of Cusa, 
 (a village near Treves,) a cardinal and bishop, who, 
 in the first half of the fifteenth century, was' very 
 eminent as a divine and mathematician ; and who 
 in a work, De Doctd Ignorantid, propounded the 
 doctrine of the motion of the earth ; more, how- 
 ever, as a paradox than as a reality. We cannot 
 consider this as any distinct anticipation of a pro- 
 found and consistent view of the truth. 
 
 We shall now examine further the promulgation 
 of the Heliocentric System by Copernicus, and its 
 consequences. 
 
 CC2 
 
388 
 
 CHAPTER II. 
 
 INDUCTION OF COPERNICUS. THE HELIOCENTRIC 
 THEORY ASSERTED ON FORMAL GROUNDS. 
 
 IT will be recollected that the formal are opposed 
 to the physical grounds of a theory; the former 
 term indicating that it gives a satisfactory account 
 of the relations of the phenomena in Space and 
 Time, that is, of the Motions themselves; while 
 the latter expression implies further that we in- 
 clude in our explanation the Causes of the motions, 
 the laws of Force and Matter. The strongest of 
 the considerations by which Copernicus was led 
 to invent and adopt his system of the universe 
 were of the former kind. He was dissatisfied, he 
 says, in his Preface addressed to the Pope, with 
 the want of symmetry in the Eccentric Theory, 
 as it prevailed in his days; and weary of the 
 uncertainty of the mathematical traditions. He 
 then sought through all the works of philosophers, 
 whether any had held opinions concerning the mo- 
 tions of the world, different from those received in 
 the established mathematical schools. He found, in 
 ancient authors, accounts of Philolaus and others, 
 who had asserted the motion of the earth. "Then," 
 he adds, " I, too, began to meditate concerning the 
 motion of the earth : and though it appeared an 
 
INDUCTION OF COPERNICUS. 38$ 
 
 absurd opinion, yet since I knew that, in previous 
 times, others had been allowed the privilege of 
 feigning what circles they chose, in order to explain 
 the phenomena, I conceived that I also might take 
 the liberty of trying whether, on the supposition of 
 the earth's motion, it was possible to find better 
 explanations than the ancient ones, of the revolu- 
 tions of the celestial orbs. 
 
 "Having then assumed the motions of the 
 earth, which are hereafter explained, by laborious 
 and long observation I at length found, that if the 
 motions of the other planets be compared with the 
 revolution of the earth, not only their phenomena 
 follow from the suppositions, but also that the 
 several orbs, and the whole system, are so con- 
 nected in order and magnitude, that no one part 
 can be transposed without disturbing the rest, and 
 introducing confusion into the whole universe." 
 
 Thus the satisfactory explanation of the ap- 
 parent motions of the planets, and the simplicity 
 and symmetry of the system, were the grounds on 
 which Copernicus adopted his theory ; as the crav- 
 ing for these qualities was the feeling which led 
 him to seek for a new theory. It is manifest that 
 in this, as in other cases of discovery, a clear and 
 steady possession of abstract Ideas, and an aptitude 
 in comprehending real Facts under these general 
 conceptions, must have been leading characters in 
 the discoverer's mind. He must have had a good 
 geometrical head, and great astronomical know- 
 
390 HISTORY OF FORMAL ASTRONOMY. 
 
 ledge. He must have seen, with peculiar distinct- 
 ness, the consequences which flowed from his sup- 
 positions as to the relations of space and time, the 
 apparent motions which resulted from the assumed 
 real ones; and he must also have known well all 
 the irregularities of the apparent motions for which 
 he had to account. We find indications of these 
 qualities in his expressions. A steady and calm 
 contemplation of the theory is what he asks for, as 
 the main requisite to its reception. If you suppose 
 the earth to revolve and the heaven to be at rest, 
 you will find, he says, "si serio animadvertas" if 
 you think steadily, that the apparent diurnal motion 
 will follow. And after alleging his reasons for his 
 system, he says 1 , "We are, therefore, not ashamed 
 to confess, that the whole of the space within the 
 orbit of the moon, along with the center of the 
 earth, moves round the sun in a year among the 
 other planets ; the magnitude of the world being so 
 great, that the distance of the earth from the sun 
 has no apparent magnitude when compared with 
 the sphere of the fixed stars." " All which things, 
 though they be difficult and almost inconceivable, 
 and against the opinion of the majority, yet, in the 
 sequel, by God's favour, we will make clearer than 
 the sun, at least to those who are not ignorant 
 of mathematics." 
 
 It will easily be understood, that since the ancient 
 
 1 Nicolai Copernici Torinensis de Revolutionibus Orbium 
 Ccelestium. Norimbergae. M.D.XLIII. p. 9. 
 
INDUCTION OF COPERNICUS 391 
 
 geocentric hypothesis ascribed to the planets those 
 motions which were apparent only, and which really 
 arose from the motion of the earth round the sun 
 in the new hypothesis, the latter scheme must much 
 simplify the planetary theory. Kepler" enumerates 
 eleven motions of the Ptolemaic system, which are 
 at once exterminated and rendered unnecessary by 
 the new system. Still, as the real motions, both of 
 the earth and the planets, are unequable, it was 
 requisite to have some mode of representing their 
 inequalities; and, accordingly, the ancient theory 
 of eccentrics and epicycles was retained, so far as 
 was requisite for this purpose. The planets revolved 
 round the sun by means of a Deferent, and a great 
 and small Epicycle ; or else by means of an Eccen- 
 tric and Epicycle, modified from Ptolemy's, for rea- 
 sons which we shall shortly mention. This mode 
 of representing the motions of the planets con- 
 tinued in use, till it was expelled by the discoveries 
 of Kepler. 
 
 Besides the daily rotation of the earth on its 
 axis, and its annual circuit about the sun, Coper- 
 nicus attributed to the axis a " motion of declina- 
 tion," by which, during the whole annual revo- 
 lution, the pole was constantly directed towards the 
 same part of the heavens. This constancy in the 
 absolute direction of the axis, or its moving parallel 
 to itself, may be more correctly vie\ved as not indi- 
 cating any separate motion. The axis continues in 
 
 2 Myst. Cosm. cap. 1. 
 
392 HISTORY OF FORMAL ASTRONOMY. 
 
 the same direction, because there is nothing to 
 make it change its direction ; just as a straw, lying 
 on the surface of a cup of water, continues to point 
 nearly in the same direction when the cup is carried 
 round a room. And this was noticed by Coper- 
 nicus's adherent, Rothman 3 , a few years after the 
 publication of the work De ftewlutionibus. " There 
 is no occasion," he says, in a letter to Tycho Brahe, 
 u for the triple motion of the earth : the annual and 
 diurnal motions suffice." This errour of Copernicus, 
 if it be looked upon as an errour, arose from his 
 referring the position of the axis to a limited space, 
 which he conceived to be carried round the sun 
 along with the earth, instead of referring it to fixed 
 or absolute space. When, in a Planetarium, the 
 earth is carried round the sun by being fastened to 
 a material radius, it is requisite to give a motion to 
 the axis by additional machinery, in order to enable 
 it to preserve its parallelism. A similar confusion 
 of geometrical conception, produced by a double 
 reference to absolute space and to the center of 
 revolution, often leads persons to dispute whether 
 the moon, which revolves about the earth, always 
 turning to it the same face, revolves about her axis 
 or no. 
 
 It is also to be noticed that the precession of 
 
 the equinoxes made it necessary to suppose the 
 
 axis of the earth to be not exactly parallel to itself, 
 
 but to deviate from that position by a slight annual 
 
 3 Tycho. Epist. i. p. 184, A. D. 1590. 
 
INDUCTION OF COPERNICUS. 393 
 
 difference. Copernicus erroneously supposes the 
 precession to be unequable ; and his method of 
 explaining this change, which is simpler than that 
 of the ancients, becomes more simple still, when 
 applied to the true state of the facts. 
 
 The tendencies of our speculative nature, which 
 carry us onwards in pursuit of symmetry and rule, 
 and which thus produced the theory of Copernicus, 
 as they produce all theories, perpetually show their 
 vigour by overshooting their mark. They obtain 
 something by aiming at much more. They detect 
 the order and connexion which exist, by imagining 
 relations of order and connexion which have no 
 existence. Real discoveries are thus mixed with 
 baseless assumptions; profound sagacity is com- 
 bined with fanciful conjecture ; not rarely, or in pe- 
 culiar instances, but commonly, and in most cases ; 
 probably in all, if we could read the thoughts of 
 the discoverers as we read the books of Kepler. 
 To try wrong guesses is apparently the only way to 
 hit upon right ones. The character of the true 
 philosopher is, not that he never conjectures hazard- 
 ously, but that his conjectures are clearly conceived 
 and brought into rigid contact with facts. He sees 
 and compares distinctly the ideas and the things, 
 the relations of his notions to each other and to 
 phenomena. Under these conditions it is not only 
 excusable, but necessary for him, to snatch at every 
 semblance of general rule ; to try all promising 
 forms of simplicity and symmetry. 
 
394 HISTORY OF FORMAL ASTRONOMY. 
 
 Copernicus is not exempt from giving us, in his 
 work, an example of this character of the inventive 
 spirit. The axiom that the celestial motions must 
 be circular and uniform, appeared to him to have 
 strong claims to acceptation ; and his theory of the 
 inequalities of the planetary motions is fashioned 
 upon it. His great desire was to apply it more 
 rigidly than Ptolemy had done. The time did not 
 come for rejecting the axiom, till the observations 
 of Tycho Brahe and the calculations of Kepler had 
 been made. 
 
 I shall not attempt to explain, in detail, Coper- 
 nicus' s system of the planetary inequalities. He 
 retained epicycles and eccentrics, altering their 
 centers of motion ; that is, he retained what was 
 true in the old system, translating it into his own. 
 The peculiarities of his method consisted in making 
 such a combination of epicycles as to supply the 
 place of the equant\ and to make all the motions 
 equable about the centers of motion. This device 
 was admired for a time, till Kepler's elliptic theory 
 expelled it, with all other forms of the theory of 
 epicycles: but we must observe that Copernicus 
 was aware of some of the discrepancies which be- 
 longed to that theory as it had, up to that time, 
 been propounded. In the case of Mercury's orbit, 
 which is more eccentric than that of the other 
 planets, he makes suppositions which are complex 
 indeed, but which show his perception of the im- 
 4 See p. 235. 
 
INDUCTION Of COPERNICUS. 3{)f> 
 
 perfection of the common theory ; and he proposes 
 a new theory of the moon, for the very reason 
 which did at last overturn the doctrine of epicycles, 
 namely, that the ratio of their distances from the 
 earth at different times was inconsistent with the 
 circular hypothesis 5 . 
 
 It is obvious, that, along with his mathematical 
 clearness of view, and his astronomical knowledge, 
 Copernicus must have had great intellectual bold- 
 ness and vigour, to conceive and fully develope a 
 theory so different as his was, from all received 
 doctrines. His pupil and expositor, Rheticus, says 
 to Schener, "I beg you to have this opinion con- 
 cerning that learned man, my Preceptor; that he 
 was an ardent admirer and follower of Ptolemy; 
 but when he was compelled by phenomena and 
 demonstration, he thought he did well to aim at 
 the same mark at which Ptolemy had aimed, though 
 with a bow and shafts of a very different material 
 from his. We must recollect what Ptolemy says, Ae7 
 
 c eXevOepov elvai Trf yvcofirj TQV /ueXAoi/Ta (pt\ocro(j)it>. 
 
 ' He who is to follow philosophy must be a free- 
 man in mind.'" Rheticus then goes on to defend 
 his master from the charge of disrespect to the 
 ancients: "That temper," he says, "is alien from 
 the disposition of every good man, and most espe- 
 cially from the spirit of philosophy, and from no 
 one more utterly than from my Preceptor. He 
 5 De Rev. iv. c. 2. 
 
396 HISTORY OF FORMAL ASTRONOMY. 
 
 was very far from rashly rejecting the opinions 
 of ancient philosophers, except for weighty reasons 
 and irresistible facts, through any love of novelty. 
 His years, his gravity of character, his excellent 
 learning, his magnanimity and nobleness of spirit, 
 are very far from having any liability to such a 
 temper, which belongs either to youth, or to ardent 
 and light tempers, or to those T&V /u.eya (ppovovvrtk 
 7rl Oewpiq. lAMpy, 6 who think much of themselves and 
 know little,' as Aristotle says." Undoubtedly this 
 deference for the great men of the past, joined with 
 the talent of seizing the spirit of their methods when 
 the letter of their theories is no longer tenable, is 
 the true mental constitution of discoverers. 
 
 Besides the intellectual energy which was re- 
 quisite in order to construct a system of doctrines 
 so novel as those of Copernicus, some courage was 
 necessary to the publication of such opinions ; cer- 
 tain, as they were, to be met, to a great extent, 
 by rejection and dispute, and perhaps by charges 
 of heresy and mischievous tendency. This last 
 danger, however, must not be judged so great as 
 we might infer from the angry controversies and 
 acts of authority which occurred in Galileo's time. 
 The Dogmatism of the stationary period, which 
 identified the cause of philosophical and religious 
 truth, had not yet distinctly felt itself attacked by 
 the advance of physical knowledge ; and therefore 
 had not begun to look with alarm on such move- 
 
INDUCTION OF COPERNICUS. 397 
 
 ments. Still, the claims of Scripture and of eccle- 
 siastical authority were asserted as paramount on 
 all subjects ; and it was obvious that many persons 
 would be disquieted or offended, with the new 
 interpretation of many scriptural expressions, which 
 the true theory would make necessary. This evil 
 Copernicus appears to have foreseen ; and this and 
 other causes long withheld him from publication. 
 He was himself an ecclesiastic; and, perhaps by 
 the patronage of his maternal uncle, was preben- 
 dary of the church of St. John at Thorn, and a 
 canon of the church of Frawenburg, in the diocese 
 of Ermeland 6 . He was a student at Bologna, a 
 professor of mathematics at Rome in the year 
 1500, and afterwards pursued his studies and ob- 
 servations at Fruemburg, at the mouth of the Vis- 
 tula 7 . His discovery of his system must have 
 occurred before 1507, for in 1543 he informs Pope 
 Paulus the Third, in his dedication, that he had 
 kept his book by him for four times the nine years 
 recommended by Horace, and then only published 
 it at the earnest entreaty of his friend Cardinal 
 Schomberg, whose letter is prefixed to the work. 
 " Though I know," he says, " that the thoughts of 
 a philosopher do not depend on the judgment of 
 the many, his, study being to seek out truth in all 
 things as far as that is permitted by God to human 
 reason : yet when I considered," he adds, " how 
 
 6 Rheticus, Nar. p. 94. 7 Riccioli. 
 
398 HISTORY OF FORMAL ASTRONOMY. 
 
 absurd my doctrine would appear, I long hesitated 
 whether I should publish my book, or whether it 
 were not better to follow the example of the 
 Pythagoreans and others, who delivered their doc- 
 trines only by tradition and to friends." It will 
 be observed that he speaks here of the opposition 
 of the established school of Astronomers, not of 
 Divines. The latter, indeed, he appears to con- 
 sider as a less formidable danger. " If perchance," 
 he says at the end of his preface, "there be na- 
 ratoXoyoi, vain babblers, who knowing nothing of 
 mathematics, yet assume the right of judging on 
 account of some place of Scripture perversely 
 wrested to their purpose, and who blame and attack 
 my undertaking ; I heed them not, and look upon 
 their judgments as rash and contemptible." He 
 then goes on to show that the globular figure of 
 the earth (which was, of course, at that time, an 
 undisputed point among astronomers,) had been 
 opposed on similar grounds by Lactantius, who, 
 though a writer of credit in other respects, had 
 spoken very childishly in that matter. In another 
 epistle prefixed to the work (apparently from ano- 
 ther hand, and asserted by Kepler" to be by Andreas 
 Osiander), the reader is reminded that the hypo- 
 theses of astronomers are not necessarily asserted 
 to be true, by those who propose them, but only 
 to be a way of representing facts. We may ob- 
 
 8 See the motto to Kepler's De Stella Martis. 
 
INDUCTION OF COPERNICUS. 399 
 
 serve that, in the time of Copernicus, when the 
 motion of the earth had not been connected with 
 the physical laws of matter and motion, it could 
 not be considered so distinctly real as it necessarily 
 was held to be in after times. 
 
 The delay of the publication of Copernicus's 
 work brought it to the end of his life : he died 
 in the year 1543, in which it was published. His 
 system was, however, to a certain extent, promul- 
 gated, and his fame diffused before that time. Car- 
 dinal Schomberg, in his letter of 1536, which has 
 been already mentioned says, "Some years ago, 
 when I heard tidings of your merit by the constant 
 report of all persons, my affection for you was 
 augmented, and I congratulated the men of our 
 time, among whom you flourish in so much honour. 
 For I had understood that you were not only 
 acquainted with the discoveries of ancient mathe- 
 maticians, but also had formed a new system of 
 the world, in which you teach that the earth 
 moves, the sun occupies the lowest, and conse- 
 quently, the middle place, the sphere of the fixed 
 stars remains immoveable and fixed." He then 
 proceeds to entreat him earnestly to publish his 
 work. The book appears to have been written 
 in 1539 9 , and is stated to have been sent in 1540 
 by Achilles P. Gessarus of Feldkirch to Dr. Voge- 
 linus of Constance, as a Palingenesia, or New Birth 
 of Astronomy. At the end of the De Revolutioni- 
 
 9 Ma3stlin. 
 
400 HISTORY OF FORMAL ASTRONOMY. 
 
 bus is the Narratio of Rheticus, already quoted. 
 Rheticus, it appears, went to Copernicus for the 
 purpose of studying his theory, and speaks of his 
 fc ' Preceptor" with strong admiration, as we have 
 seen. " He appears to me," says he, " more to re- 
 semble Ptolemy than any other astronomer." This, 
 it must be recollected, was selecting the highest 
 known subject of comparison. 
 
401 
 
 CHAPTER III. 
 
 SEQUEL TO COPERNICUS. THE RECEPTION AND DE- 
 VELOPMENT OF THE COPERNICAN THEORY. 
 
 Sect. 1. First Reception of the Copernican Theory. 
 
 THE theories of Copernicus made their way 
 among astronomers, in the manner in which 
 true astronomical theories always obtain the assent 
 of competent judges. They led to the construction 
 of Tables of the motion of the sun, moon, and 
 planets, as the theories of Hipparchus and Ptolemy 
 had done ; and the verification of the doctrines was 
 to be looked for, from the agreement of these 
 Tables with observation, through a sufficient course 
 of time. The work De Revolutionibus contains such 
 Tables. In 1551 Reinhold improved and repub- 
 lished Tables founded on the principles of Coper- 
 nicus. "We owe," he says in his preface, "great 
 obligations to Copernicus, both for his laborious 
 observations, and for restoring the doctrine of the 
 Motions. But though his geometry is perfect, the 
 good old man appears to have been, at times, care- 
 less in his numerical calculations. I have, there- 
 fore, recalculated the whole, from a comparison of 
 his observations with those of Ptolemy and others, 
 VOL. i. D D 
 
402 HISTORY OF FORMAL ASTRONOMY. 
 
 following nothing but the general plan of Coperni- 
 cus's demonstrations." These Prutenic Tables were 
 republished in 1571 and 1585, and continued in 
 repute for some time; till superseded by the Ru- 
 dolphine Tables of Kepler in 1627. The name 
 Prutenic, or Prussian, may be considered as a 
 tribute to the fame of Copernicus, for it shows that 
 his discoveries had inspired his countrymen with 
 the ambition of claiming a place in the literary 
 community of Europe. In something of the same 
 spirit, Rheticus wrote an Encomium Borussice 
 which was published along with his Narratio. 
 
 The Tables founded upon the Copernican sys- 
 tem were, at first, much more generally adopted 
 than the heliocentric doctrine on which they were 
 founded. Thus Magin published at Venice, in 1587, 
 New Theories of the Celestial Orbits, agreeing 
 with the Observations of Nicholas Copernicus. But 
 in the preface, after praising Copernicus, he says, 
 " Since, however, he, either for the sake of show- 
 ing his talents, or induced by his own reasons, has 
 revived the opinion of Nicetas, Aristarchus, and 
 others, concerning the motion of the earth, and 
 has disturbed the established constitution of the 
 world, which was a reason why many rejected, or 
 received with dislike, his hypotheses, I have thought 
 it worth while, that, rejecting the suppositions of 
 Copernicus, I should accommodate other causes to 
 his observations, and to the Prutenic tables." 
 
 This doctrine, however, was, as we have shown, 
 
SEQUEL TO COPERNICUS. 403 
 
 received with favour by many persons, even before 
 its general publication (p). We have already seen 
 the enthusiasm with which Rheticus, who was Co- 
 pernicus's pupil in the latter years of his life, speaks 
 of him. " Thus," says he, " God has given to my 
 excellent preceptor a reign without end; which 
 may He vouchsafe to guide, govern, and increase, 
 to the restoration of astronomical truth. Amen." 
 
 Of the immediate converts of the Copernican 
 system, who adopted it before the controversy on 
 the subject had attracted attention, I shall only 
 add Msestlin, and his pupil, Kepler. Maestlin pub- 
 lished in 1588 an Epitome Astronomies, in which 
 the immobility of the earth is asserted; but in 1596 
 he edited Kepler's Mysterium Cosmogmphicum, 
 and the Narratio of Rheticus; and in an epistle 
 of his own, which he inserts, he defends the Coper- 
 nican system by those physical reasonings which 
 we shall shortly have to mention, as the usual 
 arguments in this dispute. Kepler himself, in the 
 outset of the work just named, says, " When I was 
 at Tiibigen, attending to Michael Msestlin, being 
 disturbed by the manifold inconveniences of the 
 usual opinion concerning the world, I was so de- 
 lighted with Copernicus, of whom he made great 
 mention in his lectures, that I not only defended 
 his opinions in our disputations of the candidates, 
 but wrote a thesis concerning the First Motion 
 which is produced by the revolution of the earth." 
 This must have been in 1590. 
 
 DD2 
 
404 HISTORY OF FORMAL ASTRONOMY. 
 
 The differences of opinion respecting the Coper- 
 nican system, of which we thus see traces, led to 
 a controversy of some length and extent. This 
 controversy turned principally upon physical con- 
 siderations, which were much more distinctly dealt 
 with by Kepler, and others of the followers of 
 Copernicus, than they had been by the discoverer 
 himself. I shall, therefore, give a separate consi- 
 deration to this part of the subject. It may be 
 proper, however, in the first place, to make a few 
 observations on the progress of the doctrine, in- 
 dependently of these physical speculations. 
 
 Sect. 2. Diffusion of the Copernican Theory. 
 
 THE diffusion of the Copernican opinions in the 
 world did not take place rapidly at first. Indeed, 
 it was necessarily some time before the progress of 
 observation, and of theoretical mechanics, gave the 
 heliocentric doctrine that superiority in argument, 
 which now makes us wonder that men should have 
 hesitated when it was presented to them. Yet there 
 were some speculators of this kind, who were at- 
 tracted at once by the enlarged views of the uni- 
 verse which it opened to them. Among these was 
 the unfortunate Giordano Bruno of Nola, who was 
 burnt as a heretic at Rome in 1600. The heresies 
 which led to his unhappy fate were, however, not 
 his astronomical opinions, but a work which he 
 published in England, and dedicated to Sir Philip 
 
SEQUEL TO COPERNICUS. 405 
 
 Sydney, under the title of Spaccio delict Bestia 
 Trionfante, and which is understood to contain a 
 bitter satire of the Catholic religion and the papal 
 government. Montucla conceives that, by his rash- 
 ness in visiting Italy after putting forth such a 
 work, he compelled the government to act against 
 him. Bruno embraced the Copernican opinions at 
 an early period, and connected with them the 
 belief in innumerable worlds besides that which we 
 inhabit ; as also certain metaphysical or theological 
 doctrines, which he called the Nolan Philosophy. 
 In 1591 he published De innumerabilibm Mundis 
 et infigurabili, sen de Universo et Mundis, in 
 which he maintains that each star is a sun, about 
 which revolve planets like our earth; but this opi- 
 nion is mixed up with a large mass of baseless 
 verbal speculations. 
 
 Giordano Bruno is a disciple of Copernicus on 
 whom we may look with peculiar interest, since he 
 probably had a considerable share in introducing 
 the new opinions into England 1 . He visited this 
 country in the reign of Queen Elizabeth, and speaks 
 of her and of her councillors in terms of praise, 
 which appear to show that his book was intended 
 for English readers ; though he describes the mob 
 which was usually to be met with in the streets 
 of London, with expressions of great disgust: "Una 
 plebe la quale in essere irrespettevole, incivile, 
 
 1 See Burton's Anal. Mel., Pref. "Some prodigious tenet or 
 paradox of the earth's motion," &c. " Bruno," c. 
 
406 HISTORY OF FORMAL ASTRONOMY. 
 
 rozza, rustica, selvatiea, et male allevata, non cede 
 ad altra che pascer possa la terra nel suo senoV 
 The work to which I refer is La Cena de le Cenere, 
 and narrates what took place at a supper held on 
 the evening of Ash Wednesday (about 1583, see 
 p. 145 of the book), at the house of Sir Fulk Gre- 
 ville, in order to give " II Nolano" an opportunity 
 of defending his peculiar opinions. His principal 
 antagonists are two " Dottori d' Oxonia," whom 
 Bruno calls Nundinio and Torquato. The subject 
 is not treated in any very masterly manner on 
 either side ; but the author makes himself have 
 greatly the advantage not only in argument, but 
 in temper and courtesy : and in support of his 
 representations of " pedantesca, ostinatissima igno- 
 ranza et presunzione, mista con una rustica inci- 
 vilita, che farebbe prevaricar la pazienza di Giobbe," 
 in his opponents, he refers to a public disputation 
 which he had held at Oxford with these doctors 
 of theology, in presence of Prince Alasco, and 
 many of the English nobility 3 . 
 
 Among the evidences of the difficulties which 
 still lay in the way of the reception of the Coper- 
 nican system, we may notice Bacon, who, as is 
 well known, constantly refused his assent to it. 
 It is to be observed, however, that he does not 
 reject the opinion of the earth's motion in so pe- 
 remptory and dogmatical a manner as he is some- 
 times accused of doing: thus in the Thema Cceli 
 
 2 Opere di Giordano Bruno, vol. i. p. 146. 3 vol. i, p. 179. 
 
SEQUEL TO COPERNICUS. 407 
 
 he says, "The earth, then, being supposed to be 
 at rest (for that now appears to us the more true 
 opinion)." And in his tract On the Cause of the 
 Tides, he says, " If the tide of the sea be the ex- 
 treme and diminished limit of the diurnal motion 
 of the heavens, it will follow that the earth is 
 immovable ; or at least that it moves with a much 
 slower motion than the water." In the Descriptio 
 Globi Intellectualis he gives his reasons for not 
 accepting the heliocentric theory. " In the system 
 of Copernicus there are many and grave diffi- 
 culties: for the threefold motion with which he 
 encumbers the earth is a serious inconvenience; 
 and the separation of the sun from the planets, with 
 which he has so many affections in common, is 
 likewise a harsh step : and the introduction of so 
 many immovable bodies into nature, as when he 
 makes the sun and the stars immovable, the bodies 
 which are peculiarly lucid and radiant; and his 
 making the moon adhere to the earth in a sort 
 of epicycle ; and some other things which he as- 
 sumes, are proceedings which mark a man who 
 thinks nothing of introducing fictions of any kind 
 into nature, provided his calculations turn out 
 well." We have already explained that, in attri- 
 buting three motions of the earth, Copernicus had 
 presented his system encumbered with a complexity 
 not really belonging to it. But it will be seen 
 shortly, that Bacon's fundamental objection to this 
 system was his wish for a system which could be 
 
408 HISTORY OF FORMAL ASTRONOMY. 
 
 supported by sound physical considerations; and 
 it must be allowed, that at the period of which we 
 are speaking, this had not yet been done in favour 
 of the Copernican hypothesis. We may add, how- 
 ever, that it is not quite clear that Bacon was 
 in full possession of the details of the astronomical 
 systems which that of Copernicus was intended to 
 supersede ; and that thus he, perhaps, did not see 
 how much less harsh were these fictions, as he 
 called them, than those which were the inevitable 
 alternatives. Perhaps he might even be liable to a 
 little of that indistinctness, with respect to strictly 
 geometrical conceptions, which we have remarked 
 in Aristotle. We can hardly otherwise account 
 for his not seeing any use in resolving the appa- 
 rently irregular motion of a planet into separate 
 regular motions. Yet he speaks slightingly of this 
 important step 4 . "The motion of planets, which 
 is constantly talked of as the motion of regression, 
 or renitency, from west to east, and which is 
 ascribed to the planets as a proper motion, is not 
 true ; but only arises from appearance, from the 
 greater advance of the starry heavens towards the 
 west, by which the planets are left behind to the 
 east." Undoubtedly those who spoke of such a 
 motion of regression, were aware of this ; but they 
 saw how the motion was simplified by this way of 
 conceiving it, which Bacon seems not to have seen. 
 Though, therefore, we may admire Bacon for the 
 4 Thema Cceli, p. 246. 
 
SEQUEL TO COPERNICUS. 409 
 
 stedfastness with which he looked forwards to phy- 
 sical astronomy as the great and proper object of 
 philosophical interest, we cannot give him credit 
 for seeing the full value and meaning of what 
 had been done, up to his time, in Formal Astro- 
 nomy. 
 
 Bacon's contemporary, Gilbert, whom he fre- 
 quently praises as a philosopher, was much more 
 disposed to adopt the Copernican opinions, though 
 even he does not appear to have made up his 
 mind to assent to the whole of the system. In his 
 work, De Magnete, (printed 1600,) he gives the 
 principal arguments in favour of the Copernican 
 system, and decides that the earth revolves on its 
 axis 5 . He connects this opinion with his magnetic 
 doctrines ; and especially endeavours by that means 
 to account for the precession of the equinoxes. 
 But he does not seem to have been equally con- 
 fident of its annual motion. In a posthumous work, 
 published in 1651, (De Mundo Nostro Sublunari 
 Philosophia Nova) he appears to hesitate between 
 the systems of Tycho and Copernicus". Indeed, it 
 is probable that at this period many persons were 
 in a state of doubt on such subjects. Milton, at 
 a period somewhat later, appears to have been still 
 undecided. In the opening of the eighth book of 
 the Paradise Lost, he makes Adam state the dif- 
 ficulties of the Ptolemaic hypothesis, to which the 
 archangel Raphael opposes the usual answers ; but 
 
 5 Lib. vi. capp. 3, 4. 6 Lib. ii. cap. 20 
 
410 HISTORY OF FORMAL ASTRONOMY. 
 
 afterwards suggests to his pupil the newer sys- 
 tem: 
 
 . . . . What if seventh to these 
 
 The planet earth, so stedfast though she seem, 
 
 Insensibly three different motions move? 
 
 Par. Lost, B. viii. 
 
 Milton's leaning however, seems to have been 
 for the new system ; we can hardly believe that he 
 would otherwise have conceived so distinctly, and 
 described with such obvious pleasure, the motion 
 of the earth : 
 
 Or she from west her silent course advance 
 With inoffensive pace, that spinning sleeps 
 On her soft axle, while she paces even, 
 And bears thee soft with the smooth air along. 
 
 Par. Lost, B. viii. 
 
 Perhaps the works of the celebrated Bishop 
 Wilkins tended more than any others to the dif- 
 fusion of the Copernican system in England, since 
 even their extravagancies drew a stronger attention 
 to them. In 1638, when he was only twenty-four 
 years old, he published a book entitled The Dis- 
 covery of a New World; or, a Discourse tending 
 to prove that it is probable there may be another 
 habitable World in the Moon ; with a Discourse 
 concerning the possibility of a passage thither. The 
 latter part of his subject was, of course, an obvious 
 mark for the sneers and witticisms of critics. Two 
 years afterwards, in 1640, appeared his Discourse 
 concerning a new Planet ; tending to prove that it 
 
SEQUEL TO COPERNICUS. 411 
 
 is probable our Earth is one of the Planets : in 
 which he urged the reasons in favour of the helio- 
 centric system ; and explained away the opposite 
 arguments, especially those drawn from the sup- 
 posed declarations of Scripture. Probably a good 
 deal was done for the establishment of those 
 opinions by Thomas Salusbury, who was a warm 
 admirer of Galileo, and published, in 1661, a trans- 
 lation of several of his works bearing upon this 
 subject. The mathematicians of this country, in 
 the seventeenth century, as Napier and Briggs, 
 Horrox and Crabtree, Oughtred and Ward, Wallis 
 and Wren, were probably all decided Copernicans. 
 Kepler dedicates one of his works to Napier, and 
 Ward invented an approximate method of solving 
 Kepler's problem, still known as " the simple ellip- 
 tical hypothesis." Horrox wrote, and wrote well, 
 in defence of the Copernican opinion, in his Kep- 
 lerian Astronomy defended and promoted, com- 
 posed (in Latin) probably about 1635, but not 
 published till 1673, the author having died at the 
 age of twenty-two, and his papers having been lost. 
 But Salusbury's work was calculated for another 
 circle of readers. " The book," he says in the intro- 
 ductory address, "being, for subject and design, 
 intended chiefly for gentlemen, I have been as care- 
 less of using a studied pedantry in my style, as 
 careful in contriving a pleasant and beautiful im- 
 pression." In order, however, to judge of the 
 advantage under which the Copernican system now 
 
412 HISTORY OF FORMAL ASTRONOMY. 
 
 came forwards, we must consider the additional 
 evidence for it which was brought to light by Gali- 
 leo's astronomical discoveries. 
 
 Sect. 3. The Heliocentric Theory confirmed by 
 Facts. Galileos Astronomical Discoveries. 
 
 THE long interval which elapsed between the last 
 great discoveries made by the ancients and the first 
 made by the moderns, had afforded ample time for 
 the developement of all the important consequences 
 of the ancient doctrines. But when the human 
 mind had been thoroughly roused again into acti- 
 vity, this was no longer the course of events. Dis- 
 coveries crowded on each other; one wide field 
 of speculation was only just opened, when a richer 
 promise tempted the labourers away into another 
 quarter. Hence the history of this period contains 
 the beginnings of many sciences, but exhibits none 
 fully worked out into a complete or final form. 
 Thus the science of statics, soon after its revival, 
 was eclipsed and overlaid by that of dynamics ; and 
 the Copernican system, considered merely with re- 
 ference to the views of its author, was absorbed in 
 the commanding interest of physical astronomy. 
 
 Still, advances were made which had an impor- 
 tant bearing on the heliocentric theory, in other 
 ways than by throwing light upon its physical prin- 
 ciples. I speak of the new views of the heavens 
 which the Telescope gave ; the visible inequalities 
 
SEQUEL TO COPERNICUS. 413 
 
 of the moon's surface ; the moon-like phases of the 
 planet Venus; the discovery of the satellites of 
 Jupiter, and of the ring of Saturn. These dis- 
 coveries excited at the time the strongest interest ; 
 both from the novelty and beauty of the objects 
 they presented to the sense ; from the way in which 
 they seemed to gratify man's curiosity with regard 
 to the remote parts of the universe ; and also from 
 that of which we have here to speak, their bearing 
 upon the conflict of the old and the new philo- 
 sophy, the heliocentric and geocentric theories. It 
 may be true, as Lagrange and Montucla say, that the 
 laws which Galileo discovered in mechanics implied 
 a profounder genius than the novelties he detected 
 in the sky : but the latter naturally attracted the 
 greater share of the attention of the world, and 
 were matter of keener discussion. 
 
 It is not to our purpose to speak here of the 
 details and of the occasion of the invention of the 
 Telescope ; it is well known that Galileo constructed 
 his about 1609, and proceeded immediately to apply 
 it to the heavens. The discovery of the Satellites 
 of Jupiter was almost immediately the reward of 
 this activity : and these were announced in his 
 Nuncius Sidereus, published at Venice in 1610. 
 The title of this work will best convey an idea of 
 the claim it made to public notice : " The Sidereal 
 Messenger, announcing great and very wonderful 
 spectacles, and offering them to the consideration 
 of every one, but especially of philosophers and 
 
414 HISTORY OF FORMAL ASTRONOMY. 
 
 astronomers ; which have been observed by Galileo 
 Galilei, &c. &c., by the assistance of a perspective 
 glass lately invented by him ; namely, in the face of 
 the moon, in innumerable fixed stars in the milky- 
 way, in nebulous stars, but especially in four planets 
 which revolve round Jupiter at different intervals 
 and periods with a wonderful celerity; which, 
 hitherto not known to any one, the author has 
 recently been the first to detect, and has decreed to 
 call the Medicean stars" 
 
 The interest this discovery excited was intense : 
 and men were at this period so little habituated to 
 accommodate their convictions on matters of sci- 
 ence to newly-observed facts, that several of " the 
 paper-philosophers," as Galileo termed them, appear 
 to have thought they could get rid of these new 
 objects by writing books against them. The effect 
 which the discovery had upon the reception of the 
 Copernican system was immediately very consider- 
 able. It showed that the real universe was very 
 different from that which ancient philosophers had 
 imagined, and suggested at once the thought that it 
 contained mechanism more various and more vast 
 than had yet been conjectured. And when the sys- 
 tem of the planet Jupiter thus offered to the bodily 
 eye a model or image of the solar system according 
 to the views of Copernicus, it supported the belief 
 of such an arrangement of the planets, by an 
 analogy all but irresistible. It thus, as a writer 7 of 
 
 7 Sir J. HeracheL 
 
SEQUEL TO COPERNICUS. 415 
 
 our own times has said, "gave the holding turn to 
 the opinions of mankind respecting the Copernican 
 system." We may trace this effect in Bacon, even 
 though he does not assent to the motion of the 
 earth. "We affirm," he says 8 , "the sun-following 
 arrangement (solisequium) of Venus and Mercury ; 
 since it has been found by Galileo that Jupiter also 
 has attendants." 
 
 The Nuncius Sidereus contained other disco- 
 veries which had the same tendency in other ways. 
 The examination of the moon showed, or at least 
 seemed to show, that she was a solid body, with 
 a surface extremely rugged and irregular, This, 
 though perhaps not bearing directly upon the ques- 
 tion of the heliocentric theory, was yet a blow to 
 the Aristotelians, who had, in their philosophy, 
 made the moon a body of a kind altogether dif- 
 ferent from this, and had given an abundant quan- 
 tity of reasons for the visible marks on her surface, 
 all proceeding on these preconceived views. Others 
 of his discoveries produced the same effect; for 
 instance, the new stars invisible to the naked eye, 
 and those extraordinary appearances called nebula. 
 
 But before the end of the year, Galileo had new 
 information to communicate, bearing more decid- 
 edly on the Copernican controversy. This intelli- 
 gence was indeed decisive with regard to the mo- 
 tion of Venus about the sun ; for he found that that 
 planet, in the course of her revolution, assumes the 
 
 8 Thema Cceli, ix. p. 253. 
 
416 HISTORY OF FORMAL ASTRONOMY 
 
 same succession of phases which the moon exhibits 
 in the course of a month. This he expressed by a 
 Latin verse : 
 
 Cynthiae figuras aemulatur mater amorum : 
 
 The queen of love like Cynthia shapes her forms: 
 
 transposing the letters of this line in the published 
 account, according to the practice of the age; which 
 thus showed the ancient love for combining verbal 
 puzzles with scientific discoveries, while it betrayed 
 the newer feeling, of jealousy respecting the priority 
 of discovery of physical facts. 
 
 It had always been a formidable objection to 
 the Copernican theory that this appearance of the 
 planets had not been observed. The author of that 
 theory had endeavoured to account for this, by 
 supposing that the rays of the sun passed freely 
 through the body of the planet; and Galileo takes 
 occasion to praise him for not being deterred from 
 adopting the system which, on the whole, appeared 
 to agree best with the phenomena, by meeting with 
 some appearances which it did not enable him to 
 explain 9 . Yet while the fate of the theory was yet 
 undecided, this could not but be looked upon as a 
 weak point in its defences. 
 
 The objection, in another form also, was embar- 
 rassing alike to the Ptolemaic and Copernican sys- 
 tems. Why, it was asked, did not Venus appear 
 four times as large when near her perigee, as when 
 near her apogee? The author of the epistle pre- 
 9 L. U. K. Life of Galileo, p. 35. 
 
SEQUEL TO COPERNICUS. 417 
 
 fixed to Copernicus's work had taken refuge in this 
 argument from the danger of being supposed to 
 believe in the reality of the system ; and Bruno had 
 attempted to answer it by saying, that luminous 
 bodies were not governed by the same laws of per- 
 spective as opaque ones. But a more satisfactory 
 answer now readily offered itself. Venus does not 
 appear four times as large when she is four times 
 as near, because her bright part is not four times 
 as large, though her visible diameter is ; and as she 
 is too small for us to see her shape with the naked 
 eye, we judge of her size only by the quantity of light. 
 
 The other great discoveries made in the heavens 
 by means of telescopes, as that of Saturn's ring 
 and his satellites, the spots in the sun, and others, 
 belong to the further progress of astronomy. But 
 we may here observe, that this doctrine of the 
 motion of Mercury and Venus about the sun was 
 further confirmed by Kepler's observation of the 
 transit of the former planet over the sun in 1631. 
 Our countryman Horrox was the first person who, in 
 1639, had the satisfaction of seeing a transit of Venus. 
 These events are a remarkable instance of the 
 way in which a discovery in art, (for at this period, 
 the making of telescopes must be mainly so con- 
 sidered,) may influence the progress of science. We 
 shall soon have to notice a still more remarkable 
 example of the way in which two sciences (Astro- 
 nomy and Mechanics) may influence and promote 
 the progress of each other. 
 
 VOL. i. E E 
 
418 HISTORY OF FORMAL ASTRONOMY. 
 
 Sect. 4. The Copernican System opposed on 
 Theological Grounds. 
 
 THE doctrine of the Earth's motion round the Sun, 
 when it was asserted and promulgated by Coper- 
 nicus, soon after 1500, excited no visible alarm 
 among the theologians of his own time. Indeed, it 
 was received with favour by the most intelligent 
 ecclesiastics ; and lectures in support of the helio- 
 centric doctrine were delivered in the ecclesiastical 
 colleges. But the assertion and confirmation of 
 this doctrine by Galileo, about a century later, 
 excited a storm of controversy, and was visited with 
 severe condemnation. Galileo's own behaviour 
 appears to have provoked the interference of the 
 ecclesiastical authorities ; but there must have been 
 a great change in the temper of the times to make 
 it possible for his adversaries to bring down the 
 sentence of the Inquisition upon opinions which 
 had been so long current without giving any serious 
 offense (Q). 
 
 The heliocentric doctrine had for a century 
 been making its way into the minds of thoughtful 
 men, on the general ground of its simplicity and 
 symmetry. Galileo appears to have thought that 
 now, when these original recommendations of the 
 system had been reinforced by his own discoveries 
 and reasonings, it ought to be universally acknow- 
 ledged as a truth and a reality. And when argu- 
 ments against the fixity of the sun and the motion 
 
SEQUEL TO COPERNICUS. 419 
 
 of the earth were adduced from the expressions of 
 scripture, he could not be satisfied without main- 
 taining his favourite opinion to be conformable to 
 scripture as well as to philosophy; and he was very 
 eager in his attempts to obtain from authority a 
 declaration to this effect. The ecclesiastical autho- 
 rities were naturally averse to express themselves 
 in favour of a novel opinion, startling to the com- 
 mon mind, and contrary to the most obvious mean- 
 ing of the words of the Bible ; and when they were 
 compelled to pronounce, they decided against Gali- 
 leo and his doctrines. He was accused before the 
 Inquisition in 1615 ; but at that period the result 
 was that he was merely recommended to confine 
 himself to the mathematical reasonings upon the 
 system, and to abstain from meddling with the 
 scripture. Galileo's zeal for his opinions soon led 
 him again to bring the question under the notice of 
 the Pope, and the result was a declaration of the 
 Inquisition that the doctrine of the earth's motion 
 appeared to be contrary to the sacred scripture. 
 Galileo was prohibited from defending and teaching 
 this doctrine in any manner, and promised obedi- 
 ence to this injunction. But in 1632 he published 
 his Dialogo delli due Massimi Sistemi del Hondo, 
 Tolemaico e Copernicano:" and in this, he defended 
 the heliocentric system by all the strongest argu- 
 ments which its admirers used. Not only so, but he 
 introduced into this Dialogue a character under the 
 name of Simplicius, in whose mouth was put the 
 
 EE 2 
 
420 HISTORY OF FORMAL ASTRONOMY. 
 
 defence of all the ancient dogmas, and who was 
 represented as defeated at all points in the discus- 
 sion ; and he prefixed to the Dialogue a notice, To 
 the Discreet Reader, in which, in a vein of trans- 
 parent irony, he assigned his reasons for the pub- 
 lication. " Some years ago," he says, " a wholesome 
 edict was promulgated at Rome, which, in order to 
 check the perilous scandals of the present age, 
 imposed silence upon the Pythagorean opinion of 
 the motion of the earth. There was not wanting," 
 he adds, "persons who rashly asserted that this 
 decree was the result, not of a judicious inquiry, 
 but of a passion ill-informed ; and complaints were 
 heard that counsellors, utterly unacquainted with 
 astronomical observations, ought not to be allowed, 
 with their undue prohibitions, to clip the wings of 
 speculative intellects. At the hearing of rash la- 
 mentations like these, my zeal could not keep 
 silence." And he then goes on to say that he 
 wishes, by the publication of his Dialogue, to show 
 that the subject had been fully examined at Rome. 
 The result of this was that Galileo was condemned 
 for his infraction of the injunction laid upon him in 
 1616; his Dialogue was prohibited; he himself 
 was commanded to abjure on his knees the doc- 
 trine which he had taught ; and this abjuration he 
 performed (R). 
 
 This celebrated event must be looked upon 
 rather as a question of decorum than a struggle in 
 which the interests of truth and free inquiry were 
 
SEQUEL TO COPERNICUS. 421 
 
 deeply concerned. The general acceptance of the 
 Copernican System was no longer a matter of 
 doubt. Several persons in the highest positions, 
 including the Pope himself, looked upon the doc- 
 trine with favourable eyes; and had shown their 
 interest in Galileo and his discoveries. They had 
 tried to prevent his involving himself in trouble 
 by discussing the question on scriptural grounds. It 
 is probable that his knowledge of those favourable 
 dispositions towards himself and his opinions led 
 him to suppose that the slightest colour of pro- 
 fessed submission to the church in his belief would 
 enable his arguments in favour of the system to 
 pass unvisited : the notice which I have quoted, 
 in which the irony is quite transparent and the 
 sarcasm glaringly obvious, was deemed too flimsy 
 a veil for the purpose of decency, and indeed must 
 have aggravated the offense. But it is not to be 
 supposed that the inquisitors believed Galileo's ab- 
 juration to be sincere, or even that they wished it 
 to be so. It is stated that when Galileo had made 
 his renunciation of the earth's motion, he rose from 
 his knees, and stamping on the earth with his foot, 
 said, E pur si muove " and yet it does move." 
 This is sometimes represented as the heroic soli- 
 loquy of a mind cherishing its conviction of the 
 truth in spite of persecution : I think we may more 
 naturally conceive it uttered as a playful epigram 
 in the ear of a cardinal's secretary, with a full 
 
422 HISTORY OF FORMAL ASTRONOMY. 
 
 knowledge that it would be immediately repeated 
 to his master. 
 
 The ecclesiastical authorities having once de- 
 clared the doctrine of the earth's motion to be 
 contrary to scripture and heretical, long adhered 
 in form to this declaration, and did not allow the 
 Copernican system to be taught in any other way 
 than as a "hypothesis." The Padua edition of 
 Galileo's works, published in 1744, contains the 
 Dialogue which now, the editors say, "Esce final- 
 mente alia luce colle debite license ;" but they add, 
 " quanto allo Quistione principale del moto della 
 terra, anche noi ci conformiamo alia ritrazione et 
 protesta dell' autore dichiarando nella piu solenne 
 forma, che non pero ne dee ammetersi se non come 
 pura Ipotesi Mathematice, che serve a spiegare piu 
 agevolamento certi fenomeni." And in the edition 
 of Newton's Principia, published in 1760, by Le 
 Sueur and Jacquier, of the Order of Minims, the edi- 
 tors prefix to the Third Book their Dedaratio, that 
 though Newton assumes the hypothesis of the mo- 
 tion of the earth, and therefore they had used 
 similar language, they were, in doing this, assuming 
 a character which did not belong to them. " Hinc 
 alienam coacti sumus gerere personam." They add, 
 "Ca3terum latis a summis Pontificibus contra tel- 
 luris motum Decretis, nos obsequi profitemur." 
 
 By thus making decrees against a doctrine 
 which in the course of time was established as an 
 
SEQUEL TO COPERNICUS. 423 
 
 indisputable scientific truth, the See of Rome was 
 guilty of an unwise and unfortunate stretch of eccle- 
 siastical authority. But though we do not hesitate 
 to pronounce such a judgment on this case, we 
 may add that there is a question of no small real 
 difficulty, which the progress of science often brings 
 into notice, as it did then. The Revelation on 
 which our religion is founded, seems to declare, 
 or to take for granted, opinions on points on 
 which Science also gives her decision; and we then 
 come to this dilemma, that doctrines, established 
 by a scientific use of reason, may seem to con- 
 tradict the declarations of revelation, according to 
 our view of its meaning; and yet, that we can- 
 not, in consistency with our religious views, make 
 reason a judge of the truth of revealed doctrines. 
 In the case of Astronomy, on which Galileo was 
 called in question, the general sense of cultivated 
 and sober-minded men has long ago drawn that 
 distinction between religious and physical tenets, 
 which is necessary to resolve this dilemma. On 
 this point, it is reasonably held, that the phrases 
 which are employed in Scripture respecting astro- 
 nomical facts, are not to be made use of to guide 
 our scientific opinions; they may be supposed to 
 answer their end if they fall in with common no- 
 tions, and are thus effectually subservient to the 
 moral and religious import of revelation. But the 
 establishment of this distinction was not accom- 
 plished without long and distressing controversies. 
 
424 HISTORY OF FORMAL ASTRONOMY. 
 
 Nor, if we wish to include all cases in which the 
 same dilemma may again come into play, is it easy 
 to lay down an adequate canon for the purpose. 
 For we can hardly foresee, beforehand, what part 
 of the past history of the universe may eventually 
 be found to come within the domain of science ; 
 or what bearing the tenets, which science esta- 
 blishes, may have upon our view of the provi- 
 dential and revealed government of the world. But 
 without attempting here to generalize on this sub- 
 ject, there are two reflections which may be worth 
 our notice : they are supported by what took place 
 in reference to Astronomy on the occasion of which 
 we are speaking; and may, at other periods, be 
 applicable to other sciences. 
 
 In the first place, the meaning which any gene- 
 ration puts upon the phrases of Scripture, depends, 
 more than is at first sight supposed, upon the 
 received philosophy of the time. Hence, while 
 men imagine that they are contending for Reve- 
 lation, they are, in fact, contending for their own 
 interpretation of Revelation, unconsciously adapted 
 to what they believe to be rationally probable. 
 And the new interpretation, which the new phi- 
 losophy requires, and which appears to the older 
 school to be a fatal violence done to the authority 
 of religion, is accepted by their successors without 
 the dangerous results which were apprehended. 
 When the language of Scripture, invested with its 
 new meaning, has become familiar to men, it is 
 
SEQUEL TO COPERNICUS. 
 
 found that the ideas which it calls up, are quite 
 as reconcileable as the former ones were, with the 
 soundest religious views. And the world then 
 looks back with surprize at the errour of those 
 who thought that the essence of Revelation was 
 involved in their own arbitrary version of some 
 collateral circumstance. At the present day we 
 can hardly conceive how reasonable men should 
 have imagined that religious reflections on the sta- 
 bility of the earth, and the beauty and use of the 
 luminaries which revolve round it, would be inter- 
 fered with by its being acknowledged that this rest 
 and motion are apparent only. 
 
 In the next place, we may observe that those 
 who thus adhere tenaciously to the traditionary or 
 arbitrary mode of understanding Scriptural expres- 
 sions of physical events, are always strongly con- 
 demned by succeeding generations. They are looked 
 upon with contempt by the world at large, who 
 cannot enter into the obsolete difficulties with 
 which they encumbered themselves ; and with pity 
 by the more considerate and serious, who know 
 how much sagacity and right-mindedness are re- 
 quisite for the conduct of philosophers and religious 
 men on such occasions; but who know also how 
 weak and vain is the attempt to get rid of the 
 difficulty by merely denouncing the new tenets as 
 inconsistent with religious belief, and by visiting 
 the promulgators of them with severity such as the 
 state of opinions and institutions may allow. The 
 
426 HISTORY OF FORMAL ASTRONOMY. 
 
 prosecutors of Galileo are still held up to the scorn 
 and aversion of mankind ; although, as we have 
 seen, they did not act till it seemed that their 
 position compelled them to do so, and then pro- 
 ceeded with all the gentleness and moderation 
 which were compatible with judicial forms. 
 
 Sect. 5. The Heliocentric Theory confirmed on 
 Physical considerations. (Prelude to Kepler s 
 Astronomical Discoveries.) 
 
 BY physical views, I mean, as I have already said, 
 those which depend on the causes of the motions 
 of matter, as, for instance, the consideration of the 
 nature and laws of the force by which bodies fall 
 downwards. Such considerations were necessarily 
 and immediately brought under notice by the exa- 
 mination of the Copernican theory ; but the loose 
 and inaccurate notions which prevailed respecting 
 the nature and laws of force, prevented, for some 
 time, all distinct reasoning on this subject, and 
 gave truth little advantage over errour. The for- 
 mation of a new Science, the Science of Motion 
 and its Causes, was requisite, before the heliocen- 
 tric system could have justice done it with regard 
 to this part of the subject. 
 
 This discussion was at first carried on, as was 
 to be expected, in terms of the received, that is, 
 the Aristotelian doctrines. Thus, Copernicus says 
 that terrestrial things appear to be at rest when 
 they have a motion according to nature, that is, 
 
SEQUEL TO COPERNICUS. 427 
 
 a circular motion; and ascend or descend when 
 they have, in addition to this, a rectilinear motion 
 by which they endeavour to get into their own 
 place. But his disciples soon began to question 
 the Aristotelian dogmas, and to seek for sounder 
 views by the use of their own reason. " The great 
 argument against this system," says Msestlin, "is 
 that heavy bodies are said to move to the center 
 of the universe, and light bodies from the center. 
 But I would ask, where do we get. this experience 
 of heavy and light bodies ? and how is our know- 
 ledge on these subjects extended so far that we 
 can reason with certainty concerning the center 
 of the whole universe ? Is not the only residence 
 and home of all the things which are heavy and 
 light to us, the earth and the air which surrounds 
 it? and what is the earth and the ambient air 
 with respect to the immensity of the universe ? It 
 is a point, a punctule, or something, if there be 
 anything, still less. As our light and heavy bodies 
 tend to the center of our earth, it is credible that 
 the sun, the moon, and the other lights, have a 
 similar affection, by which they remain round as 
 we see them, but none of these centers is necessarily 
 the center of the universe." 
 
 The most obvious and important physical diffi- 
 culty attendant upon the supposition of the motion 
 of the earth was thus stated. If the earth move, 
 how is it that a stone, dropped from the top of 
 a high tower, falls exactly at the foot of the 
 
428 HISTORY OF FORMAL ASTRONOMY. 
 
 tower? since the tower being carried from west 
 to east by the diurnal revolution of the earth, 
 the stone must be left behind to the west of the 
 place from which it was let fall. The proper 
 answer to this was, that the motion which the fall- 
 ing body received from its tendency downwards 
 was compounded with the motion which, before it 
 fell, it had in virtue of the earth's rotation : but 
 this answer could not be clearly made or appre- 
 hended, till Galileo and his pupils had established 
 the laws of such compositions of motion arising 
 from different forces. Roth man, Kepler, and other 
 defenders of the Copernican system, gave their 
 reply somewhat at a venture, when they asserted 
 that the motion of the earth was communicated to 
 bodies at its surface. Still, the facts which indicate 
 and establish this truth are obvious, when the sub- 
 ject is steadily considered; and the Copernicans 
 soon found that they had the superiority of argu- 
 ment on this point as well as others. The attacks 
 upon the Copernican system by Durret, Morin, 
 Riccioli, and the defence of it by Galileo, Lansberg, 
 Gassendi 10 , left on all candid reasoners a clear 
 impression in favour of the system. Morin at- 
 tempted to stop the motion of the earth, which he 
 called breaking its wings; his Alee Terrce Fractce 
 was published in 1643, and answered by Gassendi. 
 And Riccioli, as late as 1653, in his Almagestum 
 Novum, enumerated fifty-seven Copernican argii- 
 10 Del. A. M. vol. i. p. 594. 
 
SEQUEL TO COPERNICUS: 429 
 
 ments, and pretended to refute them all : but such 
 reasonings now made no converts ; and by this 
 time the mechanical objections to the motion of 
 the earth were generally seen to be baseless, as 
 we shall relate when we come to speak of the pro- 
 gress of mechanics as a distinct science. In the 
 mean time, the beauty and simplicity of the helio- 
 centric theory were perpetually winning the admi- 
 ration even of those who, from one cause or other, 
 refused their assent to it. Thus Riccioli, the last 
 of its considerable opponents, allows its superiority 
 in these respects ; and acknowledges (in 1653) that 
 the Copernican belief appears rather to increase 
 than diminish under the condemnation of the de- 
 crees of the Cardinals. He applies to it the lines 
 of Horace 11 : 
 
 Per damna per caedes, ab ipso 
 Sunrit opes animumque ferro. 
 
 Untamed its pride, unchecked its course, 
 From foes and wounds it gathers force. 
 
 We have spoken of the influence of the motion 
 of the earth on the motions of bodies at its surface ; 
 but the notion of a physical connexion among the 
 parts of the universe was taken up by Kepler in 
 another point of view, which would probably have 
 been considered as highly fantastical, if the result 
 had not been, that it led to by far the most magni- 
 ficent and most certain train of truths which the 
 whole expanse of human knowledge can show. I 
 
 11 Almag. Nov. p. 102. 
 
430 HISTORY OF FORMAL ASTRONOMY. 
 
 speak of the persuasion of the existence of numeri- 
 cal and geometrical laws connecting the distances, 
 times, and forces of the bodies which revolve about 
 the central sun That steady and intense conviction 
 of this governing principle, which made its deve- 
 lopement and verification the leading employment 
 of Kepler's most active and busy life, cannot be 
 considered otherwise than as an example of pro- 
 found sagacity. That it was connected, though 
 dimly and obscurely, with the notion of a central 
 agency or influence of some sort, emanating from 
 the sun, cannot be doubted. Kepler, in his first 
 essay of this kind, the Mysterium Cosmographicum, 
 says, " The motion of the earth, which Copernicus 
 had proved by mathematical reasons, I wanted to 
 prove by physical, or, if you prefer it, metaphy- 
 sical." In the twentieth chapter of that work, he 
 endeavours to make out some relation between the 
 distances of the planets from the sun and their 
 velocities. The inveterate yet vague notions of 
 forces which preside in this attempt, may be judged 
 of by such passages as the following : " We must 
 suppose one of two things : either that the moving 
 spirits, in proportion as they are more removed 
 from the sun, are more feeble ; or that there is one 
 moving spirit in the center of all the orbits, namely, 
 in the sun, which urges each body the more vehe- 
 mently in proportion as it is nearer; but in more 
 distant spaces languishes in consequence of the 
 remoteness and attenuation of its virtue." 
 
SEQUEL TO COPERNICUS. 431 
 
 We must not forget, in reading such passages, 
 that they were written under a belief that force 
 was requisite to keep up, as well as to change the 
 motion of each planet ; and that a body, moving in 
 a circle, would stop when the force of the central 
 point ceased, instead of moving off in a tangent to 
 the circle, as we now know it would do. The force 
 which Kepler supposes is a tangential force, in the 
 direction of the body's motion, and nearly perpen- 
 dicular to the radius ; the force which modern phi- 
 losophy has established, is in the direction of the 
 radius, and nearly perpendicular to the body's path. 
 Kepler was right no further than in his suspicion of 
 a connexion between the cause of motion and the 
 distance from the center; not only was his know- 
 ledge imperfect in all particulars, but his most 
 general conception of the mode of action of a cause 
 of motion was erroneous. 
 
 With these general convictions and these phy- 
 sical notions in his mind, Kepler endeavoured to 
 detect numerical and geometrical relations among 
 the parts of the solar system. After extraordinary 
 labour, perseverance, and ingenuity, he was emi- 
 nently successful in discovering such relations ; but 
 the glory and merit of interpreting them according 
 to their physical meaning, was reserved for his 
 greater successor, Newton. 
 
432 
 
 CHAPTER IV. 
 INDUCTIVE EPOCH OF KEPLER. 
 
 Sect. 1. Intellectual Character of Kepler. 
 
 SEVERAL persons 1 , especially in recent times, 
 who have taken a view of the discoveries of 
 Kepler, appear to have been surprized and some- 
 what discontented that conjectures, apparently so 
 fanciful and arbitrary as his, should have led to 
 important discoveries. They seem to have been 
 alarmed at the Moral that their readers might 
 draw, from the tale of a Quest of Knowledge, in 
 which the Hero, though fantastical and self-willed, 
 and violating in his conduct, as they conceived, all 
 right rule and sound philosophy, is rewarded with 
 
 1 Laplace, Precis, de I' Hist. d'Asl. p. 94. " II est affligeant 
 pour 1'esprit humain de voir ce grand homme, meme dans ses 
 dernieres ouvrages, se complaire avec delices dans ses chimeriques 
 speculations, et les regarder comme Tame et la vie de 1'astronomie.' 
 Hist, of Art., L. U. K., p. 53. "This success [of Kepler] 
 may well inspire with dismay those who are accustomed to 
 consider experiment and rigorous induction as the only means 
 to interrogate nature with success." 
 
 Life of Kepler, L. U. K., p. J4, " Bad philosophy." P. 15, 
 " Kepler's miraculous good fortune in seizing truths across the 
 wildest and most absurd theories." P. 54, " The danger of 
 attempting to follow his method in the pursuit of truth." 
 
INDUCTIVE EPOCH OF KEPLER. 4M:} 
 
 the most signal triumphs. Perhaps one or two 
 reflections mav in some measure reconcile us to 
 
 / 
 
 this result. 
 
 In the first place, we may observe that the 
 leading thought which suggested and animated all 
 Kepler's attempts was true, and we may add, saga- 
 cious and philosophical ; namely, that there must 
 be some numerical or geometrical relations among 
 the times, distances, and velocities of the revolving 
 bodies of the solar system. This settled and con- 
 stant conviction of an important truth regulated all 
 the conjectures, apparently so capricious and fanci- 
 ful, which he made and examined, respecting par- 
 ticular relations in the system. 
 
 In the next place, we may venture to say, that 
 advances in knowledge are not commonly made 
 without the previous exercise of some boldness and 
 license in guessing. The discovery of new truths 
 requires, undoubtedly, minds careful and scrupulous 
 in examining what is suggested ; but it requires, no 
 less, such as are quick and fertile in suggesting. 
 What is Invention, except the talent of rapidly 
 calling before us many possibilities, and selecting 
 the appropriate one? It is true, that when we 
 have rejected all the inadmissible suppositions, they 
 are quickly forgotten by most persons; and few 
 think it necessary to dwell on these discarded hypo- 
 theses, and on the process by which they were con- 
 demned, as Kepler has done. But all who discover 
 truths must have reasoned upon many errors, to 
 VOL. i. F F 
 
434 HISTORY OF FORMAL ASTRONOMY. 
 
 obtain each truth ; every accepted doctrine must 
 have been one selected out of many candidates. In 
 making many conjectures, which on trial proved 
 erroneous, Kepler was no more fanciful or unphilo- 
 sophical than other discoverers have been. Dis- 
 covery is not a "cautious" or "rigorous" process, in 
 the sense of abstaining from such suppositions. But 
 there are great differences in different cases, in the 
 facility with which guesses are proved to be errours, 
 and in the degree of attention with which the 
 errour and the proof are afterwards dwelt on. 
 Kepler certainly was remarkable for the labour 
 which he gave to such self-refutations, and for the 
 candour and copiousness with which he narrated 
 them ; his works are in this way extremely curious 
 and amusing ; and are a very instructive exhibition 
 of the mental process of discovery. But in this 
 respect, I venture to believe, they exhibit to us the 
 usual process (somewhat caricatured) of inventive 
 minds : they rather exemplify the rule of genius 
 than (as has generally been hitherto taught,) the 
 exception. We may add, that if many of Kepler's 
 guesses now appear fanciful and absurd, because 
 time and observation have refuted them, others, 
 which were at the time equally gratuitous, have 
 been confirmed by succeeding discoveries in a man- 
 ner which makes them appear marvellously saga- 
 cious ; as, for instance, his assertion of the rotation 
 of the sun on his axis, before the invention of the 
 telescope, and his opinion that the obliquity of the 
 
INDUCTIVE EPOCH OF KEPLER. 435 
 
 ecliptic was decreasing, but would, after a long-con- 
 tinued diminution, stop, and then increase again 2 . 
 Nothing can be more just, as well as more poetically 
 happy, than Kepler's picture of the philosopher's 
 pursuit of scientific truth, conveyed by means of an 
 allusion to Virgil's shepherd and shepherdess : 
 
 Malo me Galatea petit, lasciva puella 
 
 Et fugit ad salices et so cupit ante videri. 
 
 Coy yet inviting, Galatea loves 
 To sport in sight, then plunge into the groves ; 
 The challenge given, she darts along the green, 
 Will not be caught, yet would not run unseen. 
 
 We may notice as another peculiarity of Kep- 
 ler's reasonings, the length and laboriousness of the 
 processes by which he discovered the errours of his 
 first guesses. One of the most important talents 
 requisite for a discoverer, is the ingenuity and skill 
 which devises means for rapidly testing false sup- 
 positions as they offer themselves. This talent 
 Kepler did not possess : he was not even a good 
 arithmetical calculator, often making mistakes, 
 some of which he detected and laments, while 
 others escaped him to the last. But his defects in 
 this respect were compensated by his courage and 
 perseverance* in undertaking and executing such 
 tasks ; and, what was still more admirable, he never 
 allowed the labour he had spent upon any con- 
 jecture to produce any reluctance in abandoning 
 the hypothesis, as soon as he had evidence of its 
 2 Bailly, A. M. iii. 175. 
 
 FF2 
 
436 HISTORY OF FORMAL ASTRONOMY. 
 
 inaccuracy. The only way in which he rewarded 
 himself for his trouble, was by describing to the 
 world, in his lively manner, his schemes, exertions, 
 and feelings. 
 
 The mystical parts of Kepler's opinions, as his 
 belief in astrology, his persuasion that the earth 
 was an animal, and many of the loose moral and 
 spiritual as well as sensible analyses by which he 
 represented to himself the powers which he sup- 
 posed to prevail in the universe, do not appear to 
 have interfered with his discovery, but rather to 
 have stimulated his invention, and animated his 
 exertions. Indeed, where there are clear scientific 
 ideas on one subject in the mind, it does not appear 
 that mysticism on others is at all unfavourable to 
 the successful prosecution of research. 
 
 I conceive, then, that we may consider Kepler's 
 character as containing the general features of the 
 character of a scientific discoverer, though some of 
 the features are exaggerated, and some too feebly 
 marked. His spirit of invention was undoubtedly 
 very fertile and ready, and this and his perseverance 
 served to remedy his deficiency in mathematical 
 artifice and method. But the peculiar physiognomy 
 is given to his intellectual aspect by his dwelling in 
 a most prominent manner on those erroneous trains 
 of thought which other persons conceal from the 
 world, and often themselves forget, because they 
 find means of stopping them at the outset. In the 
 beginning of his book (Argumenta Capitum) he 
 
INDUCTIVE EPOCH OF KEPLER. 437 
 
 says, " if Christopher Columbus, if Magellan, if the 
 Portuguese when they narrate their wanderings, are 
 not only excused, but if we do not wish these pas- 
 sages omitted, and should lose much pleasure if 
 they were, let no one blame me for doing the 
 same." Kepler's talents were a kindly and fertile 
 soil, which he cultivated with abundant toil and 
 vigour; but with great scantiness of agricultural 
 skill and implements. Weeds and the grain throve 
 and flourished side by side almost undistinguished ; 
 and he gave a peculiar appearance to his harvest, 
 by gathering and preserving the one class of plants 
 with as much care and diligence as the other. 
 
 Sect. 2. Kepler's Discovery of his Third Law. 
 
 I SHALL now give some account of Kepler's specu- 
 lations and discoveries. The first discovery which 
 he attempted, the relation among the successive dis- 
 tances of the planets from the sun, was a failure ; 
 his doctrine being without any solid foundation, 
 although propounded by him with great triumph, 
 in a work which he called Mysterium Cosmogra- 
 phicum, and which was published in 1596. The 
 account which he gives of the train of his thoughts 
 on this subject, namely, the various suppositions 
 assumed, examined, and rejected, is curious and 
 instructive, for the reasons just stated ; but we shall 
 not dwell upon these essays, since they led only to 
 an opinion now entirely abandoned. The doctrine 
 
438 HISTORY OF FORMAL ASTRONOMY. 
 
 which professed to give the true relation of the 
 orbits of the different planets, was thus delivered 3 
 " The orbit of the earth is a circle ; round the 
 sphere to which this circle belong describe a dode- 
 cahedron; the sphere including this will give the 
 orbit of Mars. Round Mars describe a tetrahedron ; 
 the circle including this will be the orbit of Jupiter. 
 Describe a cube round Jupiter's orbit; the circle 
 including this will be the orbit of Saturn. Now 
 inscribe in the Earth's orbit an icosahedron; the 
 circle inscribed in it will be the orbit of Venus. 
 Inscribe an octahedron in the orbit of Venus ; the 
 circle inscribed in it will be Mercury's orbit. This 
 is the reason of the number of the planets." The 
 five kinds of polyhedral bodies here mentioned are 
 the only " regular solids." 
 
 But though this part of the Mysterium Cosmo- 
 grapliicum was a failure, the same researches con- 
 tinued to occupy Kepler's mind; and twenty-two 
 years later led him to one of the important rules 
 known to us as "Kepler's laws;" namely, to the 
 rule connecting the mean distances of the planets 
 from the sun with the times of their revolutions. 
 This rule is expressed in mathematical terms by 
 saying that the squares of the periodic times are in 
 the same proportion as the cubes of the distances ; 
 and was of great importance to Newton in leading 
 him to the law of the sun's attractive force. We 
 may properly consider this discovery as the sequel 
 3 L. TJ.-K. Kepler, 6. 
 
INDUCTIVE EPOCH OF KEPLER. 439 
 
 of the train of thought already noticed. In the 
 beginning of the My sternum, Kepler had said, " In 
 the year 1595, I brooded with the whole energy of 
 my mind on the subject of the Copernican system. 
 There were three things in particular of which I 
 pertinaciously sought the causes why they are not 
 other than they are ; the number, the size, and the 
 motion of the orbits." We have seen the nature of 
 his attempt to account for the two first of these 
 points. He had also made some essays to connect 
 the motions of the planets with their distances, but 
 with his success in this respect he was not himself 
 completely satisfied. But in the fifth book of the 
 Harmonice Mundi, published in 1619, he says, 
 "What I prophesied two-and-twenty years ago as 
 soon as I had discovered the five solids among the 
 heavenly bodies; what I firmly believed before I 
 had seen the Harmonics of Ptolemy ; what I pro- 
 mised my friends in the title of this book (On the 
 most perfect Harmony of the Celestial Motions), 
 which I named before I was sure of my discovery ; 
 what sixteen years ago I regarded as a thing to be 
 sought; that for which I joined Tycho Brahe, for 
 which I settled in Prague, for which I have devoted 
 the best part of my life to astronomical contem- 
 plations; at length I have brought to light, and 
 have recognized its truth beyond my most sanguine 
 expectations." 
 
 The rule thus referred to is stated in the third 
 chapter of this fifth book. "It is," he says, "a 
 
440 HISTORY OF FORMAL ASTRONOMY. 
 
 most certain and exact thing that the proportion 
 which exists between the periodic times of any 
 two planets is precisely the sesquiplicate of the 
 proportion of their mean distances ; that is, of the 
 radii of the orbits. Thus, the period of the earth is 
 one year, that of Saturn thirty years ; if any one 
 trisect the proportion, that is, take the cube root of 
 it, and double the proportion so found, that is, 
 square it, he will find the exact proportion of the 
 distances of the earth and of Saturn from the sun. 
 For the cube root of 1 is 1, and the square of this 
 is 1 ; and the cube root of 30 is greater than 3, and 
 therefore the square of it is greater than 9. And 
 Saturn at his mean distance from the sun is at 
 a little more than 9 times the mean distance of 
 the earth." 
 
 When we now look back at the time and exer- 
 tions which the establishment of this law cost Kep- 
 ler, we are tempted to imagine that he was strangely 
 blind in not seeing it sooner. His object, we might 
 reason, was to discover a law connecting the dis- 
 tances and the periodic times. What law of con- 
 nexion could be more simple and obvious, we might 
 say, than that one of these quantities should vary 
 as some power of the other, or as some root, or as 
 some combination of the two, which in a more 
 general view, may still be called a power f And if 
 the problem had been viewed in this way, the 
 question must have occurred, to what power of the 
 periodic times are the distances proportional ? And 
 
INDUCTIVE EPOCH OF KEPLER. 441 
 
 the answer must have been, that they are propor- 
 tional to the square of the cube root. This ex-post- 
 facto obviousness of discoveries is a delusion to 
 which we are liable with regard to many of the 
 most important principles. In the case of Kepler, 
 we may observe, that the process of connecting two 
 classes of quantities by comparing their powers, is 
 obvious only to those who are familiar with general 
 algebraical views ; and that in Kepler's time, alge- 
 bra had not taken the place of geometry, as the 
 most usual vehicle of mathematical reasoning. It 
 may be added, also, that Kepler always sought his 
 formal laws by means of physical reasonings; and 
 these, though vague or erroneous, determined the 
 nature of the mathematical connexion which he 
 assumed. Thus in the Mysterium he had been led 
 by his notions of moving virtue of the sun to this 
 conjecture, among others, that, in the planets, the 
 increase of the periods will be double of the dif- 
 ference of the distances; which supposition he 
 found to give him an approach to the actual pro- 
 portion of the distances, but one not sufficiently 
 close to satisfy him. 
 
 The greater part of the fifth Book of the Har- 
 monics of the Universe consists in attempts to ex- 
 plain various relations among the distances, times, 
 and eccentricities of the planets, by means of the 
 ratios which belong to certain concords and dis- 
 cords. This portion of the work is so complex and 
 laborious, that probably few modern readers have 
 
442 HISTORY OF FORMAL ASTRONOMY. 
 
 had courage to go through it. Delambre 4 acknow- 
 ledges that his patience often failed him during the 
 task; and subscribes to the judgment of Bailly; 
 "After this sublime effort, Kepler replunges himself 
 in the relations of music to the motions, the dis- 
 tance, and the eccentricities of the planets. In all 
 these harmonic ratios there is not one true rela- 
 tion ; in a crowd of ideas there is not one truth : he 
 becomes a man after being a spirit of light." Cer- 
 tainly these speculations are of no value, but we 
 may look on them with toleration, when we recol- 
 lect that Newton has sought for analogies between 
 the spaces occupied by the prismatic colours and 
 the notes of the gamut 5 . The numerical relations 
 of concords are so peculiar that we can easily sup- 
 pose them to have other bearings than those which 
 first offer themselves. 
 
 It does not belong to my present purpose to 
 speak at length of the speculations concerning the 
 forces producing the celestial motions by which 
 Kepler was led to this celebrated law, or of those 
 which he deduced from it, and which are found in 
 the Epitome Astronomies Copernicance, published 
 1622. In that work also (p. 554), he extended this 
 law, though in a loose manner, to the satellites of 
 Jupiter. These physical speculations were only a 
 vague and distant prelude to Newton's discoveries ; 
 and the law, as a formal rule, was complete in 
 itself. We must now attend to the history of 
 4 A. M. a. 35a 6 Opticks, B. 2. p. iv. Obs 5. 
 
INDUCTIVE EPOCH OF KEPLER. 443 
 
 the other two laws with which Kepler's name is 
 associated. 
 
 Sect. 3. Kepler's Discovery of Ms First and Second 
 Lares. Elliptical Theory of the Planets. 
 
 THE propositions designated as Kepler's first and 
 second laws are these: that the orbits of the 
 planets are elliptical; and that the areas de- 
 scribed, or swept, by lines drawn from the sun to 
 the planet are proportional to the times employed 
 in the motion. 
 
 The occasion of the discovery of these laws was 
 the attempt to reconcile the theory of Mars to the 
 theory of eccentrics and epicycles; the event of it 
 was the complete overthrow of that theory, and the 
 establishment, in its stead, of the Elliptical Theory 
 of the planets. Astronomy was now ripe for such 
 a change. As soon as Copernicus had taught men 
 that the orbits of the planets were to be referred to 
 the sun, it obviously became a question, what was 
 the true form of these orbits, and the rule of 
 motion of each planet in its own orbit. Copernicus 
 represented the motions in longitude by means of 
 eccentrics and epicycles, as we have already said; 
 and the motions in latitude by certain librations, or 
 alternate elevations and depressions of epicycles. 
 If a mathematician had obtained a collection of 
 true positions of a planet, the form of the orbit, and 
 the motion of the star would have been determined 
 
444 HISTORY OF FORMAL ASTRONOMY. 
 
 with reference to the sun as well as to the earth; 
 but this was not possible, for though the geocentric 
 position, or the direction in which the planet was 
 seen, could be observed, its distance from the earth 
 was not known. Hence, when Kepler attempted to 
 determine the orbit of a planet, he combined the 
 observed geocentric places with successive modifi- 
 cations of the theory of epicycles, till at last he was 
 led, by one step after another, to change the epicy- 
 clical into the elliptical theory. We may observe, 
 moreover, that at every step he endeavoured to 
 support his new suppositions by what he called, in 
 his fanciful phraseology, " sending into the field a 
 reserve of new physical reasonings on the rout and 
 dispersion of the veterans (s) :" that is, by connect- 
 ing his astronomical hypotheses with new imagina- 
 tions, when the old ones became untenable. We 
 find, indeed, that this is the spirit in which the 
 pursuit of knowledge is generally carried on with 
 success: those men arrive at truth who eagerly 
 endeavour to connect remote points of their know- 
 ledge, not those who stop cautiously at each point 
 till something compels them to go beyond it. 
 
 Kepler joined Tycho Brahe at Prague in 1600, 
 and found him and Longomontanus busily employed 
 in correcting the theory of Mars ; and he also then 
 entered upon that train of researches which he 
 published in 1609 in his extraordinary work On the 
 Motions of Mars. In this work, as in others, he 
 gives an account, not only of his success, but of his 
 
INDUCTIVE EPOCH OF KEPLER. 445 
 
 failures, explaining, at length, the various suppo- 
 sitions which he had made, the notions by which he 
 had been led to invent or to entertain them, the 
 processes by which he had proved their falsehood, 
 and the alternations of hope and sorrow, of vexa- 
 tion and triumph, through which he had gone. It 
 will not be necessary for us to cite many passages of 
 these kinds, curious and amusing as they are. 
 
 One of the most important truths contained in 
 the motions of Mars is the discovery that the plane 
 of the orbit of the planet should be considered 
 with reference to the sun itself, instead of referring 
 it' to any of the other centers of motion which the 
 eccentric hypothesis introduced; and that, when 
 so considered, it had none of the librations which 
 Ptolemy and Copernicus had attributed to it. The 
 fourteenth chapter of the second part asserts, 
 " Plana eccentricorum esse ardXavra ;" that the 
 planes are unlibrating ; retaining always the same 
 inclination to the ecliptic, and the same line of 
 nodes. With this step Kepler appears to have been 
 justly delighted. His reflections on it are very phi- 
 losophical. "Copernicus," he says, "not knowing 
 the value of what he possessed (his system), under- 
 took to represent Ptolemy, rather than Nature, to 
 which, however, he had approached more nearly 
 than any other person. For being rejoiced that 
 the quantity of the latitude of each planet was in- 
 creased by the approach of the earth to the planet, 
 according to his theory, he did not venture to 
 
446 HISTORY OF FORMAL ASTRONOMV. 
 
 reject the rest of Ptolemy's increase of latitude, 
 but in order to express it, devised librations of the 
 planes of the eccentric, depending not upon its own 
 eccentric, but (most improbably) upon the orbit 
 of the earth, which has nothing to do with it. I 
 always fought against this impertinent tying to- 
 gether of two orbits, even before I saw the obser- 
 vations of Tycho ; and I therefore rejoice much 
 that in this, as in others of my preconceived 
 opinions, the observations were found to be on my 
 side." Kepler established his point by a fair and 
 laborious calculation of the results of observations 
 3f Mars made by himself and Tycho Brahe; and 
 had a right to exult when the result of these cal- 
 culations confirmed his views of the symmetry and 
 simplicity of nature. 
 
 We may judge of the difficulty of casting off 
 the theory of eccentrics and epicycles, by recollect- 
 ing that Copernicus did not do it at all, and that 
 Kepler only did it after repeated struggles; the 
 history of which occupies thirty-nine chapters of 
 his book. At the end of them he says, " This 
 prolix disputation was necessary, in order to pre- 
 pare the way to the natural form of the equations, 
 of which I am now to treat 6 . My first errour was, 
 that the path of a planet is a perfect circle ; an 
 opinion which was a more mischievous thief of my 
 time, in proportion as it was supported by the 
 authority of all philosophers, and apparently agree- 
 
 6 De Stella Martis, iii. 40. 
 
INDUCTIVE EPOCH OF KEPLER. 447 
 
 able to metaphysics." But before he attempts to 
 correct this erroneous part of his hypothesis he 
 sets about discovering the law according to which 
 the different parts of the orbit are described in 
 the case of the earth, in which case the eccentricity 
 is so small that the effect of the oval form is in- 
 sensible. The result of this inquiry was 7 the Rule, 
 that the time of describing any arc of the orbit 
 is proportional to the area intercepted between the 
 curve and two lines drawn to the extremities of 
 the arc. It is to be observed that this rule, at 
 first, though it had the recommendation of being 
 selected after the unavoidable abandonment of 
 many, which were suggested by the notions of those 
 times, was far from being adopted upon any very 
 rigid or cautious grounds. A rule had been proved 
 at the apsides of the orbit, by calculation from 
 observations, and had then been extended by con- 
 jecture to other parts of the orbit; and the rule 
 of the areas was only an approximate and inac- 
 curate mode of representing this rule, employed 
 for the purpose of brevity and convenience, in 
 consequence of the difficulty of applying, geome- 
 trically, that which Kepler now conceived to be 
 the true rule, and which required him to find the 
 sum of the lines drawn from the sun to every 
 point of the orbit. When he proceeded to apply 
 this rule to Mars, in whose orbit the oval form is 
 7 Ibid. p. 194. 
 
448 HISTORY OF FORMAL ASTRONOMY. 
 
 much more marked, additional difficulties came in 
 his way ; and here again the true supposition, that 
 the oval is of that special kind called ellipse, was 
 adopted at first only in order to simplify calcu- 
 lation 8 , and the deviation from exactness in the 
 result was attributed to the inaccuracy of those 
 approximate processes. The supposition of the 
 oval had already been forced upon Purbach in the 
 case of Mercury, and upon Reinhold in the case of 
 the Moon. The center of the epicycle was made 
 to describe an egg-shaped figure in the former case, 
 and a lenticular figure in the latter 9 . 
 
 It may serve to show the kind of labour by 
 which Kepler was led to his result, if we here enu- 
 merate, as he does in his forty-seventh chapter 10 , 
 six hypotheses, on which he calculated the longi- 
 tudes of Mars, in order to see which best agreed 
 with observation. 
 
 1. The simple eccentricity. 
 
 2. The bisection of the eccentricity, and the 
 duplication of the superior part of the equation. 
 
 3. The bisection of the eccentricity and a sta- 
 tionary point of equations, after the manner of 
 Ptolemy. 
 
 4. The vicarious hypothesis by a free section 
 of the eccentricity made to agree as nearly as pos- 
 sible with the truth. 
 
 8 De SteM Martis, iv. c. 47- 9 L. U. K. Kepler, p. 30. 
 10 De Stella Martin, p. 228. 
 
INDUCTIVE EPOCH OF KEPLER. 44<) 
 
 5. The physical hypothesis on the supposition 
 of a perfect circle. 
 
 6. The physical hypothesis on the supposition 
 of a perfect ellipse. 
 
 By the physical hypothesis, he meant the doc- 
 trine that the time of a planet's describing any 
 part of its orbit is proportional to the distance of 
 the planet from the sun, for which supposition, as 
 we have said, he conceived that he had assigned 
 physical reasons. 
 
 The two last hypotheses came the nearest to 
 the truth, and differed from it only by about eight 
 minutes, the one in excess and the other in defect. 
 And, after being much perplexed by this remaining 
 error, it at last occurred to him 11 that he might 
 take another ellipsis, exactly intermediate between 
 the former one and the circle, and that this must 
 give the path and the motion of the planet. Making 
 this assumption, and taking the areas to represent 
 the times, he now saw 12 that both the longitude 
 and the distances of Mars would agree with ob- 
 servation to the requisite degree of accuracy. The 
 rectification of the former hypothesis, when thus 
 stated, may, perhaps, appear obvious. And Kepler 
 informs us that he had nearly been anticipated in 
 this step. (c. 55.) "David Fabricius, to whom I 
 had communicated my hypothesis of cap. 45, was 
 able, by his observations, to show that it erred in 
 
 11 De StelM Martis, c. 58 12 Ibid. p. 235. 
 
 VOL. I. G G 
 
450 HISTORY OF FORMAL ASTRONOMY. 
 
 making the distances too short at mean longitudes ; 
 of which he informed me by letter while I was 
 labouring, by repeated efforts, to discover the true 
 hypothesis. So nearly did he get the start of me 
 in detecting the truth." But this was less easy 
 than it might seem. When Kepler's first hypothesis 
 was enveloped in the complex construction re- 
 quisite in order to apply it to each point of the 
 orbit, it was far more difficult to see where the 
 errour lay, and Kepler hit upon it only by noticing 
 the coincidences of certain numbers, which, as he 
 says, raised him as if from sleep, and gave him 
 a new light. We may observe, also, that he was 
 perplexed to reconcile this new view, according to 
 which the planet described an exact ellipse, with 
 his former opinion, which represented the motion 
 by means of libration in an epicycle. "This," he 
 says, "was my greatest trouble, that, though I 
 considered and reflected till I was almost mad, I 
 could not find why the planet to which, with so 
 much probability, and with such an exact accord- 
 ance of the distances, the libration in the diameter 
 of the epicycle was attributed, should, according 
 to the indication of the equations, go in an ellip- 
 tical path. What an absurdity on my part ! as if 
 libration in the diameter might not be a way to 
 the ellipse!" 
 
 Another scruple respecting this theory arose 
 from the impossibility of solving, by any geome- 
 
INDUCTIVE EPOCH OF KEPLER. 451 
 
 trical construction, the problem to which Kepler 
 was thus led, namely, " to divide the area of a semi- 
 circle in a given ratio, by a line drawn from any 
 point of the diameter." This is still termed " Kep- 
 ler's Problem," and is, in fact, incapable of exact 
 geometrical solution. As, however, the calculation 
 can be performed, and, indeed, was performed by 
 Kepler himself, with a sufficient degree of accuracy 
 to show that the elliptical hypothesis is true, the 
 insolubility of this problem is a mere mathematical 
 difficulty in the deductive process, to which Kepler's 
 inductions gave rise. 
 
 Of Kepler's physical reasonings we shall speak 
 more at length on another occasion. His numerous 
 and fanciful hypotheses had discharged their office, 
 when they had suggested to him his many lines 
 of laborious calculation, and encouraged him under 
 the exertions and disappointments to which these 
 led. The result of this work was the formal laws 
 of the motion of Mars, established by a clear in- 
 duction, since they represented, with sufficient ac- 
 curacy, the best observations. And we may allow 
 that Kepler was entitled to the praise which he 
 claims in the motto on his first leaf. Ramus had 
 said that if any one would construct an astronomy 
 without hypothesis he would be ready to resign 
 to him his professorship in the University of Paris. 
 Kepler quotes this passage, and adds, "it is well, 
 Ramus, that you have run from this pledge, by 
 
 GG2 
 
452 HISTORY OF FORMAL ASTRONOMY. 
 
 quitting life and your professorship 13 ; if you held 
 it still, I should, with justice, claim it." This was 
 not saying too much, since he had entirely over- 
 turned the hypothesis of eccentrics and epicycles, 
 and had obtained a theory which was a mere re- 
 presentation of the motions and distances as they 
 were observed. 
 
 13 Ramus perished in the Massacre of St. Bartholomew. 
 
453 
 
 CHAPTER V. 
 
 SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, 
 VERIFICATION, AND EXTENSION OF THE ELLIPTI- 
 CAL THEORY. 
 
 Sect. 1. Application of the Elliptical Theory to 
 the Planets. 
 
 THE extension of Kepler's discoveries concern- 
 ing the orbit of Mars to the other planets, 
 obviously offered itself as a strong probability, 
 and was confirmed by trial. This was made in 
 the first place upon the orbit of Mercury ; which 
 planet, in consequence of the largeness of its eccen- 
 tricity, exhibits mere clearly than the others the 
 circumstances of the elliptical motion. These and 
 various other supplementary portions of the views 
 to which Kepler's discoveries had led, appeared in 
 the latter part of his Epitome Astronomice Coper - 
 nicance, published in 1622. 
 
 The real verification of the new doctrine con- 
 cerning the orbits and motions of the heavenly 
 bodies was, of course, to be found in the construc- 
 tion of tables of those motions, and in the con- 
 tinued comparison of such tables with observation. 
 Kepler's discoveries had been founded, as we have 
 
454 HISTORY OF FORMAL ASTRONOMY. 
 
 seen, principally on Tycho's observations. Longo- 
 montanus (so called as being a native of Langberg 
 in Denmark,) published in 1621 in his Astronomia 
 Danica, tables founded upon the theories as well 
 as the observations of his countryman. Kepler 1 in 
 1627 published his tables of the planets, which he 
 called Rudolphine Tables, the result and applica- 
 tion of his own theory. In 1633, Lansberg, a Bel- 
 gian, published also Tabulae Perpetuce, a work which 
 was ushered into the world with considerable pomp 
 and pretension, and in which the author cavils very 
 keenly at Kepler and Brahe. We may judge of the 
 impression made upon the astronomical world in 
 general by these rival works, from the account 
 which our countryman Jeremy Horrox has given of 
 their effect on him. He had been seduced by the 
 magnificent promises of Lansberg, and the praises 
 of his admirers, which are prefixed to the work, 
 and was persuaded that the common opinion which 
 preferred Tycho and Kepler to him was a prejudice. 
 In 1636, however, he became acquainted with Crab- 
 tree, another young astronomer, who lived in the 
 same part of Lancashire. By him Horrox was 
 warned that Lansberg was not to be depended on ; 
 that his hypotheses were vicious, and his observa- 
 tions falsified or forced into agreement with his 
 theories. He then read the works and adopted the 
 opinions of Kepler; and after some hesitation which 
 he felt at the thought of attacking the object of his, 
 
 1 Rheticus, Narratio, p. 98. 
 
SEQUEL TO THE EPOCH OF KEPLER. 455 
 
 former idolatry, he wrote a dissertation on the 
 points of difference between them. It appears that, 
 at one time, he intended to have offered himself as 
 the umpire who was to adjudge the prize of excel- 
 lence among the three rival theories of Longomon- 
 tanus, Kepler and Lansberg ; and, in allusion to the 
 story of ancient mythology, his work was to have 
 been called Paris Astronomicus ; we easily see that 
 he would have given the golden apple to the Kep- 
 lerian goddess. Succeeding observations confirmed 
 his judgment : and the Rudolphine Tables, thus 
 published seventy-six years after the Prutenic, which 
 were founded on the doctrines of Copernicus, were 
 for a long time those universally used. 
 
 Sect. 2. Application of the Elliptical Theory 
 to the Moon. 
 
 THE reduction of the moon's motions to rule was a 
 harder task than the formation of planetary tables, 
 if accuracy was required ; for the moon's motion is 
 affected by an incredible number of different and 
 complex inequalities, which, till their law is de- 
 tected, appear to defy all theory. Still, however, 
 progress was made in this work. The most impor- 
 tant advances were due to Tycho Brahe. In addi- 
 tion to the first and second inequalities of the moon 
 (the Equation of the Center, known very early, and 
 the Evection which Ptolemy had discovered), Tycho 
 proved that there was another inequality, which he 
 
456 HISTORY OF FORMAL ASTRONOMY. 
 
 termed the Variation", which depended on the 
 moon's position with respect to the sun, and which 
 at its maximum was forty minutes and a half, 
 about a quarter of the evection. He also perceived, 
 though not very distinctly, the necessity of another 
 correction of the moon's place depending on the 
 sun's longitude, which has since been termed the 
 Annual Equation. 
 
 These steps concerned the Longitude of the 
 Moon ; Tycho also made important advances in the 
 knowledge of the Latitude. The Inclination of the 
 Orbit had hitherto been assumed to be the same at 
 all times; and the motion of the Node had been 
 supposed uniform. He found that the inclination 
 increased and diminished by twenty minutes, ac- 
 cording to the position of the line of nodes ; and 
 that the nodes, though they regress upon the whole, 
 sometimes go forwards and sometimes go back- 
 wards. 
 
 Tycho's discoveries .concerning the moon are 
 given in his Progymnasmata, which was published 
 in 1603, two years after the author's death. He 
 represents the moon's motion in longitude by means 
 of certain combinations of epicycles and eccentrics. 
 But after Kepler had shown that such devices are 
 to be banished from the planetary system, it was 
 
 3 We have seen (Chap, in), that Aboul-Wefa, in the tenth 
 century, had already noticed this inequality; but his discovery 
 had been entirely forgotten long before the time of Tycho, and 
 has only recently been brought again into notice. 
 
SEQUEL TO THE EPOCH OF KEPLER. l.~>7 
 
 impossible not to think of extending the elliptical 
 theory to the moon. Horrox succeeded in doing 
 this ; and in 1638 sent this essay to his friend Crab- 
 tree. It was published in 1673, with the numerical 
 elements requisite for its application added by 
 Flamsteed. Flamsteed had also (in 1671 and 2) 
 compared this theory with observation, and found 
 that it agreed far more nearly than the Pliilolaic 
 Tables of Bullialdus, or the Carolinian Tables of 
 Street (Epilogus ad Tabulas}. Moreover Horrox, 
 by making the center of the ellipse revolve in an 
 epicycle, gave an explanation of the evection, as 
 well as of the equation of the center (T). 
 
 Modern astronomers, by calculating the effects 
 of the perturbing farces of the solar system, and 
 comparing their calculations with observation, have 
 added many new corrections or equations to those 
 known at the time of Horrox; and since the mo- 
 tions of the heavenly bodies were even then affected 
 by these variations as yet undetected, it is clear 
 that the tables of that time must have shown some 
 errours when compared with observation. These 
 errours much perplexed astronomers, and naturally 
 gave rise to the question whether the motions of 
 the heavenly bodies really were exactly regular, or 
 whether they were not affected by accidents as little 
 reducible to rule as wind and weather. Kepler had 
 held the opinion of the casualty of such errours ; 
 but Horrox, far more philosophically, argues against 
 this opinion, though he allows that he is much 
 
458 HISTORY OF FORMAL ASTRONOMY. 
 
 embarrassed by the deviations. His arguments 
 show a singularly clear and strong apprehension of 
 the features of the case, and their real import. He 
 says 3 , " these errours of the tables are alternately in 
 excess and defect; how could this constant com- 
 pensation happen if they were casual ? Moreover, 
 the alternation from excesg to defect is most rapid 
 in the moon, most slow in Jupiter and Saturn, in 
 which planets the errour continues sometimes for 
 years. If the errours were casual, why should they 
 not last as long in the moon as in Saturn ? But if 
 we suppose the tables to be right in the mean 
 motions, but wrong in the equations, these facts are 
 just what must happen ; since Saturn's inequalities 
 are of long period, while those of the moon are 
 numerous, and rapidly changing." It would be 
 impossible, at the present moment, to reason better 
 on this subject; and the doctrine, that all the appa- 
 rent irregularities of the celestial motions are really 
 regular, was one of great consequence to establish 
 at this period of the science. 
 
 Sect. 3. Causes of the further Progress of 
 Astronomy. 
 
 WE are now arrived at the time when theory and 
 observation sprang forwards with emulous energy. 
 The physical theories of Kepler, and the reasonings 
 of other defenders of the Copernican theory, led 
 
 3 Astron. Kepler. Proleg. p. 17- 
 
'SEQUEL TO THE EPOCH OF COPERNICUS. 459 
 
 inevitably, after some vagueness and perplexity, to 
 a sound science of mechanics ; and this science in 
 time gave a new face to astronomy. But in the 
 mean time, while mechanical mathematicians were 
 generalizing from the astronomy already establish- 
 ed, astronomers were accumulating new facts, which 
 pointed the way to new theories and new gene- 
 ralizations. Copernicus, while he had established 
 the permanent length of the year, had confirmed 
 the motion of the sun's apogee, and had shown that 
 the eccentricity of the earth's orbit, and the obli- 
 quity of the ecliptic, were gradually, though slowly, 
 diminishing. Tycho had accumulated a store of 
 excellent observations. These, as well as the laws 
 of the motions of the moon and planets already 
 explained, were materials on which the Mechanics 
 of the Universe was afterwards to employ its most 
 matured powers. In the mean time, the telescope 
 had opened other new subjects of notice and specu- 
 lation ; not only confirming the Copernican doctrine 
 by the phases of Venus, and the analogical examples 
 of Jupiter and Saturn, which with their satellites ap- 
 peared like models of the solar system; but disclosing 
 unexpected objects, as the ring of Saturn, and the 
 spots of the sun. The art of observing made rapid 
 advances, both by the use of the telescope, and by the 
 sounder notions of the construction of instruments 
 which Tycho introduced. Copernicus had laughed 
 at Rheticus, when he was disturbed about single 
 minutes ; and declared that if he could be sure to 
 
460 HISTORY OF FORMAL ASTRONOMY. 
 
 ten minutes of space, he should be as much de- 
 lighted as Pythagoras was when he discovered the 
 property of the right-angled triangle. But Kepler 
 founded the revolution which he introduced on a 
 quantity less than this. "Since," he says 4 , " the divine 
 goodness has given us in Tycho an observer so exact 
 that this errour of eight minutes is impossible, we 
 must be thankful to God for this, and turn it to 
 account. And these eight minutes, which we must 
 not neglect, will, of themselves, enable us to recon- 
 struct the whole of astronomy." In addition to 
 other improvements, the art of numerical calcu- 
 lation made an inestimable advance by means of 
 Napier's invention of Logarithms ; and the progress 
 of other parts of pure mathematics was propor- 
 tional to the calls which astronomy and physics 
 made upon them. 
 
 The exactness which observation had attained 
 enabled astronomers both to verify and improve the 
 existing theories, and to study the yet unsystema- 
 tized facts. The science was, therefore, forced along 
 by a strong impulse on all sides. We now proceed 
 to speak of the new path into which this pressure 
 forced it ; but, in order to this, we must first trace 
 the rise and progress of the Science of Mechanics. 
 
 4 De Stella Martis, c. 19. 
 
461 
 
 NOTES TO BOOK V. 
 
 (p.) p. 403. THE doctrine of the motion of the 
 earth was first publicly maintained at Rome by Wil- 
 manstadt, who professed to have received it from Co- 
 pernicus. See Venturi, Essai sur les Outrages Physico- 
 Mathematiques de Leonard da Vinci, awe des Fragmens 
 tires de ses Manuscrits apportes d'ltalie. Paris, 1797 : 
 and, as there quoted, Marini Arcliiatri Pontificii, Tom. n. 
 p. 251. 
 
 Leonardo da Vinci himself, about 1510, explained 
 how a body by describing a kind of spiral, might de- 
 scend towards a revolving globe, so that its apparent 
 motion relative to a point in the surface of the globe, 
 might be in a straight line leading to the center. He 
 thus showed that he had entertained in his thoughts 
 the hypothesis of the eartfr's rotation, and was employed 
 in removing the difficulties which accompanied this sup- 
 position, by means of the consideration of the composition 
 of motions. 
 
 Regiomontanus (who died in 1476) is said to have 
 been inclined to this hypothesis, but to have combated 
 it ex professo : \ 
 
 (Q.) p. 418. It appears to me that the different de- 
 gree of toleration accorded to the heliocentric theory in 
 the time of Copernicus and of Galileo, must be ascribed 
 in a great measure to the controversies and alarms which 
 had in the mean time arisen out of the Reformation in 
 
 5 Schoneri Opera, Part n. Art. 127. 
 
462 NOTES TO BOOK V. 
 
 religion, and which had rendered the Romish Church 
 more jealous of innovations in received opinions than it 
 had previously been. It appears too that the discussion 
 of such novel doctrines was, at that time at least, less 
 freely tolerated in Italy than in other countries. In 
 1597, Kepler writes to Galileo thus: "Confide Galilaee 
 et progredere. Si bene conjecto, pauci de prsecipuis Eu- 
 ropse Mathematicis a nobis secedere volent ; tanta vis est 
 veritatis. Si tibi Italia minus est idonea ad publica- 
 tionem et si aliqua habitures es impedimenta, forsan 
 Germania nobis hanc libertatem concedet." Venturi, 
 Mem. di Galileo. Vol. i. p. 19. 
 
 I would not however be understood to assert the 
 condemnation of new doctrines in science to be either 
 a general or a characteristic practice of the Romish 
 Church. Certainly the intelligent and cultivated minds 
 of Italy, and many of the most eminent of her ecclesi- 
 astics among them, have always been the foremost in 
 promoting and welcoming the progress of science: and, 
 as I have stated, there were found, among the Italian 
 ecclesiastics of Galileo's time many of the earliest and 
 most enlightened adherents of the Copernican system. 
 The condemnation of the doctrine of the earth's motion, 
 is, so far as I am aware, the only instance in which the 
 Papal authority has pronounced a decree upon a point 
 of science. And the most candid of the adherents of 
 the Romish Church condemn the assumption of autho- 
 rity in such matters, which in this one instance, at least, 
 was made by the ecclesiastical tribunals. The author of 
 the Ages of Faith (Book vm. p. 248) says, " A congre- 
 gation, it is to be lamented, declared the new system 
 to be opposed to Scripture, and therefore heretical/' In 
 
NOTES TO BOOK V. 4G3 
 
 more recent times, as I have elsewhere remarked* 5 the 
 Church of Authority and the Church of Private Judgment 
 have each its peculiar temptations and dangers, when there 
 appears to be a discrepance between Scripture and Philo- 
 sophy. 
 
 But though we may acquit the popes and cardinals in 
 Galileo's time of stupidity and perverseness in rejecting 
 manifest scientific truths, I do not see how we can acquit 
 them of dissimulation and duplicity. Those persons appear 
 to me to defend in a very strange manner the conduct of 
 the ecclesiastical authorities of that period, who boast of 
 the liberality with which Copernican professors were placed 
 by them in important offices, at the very time when the 
 motion- of the earth had been declared by the same 
 authorities contrary to Scripture. Such merits cannot 
 make us approve of their conduct in demanding from 
 Galileo a public recantation of the system which they 
 thus favoured in other ways, and which they had re- 
 peatedly told Galileo he might hold as much as he pleased. 
 Nor can any one, reading the plain language of the sen- 
 tence passed upon Galileo, and of the abjuration forced 
 from him, find any value in the plea which has been 
 urged, that the opinion was denominated a heresy only 
 in a wide, improper, and technical sense. 
 
 But if we are thus unable to excuse the conduct of 
 Galileo's judges, I do not see how we can give our uncon- 
 ditional admiration to the philosopher himself. Perhaps 
 the conventional decorum which, as we have seen, was 
 required in treating of the Copernican system, may 
 excuse or explain the furtive mode of insinuating his 
 doctrines which he often employs, and which some of his 
 
 6 Phil. Ind. Sci. Book x. Chap. 4. 
 
464 NOTES TO BOOK V. 
 
 historians admire as subtle irony, while others blame it 
 as insincerity. But I do not see with what propriety 
 Galileo can be looked upon as a "martyr of science." 
 Undoubtedly he was very desirous of promoting what he 
 conceived to be the cause of philosophical truth ; but it 
 would seem that, while he was restless and eager in urging 
 his opinions, he was always ready to make such submis- 
 sions as the spiritual tribunals required. He would really 
 have acted as a martyr, if he had uttered his " e pur si 
 muove," in the place of his abjuration, not after it. But 
 in this case he would have been a martyr to a cause of 
 which the merit was of a mingled character ; for his own 
 special and favourite share in the reasonings by which the 
 Copernican system was supported, was the argument) drawn 
 from the flux and reflux of the sea, which argument is 
 altogether false. He considered this as supplying a me- 
 chanical ground of belief, without which the mere astrono- 
 mical reasons were quite insufficient ; but in this case he 
 was deserted by the mechanical sagacity which appeared 
 in his other speculations. 
 
 (R.) p. 400. Throughout the course of the proceed- 
 ings against him, Galileo was treated with great courtesy 
 and indulgence. He was condemned to a nominal impri- 
 sonment. " Te damnamus ad formalem carcerem hujus 
 S. officii ad tempus arbitrio nostro limitandum ; et titulo 
 poenitentia salutaris praecipimus ut tribus annis futuris 
 recites semel in hebdomada septem psalmos penitentiales." 
 But this confinement was reduced to his being placed 
 under some slight restrictions, first at the house of Nico- 
 lini, the ambassador of his own sovereign, and afterwards 
 at the country seat of Archbishop Piccolomini, one of his 
 own warmest friends. . 
 
NOTES TO BOOK V. 405 
 
 It has sometimes been asserted or insinuated that 
 (Jalileo was subjected to bodily torture. An argument 
 has been drawn from the expressions used in his sen- 
 tence: " Cum vero nobis videretur non esse a te integram 
 veritatem pronunciatam circa tuam intentionem ; judi- 
 cavimus necesse esse venire ad rigorosum examen tui, in 
 quo respondisti catholice." It has been argued by M. 
 Libri (Hist, des Sciences Mathematiques en Italie, vol. iv. 
 p. 259,) and M. Quinet (ISUltramontanisme, iv. Le9on, 
 p. 104,) that the rigorosum examen necessarily implies 
 bodily torture, notwithstanding that no such thing is 
 mentioned by Galileo and his contemporaries, and notwith- 
 standing the consideration with which he was treated in 
 all other respects : but M. Biot more justly remarks, 
 (Biogr. Univ. Art. Galileo,) that such a procedure is 
 incredible. 
 
 To the opinion of M. Biot, we may add that of 
 Delambre, who rejects the notion of Galileo's having been 
 put to the torture, as inconsistent with the general con- 
 duct of the authorities towards him, and as irreconcilable 
 with the accounts of the trial given by Galileo himself, 
 and by a servant of his, who never quitted him for an 
 instant. He adds also, that it is inconsistent with the 
 words of his sentence, u ne tuus iste gravis et perniciosus 
 error ac transgressio remaneat omnino impunitus ,*" for the 
 errour would have been already very far from impunity, if 
 Galileo had been previously subjected to the rack. He 
 adds, very reasonably, " il ne faut noircir personne sans 
 preuve, pas meme requisition." 
 
 (s.) p. 444. I will insert this passage, as a specimen of 
 Kepler's fanciful mode of narrating the defeats which he 
 received in the war which ho carried on with Mars. 
 VOL. I. H H 
 
466 NOTES TO BOOK V. 
 
 " Dum in hunc modum de Martis motibus triumpho^ 
 eique ut plane devicto tabularum carceres et equationum 
 compedes necto, diversis nuntiatur locis, futilem victoriam 
 ut bellum tota mole recrudescere. Nam domi quidem 
 hostis ut captivus contemptus, rupit omnia equationum 
 vincula, career esque tabularum effregit. Foris specula- 
 tores profligerunt meas causarum physicarum arcessitas 
 copias earumque jugum excusserunt resumta libertate. 
 Jamque parum abfuit quia hostis fugitivus sese cum rebel- 
 libus suis conjungeret meque in desperationem adigeret : 
 nisi raptim, nova rationum physicarum subsidia, fusis et 
 palantibus veteribus, submisissem, et qua se captivus pro- 
 ripuisset, omni diligentia, edoctus vestgiis ipsius nulla 
 mora interposita inhaesisserem." 
 
 (T.) p. 457. Horrox (Horrockes as he himself spelt 
 his name) gave a first sketch of his theory in letters to 
 his friend Crabtree in 16.38: in which the variation of the 
 excentricity is not alluded to. But in Crabtree^s letter 
 to Gascoigne in 1642, he gives Horrox's rule concerning 
 it ; and Flamsteed in his Epilogue to the Tables, pub- 
 lished by Wallis along with Horrox's works in 1673, 
 gave an explanation of the theory which made it amount 
 very nearly to a revolution of the center of the ellipse 
 in an epicycle. Halley afterwards made a slight altera- 
 tion; but hardly, I think, enough to justify Newton's 
 assertion ; (Princip. Lib. iii. Prop. 35. Schol.) " Halleius 
 centrum ellipseos in epicyclo locavit." See Baily's Flam- 
 steed, p. 683. 
 
 END OF VOL. I. 
 


 
 
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