XII 



jVA TURE 



[/, 



Supplement, 

 aiiuary i8. i8( 



no hesitation in stating that he is certainly justified in 

 hoping, as he does in the preface, '"that the present 

 volume may . . . further the advancement of, and prove 

 not altogether unworthy of, the present position of 

 Physiology in England." J. S. Edkins. 



AN ESSAY ON NEWTOA'S '' PRINCIPIAr 



An Essay on Newton's '■^ Principia.'^ By W. W. Rouse 

 Ball. (London : Macmillan and Co., 1893.) 



1"* HE name of Newton has become now quite a house- 

 hold word amongst us, and one instance of its 

 familiarity was strikingly brought home in an answer 

 given by a small child, who when asked who was Newton, 

 replied, "the man who found the first apple!" That 

 two important epochs in the world's history should 

 have been marked by the presence of this fruit, seems 

 curious indeed ; and Mr. Ball informs us that the apple 

 anecdote in Newton's case rests on good authority, for 

 besides written evidence, local tradition confirms it by 

 the careful treatment the tree received, which kept it 

 alive until the year 1820. 



For the essay which we have before us, Mr. Ball should 

 receive the thanks of ail those to whom the name of 

 Newton recalls the memory of a great man. The '■ Prin- 

 cipia,'' besides being a lasting monument of Newton's 

 life, is also to-day the classic of our mathematical 

 writings, and will be so for some time to come. During 

 Newton's lifetime three editions of this great work were 

 brought out, the first appearing in 1687 ; the second, 

 edited by Cotes, in 1713 ; and the third, by Pemberton, 

 in 1726. Since the last-mentioned date, the history of the 

 " Principia" has been discussed by Sir David Brewster 

 and Prof S. P. Rigaud, but both of these works are now 

 ■out of print and very scarce. At the present time, as Mr. 

 Ball informs us, it seems fitting to collect, from these and 

 other sources, the references to the leading events in the 

 preparation and publication of the " Principia," and the 

 present volume contains the result of his labours. In 

 the subject-matter, of course, there is much th it is not 

 new, but the value of the work lies in the fact that, be- 

 sides containing a few as yet unpublished letters, there 

 are collected in its pages quotations from all documents, 

 thus forming a co nplete summary of everything that is 

 known on the subject. 



Mr, Ball divides his essay into six main sections, 

 dealing with Newton's investigations in 1666, in 1679, in 

 1684, in 16S5-1687, compilation and publication of the 

 " Principia," the two last treating of the contents of the 

 '■ Principia," and the subsequent history and preparation 

 of later editions. 



Mr. Ball commences with the works of Newton at the 

 •time when the latter had taken his degree at Cambridge, 

 and therefore had more leisure to pursue his studies in 

 his own way. The reader is made acquainted with New- 

 ton's early views, and there are several interesting quota- 

 tions from some original manuscripts inserted. The 

 investigations of 1879 refer, in great part, to the corre- 

 spondence he had with Hooke, which turned his attention 

 to the problem of planetary motion. It was in this year 

 that Newton suggested the method of demonstrating the 

 earth's motion of rotation on its axis by the letting fall of 

 NO. 1264 VOL. 49] 



a stone from a high position, and observing the direction 

 of the deviation from the vertical ; he also repeated his 

 calculations (with new data) for finding the relation be- 

 tween terrestrial gravity and the centripetal force which 

 retained the moon in her orbit. 



In 1684, Halley. after attempting to deduce the motion 

 of the heavenly bodies from Kepler's laws, with unsuccess- 

 ful ie;ults, made a visit to Cambridge, when he found that 

 Newton " had brought this demonstration to perfection." 

 During that year Newton gave in his professional lectures 

 an account of his work then in manuscript form, en- 

 titled, " De Motu Corporum," which may be said to be 

 "a rough draft of the beginning of the first book of the 

 'Principia.'" This period includes also Halley's second 

 visit to Cambridge with reference to Newton's publication 

 of this tract, and it was at this time also that Halley asked 

 him to communicate his results to the Royal Society. 

 The tract which Newton finally communicated was en- 

 titled, " Propositiones de Motu," and may be looked upoa 

 as marking the point at which Newton had arrived 

 about the end of this year. Mr. Ball reproduces this 

 tract in exienso, as it has only once been printed, and 

 copies of it are scarce. 



The fifth chapter deals with the investigations from 

 1685 to 1687, during which time Newton was preparing 

 the " Principia." A most interesting account is given 

 of the details concerned in the preparation of the subject- 

 matter, while he refers also, by no means too fully, to the 

 extreme generosity that Halley displayed, both as regards 

 the cost of printing the books, and also to the interest he 

 took in their progress, criticising some parts, and revising 

 sheets for press. Rigaud, in his essay on the first publi- 

 cation of the " Principia," referring to this point, says, 

 "that under the circumstances it is hardly possible to 

 form a sufficient estimate of the immense obligation 

 which the world owes in this respect to Halley, with- 

 out whose great zeal, able management, unwearied 

 perseverance, scientific attainments, and disinterested 

 generosity the ' Principia' might never have been pub- 

 lished." Mr. Ball also discusses here briefly Newton's 

 controversy with Hooke, "the universal claimant," as he 

 was called. 



Chapter vi. is devoted to an analysis of the " Principia," 

 a few words of introduction relating to the main differ- 

 ences between the first editions being given. Mr. Ball 

 limits himself in the main to a statement of the pro- 

 positions, lemmas, &c., but occasionally he breaks in 

 with a i^w words of explanation, or of historical interest. 



The remaining period, ending with the year 1726, 

 contains matter dealing with the large correspondence 

 Newton had on the contents of his " Principia," to his 

 revision of the whole work, the extension of some of the 

 results, and finally to the preparations of the two later 

 editions. 



The appendices contain the correspondence between 

 Newton and Hooke and Halley, besides some memoranda 

 on the correspondence concerning the production of the 

 second and third editions. 



From the above brief sketch of the contents of this 

 essay, our readers may perhaps gather some idea of the 

 ground it covers. The author is so well known a writer 

 on anything connected with the history of mathematics, 

 that we need make no mention of the thoroughness 



