THE SCIENTIFIC SPIRIT IN FRANCE. 



101 



instrument, afterwards called "the method of fluxions"; 

 but he had not made it generally known before the 

 invention of Leibniz was published. 1 This, though much 

 later in time, had been perfected and applied by his 

 friends and followers in a most extensive manner, and 

 had, in fact, become the recognised mathematical lan- 

 guage of the Continent. No learned body did more than 

 the Paris Academicians to perfect (with purely scientific 



1 Leibniz seems to have been in 

 possession of his method as early 

 as 1675, and communicated it to 

 Collins in 1677. It was, however, 

 not published before 1684 in the 

 ' Acta Eruditorum,' and then prob- 

 ably only on account of some writ- 

 ings of Tschirnhausen trenching on 

 the same subject. Newton seems 

 to have been in possession of his 

 methods as early as 1665, fully ten 

 years before Leibniz made use of 

 his. Immediately after the publi- 

 cation of Leibniz's paper in 1684, 

 the differential calculus was taken 

 up by the Continental mathema- 

 ticians, especially by James Ber- 

 noulli (1654-1705) and John Ber- 

 noulli (1667-1748), and the Mar- 

 quis de 1'Hopital, who published 

 the first treatise on the new calculus 

 in 1696. Newton did not publish 

 any account of his method, though 

 he must have used it extensively in 

 arriving at the results contained 

 in the ' Principia.' Different views 

 have been expressed on the reasons 

 which induced Newton to withhold 

 from publication his new methods, 

 and the question to what extent 

 Leibniz owed the first suggestions 

 of his method to Newton remains 

 also undecided. Those who take 

 an interest in the personal question 

 should refer to the original docu- 

 ments, the ' Commercium Epistoli- 

 cum,' published by the Royal Society 

 in 1715 ; the pamphlet of Gerhardt, 



' Die Erfindung der Differential- 

 rechnuiig' (Halle, 1848). An ex- 

 treme view, unfavourable to Leib- 

 niz's originality, is taken by Sloman, 

 'Leibnitzens Anspruch auf die 

 Erfindung der Differentialrech- 

 nung' (Leipzig, 1857); but it has 

 not been generally adopted by those 

 who have examined into the subject. 

 As to the superiority of the Conti- 

 nental notation for practical pur- 

 poses, this seems to have been 

 generally admitted at the beginning 

 of this century, when it was intro- 

 duced into English mathematical 

 works. In the school of W. R. 

 Hamilton of Dublin the notation 

 used by Newton acquired a peculiar 

 importance, and it is still occasion- 

 ally used in some important works 

 like Tait and Steele's 'Dynamics 

 of a Particle,' and Thomson and 

 Tait's ' Natural Philosophy.' See 

 on this Tait's article on Hamilton in 

 the ' North British Review ' (Sept. 

 1866). The importance of the 

 labours of the Continental school, 

 headed by Leibniz, for the diffusion 

 of the new methods, is well de- 

 scribed by Remont de Montmort in 

 a letter to Brook Taylor, dated 18th 

 December 1718, and given in the 

 appendix to Brewster's ' Life of 

 Newton ' (vol. ii. p. 511, &c.) Those 

 who take more interest in the fate 

 of ideas and the progress of thought 

 than in personal matters will do 

 well to read this letter. 



