I 



of Injinitesimals in England. 327 



3Iy copy of Craig's second tract has written on the title-page 

 " Is. Walton Doniim Authoris. Jun : 7. 1693." The form of 

 this inscription^ especially the date, shows that it was made by 

 the receiver, and not by the giver. Supposing this receiver to 

 be I. Walton, who afterwards took part in the Analyst contro- 

 versy, the book was in Ireland on the 7th of June, and had most 

 probably been published many weeks before. The imprimatur 

 of Wallis's second volume is dated August 28, and the preface 

 July 12. The volume has 880 pages; the printing began, as 

 the preface informs us, in 1692, and Newton's contribution (a 

 most evident interpolation) is at page 390. If Craig's tract 

 were seen by Newton, as would seem most likely, at the end of 

 1692, an immediate communication to Wallis would have arrived 

 in sufficient time to appear where it actually does. Further, 

 Craig is mentioned in Newton's contribution as having written 

 to Newton for a series which was to be communicated to David 

 Gregoiy. Now Craig, in the preface of 1718, gives an account 

 of this correspondence, as some months posterior to the exami- 

 nation of his manuscript by Newton ; consequently, Newton's 

 contribution to Wallis is posterior to his having seen Craig's 

 manuscript. I conclude, then, that Newton, seeing the progress 

 the differential calculus was likely to make in England, procured 

 the entire suppression of his own name in Craig's tract, and 

 made up his inhid to insert a part of his own treatise in the 

 forthcoming work of Wallis. This will explain why Craig did 

 not then mention either Newton's examination of the manuscript, 

 or his supply of examples : the tone in which he attacks Tschirn- 

 hauss is so acrimonious, that we may be sure Newton would have 

 desired not to appear, even indirectly. It is true that Newton 

 (Edleston, p. 176) speaks of the contribution as sent in 1692, at 

 Wallis's request. That it must have been the very end of 1692, 

 which is quite consistent with my suppositions, appears from 

 this, that the contribution itself, or a parenthesis of Wallis, refers 

 to previous letters of August and Septcmbei-, from Newton to 

 Wallis, apparently on series. 



Craig continued to write in the Philosophical Transactions, 

 and he uses the differential calculus in 1701 in No. 268, in 1703 

 in No. 284, in 170-1 in No. 289, and in 1708 in No. 314. In the 

 second of these papers, he treats the differential calculus as uni- 

 versally established : ut omnibus notum, zy—J: ydz-=J: zdy. He 

 also wrote one or more papers in the Leipsic acts. His third 

 separate publication followed the great controversy : it is De 

 calculo Jlueniium libri duo. Quibus subjunguntur libri duo de optica 

 analytica. London, 1718, 4to (pp. viii + 92). We have now 

 nothing but fluxions ; not a word of the 'differential calculus : 



