38 LIMITS AND FLUXIONS 



tributed also several papers to the Philosophical 

 Trans act io ns {l^ondon), but never, before 17 18, did 

 he use fluxional symbols. In preparing the book 

 of 1685 he had received from Newton the binomial 

 theorem which he used before it had appeared in 

 print, but he had no communication about fluxions. 

 ''We have here the singular indifference, " says De 

 Morgan, "which Newton at that time, and long 

 afterwards, showed toward his own calculus."^ 

 Craig wrote a tract in 1693, and articles for the 

 Philosophical Transactzons \niy 01, 1703, 1704, 1708, 

 using the differential calculus ali this time. In the 

 issue No. 284, 1703, he employs the Leibnizian 

 sign of integration /. Craig submitted to Newton 

 one of his early manuscripts (probably the one 

 printed in 1693). With regard to this event De 

 Morgan wrote to Hamilton, the inventor of quater- 

 nions : *' Few of us know that Leibniz was perfectly 

 well known in England before the dispute, and that 

 Newton's first provocative to an imperfect publica- 

 tion was ds and infinitely small quantities paraded 

 under his own eyes by an English writer (Craig), 

 who lent him his MSS. to read."^ Craig's publica- 

 tion of 17 18 foUowed the great controversy on the 

 invention of the calculus ; now he uses fluxions 

 exclusively and says not a word on the differential 

 calculus. The book does not discuss fundamentals, 

 and no explanation of x is given. As conjectured 



^ De Morgan, Philosophùaì Magazine, 4 S., voi. iv, 1S52, p. 

 326. 



'^ Life of Str IVilliam Rowan Hamilton, by Robert F. Graves, 

 voi. iii, 1889, p. 415. 



