Dr. Dlcifon's Replj to Mr. Clarh. 6f 



In the firft place, I folemnlv declare that this charge is 

 falfe and groundlefs in every poffible refpe6l. 



Sccondl)', I deny that I have there " (hown a general me- 

 thod of finding the fluxions of quantities." I have only in- 

 ferted in a note, " a Jpecimen'" — " a /light and irnperfe^i 

 general outline" — of a I'cry eaf)', and m J'ome meafure neiv, 

 manner of treating the fundamental procefles of fluxions, 

 which I long ago mentioned to yourfelf; and which, with 

 fome thoughts on Prime and Ultimate Ratios, I intended 

 to offer vou for publication/' 8cc.* The fubftance of the 

 paper here alluded to, which you may recolleft my men- 

 tionino;, I fubmitted to a certain Gentleman whofe education 

 does honour to the Univerfity of Cambridge. But the paper 

 itfelf, owing to my indifpofition and avocations, is not yet 

 finiflied ; and, owing to the treatment I have received, is 

 likely never to be printed, any more than fome analogous 

 pieces of more confequence, which I intended for the prefs. 

 This, Mr. Clarke will fay, perhaps very truly, is no lofs to 

 the public. But unlefs he can divine the contents of a piece, 

 which has no public exiftence, his charge of plagiarifm muft 

 become impotent, or can only afi'eft it's fabricator. 



Thirdly^ Whether even the " fpecimen" of the method 

 which I promifed, be, or be not, " the very fame" with Air. 

 Clarke's, is a matter of faSi, of which thofe perfons who 

 compare them can judge; and fuch I leave to determine. 

 Whether they know any book from which that "fpecimen" 

 differs fo widely as it does from that of Mr. Clarke. 



I pretended not to a method entirely, or even in a great 

 meafure, new. My principal objeft was facility, which is 

 but too much neglefted by great mathematicians. I thought, 

 however, that mv firit way of finding the fluxion of a fraction 

 was my own, as I fl;ill think the fecond is. Certainly, I never 

 received either of them from any man, or from any book. 

 The firfl: is as follows : 



" The fluxion of a fraftion may be found by confidering 

 it as the produ6t of the numerator and denominator, giving 



X -*■ I 



the latter a negative index. Thus — is equivalent Xoy X ;r; 

 and, as the fluxion of .xy is ;.r + -"(y, fo the fluxion of 

 — , or of its equivalent^ X -t, mufl: be 



(y X*) + (.vX-^ y)=—^-^l.^y—-JL^ 

 • See my Tranflation of Carhot, notes p. 4s and 49. 



F a This 



