72 LIMITS AND FLUXIONS 



nothing, " Walton states that the fluxional calculus 

 assumes that '^Ouantities can be generateci by 

 Motion . . . and consequently they may also by 

 Motion be destroy'd." 



93. Walton's Vindication foUows Newton's ex- 

 position closely ; Berkeley's claim that Walton 

 followed in Jurin's track and borrowed from him, 

 is, I believe, incorrect. Take the vital question of 

 rejecting infinitesimals : Jurin claims that, being 

 so very small, they do not appreciably affect the 

 result ; Walton takes the stand that there is no 

 rejection whatever of infinitesimals. The main 

 criticism to be passed on Walton's first essay con- 

 sists, in our judgment, in a failure to meet 

 Berkeley's objections squarely and convincingly. 



Beì'kelefs Reply to Jurin and Walton 



94. Jurin's and Walton's articles were answered 

 by Berkeley in a publication entitled, A Dcfence of 

 Free- TJiinking in Mathematics. ^ 



Berkeley restates the purpose he liad in writing 

 the Analyst '. " Novv, if it be shewn that fluxions 

 are really most incomprehensible mysteries, and 

 that those who believe them to be clear and scien- 

 tific do entertain an implicit faith in the aiithor of 

 that method : will not this furnish a fair argumen- 

 tum ad hominem against men who reject that very 

 thing in religion which they admit in human learn- 



^ A Defence of Frec-'J'hitikmi^ in A/athet/iaiics. In Ansivo- io a 

 Pamphlet of Philalethes Cantabrigiensis. . . . Also an Appendix 

 concernine; Mr. Walton^ s Vindication. . . . By the Author of " 7'he 

 Minute Philosopher,'' Dublin, 1735. 



