8o LIMITS AND FLUXIONS 



which it had in those Parts when moving forward 

 to generate it ; in the Instant the Line vanishes as 

 a Length . . . the generating point will remain, 

 together with the Velocity it had at the very 

 Beginning of its Motion, And the Case is the 

 very same with respect to the Rectangle increas- 

 ing by the Motion of its Sides." This point is 

 elaborated with great fullness. After some illustra- 

 tions, Walton exclaims : *'This is a full and clear 

 Answer to this part of the catechism, and shows 

 that its Author has been greatly mistaken in 

 supposing that I explained the Doctrine of Fluxions 

 by the Ratio of Magnitudes infinitdy diminish' d, or 

 by Proportions between nothings. ... I do not 

 wonder that this Author should bave no clear Ideas 

 or Conceptions of second, third or fourth Fluxions, 

 when he has no clear Conceptions of the common 

 Principles of Motion, nor of the first and last Ratios 

 of the isochronal Increments of Quantities generated 

 and destroyed by Motion. ... In order to prevent 

 my being Catechised any more by this Author," 

 Walton makes a confession *'of some Part of my 

 Faith in Religion." 



Jurin's Second Reply to Berkeley 



102. Jurin brought out a second publication,^ of 

 1 1 2 pages, which was in reply to Berkeley's Defence 

 of Free-Thinking. Passing by unimportant pre- 

 liminaries, we come to Jurin's definitions of '*flow- 



' Tlìi' Minute Matheinatìclaii : or. The FrecThiither no Jiist- 

 Thinkei. By Philaleihes Cantabiigiensis. London, 1735. 



