BERKELETS ANALYST (1734) 69 



without the first, gives 2x{2y)-^{2y + (fy). Both 

 these expressions are equal to 2.r, " which is the 

 result either of two errors, or of none at ali." li 

 you claim that 2x{2y + dy)-^{2y)> 2x, how much 

 greater is it, supposing 2,r= 1000 miles ? Not as 

 much as the thousand-millionth part of an inch. 

 Jurin ends vvith a discussion of Lock on abstract 

 ideas. 



Wa/ton's First Reply to Berkeley 



90. Little is known about John Walton. He 

 was Professor of Mathematics in Dublin, and partici- 

 pated in this controversy. Otherwise, practically 

 nothing about him has been handed down. 



His reply to Berkeley was published in 1735 at 

 Uublin.i Berkeley attacked the method of fluxions 

 more particularly as given in Newton's earlier 

 exposition ; Walton defended the theory on the 

 basis of the later treatment as given by Newton 

 in his Quadratura Curvaruni (1704), and in the 

 Prmcipia, Book II. 



91. Walton begins by stating that inasmuch as 

 the credulous may " become infected" by Berkeley's 

 attack on fluxions, it seems necessary to give a 

 short account of the nature of fluxions. "The 

 momentaneous Increments or Decrements of flow- 



^ A Vindiiatioìi of Sii- Isaac Neiuton x l'timiples of Fluxions, 

 agaiusi the Oift'idotis lontaiiied in fhe Analyst. By J. Walton. — 

 Siquid novisti reclius isiis, candidus imperti : bi non, his utere inecum. 

 Hor. In the fuhiess of his Suftìciency he shall he in Straits : Every 

 Hand of the IVickcd shall come upon him. y<^/^— Duhlin, Printed ; 

 and reprinted at London, and sold by J. Robcrts in Warwick-Lane. 

 1735- [Price Six Pence.] 



