244 LIMITS AND FLUXIONS 



CoUins's Commercium Epistolicurn in the Philosophical 

 TransactionSy 17 17. Though following Newton 

 closely, variations were bound to arise. Thus, 

 Holliday says (p. 73), *' Fluxions are not magnitudes 

 but the velocities with which magnitudes, varying by 

 a continuai motion, increase or decrease." It cannot 

 be claimed that HoUiday made any contribution to 

 the philosophy of fluxions, nor even that he profited 

 as much as he might by the refinements in the logie 

 which had been made by English writers since the 

 time of Newton. 



Charles Hutton, 1796, 1798 



211. In his M athematical Dictionary^ London, 

 1796, Charles Hutton makes reference to the 

 advantage of Simpson's definition of a fluxion as a 

 magnitude uniformly generated in a finite time, the 

 imagination being now no longer confined to a single 

 point and to the velocity at that point ; moreover, 

 * ' higher orders of Fluxions are rendered much more 

 easy and inteUigible. " 



212. From the part on fluxions in Hutton's Course 

 of Mathematics ^ we take the following : 



* * The rate or proportion according to which 

 any flowing quantity increases, at any position or 

 instant, is the Fluxion of the said quantity, at 

 that position or instant : and it is proportional to 

 the magnitude by which the flowing quantity would 

 be uniformly increased, in a given time with the 



^ A Coìirseof Mathematics. By Charles Hutton. London, 4th ed., 

 1803-1804, voi. ii, p. 279. [First ed., 1798-1801.] 



