88 LIMITS AND FLUXIONS 



[a point's] Velocity will exist in a Point, and 

 successively will exist in every Point of Space 

 through which the Point moves " (p. 37). Berkeley 

 thinks that " from the generateci Velocity not 

 being the same in any two different Points of the 

 described Space it will not foUow that Velocity 

 can exist in a Point of Space. But in this he is 

 mistaken. P'or the continuai Action of a Moving 

 Force necessarily preserves a continuai Velocity ; 

 and if the generated Velocity be not the same in 

 any two different Points of the described Space, a 

 Velocity must of Consequence exist in every Point 

 of that Space" (p. 38). This account of velocity 

 " is agreeable to Sir Isaac Newton's Notion of 

 Velocity ; who constantly excludes described Space 

 from his Idea of that Term." Motion being 

 measured by QV, **the continuai translation of a 

 Body therefore into a new Place is, . . . an Effect 

 of this Tendency forward in the Body, and not the 

 Tendency itself ; consequently Space described is 

 an Effect of Velocity, and not Velocity itself" 

 (p. 47). On the question of first and last ratios it 

 cannot be said that Walton here throws new light. 

 He insists that he explained fluxions not ''by the 

 Ratio of Magnitudes infinitely diminish'd, but by 

 the first and last Ratios of Increments generated or 

 destroyed in equal times : that is, by the Ratios of 

 the Velocities with which those Increments begin 

 or cease to exist" (p. 53). To Berkeley 's charge 

 that Walton " supposed. two Points to exist at the 

 same Time in one Point, and to be moved different 



