200 LIMITS AND FLUXIONS 



position Rowning says (p. 88), '*that the Velocity 

 of any Body is the same at any one Point, or at any 

 one Time, whether the Body moves with an uniform, 

 accelerated, or with a retarded Motion at that Point 

 or Time." This is elucidated by reference to geo- 

 metrie figures, and amounts, in the main, to the 

 explanation given by Rowe in finding the fluxion 

 of xy. One objection to such explanations, which 

 had been raised by Berkeley, was that one could not 

 speak of the velocity a body had at a point of space. 

 That such a phraseology is admissible is tacitly 

 assumed by Rowning. What the latter emphasises 

 is that no use is made of the concept of the 

 * ' infinitely little. " As to Berkeley's second objec- 

 tion, that the supposition which is made at the 

 beginning of the process is later displaced by its 

 contrary, as when the symbol o is at first made an 

 actual increment and later in the same process taken 

 as no increment, Rowning argues that terms involv- 

 ing factors oo^ ooo, etc. , "do arise in consequence 

 of the Acceleration wherewith the Power of ;ir flows, 

 when X itself flows uniformly ; and consequently 

 that they arise from the second and higher Fluxions 

 of that Power ; and that, therefore, when the first 

 Fluxion of that power is only inquired after . . . 

 they are to be left out and rejected, as appertain- 

 ing to another Account." It can hardly be claimed 

 that Rowning made a contribution to the theory 

 of fluxions. However, he has a pleasant way of 

 expressing himself. His book was favourably re- 

 viewed in the Monthly Review (voi. xiv, p. 2 86). 



