256 LIMITS AND FLUXIONS 



motion, however, we inquire what velocity is ; and 



here it is defined to be the relation between the 



space which would be described were the motion 



continued uniform from any point, and the time. 



Stili difficulties remained ; this definition might con- 



vey to the mind a general idea of the nature of 



velocity, but was of no mathematical use, since the 



space which would be described could not be immedi- 



ately ascertained and determined. Another step 



was therefore to be made, and which was made by 



establishing this proportion ; if V be the velocity, 



S the space, which would be described, and T the 



time, S' the space really described, and T' the 



S 

 corresponding time; then V = ^ = ultimate rjatio of 



S' 



, when S' and T' are indefinitely diminished. " 



Again he says : 



*' On the ground of perspicuity and evidence, the 

 understanding is not much assisted by being directed 

 to consider ali quantity as generated by motion ; 

 . . . when such quantities as weight, density, force, 

 resistance, etc. , become the object of inquiry . . . 

 then the true end of the figurative mode of speech, 

 illustration, is lost. . . . That which happened to 

 Aristotle has happened to Newton ; his foUowers 

 have bowed so implicitly to his authority, that they 

 have not exercised their reason. The method of 

 fluxions had never so acute, so learned, and so 

 judicious a defender as Maclaurin : — yet who- 

 ever consults it . . . finds the author speaking of 



