31 



As may also be considered as consisting of two parts, one 



part ( = ^^ A f ) is independent of the two forces R and P, which 



between P and Q are variable both in quantity and in direction, 

 and the other part arises from the action of these forces during the 

 time A t. This part we may suppose also produced by an equivalent 

 constant force acting during the time a ^ in a direction perpendi- 

 cular to PE, and we may represent this force hy P + q i^ t, q 

 being a variable but determinate quantity, then by the property 

 of uniformly accelerated motion 



^^ = t^t+'~iP+qAt)^t' (4) 



comparing equations (3) and (4) 



or taking the limits of this equation 



d'z _ Px „ Pxdt'' 



jT^-^ov d^z = -^ (5) 



ButJ^=lim.f->|%rd. = l^" (6) 



Multiplying together equations (5) and (6) 



and by integration 



dz'- = (h+y— dv)dt^ (7) 



h being a constant quantity. 



Then from equations (7) (2) and ("1) we obtain 



do — 



W— X _i _1 (^) 



\ i k+fiPx^d, * 



also by equations (7) and (6) 



