352 ON PHYSICAL DATA 



Let M & M' be the 

 masses of the bodies ^ a c b 



A & B respectively 

 OAr:*' & OB=x' 



being a fixed point in the line A B produced 

 t ~ time the bodies arrive at distances <2? and s^ 

 respectively. 



The effective force of A upon B is (m<om') ,\ ~^^ 



Ditto B upon A is (mtnm}) . 1 ~ y 



.:M^j^=im.m^)-^rz^ (2) 



o ,., d^ x^ ^ ,. f(x^—x ,., . 



^^^^=--(^'^'""^)(k:^^ (3) 



by the equations of motion. 



Add together equations (2) and (3), and wc 

 shall have 



M -^-|- + M' -^^^ = 0. Integrate this 



equation with respect to t, and we shall have 



M4f+M'4^ = C (4) 



Where C must be determined from the initial 

 circumstances of motion. Put v and w' to repre- 



