354 ON PHYSICAL DATA 



Substitute these values in equation (7), and we 

 shall have 



X-A=(«^±^V (8) 



M +M' 

 When V and v^ are nothing, we shall have 



Ma; + M'a; = Ma + M'a' (A) 



Hence, the motion or the space which the centre 

 of gravity moves through is proportional to the 

 time. 



If we consider M = M' ; we shall have 



X-A = ^^.t (9) 



Let us next examine the equation (1) viz.f(j») =: 

 Put, f(p) zzp'^ + Hip + n.2zz0 





'^ 2 



Hence there are two values of j9, namely 



— w, + v^n? — 4^2 and — n, — V'n? — 4^2 



2 " 2 



Equation (8) contains the conclusion arrived at by Newton. 

 See Principia, pa^e 27, vol. 1. 



