APPLICABLE TO MATHEMATICS, &C. 353 



sent the velocities of A and B at distances a and 

 a^ respectively. 



.-. C = M v + M' «' 



Consequently equation (4) may be written 



M-^+W~= Mv+Wv' (5) 



at at ^ ■' 



Integrate this equation, and we have 



M X -\- M.' x' = (Mv -\- M} v') t + C (6) 



To determine C\ we have the values of o! and .2?* 

 when ^ = 



.-. M a + M* a' = C* ; consequently 

 Mar + M'a;> = (M« + M'«')< + Ma + M'a' (7) 



If X be the distance to the centre of gravity 

 of M and M' at any time t ; and A be the dis- 

 tance of the centre of gravity at the commence- 

 ment of motion, we shall have 



Mx-\-Wx= (M. + W)X 



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

 z z 



