38 OUTLINES OF NATURAL PHILOSOPHY. 



If the bodies move in opposite directions, one of the 

 velocities, as b, must be made negative. 



If the bodies are equal, the velocity of A after the 

 stroke is 6, and that of B is a. The bodies 

 therefore exchange velocities. 



When the velocity of either body, after collision, 

 comes out negative, we are to understand its direc- 

 tion to be contrary to that which is accounted all 

 .firmative. 



79- The difference of the velocities of two per- 

 fectly elastic bodies, is the same before and after 

 collision ; but the body which had the greatest velo- 

 city before collision, has the least after it. 



If A and B be the masses of the bodies, a and b 

 their velocities before collision, a and b' their 

 velocities after it; a b = b' a. Hence, also, 

 a + ct b -|- b'. 



Hence, too, the relative motion of the bodies is not 

 changed by their collision. 



SO. In perfectly elastic bodies, the sum of the 

 products made by multiplying each of the bodies 

 into the square of its velocity, is the same after col- 

 lision that it was before it. 



For 



