Collision ofunelastic Bodies. 183 



the body m, n will always draw m for a certain time, after which 

 tfi will prevail, and draw n in its turn. 



Indeed, whatever may be the quantity of motion n T>, impress- 

 ed upon w, so long as it is of a finite value, it is evident that it 

 would always be necessary, in order to counteract it, that gravi- 

 ty should act for a certain time, for it only acts by degress infi- 

 nitely small at each instant. 



If we would know at the expiration of what time m will cease 

 to ascend, we should proceed thus. Let if be the time employed 

 by a heavy body, falling freely, in acquiring the velocity i> ; ac- 

 cording to article 263, we shall have 



therefore the velocity of n will be changed to 



n g t' m n 



m -f- n m -f- n & 



which being put equal to zero, gives 

 n g t' = (m n 



from which we deduce 



n t' 



If, for example, the velocity T, supposed to be impressed upon w, 

 is such as a heavy body would acquire in one second, we should 

 have t' = I". Suppose m = 100 lb , and n = I 1 *, we should 

 have 



t = 



1001 99 



that is, the body n would draw the body m only during one 

 ninety-ninth of a second ; still it would draw it. 



We see, therefore, that there is not a finite force, however 

 small, which is not capable of overcoming the weight of a body; 

 and that it is not possible for a body actually in motion, to be 

 placed in equilibrium with the weight of another body, that is, 

 with a body that has the simple tendency of gravity. The for- 



