182 Dynamics. 



n 



m+n :m-n : : g : -^-- g. 



If, therefore, we call w the velocity of m at the expiration of a 

 264. number t of seconds, we shall have 



m 



267. and the space which it will have described, will be 



^x 



which is readily found, by putting for t the given number of sec- 

 276. onds, and for g 32,2 feet. 



293. If at the first instant the body ?i, supposed to have less 

 mass than the other, receive an impulse or velocity T, that is, if 

 it were struck in such a manner, that, being considered free and 

 without gravity, it would pass over in a second a number of feet 

 denoted by , it would divide this action with the body m which 

 it would draw during a certain time. In order to determine how 

 the action in question would be divided, it must be remarked, 

 that at the first instant the action of gravity being infinitely small 

 or nothing, the body n, urged with a velocity i>, acts upon the 

 body m as if this last were at rest. It is necessary, therefore, 

 in order to find the velocity remaining after the action, to divide 

 28. the quantity of motion n v by the sum of the masses, which gives 



for the velocity with which n would draw m, if gravity 



m -f- n 



did not act in the following instants. But as we have seen that 

 it would act in such a manner as to give to the body m, in 



m n . , 

 the opposite direction, the velocity g t in the time / ; it 



follows that, at the expiration of the time , the body n will have 

 only the velocity 



Whence it will be seen, that however small n may be, and how- 

 ever small the velocity -y, and however considerable the mass of 



