178 Dynamics. 



m {u -r u') = n u'. 

 from which we deduce 



771 U 

 U' = - , 



in -j- n 



the same as the expression above obtained from the general for- 

 mula. 



289. When the bodies move in opposite directions, in order 

 to find the velocity after collision, it is only necessary to suppose 

 in the first formula, that v is negative, which gives 



. mu nv 

 u' = 



m + n 



that is, when the bodies move in opposite directions, in order to find 

 the -velocity after collision, we take the difference of the quantities of 

 motion belonging to the bodies before collision, and divide by the sum 

 of the masses ; and, this velocity will take place in the direction of that 

 body which had the greater quantity of motion. 



We might also obtain this result directly by proceeding as in 

 the above example. 



Thus the laws of the direct collision of unelastic bodies reduce 

 themselves in all cases to this single rule ; tJie velocity after collis- 

 ion is equal to the sum or to the difference of the quantities of motion 

 before collision (according as the bodies move in the same or in op- 

 posite directions), divided by the sum of the masses. 



Of the Force of Inertia. 



290, We have supposed in what we have said, that indepen- 

 dently of gravity, the resistance of the air, and other obstacles, 

 one of the two bodies opposes a resistance to the other, and 

 makes it lose a part of its velocity. But how can a body with- 

 out gravity, and which is confined by no obstacle, oppose a re- 

 sistance ? Does not this seem to imply that it would be capable 

 of giving motion ? 



