Collision. 175 



But it must be recollected that, in the equation g dt* = d ds, 

 it is supposed that d t is constant. When d t is variable, we make 

 use of the equation 



Occasions will occur in which these formulas will be of great 

 use. But we must not forget that the quantity g which they 

 contain, represents, for each instant, the velocity which the ac- 

 celerating force is capable of giving to the moving body in a 

 known interval of time, as one second, if during the second, it 

 were to act with a uniformly accelerating force ; so that as each 

 quantity g measures for each instant, the effect of which the ac- 

 celerating force is capable, we shall give it, for brevity's sake, the 

 name of accelerating force. 



Of the direct Collision of Bodies. 



285. We suppose, in what follows, that no account is taken 

 of the gravity of bodies, of friction, or other resistance. 



We suppose also that the bodies, whose collision is the sub- 

 ject of consideration, act the one upon the other according to 

 the same straight line, passing through their centres of gravity, 

 and that this straight line, is perpendicular to the plane touching 

 their surfaces at the point where they meet. 



We shall consider bodies as divided into two classes, denom* 

 inated unelastic and elastic ; the former are supposed to be such 

 that no force can change their figure ; the latter are regarded as 

 capable of having their figure changed, that is, of being com- 

 pressed, but as endued at the same time with a property by 

 which this figure is resumed after the compressing force is re- 

 moved. 



Although there are not in nature bodies of a sensible mass 3 

 that answer perfectly to either of these descriptions, yet it is only 

 by proceeding upon such suppositions, that we are able to de- 

 termine the action of such bodies as are actually presented to 

 our observation. 



