1821.] Phcenomena of Heat J Gases f Gravitation, S^c. 287 



or even a philosophical way of estabUshing the question ; but in 

 a case of this kind, where I thought my prejudices might 

 influence my judgment, it appeared no bad method of examining: 

 the soundness of my opinion by the standard of other people's.^ 

 From all these circumstances, it appears that the vulgar doc- 

 trine of the collision of hard bodies is, in this particular case, 

 incorrect, by making the intensity of the stroke only the half of 

 what it should be. For the bodies remaining together after the 

 impulse, the force of the stroke upon each must be equivalent to 

 the motion destroyed ; that is, to the momentum of either of 

 them. But the force upon each is the force with which they 

 come in contact ; the force, therefore, with which they come in 

 contact is equal to the momentum of one of the balls ; that is, 

 agreeable to both theories, to the force with which either ball 

 alone would, with the same momentum, strike a fixed plane. 



Prop. III. 



If a hard ball strike another hard ball at rest in the line 

 of their centres of gravity, an exchange of state will take 

 place ; the former will remain at rest after the stroke, and the 

 latter will proceed in the same direction in which the first was 

 moving, and with the same momentum. 



If this be not the case, the first body must, after the impact, 

 either move backwards or forwards in the direction of the other 

 body, with an equal or less velocity. But it cannot move back- 

 wards, because the intensity of the stroke itself on a quiescent 

 body can evidently never exceed the momentum ; therefore, if it 

 move at all after the stroke, it must follow the other body, with 

 an equal or less velocity than this body acquires from the 

 impulse. Suppose it be with a velocity /;, either equal to, or 

 less than, that acquired by the other body ; and suppose A 

 represent the first body, and a its velocity before the impact. 

 Then because (a — h), A is the motion lost by A, on account of 

 the impact, and consequently the motion gained by B, the other 

 body. This quantity represents the intensity of the impulse. 

 And in any other case {a' — h') K' represents also the intensity 

 of the impulse ; but if the quiescent bodies be equal, and if the 

 momenta A «, -k! a , of A and A', before the impact be equal, 

 the strokes themselves, by cor. to prop. 1 will likewise be equal ; 

 that is, « A — 6 A = a' k! -^ h' A^, and, consequently, h A. ■=. 

 y k' ; or the motion which is left to each of the bodies. A, A'', 

 after the impulses, will be the same. Now whatever be the value 

 of the momentum A «, if we imagine the body A to be vastly less 

 than B, the velocity of B after the impulse must be vastly 

 less than that of A before the impulse ; and, therefore, the 

 motion h A, which remains to A after the impulse must be 

 vastly less than A a, the motion of A before the impulse. And 

 if we suppose A so small as to have a ratio to B less than any 

 assignable ratio, the ratio of A 6 ; and, therefore, of A' h' to A «, 

 or A' a', will also be less than any assignable ratio. Therefore, 



