244 M. Poiasot oji the Percussion of Bodies. 



of the hammer must have the value itIq rr^ 5, and its velocity 



K^ + o?^ i^ +•*■ 



V the value Vq — v¥~) ^^ order that by the shock the same quan- 

 tity of motion M 



° "M + Wq 



may be transmitted to the body M, that is to say, in order that 

 the same constant velocity 



OM + OTo 



may be communicated to the centre of gravity G of M. 



3. But if the same velocity is imparted to the centre G, what- 

 ever may be the distance x of the point of impact, the same ve- 

 locity of rotation around G will not be communicated; for this 

 velocity, which, according to art. ], is expressed by 



M («+l)K'^ + na;2' 



clearly depends upon x ; in fact, putting for m, v, and n the pre- 

 ceding values, 6 becomes 



and consequently is proportional, as it clearly should be, to the 

 distance x from the centre G at which the stroke is applied. 



4. If we suppose the mass of the point m to be infinitely 

 small, aud its velocity v infinitely great, so that the product mv 

 may be equal to a finite quantity P, we shall find, by putting 

 n = 0, that the force m[v — u) transmitted to M becomes 



m(v — u)=^V, 



that is to say, equal to the force mv itself; which latter, therefore, 

 is entirely iu) parted to the body M. 



On this hypothesis we may form a natural idea of what is 

 meant by a force being impressed upon a body. We may con- 

 sider the same as the percussion of an infinitely small corpuscle 

 which strikes the body with an infinitely great velocity. Since 

 the finite mass M is not augmented by the addition of the cor- 

 puscle, we may assume that after the shock the latter remains 

 attached to the body, and thus that all the force passes to M. 



In this manner we can conceive why the force is proportional 

 to the velocity. For if we regard this force as proceeding from 

 the action of several equal corpuscles which strike the body suc- 

 cessively with equal and infinite velocities, we see that, since the 

 first simply gives a finite velocity to the body M before at rest, 

 the second corpuscle, which arrives with infinite velocity, will 



