M. Poinsot on the Percussion of Bodies. 269 



remain motionless^ we must nevertheless assume that it has re- 

 ceived a finite quantity of motion, which has been entirely trans- 

 ferred there ; and hence that the force applied has not been de- 

 stroyed, but still subsists without the least alteration. 



Whenever, therefore, on encountering some fixed point, a body 

 is seen to become animated with a velocity greater than it for- 

 merly possessed, we must, if we vv'ish to know the quantity of 

 motion which exists after the shock, not only consider the quan- 

 tity which the body possesses, but also that which it has im- 

 parted, in a contrary direction, to the fixed point in question. 

 And if we take the difference between these two quantities of 

 motion, as we ought to do in this case, we shall find precisely 

 the same quantity as existed before the shock ; so that the ge- 

 neral principle of the conservation of force remains intact. It 

 may easily be shown, too, that the principle of the conservation 

 of areas is likewise observed, provided the movement of the fixed 

 point — or rather of the free point, with an infinitely great mass 

 — be taken into consideration. Thus, as soon as we take cogni- 

 zance, not of the moveable body alone, but of the system com- 

 posed of that body and of the material point in question, all 

 paradox disappears. 



51. But to return to the peculiar motion of the body irrespect- 

 ive of that of the fixed point, which is insensible, it may be well 

 to make, or rather to recall, one more important remark, although 

 the reader will probably have ah-eady done so. This capability 

 of being reflected on encountering an obstacle, or of being pro- 

 jected forwards with a greater velocity than before, proceeds, 

 essentially, from the rotation of the body around its own centre 

 of gravity. For if the body be endued with a simple movement 

 of translation alone, it will neither be capable of any reflexion by 

 means of any of its points, nor of any progression with a velo- 

 city superior to its own. By the presentation of an obstacle, the 

 motion of the centre of gravity of the body must, necessarily, be 

 retarded, and it will be altogether arrested if the obstacle be 

 presented in a direction passing through the centre of gravity. 

 But when the body turns on itself, it becomes, so to speak, en- 

 dued with a kind of elasticity, such as we have already described, 

 and it may then present those curious effects which we observe 

 whenever a body in motion encounters an obstacle, or a series of 

 obstacles successively presented to it. 



But to complete our theory, we must now consider the points 

 of the Ijody from a second point of view, relative to the conversion 

 or new rotation which it assumes on encountering a fixed point. 

 On the centre of maximum conversion. 



52. We have seen (art. 31) that when the obstacle or fixed 

 point is presented to the movement of the body in a direction 



