176 M. Poinsot on the Percussion of Bodies. 



fraction equal to unity, it follows that the centre of gravity is the 

 only point with respect to which it can be affirmed that the body 

 strikes as if its wiJole mass were concentrated in the point of 

 impact. The quantity of this percussion is Ma9. 



29. If we consider the centre of percussion C, corresponding 

 to a: = h, we shall find for the force of percussion at this point, 

 the- expression 



whence we sec that this centre C strikes as would a free point 

 moving with the same velocity W, and charged with the fraction 



y of the mass of the body. If we consider its quantity merely, 



this percussion is also Ma6, that is to say, it is the same as that 

 which appertains to the centre of gravity ; it diifers from the 

 latter, however, in being the percussion of a less mass moving 

 with a greater velocity. If the obstacle is an absolutely fixed 

 point, these two percussions may be regarded as perfectly equi- 

 valent, since in both cases the same quantity of motion is de- 

 stroyed. But if the obstacle is a free massive point opposed to 

 the movement of the body, the two 'percussions in question can 

 no longer be regarded as identical. For it is evident that the 

 body, by striking with its centre of percussion C, would impart 

 to the massive point /j, the velocity 



v=— J 



-ii/r « 



f^ + Mj 



whereas by striking with its centre of gravity it would only im- 

 part to the point the velocity 



_ Mad 



which is less than the foregoing in consequence of I being 

 greater than a. 



30. We sec, then, that by striking with its centre of percus- 

 sion, a body imparts more motion to a free point /m, previously 

 at rest, than if it had struck the same with its centre of gravity. 

 But the centre C of percussion is not on this account the point 

 by means of which the body could communicate the greatest 

 possible velocity to the point /x ; neither does the centre T of 

 maximum percussion possess this property, but another new 

 point, whose distance from the centre of gravity depends upon 

 the ratio between the masses M and //,. In fact let V be the 

 velocity imparted to the massive point fj, when the body M strikes 

 the same with a point at the distance x from the centre of gra- 



