M. Poinsot on the Percussion of Bodies. 173 



at once remarked, as will also the accordance between the latter 

 and the precise notion of percussion which we ought to possess. 

 Take, for instance, the case of a body turning around its own 

 centre of gravity ; if we were to seek, according to the old theory, 

 the particular point known as the centre of percussion, we should 

 find it to be situated at an infinite distance from the centre of 

 gravity, and that the force of percussion altogether vanishes. 

 From this one might conclude that a rotating body, whose centre 

 of gravity is at rest, is not capable of striking an obstacle or of 

 communicating motion to any material point which is presented 

 to it, a conclusion as opposed to experience as it is to our theory. 

 In fact, we find that if a body turns around its own centre of 

 gravity with an angular velocity 0, or, in other words, if the 

 body is animated by a couple whose measure is MK^. 6, it is 

 capable of striking at a distance x from its centre of gravity with 

 a force r 



that the maximum percussion takes place at the distance x = K. 

 precisely, and that the intensity of the same is measured by the 

 quantity of motion 



so that the body strikes with this centre just as if the half of its 

 mass M were there concentrated. 



In the same manner we find that the reciprocal point on the 

 other side of G, at the distance a; = — K, is also capable of striking 

 in an opposite direction, as if the other half of the body's mass 

 were there concentrated ; hence we see that during the motion 

 of the body its whole mass is, as it were, appropriated in equal 

 shares by these two reciprocal centres. In the next article, 

 however, we shall show that this last property is merely a parti- 

 cular case of a general one which all pairs of reciprocal points 

 possess. 



V. New properties of any two mutually reciprocal centres 



IN A BODY. 



26. It has been already shown (art. 15), that when animated 

 by an impulse P passing at the distance h from its centre of 

 gravity, the body strikes at C, whose distance from G is x, with 

 a force Q expressed by 



hx+K\ 



and at the point 0', reciprocal to C, with a force 



