354 M. Poiusot on the Percussion of Bodies. 



On the centre of maximum percussion. 

 31. The percussion due to a couple, whose two moments with 

 respect to the two principal axes a and /3 arc L and M, being 

 expressed by 



and the coordinates x and y of the centre J), where the percus- 

 sion is a maximum, satisfying the equations 



we easily find 



dQ ^ .dQ ^ 

 -^ =0, and -r- =0, 

 dx dy 



from which we immediately deduce 

 x:y = L:M, 



u^x^ + l3^y^ = u^^. 

 The centre of maximum percussion, therefore, is at once upon 

 the central ellipse and upon the intersection of a plane through 

 the origin G, parallel to the plane of the couple. Consequently 

 each extremity of the diameter 3S determined by the plane of 

 the couple is such a centre. 



If we represent by (Q) the value of this maximum percussion, 

 the preceding equations give 



^^)= 2^ ' 



or, since 



6 -X +y - ^2L2^^2|^2 > 



the simpler expression ^____ 



^L^ + M^ 

 (^^- 28 ' 



which is nothing more than the moment of the couple of impul- 

 sion divided by the length of the diameter parallel to its plane. 

 Hence when a body is animated solely by the impulse of a 

 couple perpendicular to one of its three principal planes, or, in 

 other words, when a body actually turns around a diameter 2S' 

 of the central ellipse described in this plane, the point where it 

 strikes with the greatest violence is at one of the extremities of 



