M. Poiasot on the Percussion of Bodies. 169 



P being the impulse with which the body is moved, and h the 

 distance CG of this impulse from the centre of gravity. 



16. We may remark, enjiassant, that if wc suppose 



that is to say, if the obstacle C be presented at the spontaneous 

 centre 0, the percussion Q becomes zero, as it ought to do. 



17. If we suppose .r=0, that is, if we place the obstacle before 

 the centre of gravity, the percussion Q is equal to the force P 

 itself. 



If we suppose x=h, in which case the obstacle C is applied 

 at the point C, the percussion Q is again equal to P. 



Thus with its centre of percussion the body does not strike 

 more forcibly than with its centre of gravity. There is this dif- 

 ference between the two cases, however : when the body strikes 

 with its centre of percussion, its whole motion is entirely arrested ; 

 whereas when it strikes with its centre of gravity, it loses its 

 motion of translation merely and, after the impact, preserves its 

 former rotation d around the centre of gravity G. 



18. It will also be seen that when x is negative and greater 



than — or «,— in which case the obstacle C is placed on the same 



side of the centre of gravity as the spontaneous centre 0, and 

 beyond the same, — the percussion Q becomes negative or contrary 



in direction to the impulse P ; so that, to be struck by the body 

 at all, the obstacle C must then be presented on the other side, 

 or in the rear of the body with respect to its translation in space. 



But the question at present before us is, to find the distance 

 X of the point T where the percussion Q is a maximum. 



19. To find this remarkable point, we have merely to diflfer- 



entiate the preceding expression P . Y.i-^<i, * l^eing thereby re- 

 garded as the sole variable, and to equate the resulting expression 

 for -y^ to zero : this gives us the quadratic equation 



or, smce -^ = a, ^, ^ 3^^ - K^ = 0, 



whence we deduce 



x=-a± ^K^ + a^, 



the required distance of the point T from the centre of gravity G 

 (sec figure, art. 15). 



