M. Poinsot on the Percussion of Bodies. 253 



-r- aud — : for the first, wlierem i and K are both variable with 



/i, represents a /mVe line l=d+-^f whereas the second, in 



which sn is independent of fi, denotes an infinite line when x=0. 

 These delicate distinctions are as necessary in dynamics as they 

 are in analysis ; in both the gravest errors are incurred by ne- 

 glecting them. 



10. To give an example, let us suppose that, our system hav- 

 ing received the impulse of a given couple N, we require to know 

 the force Q with which the body would strike a fixed point T 

 presented to it at any distance x from the centre of gravity g. 

 It has been shown in another place* that this percussion Q has 

 the value 



and that the maximum of Q is at the point T which corresponds 

 to ^ = K, that is to say, at the extremity of the arm of inertia K 

 of the system. Now since this line K is zei'o in the present case, 

 one might conclude that the centre T of maximum percussion 

 coincides with the centre of gravity ff, — a conclusion which, in 

 dynamics, would be a great error; for it is easy to see that at 

 the point g the percussion is zero, whilst at the point T {x = K), 

 although infinitely near to ff, the percussion is infinite. 

 In fact the expression 



a;-] 



w 



becomes, for x = 0, 



as it clearly should, since the system actually turns on its centre 

 of gravity, and tlicreforc can cause no percussion at this point. 

 But, making x = K, the expression becomes 



whence, on taking for K its value, which is here zero, we have 



11. Similarly, if the body, instead of being animated by a 

 * See Chap. I. art. 23. 



