M. Poinaot on the Percussion of Bodies. 24iT 



upon F, proceeding from the motion q imparted to M, is the 

 only one considered. 



9. If we suppose m and M to become attached, the percussion 

 produced at /, whose distance from the centre G of M is h, will 

 be found to be 



^-"*^'K2 + A2 + „(a;-A)2' 



as may be easily verified by seeking the force P with which a com- 

 pound body ]M + in, animated by a force mv applied at the distance 

 X from the centre G of M, and consequently at the distance 



^ from the centre g of M + ?«, would strike a point /at the 



distance h from G, and therefore at the distance h r from 



' n + 1 



the centre ^ of M + 7n. 



10. Setting x = /i, we have V = mv, as it should be when the 

 shock takes place at the point / itself. 



As ^ increases from x = to .r = k, the numerator of the fraction 

 increases and the denominator decreases ; for both which reasons 



the percussion P increases from P= ^^yrn — y^ — -— ^ to V = mv. 



K- 



When sc= — —, P = 0, as it should be; for then the point m 



strikes at a point or centre of percussion 0, with respect to which 

 /is a spontaneous centre of rotation, and under such circum- 

 stances/can suffer no percussion. 



When x = x , P is again zero, so that there is a point which 

 corresponds to a maximum of P. 



11. To find the distance x which corresponds to this maximum 

 of P, wc have 



7H 



or, putting for 7i its value ^, 



x^ + ^^x - fsK^ + A^ 4- - (K' + /*')] = ; 



It Lm tit J 



or, making Yi^=nh and a-{-k = l, 



x^-'r2ax-(hl'^^^ + ah^=0. 



This equation gives two values of x corresponding to points situ- 

 ated at equal distances from, and ou different sides of 0, for 

 which x= — a. 



12. As an cxamjde, let us take the case of ?i=l or ?« = M, 

 and h = K. Here the masses m and M are equal, and the sup- 



