M. Poinsot on the Percussion of Bodies. 345 



again have the same action on ]\I as if this body were at rest, 

 and consequently will impart to the same a new velocity equal 

 to the first, and so on. 



5. Let us next suppose the body M to be placed upon a fixed 

 support, applied at a point F whose distance ft-om the centre of 

 gravity G is h. If the body were struck with any force Q at the 

 point F and at right angles to the support, it is evident that the 

 direct percussion upon the obstacle would be measured by the 

 force Q itself. 



But if the body were struck with the same force, and in a 

 parallel direction, at another poiut C taken on the line GF at 

 the distance x from G, the percussion on the obstacle would no 

 longer be the same as before, but would be dependent upon the 

 distance x in a manner which requires to be determined. 



Regarding F as a centre of percussion, let the corresponding 

 spontaneous centre of rotation be sought. To determine its 

 distance OG = a, we have the equation «/i = K^, which at once 



gives a= -J-*. 



This found, imagine the force Q, which strikes at C at the 

 distance x from the centre G, decomposed into two other parallel 

 forces P and R, striking respectively at F and 0. It is evident 

 that this latter component which acts at can produce no per- 

 cussion on the support applied at F, for F is a spontaneous 

 centre of rotation with respect to regarded as a centre of per- 

 cussion. The component P, therefore, which falls directly at F is 

 the only one which causes a percussion against the fixed obstacle. 



But by the composition of forces we have 



Q, : V = a + h : a -\- X, 

 whence results, on putting for a its value -r-, 



Such is the percussion produced upon a fixed support, placed at 

 the distance h from the centre of gravity of a body, by a given 

 force Q which strikes that body at a distance x from the same 

 centre. 



G. From this expression it will be seen that, by applying one 

 and the same force Q at a convenient distance from the centre 

 G, we may produce upon a fixed obstacle a percussion of any 

 magnitude, and that in any direction, — a theorem which appears 

 to be worthy of note. 



If we suppose x = h, we have P = Q, as it clearly should be; 

 for then the force Q strikes the object itself directly. 

 * Sec Chap. I. art. 5, 



