M. Poinsot on the Percussion of Bodies, 175 



with the same capability of percussion as the body Itself. For 

 the rod would, as we have just seen, not only have the same 

 mass and the same centre of gravity, but it would also have the 

 same moment of inertia with respect to this centre G. In fact, 

 the moment of inertia of the two massive points m and n is 



mx^ + n . — 5- ; 



replacing, however, the first term mx^ by its equal nK^, and the 

 factor tiK^ of the second term by its equal mx'^, this expression 

 becomes 



K2 ■ 



«K2 + 7nx^ . ^ = (m + n) K2 = MK^ ; 



that is to say, the moment of inertia in question is equal to that 

 of the body. 



Our ideal rod, therefore, under the influence of the same im- 

 pulse P, would have the same spontaneous centre and the same 

 angular velocity; it would consequently be capable, at each of 

 its points, of the same force of percussion as is the body at each 

 of the corresponding points. 



Corollary. 

 On the centre of oscillation of a heavy body. 

 Hereby we may see why a heavy body suspended from a point 

 oscillates exactly as would a simple pendulum of the length OC 

 equal to the distance from the point to its reciprocal C in the 

 body ; for we may conceive the body to be replaced by an imma- 

 terial rod CO, loaded at its two ends with the portions m and n 

 of the body's mass, and in virtue of the same applied force P, 

 the movement of this rod will be exactly the same as that of the 

 body itself. But since the force P is here equal to the weight 

 of the body, its direction passes through the centre of gravity G, 

 which is at the same time that of the massive points m and n ; 

 whence it follows that the force P may be resolved into two, p 

 and q, applied at these points, and proportional to their respect- 

 ive masses m and n. If the point becomes fixed, therefore, the 

 movement of the point 7n is destroyed, and the point w at C 

 remains abandoned to the simple force q which is its natural 

 weight. 



Remark. 



28. Since, when the body moves, the point C taken at the 

 distance x from its centre of gravity strikes with the same force 



as if the fraction -o — ^, of the mass M were there collected, 



x-'+lS.'' 



and since a?=0 is the only value of x wliich can render tliia 



