M. Poinsot on the Percussion of Bodies. 249 



support / by means of an interposed free body M placed on the 

 same, with its centre of gravity G at the distance K from the point 

 of contact /, we must strike, not at the point / itself, but at a 

 distance K v^6— 2K beyond the same. 

 If, in the general expression 



K^ + hx 

 ^-'«^K2 + A2 + n(a?-A)2' 



we suppose m infinitely small and v infinitely great, whilst mv 

 I'emains equal to a finite quantity Q, we have, since h = 0, 



which agrees perfectly with a previous result in art. 5. 



Chapter IV. 



On the method of reducing to the theory of the motion of free bodies 

 that of bodies supposed to be impeded by fixed obstacles, 



1. Hitherto we have considered perfectly free bodies alone ; 

 but in mechanics it is often necessary to consider bodies which 

 are only free to turn around a fixed point or axis, to slide over 

 an immoveable plane, and so forth. Instead of new principles 

 being required for the solution of problems of this kind, it will 

 be seen that the preceding ones suffice, and that our theory may 

 be applied in the most direct and wfl^wra^ manner to the singular 

 cases where some fixed obstacle is supposed to impede the move- 

 ments of the body. 



2. In fact there is no fixed body in nature. A so-called fixed 

 point is in reality merely a point invariably attached to some 

 body whose mass, being very great, is regarded as infinite in 

 comparison with that of the moving body under consideration. 

 In place of a so-caWed fixed point, then, we may always conceive 

 a free point endued with an infinitely great mass ; in other words, 

 a point in which an infinite quantity of matter is supposed to be 

 concentrated. 



In this manner, instead of a body of any figure and finite mass 

 M moveable around a point I supposed to be fxed, we have 

 merely to consider a free system composed of the same body M, 

 and of a material point of infinite mass yu, attached to M at the 

 point I. 



3. It is evident that the centre of gravity r/ of such a body or 

 system will fall infinitely near the point I ; and that this centre, 

 being charged with an infinite mass fi + M, can only receive an 

 infinitely small motion in virtue of the action of any finite forces 

 supposed to be applied to it. This centre of gravity y, therefore, 



