<-^) ' 



252 M. Poinsot on the Percussion of Bodies, 



(i\ 1 + 

 whence is deduced, on making /i, = co , 



i ~ d ~ d ~ ' 



This is precisely the expression for the distance IC between the 

 point I and the centre C of oscillation of the body M around I. 



8. Herefrom we learn that the same point C, which, in the 

 simple body M, is reciprocal to the point I, is also reciprocal to I 

 in the system composed of the same body M and of the material 

 point of infinite mass /x placed at I. If, then, we suppose the 

 system to be struck at an infinitely small distance i, to the right or 

 left of the centre y, the spontaneous centre of rotation C will be on 



the other side of _y at a finite distance l=d+ —r-. But however 



small the distance i between the point of impact and the centre 

 g may be, we may always conceive another point to be situ- 

 ated between the two at a distance x from g infinitely small with 



K2 

 respect to i, so that the expression — shall be infinitely great 



in comparison to -^; hence since the latter corresponds to a 



^ K2 . 



finite line I, the former — will represent an infinite line ; and 



the spontaneous centre C of rotation which corresponds to the 

 centre of percussion 0, will be at an infinite distance from the 

 centre of gravity g. Whenever, then, in our formulae we en- 



counter the expression — , wherein we have to make the inde- 



. ^ K^ 



jjendent variable x equal to zero, we must take — =30, although 



. K2 .^ . 



the similar expression -:- corresponds to a finite line I when the 



variable i, which in this case depends upon K, becomes also equal 

 to zei'o. 



9. In dynamics, therefore, we must guard against confound- 

 ing this infinitely small line K, which represents the arm of 

 inertia of the system, with the infinitely small line i which de- 

 termines the distance from the centre of gravity g of the material 

 point fi attached at I, although both these lines become zero 

 under our hypothesis of /x = oo. At the same time we must 

 carefully distinguish between the true values of the expressions 



