M. Poinsot on the Percussion of Bodies. 



255 



from the centre of gravity G of the system of the two masses M 

 and [I. 



Setting the length of the Hne GO = l, and G0 = ?, the moment 

 of inertia of the system around its centre G will be 



where K represents the arm of inertia ; we have^ further, 

 i = l^ and l—i=I—-^ — , 



so that 





whence we deduce 



K^=l^^^^ = i(l-'i). 



The percussion Q produced at T, at the distance x from G, is 

 expressed by 



K^ + x{l-i) 

 ^~^ • K^ + x^ ' 



and the value of x which corresponds to a maximum of the 

 percussion Q is easily found to be 



XQ=—i+ Vil; 



whence, substituting this value of x in the expression for Q, the 

 maximum percussion Q^ will have the value 



Q.=|(i±v/i+V). 



or, as otherwise expressed, 



Example. — Let us take the case of ]\I = 1, /i, = 9999, which 

 gives 1^ =9999; we have at once 



