256 M. Poinsot on the Percussion of Bodies. 



9999 



i=l. 



100002 



1 



10000' 



whence 



K'^_ 9999 

 i "10000 



The abscissa w,y of the point T, wliere the greatest percussion 

 takes placCj is 



''°~\ 10000 ±100/' 



this maximum percussion itself is 



p p 



Qo= 2 (1 + '/lOOOO) = 101 ~ 



at the point T when it acts in the same direction as V ; and at 

 the point T', reciprocal to T, its intensity is 



Qo=-^(l- 'v/lOOOOj=-99-5-, 



ami its direction opposite to that of P. 



In this example, then, where the rod OC is loaded at its two 

 extremities with material points /n and M, whose masses are in 

 the ratio of 9999 to 1, and where the point M is struck by a 

 force V, the maximum percussion is SOg times the impulse P; 

 and at the point T', reciprocal to T, it is 49| times this force P, 

 but in an opposite direction to the same. 



The point T of greatest percussion is between the centi'es G 

 and C ; the other point T' of maximum negative percussion is 

 on the other side of the centre G. These two points, T and T', 

 are very near to the centre of gravity G ; the hrst T being at a 



99 

 distance GT equal to of OC, the other T' at a distance 



GT' equal toyKT^KT, of the same line OC : their mutual distance 

 TT' is therefore I— —I 



The arm of inertia K of the body around G is / J^^^^^ = -^ / 



10000 100 



nearly, and TV=Xq + x'q is exactly double the arm of inertia K' 

 with respect to ; for 



