356 M. Poinsot on the Percussion of Bodies. 



are to the right and left of this spontaneous axis, and at a distance 

 X sin from the same precisely equal to the arm K of inertia of 

 the body with respect to this axis. This property, together with 

 that of being situated in the diameter of the central ellipse con- 

 jugate to the direction of the spontaneous axis, completely deter- 

 mine the positions of these centres of maximum percussion. 



This theorem, therefore, applies to all possible positions of the 

 spontaneous axis in the principal plane under consideration. 

 When this axis passes through the body's centre of gravity, as 

 was the case in the preceding article, we have A = 0, and the 

 distance \ sin <^ = K reduces itself to + 8 sin <^, as already found 

 in art. 31. 



Corollary VI. 



On a new expression for the force Q with which each point 

 is endued in virtue of the rotation of the body. 



33. In art. 18 we found that when a and b represent the 

 coordinates of the point C where the body received the impulse 

 P to which it owes its motion, and x and y the coordinates of 

 any point D, the force Q with which the body strikes an obstacle 

 presented at D may be expressed by 



^ <fax+^by + a^ 



If from the point D, whose coordinates are x and y, we let fall 

 a perpendicular upon the spontaneous axis whose equation is 



u^at + /3^bu + u^/3'^=0, 



its length tt will be found to be 



_ ^ax+^y + u^J^ 



and the above expression for Q will take the form 



Q=P ^''"'"''^ 



but, in virtue of the preceding expressions. 



CG=H= Va^ + b^, 



aV + ^2^2' 



and of the relation 



A.Ii = S^ 



the radical which enters into the expression of Q will have the 



