M. Poinsot on the Percussion of Bodies. 351 



Corollary IV. 

 Particular cases of the foregoing theorems. 



25. If, in the general expression 



^~ aV^+/Sy^-«^/3^- 

 (see art. 18), we suppose « = and b = 0, we have the particular 

 case where the impulsion P passes through the centre of gravity 

 G of the body, and consequently where the body is animated 

 only by a translatory motion in the direction of its principal 

 axis GZ. 



In this particular case, therefore^ the percussion which the 

 body is capable of producing at any point of the principal plane 

 XYis „2^2 



the maximum of which corresponds to ,r=0 and ?/=0; so that 

 the centre of maximum percussion then coincides — as it clearly 

 should — with the centre of gravity itself. 



26. The curve formed by the points of equal given percussion 

 nP will now be represented by the equation 



«V-* + 



/3y=«^/3^(i-l), 



whence we see that these points are situated on an ellipse similar 

 to the central ellipse, described around the same centre as the 

 latter, and placed in a similar manner. The magnitude of this 

 ellipse will depend upon the constant value nV given to Q, which 

 value, however, must not be assumed greater than P, since P is 

 now the greatest force of percussion that the body can produce. 

 If, for example, we suppose 



we shall have 



the equation of the central ellipse ; whence we conclude that the 

 contour of this ellipse is the locus of the points at or with which 

 the body strikes with a force equal to half that of the impulse 

 by which it is animated. 



Corollary V. 

 On the particular case where the body is animated solely by 

 the impulsion of a couple. 

 27. Let us give to the general expression for Q the form 



Q=P«- "" 



aV + ySV + «^/32' 



