M. Poiusot on the Percussion of Bodies, 289 



the centre of gravity G, we have 



«^/3^ _A 



for, by art. 2, the first term expresses the ratio of the abscissae 

 or ordinates of the two reciprocal points C and O^ and this ratio 

 is evidently the same as that of the two lines H and A. 



Employing this simpler expression, the equation for determi- 

 ning V becomes 



«;H3Av-AH = 0, 

 and gives 



v=-k± \/A2 + AH. 



There are, therefore, two centres oi maximum percussion, one to 

 the right, and the other to the left of the centre of gravity G. 



In order to refer these two points to the spontaneous centre of 

 rotation 0, we have only to make 



in order at once to deduce 



X= ± a/AL, 



where for brevity L represents the line OC = A + H. We are thus 

 led to the following theorem : — 



The centre of maximum jjercussioii is upon the line passing 

 through the body's centres of impulsion and gravity, audits distance 

 Xfrom the spontaneous ceritre of rotation is the geometric mean 

 between the distances of the centre of gravity and of the centre of 

 impulsion from the same spontaneous centre. This theorem is 

 precisely similar to the one before found in the particular case 

 where spontaneous rotation takes place around an axis parallel 

 to one of the principal axes of the body. 



22. As to the value (Q) of the maximum percussion, it is ex- 

 pressed by 



(Q)=P. 15 ^, 



as will be easily found from the general expression for Q by 

 there substituting, in the first place, for x and y their values in 

 V, and afterwards for v the value 



r=-A+ i/A2 + AH, 



which corresponds to the maximum. 



The first value (Q), which is positive, corresponds to the centre 

 D situated between C and G ; it gives a percussion in the same 

 direction as, and always greater than the impulsion P. 



Phil. Mag. S. 4. Vol. 15. No. 100. April 1858. U 



