M. Poiasot on the Percussion of Bodies. 273 



whence 



a; = or a?=— a; 

 it is, in fact, evident that if we were to present the obstacle 

 either at the centre of gravity or at the spontaneous centre of 

 rotation, the new rotation which the body would assume would 

 be the same as that which it possesses, in other words, the ori- 

 ginal rotation of the body would suffer no alteration, &c. 



Remark. 



61. It is useless, however, to continue the further enumera- 

 tion of these centres of a given conversion ; their research is 

 analogous to that of the centres of reflexion, and presents no 

 difficulty whatever. We must remark, however, that all points, 

 such as the above, which have reference to certain given arbi- 

 trary quantities, are not veritable centres such as those first con- 

 sidered ; in other words, they are not unique points of the body 

 determined solely by the movement under consideration. Their 

 number is, in fact, infinite : for example, the points by means of 

 which a body in motion is capable of striking with a given force, 

 are not i-estricted to the two above determined ; on the contrary, 

 there are innumerable others which possess the same property, 

 and, as we shall afterwards see, all such points of equal percussion 

 are situated on the circumference of a certain ellipse within the 

 body. But the points of maximum percussion, maximum reflexion, 

 &c. are unique ; they are, properly speaking, the only ones to 

 which the term centre is applicable, and which, as such, desei've 

 to be particularly noticed. 



The position of, and mutual dependence between these several 

 centres in any body may be rendered clear and, as it wei'e, visible 

 by means of an extremely simple geometrical figure; in this 

 manner, too, the theorems may be very easily remembered. 



Geometrical expression of the principal results of the 

 foregoing memoir. 



62. Let G be the centre of gravity, and C the centre of per- 

 cussion of the body, that is to say, the centre of the original 

 impulse which it has received. Join C and G, and at G erect a 



^A- 



T' O S' G T C 8 



perpendicular to C G, making its length G A equal to K the arm 

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



