274 M. Poinsot on the Percussion of Bodies. 



of inertia of the body. If, upon C A as chord, a circle be de- 

 scribed so that its centre is in the direction of C G, this line pro- 

 duced will cut the circumference in a point 0, which will be the 

 spontaneous centre of rotation. 



And, conversely, starting from the point 0, as given, we may 

 find the corresponding centre of percussion C by joining O and 

 A, and upon O A as chord describing a circle, whose diameter 

 shall coincide with G ; O G produced will cut the circumfe- 

 rence of this circle in the point C required. 



The two reciprocal centres C and O, therefore, between which 

 the centre of gravity is situated, may be considered as the two 

 extremities of the diameter of a circle whose ordinate G A, cor- 

 responding to the point G, represents the line K which deter- 

 mines the moment of inertia of the body. 



63. If now from as centre, and with radius A, a circle be 

 drawn cutting the direction of the diameter in the points T and 

 T', we shall obtain the two centres of greatest percussion ; that 

 is to say, T will be the centre of greatest percussion in the direc- 

 tion of the translation of the body, and T' that of greatest per- 

 cussion in the opposite direction, in other words, when the body 

 strikes in the rear of its motion through space. 



64. These points T and T' will be at the same time the two 

 centres oi greatest reflexion ; the first T will be that of a veritable 

 reflexion of the centre of gravity, whilst the second T' will be 

 that of a negative reflexion, in other words, of a progression of 

 the centre of gravity in the same direction as it at present 

 moves. 



65. In the second place, the circle described around C as 

 centre, with the radius C A, cuts the diameter in two points S 

 and S', which will be the two centres of greatest conversion : the 

 first S, which is in the production of the diameter, is the centre 

 of maximum positive conversion ; that is to say, the point by 

 which, if an obstacle be there presented, the body will be made 

 to rotate, after the shock, in a direction contrary to that of its 

 present rotation, and with the greatest possible velocity; the 

 other centre S' is that of maximum negative conversion, or the 

 point by means of which, after the shock, the greatest possible 

 rotation will be given to the body in the same direction as it at 

 present turns. 



66. Thus the simple and well-known figure of a right-angled 

 triangle, with the perpendicular let fall from the right angle 

 upon the hypothenuse, supplies everything with respect to the 

 position of, and mutual dependence between the several centres 

 we have considered in a body which turns around one of its 

 principal axes at the same time that its centre of gravity is trans- 

 lated through space in a direction perpendicular to this axis. 



