M. Poinsot on the Percussion of Bodies. 275 



The figure clearly shows, too, what takes place when the body 

 is endued with only one of these two motions. For : 



First. If the impulse which the body has received is due, solely, 

 to a simple force passing through the centre of gravity, the cen- 

 tre C of percussion will coincide with the point G, the side CA 

 with the perpendicular GA = K, and the other side AO of the 

 right-angled triangle with the line through A parallel to the 

 hypothenuse. The centre T of greatest positive percussion, 

 therefore, now coincides — as it clearly should do— with the point 

 G, and the other centre T' of greatest negative percussion is at 

 an infinite distance ; lastly, the two centres S and S' of greatest 

 conversion are situated at the distance CA = GA=+K from 

 the same centre G. 



Secondly. If the body has received the impulse of a couple 

 merely, the spontaneous centre O will coincide with the centre 

 of gravity, the side OA with the perpendicular GA, and the side 

 AC mth the parallel through A to the hypothenuse. The two 

 centres T and T' of maximum percussion are now at the distance 

 0A= +K from the centre G; and of the two centres S and S' 

 of greatest conversion, the first S is infinitely distant, and the 

 second S' coincides with the same centre G. 



67. Lastly, in order to have a clear idea of the force or action at 

 any point x of the body taken arbitrarily on the hypothenuse CO, 

 we have only to join x with the vertex 



A of the right angle of the triangle and A 



, . . AG2 ^ ^ 



determme the fraction ^=2 of the whole 

 Kx 



mass M of the body. We may then say 

 that the point x acts as would a free q 

 point charged with this fraction of the 

 whole mass M. We see, too, that the point O reciprocal to x 

 would act as a free point charged with the remainder of this 

 mass ; so that these two reciprocal points x and divide the 

 mass of the body into two parts reciprocally proportional to xk^ 

 and OA , or — what amounts to the same thing — into two parts 

 inversely proportional to their distances OG and xG: from the 

 centre of gravity G of the body. 



68. It appears to us that truths so evident, and so easy of ex- 

 pression as the above, are as new elements added to science, and 

 cannot fail to contribute to its advancement. For we must 

 admit that the human understanding advances but little, other- 

 wise than by the aid of such simpler ideas or more convenient 

 instruments which it invents and, so to speak, handles with 

 greater facility. These new questions, therefore, appear to us 

 not unworthy of the attention of geometricians, and tlieir novelty 



T2 



