368 M. Poinsot on the Percussion of Bodies. 



centre of a given percussion Q, i. e. if we please, of a velocity 



^ lost, is also the centre of a given reflexion or velocity ^. 



These two centres, therefore, coincide with one and the same 

 point, which is considered from two different points of view, but 

 determined in the same manner. Nevertheless, the considera- 

 tion of these centres with reference to the reflexion which the 

 body sufi'ers when an obstacle is there presented merited the 

 space we have devoted to the same, as well on account of the 

 new^ dynamical questions thus presented, as on account of the 

 curious similarity thereby established between hard and elastic 

 bodies. In fact, it is well worthy of notice that a perfectly hard 

 body, in virtue purely of the motion it possesses, may be gifted 

 with a certain kind of elasticity at its several points, so that by 

 collision with an obstacle the centre of gravity of the body may 

 be reflected in the rear of its former motion, or precipitated forward 

 with a new velocity, just as if some elastic spring had been inter- 

 posed at the point of impact. It is also not less remarkable, that 

 this velocity of reflexion may not only be equal to the incident 

 velocity of the centre of gravity, as in the case of perfectly 

 elastic bodies, but may even surpass the same, and become as 

 great as we please, provided the rotation of the body on itself be 

 sufficiently rapid. 



50. This increase of velocity, which the centre of gravity of a 

 body may acquire by the mere presence of a fixed point which 

 the body encounters, appears somewhat paradoxical. It seems 

 as if the quantity of movement which exists in a body, and 

 which is always estimated by the product of the mass into the 

 velocity of the centre of gravity, could never be augmented 

 otherwise than by the accession of some new active force applied 

 to the body. But here we see only a fixed point capable of de- 

 stroying, but not of producing motion, and still it is a fact that 

 on encountering this fixed point, a moving body, far from losing 

 any portion of its velocity, may suddenly become endued with a 

 velocity at once greater than, and in the same direction as, that 

 of its original projection. Here, therefore, in apparent contra- 

 diction to the general principles of dynamics, we have, in some 

 measure, a creation, instead of a pure loss of motion as one 

 would have anticipated. 



We must observe, however, that in nature there is no such 

 thing as 2i fixed point ; that a point considered by us as fixed, is 

 in reality a free point, which we assume to be charged with a 

 mass extremely great, infinite indeed, in comparison to the mass 

 of the body iinder consideration ; consequently, that if, by the 

 action of a finite force applied to it, this material point receives 

 merely an infinitely small velocity, and thus appears to us to 



