162 M. Poinsot on the Percussion of Bodies. 



Hence at the same distance from its centre of gravity G, 

 there will always exist a centre of percussion C in the body; 

 that is to say, a point to which, if the body were at rest, a single 

 force might be applied which would be capable of producing the 

 motion which actually exists, and hence there will always be a 

 point by means of which the movement of the body may be 

 arrested, either by there applying a single force equal and con- 

 trary to the original impulse, or by there presenting an obstacle 

 or fixed point for the body to strike against. 



3. But although a body whose motion is due to a single im- 

 pulse preserves a centre of percussion throughout its subsequent 

 motion, we cannot affirm that there is always a centre of percus- 

 sion in a moving body ; for its motion may have arisen from the 

 action of forces incapable of reduction to a single one, in which 

 case no single force can exist capable of giving to the body the 

 precise motion it possesses, and consequently there can be no 

 centre of percussion in the body. In another place we shall ex- 

 amine the motion of a body animated by any forces whatever ; 

 here we shall merely consider the particular case where the body 

 in question has been set in motion by a single impulse P, and 

 we shall, moreover, assume the direction of this impulse to be 

 contained in a plane passing through the centre of gravity G, 

 and perpendicular to one (G Z) of the three principal axes of the 

 body. 



4. Let M always represent the mass of the body, and MK^ its 



memoir is superfluous ; for their use, au English version of this memoir is 

 certainly not called for. 



Nevertheless, the works of the able author of the Theorie nouvelle de la 

 rotation des corps are far from being so familiar to Englishmen generally 

 as they deserve to be. Even apart from the results they contain, and solely 

 in virtue of the method they manifest, Poinsot's memoirs, attentively 

 studied, have a peculiar value, especially to a student whose own method of 

 working has not yet become habitual. 



Nowhere do we meet with greater clearness in the treatment of the sub- 

 ject, nowhere with closer reasoning on the problem in hand, or a happier 

 combination of veritable analysis and synthesis. Calculus, — that general 

 servant whose convenient readiness is often abused — is always at hand to 

 assist and confirm, but never to direct. Poinsot may be said alwaj's to 

 work with, but never to entrust work to, this his servant ; he knows too 

 well, indeed, how invaluable, for a full grasp of the whole question, is that 

 insight which is alone the reward of hard, close, and attentive reasoning. 



The translation of the following memoir, with the consent of the author 

 and with the advantage of occasional suggestions from him, has been an 

 easy, and certainly a pleasant task. The original research, it may be well 

 to state, was virtually completed no less than twenty years ago, although it 

 has been published but a few months ; a knowledge of this fact may ex- 

 plain some things, and will certainly not diminish the value of the whole. 

 With respect to the occasional notes and references which will be found 

 throughout the memoir, it is only fair to add that none of them appear in 

 the original,— T. A. Hibst. 



