346 M. Poinsot on the Percussion of Bodies. 



U x=—a= J-, then P = 0; tliat is to say, a force applied 



at causes no percussion on the support F, — a consequence 

 which is also evident. 



Putting a-\-x = y, and representing the line a-\-h by /, the 

 preceding expression for P takes the simple form 



whence it is visible that from the point 0, regarded as the origin 

 of the distances y at which the body M is struck by the force Q, 

 the percussion produced on F increases uniformly, like the ordi- 

 nates of a right line, and that it has the same values on the 

 right and on the left of this origin, except that the signs arc 

 changed. 



7. It will no doubt appear remarkable that with the aid of a 

 free body M placed upon a support, and by employing the same 

 force Q, it is possible to produce a percussion on this support 

 not only greater than the force Q itself, but greater than any 

 given percussion. But this theorem supposes that the force Q, 

 at whatever distance it may be applied, is entirely transmitted 

 to the body M. It would be incorrect to conclude that, with a 

 hammer of the same mass m striking with the same velocity r, 

 any required percussion could be produced upon an obstacle by 

 means of an interposed body M ; for the force mv of the hammer 

 would only be partially transmitted to the body, and this part 

 would diminish as the distance of the point of impact increased. 



But if the hammer and the velocity of its stroke be changed 

 at each distance x, so that m may be inversely, and v directly 

 proportional to K- + x^, the quantity of motion transmitted to M 

 will always be the same (art. 2). llepreseutiug, then, by q this 

 constant quantity of motion imparted to the body M, the per- 

 cussion against the support F will be expressed by 



whence we learn that, with the aid of an interposed body M, it 

 is possible to produce a given percussion of any magnitude ujjon 

 a fixed support by means of the shock of a material point endued 

 with a convenient mass and velocity. The hammer-stroke may 

 here be regarded as the same, for the product mv is constant. 



8. On making a,' = A, we find P = (7; and yet, since the shock 

 is then direct, we ought to have P = ?hz;=:Q. To explain this, it 

 is necessary to remark that throughout this analysis it has been 

 assumed that, after the shock of m upon M, the residual force 

 mu in the hammer is no longer employed, so that the percussion 



