TH,E 

 LONDON, EDINBURGH axd DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



OCTOBER 1859. 



XXXVII. On the Percussion of Bodies. % M. L. Poinsot*/ 



Chapter IILf 



On the quantity of motion impai-ted to a body by the shock of a material 

 point which strikes the body in a given direction. 



1. T ET M be the mass of the body, G its centre of gi-avity, 

 JL^ and through this centre let a plane be drawn perpen- 

 dicular to one of the three principal axes of the body. At a point 

 C in this plane the body is supposed to be struck by a material 

 point having the mass m, and moving with a given velocity v in 

 a direction perpendicular to the line C G J ; required the quan- 

 tity of motion which will be imparted to the body M in conse- 

 quence of this shock. 



In the first place it is clear that the material point m, which 

 befoi'e impact has the velocity v, will only retain a certain velo- 

 city u after the shock, and that it will then cease to act upon M 

 because the point C will recede before it with the same velocity. 

 The quantity of motion imparted to M by the shock will there- 

 fore be equal to the quantity m{v — u) which m loses. 



The question reduces itself, then, to finding the velocity u 

 which m retains after impact. Now so long as m acts upon M, 

 these bodies are necessarily in contact ; and since they are in 

 contact, they may be supposed to be attached to each other 

 during the time of action, however short that time may be. 

 Hence the velocity u assumed by the point C of the body M, is 



* Translated by Dr. T. A. Hirst from the Comntes Rendus, vol. xlviii. 

 p. 1127. 



t For the first and second chapters see Phil. Mag. vol. xv. 



4 The direction in which the material point moves is also in the plane 

 perpendicular to the same principal axis. 



Phil. Mag. S. 4. Vol. 18. No. 120. Oct. 1859. R 



