DYNAMICS. 41 



83. If two elastic spherical bodies A and B, 

 (fig. 6.) moving in directions, and with velocities re- 

 presented by the lines AA', BB', come into contact 

 when at A' and B', and if AB' be the line which 

 joins their centres at that moment : Then if the ve- 

 locity of A be resolved into two, AC, A'C, the one 

 perpendicular to AB', and the other parallel to it ; 

 and if the velocity of B be resolved in like manner 

 into BD, B'D ; after collision A will retain the velo- 

 city represented by AC, and B that represented by 

 BD, unchanged ; but the velocities A'C, B'D, will 

 be changed by the collision, into others which may 

 be found by article 78, and if these be a' and b' ; 

 then the path of A after the stroke will be the dia- 

 gonal of a rectangle under A'E (~AC) and a', and 

 the path of B, the diagonal of a rectangle under 

 B'F (zrBD) and V. 



Thus the paths of the bodies after collision are deter- 

 mined. 



84. If the bodies are imperfectly elastic, that is, 

 if, in restoring their figures, they do not generate 

 velocities equal to those which were destroyed in 

 altering them, their motions after collision are de- 

 termined, by supposing that the motion lost or gain- 

 ed is not double, but has a given ratio to tjiat which 

 would be gained or lost if the bodies were perfectly 

 hard, as at $ 75, 



When 



