CHAPTER III. 



Collisions. 



19. If two bodies (stars or molecules) having the masses and come 

 into collision and tlie bodies are unelastic, then the velocities and the velocity com 

 ponents of the two bodies after the collision are identical. If the values of the 

 variables after the collision are denoted by u^, ti^, etc. we hence have 



(38) . u^ = u^, v^=v.^\ w^ = w^ 

 and 



(38*) ^: = <. 



The integrals of the centre of gravity may be supposed to subsist at the 

 collision, so that 



(39) + y./ = + ^2' 



Wy -|- tv^ = -|- m.^ w.^. 



Combining (38) and (39) we get 



m, + m„ M,, , 

 — — S = "2 



m, V, -\- m„ V , 



^ ' , ^ = ^2 



m. u). + w., Wç. , 



— — —, — ^ = w„ . 



+ 



These formulae show that at collisions the velocities after the colHsion are 

 unequivocally determined by the velocities before the collisions without introducing 

 any parameters, whereas at passages two parameters h and enter into these 

 relations. 



If, on the other hand, the velocities u.^', etc. after the collision are known, 

 we cannot from (40) compute their velocities before the collision. We are, indeed, 

 only able to compute the velocity of the centre of gravity of the two bodies, which 

 is unaltered at the collision. 



= 



(40) V,' = 



