ov coLLisiaN. 77 



descend through equal arcs, so as to meet each other with equal velocities. 

 They recede from each other after collision with the same velocities, and rise 

 to the points from which they before descended, with a small deduction for 

 the resistance of the surrounding bodies. 



"When a ball at rest is struck by another eqnal ball, it receives a velocity 

 equal to that of the ball which strikes it, and this ball remains at rest. And 

 if two equal balls meet or overtake each other with any unequal velocities, 

 their motions will be exchanged, each rising to a height equal to that from 

 which the other descended. 



The effect of collision takes place so rapidly, that if several equal balls be 

 disposed in a right line, in apparent contact with each other, and another 

 ball strike the first of them, they will all receive in succession the whole velo- 

 city of the moving ball before they begin to act on the succeeding ones ; they 

 will then transmit tlie whole velocity to the succeeding balls, and remain en- 

 tirely at rest, so that the last ball only will fly off. 



In the same manner, if two or more equal balls, in apparent contact, be in 

 motion, and strike against any number of others placed in a line, the first of 

 the moving balls will first drive off the most remote, and then the second the 

 last but one, of the row of balls which Avere at rest: so that the same number 

 of balls will fly off together on one side, as descended to strike the row of 

 balls on the other side ; the others remaining at rest. 



If the line of balls, instead of being loosely in contact, had been firmly 

 united, they would have been impelled with a smaller velocity, and the ball 

 striking them would have been reflected. For when a smaller elastic body 

 strikes a larger, it rebounds with a velocity less than its first velocity, and the 

 larger body proceeds also with a less velocity than that of the body striking it. 

 But if a larger body strikes a smaller, it still proceeds with a smaller velocity, 

 and the smaller body advances with a greater. 



The momentum communicated by a smaller elastic body to a larger one is 

 greater than its own, and when the first body is of a magnitude comparatively 

 inconsiderable, it rebounds with a velocity nearly as great as the velocity of 



