ON COLLISION. 59 



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 were 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 compa- 

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

 velocity of its impulse, and the second body acquires a momentum nearly 

 twice as great as that of the first. When a larger body strikes a smaller 

 one, it communicates to it only as much momentum as it loses. 



In the communication of motion between inelastic bodies, the want of a 

 repulsive force, capable of separating them with an equal relative velocity, 

 is probably owing to a permanent change of form ; such bodies receiving and 

 retaining a depression at the point of contact. When the velocity is too 

 small to produce this change of form, the bodies, however inelastic, may 

 usually be observed to rebound a little. 



Bodies which are perfectly inelastic, remain in contact after collision ; 

 they must therefore proceed with the same velocity as the centre of inertia 

 [gravity] had before collision. Thus, if two equal balls meet, with equal 

 velocities, they remain at rest ; if one is at rest, and the other strikes it, 

 they proceed with half the velocity of the ball which was first in motion. 

 If they are of unequal dimensions, the joint velocity is as much smaller 

 than that of the striking ball, as the weight of this ball is smaller than the 

 sum of the weights of both balls. And in a similar manner the effects of 

 any given velocities in either ball may be determined. 



It follows immediately from the properties of the centre of inertia [gra- 

 vity] that in all cases of collision, whether of elastic or inelastic bodies, 

 the sum of the momenta of all the bodies of the system, that is of their 

 masses or weights multiplied by the numbers expressing their velocities, is 

 the same, when reduced to the same direction, after their mutual collision, 

 as it was before their collision. When the bodies are perfectly elastic, it 

 may also be shown that the sum of their energies or ascending forces, in 

 their respective directions, remains also unaltered. 



The term energy may be applied, with great propriety, to the product of 

 the mass or weight of a body, into the square of the number expressing its 

 velocity. Thus, if a weight of one ounce moves with the velocity of a foot 

 in ^a second, we may call its energy 1 ; if a second body of two ounces 

 have a velocity of three feet in a second, its energy will be twice the square 

 of three, or 18. This product has been denominated the living or ascend- 

 ing force [the vis viva], since the height of the body's vertical ascent is in 



