78 LECTURE vrri. 



its impulse, and tlie second body acquires a momentum nearly twice as great 

 as that of the first. When a larger body strikes a smaller one, it communi- 

 cates 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 cliange of form ; such bodies receiving and 

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

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

 usually be observed to rebound a little. 



Bodies, which ai-e perfectly inelastic, remain in contact after collision; they 

 must therefore proceed with tlie same velocity as the centre of inertia had 

 before •colHsion. 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 un- 

 equal dimensions, the joint velocity is as much smaller than that of the strik- 

 ing 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, 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 re- 

 duced 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 direc- 

 tions, remains also unaltered. 



The tenn 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 ve- 

 locity. Thus, if a weight of one ounce moves Avith a velocity of a foot in a 

 second, we may call its energy 1 ; if a second body of two ounces have a ve- 

 locity 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 ascending force, 



