1821.] Phenomena of Heat y Gases, Gravitation, S^c. 285 



the other body would have come in contact with the plane, and^ 

 therefore, makes the stroke twice as great. 



This might probably be made more obvious thus : Suppose a 

 hard plane, or other body, be held against a fixed hard body, 

 and in this way receive the impulse of the ball ; then, because 

 that part of the intermediate body which is against the fixture is 

 not urged any way by that fixture, the force with which the ball 

 comes in contact with the other side is the force with which the 

 sides of this intermediate body are driven together; but this 

 force is the monumentum of the ball; therefore, that momentum 

 is the force of constipation in this case. But if we now fix the 

 intermediate body, and instead of the fixed body on one side of 

 it imagine another equal ball to come in contact with it at the 

 same time as the former, and with an equal momentum, then the 

 force with which each surface of this intermediate body is urged 

 towards its centre is equal to the momentum of each of the balls; 

 and, therefore, the force with which the two surfaces are urged 

 together is equal to the sum of these momenta, or to twice one 

 of them ; but this force is manifestly the force with which the 

 two balls would have come in contact if there had been no inter- 

 mediate body; therefore, that force is the double of the force 

 with which either body would have struck a fixed plane. 



Cor. 3. — Hence if two hard and equal balls come in contact 

 with equal and opposite momenta, they will separate after the 

 stroke with the same velocity with which they met. For since 

 the intensity of the stroke is the force with which each of the 

 balls is acted on in a direction opposite to that in which it came 

 at the time of the contact ; and since that intensity is by the 

 preceding cor. equal to twice the momentum of either ball, each 

 ball at the time of the contact might be conceived to be acted on 

 by two opposite forces, one its momentum, impelhng it towards 

 the other ball ; and the other, the force of the contact equal to 

 twice its momentum impelling it in an opposite direction. The 

 difference between these two forces, therefore, or the value of 

 one momentum, is the force with which each ball retraces its 

 path ; and, consequently, the velocity of the separation of the 

 balls is equal to the velocity of their approach. This coincides 

 with the theories of Wren and Huygens. 



Scholium, 



By the old theory of collision, two hard bodies coming in con- 

 tact with equal opposite momenta will not separate after the 

 collision, but will continue together ; and the reason assigned for 

 this is, that being unelastic, they cannot, when they meet, exert 

 themselves to separate, and, therefore, must remain together. 

 Such a method as this is not reasoning from the property of 

 hardness, the physical force of the impulse, and the eflfect which 

 that force would have upon the motions of the bodies ; but from 

 the absence of a property which does not belong to this class of 



