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(55.) If a mass A, fig.4., moving towards C, impinge upon an equal mass, which is quiescent at B, the two masses will move together towards C after the impact. But it will be observed, that their speed after the impact will be only half that of A before it. Thus, after the impact, A loses half its velocity; and B, which was before quiescent, receives exactly this amount of motion. It appears, therefore, in this case, that B receives exactly as much motion as A loses: so that the real quantity of motion from B to C is the same as the quantity of motion from A to B.

Now, suppose that B consisted of two masses, each equal to A, it would be found that in this case the velocity of the triple mass after impact would be one-third of the velocity from A to B. Thus, after impact, A loses two-thirds of its velocity and, B consisting of two masses each equal to A, each of these two receives one-third of A’s motion; so that the whole motion received by B is two-thirds of the motion of A before impact. By the impact, therefore, exactly as much motion is received by B as is lost by A.