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By this calculation it appears that in the impact A has lost a quantity of motion expressed by 24, and that B has received exactly that amount. The effect, therefore, of the impact is a transfer of motion from A to B; but no new motion is produced in the direction AC which did not exist before. This is obviously consistent with the property of inertia, and indeed an inevitable result of it.

These results may be generalised and more clearly and concisely expressed by the aid of the symbols of arithmetic.

Let a express the velocity of A.

Let b express the velocity of B.

Let x express the velocity of the united masses of A and B after impact, each of these velocities being expressed in feet per second, and the masses of A and B being expressed by the weight in pounds.

We shall then have the momenta or moving forces of A and B before impact, expressed by A × a and B × b, and the moving force of the united mass after impact will be expressed by (A + B)×x.

The moving force of A after impact is A × x, and therefore the force it loses by the collision will be (A × a - A × x). The force of B after impact will be B × x, and therefore the force it gains will be B × x - B × b. But since the force lost by A must be equal to the force gained by B, we shall have