This law is the basis not only of the doctrine of impact in mechanics, but also of that of equilibrium in statics. From the force of impact which two bodies with the same velocity exert the relation of their masses to each other may be determined. Thus of two hammers striking with the same velocity, the one which has the greater mass will drive the nail deeper into the wall or the post deeper into the earth. For example, a hammer weighing six pounds with a velocity = 6 effects as much as a hammer weighing three pounds with a velocity = 12, for in both cases the quantity of motion or the momentum = 36. Of two balls rolling at the same pace, the one which has the greater mass will impel a third ball at rest to a greater distance than the ball of less mass can. For the mass of the first multiplied by the same velocity gives a _greater quantity of motion_, or a _greater momentum_. The cannon carries further than the gun, because an equal velocity communicated to a much greater mass gives a much _greater quantity of motion_, which resists longer the retarding effect of gravity. For the same reason, the same arm will throw a lead bullet further than a stone one of equal magnitude, or a large stone further than quite a small one. And therefore also a case-shot does not carry so far as a ball-shot. The same law lies at the foundation of the theory of the lever and of the balance. For here also the smaller mass, on the longer arm of the lever or beam of the balance, has a greater velocity in falling; and multiplied by this it may be equal to, or indeed exceed, the _quantity of motion_ or the _momentum_ of the greater mass at the shorter arm of the lever. In the state of rest brought about by _equilibrium_ this velocity exists merely in intention or virtually, _potentiâ_, not _actu_; but it acts just as well as _actu_, which is very remarkable. The following explanation will be more easily understood now that these truths have been called to mind.