Page:The World as Will and Idea - Schopenhauer, tr. Haldane and Kemp - Volume 2.djvu/236

226 principal passage of this communication is quoted in Dugald Stewart's "Philosophy of the Human Mind," and is probably taken from Robert Hooke's Posthumous Works. The history of the matter, and how Newton got into difficulty by it, is also to be found in the "Biographie Universelle," article Newton. Hooke's priority is treated as an established fact in a short history of astronomy, Quarterly Review, August 1828. Further details on this subject are to be found in my "Parerga," vol. ii., § 86 (second edition, § 88). The story of the fall of an apple is a fable as groundless as it is popular, and is quite without authority.

(2) To No. 18 of Matter.

The quantity of a motion (quantitas motus, already in Descartes) is the product of the mass into the velocity.

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.

The quantity of a given matter can only be estimated in general according to its force, and its force can only be known in its expression. Now when we are considering matter only as regards its quantity, not its quality, this expression can only be mechanical, i.e., it can only consist in motion which it imparts to other matter. For only in motion does the force of matter become, so to speak, alive; hence the expression vis viva for the manifestation of force of matter in motion. Accordingly the only measure of the quantity of a given matter is the quantity of its motion, or its momentum. In this, however, if it is given, the quantity of matter still appears in