Fifthly, a stone created originally on the brink of a precipice would be ready to fall into it, although it has never been thrown up; on the contrary, a stone thrown up to such a height as to reach the limits of the moon's effectual attraction would never come down again, notwithstanding the enormous amount of pretended "actual energy" expended in the mighty ascent. Hence the upward flight has nothing whatever to do with any so-called "potential energy." It is, therefore, a gross delusion to hold that by allowing the stone again to fall, "we may change the potential energy into actual energy," it being evident that the actual velocity of the falling stone is not a result of transformation, but the product of continuous action.
We cannot, then, adopt the phrase "potential energy" in metaphysics. The phrase means nothing; for there is nothing in nature which can be designated by such a name. Energy is synonymous with power; and power cannot be in a potential state. To be in potency to receive any amount of velocity is not energy, but passivity. On the other hand, the power of doing work is not a mere force, as assumed by the modern theory, but is something much higher and better. Forces are only variable quantities of action; the power, on the contrary, in one and the same body is always the same, and yet is competent to do more or less work, according as it is exerted under more or less favorable conditions. The stone that is hurled against a pane of glass exerts, in breaking it, the very same power which it exerted before being hurled; only the conditions of the exertion are quite different, inasmuch as its velocity brings it against the glass at such a rate that, before its movement can be checked by the action of the glass, the stone has time to outrun it, dashing it to pieces. Yet it is by its action, not by its velocity, that it does such a work. Of course, its action is proportional to its velocity, and its work is proportional to the square of its velocity; and thus the velocity serves to measure both the work and the action, but it does not follow that the velocity is the active power. Velocity is an accidental mode of being; and nothing accidental is active. This important philosophical truth can be easily established as follows:
In all things the principle of being is the principle of operation, as philosophers agree; whence the axioms, "By what a thing is, by that it acts," and "Everything has active power inasmuch as it has being." Now, all substance has its being independently of accidents; therefore, all substance has its active power independently of accidents. On the other hand, accidents give to the substance a mode of being, and nothing more; therefore, they also determine its mode of acting, and nothing more. But as to be in this or that state presupposes being, so also to have a power ready to act in this or that manner presupposes power. Hence no accident gives active power to the substance of which it is the accident; or, in other terms, accidents are nothing more than conditions determining the mode of application of the active powers that pre-exist in the substance.
Again, all natural accidents[272] are reducible to three classes; as some of them are accidental acts produced by some agent and passively received in some subject, others are intrinsic modes of being resulting from the reception of such accidental acts, and, lastly, a great many are mere relativities or relative modes. Now, that relativities can act no one has ever pretended to assert. That intrinsic modes of being can act, is implicitly assumed by all who consider velocity as an active power; for velocity is an intrinsic mode of being. Yet if we ask them whether the existence of things is competent to act, they will certainly answer no; and they will be right. But, I say, if existence cannot act, still less can a mere mode of existing act. For a mode of existing is a reality incomparably less than existence itself. Accordingly, since they concede that not the existence, but the thing existing, is a principle of action, they must also à fortiori concede that the thing modified, and not its mode, is a principle of action. Finally, with regard to the accidental act, it is evident that its reception in the substance cannot impart to it any new activity, since its formal effect simply consists in a new mode of being, which, as we have just seen, is not active. It is clear, then, that no natural accident has active power.
Omitting other reasons drawn from theoretical considerations, and which might be usefully developed in special metaphysics, I will only add an à posteriori proof, which physicists will probably find more congenial to their habit of thought. It consists in the fact that bodies act on one another without being animated by velocity, or without their velocity having any share in the production of the effect. Thus a book at rest on a table acts on the table; and a liquid, or a gas, at rest in a jar acts on the jar. On the other hand, the earth, though not at rest, attracts bodies, not by its diurnal rotation or by its annual revolution, but by a power dependent only on its mass; and the same is to be said of the sun and the planets. This shows that the power from which the motive action of bodies proceeds is not their velocity; whence it follows that velocity is only an affection of bodies, and has no bearing upon the active powers of the same, but only on the mode of their application. Now, since all the accidents which have been supposed to involve active power can be resolved into kinds of movement, it must be owned that such accidents have no real activity; for all kinds of movements consist of velocity, and velocity does not act.
Hence, whatever scientists may say to the contrary, heat, light, electricity, etc., are not efficient powers, but modes of movement, on which the mode of acting of bodies depends. When heat was thought to be a subtle imponderable substance, philosophers could consistently call it an efficient power; but since it is now decided that heat is only "a mode of motion," how can we still attribute to it what is the exclusive property of substances? If heat is only a mode of motion, a bar of iron, when hot, has no greater powers than when cold; it has only a greater movement. So also, if light is only a mode of motion, luminiferous æther has no greater power when undulating in the open air than when at rest in a dark room. In the same manner air, when perfectly still, has the same powers as when actually propagating any variety of sounds. When, therefore, physicists speak to us of such movements as powers, let us not be imposed upon by their phraseology, if we wish to be consistent in our reasonings, and avoid useless and troublesome disputes.
Yet it was to be expected that our physicists in their technical language would confound heat, light, and other modes of movement with forces and powers. The correlation between such movements and the actions of the bodies subjected to them is, in fact, such as to allow of the former being taken for measure of the latter. Thus a given amount of mechanical action may give rise to a definite amount of heat, and vice versa; hence the one can be technically considered as the equivalent of the other, inasmuch as the one is the measure of the other. But does it follow that action and heat belong to the same category? Certainly not. It is not the action itself, but its mechanical effect, that should be taken as the true equivalent of the heat generated. And when we are told that "heat is expended in generating mechanical movement," we must not fancy that calorific movement causes another kind of movement, as the phrase seems to imply, but only that, while the calorific movement is diminished by a given cause, the same cause generates the mechanical movement. We should always bear in mind that the language of modern science, though correctly expressing the correspondence of effects to effects, is very far from expressing as correctly the relation of effects to causes. Physicists should learn to distinguish between efficient causes and conditions determining the mode of their causation. Heat is one of such conditions, and to call it a force is to endow it with efficient causality; for the term force always conveys the idea of causation. They should either cease to describe heat as a force, or, if this cannot be done, explain more explicitly than they do the technical restrictions modifying the philosophical meaning of the word. We can hardly expect that they will follow our advice; but, at any rate, it is to be hoped that philosophers at least will take care to follow it, and guard against the corruption of their own terminology.
Besides heat, light, electricity, and magnetism, there are many other modes of being technically called forces. Centrifugal force is one of them; for, in fact, centrifugal force, in spite of the name, is nothing more than "that quantity of movement which is extinguished by centripetal action in the unit of time."
The force of inertia—vis inertiæ—is another technical or conventional force. For it is plain that inertia cannot act; and thus it is impossible to conceive any true force of inertia. But, technically, vis inertiæ means "the quantity of the effort by which a body, when enduring violence from without, resists compression, traction, or any other alteration of its molecular structure." This effort proceeds, not from inertia, but from the active powers residing in the molecules of the body; and yet it has received the name of vis inertiæ, because it develops itself in the lapse of time during which the body, inasmuch as inert—i.e. incapable of leaving its place before the whole mass has acquired a common velocity—is still loth to start, and thus compelled to struggle against the invading body. Philosophers, by keeping in sight this definition of vis inertiæ, will be able to solve many sophisms of modern scientific writers.
Again, the weight of a body is called a force, and is represented by the product of the mass of the body into a velocity which it has not, but which it would acquire through the action of gravity in a second of time, if it were free to fall. If the mass be called M, and the velocity which it would acquire g, the product Mg will represent the weight of the body. Now, when the body is at rest on a table, the pressure exercised by it on the table is said to be Mg. Does this mean that the weight of the body acts on the table? Not at all; for the body does not act by its weight, which is not an active power. The truth is that the table by its resistance prevents the body from acquiring the momentum Mg; and since this resistance of the table must be equal to the pressure exercised on it by the body, hence the pressure itself is also equal to Mg; and thus a true force—a quantity of pressure—is technically identified with the weight of the pressing body. This identification tends to give a false idea of the nature of the fact, and therefore should be carefully avoided in philosophy.