VIII. THE CONSERVATION OF ENERGY

"If the given cause c has produced an effect e equal to itself, it has in that very act ceased to be—c has become e. If, after the production of e, c still remained in the whole or in part, there must be still further effects corresponding to this remaining cause: the total effect of c would thus be > e, which would be contrary to the supposition c = e. Accordingly, since c becomes e, and e becomes f, etc., we must regard these various magnitudes as different forms under which one and the same object makes its appearance. This capability of assuming various forms is the second essential property of all causes. Taking both properties together, we may say, causes an INDESTRUCTIBLE quantitatively, and quantitatively CONVERTIBLE objects.

"There occur in nature two causes which apparently never pass one into the other," said Mayer. "The first class consists of such causes as possess the properties of weight and impenetrability. These are kinds of matter. The other class is composed of causes which are wanting in the properties just mentioned— namely, forces, called also imponderables, from the negative property that has been indicated. Forces are therefore INDESTRUCTIBLE, CONVERTIBLE, IMPONDERABLE OBJECTS.

"As an example of causes and effects, take matter: explosive gas, H + O, and water, HO, are related to each other as cause and effect; therefore H + O = HO. But if H + O becomes HO, heat, cal., makes its appearance as well as water; this heat must likewise have a cause, x, and we have therefore H + O + X = HO + cal. It might be asked, however, whether H + O is really = HO, and x = cal., and not perhaps H + O = cal., and x = HO, whence the above equation could equally be deduced; and so in many other cases. The phlogistic chemists recognized the equation between cal. and x, or phlogiston as they called it, and in so doing made a great step in advance; but they involved themselves again in a system of mistakes by putting x in place of O. In this way they obtained H = HO + x.

"Chemistry teaches us that matter, as a cause, has matter for its effect; but we may say with equal justification that to force as a cause corresponds force as effect. Since c = e, and e = c, it is natural to call one term of an equation a force, and the other an effect of force, or phenomenon, and to attach different notions to the expression force and phenomenon. In brief, then, if the cause is matter, the effect is matter; if the cause is a force, the effect is also a force.

"The cause that brings about the raising of a weight is a force. The effect of the raised weight is, therefore, also a force; or, expressed in a more general form, SEPARATION IN SPACE OF PONDERABLE OBJECTS IS A FORCE; and since this force causes the fall of bodies, we call it FALLING FORCE. Falling force and fall, or, still more generally, falling force and motion, are forces related to each other as cause and effect—forces convertible into each other—two different forms of one and the same object. For example, a weight resting on the ground is not a force: it is neither the cause of motion nor of the lifting of another weight. It becomes so, however, in proportion as it is raised above the ground. The cause—that is, the distance between a weight and the earth, and the effect, or the quantity of motion produced, bear to each other, as shown by mechanics, a constant relation.

'Gravity being regarded as the cause of the falling of bodies, a gravitating force is spoken of; and thus the ideas of PROPERTY and of FORCE are confounded with each other. Precisely that which is the essential attribute of every force—that is, the UNION of indestructibility with convertibility—is wanting in every property: between a property and a force, between gravity and motion, it is therefore impossible to establish the equation required for a rightly conceived causal relation. If gravity be called a force, a cause is supposed which produces effects without itself diminishing, and incorrect conceptions of the causal connections of things are thereby fostered. In order that a body may fall, it is just as necessary that it be lifted up as that it should be heavy or possess gravity. The fall of bodies, therefore, ought not to be ascribed to their gravity alone. The problem of mechanics is to develop the equations which subsist between falling force and motion, motion and falling force, and between different motions. Here is a case in point: The magnitude of the falling force v is directly proportional (the earth's radius being assumed—oo) to the magnitude of the mass m, and the height d, to which it is raised—that is, v = md. If the height d = l, to which the mass m is raised, is transformed into the final velocity c = l of this mass, we have also v = mc; but from the known relations existing between d and c, it results that, for other values of d or of c, the measure of the force v is mc squared; accordingly v = md = mcsquared. The law of the conservation of vis viva is thus found to be based on the general law of the indestructibility of causes.