When we wonder, therefore, at the discovery that heat is motion, we wonder at something that was never discovered. It is perfectly indifferent and possesses not the slightest scientific value, whether we think of heat as a substance or not. The fact is, heat behaves in some connexions like a substance, in others not. Heat is latent in steam as oxygen is latent in water.
V. THE CONFORMITY IN THE DEPORTMENT OF THE ENERGIES.
The foregoing reflexions will gain in lucidity from a consideration of the conformity which obtains in the behavior of all energies, a point to which I called attention long ago.[56]
A weight P at a height H1 represents an energy W1 = PH1. If we suffer the weight to sink to a lower height H2, during which work is done, and the work done is employed in the production of living force, heat, or an electric charge, in short, is transformed, then the energy W2 = PH2 is still left. The equation subsists
W1/H1 = W2/H2, (2) or, denoting the transformed energy by W' = W1-W2 and the transferred energy, that transported to the lower level, by W = W2,
W'/(W' + W) = (H1-H2)/H1, (3)
an equation in all respects analogous to equation (1) at page 165. The property in question, therefore, is by no means peculiar to heat. Equation (2) gives the relation between the energy taken from the higher level and that deposited on the lower level (the energy left behind); it says that these energies are proportional to the heights of the levels. An equation analogous to equation (2) may be set up for every form of energy; hence the equation which corresponds to equation (3), and so to equation (1), may be regarded as valid for every form. For electricity, for example, H1, H2 signify the potentials.
When we observe for the first time the agreement here indicated in the transformative law of the energies, it appears surprising and unexpected, for we do not perceive at once its reason. But to him who pursues the comparative historical method that reason will not long remain a secret.
Since Galileo, mechanical work, though long under a different name, has been a fundamental concept of mechanics, as also a very important notion in the applied sciences. The transformation of work into living force, and of living force into work, suggests directly the notion of energy—the idea having been first fruitfully employed by Huygens, although Thomas Young first called it by the name of "energy." Let us add to this the constancy of weight (really the constancy of mass) and we shall see that with respect to mechanical energy it is involved in the very definition of the term that the capacity for work or the potential energy of a weight is proportional to the height of the level at which it is, in the geometrical sense, and that it decreases on the lowering of the weight, on transformation, proportionally to the height of the level. The zero level here is wholly arbitrary. With this, equation (2) is given, from which all the other forms follow.