There are many other manifestations of electricity, all of which have been more or less studied, and they lead to the formation of theories of its nature, theories which fit in, to a greater or less extent, with the observed facts. The electrification of a body is a physical quantity capable of measurement, and two or more electrifications can be combined experimentally with a result of the same kind as when two quantities are added algebraically. We, therefore, are entitled to use language fitted to deal with electrification as a quantity as well as a quality, and to speak of any electrified body as "charged with a certain quantity of positive or negative electricity."

While admitting electricity to the rank of a physical quantity, we must not too hastily assume that it is, or is not, a substance, or that it is, or is not, a form of energy, or that it belongs to any known category of physical quantities. All that we have proved is that it cannot be created or annihilated, so that if the total quantity of electricity within a closed surface is increased or diminished, the increase or diminution must have passed in or out through the closed surface.

This is true of matter, but it is not true of heat, for heat may be increased or diminished within a closed surface, without passing in or out through the surface, by the transformation of some form of energy into heat, or of heat into some other form of energy. It is not true even of energy in general if we admit the immediate action of bodies at a distance.

There is, however, another reason which warrants us in asserting that electricity, as a physical quantity, synonymous with the total electrification of a body, is not, like heat, a form of energy. An electrified system has a certain amount of energy, and this energy can be calculated. The physical qualities, "electricity" and "potential," when multiplied together, produce the quantity, "energy." It is impossible, therefore, that electricity and energy should be quantities of the same category, for electricity is only one of the factors of energy, the other factor being "potential."

Electricity is treated as a substance in most theories of the subject, but as there are two kinds of electrification, which, being combined, annul each other, a distinction has to be drawn between free electricity and combined electricity, for we cannot conceive of two substances annulling each other. In the two-fluid theory, all bodies, in their unelectrified state, are supposed to be charged with equal quantities of positive and negative electricity. These quantities are supposed to be so great than no process of electrification has ever yet deprived a body of all the electricity of either kind. The two electricities are called "fluids" because they are capable of being transferred from one body to another, and are, within conducting bodies, extremely mobile.

In the one-fluid theory everything is the same as in the theory of two fluids, except that, instead of supposing the two substances equal and opposite in all respects, one of them, generally the negative one, has been endowed with the properties and name of ordinary matter, while the other retains the name of the electric fluid. The particles of the fluid are supposed to repel each other according to the law of the inverse square of the distance, and to attract those of matter according to the same law. Those of matter are supposed to repel each other and attract those of electricity. This theory requires us, however, to suppose the mass of the electric fluid so small that no attainable positive or negative electrification has yet perceptibly increased or diminished the mass or the weight of a body, and it has not yet been able to assign sufficient reasons why the positive rather than the negative electrification should be supposed due to an excess quantity of electricity.

For my own part, I look for additional light on the nature of electricity from a study of what takes place in the space intervening between the electrified bodies. Some of the phenomena are explained equally by all the theories, while others merely indicate the peculiar difficulties of each theory. We may conceive the relation into which the electrified bodies are thrown, either as the result of the state of the intervening medium, or as the result of a direct action between the electrified bodies at a distance. If we adopt the latter conception, we may determine the law of the action, but we can go no further in speculating on its cause.

If, on the other hand, we adopt the conception of action through a medium, we are led to inquire into the nature of that action in each part of the medium. If we calculate on this hypothesis the total energy residing in the medium, we shall find it equal to the energy due to the electrification of the conductors on the hypothesis of direct action at a distance. Hence, the two hypotheses are mathematically equivalent.

On the hypothesis that the mechanical action observed between electrified bodies is exerted through and by means of the medium, as the action of one body on another by means of the tension of a rope or the pressure of a rod, we find that the medium must be in a state of mechanical stress. The nature of the stress is, as Faraday pointed out, a tension along the lines of force combined with an equal pressure in all directions at right angles to these lines. This distribution of stress is the only one consistent with the observed mechanical action on the electrified bodies, and also with the observed equilibrium of the fluid dielectric which surrounds them. I have, therefore, assumed the actual existence of this state of stress.