The answer to this question will suggest itself at once to those who have properly apprehended the principle of the essential relativity of all material existence. A material object is, in every one of its aspects, but one term of a relation; its whole being is a presupposition of correlates without; all things are, figuratively speaking (if I may resort to such a figure without incurring the charge of illustrating obscurum per obscurius) shadows of each other. Every change of a body, therefore, presupposes a corresponding change in its correlates. If the state of any material object could be changed without a corresponding change of state in other objects without, this object would, to that extent, become absolute. But this is utterly unthinkable, and therefore utterly impossible, as we have already seen. At the same time it is also evident that, while every change of a body is thus conditioned by changes without, these latter changes are equally conditioned by it; that all material action, therefore, is mutual; that reaction is invariably equal to action. A corollary from, or rather an application of this is the well-known theorem that the forces within a body or conservative system can alter only the positions of its constituent parts, but cannot change the position of the body as a whole; and that, whenever such an internal change takes place, the momentum accruing in one direction has its counterpart in an equal momentum accruing in the opposite direction. If we apply this theorem to the universe as a whole, i. e., as a single dynamical system, and if we bear in mind that, mechanically speaking, all force properly so called, i. e., all potential energy, is energy of position, we see at once that whatever energy is spent in actual motion is gained in position—that the system, therefore, is absolutely conservative; and we are thus led, by a very simple approach, to the principle of the conservation of energy.
After this summary discussion of the first conceptual element of matter, inertia, I proceed to the consideration of the other element, force. In the canonical text-books on physics, force is defined as the cause of motion. "Any cause," says Whewell ("Mechanics," p. 1), "which moves or tends to move a body, or which changes or tends to change its motion, is called force." Similarly Clerk Maxwell ("Theory of Heat," p. 83): "Force is whatever changes or tends to change the motion of a body by altering either its direction or its magnitude." Taking either of these definitions as correctly representing the re-
- If the term "force" is restricted, as it ought to be, to the designation of potential energy, or mere tension, the expression "persistence or conservation of force" becomes inaccurate; for the sum of the forces in the universe, in this sense, is by no means constant. The "persistence of force" or, more properly, the "conservation of energy," simply imports that the sum of actual or kinetic energy (energy in motion) and potential energy (energy of position or energy in tension) in the material universe is invariable. This, as is shown in the text, is but an amplification of the theorem that in any limited conservative system the sum of the potential and kinetic energies of its parts is never changed by their mutual actions.