When the quantity of power is expressed by a number, its value is determined, as we have stated, by the intensity of its efficiency in a given time and fixed conditions. The unit of intensity by which the amount of the effect produced is measured is arbitrary; for there is no natural unit for the degrees of intensity, it being evident that such degrees can be divided and subdivided without end, just like the continuum. Hence the numbers by which we express degrees of intensity are only virtually discrete, just as those by which we express continuous quantities. The ordinary unit assumed for the measure of intensity is that degree of intensity which causes a unit of weight to measure a unit of distance in a unit of time. As all these units are arbitrary, it is evident that such is also the unit of intensity.
Let us remark, also, that the power of natural causes has in its action a twofold continuity—that is, with regard both to space and to duration. As long as a natural cause exists, it acts without interruption, owing to its intrinsic determination, provided there be, as there is always in fact, some subject capable of being acted upon by it. This constitutes the continuity of action with regard to duration. On the other hand, the motive power of such natural causes is exerted, according to the Newtonian law, throughout an indefinite sphere, as we have shown in another place;[155] and this constitutes the continuity of action through space. Moreover, if the point acted upon approaches the agent or recedes from it, the continuous change of distance will be accompanied by a continuous change of action; and thus the intensity of the act produced by the agent will increase or decrease in a continuous manner through infinitesimal degrees corresponding to the infinitesimal changes of local relations occurring in infinitesimal instants of time. This relation of changes is the base of dynamics. But enough on this point.
Origin of movement.—We may now pass to the conclusions concerning movement as dependent on its proximate cause. The power by which the natural causes produce momentums of movement is called “motive power.” This power is to be found both in material and in spiritual beings; but as in spiritual substances the exercise of the motive power is subject to their will, and consists in the application of a nobler power to the production of a lower effect, we do not and cannot consider the power of spiritual beings as merely “motive,” for it is, above all, intellective and volitive. Material things, on the contrary, because they possess no other power than that of moving, are characterized by it, and are naturally determined to exercise it according to a law which they cannot elude. It is of these beings in particular that the following conclusions are to be understood.
1st. There is in all material creatures a motive power—that is, a first act of moving—which, considered in its absolute state, has no need of extrinsic termination, that is, of producing a momentum of movement.
2d. This motive power is an objective reality.
3d. The same power is nothing accidentally superadded to the being of which it is the power.
4th. This power is the virtuality, or extrinsic terminability, of the act by which the agent is.
5th. This power is not modified by the production of momentums in extrinsic terms.
6th. The momentums thus produced are second acts of the motive power, extrinsic to it; and though, owing to their intensity, which may be greater or less, they can be related to one another through an intrinsic foundation, yet their entitative distances have only an extrinsic foundation—to wit, the agent’s power.
Some of these propositions are quite evident; but our present object is not only to explain what may require a special discussion, but also, and principally, to dissect our subject in such a manner as to make it manifest that a perpetual analogy exists between the conditions and the principles of all kinds of continuum, and that in all of them the transition from the absolute to the relative, from the cause to the effect, and from the formal reason to its formal result, is made through a like process and through similar degrees. For this reason we think that even those conclusions which seem too obvious to deserve mention become interesting and serve a good purpose; for in the parallel treatment of analogous subjects, those things which are clearer throw light on those which are more abstruse, and about which we often feel a certain hesitation.