That a primitive element cannot have two different laws of action will be manifest by considering that the law which an element obeys in its actions results from the intrinsic determination of its nature—that is, from its formal constitution—inasmuch as the principle of action is, in every primitive substance, the formal principle of its very being: Principium essendi est principium operandi. Now, a primitive element has but one formal principle of being; for it is entitatively one, and therefore it has but one formal determination to act, which, as resulting from its essential constitution, is unchangeable and inviolable. But it is evident that from one formal determination to act only one law of action can possibly result. Two laws would be two formal results, and would require two formal principles giving two different determinations. Accordingly, since each primitive element has but one formal principle, it cannot have two laws of action. And therefore the Newtonian law, which primitive elements follow at astronomical distances, must prevail also at all other distances.
Let the reader observe that this conclusion regards the action of primitive elements, not the action of molecules. That molecular actions at molecular distances are not inversely proportional to the square of the distance is a known fact. Molecular cohesion, for instance, is immensely greater than it could possibly be by the Newtonian law; so also molecular repulsion. This is what prevented physicists from recognizing the applicability of the Newtonian law at molecular distances. As long as the primitive elements were confounded, under the name of atoms, with the molecules of the so-called primitive bodies, hydrogen, oxygen, carbon, etc., it was impossible to recognize in the molecular actions any trace of the Newtonian law; hence came the division of attraction into universal and molecular, the first following a known law, the second following some other law or laws which physicists could never discover. Their embarrassment was a necessary consequence of an incomplete analysis of the material [pg 730] compound. The molecule of a given substance, though often called an atom, is a system of primitive elements; and elements acting according to the Newtonian law can give rise to molecular systems which, at very small distances, will act according to any other law that may be indicated by molecular phenomena. This other law depends entirely on the number, kind, strength, and geometrical arrangement of the primitive elements which enter into the constitution of the molecule; and since molecules of different primitive substances are very differently constituted, every kind of molecule must have its own peculiar law of acting at molecular distances—a fact on which the scientific explanation of the different physical and chemical properties of different substances entirely depends. Hence it is clear that all the attempts at finding a general law of molecular attraction were, from the very nature of the case, destined to fail. The only general law of action which all matter obeys is the Newtonian law; and what was once considered to form an exception to it is now acknowledged to be the result of its application to a complex system of attractive and repulsive elements.
From the fact that the actions of all elements are proportional to the inverse squares of the distances, it follows that the sphere of activity of material elements extends beyond any assignable limit. The intensity of the action cannot, in fact, become = 0 unless the distance becomes infinite. The objections to which this corollary of the Newtonian law may give rise will be answered in our next article, where all the difficulties concerning the actio in distans will be solved.
Mode of action.
A last question remains here to be examined respecting the action of primitive material elements—viz., whether such an action needs a medium through which it may be transmitted and communicated to distant bodies, or whether, on the contrary, it is exerted upon them directly without dependence on any material medium.
In answering this question we must be careful not to confound action with movement. Movement, though not properly transmitted, is propagated, as we shall explain; and this cannot take place where there is no movable matter. Those who are wont to identify movement with force, and force with action, as is unfortunately the fashion even in scientific treatises, will no doubt imagine that actions must be transmitted or propagated through a material medium, just as sound through air, or as light through luminiferous ether. But action is not movement; and therefore the question how elementary actions—that is, how attractions or repulsions—reach distant bodies has to be resolved on its own merit, as one altogether distinct from the question about the propagation of movement. This premised, we are going to show that the elementary actions are independent of all material medium of communication.
In the first place, there is no reason why we should assume that the elementary action (attraction or repulsion) depends on a medium of communication, except inasmuch as we may apprehend that the action itself, or the active power whence it proceeds, is in need of being transmitted to some matter located at a certain distance. But neither the elementary power nor the elementary action can be [pg 731] transmitted to the distant matter. And therefore neither the power nor the action can be dependent on a medium of communication.
In this syllogism the major is evident; and the minor can be proved in two manners: First, because the power and the action are, of their own nature, intransmissible. Secondly, because, prescinding from their intransmissibility, no medium can be assigned which would be capable of transmitting them. And as to the first, we know that nothing can be transmitted to a distant place except by local movement; but neither the active power nor the elementary action is capable of receiving local movement; for there is no other subject capable of local movement than matter alone, on account of its passive potentiality. Hence neither power nor action can be transmitted. And in the second place, even were they transmissible, what medium could be found for their transmission? If any such medium could be found, it would consist of some matter like ether or air, this being the view of those who admit the necessity of such a medium. On the other hand, a material substance is not a suitable medium for transmitting action or power. For whenever an active power is exerted upon matter, the result of the exertion is nothing but a determination to a change of place; as it is well known that matter cannot receive any other determination. And therefore it is not the power that is received in the matter acted on, but only the act produced by its exertion, which act is otherwise called a momentum either statical or dynamical. Strictly speaking, not even the action itself is received in the matter, although we are wont to tolerate such an expression; for the action properly so called is the production of an act, and the matter receives, indeed, the act produced, but not its production. And thus the action, properly speaking, is terminated to the matter, and not received in it. Hence we see that neither the power of the agent nor its exertion is received in the matter acted on; it is merely the produced accidental act, or, in other terms, the momentum, that is received. But evidently matter cannot transmit what it does not receive. And therefore matter cannot be a medium for transmitting either power or action. Whether it can transmit movement we shall examine at the end of the present question.
This argument would suffice to show that elementary actions are quite independent of a material medium. Yet as the prejudice against which we are fighting is ancient, popular, and deeply rooted, we think it will not be superfluous to confirm our proof by a few other considerations.
Those who maintain the transmission of forces admit a material medium, in which, by successive contact of particles with particles, the transmission of the force to a distant body is supposed to be carried on. By the word “force” they understand action as well as movement. Now, let us ask them whether the particles of their material medium come into mathematical contact or not. If they do not come into mathematical contact, then the action is not transmitted by the medium from one particle to another, for there will be a vacuum between them; and vacuum is not a material medium. If, on the contrary, the particles come into mathematical contact with their own matter, then, as we have already shown in our past article, [pg 732] they cannot by such a contact communicate any movement to each other; and since the transmission in question should be carried on by successive communications of movement, it is plain that no such transmission will be possible. And accordingly the theory of the transmission of actions through a medium must be rejected.