The activity of material substance is a very interesting subject of investigation; its nature, its mode of working, the law of its exertion, and the conditions on which the production of its effects depends, give rise to many important questions, which, owing to philosophical discords, have not yet received a satisfactory solution. The first of these questions is: Does material substance act at a distance, or does it require, as a condition sine qua non for acting, a mathematical contact of its matter with the matter acted upon?
Philosophers and scientists have often examined this grave subject, but their opinions are still divided. Those philosophers who form their physical views from the scholastic system, commonly hold that a true material contact is an indispensable condition for the action of matter upon matter, and think it to be an evident truth. But physicists, “with few exceptions,” as Prof. Faraday remarks, admit that all action of matter upon matter is [pg 584] an actio in distans, and he himself supports the same doctrine, although suggesting that it should be expressed in somewhat different terms. We propose to show that this latter solution is the only one consistent with the principles both of science and of philosophy. And as the opposite view owes its origin, and in a great measure its plausibility, to the known theory of kinetic forces as deduced from the impact of bodies, we shall argue from the same theory in support of our conclusion.
Here is our argument. When a body impinges upon another body, if any communication of movement is made by a true and immediate contact of matter with matter, its duration must be limited to that indivisible instant of time in which the distance between the struggling particles of matter becomes = 0. But in an indivisible instant of time no finite velocity can be communicated. And therefore no real movement can be caused in the impact of bodies by a true and immediate contact of matter with matter.
We think that this argument admits of no reply. Its major proposition is the statement of an obvious geometric truth. Nor can it be gainsaid by assuming that the duration of the action can be prolonged; for the action, in the opinion of those against whom we now are arguing, is supposed to require true material contact; and it is plain that two particles of matter coming into contact cannot remain in contact for any length of time, however inappreciable, unless in the very first instant of their meeting their velocities have become equal; it being evident that two particles of matter animated by different velocities cannot preserve for any length of time the same relation in space. To assume, therefore, that the contact can be prolonged, is to assume that from the very first instant of the collision the unequal velocities of the struggling particles have been equalized, or, in other terms, that the velocity imparted has been communicated in the very first instant of the impact. But if so, then the assumption of a prolonged contact, as a means of communicating the velocity, is altogether useless, and involves an evident contradiction. It is therefore necessary to concede that, if the velocity is communicated by a true and immediate contact of matter with matter, the communication must be made in an indivisible instant of time.
The minor proposition of our syllogism is equally evident. For it is one of the fundamental axioms of mechanics that actions, all other things being equal, are proportional to their respective duration; whence it is plain that an action of which the duration is infinitesimal cannot produce more than an infinitesimal effect. And therefore no finite velocity can be produced by true material contact.
Against this argument four objections may be advanced: First, that although in the contact of one point with another point no finite velocity can be communicated, yet in the case of a multitude of material points coming into collision the effect might be appreciable. Secondly, that a particle of matter may be carried straight away by another particle which impinges upon it with sufficient velocity. Thirdly, that a distinction is to be made between continuous and instantaneous actions, and that, although a continuous action produces an effect proportional to its [pg 585] duration, as in the case of universal attraction, yet instantaneous actions, as in the case of impact, may not necessarily follow the same law. Lastly, that even admitting the impossibility of producing finite velocity in an infinitesimal unit of time, yet finite velocity might still be communicated in an infinitesimal unit of time without any new production, as modern scientists assume.
To the first objection we answer that, if each material point cannot, in the instant of the contact, acquire more than an infinitesimal velocity, the whole multitude will have only an infinitesimal velocity; and thus no movement will ensue.
To the second we answer that a particle cannot be carried straight away unless it receives a communication of finite velocity; and such a communication, as we have already shown, cannot be made in the instant of the contact.
The third objection we answer by denying that there is any rigorously instantaneous action. When physicists speak of “instantaneous” actions, they mean actions having a finite duration, which, however, is so short that it cannot be appreciated or measured by our means of observation. And therefore what is called an “instantaneous” action is nothing but a continuous action of a short duration. Now, a difference of duration is not a difference in kind; and accordingly, if actions are proportional to their duration when their duration is longer, they are no less so when their duration is shorter.
The last objection takes for granted that there can be a communication of velocity without production of velocity; which amounts to saying that the velocity of the impinging body is transmitted identically to the body impinged upon. This is, however, a mere delusion. The velocity acquired by the body impinged upon has no previous existence in the impinging body; and accordingly its communication implies its real production, as we have proved in one of our past articles.[133]