It might be urged, as a fourth objection, that if an attractive and a repulsive power differ in kind, then a repulsive element and an attractive element will be two kinds of material substance; which is inadmissible. For we cannot admit two kinds of primitive material beings essentially different, as the essence of matter must be the same in all the elements.
To this we answer that although there are two kinds of elements, there are not two kinds of matter. In other terms, an attractive element differs from a repulsive one as [pg 727] to the principle of action, but not as to the matter itself. In fact, the essence of a material being as such requires nothing more than a form giving existence to matter; hence, wherever there is a form giving existence to matter, there also is the essence of matter. Now, matter is as much and as completely actuated by a form or act which is a principle of attraction as by a form or act which is a principle of repulsion. For the actuation of the matter by its form is not efficient, but formal; and its result is not to approach by attraction or to recede by repulsion, but to be simply and absolutely; so that neither attractivity nor repulsivity has any bearing on the essential constitution of a material element as such—that is, inasmuch as it is material. Accordingly, two elements of opposite natures differ in kind as agents, but not as material beings; and thus the essence of matter as such remains one and the same in all the elements. Matter, as we have already shown, is the centre of a sphere of activity; and it is evident that, by this activity of an attractive or of a repulsive nature, the centre remains a centre, and the sphere a sphere, without the least alteration. Gold and ivory differ in kind; but a sphere of ivory and a sphere of gold do not differ in kind as spheres, and their centres do not differ in kind as centres. In a like manner the sphere of activity of an attractive element does not differ from the sphere of activity of a repulsive element, nor the centre of the one from the centre of the other. And therefore two elements, however different in their nature as agents, do not cease to be of the same kind as material. Their form is different, but informs equally, and their matter is exactly the same.
We have stated that Boscovich was led to admit two opposite powers in the same element, because he thought this to be the only means of accounting for the impenetrability of bodies. We observe that, although the impenetrability of bodies peremptorily proves the existence of repulsive powers, it by no means proves that the repulsive power coexists with the attractive in the same primitive element. Hence Boscovich's inference is not legitimate. Molecules, as we have already remarked, may possess both powers, as their composition involves a great number of elements, which can be of different natures. And this suffices to explain the impenetrability of bodies, and all other properties dependent on molecular actions, without need of arbitrary hypotheses.
A last objection against the doctrine we have established might be drawn from the difficulty of reconciling the existence of repulsive elements with universal attraction; for if we admit that repulsion can be exercised at astronomical distances, it will be difficult to see how the celestial bodies can attract one another in the direct ratio of their masses, as the law of attraction requires.
The answer is obvious. If all matter were repulsive, universal repulsion would be the consequence. But if bodies are made up partly of attractive and partly of repulsive elements, then will either universal repulsion or universal attraction prevail, according as the number and power of the repulsive elements is greater or smaller than that of the attractive ones. Hence, from the fact that in the solar system and elsewhere attraction prevails, it follows, indeed, that the attractive powers are the stronger, but it [pg 728] does not follow that they are the whole stuff of which bodies are compounded.
As to the law of attraction in the direct ratio of the masses, a distinction is to be made. The law is certainly true if by masses we mean the masses acted on; not so, however, if for the masses acted on we substitute the masses of the attracting bodies. The fact of universal attraction shows that two planets, all other things being equal, must be attracted by the sun in the direct ratio of their masses. This is an established truth. But to say that, all other things being equal, the sun and the earth would attract the moon in the direct ratio of their absolute masses, is to assume what no fact whatever gives us the right to assert. Physicists very commonly admit this second assumption, and consider it a part of the law of attraction; but they would be not a little embarrassed were they required to undertake its demonstration. They take for granted that all the particles of matter are equally and uniformly attractive. Now, this assumption has never been established by facts; it simply arises from an unlawful generalization—that is, from the extension of the law of kinetic forces to dynamical actions. The momenta of two bodies animated by equal velocities are proportional to the masses of the same bodies; but nothing justifies the inference that therefore the attractive powers must be proportional to the masses. Indeed, it is scarcely possible to believe that equal masses of lead, iron, and zinc possess equal powers. Their properties are, in fact, so different that we cannot assume their constitution to be the result of an assemblage of equal powers. Hence we maintain that, unless two bodies have the same molecular constitution, their attractions cannot be proportional to their masses.[162]
Universal attraction being also proportional to the inverse squares of the distances, as we are going to show, we may add that the existence of repulsive elements in the sun and in the planets by no means interferes with this law. In fact, the total action of one celestial body on another, on account of the great distance at which the law of universal attraction is applied, equals the algebraic sum of all the actions by which one body makes an impression upon the other. Hence, if all the elements of which the body consists, whether they be attractive or repulsive, act proportionally to the inverse square of the distance, it is evident that the resultant of all such actions will also be proportional to the inverse square of the distance, whenever the form of the body is spherical, or nearly so, as is the case with the celestial bodies. And thus it is plain that no valid objection can be drawn from universal attraction against the existence of repulsive elements.
Law of elementary actions.
We have now to establish the general law of elementary attraction and repulsion. We hold that the actions of every primitive element are always inversely proportional to the squares of the distances, no matter whether such distances be great or small, astronomical or molecular.
This proposition can be briefly proved in the following manner: Astronomy teaches us that the Newtonian law, according to which the actions are inversely proportional to the squares of the distances, is true for all the celestial bodies. Now, the total action of one celestial body upon another is a resultant of elementary actions, and arises from the algebraic sum of them all. Hence it follows that every element of matter, when acting from certain distances, obeys the Newtonian law; for it is evident, from the theory of the composition of forces, that the sum of the elementary actions cannot follow the Newtonian law unless these actions themselves follow it. But if the law is true in the case of astronomical distances, it must be true also in the case of microscopical and molecular distances. For as a primitive element cannot have two laws of action, so neither can it follow at molecular distances any other law than that which it follows at all other distances.