It is not true, therefore, that the weight is not “the presentation of an absolute substantive entity,” as the author pretends. Weight implies mass and gravitation, and presents the one as subject to the other. Now, the mass is an “absolute substantive entity,” as we have shown. Nor is it true that weight is “the mere expression of a relation between two bodies mutually attracting each other,” as the author imagines. The pound of carbon is a pound not because of an attraction exercised by the carbon upon the earth, but merely because of the attraction exercised by the earth on the mass of the carbon. Were it otherwise, the mathematical expression of weight should contain, besides the mass of the body weighed and the action of gravity upon it, a third quantity representing the action [pg 789] of the body upon the earth, and the gravitation of the earth towards the body.
The writer proceeds: “Masses find their true and only measure in the action of forces, and the quantitative persistence of the effect of this action is the simple and accurate expression of the fact which is ordinarily described as the indestructibility of matter. It is obvious that this persistence is in no sense explained or accounted for by the atomic theory” (p. 708).
We admit that, owing to our inability to determine the absolute number of primitive elements in a body, we resort to the persistence of the weight in order to ascertain the persistence of a certain quantity of matter in the body. But this does not show that the action of forces is the “only measure” of masses. A mass is a number of material units; its true measure is one of such units, and it is only in order to determine the relative number of such units in different bodies that we have recourse to their weights. It is not the quantity of matter that follows the weight of the body, but it is the weight of the body that follows the quantity of matter; and therefore, although we determine the relative quantities of matter by the relation of their weights, it is not the weight that measures the quantity of matter, but it is the quantity of matter that measures the weight. In other terms, the persistence of the mass is merely known through the persistence of the weight, but the persistence of the weight is itself a consequence of the persistence of the mass. Hence the persistence of the mass is perfectly accounted for by the atomic theory, notwithstanding Mr. Stallo's contrary assertion.
He says: “The hypothesis of ultimate indestructible atoms is not a necessary implication of the persistence of weight, and can at best account for the indestructibility of matter if it can be shown that there is an absolute limit to the compressibility of matter—in other words, that there is an absolutely least volume for every determinate mass” (p. 708). Both parts of this proposition are false. The first is false, because the weight of a body is the result of the gravitation of all its particles; and, therefore, it cannot persist without the persistence of the gravitating particles. The second part also is false, because the persistence of the weight implies the persistence of the mass independently of all considerations concerning a limit of compressibility or an absolute minimum of volume. Hence, whatever the author may say to the contrary, it is quite certain of scientific certainty that there can be, and there is, in all bodies, “an absolute constant of mass.”
Atomic theory.—The writer objects to the atomic theory on the ground that it does not explain impenetrability, and that it misconceives the nature of reality. He begins by remarking that “the proposition, according to which a space occupied by one body cannot be occupied by another, implies the assumption that space is an absolute, self-measuring entity, and the further assumption that there is a least space which a given body will absolutely fill so as to exclude any other body” (p. 709). We think that the proposition implies nothing of the kind. The space occupied by one body cannot naturally be occupied by another, because all bodies are made up of molecules which at very small distances repel one another with actions of greater and greater intensities, thus preventing compenetration, while successfully struggling for the preservation of their own individuality. This the molecules can [pg 790] do, whether space can be filled or not, and whether space is a self-measuring entity or not. Hence the remark of the author has no foundation.
But he continues: “The atomic theory has become next to valueless as an explanation of the impenetrability of matter, since it has been pressed into the service of the undulatory theory of light, heat, etc., and assumed the form in which it is now held by the majority of physicists. According to this form of the theory, the atoms are either mere points, wholly without extension, or their dimensions are infinitely small as compared with the distances between them, whatever be the state of aggregation of the substances into which they enter. In this view, the resistance which a body, i.e., a system of atoms, offers to the intrusion of another body is due not to the rigidity or unchangeability of volume of the individual atoms, but to the relation between the attractive and repulsive forces with which they are supposed to be endowed. There are physicists holding this view, who are of opinion that the atomic constitution of matter is consistent with its compenetrability—among them M. Cauchy, who in his Sept Leçons de physique générale (ed. Moigno, Paris, 1868, p. 38), after defining atoms as material points without extension, uses this language: ‘Thus, this property of matter, which we call impenetrability, is explained when we consider the atoms as material points exerting on each other attractions and repulsions which vary with the distances that separate them.... From this it follows that, if it pleased the Author of nature simply to modify the laws according to which the atoms attract or repel each other, we might instantly see the hardest bodies penetrate each other, the smallest particles of matter occupy immense spaces, or the largest masses reduce themselves to the smallest volumes, the entire universe concentrating itself, as it were, in a single point’ ” (p. 710).
We think that the author's notion of the form in which the atomic theory is now held by physicists is not quite correct. The chemical atoms are now considered as dynamical systems of material points, so that the atomic theory is now scarcely distinguishable from the molecular theory. That such a theory “has become next to valueless as an explanation of the impenetrability of matter” is not true. Of course two primitive elements of matter, if attractive, would, according to the theory, as we understand it, pass through one another; as nothing can oppose their progress except repulsion, which is not to be thought of in the case of attractive elements. But the case is different with molecules; for every molecule of any special substance contains a number of repulsive elements, and possesses a repulsive envelope[182] which resists most effectually all attempt at compenetration on the part of other molecules. Hence the impenetrability of bodies (not of matter, as the author says) is a simple result of the molecular constitution of bodies, as explained in the atomic theory of the modern chemists.
That the resistance which a body offers to the intrusion of another body is due “not to the rigidity or unchangeability of volume of individual atoms, but to the relation between the attractive and repulsive forces with which they are supposed to be endowed,” is an obvious truth. We do not see by what kind of reasoning the author can infer from it [pg 791] that “the atomic theory has become next to valueless as an explanation of impenetrability.” We rather maintain that the theory is correct, and that no other theory has yet been found which explains impenetrability without assuming much that philosophy condemns. As to M. Cauchy's views, we remark that, when he defines atoms as “material points without extension,” he does not speak of the chemical atoms, or equivalents, but of the primitive elements of which such atoms or equivalents are composed.
The author says: “The assumption of atoms of different specific gravities proves to be not only futile, but absurd. Its manifest theoretical ineptitude is found to mask the most fatal inconsistencies. According to the mechanical conception which underlies the whole atomic hypothesis, differences of weight are differences of density; and differences of density are differences of distance between the particles contained in a given space. Now, in the atom there is no multiplicity of particles and no void space; hence differences of density or weight are impossible in the case of atoms” (p. 715).
This conclusion would be quite inevitable, if it were true that the atom of the chemists contains no multiplicity of particles and no void space; but the truth is that chemical atoms are nothing but equivalents, or molecules—that is, dynamical systems of material points intercepting void space. Hence the author's argument has no foundation. The very fact that men of science unanimously agree in attributing to different atoms a different weight, should have warned Mr. Stallo that the word “atom” could not be considered by them as a simple material point.