Body and ether atoms probably repel one another at molecular distances. It used to be assumed that they attracted one another at the ordinary molecular distances, and that this attraction was only converted into repulsion in the most immediate vicinity; this supposition is also still the common one in the elementary manuals. Up to a certain point, the phenomena are equally well explained by either of the hypotheses; but since, for the sake of calculation, a decision must be made in favour of one, attraction was accidentally chosen. Wiener has shown (comp. Poggendorff’s “Amalen,” vol. cxviii. p. 79, and Wiener, “Die Grundzüge der Weltordnung,” first book) that the hypothesis of repulsion offers essential advantages for the explanation of the fluid state of aggregation, and that this generally agrees better with our other physical views. There is, according to this supposition, not as in Redtenbacher’s “System of Dynamids,” a thick envelope of ether-atoms about every material molecule, but, on the contrary, the ether is thinnest in the immediate neighbourhood of the corporeal molecules, accordingly thinner within the body than in empty space, because the densely packed corporeal molecules partially repel the ether. As we shall see later on that at all events attraction takes place at greater distances between body and ether atoms, the difference of the two opposed views in strictness only consists of a divergence in respect of the magnitude of that distance where attraction is converted into repulsion; and, moreover, according to both views, this distance must be so small that it must be designated molecular distance.
The atomic theory, in the present phase of its development, explains in a surprising way the laws of heat and the different states of aggregation induced by changes of heat (see Wiener, “Grundzüge der Weltordnung,” first book; and for a more mathematical treatment, Ch. Briot, “Lehrbuch der mechanischen Wärmetheorie”). It has the advantage of representing all the many so-called forces of matter, as gravitation, elasticity, heat, galvanism, chemistry, &c., as manifestations of molecular and atomic forces—i.e., that one also actually sees and calculates the evolution of the one from the other,—whereas that Dynamism, which, like the Kantian, will know nothing of atoms and atomic forces, only merely asserts the origin of the higher material forces from attraction and repulsion, but cannot in the least say how it comes to pass.—
There still remains one material force to be mentioned, vis inertiœ, of which Atomism has hitherto wrongly denied that it comes under the conception of force, or which it has treated as an additional force, whereas it might have already learnt from Kant (“New System of Best and Motion,” comp. Kant’s Werke, vol. v. pp. 282–284, 287–289, and 409–417) what vis inertiœ is, namely, that it depends simply and entirely on the reciprocity or relativity of movement, which had been previously clearly stated by Leibniz (Mathemat. Werke, vi. p. 252). To wit, if one imagines an atom alone in space, the notion of rest or motion cannot at all apply to the same, because it has no definite place in space; thus also cannot change this place. There is, accordingly, no absolute, but only relative, rest and motion. It follows from that, that one has no more right to say, A moves towards B, than B moves towards A; the ball moves towards the target, than the target moves towards the ball; that thus the resistance which the target opposes to the ball is not so much a resistance of the resting as of the moved target, or its vis viva. What here in the case of impact immediately strikes the eye takes place again in pushing and pulling, only as an integration of infinitely numerous single moments of repulsion or attraction of atoms and molecules. In both cases the resistance of the vis inertiœ to be overcome depends on the reciprocity of attraction and repulsion and the relativity of motion.
To explain Inertia we thus, in fact, need, notwithstanding that it itself acts as an opposing force, no new force; we can get along perfectly well with the attraction and repulsion of corporeal and ethereal atoms.—Let us now see how, on closer inspection, the principles previously adduced assume of themselves a simpler form.—
If we imagine two corporeal atoms, A and B, they would even then still move towards one another if only A possessed attractive power; for in that A attracts the atom B, it necessarily, on account of the relativity of motion, just as much moves towards B as it draws B towards itself. The same holds good, however, for B. Since now both A and also B possess attraction, each of them produces the mutual approximation, thus their actual attraction will be the sum of their individual forces. The same holds good for the repulsion of etheratoms. But now curiously one and the same corporeal atom is said to possess two opposite forces, namely, energy of attraction for corporeal atoms, and repulsive force for ether-atoms. An ether-atom has thus either a corresponding special repulsive force for ether-atoms, and a special repulsive force for corporeal atoms; or, however, its repulsive force is equally great for corporeal and ether atoms, i.e., one and the same. The latter supposition has nothing against it; it will therefore, as the simpler, in any case deserve the preference, for principia non sunt multiplicanda prœter necessitatem. According to the latter assumption, then, an ether-atom is similarly repellently related to every other atom, no matter what other forces may belong to this atom; i.e., if a corporeal atom meets it, it repels this just as much as an ether-atom, no matter how great the force may be with which the corporeal atom repels the ether-atom, as compared with the repulsive force of an ether-atom. Of course the total mutual repulsion is the sum of the two forces. But if the magnitude of the repellent force of the corporeal atom is indifferent with regard to the repulsive force of the ether-atom, it must also be indifferent to it if this force becomes = 0, or if it becomes negative, i.e., attractive, always supposing that the total repulsion of the two is the sum of the single forces. In the latter case the total result would remain repulsion, as long as the repulsive force of the ether-atom is greater than the attractive force of the corporeal atom; in the converse case it would be attraction. But herewith we at once get rid of the unnatural assumption of two mutually contradictory forces in this corporeal atom; for the repulsion between ethereal and corporeal atom remains as such for all small distances, when the repulsion of the former is stronger than the attraction of the latter, and the body-atom is similarly related to every other atom by attraction, just as the ether-atom is repellently related to every other atom in the same way. That, however, in fact, ethereal and corporeal atoms do not repel one another at all, but only at smaller, distances, seems to me evidently to result from the following: The material system is unconditionally to be regarded as finite, both from à priori considerations and on astronomical grounds.1 The ether, however, must extend into the infinite, if there be no limit, where the attraction of all the corporeal atoms prevails over the repulsion of all the ether atoms; a rotation of the system about one or more axes (so far as such an one is at all conceivable under the supposition of the relativity of motion) would only strengthen the continual efflux of the ether-atoms by centrifugal force; and even on the inadmissible assumption of an infinite number of ether-atoms to a finite number of corporeal atoms, the constant efflux of ether-atoms in infinite space would induce a continuously increasing rarefaction of the ether in the world-system, for which there is nothing to be said.
Accordingly, if we are compelled by the finiteness of the material world-system to assume a definite finite distance, where the repulsion of the ether-atom from the corporeal atom is equal to the attraction of the corporeal atom to the ether-atom, we immediately get what we want, namely, that at less distances repulsion must prevail over attraction, since the repulsion of the ether-atom diminishes much more quickly with diminution of the distance than the attraction of the corporeal atom. However, then, one may regard the matter, in every respect the simplest assumption most recommends itself, that the corporeal atom has only attractive force, the ether-atom only force of repulsion, which is uniformly manifested towards both kinds of atoms. At a particular distance (which manifestly must be determined by the magnitude of the intended world) they are equal to one another; the different law of their change with the distance causes at greate
r distances attraction, at lesser repulsion increasingly to predominate. At the distances at which they exist between the molecules of a body, repulsion probably immensely preponderates. This is, however, also necessary if, according to the assumption of Wiener, the ether-atoms are distributed within the body far more sparsely than in empty space, and nevertheless must suffice to hold in equilibrium the mutual attraction of the so thickly packed corporeal molecules.
Since, if one steers clear of the contradiction of an already existing, i.e., completed infinity, the number of the ether-atoms, as that of the corporeal atoms, must be finite, we have no ground at all to assume that the number of both is different; we may, on the contrary, rather hold them to be equal, since what the ether-atoms seem to gain in greater distribution through space the corporeal atoms acquire in density of cohesion. We have then for every body-atom an ether-atom, which are distinguished, apart from the law of their change of force with distance, only by the positive and negative direction of their forces. If one conceived every corporeal atom and every ethereal atom fused together, all force would suddenly disappear from the world, for their antagonism would have been neutralised. Thus we see here the sundering into a polar dualism to be the principle which produces the material world.
Let us further inquire what we are to understand by the mass of a body. We chiefly measure mass by weight. As soon, however, as science reached the assumption of the ether, which, because it has no attraction, can also have no weight, it was necessary to take something else instead of weight as the measure of mass, and, moreover, somewhat that is common to ether and body; as such, only vis inertiœ is offered. But now, even if we can thus measure mass, we still get no notion of mass unless we are content to grasp it as the unknown substratum of equal persistent forces. But assuredly no one is really satisfied with this. Physical science explains mass to be the product of volume and density, and this certainly leads to the mode in which all unprejudiced thinking conceives the notion of mass, provided that, in the explanation of density, one avoids the circle and does not again employ the notion of mass. Then is density only to be apprehended as the keeping asunder of equivalent particles. If, now, the product of volume and density remain unchanged, it is clear that this is only possible by the number of equivalent particles remaining unchanged. We may then define mass absolutely as the number of equivalent particles, supposing that in all things to be compared we continue the division until we everywhere come to equivalent particles. It is immediately evident that only the original atoms answer this requirement; but this they really do: even the ethereal and corporeal atoms are to be regarded as equivalent, since each ether-atom just as much repels each body-atom as each ether-atom, and inversely; consequently the reciprocity of their forces, i.e., their vis inertiœ, is equal. We have, then, now to define the mass of a thing as the number of its atoms, and herewith furnish the only possible strictly scientific expression for that which each one more or less clearly conceives by the word mass. It follows, however, directly from this, that there is no longer any sense in talking of the mass of an atom, for one would then have to imagine the same again decomposed into equivalent parts, and thereby would get no farther than one already is. One may possibly speak of the mass of a molecule, for this just consists of atoms; one may also say, by way of comparison, a corporeal molecule is of very much greater mass than an ether-atom; but the masses of two atoms cannot be compared, for each of them is the mass-unit. Further, it would be conceivable that, without interposed ether-atoms, n body-atoms should unite into a single one, so as to become inseparable; then an ether-atom would repel each of these united atoms with a single, the compound with n-fold force, and the compound would certainly have the mass n; but just on that account would it be erroneous to call it One atom with n-fold mass; there always remains, so long as the atoms are conceived as material, impenetrable balls, a complex of n atoms.—For the rest, we have no occasion at all to believe in the real existence of such direct fusions of body-atoms, for it is to be assumed that the body-atoms in the molecule of a so-called chemical element are just as much kept asunder by ether-atoms as the molecules of the chemical elements in the molecule of their chemical compound, which last is proved by this, that they may be again separated by ether-vibrations (heat, galvanism, &c.) With respect to the great differences of the atomic weights, we must also imagine the number of the body-atoms united in an elementary molecule to be very great, in conformity with the fact that often hundreds of elementary molecules are united in the molecule of a higher organic combination.
The result of all this is, that the atom is the unit of which every mass is composed, just as all numbers are compounds of One; that it is therefore just as sensible to ask what is the mass of an atom as what is the number of unity.—
We come now to the last and most difficult question: Is the atom anything else but force? has the atom substance, and what are we to understand by this term?—Let us recall the way in which we arrived at the atom. As children, we knock our heads and feel pain; we touch things, and get visual and other impressions from them. For these instinctively localised projected perceptions we just as instinctively suppose causes which we call things. We suppose things outside us which act upon us, but especially that against which we push outside we call matter or substance. Science does not stop at this crude, instinctively sensuous, and practically sufficing hypothesis, but pursues the causes of our perceptions farther, and examines them more carefully. It shows us that visual perceptions are excited by ethereal vibrations, auditory perceptions by aerial vibrations, olfactory and gustatory perceptions by chemical vibrations in our sense-organs; that thus all these perceptions by no means concern a matter, but a motion, for whose explanation it must again suppose forces, which in the last resort turn out to be manifestations of combined molecular and atomic forces. It shows us further that the foundation of all our tactile perceptions, the so-called impenetrability of matter, or the resistance which it opposes to foreign bodies in attempting to approach beyond certain limits, may be the result of the repulsion of the ether-atoms, which at infinitely small distances become infinitely greater than the attractive force of the corporeal atoms; that, however, a direct contact of the atoms, therefore an impenetrability, not as consequence of force, but inhering in matter as such, nowhere occurs at all. All the explanations which physical science gives or attempts to give rest on forces; substance or matter remains thereby, at the most, a spectre idly lurking in the background, which, however, is always only able to assert itself at obscure places, where the light of knowledge has not yet penetrated; the further knowledge, i.e., the explanation of phenomena, spreads its light, the more in the course of history does matter, which in the naïve sensuous intuition still occupies the whole outer space of perception, withdraw into the background.
Never, however, as far as physical science reaches, or will reach, can it require anything else than forces for its explanation. On the contrary, where, at the present day, it wants the word substance, it understands thereby, as by matter, only a system of atomic forces, a dynamic system, and only employs the words substance and matter as indispensable summary signs or formulæ for these systems of forces.
As, now, scientific hypothesis should never extend farther than the need of explanation requires, but the concept Matter serves and can serve no scientific need of explanation, it follows from this that a concept Matter which means anything else than a system of forces has no warrant and no place in physical science, since it has indeed itself proved all that which sensuous apprehension calls effects of matter to be effects of forces.
Undoubtedly nothing is more difficult than to free ourselves from the immediate ideas of sense, which we have imbibed, as it were, with our mother’s milk, which have been instinctively laid hold of as first crude but practically sufficient hypotheses, and which by the habit of a lifetime have become a part of ourselves. There is need of industry, tranquillity, clearness, and force of thought to perceive the prejudices of sense and other prej
udices of thought as such; still more courage does it require to break for good and all with that which has been once surmounted in all its consequences; but even when one has done all this, there is still required an almost superhuman energy of intelligence and character never again to be prejudiced, or at least secretly influenced, by what has been absolutely discredited; for there is no task more difficult than this, to conquer for ourselves only a full, negative freedom of thought. Precisely because the prejudices springing from sense are not conscious conclusions of the understanding, but instinctive, practically sufficing suggestions, are they so difficult to be destroyed and set aside by conscious thought. One may say to oneself a thousand times that the moon at the horizon has the same angular magnitude, has the same apparent size, as high up in the sky; that it is an error of the understanding to hold it to look smaller up in the sky than down at the level—the same error which does not allow the vault of heaven to appear as hemisphere, but as flattened spheroid—all that cannot bring a single individual to see the moon in both cases as of equal magnitude, just because, in spite of better conscious knowledge, the instinctive assumption asserts itself.
Such an instinctive prejudice springing from sensibility is Matter. No natural philosopher has, in his science, anything to do with matter, except in so far as he decomposes it into forces, whereby accordingly the apparent material effects turn out energies, i.e., matter is more and more resolved into force. Thus, even at the present day, few natural philosophers will be found who would grant the final consequence of their own science, that matter is nothing but a system of forces; and the reason of this lies simply in sensuous prejudice. One forgets that we indeed just as little directly perceive matter as atoms, but only its pressure, impact, vibrations, &c.; that this matter is indeed also merely a hypothesis, which must justify itself before the tribunal of physical science; but this justification is not merely never forthcoming, but instead of it after every inquiry instituted in any quarter whatsoever evaporates into forces. This is forgotten because one accidentally knocks one’s elbow, and instinctive sensibility shrieks at once “Matter” into the reasoning.—If, now, we seriously attack such a prejudice, it tries to maintain itself with sophisms; the natural philosopher forgets the rules of his method, and even advances à priori reasons in order only to save his favourite prejudice.
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