first appeared in the Philosophical Magazine, Sept. 1877, to replace the arbitrarily assumed atom streams of Le Sage and Lord Kelvin by a motion which is exactly analogous to that which belongs to the kinetic theory of gases. In that way the most obscure assumption of Le Sage's theory finds an unforced explanation-namely, how the symmetrical motion of the atoms under the continual changes of their direction produced by their collisions against gross matter, is kept up. : Now it has already been mathematically demonstrated in the case of ordinary gases, that an automatic correction goes on in a system of bodies or particles in free collision, and such a one that the particles are forced to move equally in all directions and this is the absolutely necessary condition for equal pressure in all directions. The rate of establishment of this automatic correction, which is chiefly brought about by the oblique encounters, has, in fact, been calculated mathematically by Prof. Ludwig Boltzmann for ordinary gases. This adjustment (or correction) is in fact of such a stable character, that if the motion of the gas particles were artificially disturbed, the particles would of themselves equalize the motion again, so that an equal number of particles are moving in any two opposite directions. The motion can also be described so, that if we think of any small point situated anywhere in space, the atoms are at every instant flying towards and from this point, exactly as if it were a luminous point. Hence it follows that when a system of atoms is left to itself, it will, by the principles of dynamics, automatically adjust the character of its motion in such a way that this motion is adapted to produce the gravitation effects. The motion of streams of atoms equally at all angles, which Le Sage gave forth as an arbitrary postulate, is attainable in a gas without any postulate. Instead of streams, each of which for itself maintains a constant direction of motion, and which cease to flow after a long epoch of time, we have a permanent motion of atoms correcting itself in a self-acting manner; and which fulfils the wished-for object. So, therefore, we have succeeded, by starting from a very simple and thoroughly natural foundation, in establishing all those conditions which Le Sage needs for his theory. Nevertheless there are certain assumptions concerning quantitative relations to be added. In the first place, the mean length of path of an æther atom must be assumed to be exceedingly great. If, namely, the same were small in proportion to the distance between two influencing masses, then in the intervening space between these masses, by the collisions of the æther atoms among themselves, the normal proportionality between translatory and internal motion of the atoms would be nearly restored (by encounters), and therefore the mutual shelter of the two masses would nearly be nullified. The range of gravitation (its sphere of action) is therefore conditioned by the mean length of path of the atoms, and this may be regarded as an interesting deduction from the theory. Accordingly, on the assumption that the mean distances of the stars (excepting, of course, the relatively approximated double stars) are large in proportion to the mean length of path of the atoms, the inference would follow that the stars do not gravitate towards each other-and apparently in that way the universe would rather gain than lose in stability. One sees then that the mean length of path of the ather atoms must be great in comparison with those distances across which Newton's law has been demonstrated to apply with exactness. In an article in the Encyc. Brit. 1875 (or Scientific Papers, vol. ii. p. 476) Maxwell raises the objection that by the atomic encounters gross matter would be raised to a white heat; he grounds this inference on the theorem that for thermal equilibrium between atoms or molecules the mean energy of translatory motion must be equal. Now the pressure (to take some symbol) is equal to the product of the mean energy of translatory motion L of an atom into the number N of atoms contained in the unit of volume. If, therefore, the mean energy of translatory motion of an æther atom be equal to that of a molecule of gross matter, which we can calculate in the case of ordinary gases, then N for the æther must have an enormous value, in order to be able to account for the gravitation pressure. Now Maxwell says: we are tolerably certain that N for the æther is small compared with the value of N for gross matter. From this he concludes that in order to explain the gravitation pressure, it is necessary to assume Lenormously great. And according to the theorem that for thermal equilibrium L must be the same for all atoms (or molecules), it would follow that L also for the molecules of gross matter must finally assume a value which is much greater than that which we find in the case of gases. In other words, that all gross matter must be raised to a white heat by the collisions of the æther atoms. But, independently of the fact that the above-named theorem, relating to thermal equilibrium, for molecules or atoms of very different size is still contested, it seems to me that no cogent reason exists for the assumption that N is smaller for the æther than for gross matter. One can, in fact, imagine the æther atoms as small as one pleases; then an enormous number of them can exist in the unit of volume combined with an enormously great length of path. In general, in putting forward a theory of this kind, we should see no improbability in the assumption of either a very great or a very small number. Our objection to uncommonly great or uncommonly small numbers rests in fact upon custom, and regularly disappears as soon as the theory in question has further introduced itself. There exists in space field enough, when necessary, for finer material, as our conceptions are not limited in the direction of smallness, and the smaller the particles, the quicker is their natural speed of motion, and the more intense the enclosed store of concealed energy also the whole arrangement becomes all the less appreciable by our senses. The effects-called gravitational effects-on the other hand, do not escape detection by our senses; and reasoning from these effects, we trace and infer the invisible causes which lie at the basis of these effects. Evidently there exists just as little an obstacle in space to smallness of size as to any given velocity of motion, and there are reasons for supposing that gravity must propagate itself with great velocity. Precisely because the normal velocity of the atoms is great, the material concerned in producing gravity can be very limited in quantity, and notwithstanding that exert a very considerable pressure. The atoms are therefore to be assumed very small, almost points, the condition adapted for a great length of path. The analogy of this gravitation mechanism (at least in principle) with the generally assumed structure of our atmosphere, may be regarded as a recommendation to the theory. A further objection of Maxwell's, that according to this theory the action of gravity could only be kept up by an enormous expenditure of external work little short of ruinous, applies in fact to the theory of Le Sage in the form presented by Lord Kelvin; also to the theories of Isenkrahe and Bock considered further on; not, however, to the theory set forth by the present writer, because, according to this latter theory, the maintenance of the motion of the æther atoms demands just as little an expenditure of energy as the maintenance of the motion of the molecules of a gas in the ordinary gas theory. Moreover, the "shelter" of one mass by another is explained without any absorption of energy. The large store of energy contained in the æther atoms is moreover of use for the explanation of the most varied natural phenomena; and it may be observed that the intervention of a medium is wanted in other respects, for instance for the elucidation of magnetic and electric phenomena. It may be mentioned, further, that the explanation of gravitation carries with it the great advantage of rendering superfluous the idea of the existence of two (inherently different) kinds of matter, "ponderable" and "imponderable." The smaller atoms in space do not gravitate, only because the mechanism of gravitation cannot itself be subject to the conditions for producing gravitation. So, therefore, disappear the almost contradictory properties, "ponderable" and "im ponderable," which have been arbitrarily attributed to matter: and we have therefore no reason for believing that the atoms diffused in space differ essentially from gross molecules, excepting in their dimensions. To the abandonment of the idea of two inherently different kinds of matter, the abandonment of two supposed different kinds of energy is analogousviz., energy with motion, and energy without motion. Accordingly there would remain only one kind of energy, namely, that which a moving body possesses. Another important quantitative relation is so conditioned that the "shelter" is evidently proportional to the surface exposed to the moving atoms; the gravitational effect, on the other hand, is proportional to the mass, as experiment shows. This result can only be achieved by supposing gross matter to possess a very porous structure. In that way, the gross molecules inside a body are reached or affected by the penetrating æther atoms almost with the same facility as the external molecules of the body. If we assume that the quantity of material contained in the substance of any molecule is very small compared with the vacant space contained in that same molecule, and if one does not suppose any superfluous material in the structure of the molecule; the proportionality existing between gravitation and mass can be satisfied as closely as observation requires. Some Remarks on Crystal Structure. Even Le Sage recognized that for the elucidation of the gravitational effects the assumption of a porous or open structure in matter is necessary. Lord Kelvin draws a curious inference from this. In the Philosophical Magazine, May 1873, postscript p. 331, Lord Kelvin supposes that it might be probable that bi-axial crystals would not be penetrable with equal facility in all directions by the æther atoms. If that were so, such crystals would possess a (even if very small) difference of weight, according as the one or the other axis is vertical. Have, however, sufficiently delicate experiments been made on this point? A contribution published by me in the Philosophical Magazine for April 1880 on crystalline structure might be mentioned here. I have tried to define further this open structure, so that it appears to be well adapted for the explanation of cohesion, adhesion, and chemical affinity. One knows how the cells of bees are formed by pressure, and how by pressure elastic spheres may be converted into angular, such as hexagonal-shaped, bodies. As remarked, the gravitation theory (and many independent facts) demand that the molecules of bodies shall possess an open structure; which also satisfies the conditions of lightness and economy of material. As crystals exist, it is sometimes supposed that the molecules of bodies (whose open structure is often illustrated by cubes and other figures formed of wire) themselves represent the shapes of the crystals. We do not, however, need to assume that the molecules possess exactly such shapes, because if the separate molecules themselves possessed even a rounded structure, they must be pressed into angular forms as soon as two or more of them were pressed together by impacts of the æther atoms. Let us take for illustration the simplest open structure, viz. rings; although it is not thereby implied that this is the sole groundform of the molecules. Elastic molecules of any very open structure of three dimensions would probably give a greater stability to the crystal mass formed out of them. Simple elastic rings can then by pressure of their boundaries against each other (as caused by the flying of very minute Fig. 1. æther atoms through the structure) conceivably be changed into hexagonal, square figures, &c. Fig. 1 may serve to |