7. Clausius, as is known, has investigated a relation between the mean length of path of the particles of a gas and the diameter of the particles. From this investigation it follows that the mean length of path of the particle of a gas (i.e. the average distance which the particle moves before encountering another particle) increases in proportion as the square of the diameter of the particle diminishes. Thus by making the particle small enough, its mean length of path may be increased to any extent. No objection, evidently, can be made to this, for à priori one size of particle is just as likely as another. This minute size would render it possible for the particle to possess a high velocity without producing thereby disturbance or displacement among the molecules of ordinary matter ; and this high velocity is necessary to accord with the observed facts of gravity. One velocity cannot be said à priori to be more likely than another. We must just be guided by the teaching of facts as to what the velocity is.[1]
8. It is an interesting fact pointed out by Sir William Thomson (Phil. Mag. May 1873) that the distance through which gravity is effective would depend on the distance through which the gravific particles move before being intercepted by collision with each other (which is equivalent to the mean length of path of the particles). By assuming the distance of the stars to be a multiple of the mean length of path of the particles, it would therefore follow that the stars do not gravitate towards each other—this satisfying the condition for the stability of the universe. The assumption of all the bodies of the universe gravitating towards each other is evidently quite inconsistent with stability (as already pointed out by Professor Challis). All that we require to admit is that the effects of gravity hold through as great distances as we have observed them.
9. The distance through which gravity has been observed to act is well known to be but an infinitesimal fraction of the distance of the stars. It may therefore well be that the mean length of path of the particles of the medium producing gravity may be but an infinitesimal fraction of this distance. The column of the gravific medium intercepted between two stars would therefore on the whole be at rest, just as a column of gas is at rest between two bodies a visible distance apart (i.e. a distance which is a large multiple of the mean length of path of the particles of gas). Le Sage appears to have assumed that the mean length of path of the gravific particles swept through the universe ; or he assumed that streams of matter came from the depths of space and passed entirely through the visible universe into space beyond.[2]
This [211] assumption cannot but be regarded as fantastic, and, as we observe, is by no means necessary. The mean length of path of the particles, so far from being comparable to the dimensions of the visible universe, may be but an infinitesimal fraction of the distance of two of its primary components. All we require to admit is that the mean length of path of the particles of the medium is at least as great as the very limited range through which gravity has been observed to act ; or, in order to explain all the observed facts, it is sufficient to admit that the universe is immersed in a gas (or medium constituted according to the kinetic theory) the mean length of path of whose particles is so adjusted as to cause the minor or secondary portions of the universe to gravitate towards each other.[3] Under the simple conception of a variation in the diameter of the particles of a medium, the mean length of path of the particles (and with it the range of gravity) is capable of adjustment with precision to any range. It would probably be difficult to imagine any more simple condition as a mechanical means to an end than this.
10. It is a necessary condition to Le Sage's theory (in order [212] that gravity may be sensibly proportional to mass) that the total volume of free space in a substance, in the form of interstices between the molecules or in their structure, must be great compared with the total volume of matter contained in the molecules themselves. Le Sage assumed the molecules of substances to have a sort of open structure in the form of cages with wide interstices. This condition of free interstices would be equally satisfied by assuming the molecules to be small relative to their mean distance, or on the condition of the vortex-ring atom theory, without any necessity for making the above somewhat fantastic assumption of cage-structure.
11. It is necessary to assume that the particles producing gravity are in very close proximity compared with molecules, otherwise the particles would be unable by their motion to produce a perfectly equable pressure upon the molecules of matter. It might be thought that, because the particles of the gravific medium are so close, and the molecules of ordinary matter relatively far apart, therefore the quantity of matter in the form of gravific particles enclosed in a given volume of space must be very great compared with the quantity of ordinary matter that that same volume of space would contain—or, in other words, that there must be a relatively enormous quantity of matter in the form of gravific particles. This by no means follows; for although the gravific particles may be very close, Ihe relative quantity of matter in them may be very small, provided the particles themselves are small. Indeed by simply conceiving an extreme degree of subdivision, the particles pervading a given volume of space may by continued subdivision be conceived to be brought into as close proximity as we please ; and though the space itself is large, the total quantity of matter thus used may be conceived as small as we please. No consequence how minute the size (or mass) of a particle may be, the effect produced by its motion remains as great, provided its velocity be adequately augmented. The minute size is the very condition adapted to a high velocity; and this minute size is at the same time the necessary condition for a long mean path. Thus we may observe that the mechanical conditions of the problem fit into each other. The matter of the gravific medium is in such a finely subdivided state, and its motion so rapid, that its presence necessarily eludes detection. The pressure (termed "gravity") due to the motion of the particles of the gravific medium is no more difficult of realization than the pressure due to the motion of the molecules of air. If the motion of the molecules of air be unrecognized by the senses, how much more must this be the fact with the minute gravific particles; indeed it is difficult to see what mechanical objection can be urged against this realization of the problem, which is extremely simple.
12. The theory of "action at a distance" being rejected, which is necessary in order to explain the facts at all, the effects of gravity can in principle be referred to only two conceivable causes. The tendency of two molecules of matter to approach each other can be referred (1) to a motion possessed by the molecules themselves disturbing the equilibrium of pressure of the medium between them ; (2) to a motion possessed by the medium itself (in the form of streams or currents) acting upon the molecules. The first of these two conditions appears to be inadmissible, from the fact that we cannot interfere with or modify gravity at will, whereas we can very readily interfere with or modify the motion of the molecules of matter (as by adding or subtracting heat, for example). It therefore would appear that gravity must be due to some motion that we cannot interfere with, i.e. to a motion in the external medium which we cannot handle or which is beyond our control. Only one conclusion appears therefore to be possible here ; and therefore it would seem that the theory of Le Sage can scarcely be regarded as a mere hypothesis, but rather as an irresistible deduction which is forced upon us in the absence of any other conceivable inference. Certainly, if simplicity be a recommendation, the theory needs no recommendation on that ground.
London, July 1877.
1 ↑ I have shown (Phil. Mag. June 1877) that a physical relation exists between the velocity of the particles of a medium constituted according to the kinetic theory and the velocity of propagation of a wave in the medium. Professor Maxwell has calculated (as given in postscript to the paper) the numerical value of this relation at . Thus it appears that if the velocity of propagation of a wave in any medium constituted according to the kinetic theory can be measured, then the velocity of the particles of the medium is given by dividing this velocity by . So, for example, the velocity of the molecules of air is given by dividing the » velocity of sound in air by ; so of other gases. Thus it appears that the velocity of a wave in any medium constituted according to the kinetic theory (such as the velocity of a wave of sound in air) is solely dependent on and proportional to the velocity of the particles of the medium ; and this velocity of the wave is independent of the density or pressure of the medium, or of any thing else excepting the velocity of its particles.