No. 15.

Stability of the Cosmos.

On the Development of Potential Energy.

There can be no doubt that generally, with moving bodies (if we except bodies in orbits), as we descend in the scale of velocity, the numbers of such bodies increase. This is easily shewn to be the case, there are three causes acting together to produce this result. Suppose a particle proceeding outwards from a central mass to the limits of effective attraction, when near the mass its velocity is high, its velocity being high it quickly passes from great attraction; but attraction varies inversely as the square of the distance, therefore, from this cause, at small distances attraction diminishes quickly, and at great distances slowly. Therefore the time a particle occupies any high velocity is incomparably shorter than the time it occupies a low velocity; in fact, taking all the free particles, it is probable that the numbers having any given velocity is about inversely proportionate to the square of the velocity, except at both ends of the series. Thus the number of free particles of gas, which is at extremely low velocity, is doubtless very large indeed; probably fully sufficient for the purpose of rendering bodies capable of absorbing the lowest order of radiation, thus shewing that the dissipation of energy is not a necessary result. There are some extremely interesting speculations as to the state of those substances, whose free particles are below the temparature of liquid or even the solid state. What is this physical state? I shall probably discuss this most interesting question in a future letter. There are many puzzling points about it. Thus then we see that generally small bodies will be moving slowly, and also that the higher the potential of space, or position of least attraction, the slower the particles will generally be moving. I will put this statement in another way. Let us suppose a portion of space which has been drained of matter by gravitation, it is clear that here attraction will be least or potential highest. Therefore particles approaching this space will do more work than in moving in any other direction. They will therefore move more slowly. Again suppose all particles to have a motion without any order, it is evident that in any place where the bodies move slowly, they will tend to accumulate, as going at walking pace past any spot tends to block the road, so that with particles travelling equally in every direction, in those positions in space where they move slowest, they will be in increasing numbers. Thus, although gravitation tends to aggregations, we have in the slower movements of bodies, at high potential, a means of filling the drained parts of space, and a constant tendency to an equilibrium of matter. I have already shown how partial impacts tends to separate large masses into smaller ones, and also how the principles of selective escape—tends in all considerable impacts to render a large number of molecules free from the attractive influence of the general mass, I have also page 16 shewn how, in the case of very partial impacts—of very large bodies—the heat may absolutely dissipate every molecule of the coalesced part, and so convert all the heat into potential energy, so that altogether it appears there is a roughly compensating fiction going on throughout space. Gravity aggregates, velocity divides, gravity drains spaces, slowly travelling bodies tend to fill these spaces. Radiant heat warms the matters of space, gas near zero cools these bodies, and in turn converts this energy into potential energy or available heat. So it is thus possible that the cosmos flows on in an ever varying, ever constant, rhythmic stream, without evidence of a beginning, or promise of an end, infinite and immortal.

Thus ends the series of letters, Since the earlier ones were written, the evidence that has accumulated on many of the points appear to suffice for an absolute demonstration; but I shall wait for discussion before renewing them, when I hope, with greater space, to give more logical proofs of the propositions I have offered.