TRANSACTIONS OF SECTION A. 621 



vibrations, of elastic solids, and the transmission of waves like those of light 

 through an extended quasi-elastic solid medium. But unfortunately for this idea 

 the equilibrium is essentially unstable, both in the case of magnets and, not- 

 withstanding the fact that the forces are oppositely directed, in the hydrokinetic 

 analogue also, when the several movable bodies (two or any greater number) are 

 so placed relatively as to be in equilibrium. If, however, we connect the perforated 

 bodies with circulation through them in the hydrokinetic system, by jointed rigid 

 connecting links, we may arrange for configurations of stable equilibrium. Tims 

 without fly-wheels, but with fluid circulations through apertures, we may make a 

 model spring balance, or a model luminiferous ether, either without or with the 

 rotational quality corresponding to that of the true luminiferous ether in the 

 magnetic fluid — in short, do all by the perforated solids with circulations through 

 them that we saw we could do by means of linked gyrostats. But something that 

 ■we cannot do by linked gyrostats we can do by the perforated bodies with fluid 

 circulation. "We can make a model gas. The mutual action at a distance, repul- 

 sive or attractive according to the mutual aspect of the two bodies when passing 

 within collisional distance l of one another, suffices to produce the change of direc- 

 tion of motion in collision, which essentially constitutes the foundation of the 

 kinetic theory of gases ; and which, as we have seen before, may as w r ell be due to 

 attraction as to repulsion, so far as we know from any investigation hitherto made 

 in this theory. 



There remains, however, as we have seen before, the difficulty of providing for 

 the case of actual impacts between the solids ; which must be done by giving them 

 massless spring buffers, or, which amounts to the same thing, attributing to them 

 repulsive forces sufficiently powerful at very short distances to absolutely prevent 

 impacts between solid and solid ; unless we adopt the equally repugnant idea of 

 infinitely small perforated solids, with infinitely great fluid circulations through 

 them. "Were it not for this fundamental difficulty, the hydrokinetic model gas 

 would be exceedingly interesting ; and, though we could scarcely adopt it as conceiv- 

 ably a true representation of what gases really are, it might still have some im- 

 portance as a model configuration 0I * solid and liquid matter, by which without 

 elasticity the elasticity of a true gas might be represented. 



But lastly, since the hydrokinetic model gas with perforated solids and fluid 

 circulations through them fails because of the impacts between the solids, let us 

 annul the solids and leave the liquid performing irrotational circulation round 

 vacancy, 2 in the place of the solid cores which we have hitherto supposed; or let 

 us annul the rigidity of the solid cores of the rings, and give them molecular rota- 

 tion according to Helmholtz's theory of vortex motion. For stability the molecular 

 rotation must be such as to give the same velocity at the boundary of the rotational 

 fluid core as that of the irrotationally circulating liquid in contact with it, 

 because, as I have proved, frictional slip between two portions of liquid in 

 contact is inconsistent with stability. There is a further condition, upon which 

 I cannot enter in detail just now, but which may be understood in a general 

 way when I say that it is a condition of either uniform or of increasing 

 molecular rotation from the surface inwards, analogous to the condition that 

 the density of a liquid, resting for example under the influence of gravity, 

 must either be uniform or must be greater below than above for stability of 



1 According to this view there is no precise distance, or definite condition respect- 

 ing the distance, between two molecules at which apparently they come to be in 

 collision, or when receding from one another they cease to be in collision. It is con- 

 venient, however, in the kinetic theory of gases, to adopt arbitrarily a precise defini- 

 tion of collision, according to which two bodies or particles mutually acting at a 

 distance may be said to be in collision when their mutual action exceeds some 

 definite arbitrarily assigned limit, as, for example, when the radius of curvature of 

 the path of either body is less than a stated fraction (1/100, for instance) of the 

 distance between them. 



- Investigations respecting coreless vortices will be found in a paper by the author, 

 « Vibrations of a Columnar Vortex,' Proc. R. S. E. March 1, 1880 ; and a paper by 

 Hicks, recently read before the Royal Society. 



