ro-kinetic 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,[1] 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 rotation 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 into 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 inward,
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 equilibrium. All that I have said
in favor of the model vortex gas composed of perforated solids with fluid
circulations through them holds without modification for the purely
hydro-kinetic model, composed of either Helmholtz cored vortex rings or of
coreless vortices, and we are now troubled with no such difficulty as that
of the impacts between solids. Whether, however, when the vortex theory of
gases is thoroughly worked out, it will or will not be found to fail in a
manner analogous to the failure which I have already pointed out in
connection with the kinetic theory of gases composed of little elastic
solid molecules, I cannot at present undertake to speak with certainty. It
seems to me most probable that the vortex theory cannot fail in any such
way, because all I have been able to find out hitherto regarding the
vibration of vortices,[2] whether cored or coreless, does not seem to imply
the liability of translational or impulsive energies of the individual
vortices becoming lost in energy of smaller and smaller vibrations.

[Footnote 1: 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.]

[Footnote 2: See pap