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 papers by the author “On Vortex Motion.” Trans.  R.S.E.  April, 1867, and “Vortex Statics,” Proc.  R.S.E.  December, 1875; also a paper by J.J.  Thomson, B.A., “On the Vibrations of a Vortex Ring,” Trans.  R.S.  December, 1881, and his valuable book on “Vortex Motion.”]

As a step toward kinetic theory of matter, it is certainly most interesting to remark that in the quasi-elasticity, elasticity looking like that of an India-rubber band, which we see in a vibrating smoke-ring launched from an elliptic aperture, or in two smoke-rings which were circular, but which have become deformed from circularity by mutual collision, we have in reality a virtual elasticity in matter devoid of elasticity, and even devoid of rigidity, the virtual elasticity being due to motion, and generated by the generation of motion.

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APPLICATION OF ELECTRICITY TO TRAMWAYS.

By M. HOLROYD SMITH.

Last year, when I had the pleasure of reading a paper before you on my new system of electric tramways, I ventured to express the hope that before twelve months had passed, “to be able to report progress,” and I am happy to say that notwithstanding the wearisome delay and time lost in fruitless negotiations, and the hundred and one difficulties within and without that have beset me, I am able to appear before you again and tell you of advance.