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.

[1]Meeting of the British Association, Montreal. 1884. Section A. Mathematical and Physical science. Opening Address by Prof. Sir William Thomson, M.A., LL.D., D.C.L., F.R.SS.L. and E., F.R.A.S., President of the Section.[2]"Preuve de la supposition que j'ay faite: Que la matiere subtile ou etheree est necessairement composee de PETITS TOURBILLONS; et qu'ils sont les causes naturelles de tous les changements qui arrivent a la matiere; ce que je confirme par i'explication des effets les plus generaux de la Physique, tels que sont la durete des corps, leur fluidite, leur pesanteur, legerete, la lumiere et la refraction et reflexion de ses rayons." - Malebranche, "Recherche de la Verite," 1712.[3]Proc. R.S.E., March 2, 1874, and July 5, 1875.[4]On the other hand, in liquids, on account of the crowdedness of the molecules, the diffusion of heat must be chiefly by interchange of energies between the molecules, and should be, as experiment proves it is, enormously more rapid than the diffusion of the molecules themselves, and this again ought to be much less rapid than either the material or thermal diffusivities of gases.

Thus the diffusivity of common salt through water was found by Fick to be as small as 0.0000112 square centimeter per second; nearly 200 times as great as this is the diffusivity of heat through water, which was found by J.T. Bottomley to be about 0.002 square centimeter per second. The material diffusivities of gases, according to Loschmidt's experiments, range from 0.98 (the interdiffusivity of carbonic acid and nitrous oxide) to 0.642 (the interdiffusivity of carbonic oxide and hydrogen), while the thermal diffusivities of gases, calculated according to Clausius' and Maxwell's kinetic theory of gases, are 0.089 for carbonic acid, 0.16 for common air of other gases of nearly the same density, and 1.12 for hydrogen (all, both material and thermal, being reckoned in square centimeters per second).[5]Republished in Sir W. Thomson's "Mathematical and Physical Papers," vol. i., article xlix., p. 381.[6]That this is a mere hypothesis has been scarcely remarked by the founders themselves, nor by almost any writer on the kinetic theory of gases.

No one has yet examined the question, What is the condition as regards average distribution of kinetic energy, which is ultimately fulfilled by two portions of gaseous matter, separated by a thin elastic septum which absolutely prevents interdiffusion of matter, while it allows interchange of kinetic energy by collisions against itself? Indeed, I do not know but, that the present is the very first statement which has ever been published of this condition of the problem of equal temperatures between two gaseous masses.[7]Paper on "Vortex Atoms," Proc. R.S.E. February. 1867: abstract of a lecture before the Royal Institution of Great Britain, March 4, 1881, on "Elasticity Viewed as possibly a Mode of Motion"; Thomson and Tait's "Natural Philosophy," second edition, part 1, §§ 345 viii. to 345 xxxvii.; "On Oscillation and Waves in an Adynamic Gyrostatic System" (title only), Proc. R.S.E. March, 1883.[8]In Fig. 1 the two hooked rods seen projecting from the sphere are connected by an elastic coach-spring. In Fig. 2 the hooked rods are connected one to each of two opposite corners of a four-sided jointed frame, each member of which carries a gyrostat so that the axis of rotation of the fly-wheel is in the axis of the member of the frame which bears it.

Each of the hooked rods in Fig. 2 is connected to the framework through a swivel joint, so that the whole gyrostatic framework may be rotated about the axis of the hooked rods in order to annul the moment of momentum of the framework about this axis due to rotation of the fly-wheels in the gyrostat.[9]The integral of tangential component velocity all round any closed curve, passing once through the aperture, is defined as the "cyclic-constant" or the "circulation" ("Vortex Motion," § 60 (a), Trans. R.S.E., April 29, 1867). It has the same value for all closed curves passing just once through the aperture, and it remains constant through all time, whether the solid body be in motion or at rest.[10]According to this view, there is no precise distance, or definite condition respecting 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 convenient, however, in the kinetic theory of gases, to adopt arbitrarily a precise definition 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 (one one-hundredth, for instance) of the distance between them.[11]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.[12]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."