one another in sharply concave curves round their common center of gravity, they fly asunder again. A careless onlooker might imagine they had repelled one another, and might not notice the difference between what he actually sees and what he would see if the two bodies had been projected with great velocity toward one another, and either colliding and rebounding, or repelling one another into sharply convex continuous curves, fly asunder again. Joule, Clausius, and Maxwell, and no doubt Daniel Bernoulli himself, and I believe every one who has hitherto written or done anything very explicit in the kinetic theory of gases, has taken the mutual action of molecules in collision as repulsive. May it not after all be attractive? This idea has never left my mind since I first read Davy's "Repulsive Motion," about thirty-five years ago, and I never made anything of it, at all events have not done so until to-day (June 16, 1884)--if this can be said to be making anything of it--when, in endeavoring to prepare the present address, I notice that Joule's and my own old experiments[1] on the thermal effect of gases expanding from a high-pressure vessel through a porous plug, proves the less dense gas to have greater intrinsic _potential_ energy than the denser gas, if we assume the ordinary hypothesis regarding the temperature of a gas, according to which two gases are of equal temperatures [2] when the kinetic energies of their constituent molecules are of equal average amounts per molecule. [Footnote 1: Republished in Sir W. Thomson's "Mathematical and Physical Papers," vol. i., article xlix., p. 381. ] [Footnote 2: 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.]