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.]

Think of the thing thus. Imagine a great multitude of particles inclosed by
a boundary which may be pushed inward in any part all round at pleasure.
Now station an engineer corps of Maxwell's army of sorting demons all round
the inclosure, with orders to push in the boundary diligently everywhere,
when none of the besieged troops are near, and to do nothing when any of
them are seen approaching, and until after they have turned again inward.
The result will be that, with exactly the same sum of kinetic and potential
energies of the same inclosed multitude of particles, the throng has been
caused to be denser. Now Joule's and my own old experiments on the efflux
of air prove that if the crowd be common air, or oxygen, or nitrogen, or
carbonic acid, the temperature is a little higher in the denser than in the