generally accepted theory of statistical equilibrium involving the so
called "law of equipartition," enunciated first for gases and extended to
liquids and solids.

In the first place the kinetic theory fixes the number of degrees of
freedom of each gaseous molecule, which would be three for argon, for
instance, and five for oxygen. But what prevents either from having the
six degrees to which ordinary mechanical theory entitles it? Furthermore,
the oxygen spectrum has more than five lines, and the molecule must
therefore vibrate in more than five modes. "Why," asks Poincaré, "do
certain degrees of freedom appear to play no part here; why are they, so
to speak, 'ankylosed'?" Again, suppose a system in statistical
equilibrium, each part gaining on an average, in a short time, exactly as
much as it loses. If the system consists of molecules and ether, as the
former have a finite number of degrees of freedom and the latter an
infinite number, the unmodified law of equipartition would require that
the ether should finally appropriate all energy, leaving none of it to the
matter. To escape this conclusion we have Rayleigh's law that the radiated
energy, for a given wave length, is proportional to the absolute
temperature, and for a given temperature is in inverse ratio to the fourth
power of the wave-length. This is found by Planck to be experimentally
unverifiable, the radiation being less for small wave-lengths and low
temperatures, than the law requires.

Still again, the specific heats of solids, instead of being sensibly
constant at all temperatures, are found to diminish rapidly in the low
temperatures now available in liquid air or hydrogen and apparently tend
to disappear at absolute zero. "All takes place," says Poincaré, "as if
these molecules lost some of their degrees of freedom in cooling--as if
some of their articulations froze at the limit."