This is the way I feel about it.

"I remain,
"Yours faithfully,
"J.W. GIBBS."

Professor Gibbs's criticism of the illustration of water-mixture is
evidently just. Another might well have been used where the things mixed
are not material--for instance, the value of money deposited in a bank. If
A and B each deposits $100 to C's credit and C then draws $10, there is
evidently no way of determining what part of it came from A and what from
B. The structure of "value", in other words, is perfectly continuous.
Professor Gibbs's objections to an "atomic" theory of the structure of
energy are most interesting. The difficulties that it involves are not
overstated. In 1897 they made it unnecessary, but since that time
considerations have been brought forward, and generally recognized, which
may make it necessary to brave those difficulties.

Planck's theory was suggested by the apparent necessity of modifying the
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 Poincare, "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, instea