d 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 Poincare, "as if
these molecules lost some of their degrees of freedom in cooling--as if
some of their articulations froze at the limit."

Planck attempts to explain these facts by introducing the idea of what he
calls "quanta" of energy. To quote from Poincare's paper:

"How should we picture a radiating body? We know that a Hertz resonator
sends into the ether Hertzian waves that are identical with luminous
waves; an incandescent body must then be regarded as containing a very
great number of tiny resonators. When the body is heated, these resonators
acquire energy, start vibrating and consequently radiate.

"Planck's hypothesis consists in the supposition that each of these
resonators can acquire or lose energy only by abrupt jumps, in such a way
that the store of energy that it possesses must always be a multiple of a
constant quantity, which he calls a 'quantum'--must be composed of a whole
number of quanta. This indivisible unit, this quantum, is not the same for
all resonators; it is in inverse ratio to the wave-length, so that
resonators of short period can take in energy only in large pieces, while
those of long period can absorb or give it out by small bits. What is the
result? Great effort is necessary to agitate a short-period resonator,
since this requires at least a quantity of energy equal to its quantum,
which is great. The chances are, then, that these resonators will keep
quiet, especially if the temperature is low, and it is for this reason
that there is relatively little short-wave radiation in 'black
radiation'... The diminution of specific-heats is explained similarly:
When the temperature falls, a large number of vibrators fall below their
quantum and cease to vibrate, so that the total energy diminishes faster
than the old theories require."

Here we have the germs of an atomic theory of energy. As Poincare now
points out, the trouble is that the quanta are not constant. In his study
of the matter he notes that the work of Prof. Wilhelm Wien, of Wuerzburg,
leads by theory to precisely the conclusion announced by Planck that if we
are to hold to the accepted ideas of statistical equilibrium the energy
can vary only by quanta inversely proportional to wave-length. The
mechanical p