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 property of the resonators imagined by Planck is therefore precisely that which Wien’s theory requires.  If we are to suppose atoms of energy, therefore, they must be variable atoms.  There are other objections which need not be touched upon here, the whole theory being in a very early stage.  To quote Poincare again: 

“The new conception is seductive from a certain standpoint:  for some time the tendency has been toward atomism.  Matter appears to us as formed of indivisible atoms; electricity is no longer continuous, not infinitely divisible.  It resolves itself into equally-charged electrons; we have also now the magneton, or atom of magnetism.  From this point of view the quanta appear as atoms of energy.  Unfortunately the comparison may not be pushed to the limit; a hydrogen atom is really invariable....