of the matter he notes that the work of Prof. Wilhelm Wien, of Würzburg,
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 Poincaré 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.... The
electrons preserve their individuality amid the most diverse vicissitudes,
is it the same with the atoms of energy? We have, for instance, three
quanta of energy in a resonator whose wave-length is 3; this passes to a
second resonator whose wave-length is 5; it now represents not 3 but 5
quanta, since the quantum of the new resonator is smaller and in the
transformation the number of atoms and the size of each has changed."

If, however, we replace the atom of energy by an "atom of action," these
atoms may be considered equal and invariable. The whole study of
thermodynamic equilibrium has been reduced by the French mathematical
school to a question of probability. "The probability of a continuous
variable is obtained by considering elementary independent domains of
equal probability.... In the classic dynamics we use, to find these