roperty 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.... 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
elementary domains, the theorem that two physical states of which one is
the necessary effect of the other are equally probable. In a physical
system if we represent by _q_ one of the generalized coordinates and by
_p_ the corresponding momentum, according to Liouville's theorem the
domain [double integral]_dpdq_, considered at given instant, is invariable
with respect to the time if _p_ and _q_ vary according to Hamilton's
equations. On the other hand _p_ and _q_ may, at a given instant take all
possible values, independent of each other. Whence it follows that the
elementary domain is infinitely small, of the magnitude _dpdq_.... The new
hypothesis has for its object to restrict the variability of _p_ and _q_
so that these variables will only change by jumps.... Thus the number of
ele