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
elementary domains of probability is reduced and the extent of each is
augmented. The hypothesis of quanta of action consists in supposing that
these domains are all equal and no longer infinitely small but finite and
that for each [double integral]_dpdq_ equals _h_, _h_ being a constant."

Put a little less mathematically, this simply means that as energy equals
action multiplied by frequency, the fact that the quantum of energy is
proportional to the frequency (or inversely to the wave-length as stated
above) is due simply to the fact that the quantum of action is constant--a
real atom. The general effect on our physical conceptions, however, is the
same: we have a purely discontinuous universe--discontinuous not only in
matter but in energy and the flow of time. M. Poincaré thus puts it: "A
physical system is susceptible only of a finite number of distinct states;
it leaps from one of these to the next without passing through any
continuous series of intermediate states."

He notes later:

"The universe, then, leaps suddenly from one state to another; but in the