mentary 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. Poincare 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
interval it must remain immovable, and the divers instants during which it
keeps in the same state can no longer be discriminated from one another;
we thus reach a conception of the discontinuous variation of time--the
atom of _time_."

I quote in conclusion, Poincare's final remarks:

"The present state of the question is thus as follows: the old theories,
which hitherto seemed to account for all the known phenomena, have met
with an unexpected obstacle. Seemingly a modification becomes necessary. A
hypothesis has presented itself to M. Planck's mind, but so strange a one
that one is tempted to seek every means of escaping it; these means,
however, have been sought vainly. The new theory, however, raises a host
of difficulties, many of which are real and not simply illusions due to
the indolence of our minds, unwilling to change their modes of thought....

"Is discontinuity to reign through out the physical universe, and is its
triumph definitive? Or rather shall we find that it is but apparent and
hides a series of continuous processes?... To try to give an opinion just
now on these questions would only be to waste ink."

It only remains to call attention again to the fact that this conception
of the discontinuity of energy, the acceptance of which Poincare says
would be "the most profound revolution that natural philosophy has
undergone since Newton" wa