194
THEORY OF
LIGHT
PRODUCTION
For the
distribution
of
states
of these
resonators to be uniquely
determined in
thermodynamic
equilibrium,
one
has to
assume
that there exists
an
arbitrarily small
number
of freely
moving
molecules besides the
resonators,
which
by
virtue of their collisions with the ions
can
transmit
energy
from
[9]
resonator
to
resonator;
we
will
not
take into
account
these molecules in
our
calculation
of
entropy.
We
could determine
Ev
as a
function
of temperature from
the
Maxwell-
[10]
Boltzmann
distribution
law and would thereby
obtain the invalid radiation
formula (1).
One
arrives
at
the
route
taken
by
Mr.
Planck in the
following
manner.
Let
P1,...Pn be
appropriately chosen state
variables1 that
completely
determine the
state of
a
physical
system
(e.g., in
our
case
the values
x
and
£
of
all the resonators).
At
the absolute
temperature
T,
the
entropy
S
of
this
system
is
represented
by
the
equation2
H
R
[12]
(4) S
= j
+
j
lg
e
dpy..dp
N
H
IT H
n
where
H
denotes the
energy
of the
system
at
temperature
T,
H
denotes the
energy
as
a
function
of
P1,...Pn,
and
the
integral
is
to be
extended
over
all
possible
combinations
of
the values of
P1,...Pn.
If the
system
consists
of
a
very
large
number
of
molecular
structures--
and
the formula
has
meaning
and
validity
only
in this case--then
only
those
[13]
combinations
of values of the
P1...Pn
whose
H
differs
very
little
from
H
contribute
significantly
to
the
value of the
integral
appearing
in
S.3 If
this is taken
into
account,
it is easily
seen
that,
except
for
negligible
quantities,
one can
put
R
f//+A//
[14]
S
= ji
lg
dpv..dpn
,
J ff
[11]
1A.
Einstein,
Ann.
d.
Phys.
11
(1903):
170.
2loc. cit.
§6.
3Follows from
§3
and
§4
loc. cit.