364
THE
RADIATION
PROBLEM
[30]
[31]
statistical
probability of
the individual
states
Av
of
an
isolated
system.
A
theory
yielding
values for the
probability of
a
state
that differ
from
those
obtained
in
this
way
must obviously be
rejected.
A
consideration of
the
kind indicated for
determining
certain statisti-
cal
properties
of heat radiation enclosed
in
a
cavity
had already been
carried
out
by me
in
an
earlier
paper,1
in
which
I first
presented the
theory
of
light
quanta.
However,
since
at
that
time I
started
out
from Wien's
radiation
formula, which
is valid
only
in
the
limit (for small values of
v/T),
I
shall
present
here
a
similar consideration
which
provides
a
simple
interpretation of
the
content of
Planck's radiation formula.
Let
V
and
v
be
two
interconnected
spaces
bounded
by
diffusely,
com-
pletely
reflecting walls.
Let
a
heat radiation with the
frequency
range
dv
be
enclosed
in
these
spaces. H
shall
be
the radiation
energy
existing
instantaneously in
V,
and
n
the radiation
energy
existing instantaneously
in
v.
After
some
time the
proportion
H0:
n0
=
V :
v
will then hold
permanently,
within
some
approximation. At
an
arbitrarily
chosen
instant
of
time,
n
will deviate
from
n0
according
to
a
statistical
law
that is
obtained directly
from
the relation
between
S
and
W
if
one changes
over
to
the differentials,
N
1
R
S
dW
=
const.
e dn
.
If
E
and
a
denote the
entropy
of the radiation
in
the
two
respective
spaces,
and
if
we
set
n
=
n0 +
e, we
have
and
dn
=
de
S S
+
(T Xq
+
(TQ
+
-
Because
tf(S
+
cr)
Je
e +
o
d(E
+
a)
Je
o
1
-
0
,
/2(£
+
cr)
Je1
• *
o
[29]
1Ann.
d.
Phys.
17
(1905): 132-148.