DOC.
56
365
if
one assumes
that
V
is
very
large
compared
with
v,the
second
equation
reduces
to
S
=
const.
+
1/2
"
de2
d2a
. .
0
[32]
If
we
content
ourselves with the first
nonvanishing
term of
the
series,
thus
causing
an
error
that
is the smaller the
greater
the value of
v
compared
with the
cube
of the radiation
wavelength,
we
obtain
i ä
d2r
dW
=
const.
•
e
2
R
Je*
o de [33]
From
this
we
obtain for the
mean
value
E2
of the
square
of the
energy
fluctuation
of the radiation
occurring
in
v
0
2:
N
117k"
[34]
If
the
radiation formula is
known,
we can
calculate
a
from
it.1 If
one
considers
Planck's radiation formula
as an
expression of experience,
one
obtains, after
a
simple
calculation,
f2
-
^
vhl»
+ SOT
C3
•
Id!
M
'
V
[36]
We
have
thus arrived
at
an
easily
interpretable
expression
for the
mean
value
of
the fluctuations
of
the radiation
energy
present
in
v. We
shall
now
show
that the
current
theory
of radiation is
incompatible
with this result.
According
to
the
current
theory, the fluctuations
are
due solely to
the
circumstance that the
infinitely
many
rays
traversing
the
space,
which
constitute the radiation
present in
v,
interfere with
one
another
and
thus
provide
a
momentary energy
that is
sometimes greater, sometimes
smaller than
the
sum
of the
energies
that the individual
rays
would provide
if
they
were
1Cf.,
e.g.,
Planck's
repeatedly
cited
book, Equation
(230).
[35]