DOC.
18
REPLY TO LAUE
93
sinw -m
A A
2
___ _
)sinir(v~_n)
m n
2
lv2
____________Tsin2~rv
2~
_ _
(11)
It
is
a
priori
obvious that
a
statistical
dependence
between radiation
components
can
only
be
expected
between
neighboring frequencies;
m
and
n
belong,
therefore,
into the
same
narrow
spectral range,
and the
same
holds for those
values
v
which
contribute
substantially
to
our sum.
The quotient on the right-hand side of
(11)
changes only slowly with
v
because
[p.
885]
T/6
is
a
small
quantity.
Therefore,
one can average
relative to
av2
over many [4]
{3}
sequential
terms without noticeable
error,
and the
mean
value
av
can
be
pulled as
a
constant before the
sum
since the summation extends
only
over a narrow
spectral
range.
The summation
over
the
quotients
can
then be transformed into
an integral
and
one
obtains:
AA
=120
sin2x
dx.
m n
(12)
Instead
of
taking
the
integral
between the boundaries
of
the aforesaid
spectral
range,
one
can
take it without noticeable
error
between
-
oo
and
+
oo.
The
integral
has the value
tt
for
m
=
n,
but it
always
vanishes1
when
m
=
n
(m, n being integers).
The
vanishing
of
AmAn
(for
m
=
n)
is
herewith
shown;
proofs
for the
vanishing
of
BmBn
(for
m
= n)
and for
AmBn
can
be carried out in
analogy.
From the
vanishing
of these
mean
values
follows,
according
to
§1,
the
1The
integral
is
equal
to
1/(m-n)n{|sin2x/x-mn|sin2x/x-mn}
Each
of
the last two
integrals
is
equal
to
+~
rsinzy
SI
y
dy
-n
-`J.