90 DOC.
18
REPLY TO LAUE
a;
=
..«»«
-
0
K
=
fb:f^datv\..dbP
=
0
(3)
The
resulting
radiation is
given
in the time interval 0
to
T
by
the
expression
cos
27771-
+
Bb
sin
2vn
-
n
T T
P
cos
2m+
b^
sin
2Tr/iyj
(4)
and from this follows the
validity
of
the relations
(V)
An
=
Bn
=
E
*"(v)
(5)
Which statistical law follows
now
for
the Fourier coefficients
A1...Bz?
[p.
882] Using
considerations
quite
analogous
to
the
ones
in
part
I
of
Laue's
paper, one
finds the statistical law
we are
looking
for
to
be
as
follows:
(amnAmAn
+
ßmnBmBn + 2ymnAmBn)
dW
=
const
e
mn dA1...dBz.
(6)
One
can see
from this relation that the
superposition
of
infinitely many
radiation
components
does not at all
guarantee
the statistical
independence
of
the Fourier
coefficients.
The law
(6),
however,
still allows
us
to
reduce the
question
of statistical
independence
of
the Fourier coefficients to
a
simpler one.
The statistical
indepen-
dence
is satisfied
if
and
only
if
the
exponent
in the
exponential
function contains
only
the
squares
of
the
Am
and
Bn,
not, however, any products
of these
quantities,
i.e.,
a
mn
= =
0 for
m
*
n
Y^v
=
0
(7)
must be satisfied.
It is furthermore
clear,
because
of
(3)
and
(5),
that
under
statistical
independence
the relations
AmAn
= =
0
for
1TI
*
/I
m n m n
AmBn
=
0
m n
(7a)
must
obtain.
The
number
of
conditions
(7a)
is
equal
to
the number of conditions
(7),
and all
conditions
(7a) are
mutually independent.
It
follows, therefore,
that under the