DOC.
18
REPLY TO LAUE
89
the
same
statistical law which is assumed
to
be
given.
In both
cases,
the statistical
independence
of the Fourier coefficients in
the
development
of
the
resulting
radiation
does
not
follow. From this
one
should
not-in
my
opinion-deduce
the
admissibility
of the
hypothesis
that this
independence
does
not
also exist in
natural
radiation.
After
all,
it has
not
been shown that the
degree
of disorder from this
irregular
distribution of resonators in
a
layer
of thickness
cT
has
to
be the
same as
the
one
encountered in
natural
radiation.
The
suspicion
becomes
more prominent
when
one sees
in Laue's calculations that
the
degree
of statistical
dependence
of
two terms in the
development
of
the
resulting
radiation characterized
by
indices
p
and p'
is determined
by
a
term, viz.,
Trip
-
p')r
T
i.e.,
a quantity
that
depends upon
the thickness
of
the
layer.
But
a
statistical
dependence
of
this kind in natural
radiation-if
such
dependence
could be found
there-should
have
nothing
to do with the method
of
generation
of
the radiation that
is under consideration here.
In
my
opinion,
therefore, none
of the
cases
considered
by
Laue is
equivalent
to
the disorder found in natural
radiation,
and his results do not allow
one
to conclude
[p.
881]
anything as
far
as
natural radiation is concerned.
Consequently,
I
uphold my previous
claim and will
try
to
support
it
with
a new proof,
while
utilizing
the theorems
of
probability
upon
which Laue has elaborated in his
paper.
§1.
Statistical
Properties
of Radiation
Developed by
Superposition
of
an
Infinity
of
Mutually Independently
Generated Radiations
Each
one
of
the radiation
components
to be considered shall be
represented
in the
time interval 0
to
T
by
a
Fourier
expansion
of
the form
cos
2vn-
+
b^
sin
2vn-,
(1)
{1}
n
T
T
where the coefficients
satisfy
the
probability
law
dW
=
/
(v)(a1(v)..
.az(v)..
.,b1(v)...bz(z)da1(v)...dbz(z)..., (2)
which law
can
be
a
different
one
for each radiation
component
(v).
Furthermore,
the
law
can
be such that