502 DOC.
486
MARCH
1918
the
areas
of
this
surface
but
only
certain
parts,
the total
extension of
which
I
denote
as
F'
F.
Then, according
to
you,
S
=
k
log
F'
+ const.
These two
equa-
tions
do not
contradict
each
other
only
if
F'
=
F,
i.e.,
if
the
system
is
ergodic
or
if
F'
is
nearly
=
F.
The latter
applies,
e.g.,
to
the
example you
put
forward of
a
system composed
of
a
number
of
independently
ergodic systems.
Here the total
system
is admittedly
not
ergodic.
But the
deviation from
an ergodic system,
or
the fraction F-F'/F,
is
so
small
that it
is
negligible against log
F.
II. Your assertion
that
your
oscillation consideration
is
upheld
if
a
pulverized
carbon
particle is
presupposed
to exist within
the
black-body
radiation
would be
fully
valid
only
if it
were
demonstrated
that,
upon
introducing
a
carbon
particle,
black-body
radiation
became
ergodic.[5]
However,
I believe such
proof
cannot
be
given;
for
I
consider
any system
whose
energy
partly
consists in
black-body
radiation
as
nonergodic.
I
think
this
because,
in
a
pure vacuum, processes
take
place according
to
Maxwell’s
equations,
hence
are
entirely uniquely specified,
to
be
more
precise,
are
such
that the
ones
in
the
interior
are
determined
by
the
processes
at
the
bordering
surface.
That
is
why
not all
degrees
of
freedom
phase regions may
be
regarded
as
statically
independent
dynamically possible,
and thus
an
essential
precondition
of
ergodic
behavior is removed.
III.
Regarding
the fluctuations
of
motion
of
a
diathermanous
(or reflective)
plate
in
a
radiation
space,
I
would
just
like to
venture
to make
two
comments.
1)
Certainly,
a
plate
consisting
of
a
substance
that
has
eigenfrequencies only
in
the ultraviolet
can
be considered
absolutely homogeneous
in
long-wave
ra-
diation,
yet only
under
the
condition
that the radiation
intensity is
absolutely
constant.
As
soon as
it
is subjected to
fluctuations,
however,
the
atomic
struc-
ture of
the
plate
comes
into
play,
indeed,
with
greater effect,
the
more
abruptly
the fluctuations
set in.
2)
Strictly
speaking,
a
plate is
in
statistical
equilibrium
with the
radiation
only
when
it
has
the
very
same
temperature.
But then it
may
not be
regarded
as rigid,
rather
it must take into account
the
oscillations of its
particles,
and this
amounts
to
a
considerable
complication
of
the
processes.
So, now
you
have
probably
had
enough
of
this! Therefore
only a
word
about
the
question
of
your
surviving beneficiary
conditions.[6]
I
also
am
entirely
of
your
opinion
that
you
attend
to
the
execution
of
this
yourself
and for
this
reason
would
like
to
offer
you
the
advice of
contacting
the
official
responsible
for academic af-
fairs at
our
Ministry,
Privy
Councillor Prof.
Kruss.[7]
The document in which
the
Ministry
informs the
Academy
that
you
should be
granted widow’s
and
or-
phan’s
pensions
according
to
the
provisions existing
for
the
survivors of
university