DOCS.
283,
284
SEPTEMBER
1911
205
Now to
entropy
and
probability.
You
write
very amusingly:
"The
case
with
the
particle
...
is
really very
instructive,
but
evidently
I
have
not
yet
quite
understood what
the
point
is"(!)[11]
In the
case
of
a
particle,
the
point is
to know
the
probability
for
a
volume
element dr
at height
z.
If dr
is
realized
by means
of
a rigid
screened
box,
the
osmotic forces do
not do
any
work
when
the
box
is
raised
infinitely slowly.
If the
entropy
and
probability are
referred
to
this
area r,
which
is
always
of
the
same
size,
Boltzmann's
equation
holds
exactly.
The
same
is true
if
r
is
a
function of
z.
Only
one
must
then
take
into account
the
osmotic work
when
one
determines
S.
We
see
that
the strict
application
of the
principle is
possible only
if
the
state
region
can
be
realized
physically
and
changed
oo
slowly.
But
in
the
case
of
an isochorically
heated
subsystem, one
does
not
have the
means,
in
each
and
every
state,
for
preventing
this
subsystem from leaving a
certain
energy
interval 8E.
But the
exact values
of
S
and W would have to
refer
to such
an
interval,
in such
a
way
that
they
depend
not
only on
E,
but
also
on
8E.
Of
course,
the
region
to which
one
refers
S
and
W
can
also be
unbounded
(in
the
direction of smaller
entropy
values);
such
a
choice
is
sometimes
even
advantageous (osmotic pressure),
but
it
is
not,
in
principle,
essential.-
Think about
metals!
Something
sensible
must
be found
there. The
current
state
of
affairs
is
unbearable.[12]
Many
thanks
to
Anna
and
Vero
for
their
friendly
note.
Best
regards
to all
three of
you
from
your
Albert
Enclosed
is
a
note
from
my wife.[13]
284. From
Willem Julius
[Utrecht]
17 September
[191l][1]
I hope
that
you
will
not
take
it amiss
that
a
letter
in the
name
of
our
faculty
is
being
sent to
you
in
spite
of
your
response to
my
preliminary
inquiry.[2]
It
was
simply
unthinkable
not to
mention
your name
at
the
meeting,
and
people
were
generally
of the
view that
the
reason
you
had
given
for
your
refusal
was
not
of
such
a
fundamental
nature
that
it would be
pushy or even impermissible
on our
part to
make
one more
attempt
to
win
you over.
To
all
appearances,
mathematical
physics can
thrive in
the
Netherlands;
our faculty
wishes
to
work
actively
at creating
the conditions
that
would
most
favor such
a
development,
and
is
therefore
turning
to
you.-
I have
now
studied
at
a more
leisurely pace your
noteworthy paper,
the
proofs
of
which
I
had
returned,
unfortunately,
in
too
great
a
hurry.[3]
I would
not
presume
to
make
any
objection to
the theoretical
analysis.
I would
only
like to ask
whether
it
might
be
possible
that the relative
change
of
frequency
expected
for
the sun-earth
system
is
no