DOC.
10
MAY 1914
19
If
you develop only
the data
on
the
energy
line instead of
on
the
q,
p
plane
this
is not
so
clearly
obvious!!
£
=
a2/2p2
+
B2/2q2
+
cq2
+.....)
has likewise worked with such
a G(q,
p,
a).[11]
(4)
Whether the introduction
of
such
an a
in the
a
priori
G's contradicts the
spirit
of
Boltzmann,
since
the
system
does
of
its
own
accord.........
Please, please, dear,
dear
Einstein, delay
this
question
for
a
little bit
longer.-
I believe
myself entirely equal
to
this comment
as
well-but
communicating
this
in
writing
to
you
is
much
too
hard
a
task.-
So
simply accept provisionally my
statement of the
problem,
which bases itself
on
the introduction
of
such
a
G(q,
p,
a).
Then in
any
case
the
question remains,
of
course:
(5)
For
which
G(q,
p,
a)
is
the relation
udQ
=
dlgW
satisfied?
And
now
I
could
prove
the
following
statement:[12]
Let
i(q,
p, a)
be
the
2r-dimensional
volume
enclosed in
the
2r-dimensional
(molecule)
phase space
of
that
e(q,
p,
a)
=
const.
plane
which
goes
through
the
molecule
phase
point
q1....pr.
[For
Planck
resonators
i(q, p,
a, ß)
=
1/2(a2q2+ß2p2)/(aB/2n)
And let
G(q, p,
a)
be
any pure
function
of
i(q,
p,
a)
[such
as,
e.g.,
=
i2 or
lg
i
but
not iq
or
ai
+
i2
or
(a
+
q)i][13]
G(q,
p, a)
=
r(i).
For
every
such
G(q,
p,
a)
=
r(i(q,
p, a)),
the
accompanying
“most
probable”
distributions
f =
e
(i(q,P,a))
ƒ dTe~^£V(i)