DOC.
490
DECEMBER
1913 367
for
some
kind of
independent quanta
in
empty space,
or
whether
the solution
to
the
difficulties
should
be
expected
from
filling a gap
in
our knowledge
about the mutual
interaction of
charged
particles
in matter.
Of
course many
considerations about
energy-
and
momentum-"schwankungen"
came
in
here.
{Would it
not
be
possible
to
translate
this word
by
"bobbing"?
In
my opinion
this
provides
precisely
what
is
needed:
an upward
and
downward
movement
with
an
average
level. This
average
level
is
lacking
if
one
thinks
of
oscillating,
and in
variation
a
reversal of
sign
is
implied,
which
is
unnecessary.}[4]
The
impossibility
of
reaching
absolute
zero was
another
hobby
horse
we
rode.
All this
was
still
connected
to
things
that
I
had
thought
about before.
Furthermore,
we
took
up
the
study
of
the
average energy
of
an
electrical
dipole
that
is
in
the radiation
field and
can
rotate
around
a
fixed
equatorial axis.[5]
The method
you
suggested
to
me
for
deriving a
differential
equation to
determine
a
stationary
distribution
function,
which
I
used in Ch. IV.
§5
of
my
dissertation,[6]
I have
been
able to
generalize
somewhat
for
the
case
in which
the
changing
momenta
depended
on
the
speed
and
had
an
average
different
from
zero.
For the
case
of
one
degree
of freedom
(rotation
around
a
fixed
axis)
the
differential
equation is:
aqt~t~~~
+
1ũ2!a
=
0
or
Wf(q)r WR+
(WR2] =
const
=
0.
2aq
In this
equation
q
is
a
quantity
which determines
the
state, for
example,
the
moment
of
momentum
around the rotation
axis.
Wdq
is
the number of
dipoles
between
q
and
q
+ dq.f(q) is
the decrease of
q
per
unit of
time
as a
result of
emission,
friction and
is
not
always
proportional to
the
first
power
of
q.
R
is
an
irregular
momentum,
i.e.,
the
irregular change
of
q
in
the
very
small
time
r.
The
first
equation
means
that the number
in
(q,
q
+
dq)
has not
changed
in
the time
t.
The
second
one means
that
an
equal
number of
dipoles pass through
the
value
q
in
increasing
and
decreasing
direction.
If
q
is
not assumed
to be
the
moment
of
momentum
but
if
another
quantity
is
taken
to
be
the coordinate
determining
the
state, for
example
the
energy,
generally
a
quantity
x,
so
that
q
=
f(x),
then
very satisfactorily,
the
equation
takes
on
the
same
form
in x.
With
this
equation
we
first
investigated
whether
Maxwell's
distribution function
corresponds to
the radiation
formula of
Rayleigh
and
Jeans
(which
is
needed
for
the
calculation of
R).
We did
not
achieve
agreement
as long as we
assumed
R to be
equal
to
zero.
This
seemed
so
plausible to
us.
We
eventually
realized
though
that
it
was
not
so
and I have succeeded
in
calculating
the
value
of R.
Agreement
has
now
been
achieved.
Subsequently,
I
started
to
calculate the distribution function that
corresponds
to
the
radiation formula of
Planck.
It
has
an
awkward form.
If
0)
is
the
angular
velocity
and
L
the
moment
of inertia of the
dipole,
and
if
consequently
the distribution function for
to
is
written
down,