DOC.
32
189
Thus,
the rotational
motion
produced
by
molecular
motion
decreases
much
faster with increasing
P
than
does
translational
motion.
For
P
=
0.5
mm
and
water at
17°,
the formula
yields
about
11
seconds
of
arc
for
the
angle
traversed
in
one
second
on
the
average,
and
about
11
minutes
of
arc
for that traversed in
one
hour.
For
P
=
0.5
micron and water
at 17°,
we
get
about
100 degrees
of
arc
for
t
=
1
sec. [25]
In the
case
of
a
freely
floating
suspended
particle,
three
mutually
independent
rotational
motions
of this kind take place.
The
formula derived for
A2
might
be
applied to
other
cases as
well.
For
example,
if
the
reciprocal of the electric resistance of
a
closed circuit
is substituted for
B,
the formula
shows
how much
electricity will
flow
on
the
average through
some
particular
cross
section of the conductor
during
time
t,
which
relation is connected
again
with the
limiting law
of
black-body
radia-
tion for
great
wave
lengths
and
high temperatures. However,
since I could
not [26]
find
any
additional
experimentally
verifiable
consequences, any
treatment of
further special
cases
seems
useless
to
me.
§5.
On
the limit
of
validity
of
the
formula
for
A2
[27]
It is clear that formula
(II)
cannot be
valid for
arbitrarily
small time
intervals. This is
so
because the
mean
velocity of
the
change
of
a
result-
ing
from
the thermal
process,
t
2
RTB 1
becomes
infinitely
large
for
an
infinitesimally small time interval
t, which
is
obviously impossible
because
every suspended
body
would
then
have
to
move
with infinitely
great instantaneous
velocity.
The
reason
for this is that
we
have implicitly assumed
in
our
derivation
that the
process
occurring
during
time
t
is
to
be
conceived
as an
event
that is
independent
of the
process
occurring during
the times
immediately
preceding
it.
But the
shorter the