186
REVIEW
OF
BROWNIAN MOTION
can
be
considered
as
infinitesimally
small
changes
in
the
argument
of the
function F(a).
If lengths
numerically equal to
a are
plotted
along
a
straight line
starting
from
some
specified
origin,
then
to
each
system
there
will
correspond
a
point (a)
on
this straight line.
F(a)
is the density
of
the
system–
points
(a)
on
the line.
During
time
t, exactly
as
many
system-points must
then
cross
an
arbitrary
point
(a0)
of the
line in
one
direction
as
in
the
opposite
one.
Let
a
force
corresponding
to
the
potential $
produce a change
of
magnitude
Ä1
=
-ß^t
in
a,
where
B
is
independent
of
a,
i.e.,
the
velocity
of
change
of
a
shall be proportional
to
the
operating
force
and independent
of
the value
of
the
parameter.
We
will
call the
factor
B
"the
mobility
of the
system
with
respect
to
a."
Thus,
if
the external
force
were
to operate
without the quantity
a
being
changed by
the
random
molecular thermal
process,
then
n1
=
B
Ifa
a-ÜQ
v
(r
system-points would
cross
the
point
(a0)
toward
the
negative
side
during
time
t.
Let
^(A)
be
the probability
that,
due to
the
random
thermal
process,
the
parameter
a
of
a
system
experiences
during
time
t
a
change
whose
value
lies
between
A
and
A +
dA,
where
^(A)
=
^(-A),
and
ij)
is
independent
of
a.
The number
of
system-points
crossing
the
point
(a0)
toward
the
positive
side
on
account of the
random
thermal
process during
time
t
is then
rA=00
n2
=
f(a0-A)I(A)rfA,U
A=0
where
we
have
put