DOC.
32
185
N
-
J*
v(p-
p0)gx
dW
=
const.e dx.
Thus
we
will then find that
suspended
particles
can
float in
a
liquid
if, for
values of
x
that
do
not
escape
observation because of their smallness, the
quantity
N
v(p
-
Po)9x
RT
does not have
too high
a
value-provided
that the
particles
that
have
reached
the
bottom
of the container
do
not
adhere there
due to
some
circumstance
or
other.
§3.
On
the
changes
in
the
parameter
a
caused
by
thermal motion [20]
Now we
return again
to the
general
case
discussed
in
§1,
for
which
we
derived
equation
(I).
For
the
sake
of
a
simpler
mode
of
expression and
visualization,
we
will
now assume,
however,
that
a
very
large number
(n)
of
identical
systems
of
the kind described there
are
involved; in
that
case
we
have
to
deal
with
numbers
instead
of
probabilities.
Equation
(I)
expresses
then the
following:
Of
N
systems,
there
are
(Ia)
dn
= pe
da
-
F(a)da
systems
in
which
the value
of
the
parameter
a
lies
between
a
and
a+
da
at
a
randomly
chosen
instant.
We
shall
use
this relation
to
determine the
magnitude
of the irregular
changes
of
the
parameter
a
produced
by
the
random
thermal
processes. To
that
end,
we
express
in
symbols
that, within the time
span
t,
the
function
F(a)
does not
change
under the
combined
effect
of
the force
corresponding
to
the
potential
$ and
the
random
thermal
process;
here
t
denotes
a
time
so
small
that the
corresponding
changes
of
the
quantities
a
of the individual
systems
[19]