130
MOVEMENT
OF SMALL PARTICLES
Thus,
apart
from
universal
constants and
the absolute
temperature, the
coefficient
of
diffusion
of
the
suspended
substance
depends only
on
the
coefficient of friction of the
liquid and
the size
of
the
suspended
particles.
S4.
On
the random
motion
of
particles
suspended
in
a
liquid
and
their relation
to diffusion
We
shall
now
turn to
a
closer examination
of
the
random
motions
which,
caused
by
thermal molecular
motion, give
rise
to
the diffusion
investigated
in
the last section.
Obviously,
we
must
assume
that
each
individual
particle
performs
a
motion
that is
independent
of the
motions
of all the other particles;
similarly, the
motions of
one
and
the
same
particle in
different time
intervals will
have to be
conceived
as
mutually
independent
processes
so long
as we
think of these time intervals
as
chosen not to be
too
small.
We
now
introduce into the consideration
a
time
interval
r,
which shall
be
very
small
compared
with observable time intervals but still
so
large
that
the
motions
performed
by a
particle
during two
consecutive time intervals
r
[16]
may
be
considered
as
mutually independent events.
Suppose, now,
that
a
total
of
n
particles
is
present
in
a
liquid.
In
a
time interval
r,
the Xcoordinates
of
the individual particles will increase
by A,
where
A
has
a
different (positive
or
negative)
value for
each
particle.
A
certain
frequency law
will hold for
A:
the
number dn
of
particles
experiencing
a
displacement lying
between
A
and
A+dA
in
the
time interval
r
will
be expressed
by an
equation of
the
form
dn

mp(A)dA,
where
r+oo
(p(A)dA

1,
oo
and
Q
differs
from
zero
for
very
small values of
A
only,
and
satisfies
the condition
p(A)
=
p(A).