320
THEORY OF BROWNIAN MOTION
z
X
"Sc
E E'
p r
Mr
Fig. 94 Fig. 95
We
will
denote the
distance
of the
surface
E
from
the left
end
of the
vessel
by
x,
and
the
distance
of the
surface
E'
from
the
same
end
of the
vessel
by x +
dx;
then
dx
also
equals
the
volume
of
the
liquid lamina
considered. Since
p
-
p'
is the
osmotic
pressure
acting
on
the
volume dx
of
the dissolved substance,
[5]
p-pt
- p'-p
-
dp
-
dx
dx
dx
=
Rh.', dx
-RT
is
the osmotic
force acting
on
the dissolved substance contained in the
unit
volume.
Since,
further,
the
osmotic
pressure is
given
by
the equation
=
Rh.
where
R
denotes the constant
of
the
gas
equation
(8.31.10-7),
T
the
absolute
temperature,
and v
the
number
of
dissolved
gram-molecules
per
unit
volume
we
get,
finally
the following expression
for
the osmotic
force
K
acting
on
the
dissolved substance per
unit
volume
(1)
-RT
au
dx
a
To
be
able to calculate the diffusional
motions
that these
motive
forces
can
produce,
we
must
also
know how
great
a
resistance is offered
by
the
sol-
vent to the
motion of
the dissolved substance. If
a motive
force
k
acts
on
a
molecule,
it
imparts
to
it
a
proportional velocity
v
according
to
the
equation