DOC.
16
127
But
from
the molecular
theory
of heat,
presented
in the
papers
cited1,
it
can
easily be deduced
that
dB/B
and
dB'/B are
equal
to
the
probabili-
ties that
at
an
arbitrarily
chosen
moment
the
centers
of
gravity
of the
particles will
be found
in the
regions
(dx1...dzn)
and
(dx'1...dz'n),
respectively.
If the
motions of
the individual particles
are
(in sufficient
approximation)
independent
of
each
other,
and
the liquid is
homogeneous
and
no
forces
act
upon
the particles, then the
probabilities
corresponding
to
the
two
systems
of
regions must be
the
same
if the size
of
the
regions
is the
same, so
that
we
have
dB
T
dB
But
it follows
from
this
equation and
the
one
preceding
it that
J
= j
This
proves
that J
does
not depend
on
either
V*
or
x1,
y1
...zn.
Integrating,
we
get
and from
that
and
B
=
Jdx*...
dzn
=
JV*n,
1
n
RT
F
=
-
f
{lg
J
+ n
lg
V*}
P =
-
OF
_
RT
n
_
RT
W
~
T*
It
~
T v
[10]
This consideration demonstrates that the existence of osmotic
pressure
is
a
consequence
of the molecular-kinetic
theory
of
heat,
and
that,
according
to
this
theory, at great
dilutions
numerically equal
quantities of dissolved
molecules
and
suspended
particles
behave completely
identically with
regard
to
osmotic
pressure.
1A.
Einstein,
Ann.
d.
Phys.
11
(1903): 170.
[9]