246
DOC.
9
CRITICAL OPALESCENCE
[19]
It
is
significant
that the
main
result of
our investigation, given by
the formula
(17a),
permits
the
exact
determination of the
constant
N, i.e.,
the absolute
size
of
molecules.
In
what
follows,
this
result
will be
applied
to
the
special case
of
a
homogeneous
substance, as
well
as
to
binary liquid
mixtures in
the
vicinity
of the
critical state.
§ 5.
Homogeneous
Substances
In the
case
of
a
homogeneous
substance
we
have
i|f
=
-
Jpdv,
hence
82iJ;
_
dp
dv2
dv
Further,
according
to
the Clausius-Mosotti-Lorentz
relation,
e
-
1
v
=
const.,
8+2
hence
(c
~
l)2(c
+ 2)2
dv)
9vz
Substituting
these
values in
(17a),
we
get
(17b)
Jo
_
RTo
(e
-
l)2(e
+ 2)2
(2itX
+ 2)2
(2iiY
A [
A J
(4kL
Je
N
9^
{
_dp\
\
k)
(4*0)
dv
CX)S2(p.
In this
formula,
which
gives
the ratio of the
intensity
of
the
opalescent
light
to
that of
the
excitory light,
in
case
the latter
is
measured
at distance D from
the
volume
p
originally
traversed
by
the
light, we use
the
following
notation:
R
is
the
gas
constant,
T
is
the
absolute
temperature,
N
is
the number of
molecules in
one gram-molecule,
e
is
the
square
of the refraction
exponent
for
wavelength
X,
v
is
the
specific
volume,
dp!d
is
the isothermal
derivative
of the
pressure
with
respect
to
the
volume,
p
is
the
angle
between the
electric field vector
of the
exciting wave
and
the
plane
normal
to
the
opalescence ray
under consideration.
That
dp/dv
is
the
isothermal,
and
not,
say,
the adiabatic
derivative,
has to do with the
fact
that of
all
the
states
belonging
to
a given density
distribution,
the
state
of
constant