Theories of the optical behaviour of liquids generally base themselves on the postulate that the well-known Lorentz formula (
n
2
— 1)/(
n
2
+ 2)ρ = constant correctly expresses the relation between the refractive index and density of a liquid. It has long been known, however, that this formula is at best only an approximation. The quantity (
n
2
— 1)/(
n
2
+ 2)ρ is found experimentally to be not invariable, its deviation from constancy becoming more and more marked as the density is increased. The change in the value of (
n
2
— 1)/(
n
2
+ 2)ρ in passing from the state of vapour to that of a liquid under ordinary conditions, is usually quite appreciable, as might be instanced by the case of benzene, for which Wasastjerna found for the D-line a molecular refraction of 27·20 in the vapour state, while the corresponding value for the liquid is 26·18, that is, 3·8 per cent, lower. The deviations from the Lorentz formula appear most striking when we use it to compute the change in the refractive index of a liquid produced by alterations of temperature or pressure. Here, again, we might instance the case of benzene, for which the observed value of
dn
/
dt
= —6·4 × 10
-4
per degree Centigrade for the D-line at 20° C., and that of
dn
/
dp
= —5·06 × 10
-5
per atmosphere, while the calculated values are
dn
/
dt
= —7·15 × 10
-4
and
dn
/
dp
= —5·66 × 10
-5
. The observed values are thus numerically about 10 per cent, smaller in either case, indicating that (
n
2
— 1)/(
n
2
+ 2)ρ diminishes more and more quickly as the density is increased. An expression of the form (
n
2
— 1)/(
n
2
+ 2)ρ =
a
—
b
ρ
2
where
a
and
b
are positive constants, has been found to represent the refraction of carbon dioxide over a wide range of density more closely than the original Lorentz formula. It has been deduced theoretically on certain suppositions regarding the magnitude of the polarisation field in liquids, which are, however, somewhat arbitrary in nature. Considering next the electrical behaviour of liquids, we find that the formula proposed by Debye (ε — l)/(ε + 2)ρ = A + B/T is not adequate to explain the dielectric properties of many known liquids. To illustrate this, we may again consider the case of benzene, whose dielectric constant has been determined over a wide range of temperatures and pressures. Since A and B in the formula are essentially positive constants, it follows that (ε — l)/(ε + 2)ρ should remain invariable when the liquid is compressed isothermally, and that it should
diminish
with rising temperature. Actually it is found with benzene that the quantity in question falls steadily with increasing pressure and
increases
with rising temperature. A similar apparently anomalous behaviour is shown by many other liquids whose molecules have a negligible electrical polarity. Liquids of marked electrical polarity show a diminution of (ε — l)/(ε + 2)ρ with rising temperature as demanded by the formula, but they deviate from it by showing a diminution of the same quantity when isothermally compressed, the latter effect being usually even more marked than for non-polar compounds.
The formation of mercury molecules
