the liquid can be supercooled.

We may find the value of the pressure of the saturated vapour for each T
in a geometrical way by drawing in the theoretical isothermal a straight
line parallel to the v-axis in such a way that [int] v1 to v2 pdv will
have the same value whether the straight line or the theoretical
isothermal is followed. This construction, given by James Clerk Maxwell,
may be considered as a result of the application of the general rules
for coexisting equilibrium, which we owe to J. Willard Gibbs. The
construction derived from the rules of Gibbs is as follows:--Construe
the free energy at a constant temperature, i.e. the quantity - [int]pdv
as ordinate, if the abscissa represents v, and determine the inclination
of the double tangent. Another construction derived from the rules of
Gibbs might be expressed as follows:--Construe the value of pv -
[int]pdv as ordinate, the abscissa representing p, and determine the
point of intersection of two of the three branches of this curve.

As an approximate half-empirical formula for the calculation of the
pressure,

p /Tc-T\
-log10 --- = f( ---- )
pc \ T /

may be used. It would follow from the law of corresponding states that
in this formula the value of [int] is the same for all substances, the
molecules of which do not associate to form larger molecule-complexes.
In fact, for a great many substances, we find a value for f, which
differs but little from 3, e.g. ether, carbon dioxide, benzene, benzene
derivatives, ethyl chloride, ethane, &c. As the chemical structure of
these substances differs greatly, and association, if it takes place,
must largely depend upon the structure of the molecule, we conclude from
this approximate equality that the fact of this value of [int] being
equal to about 3 is characteristic for normal substances in which,
consequently, association is excluded. Substances known to associate,
such as organic acids and alcohols, have a sensibly higher value of f.
Thus T. Estreicher (Cracow, 1896) calculates that for fluor-benzene f
varies between 3.07 and 2.94; for ether between 3.0 and 3.1; but for
water between 3.2 and 3.33, and for methyl alcohol between 3.65 and
3.84, &c. For isobutyl alcohol [int] even rises above 4. It is, however,
remarkable that for oxygen [int] has been found almost invariably equal
to 2.47 from K. Olszewski's observations, a value which is appreciably
smaller than 3. This fact makes