us again seriously doubt the correctness
of the supposition that [int] = 3 is a characteristic for
non-association.

Critical volume.

It is a general rule that the volume of saturated vapour decreases when
the temperature is raised, while that of the coexisting liquid
increases. We know only one exception to this rule, and that is the
volume of water below 4 deg. C. If we call the liquid volume v_l, and the
vapour v_v, v_v - v_l decreases if the temperature rises, and becomes
zero at Tc. The limiting value, to which vl and vv converge at Tc, is
called the _critical volume_, and we shall represent it by v_c.
According to the law of corresponding states the values both of v_l/v_c
and vv/vc must be the same for all substances, if T/Tc has been taken
equal for them all. According to the investigations of Sydney Young,
this holds good with a high degree of approximation for a long series of
substances. Important deviations from this rule for the values of vv/vl
are only found for those substances in which the existence of
association has already been discovered by other methods. Since the
lowest value of T, for which investigations on v_l and v_v may be made,
is the value of T3; and since T3/Tc, as has been observed above, is not
the same for all substances, we cannot expect the smallest value of
v_l/v_c to be the same for all substances. But for low values of T, viz.
such as are near T3, the influence of the temperature on the volume is
but slight, and therefore we are not far from the truth if we assume the
minimum value of the ratio v_l/v_c as being identical for all normal
substances, and put it at about 1/3. Moreover, the influence of the
polymerization (association) on the liquid volume appears to be small,
so that we may even attribute the value 1/3 to substances which are not
normal. The value of v_v/v_c at T = T3 differs widely for different
substances. If we take p3 so low that the law of Boyle-Gay Lussac may be
applied, we can calculate v3/v_c by means of the formula p3.v3/T3 =
k.p_c.v_c/Tc provided k be known. According to the observations of
Sydney Young, this factor has proved to be 3.77 for normal substances.
In consequence

v3 p_c T3
--- = 3.77 --- --.
v_c p3 Tc

A similar formula, but with another value of k, may be given for
associating substances, provided the saturated vapour does not contain
any complex molecules. But if it does, as is the case with acetic acid,
we m