ed, and which yet cannot be
ranged under this law, e.g. water and alcohols. The most natural thing,
of course, is to ascribe the deviation of these substances, as of the
others, to the fact that the molecules of the liquid are polymerized. In
this case we have to account for the following circumstance, that
whereas for NO2 and acetic acid in the state of saturated vapour the
degree of association increases if the temperature falls, the reverse
must take place for water and alcohols. Such a difference may be
accounted for by the difference in the quantity of heat released by the
polymerization to double-molecules or larger molecule-complexes. The
quantity of heat given out when two molecules fall together may be
calculated for NO2 and acetic acid from the formula of Gibbs for the
density of vapour, and it proves to be very considerable. With this the
following fact is closely connected. If in the pv diagram, starting from
a point indicating the state of saturated vapour, a geometrical locus is
drawn of the points which have the same degree of association, this
curve, which passes towards isothermals of higher T if the volume
diminishes, requires for the same change in T a greater diminution of
volume than is indicated by the border-curve. For water and alcohols
this geometrical locus will be found on the other side of the
border-curve, and the polymerization heat will be small, i.e. smaller
than the latent heat. For substances with a small polymerization heat
the degree of association will continually decrease if we move along the
border-curve on the side of the saturated vapour in the direction
towards lower T. With this, it is perfectly compatible that for such
substances the saturated vapour, e.g. under the pressure of one
atmosphere, should show an almost normal density. Saturated vapour of
water at 100 deg. has a density which seems nearly 4% greater than the
theoretical one, an amount which is greater than can be ascribed to the
deviation from the gas-laws. For the relation between v, T, and x, if x
represents the fraction of the number of double-molecules, the following
formula has been found ("Moleculartheorie," _Zeits. Phys. Chem._, 1890,
vol. v):

x(v - b) 2(E1 - E2)
log --------- = ---------- + C,
(1 - x)^2 R1T

from which

T /dv\ E1 - E2
------( -- ) = -2-------,
(v - b) \dT/_x R1T

which may elucidate what precedes.

Condensation of substances with l