ust also know the degree of association. It can, however, only be
found by measuring the volume itself.

Rule of the rectilinear diameter.

E. Mathias has remarked that the following relation exists between the
densities of the saturated vapour and of the coexisting liquid:--

/ T \
[rho]l + [rho]v = 2[rho]c {1 + a(1 - -- ) },
\ Tc/

and that, accordingly, the curve which represents the densities at
different temperatures possesses a rectilinear diameter. According to
the law of corresponding states, a would be the same for all substances.
Many substances, indeed, actually appear to have a rectilinear diameter,
and the value of a appears approximatively to be the same. In a _Memoire
presente a la societe royale a Liege_, 15th June 1899, E. Mathias gives
a list of some twenty substances for which a has a value lying between
0.95 and 1.05. It had been already observed by Sydney Young that a is
not perfectly constant even for normal substances. For associating
substances the diameter is not rectilinear. Whether the value of a, near
1, may serve as a characteristic for normal substances is rendered
doubtful by the fact that for nitrogen a is found equal to 0.6813 and
for oxygen to 0.8. At T = Tc/2, the formula of E. Mathias, if [rho]v be
neglected with respect to [rho]l, gives the value 2 + a for
[rho]l/[rho]c.

Latent heat.

The heat required to convert a molecular quantity of liquid coexisting
with vapour into saturated vapour at the same temperature is called
_molecular latent heat_. It decreases with the rise of the temperature,
because at a higher temperature the liquid has already expanded, and
because the vapour into which it has to be converted is denser. At the
critical temperature it is equal to zero on account of the identity of
the liquid and the gaseous states. If we call the molecular weight m and
the latent heat per unit of weight r, then, according to the law of
corresponding states, mr/T is the same for all normal substances,
provided the temperatures are corresponding. According to F. T. Trouton,
the value of mr/T is the same for all substances if we take for T the
boiling-point. As the boiling-points under the pressure of one
atmosphere are generally not equal fractions of Tc, the two theorems are
not identical; but as the values of p_c for many substances do not differ
so much as to make the ratios of the boilin