120 Preston—On the Continuity of Isothermal Transformation, &c. 
to the liquid state, Professor James Thomson, in an ingenious speculation 
(suggested by the shape of the isothermals immediately above the critical 
temperature), proposed an isothermal curve of the form represented in fig. 2, 
which embraces the idea of continuity of transformation, so much insisted on 
by Andrews. Here, in passing from B to D, the substance is supposed to be 
homogeneous throughout, and not to be partly liquid and partly vapour as in 
the corresponding part BD of the isothermal of fig. 1. The word homogeneous 
must here, however, be taken with some reservation, for although the mass, as a 
whole, may be apparently homogeneous—that is, one cubic centimetre may be 
on the whole the same as another,—yet when considered in very small portions, 
the mass may be intensely heterogeneous. For example, small portions may 
approach the gaseous state more nearly than the liquid, while others may be 
more decidedly in the liquid condition.* 
Since the time of Andrews and Thomson, various attempts have been made 
to deduce from dynamical principles a general relation connecting the volume, 
pressure, and temperature of a substance which will apply to the liquid as well 
as the gaseous condition of matter, and which will also hold throughout the 
transformation from one state to the other. Of these, the most notable examples 
are those of Van der Waals and Clausius, both of whom obtained equations 
(founded on certain assumptions), for the isothermal curves which, when traced, 
presented the characteristics of the curve suggested by James Thomson, as shown 
in fig. 2. 
A difficulty which presents itself at once to the acceptance of such a curve as 
representing a realisable series of transformations, is that the part M N represents 
conditions of the substance in which the volume and the pressure increase 
together. As a consequence, this part of the curve has been generally regarded 
as unrealisable, and direct experimental evidence of it has been nowhere found in 
nature; yet, the interesting phenomena of superheating and supersaturation are 
so well represented by the portions BM and DN, that the whole curve has been 
admitted as a possible, if not a necessary, generalisation. 
It is to this unrealisable part of the curve that I now wish to attract attention, 
and I shall endeavour to show that there is a conceivable condition of the 
substance which satisfies the extraordinary demands of the portion MN, viz., 
that the pressure and volume shall increase together, and that throughout the 
transformation the substance shall be in equilibrium, although necessarily 
unstable. 
For this purpose, let us consider the condition of the substance at any point 
of the isothermal between B and D. What really happens in practice is, that 
* This view has been put forward more than once in the Author’s Theory of Heat, e.g., p. 896. . 
