Preston—On the Continuity of Isothermal Transformation, &c. 125 
It is interesting to note, that the mass may be transformed from the condition 
B to the condition D by two distinct routes of transformation—one along the 
right line BD, in which the condition is stable, and the other along the curved 
path BMCND, in which the condition is unstable,—yet the principle of the 
conservation of energy forces us to conclude that the work done against external 
pressure, while the mass expands from B to D, must be the same in the two 
cases, and for this reason it has been concluded, that whatever the shape of the 
curve AMND may be, the area of the loop BMC must be equal to the area 
of the loop CND. At first sight we might apply the same reasoning to the 
transformation from B to C, or from D to C, and rush to the conclusion that 
the area of each loop must be zero, or else that we are here presented with a 
violation of the principle of conservation of energy. 
But it must be remarked, that although at the point C of the diagram, the 
mass, in both cases, has the same temperature, pressure, and volume, yet in 
one case all the vapour is collected into one portion of the chamber, and all 
the liquid into the other, whereas in the other case, the vapour and liquid are 
not distinctly separated from each other, but intermixed in some way so as to 
occupy the whole space as an apparently homogeneous mass. Hence the point 
C represents two distinct conditions of the mass in which the pressure, volume, 
and temperature are the same, but in which the internal energies may differ 
very considerably. Thus, although less external work is done in passing from 
B to C along the curve BMC, than in passing along the right line BC, yet in 
virtue of the arrangement of the mass, the internal energy at C, in the former 
case, may be considerably greater than in the latter. 
This, indeed, must be the case if the arrangement of the mass be of the 
bubble and drop nature here suggested. For, if a given mass, existing partly 
as liquid and partly as vapour, in such a way that the liquid is collected 
together in one part of the containing vessel, while the vapour is all collected 
in the remainder (as ordinarily occurs in practice), and if we desire to change 
it from this arrangement into one like that described above, in which the 
vapour is disseminated through the liquid in bubbles, or in which the whole 
vessel is filled with vapour and drops, a certain amount of work must be done 
in order to effect the transformation—namely, the equivalent of the surface 
energy possessed by the enormously increased surface area of the bubbles and 
drops in the new condition. Thus, although less external work is done in 
passing along the isothermal BMC than along the rectilinear path BC, yet the 
mass in the former case possesses more surface energy than in the latter, and the 
excess of external work in the latter transformation is represented in the former 
by an excess of internal work spent in generating the excess of surface film. 
Similar remarks apply to the portion CND, for in passing along this curve, 
