Transformation from the Liquid to the Gaseous State. 233 



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 through- 

 out 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 cer- 

 tain 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 realizable series of trans- 

 formations, is that the part MN 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 unrealizable, and 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, 

 generalization. 



It is to this unrealizable 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 through- 

 out the transformation the substance shall be in equilibrium, 

 although necessarily unstable. 



For this purpose, let us consider the condition of the sub- 

 stance at any point of the isothermal between B and D. 

 "What really happens in practice is, that bubbles of vapour are 

 formed in the interior of the liquid mass, and by reason of 

 the action of gravity these rise vertically upwards, and the 

 result is that the mass becomes separated into two portions, 

 the upper part of the containing vessel being filled with 

 vapour, and the lower part by the remaining liquid. The 

 action of gravity is thus to separate the vapour bubbles from 

 the liquid, and it is on this account, as we shall see, that the 

 part BD of the isothermal is, in practice, a right line as shown 

 in fig. 1. If, however, we imagine the action of gravity to 

 be removed, then a bubble of vapour when formed would 



* This view has been put forward more than once in the Author's 

 < Theory of Heat/ e . c/., p. 396, 



