472 Proceedings of the Royal Society of Edinburgh. [Sess. 
liquid and solid states into a single state, latent heat may vanish. On the 
other hand, Tammann has shown that, at a temperature of — 22° C. and 
under a pressure of over 2000 atmospheres, ice tends to assume two other 
crystalline forms ; so that multiplication of states takes place. 
It is to be noted that there is no region of instability on the complete 
isothermals corresponding to the postulated condition of entire absence of 
nuclei. To realise the condition of homogeneity referred to in section 2, it 
must be assumed that the molecules of the containing vessel exert appro- 
priate forces upon the molecules of the substance. 
To present the case of a three-state substance which expands in the 
process of liquefaction, and volatilises, below its triple-point, without the 
possibility of formation of liquid, it is only necessary to interchange the 
diagrams and the terms liquid and solid, etc. 
6. The following reasoning establishes the law of equality of areas 
given above. 
Except in so far as rapidity is concerned, the normal process of change of 
state takes place independently of the amount of nucleus present. There- 
fore the physical state of the substance is independent of the presence or 
absence of nuclei. Thus the same terminal conditions subsist whether we 
pass from p to r by the path pqr, or by the path p B q C r ; and the 
amounts of work performed are identical, so that the areas p B q and qC r 
are equal. Another alternative path is p ab qcdr. Therefore p qba 
= qc dr, and a B b — c C d. 
( Issued separately July 28, 1910.) 
