466 
Proceedings of the Royal Society of Edinburgh. [Sess. 
XXXIII. — On Continuous, and Stable, Isothermal Change of State. 
By Professor W. Peddie. 
(MS. received June 3, 1910. Bead June 6, 1910.) 
1. The three physical states of a substance, solid, liquid, and gaseous, are 
representable, as is well known, by means of three functions of pressure, 
volume, and temperature ; say 
fi(P, v , 0» / 2 fe *)> fsiP, v > t )• 
In the case of water-substance, James Thomson represented these 
functions as surfaces of his geometrical (p, v, t ) model. 
No attempt has been made to group these three functions in a single 
form F (p,v,t), though various equations combining f 2 and/ 3 , either empir- 
ically or as deductions from theory, have been given ; first, and notably, that 
of Van der Waals. In Thomson’s model the process of gradual isothermal 
and isopiestic passage from one state to another is indicated by motion of 
the representative point along a line parallel to the axis of volume. This 
gradual passage, which represents the change occurring normally in the 
processes of solidification, liquefaction, or vaporisation, does not represent a 
strictly continuous physical process. The continuous change of volume 
occurs because the associated discontinuous change of molecular arrangement 
takes place in gradual instalments. A sudden change of density occurs on an 
instantaneously infinitesimal volume scale. It is now recognised that this 
normal process of passage from one state to another is dependent on the 
presence of suitable nuclei. In the absence of suitable nuclei, abnormal 
extension of the surfaces / 2 and / 3 , at temperatures above the triple-point, 
is made evident by the phenomena of super-heated or infra-pressed water 
and of super-pressed or infra-heated steam. So also, abnormal extension 
of the surfaces f v / 2 , and / 3 , at temperatures below the triple-point, is made 
evident, in the case of / 2 , by the existence of infra-pressed or infra-heated 
water ; in the case of f v by the existence (?) of infra-pressed ice under suitable 
conditions analogous to those of Berthelot’s experiment, or (?) of super-pressed 
nucleus-free ice ; in the case of / 3 , by the existence of infra-heated or super- 
pressed vapour. 
2. Those cylindrical surfaces, which, in the (p, v, t ) model, represent 
normal conditions during change of state, do not therefore correspond to the 
