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

f1(p, v, t), f2(p, v, t), f3(p, 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 f2 and f3, either empirically 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.