398 -T. TT. Gibbs on a Representation by Sxn'faces 



that it may exist at a given temperature at pressures greater than 

 that of equilibrium between the vaj)or and its liquid meeting in a 

 plane surface at that temperature, the considerations adduced by Sir 

 W. Tliomson in his paper "On the equilibrium of a vapor at the 

 curved surface of a liquid" (Proc. Roy. iSoc. Ed., Session 1869-1870, 

 and Phil. Mag., vol. xlii, p. 448), leave no room for doubt. By exper- 

 iments like that suggested by Professor J. Thomson in his paper 

 already referred to, we may be able to carry vapors farther beyond 

 the limit of absolute stability.* As the resistance to deformation 

 characteristic of solids evidently tends to prevent a discontinuous 

 change of state from commencing within them, substances can doubt- 

 less exist in solid states very far beyond the limit of absolute stability. 

 The surface of absc^lute stability, together with the triangle repre- 

 senting a compound of three states, and the three developable sur- 

 faces which have been describe<l representing com]>ounds of two 

 states, forms a continuous sheet, which is everywhere concave upward 

 except where it is plane, and has only one value of £ for any given 

 values of v and ij. Hence, as t is necessarily positive, it has only one 

 value of 1} for any given values of v and £. If vaporization can take 

 place at every temperature except 0, p is everywhere positive, and 

 the surface has only one value of v for any given values of 7/ and s. 

 It forms the surface of dissipated energy. If we consider all the 

 points representing the volume, entropy, and energy of the body in 

 every possible state, whether of equilibrium or not, these points will 



* If we experiment with a fluid which does not wet the vessel which contains it, we 

 may avoid the necessity of keeping the vessel liotter than the vapor, in order to pre- 

 vent condensation. If a glass bulb with a stem of sufficient length be placed vertically 

 with the open end of the stem in a cup of mercury, the stem containing nothing but 

 mercury and its vapor, and the bulb nothing but the vapor, the height at which the 

 mercury rests in the stem, affords a ready and accurate means of determining the pres- 

 sure of the vapor. If the stem at the top of the column of liquid should be made hot- 

 ter than the bulb, condensation would take place in the latter, if the liquid were one 

 which would wet the bulb. But as this is not the case, it appears probalDle, that if 

 the experiment were conducted with proper precautions, there would be no condensa- 

 tion within certain limits in regard to the temperatures. If condensation should take 

 place, it would be easily observed, especially if the bulb were bent over, so that the 

 mercury condensed could not run back into the stem. So long as condensation does 

 not occur, it will be easy to give any desired (different) temperatures to the bulb and 

 the top of the column of mercury in the stem. The temperature of the latter will 

 determine the pressure of the vapor in the bulb. In this way, it would appear, we 

 may obtain in the bulb vapor of mercury having pressures greater for the tempera- 

 tures than tliose of saturated vapor. 



