48 EEPRESENTATION BY SURFACES OF THE 



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

 curved surface of a liquid" (Proc. Roy. Soc. Edinb., Session 1869-1870, 

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

 ments 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 absolute stability, together with the triangle repre- 

 senting a compound of three states, and the three developable surfaces 

 which have been described representing compounds of two states, 

 forms a continuous sheet, which is everywhere concave upward 

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

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

 value of r\ for any given values of v and e. 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 r\ and e. 

 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 

 form a solid figure unbounded in some directions, but bounded in 

 others by this surface.! 



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

 we may avoid the necessity of keeping the vessel hotter than the vapor, in prder to 

 prevent 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 

 pressure of the vapor. If the stem at the top of the column of liquid should be made 

 hotter 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 probable, 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 those of saturated vapor. 



f This description of the surface of dissipated energy is intended to apply to a sub- 

 stance capable of existing as solid, liquid, and vapor, and which presents no anomalies 

 in its thermodynamic properties. But, whatever the form of the primitive surface 

 may be, if we take the parts of it for every point of which the tangent plane does 

 not cut the primitive surface, together with all the plane and developable derived 

 surfaces which can be formed in a manner analogous to those described in the preceding 

 pages, by fixed and rolling tangent planes which do not cut the primitive surface, 



