1 74 J. W. Glbbs — EqmUhriuiin of Heterogeneous Substances. 



The surfaces detined by equations (187) and (189) may be distin- 

 guished as the v-7]-e surface, and the t-2>'C surface, of the substance to 

 which they relate. 



In the t-p-'C surface a line in which one part of the surface cuts 

 another represents a series of pairs of coexistent states. A point 

 through whicli pass three different parts of the surface represents a 

 triad of coexistent states. Through such a point will evidently pass 

 the three lines formed by the intersection of these sheets taken two 

 by two. The perpendicular projection of these lines upon the i>t 

 plane will give the curves which have recently been discussed by Pro- 

 fessor J. Thomson.* These curves divide the space about the projec- 

 tion of the triple point into six parts which may be distinguished as 

 follows : Let C^'^^, C^^', ^^*-' denote the three ordinates determined for 

 the same values of p and t by the three sheets passing through the 

 triple point, then in one of the six spaces 



^(n<Ki)<^(s,^ (191) 



in the next space, separated from the fornier by the line for which 



^(n<^(S)<^(z)^ (192) 



in the third space, separated from the last by the line for which 



^(Sj<^(n^^W (193) 



in the fourth ?(«> < ?(^) < C^''\ (194) 



in the fifth C^^> < tS^^ < ?(^), (195) 



in the sixth C<^> < ?(^) < ?(«>. (196) 



The sheet which gives the least values of 'C, is in each case that which 

 represents the stable states of the substance. From this it is evident 

 that in passing around the projection of the triple point we pass 

 through lines representing alternately coexistent stable and coexistent 

 unstable states. But the states represented by the intermediate 

 values of ? may be called stable relatively to the states represented 

 by the highest. The differences C^^^ — ^^'>, etc. represent the amount 

 of woi"k obtained in bringing the substance by a reversible process 

 from one to the other of the states to which these quantities relate, 

 in a medium having the temperature and pressure common to the 

 two states. To illustrate such a process, we may suppose a plane 

 perpendicular to the axis of temperature to pass through the points 



* See the Keports of the British Association for 1871 and 1872 ; and Philosophical 

 Magazine, vol. xlvii. (1874), p. 447. 



