EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 127 



DTE, FTG, HTA. Now we may make either sheet of the primitive 

 surface sink relatively to the other by the proper variation of 

 temperature or pressure. If the sheet to which ATB, ETF belong is 

 that which sinks relatively, these parts of the surface of dissipated 

 energy will be merged in one, as well as the developable surfaces ETC, 

 DTE, and also FTG, HTA. (The lines CTD, BTE, ATF, HTG will 

 separate from one another at T, each forming a continuous curve.) 

 But if the sheet of the primitive surface which sinks relatively is 

 that to which CTD and GTH belong, then these parts will be merged 

 in one in the surface of dissipated energy, as will be the developable 

 surfaces ETC, ATH, and also DTE, FTG. 



It is evident that this is not a case of maximum or minimum tem- 

 perature for coexistent phases under constant pressure, or of maximum 

 or minimum pressure for coexistent phases at constant temperature. 



Another case of interest is when the composition of one of three 

 coexistent phases is such as can be produced by combining the other 

 two. In this case, the primitive surface must touch the same plane 

 in three points in the same straight line. Let us distinguish the parts 

 of the primitive surface to which these points belong as the sheets (A), 

 (B), and (C), (C) denoting that which is intermediate in position. 

 The sheet (C) is evidently tangent to the developable surface formed 

 upon (A) and (B). It may or it may not intersect it at the point of 

 contact. If it does not, it must lie above the developable surface 

 (unless it represents states which are unstable in regard to continuous 

 changes), and the surface of dissipated energy will include parts of 

 the primitive sheets (A) and (B), the developable surface joining 

 them, and the single point of the sheet (C) in which it meets this 

 developable surface. Now, if the temperature or pressure is varied 

 so as to make the sheet (C) rise 

 above the developable surface 

 formed on the sheets (A) and (B), 

 the surface of dissipated energy 

 will be altered in its general 

 features only by the removal of 

 the single point of the sheet (C). 

 But if the temperature or pressure 

 is altered so as to make a part Flgl 



of the sheet (C) protrude through the developable surface formed 

 on (A) and (B), the surface of dissipated energy will have the form 

 indicated in figure 8. It will include two plane triangles ABC and 

 A'B'C', a part of each of the sheets (A) and (B), represented in the 

 figure by the spaces on the left of the line aAAV and on the right of 

 the line bBB'b', a small part CC' of the sheet (C), and developable 

 surfaces formed upon these sheets taken by pairs ACC'A', BCC'B', 



