184 J. W. Gibbs — Equilibrmm of Heterogeneous Substances. 



page 155. But on that side of the limit on which the coexistent 

 phases are possible, there will be two pairs of coexistent phases for 

 the samj values of t and />, as seen in figure 6. If the curve AA' repre- 

 sents vapor, and the curve BB' liquid, a liquid 

 (represented by) B may exist in contact with 

 a vapor A, and (at the same temperature and 

 pressure) a liquid B' in contact with a vapor 

 A', If we compare these phases in respect to 

 their composition, we see that in one case the 

 ^^' ^' vapor is richer than the liquid in a certain 



component, and in the other case poorer. Therefore, if these liquids 

 are made to boil, the effect on their composition will be opposite. If 

 the boiling is continued under constant pressure, the temperature will 

 rise as the liquids approach each other in composition, and the curve 

 BB' will rise relatively to the curve AA', until the curves are tangent 

 to each other, when the two liquids become identical in nature, as also 

 the vapors which they yield. In composition, and in the value of 'Q per 

 unit of mass, the vapor will then agree with the liquid. But if the 

 curve BB' (which has the greater curvature) represents vapor, and 

 AA' represents liquid, the effect of boiling will make the liquids A 

 and A' differ more in composition. In this case, the relations indi- 

 cated in the figure will hold for a temperature higher than that for 

 which (with tlie same pressure) the curves are tangent to one another. 

 When two coexistent phases of three component substances have 

 the same composition, they are represented by the point of contact of 

 two sheets of the primitive surface. If these sheets do not intersect 

 at the point of contact, the case is very similar to that which we have 

 just considered. The upper sheet except at the point of contact 

 represents unstable phases. If the temperature or pressure are so 

 varied that a part of the upper sheet protrudes through the lower, the 

 points of contact of a double tangent plane rolling upon the two 

 sheets will describe a closed curve on each, and the surface of dissi- 

 pated energy will include a portion of each sheet of the primitive sur- 

 face united by a ring-shaped developable surface. 



If the sheet having the greater curvatures represents liquid, and 

 the other sheet vapor, the boiling temperature for any given pressure 

 will be a maximum, and the pressure of saturated vapor for any given 

 temperature will be a minimun, when the coexistent liquid and vapor 

 have the same composition. 



But if the two sheets, constructed for the temperature and pressure 

 of the coexistent phases which have the same composition, intersect 



