126 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



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 con- 

 tinued 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 f 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 indicated 

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

 (with the 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 dissipated energy will include a portion of each sheet of the 

 primitive surface 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 minimum, 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 



at the point of contact, the whole primitive 

 surface as seen from below will in general 

 present four re-entrant furrows, radiating 

 from the point of contact, for each of which 

 a developable surface may be formed by a 

 rolling double tangent plane. The different 

 parts of the surface of dissipated energy in 

 the vicinity of the point of contact are 

 represented in figure 7. ATB, ETF are 



parts of one sheet of the primitive surface, and CTD, GTH are parts 

 of the other. These are united by the developable surfaces ETC, 



