266 MOREY ART. Q 



the difference in volume become zero, and the equation becomes 

 indeterminate. This is as should be expected; the three-phase 

 system was univariant because there were three equations 

 between the three quantities, pressure, temperature, and com- 

 position. When the two liquid phases become identical, not 

 only in composition but also in properties, there are no longer 

 three phases, but two only, and the system is no longer uni- 

 variant but divariant. In the case of calcium chloride hexa- 

 hydrate, when the liquid and solid phases had the same com- 

 position at the minimum melting point, there was still an 

 entropy difference, since it takes heat to melt a solid, and a 

 volume difference. At the temperature at which the two liquids 

 merge into one another, all distinctions between the phases 

 disappear, and there are but two phases, liquid and vapor. At 

 this temperature there may be not only the critical solution, 

 but also any other mixture of liquid phenol and water; the 

 composition of the solution or the vapor pressure must be fixed 

 in order to completely determine the system. 



The critical Hquid itself is, however, completely determined. 

 At a temperature very near to the critical solution temperature 

 of the mixture, there are still three equations, and the critical 

 solution is determined by the additional condition that the two 

 phases become identical. We have, then, four equations; three 

 of the type of (1) [97], and the additional equation expressing 

 the condition of identity between the two liquids, so this solu- 

 tion is uniquely determined. 



If from the invariant point, solid phenol + two liquids -\- 

 vapor, the water-rich layer disappears, we have the univariant 

 equilibrium, solid phenol + a phenol-rich Uquid + vapor. 

 This equilibrium will be realized if the total phenol content of 

 the mixture be greater than that of the phenol-rich liquid, and 

 constitutes another branch of the solubility curve of phenol in 

 water, or of the melting-point curve of phenol-water mixtures 

 along which the solubility of phenol in water increases uni- 

 formly, until the melting point of phenol is reached. This 

 curve does not differ in any important respect from the upper 

 portion of the H2O-KNO3 curve, except that the melting point 



