288 MOREY ART. G 



the various univariant reactions. This is evident from equation 

 [129] or from the expanded form of (6) [129] given below. The 

 method of applying this criterion is by considering what 

 curves will coincide when we vary the composition of different 

 phases. If by varying the composition of one phase in a 

 certain direction n phases get on the onefold (n), then, as proved 

 above, the p-t curves of the two univariant equilibria formed 

 by these n phases with each of the other two phases will coin- 

 cide; these two curves must be adjoining curves, and no other 

 curves can be between them. By repeating this reasoning, 

 assuming the composition of the same phase to change in other 

 directions, or assuming the composition of another phase to 

 change, the relative positions of the p-t curves, i.e., the order 

 in which they succeed one another around the invariant point, 

 can be deduced. The stable and metastable portions can be 

 distinguished by means of the theorems previously given. 



33. Order of the p-t Curves in the Ternary System, H2O- 

 K2O • SiO^-SiOi. Let us apply the above considerations to the 

 quintuple points in the ternary system, H2O-K2O • Si02-Si02, 

 and pay particular attention to the question of the sequence of 

 the p-t curves around the invariant (quintuple) point. For the 

 purpose of this discussion, we will combine the above theorems 

 in regard to the conditions under which p-t curves coincide, and 

 in regard to the factors which determine whether the curves 

 coincide stable to stable or stable to metastable, in the following 

 rule: Whenever in a ternary system three phases lie on a 

 straight line, the p-t curves of all the ternary univariant 

 equilibria containing these three phases coincide with each other 

 and with the p-t curve of the univariant binary equilibrium 

 between the three phases alone. When the other two phases at 

 the quintuple point lie on the same side of the line on which 

 lie the compositions of the three reacting phases, the curves 

 coincide stable to metastable ; when the other two phases lie on 

 opposite sides of the line on which lie the compositions of the 

 three reacting phases, the curves coincide stable to stable. 



The compositions of all the phases which are met with in 

 the ternary system, H2O-K2O • Si02-Si02, are shown in Fig. 6. 

 In treating this system we will assume that the vapor phase 



