HETEROGENEOUS EQUILIBRIUM 291 



other, their stable portions adjoining, and when the phases, L, 

 K20-Si02, and K20-2Si02, fall on a straight line these two 

 curves will coincide in their stable portions. 



The quintuple point Qz is exactly similar to Qi, but in- 

 stead of KzO-SiOa-^HsO, KaO-SiOz, and K2O -28102 we have 

 K20-Si02-H20, KaO-SiOs-IHaO, and K20-2Si02-H20, respec- 

 tively. Making these substitutions, the discussion of Qi will 



apply to Q3. 



Quintuple points Q2 and Q4 also are similar to each other. 

 Both contain the same three phases, V, K2O -28102 -1120, and 

 K2O • 28102 • At Q2 we also have the liquid represented by the 

 point Q2 and the solid phase, K2O • 8i02 • IH2O; at Qi we have the 

 liquid represented by the point Qi and the solid phase, 

 K2O • 48102 • H2O. Since in both systems the phases, V, 

 K2O • 28102 • H2O, and K2O • 28102, He on a straight line, the curve, 

 V-f K2O • 28102 • H2O + K2O • 28102 + K2O • 8102 • IH2O (7a), which 

 proceeds from Q2 to lower temperatures and pressures, and the 

 curve, V + K2O • 28102 • H2O + K20- 28102 + K2O • 48102 • H2O 

 (76 + 7a), which proceeds from Q4 to lower temperature 

 and pressure, and the curve, V + L + K2O • 28102 • H2O + 

 K20- 28102 (76 + 7c), which proceeds from both Q2 and Qa 

 to higher temperatures and pressures, coincide with each other 

 and with the dissociation-pressure curve of K2O • 28102 • H2O in 

 the binary system, HgO-KaO- 28102 (curve 7a + 76 + 7c). 

 The positions of the other curves that proceed from Qo and Q4 

 are easily found by the same mode of reasoning as that applied 

 to the curves at Qi. 



The quintuple points Qsa and Qsb* differ from the preceding 



* The compound, K2O -48102, was not met with in the original study 

 of the ternary system, by Morey and Fenner {J. Am. Chem. Soc, 39, 

 1173 (1917)), but was found later in the study of the anhydrous binary 

 system by Kracek, Bowen, and Morey (/. Phys. Chem., 33, 1857 (1929)). 

 The evidence in both studies makes it probable, though not certain, 

 that K20-4Si02-H20 has a congruent melting point. The relations 

 around quintuple points Qoa and Qiu are thus in part hypothetical, and 

 in Fig. 8 the two invariant points are not separated, nor are the two 

 curves from Qsa and Q&h to the sides of the diagram. The eutectics 

 containing K2O -48102 in the binary system, K20-8i02, are at 752° and 

 69 weight per cent silica, and at 764° and 72 per cent silica. 



