HETEROGENEOUS EQUILIBRIUM 275 



of the univariant equilibria, P' + P" + P'" + P^^ and P' + 

 P" + -P^^ + P^ , which proceed from the quintuple point, 

 P' + P" + P'" + P^^ + P^. The equation of the first of these 

 is 



H' m/ W/i niz 



H" m/' W2" ms" 



dp _ 

 dt 





F' w/ m^' rriz 

 V" my" m," m," 

 V" m,'" m^'" m,"' 



IV IV IV IV 

 mi 7712 W3 



F 



Now assume that P', P", P'" lie on a straight line in the com- 

 position diagram,* We then have the relation 



and hence also 



and 



A'P' = A"P" + A"'P"', 



nt in 

 nil > 



AW = A'W + A 

 AW = A'W' + A"W'\ 



AW = A'W' + A 





By substituting these values of mi ', ma', W3' in the above deter- 

 minants, and subtracting A" times the second row and A'" 

 times the third row from A' times the first row, we get 



* An example of this is found in Fig. 5. Here the phases are 

 K20-2Si02, K20-2Si02-H20 and V; the vapor phase contains only H2O, 

 and its composition is represented by the apex of the component 

 triangle. 



