( 191 ) 



two other phases, and u the degree of this decrease of volume. We 

 arrive at the same result if we follow the course (Verslag Kon. 

 Akad. v. Wetensch. Deel V, p. 482) indicated there, viz. : 



We find the same equation when we have three phase equilibrium 

 for a binary system of solid, liquid, and gaseous. And the course 

 of the line p=f{T) is then known. It is a line, consisting of two 

 branches lying above each other, which smoothly pass into each 

 other at a certain maximum temperature, and the upper branch of 

 which possesses maximum pressure. In this case, however, the course 

 is simpler. For the equilibrium of solid, liquid, and gaseous two 

 branches occur; on one branch the liquid is richer in one of the 

 components than the solid body, and on the other branch the reverse. 

 Where these branches meet, the value of x has the same amount 

 for the solid body and for the liquid, and in that point the line 

 p=f(T) has an element in common with the melting-point line. 



dp 



This is seen from the value of — , if e. g. x 3 = x, is put in it, in 



dT 



which case ■— = — 



dT 



And it has, therefore, often been stated 



as a fixed rule, that when two phases have the same concentration, 

 the variation of equilibrium with the temperature depends only on 

 these two phases, and is independent of. the third. Also for equi- 

 librium of 2 liquid phases and one gas phase, however, equality of 

 concentration may occur between two phases. Thus one of the liquid 

 phases may get the same concentration as the gas phase, or the two 

 liquid phases may get the same value of x. Then the above mentioned 

 rule does not hold. When a solid body has the same concentration 

 as a liquid, and e.g. x, =x t , then ij, is not equal to ?j,, and v % not 

 equal to v t . Then there are, indeed, two phases of the same con- 

 centration, but not two identical phases. But when a liquid phase 

 has the same concentration as a gas phase this expression means 

 that in the three phase triangle one of the sides has been reduced 

 to zero, and these two phases have become identical. Then we find 



13 

 Proceedings Royal Acad. Amsterdam. Vol. X. 



