101 

 In this: 



v' — [|i (a-,— A') + « (»/— ^i) + •'• //i— -''•i .'/J ^ ^ .g. 



'" = L-^-: (i?'-i?) + .'/i («-«') + «' /^— « in ^ ' 



in wliicli A is an arbitrary factor. The signiticanoc (hereof is as 

 follows: In each fourphase ecjiiilibrium F -{- F' -\- L -\- G a reaction 

 can always take place, which we represent by : 



11 quant. F -\- n' qiiant. F' -\- i)i quant. L -\- m^ quant. G = (7) 



It is evident that the four reaction coefficients in (7) cannot have 

 the same sign. With the aid of the known compositions of the four 

 phases we find from (7) that n, u', vi and 7/i, have the values given 

 in (6). The numerator of (5) therefore represents the change in 

 entropy, the denominator the change in volume occurring in reaction 

 (7). If we call the heat to be supplied or withdrawu in this reaction 

 A IF and the change occurring in volume A I^, then (5) changes into 

 the well-known relation : 



d^P AW 



T — = (8) 



dT LV ^ ^ 



which, of course, we might have deduced in a dilFcrent manner. 



Before applying this formula we will first investigate more closely 

 the liquid um and the vapoui- curve and the reactions which can 

 appear in the system F -\- F' -{- L -\- G. 



Let us first consider the point of intersection S of the liquidum 

 curve ac (^fig. 1, 2 and 3) with the line FF' ; the vapour a]iper- 

 taining to this liquid S is indicated by 6\. As the three points F, 

 F' , and *S of this four-phase equilibrium F -\- F' -\- liquid S -\- vapour 

 aSj are situated on a straight line, a reaction occurs in which the 

 vapour does not take part. According to the situation of the three 

 points F, F' , and aS in regard to each other this reaction will be 

 F-\-F':^L or F':^F-\-L or F:^F' -\- L. 



If the three points are situated as in fig. 1 or 2, the reaction is 

 F -\- F' "^ L ; the liquid S is then formed by the joint fusion of the 

 compounds F and F' , so thitt the point S is a point of the melting 

 point line of the complex F -\- F' . As this li(|uid, however, can be 

 also in equilibrium with a vapour 6'i, the point >S is the minimum 

 melting point of the complex F -\- F' . 



If the three points are situated as in fig. 3 the reaction F'^F-\-L 

 occurs ; the point >S is then the incongruent minimum melting point 

 of the complex F-{- F'. 



