1151 



Let ns assume that point F in fig. 3 (XI) represents the two 

 modifications F and F' and that A a h n is the modificationcnrve and 

 h^nj)^)!^ the vaponirnrve. 



Therefore, in the binary system two temperatures and pressures 

 of inversion occur, viz. in the points A and n. Considering the equi- 

 libria under a constant pressure, 7'/,= Tn; under their own vapour 

 pressure, however Tj, and 7'„ as well as /^/, and 7^,, are different. The 

 points A and n of fig. 3 (XI) resemble viz. ^ó and //? of fig. 1. Although 

 solid substance, liquid and gas of the equilibrium F-{-F' -\-Lh-\-(rk^ 

 and F ~\- F' + Ln-\- 6-'«i are represented by points of a straight line, 

 yet in A and n c/P=0 and dTz=z() is not the case. In order to 

 see this, we substitute in (52) — (54) « = ; from this we find : 



J. rcip\ ^.^ r s \ n'-n 



RT ' \dx):,= ~lv\ ~ 7j {ii—ii)LV—{v'—v)KH ' ' ^^^^ 



so that dP and dT in A and 7i are not zero. A V is the increase of 

 volume and A// is tlie increase of entropy when between F, L, 

 and G of the equilibrium F-^F' -\-L,-^(i,^ or F-\-F'-\- Ln-^Gh, 

 a reaction takes place, at which one volume of vapour is formed. [We 

 may also replace in (57) and (58) A F and A// by A F' and A//', 

 which indicate then the same increases when the phases i^', L, and 6^ 

 react]. When in fig. 3 (XI) A and n are situated not too close to 

 F, or in other words, when the temperatures of inversion T/j and T„ 

 are situated not too close to the melting-point Tf , A T^ is ^0 and large 

 with respect to v' — v; the denominator of (57) and (58) is then 

 generally positive. 



That there may be accordance with fig. 1. we take first v'^v. 

 In fig. 3 in the vicinity of A and A; (see A Faa^) s ^ s^ ; in the 

 vicinity of n and n^ (see A Fhh^) s<:^,s\. From (57) and (58) now 

 follows : i^and 7Mncrease along the modificationcnrve from n tow^ards A. 

 When we take v' <^v then it follows: 7' increases from A towards 

 n, P from 7i towards A. 



At last we may still consider the case, that F and consequently 

 also F' is one of the components, e.g. B. The reader can easily draw 

 himself the P, 7-diagram, which is now simpler than in fig. 1. 

 In the concentrationdiagram the modificationcnrve ends then in two 

 points, the one on BC and the other on BA. If we determine the 

 modificationcnrve under a constant pressure, T is the same in each 

 point of this curve; in this case T and 7^ will change however again 



75 



Proceedings Royal Acad. Amsterdam. Vol. XVI, 



