394 



substituting therein .v^, y, and V^ for x, y and V, and vice versa. 

 In this waj condition (6) is again obtained. From this follows : if 

 two saturation curves under their own vapour pressures touch each 

 other, then their corresponding vapour saturation curves must also 

 touch, and vice versa. This is the case when the four phase reaction 

 takes place without change of volume. 



When considering figs. 2 — 5 we have supposed that in the four- 

 phase systems always a four-phase reaction takes place. As a tran- 

 sition instance a three phase reaction may, however, also take place. 



If we limit ourselves to such reactions taking place between 

 liquid, vapour and one of the solid bodies, then we have: h) 

 F^L:^Gl)L:^F-{- Gj) F:^ Z + G B F + X ^ G I) L:^ 

 F' j^ Qm) F':^L^ G. 



In the four-phase equilibrium j^^ -|- i^' -|- liquid </-]- vapour g^ 

 (figs 2, 3 and 4) reaction It, i or j takes place, if the points F, g 

 and //i are situated in a straight line. Reaction h takes place if the 

 point (/i, reaction i if the point g, and reaction / if the point F is 

 situated between the other two points. 



If, however, the three jioints F, g and g^ are in a straight line, 

 then the pressure for the system i^-{- liquid (/-[- vapour (/j will be 

 a maximum or minimum, as we have seen before. The point g 

 will then be the point of maximum or minimum pressure for the 

 saturation curve of F, the point g^ such a one for the vapoursatu- 

 ration curve under its own vapour pressure. Consequently in fig. 

 2 the point g coincides with the point y or the point ƒ with the 

 point X. 



The previous considerations may also be expressed thus : when in 

 the equilibrium F -\- F' -\- L -^ G one of the three-phase reactions 

 h — m takes place, a point of maximum or minimum pressure of a 

 saturation curve is situated on the liquid curve of this equilibrium, 

 and a similar point of the vapour saturation curve under its own 

 vapour pressure on the vapour curve of this equilibrium. 



In connection with the previously deduced properties (communi- 

 cation VIII) we find, consequently, that if in a four phase equili- 

 brium F -f F' -\- L ^ G a three-phase reaction takes place between 

 liquid, gas and one of the solid bodies then : 



1. the four-phase curve, the limit curve of this compound and 

 the solution path of this compound belonging to this point will touch 

 one another in the P, J'-diagram. 



2. in the concentration diagram on the liquid curve of the four 

 phase equilibrium a point of maximum or minimum pressure of the 

 saturation curve of the compound will be situated, and on the 



