547 



oilier, tlicir moliisluhlc pi'oloiigatioiis ;ii-e .si(na('3«l in llie viciiiilj of 

 llie i)oiiit of intersection, both within or both outside llie corresponding 

 threephasetriangle. 



Whether the two curves themselves with respect to the other 

 phases are already metastable or not, does of course not effect the 

 validity of this rule. 



When two equilibriumcurves intersect each othei' in a point X, 

 the phase A', (liquid, gas, mixed crystal) may be in equilibrium 

 with two other phases which we shall call iM and A' (liquid, gas, 

 mixed crystal etc.). The lines XM and AW form four angles ; we 

 shall now call the angle XMX therefore, the- angle being one of 

 the angles of the three-phasetriangle, and its opposite angle, the 

 threephaseangle of the point X. 



Wc' can express now the abovementioned rule also in this way: 



When two equilibriumcurves {F and T constant) intersect each 

 other, both curves are situated in the vicinity of the point of inter- 

 section, either within or outside the threephaseangle of the point 

 of intersection. 



In the figures 1, 2, and 3 we see, that the position of the curves 

 in the vicinity of their points of intersection is in agreement with 

 this rule. 



Let us take for instance the point of intersection .v in fig. 1 or 2. 

 In this point x the curves dv and tu intersect each other and 

 therefore the equilibrium F' -f- liquid ,v -{- vapour a\ occurs. The 

 threephaseangle of the point a' therefore is /'x^xF' and its 

 opposite angle. The curves dx and ux are drawn in fig. 1 and 2 

 within this angle, in fig. 3 (herein ux is replaced by Sx) outside 

 this angle. 



Let us now take a point of intersection of three curves as for 

 instance the point ƒ in fig. 2. Taking these curves two and two, 

 we have three pairs of curves ; the abovementioned rule is appli- 

 cable to each of these pairs. 



If we contemplate the pair of curves dfe and uxf, the equilibrium 

 F' -\- liquid ƒ 4- vapour f\ occurs in ƒ. The threephaseangle 

 of the point ƒ is therefore / f\fF' and its opposite angle. The 

 curves dfe and uxf are both drawn within this angle. 



If we contemplate the pair of curves dfe and ubf, then in ƒ 

 occurs the equilibrium F -[- liquid ƒ -|- vapour /j ; the threephase- 

 angle of the point / is therefore / f^fF ^^^ i'^ opposite angle. 

 The curves dfe and uhf are both drawn within this angle. 



If we contemplate the pair of curves uxf and id)f, then in ƒ 

 occurs the equilibrium F -]- F' -\- \\([\m\ f, the threephaseangle of 



