393 



each otlior, and also thai (he (wo [)oin(s of' contact are not situated 

 on the line joining F and F' of the solid phases. Tins also follows 

 from the eqnations of these curves. 



The saturation curve under its own vapour pressure is, as we 

 have seen before [8 and 9] (II)] fixed by 



[(.t'-«) r + (//-/?) «1 civ + \{o:-a) s -f {y - /:?) q chj ^ A . clP . {\) 

 \{w, - X) r + {y-y) .] d,v. -f \{x,-ai) s + {y,-y) q dy = C . dP . (2) 

 We may write for this, after eliminating clF 

 \{,v-a) C-{.v—.v) A {rdx -f sdy) + \{ii-^)C-{y—y)A[{iidiü + tdy)=:0{^) 



For the saturation curve of F' under its own vapour pressure we 

 have : 



!(,,_«') C—{x,—x)A\{rdx + sdy)^\{y—^') C-{y,—y)A%sdx-\-tdy) = 0{^) 



If the two saturation curves under their own vapour pressures 



dy 



touch one another, then, for this point of contact, — from (3) and 



dx 



(4) must necessarily have the same value. This is the case when : 



(,,_«') C-K-.^') .4' {y-^^)C-{y-y)A!' ' ' ^^^ 

 If we substitute herein the values of A, A' and C we find after 

 reduction : 



n + n' v' 4-- m V. + m^ F^ = (6) 



where n, n', m and m^ have the same values as in (6) (VIII). 



(6) is not satisfied by a point on the line FF' ; in this case, 

 namely m^ becomes = 0, and consequently, we should have to 

 satisfy, at the same time : 



nv -{- 71 v' -\- m V=() . . (7) 



As the value of the first part of (7) is, however, dependent on 

 the volumes of the three phases F, F' and L, consequently (7) is 

 usually not satisfied. This also follows from the meaning of the first 

 part of (7); this, namely, represents the change of volume which 

 takes place in the minimum melting point of the complex F -\- F' , 

 and this is, of course, only in higlily exceptional cases equivalent 

 to zero. 



The first part of (6) represents, as we have seen before, the 

 change of volume which takes place in a reaction in the four-phase 

 system F -\- F' -\- L -\- G. In agreement with previous considera- 

 tions consequently, we see that two saturation curves under their 

 own vapour pressures touch, if the four-phase reaction takes place 

 without change of volume. 



If the condition is calculated that two vapour saturation curves 

 may touch, then a form is obtained, which is deduced from (6) by 



