286 



tares starting from the invaiiant poinl ; wlien ^j and ?., are both 

 negative, then botii curves go towards lower 7'; when A, and ^, liave 

 opposite sign, tiien liolii curves go, starling from the invariant point 

 in opposite direction of temperature. 



It follows from all this that the tangent to curve E is situated 

 within the angle, which is forme<l hy the curves [F^) and {F,). [Of 

 course we mean that angle wich is smaller than 180']. As in the 

 case of K=0 (consequently ,c, ^ 0) curve E coincides with (F^) 

 and in the case of K =z ao (consequently ,/■, =r 0) curve /i" coincides 

 with (F,) consequentiv the property' follows, whicii we have deduced 

 already in the previous communication also, viz: 



Curve E is situated between the curves (i^J and (F,) or in other 

 words: in the region [F^ F,). 



Yet also we tind, however: 



Curve E is situated nearer curve (F,) in proportion as the con- 

 centration of the new substance in the phase F^ is larger with 

 respect to that in F,; curve E is situated nearer to curve (F,) in 

 proportion as the concentration of the new substance in the phase 

 F, is greater with respect to that in F^. 



When the new substance occurs only in the phases i^, F, and 

 F,, then we tind, in accordance with previous papers that curve E 

 is situated in the region {F^ F, F,). 



When one of the curves, f.i. (F3) is between the other two (i'',) and 

 [Fj) then curve E is situated also l)etween {F,) and {F,). When, 

 however, none of the three curves is situated between the other 

 two, then curve E may go, starting from the invariant point in 

 every arbitrary direction. 



Now we consider the binary equilibrium 



E (a; = 0)^F -^ L, + L, + G 

 we represent the composition, the entropy and the volume of 



F by y i — y H and V 



Zy, ,, y, 1 — _!/, //j and F", 



L, „ y, 1— y, H, and F, 



G ,, y, i—y, H, and T, 



When we add a new substance A', then we call its concentration 

 in those phases .r .r, ,r, and .r,. 



In order to deduce the isovolumetrical and isentro[)ical reaction 

 we take two arbitrary reactions; for this we choose: 



