666 



and the curve L(P= Pc) which is not drawn, touch one another, 

 etc. Consequently curve abed touches two curves L {P = P^) viz. 

 in b curve L {P =: Pi,) and in c curve L {P = Pc). 



In the point 5 three curves touch one another viz. curve 

 L{R) = mSM, curve L[T =Ts) — iSk, and the curve L (P= P5), 

 which is not drawn. 



Some special cases. 



Before we have already drawn the attention to the fact, what 

 changes have to be made in the conditions (2) and (3) [XVIi], when 

 one or more of the phases have a constant composition. When, 

 however, ail phases have a constant composition, then the conside- 

 rations must be somewhat altered. Let us ta,ke a phases-complex 



in which all the phases have a constant composition. We now may 

 distinguish two cases, accoi'ding to the fact whether in this complex 

 a phase- reaction may occur either never or always. In the latter 

 case E passes into an equilibrium Er and the phase-reaction is 



p.^ iT, + ... + ;, i^, 4_ ... -f. ;„ F„ = 



in which ?.^ . . . are independent of P and T. 

 The condition for equilibrium becomes now : 



;i. ^, + ;., Z, + . . . -h A„ Z„ = 0. 



As Z^ . . . depend only upon Pand 7', the equilibrium is represented 

 therefore, in the P,T-diagram by a curve. The direction of this 

 curve is defined by (9). 



We may also imagine the c£lse that phases occur with limited 

 changeable composition viz. phases in which one or more components 

 have a constant composition and the other components a variable 

 composition. This is e.g. the case when two hydrates A.nHJ) 

 and B . nH^O form mixed-crystals; then thej^ have the composition 

 PA . {1 — P) B ,n H^O, in which P may change from Otol. We 

 may also represent the composition of this mixed-crystal by: 

 (xH^O-\-yA-^{\ —a— y)B, in which a—n : (n + 1) and y=P:{n-\- 1). 



When F^ represents a similar phase, in which x-^ and y^, are 



constant, 2, Wj . . . variable, then we have to omit in (3) [XVII J - — 



and — ^, and we must replace them in the first equation (2) [XVII] 

 by the corresponding quantities of another phase Fr- 



