118 



We Kiigiit jubt as well have posed instead of (3) tlie condition 

 that the reaction takes place withont addition or withdrawal of heat. 

 As the entropy remains the same then, we call snch a reaction an 

 "isentropical reaction". When we represent the entropies by tj,, tjj etc., 

 tlien the condition is: 



.'/,'j, 4- n.n^ + i/s'is + • • • + .'/„+2^i»+2 = ... (4) 



Then we have again n -\- 1 eqnations, so that also an isentropical 

 reaction between the n -\~ 2 phases of an invariant eqnilibrium is 

 completely defined. 



It is evident that the coetlicients //;, ?/, etc. in the isovoliimetrical 

 reaction (1) are others than in the isentropical reaction (1). Further 

 it is also evident that, dependent on the direction of the reaction, 

 we must add or withdraw heat with an isovoiu metrical reaction 

 and that we must change the volume with an isentropical reaction. 



Now we imagine at 1\ and under /■*„ that the n -\- '2 phases 

 lu ■ ■ • Fn+-> are together; we let the isovolumetrical or isentropical 

 reaction take place and we let this proceed nnlil one of the phases 

 disappears. Then an equilibrium of n components in // -\- 1 phases 

 arises, which is consequently monovariant. In this way n -\- 2 mono- 

 variant equilibria may occur. As in each of these equilibria one of 

 the phases of the in\ariant point fails, we represent, for the sake 

 ot abbreviation, a monovariant equilibrium by pulling between 

 parentheses the missing phase. Consequently we shall represent the 

 equilii)rium F^ -\- J'\ -{- . . . F„-i^-2 by (F^), the equilibrium F^ -^ F, -f- 

 F^ -\- . . . F,i-\-2 by {F^), etc. From the invariant equilibrium, there- 

 fore, the II -\- 2 monovariant equilibria {F^), {F^), {F^) . . . {Fu-^2) 

 may occur. 



Each mouovariant equilibrium exists at a whole series of tem- 

 peratures and corresponding pressures; consequently it is represented 

 in the ƒ", 7'-diagram by a curve, which goes through the invariant 

 point P„T„. Therefore in this point n -\- 2 curves intersect one 

 another. Each of these curves is divided by the invariant point into 

 two parts; the one represents stable conditions the other metastable 

 conditions. We shall always dot the metastable part. (See e. g. the 

 tig. 1, in which these curves are indicated in the same way as the 

 equilibria, which they represent). 



When we consider onl}' stable conditions, we may say : n -\- 2 

 mono variant curves proceed from an invariant point of a system 

 of n components. 



