725 



Of course this is also in accordance with (15); when herein we 

 put f.i. in = l and 71 = then phase F represents the com posant i^,. 



When we express the composition of a phase in its components, 

 consequently in .r and y, tlien .r and // are positive and .'' + .V^1- 

 When, however, we express its composition in composants, then m 

 and n may also be negative and also m-\-n'^l. The latter is the 

 case f.i. for a phase, represented by the point P. In (15) m and n 

 are then positive and 1 — m — n is negative. 



Wiien we have a quaternary system then similar relations exist 

 between the coordinates viz. 



x' = m /, y' =nl, :' = P h 



Till now we have assumed that each of the n composants of a 

 system of /( components contains also those 7i components. It is 

 apparent, however, that we may choose the composants also in such 

 a way that one or more or even all composants contain less than }i 

 components. Of course the n composants together must contain the 

 It components. We may consider the representation with the aid of 

 components as a special case of the representation with the aid of 

 composants; each of the composants tiien contains a single component 

 only. We shall, however, continue by calling this a representation 

 with the aid of components. When, however, there is at least one 

 composant, which contains more than one component, then we shall 

 speak of a representation with the aid of composants. 



As it is known, the deduced functions of the thermodynamical 

 potential become infinitely large when the quantities of one or more 



of the components approach to zero. In a quaternary system f.i. — 



ox 



becomes infinitely large when x or 1 — x — y — z approaches to zero; 



— when y or 1 — .v — y — z and — when : or 1 — .v — y — 2 approaches 



to zero. 



Using composants this is otherwise, however. It follows viz. 



from (1 11 that -~ ,—- and r-- become infinitely large, only then when 

 dm o?i op 



d: d: d: 



one or more of the tiinclions — , — and — are infinitelv large and 



o.r oy oz 



this may take place, as we have seen above, only when one or more 



of the conditions : 



X = y = z = 1— .r— y— ^ = . (20) 



is satisfied. In general r— , - or — become, therefore, infinitely 



077? on op 



