( 320 ) 

 i ._ ¥h < -' n ^-Ii 



n — 1 u — 1 



or 



J/e, + n[/e 3 >n— 1 . 



So the condition f : and s 2 > ensures thai the loens does not 

 take up the whole width from a? = to a," = 1. Fur the loens not 

 to exist at all the value of e l and s a must he such that : 



l/f, + "|/f 3 >« — 1 • 

 jf j/^ _|_ n|/f, = n — 1, the locus reduces to a single point. In 

 this case : 



The equation has two coinciding roots, i.e. x — -or 1 — os = . 



>t — 1 it — 1 



Perhaps these results might have heen obtained in a more lucid 



x 



way. if we had introduced the quantity A = , instead of.r into 



1 — ./■ 



the equations (a) or («'), so the number of molecules of the second 



substance present per molecule of the first substance in the binary 



mixture, which quantity must necessarily be positive. The condition 



,r-\y d 2 tf? 



that the two curves — - = and ■ =0 do not intersect at any 



cl.c'- '/'■'"' 



temperature assumes then the following form : 



_.v|i- fl - f ''";U .^* V>0.. . . (y) 



(n-l) s ( (n-l)°- | (n-iy 



For N = and X = x this condition is satistied for positive 

 gj and f.,. Bui for this equation to be satistied for any arbitrary 

 value of A' it is ret pi ire* I that : 



{n — W^V (n — l) 2 

 or 



^ (II -1)' 



or 



n— l<|/e 1 +»l/f, 



If we construct the relation between f 1 and £., as a curve, taking 

 fj and e s as coordinates, we get, for the case that the locus of the 

 points of intersection contracts to a single point : 



