( 638 ) 

 That as yet our attention lias almost exclusively been directed to 

 — - = is due to the fact that we know with certainty that a 



dv* 



given binary mixture furnishes points for the latter locus for values 



of T below Tk for that mixture, whereas the conditions for the 



d 2 lp 



existence of a locus = are not known - - and it might be 



dx* 



suspected that this remained confined to temperatures so low that 

 the solid state would have set in, and so the complications which 

 would be caused by this, could not be observed. That such a sup- 

 position is not quite unfounded may still be safely concluded from 

 the behaviour of many mixtures, which quite answer to the consi- 



d*ü) 

 derations in which the curve - is left out of account. But that 



d.v* 



the behaviour of mixtures for which more complicated phenomena 



occur, cannot be accounted for but by taking into consideration that 



can be = 0, seems also beyond doubt to me. 



da? 



The approximate equation of state gives for this quantity the 



following value : 



fdby 



.,™ MRT I — MRT 



d'ip MRT \dx) dx* dx 2 

 — — 1 ± — '— _| 



dx 2 X (1 — «?') (r — 1,)' 1 V — b V 



which I shall still somewhat simplify by assuming that b depends 



d*b 



linearly on x, and so — = 0. We can easilv derive from this form 



dx 2 



d 2 lV 



that it — — can be = 0. this will be the case in a closed curve At 

 aar 



d 2 UJ 



the boundaries of the v,x- diagram — — is certainly positive. For# = 



dx l 



and x = l even infinitely great. Also for v = b. And for v = x 



MRT 



it reduces to — -, the minimum value of which is equal to 



x (1 — x) n 



4 MRT. That, if only T is taken low enough, it can be negative, 



d*a 

 at least if — is positive, is also obvious. At exceedingly low value 



of T it can take up a pretty large part of the ?v-diagram, which 

 must especially be sought in the region of the small volumes. With 

 rise of temperature this locus contracts, and at a certain maximum 

 temperature for its existence, it reduces to a single point, So it is 

 no longer found above a certain temperature. 



{To be continued). 



