( 526 ) 



Now there are three more problems, and to this I will call atten- 

 tion in this note, which may be considered as the analogues to the 

 three above-mentioned ones. 



If in the above problems we substitute the quantity .'' Ibr /• and 



ö 2 if' d'«(» ö> 



vice versa, so that r — changes into r— ,andr-r- remains unchanged 



Oc' 2 OA- 2 OXOC 



d 8 if> d> 



then the intersection of the curves - — = and = will give 



ox* oxóv 



rise to three problems, which are of as much importance for the 



theory of the binary mixtures as the three above-mentioned problems, 



d\p d> 



which relate to the intersection of r— - = and —-^ = 0. 



Of 1 Od-Oc 



In the first place the points at which the two curves y - =0and 



— — = intersect will belong to the spinodal curve, as appears 

 dado 



d a if>d 2 if> /d> 



from — ;.— = T-T- 



o.v 2 ou 2 v.o,<()/ 



In the second place these points of intersection will have the same 



/dijA 

 significance for the course ot the curves ( t— = <7 — constant, as 



ö 2 ip d> 



the points of intersection c-r- = and x-^- = have tor the course 



1 Or 2 OiVOV 



of the curves [ v - I = — » = constant. The first point of inter- 



section will be a double-point for the q lines, whereas the other 

 point of intersection will present itself as an isolated point, the centre 

 of detached closed portions of the q lines. 



In the third place there will be a limiting temperature for the 



existence of the locus —- = (). With increasing value of 7' this curve 



dhp 

 contracts to an isolated point, just as is the case with — = with 



d 3 if> 

 maximum r J\, or as the curve -— = has a double point with 



ov' 2 



minimum r l\. 



In the fourth place there is a temperature at which the curves 



~^ = 0and T -^=0 only touch, and the two points of intersection 



o.v 2 dwdv 



have, accordingly, coincided. 



And finally, and this is the most important case, there is a tern- 



