( 449 ) 



regions oontaininj? blue (Itluc, •ii'ceii, ])iir])lo) fi-oiu the others. It 



1 

 touches tlie y-axis iji tlie poiiil -/.=:(), y= -. lis (M[iiutioii is: 



(2 y _ 3 X + 1)'^ - S (7-x) = 

 or if we (niiisfer the onjj;in (o tlie point y=l, x=[ ami therefore 

 introduce the new xariahles: x' = x — J; y' z= y — 1, wliich hi'iii^^s 

 about a simpHficatiou also for the other border curves, we get: 



(2 /_3 xT' - 8 (/--/)::= (4) 



Then we liave every wliere inside that parabola, so in the regions 



5, 6, 7: 



(2 y'_3 x'r - 8 (y'-x')< 



and outside it in the regions 1, 2, 3, 4: 



(2y'-4xr-8(y'-x')>0. 

 In consequence of this it depends on the situation inside or 

 outside the parabola, whether on the corresponding i|'-surface the 

 plaitpoint Avill enter the surface at decrease of temperature or at 

 increase of temperature and whether the spinodal curves turn their 

 convex oj" their concave sides to the side ■/■ = 0. 



I'ig- ^- For points on the parabolic border curve the plaitpoint 



occurring in the point K at the critical temperature of 

 the principal component, is to be considered as an homo- 

 geneous double plaitpoint at that moment. The projection 

 on the V, .i'-surface appears then as is indicated in tig. /;. 

 How the transition to this condition takes place may 

 be made clear by the subjoined fig. c, \viiich represents 

 the same projection for a temperature slightly below that 

 of the critical temperature of the princi|)al component 

 for the case that the x- and y-values indicate a I'ig. c. 



point, which is still situated in the green region 



6, but on the verge of the border curve of the 

 yellow region 2. 



Very near the plaitpoint /^ we find here ab-eady 

 a second plaitpoint I*', which at fu it her decrease 

 of temperature soon coincides willi l\ 



If now^ the point in the green regioji a|)|)roaches 

 the border curve of the yellow region, the two 

 points /^coincide nearer and nearer lo the critical 

 temperature of the iirincipal ("oiiipoiKMit and lo the pinnt A'. On 

 the border ciii-nc it lakes plaee in the poijit K itself". iU'ijond the 

 limit, in the yellow region, the plait of P docs not develop any 

 more and P' takes the place of /*. 



30 



Proceedings Royal Acad. Aiiiöleidaiii. V'ol. V. 



K 



