( 450 ) 



7. As second border we get in tlie graphical representation the 

 straiglit line: 



2 y'— 8 x' = (5) 



It separates tlie regions containing red 3, 4 and 7, - toi' wliicli 

 2 y' — 3 x'<^0, and where the tangent in the plaitpoint, continued in 

 the direction of tlie large volumes, inclines towards the side ./'^O — 

 from the others, where it inclines to the inner side of the ^'-surface. 



As we saw before, this inclination determines the nature of the 

 retrograde condensation. Not exclusively, however. For in the tirst 

 four cases of figure 2 the result of the same way of inclination is 

 in this regard exactly the opposite of that in the last four cases ; 

 hence the parabolic border cui-ve acts hero also as a separathig curve ; 

 so that retrograde condensation of the first kind (i.e. with temporary 

 formation of the denser phase) occurs in the regions 3, 4, 5 and 6, 

 in the tAvo first with greater i)i-op()rtion of the admixture in the 

 temporary phase, in the two last the reverse, and on the contrary 

 retrograde condensation of the second kind in the regions 1 and 2 

 (with a larger pro[)()rti()n in the temporary less dense phase) and 7 

 (with a smaller proportion in that same phase). 



8. The third border curve is a cubic curve with the equation: 



(2y'— 3>c')' — 4(4y'-3x')(2y'-3x')4- lGy'=:0. . . (G) 



It consists of two branches, which possess both on one side the 

 common asymptote : 



2 y' _ 3 >c' — 2 — . (7) 



and which run at the other side parabolically to infinity. 



The right-side branch, whose shape resembles more or less a para- 

 bola, touches the curve y' = in the point vJ = 0, y' = (x=zj , y=l)- 



Between the two branches, so in the regions 2, 4 and 6 : 

 (2 y' — 3 x')' — 4 (4 y' — 3 x') (2 y' — 3 x') + 16 y' < ; 



in all the other regions of course ]> 0. 



In the former case the tangent KP to the plaitpoint-curve of the 

 (v, a;)-diagram is directed to the side of the small volumes, in the 

 second to that of the large volumes. 



If we, however, examine, whether e.g. at decrease of temperature 

 the plaitpoint moves tOAvards the large or towards the small volumes, 

 the parabolic border curve acts again as separating curve. 



It appears then that the plaitpoint moves towards the large volumes 

 at decrease of temi)erature in the regions 2, 4, 5 and 7, at increase 

 of temperature in the others. 



