( 276 ) 



i)'-surface from the side of the small volumes, reaches the side.r = 

 at T=Ti L -,, and then passes into a plait crossing in a slanting 

 direction from v = b to x = 0. This description was accompanied 

 by remarks about limited miscibility in the gas state. 



In Suppl. N°. 15 $ 7 These Proc. March '07, p. 795 three cases 

 were distinguished for mixtures in which one component is a gas 

 with a feeble attraction. They are indicated as cases (a), (b) and (c) 

 in $ 9, These Proc. Sept. '07, p. 235. Case (a) corresponds with the 

 above mentioned one ; in case (b) a plait coming from v = b and 

 one coming from x = join to a single plait in a double plaitpoint l ) ; 

 in case (c) a plait starts from x — 0, comes in contact with v = b 



') On the suppositions mentioned in Comra. N°. 96c p. 509 and p. 510 the 

 data for the two double points in the net of spinodal curves, of which this double 

 plaitpoint is one (a node) may be found in the following way (cf. Coram. Suppl. 

 N'. 15, p. 233, note 1): 



The equation for the ü.z-projection of the spinodal curve on the molecular 

 ({/•surface : 



RTvm* = 2(1 xm) {i\u\/anM-bnM\/aMY -f 2tfj;(uj;l/a 2 2.i/-&22.Ul/aj/) 5 (1) 



(cf. Suppl. N°. 15, March '07, p. 788) gives as conditions for the appearance of 

 a double point after some obvious reductions: 



(«j/l/aiij/— b\]M\/a^y = 2buM [/auM-{^— ®M){vMV'*nM— &njtfj/aj/) -f- 



+ 26 2 2.vl/aiiJ/.*iW(«j;l/a22J7— bnsi[/au) . ... (2) 



and 



(vjj{/a 2 2M — b-22M\/aMy = 2b Li 3l V^llM • (1 — x 2>l){p mV a W hl~ *il.4/|/a,tf) + 



-f %h-2.\ya22M . xM(vM\Za 22 M— b-nu^/au) . ... (3) 



From (2) and (3) follows: 



(oj/l/ai \m— b\\ SiS/ayy (vM\/a■> 2 M—b22^J[/au) , 



Extracting the root from this equation, we may (2) and (3) reduce to: 

 I'M V a I \M — b ii m V a M 



(4) 



= 26i ijw(l - xm) ± 2b-izMXMV a v>Ml<i\\M ■ (5) 

 ya\\M 

 and 



vm VailM — b^-M V a M , , „, n > A . , ,„. 



= IbiiM^M ± *v\\M\\— > r M) lsa\\M/a-22M- (o) 



V0.1-2M 



By eliminating vm from (5) and (6) we obtain for Xm the equation (1) of Suppl. 

 N°. 15, March '07, p. 796 (cf. errata Proc. Sept. '07, p. 239). 



The further derivation of vm and T (see Suppl. N°. 15, March '07, p. 798) 

 may be left to the reader (compare with these developments van Laar, These 

 Proc. May '07, p. 38 sqq. and Arch. Teyler (2) 11 (1907) l re partie § 5). 



