( 796 ) 



cerning the equation of state and the quantities a ït l ) and ó 15 . In 

 the net of spinodal curves for a given pair of substances 2 singular 



points may then occur, belonging to the spinodal curves for different 

 temperatures. The values of x for these are determined by the 



equation : 



•?\I 3&I1M k / «22M =F -^11 M '' ":i.M"22M ~ &22M V ('n.M 



1 — "-''M — h\\\\ va-tvyi =F - (/ 'J2.M I' «11MÖ22M+ 3^22M^ "1IM 



For very small a„ we find from this two singular points with 

 ./■>!, so not belonging to that part of the ip-surface which can 

 denote phases of mixtures. Of these two singular points that for 

 which the lowest signs hold, passes through infinity for increasing 

 ",.;■ and then approaches the line x = on the other side of the 

 ^'-surface. This line is reached for: 



1 

 |! ".-j.M "i;M = -{— 1 -+- V 1 • 3 &02M l '.\\\ { = >", • (2) 



With increasing a„ a n the singular point, which appears to be a 

 double point for this region, approaches the line v = b, which line 

 is reached for: 



V ,i-,, M <M|M= — (1— /'■_>■_> m 6|iM) + V\— 622.M '' M • (622.M /'i 1 M )-= ///._. (3) 



In this we assume 602M <C éiui'). 



So it' the mutual attracti t' the molecules of the most volatile 



component and those of the other in connection with the attraction- 

 inter se attains a certain value on the assumptions made for the 

 calculation- for m = V a 2 2M/«iiM = »*, the spinodal curve for 

 T=T/ Ci will no longer touch the side in A', (cf. fig. 1 PI. I), but it 



') In this first investigation of what may be expected for mixtures of helium, 

 with a view of forming some opinion as to the conditions under which the ex- 

 periments for this purpose are to be made, we put i§ 2), &i2M = £ (bim+b-zm) 

 «i2M = l "MM'fj-jM (cf. Gomm. Suppl. No. 8, These Proc. Sept. 'of p. 227) in 

 the calculations, no data concerning a 12 and & ia for those mixtures beiiu available 

 as yet. Also Van der Waals iThese Proc. Febr. '07, p. 630) assumes that as a 

 rule «i2M < («iiM + rt2L>M). It will be necessary for a complete survey concerning 

 tlic different possibilities to make also other suppositions about avm (cf. Van der 

 Waals I.e., Kohxstamm ibid p. 642), at the same time taking care that a and b 

 are not put independent of v and T. at least not both (cf. Van der Waals, These 

 Proc. Sept. '05 p. 289) and that they may only be put quadratic functions of X 

 by approximation. 



If also for mixtures with very small 022, «i2M might be < ^ aima. 2M (cf. 

 Kohnsta.mm 1 c.) the phenomena of limited miscibility under discussion might still 

 be sooner expected. 



2 ) For &22M.> &riM the other singular point comes from side x = 1 on the 

 a-surface for a smaller value of «j_>m «mm. As probably this case does not present 

 itself for the pairs of substances with small ch ü a n known to us, we shall not discuss it. 



