( 661 ) 



temperatures of the components given there are found in the way 

 explained in § 5. 



atmospheric pressure according to Dewar (Roy. Institution Weekly Evening Meetings), 

 25 March '04) at 0.070, and let us derive the coefficient of compressibility according 

 to the principle of the corresponding states, e.g. from that of pentane at 20° C, 

 then the density at 40 atms. is 0,072. If we calculate the increase of density in 

 consequence of the solution of helium from van der Waals' equation of state for 



a binary mixture by putting bMiie = — bm\?, for this correction term, we get 



for the density of the liquid phase at the p and T mentioned if it contained 

 3% He : 0.077. 



The gas phase will have the same density at about thep and T mentioned (cf. Comm. 

 N°. 96a, Nov. '06, p. 460). The theoretical density (Avogadro-Boyle-Gay-Lussac) at 

 y=20° and p = 40 atms. = 0.0885. If we assume Van der Waals' equation of state 

 with a and b for constant x not dependent on v and T, to hold for this gas phase, 



b x ax 1 

 it follows with the above given value of the density that ; = 0.15. 



For a 2 2 = «12 = with a n y— 0.00042 (Kohnstamm, Landolt-Börnstein-Meyer- 



hoffer's Physik. Ghem. Tabellen), and with i' M = 0.0021, putting x = 0.80 for the 



gas phase, we should obtain: b — 0.21 v (/ = 0.00044. We should then, if 



we may put b^ M = *(&, 1J7 + K 2)1 ), get & 22if = 0.00033 =»/ 8 & ll M (P Mi/ = 0.00088, 



Kohnstamm 1. c). If we wish to assume positive values for a 12 and (/ 22 (cf. Comm. 

 N°. 96a, p. 460), we should have to put & 22jf > »/ 8 & 14 M for T =20°; if we 



assumed that the gas phase contained 15% He we should derive from the above 

 mentioned experiment for positive values of a u and <7 12 : b 00 ., > 0.31 b . . 



These results harmonize very well with what may be derived about b Ï/IT( . 



at 0° G. ; the ratio of the refracting powers (Rayleigh) gives: & 00 ]f = 0.31 b .„ 



while the ratio of the coefficients of viscosity and also that of the coefficients of 

 the conduction of heat lead to a greater value for &jfjj e (about Va b^jj). 



If we take b 22i ]j/b l { ^ = l / 2 , we should obtain from the above given considerations 

 (putting a [2M =\/a uM a 2 , lM ) : a 22n 'a uu = V175» so that T kUv — about 0.35°. 



This renders a value for the critical temperature of He < 0.5° probable. 



This conclusion would not hold if bril for x = 0.8 were considerably greater 

 than follows from the hypothesis that b x M varies linearly with x. This however 

 is according to the experiments of Kuenen, Keesom and Brinkman on mixtures of 

 GH3GI — G0 2 and C0 3 — 2 , not to be expected. The experiments of Verschaffelt 

 on mixtures of G0 3 — H 2 would admit the possibility, but give no indication for 

 the probability of it. [Added in the English translation]. 



So though probably b w/b n for mixtures of He and H 2 is larger, yet we shall 

 here retain the supposition made in § 5 on 6 sa/& n , with which the calculations 

 were started, because the accurate amount is not yet known to us, and we only 

 wish to give here an example for discussion ; moreover the course of the ^-sur- 

 face will not be considerably modified by this difference in any essential respect. 



