( 663 ) 



ratios of the molecular weights and of the critical volumes, ham- 

 tropic plaitpoints prove only possible (quite apart from (he question 

 whether they are physically realisable, and whether they belong to 



1 

 the gas-liquid plait) for TkJT kl <Ct • 



The barotropic plaitpoint for the ratio TtJ T kl = 0.0002 is a 



plaitpoint for a mixture, one component of which is a gas almost 

 without cohesion (Comm. No. 96/> $ 1). A further consideration of 

 it would lead us again to the region of the longitudinal plait. 



The conditions relating to barotropic plaitpoints for x bp i near I 

 furnish a contribution to the knowledge of van der Waals' tp-surface 

 for binary mixtures with a small proportion of one of the components x ). 

 We find for TkJT kl near l / A , putting x bp i = l — g: 



(1 1 ) 9 14 



* I 2 s 3* |" 7 ( 9 * ^ 



20 „., 29 „ ) 1 ( 7 315 735 ) 



_ g 2 / 3 § . . . , T,JT kl = - 1 g 1 /i H § 2 /a I . . 



9 9 ( 2/ * 4 I 2 T 16 16 j 



It is seen from the series of the ratios T k JT kl in table I, that 

 in this a maximum and a minimum occur, respectively for about 

 TkJ Ttx == 0.219 and 0.J 96. From the formulae derived for x bp i 

 near 1, a minimum and a maximum for {i is found, and hence for 

 T k JT kl , respectively at x bpi = 0.9968 and 0.969. That the latter is 

 in reality found at x bp i = 0.94 is due to following terms in the 

 development. 



For T k JT kl < 0.196 or 0.219 < T k JT ki < 0.25 one barotropic 

 plaitpoint is found, for 0.196 < T%JT kl <C 0.219 three. In connec- 

 tion with Comm. No. 96 b § 2 (Dec. '06 p. 502, cf. also this Comm. 

 § 1, Dec. '06, p. 508) it follows also from this that for the mixtures 

 considered here at lower temperature the longitudinal plait makes 

 its influence felt. 



The experiment described in Comm. N°. 96a proved that for 

 mixtures of He and H 2 at — 253°, i.e. about T = 0.65 7/,n.„ a 

 barotropic tangent chord is found on the ^-surface. If at thai 

 temperature only one barotropic tangent chord occurs, this will point 

 to this (Comm. N°. 966 p. 504) that for the mixtures of these sub- 

 stances T bp i s > 0.65 7/,!^, and therefore according to this table 

 TkELe <C 0.18 TfcHj, while the found considerable difference in con- 

 centration between the gas and the liquid phase (see Footnote 3, 



i) Gf. Comm. N'. 75 (Dec. '01), N». 79 (April '02), N°. 81 (Oct. '02), Suppl. 

 No. 6 (May, June '03). 



45 

 Proceedings Royal Acad. Amsterdam. Vol. IX. 



