( 230 ) 



the directions of the tangents the double fan-shape is very prominent. 



3". the vapour branch of the binodal line in the projection is 

 almost a straight line, and in agreement with this, according to 

 VAN DER Waals, the law of Henry holds over the whole area of 

 composition variation, while the vapour branch on the ^^I'-diagram 

 is again almost a hyperbola. 



§ 7. Simplijication of t/te determination of conditions of coexistence 

 inhen the liqidd phase is far hehio its ^) critical temperature. In order 

 to determine the binodal line of the transverse plait we need only 

 know two zones on either side of the plait. Let the border curve of 

 the homogeneous mixtures be that curve which on the V?-surface con- 

 nects the vapour and the liquid [)hases in which the mixture, with 

 the composition x taken as homogeneous, would be in equilibrium, 

 then the binodal line wanted lies beyond ^) this border curve, which 

 it meets for the compositions and x. Therefore it is more or less 

 indicated, which zone on the vapour side we ha\'e to calcidate. 



If, as in the case of methylchloride and carbon dioxide at — 25° C. 

 (or ^vith ether and hydrogen at the ordinary temperature for the ))art 

 of the ether side) the zone on the liquid side is shrunk to a plate, 

 we need only calculate a single curve on the liquid side. For then 

 the point of contact is so near the rim curve — that for which \p is 

 a minimum — that this curve may be substituted for the tp-surface. 

 The V of this curve may be easily derived for each x from the 



equation of state because — ]^ — w = 0. With the value i\,=oor 



\dvjx 



Vp=o ^ve then find by integration if'/,=o, Avhile in the way as described 



in Comm. n" 66 § 5, ') the tangent through the point %=q, Vp—o 



to the curve tf'^ on the vapour surface is drawn graphicall}' and the 



vapour tension of the homogeneous mixture is obtained. 



If we only wish to determine the pressure and the composition of 

 the coexisting phases we have also a neglection of little importance 

 in the supposition that viigx = viu^^ x -\- v//^, (1 — x), in other words 

 that the rim cur\'e lies in a plane, while in many cases we may 

 suppose that this plane coincides with the t|?i'-plane. 



In order to find the conditions of coexistence we roll a plane (piece 

 of plate-glass) over the rim of a thin plate cut after the calculated 



rim curve 



[ better still the rim curve for — j and over a model 



1) Gomp. § 1 footnote. 



2) Van der Waals Gontinuitat II p. 100. 



3) Arch. Néerl. Livre jubil. Lorentz, p. 665. 



