( 282 ) 



and a light oil with high critical temperature '), nitrogen-lithium, 

 argon -kali um, mercury-iron etc. sinking of t lie gas phase in the 

 liquid phase could be realized. 



$ 3. On the conditions for the occurrence of 'barotropic phenomena. 



It appeared in § 2 that with a suitable ratio of the limiting densities 

 the occurrence of the barotropic phenomena depends to a great extent 

 on the ratio of the attractions of the molecules of the two compo- 

 nents, hence on the ratio of the critical temperatures. The same thing 

 may also be derived in the following way, more independent of the 

 particular hypotheses which have led to the consideration of obliquely 

 crossing plaits. 



To bring about the phenomenon of the gas phase sinking in the 

 liquid phase, the gas phase will have to be much more compressible 

 than the liquid phase, and even on compression the gas phase must 

 not dissolve in the liquid phase. For this the temperature will have 

 to be pretty far below the critical temperature of the least volatile 

 component (7\), but still far above that of the second component 

 (7VJ. This points to a large difference between the critical tempe- 

 ratures of the components. 



If for the pair of substances considered retrograde condensation of 

 the first kind occurs, the coexisting phases indicated by the points 

 L and G on the if'-surface for the molecular quantity (see fig. 7) s ), 

 can only have the same density if M t ^> M v 



Only when on the plait on the molecular ijvsurface connodal 

 tangent chords appear for which the angle with the axis a? = 0: 



6 ^> — , the coexisting phases can have equal density for M, < M x . 



As the difference between x g and xi is larger, and so the connodal 

 tangent chords deflect more rapidly from the side x = 0, a smaller 

 difference between A/, and If, will suffice to establish equal densities 

 in G and L. 



This will be the more the case the more the plait extends towards 

 the side v = b. 



The latter is particularly furthered by a small ratio ao 23 ,/a I1JU - (cf. 

 Ooinm. Suppl. N°. 15 PI. I fig. 1 and PI. II), so by a small ratio of 

 the critical temperatures, b 2 n M smaller than b n31 also tending in this 

 direction. 



l ) Mr. F. M. Gilley of Boston drew our attention to mixtures of air and oil. 



*) The dotted lines indicate that the considerations of this § hold both for the 

 case that at lower temperature the plait crosses the ^-surface as a transverse plait, 

 and for the case that it extends towards v = b. 



