(194) 



rp 



the ratio — - is a high value, and for which the temperature, at 

 T h 



which = has contracted to a point, is much higher than T^. 



dx' 



As an example take the mixture helium and hydrogen investigated 

 by Kamerlingh Onnes and Keesom partly experimentally and further 

 theoretically, or the mixture helium and water. As, however, there 

 are two shapes possible, I shall describe them both, not stating as 

 yet, which of these shapes is the correct one in these cases. 



As b for hydrogen will be higher lhan b for helium, helium is 

 the first component. In the first place we observe that there must be 

 a complex plait for T <C Tjc x , which extends over the whole width. 



= has closed on the helium side for T~> 7a-,; but — = 



dv* dx* 



d'rp 

 is a closed curve, which extends outside — =0 on the helium 



dv % 



d'ty d'ty 



side, and so there is intersection of — = and — — = 0. The 



dv* dx' 



d'ty 

 spinodal curve, which remains near — - = on the side of H, , 



dv' 



moves further away from this line as we approach the helium side, 



and remains also outside — = 0. I shall continue to assume that the 

 dx' 



spinodal line remains closed on the side of the small volumes. The 



changes which must be made if this should not be the case, will 



be easily applied in the result at which we arrive. Then there are 



three plaitpoints for this T^> Tk x - With very small difference of 



T and T^ there is first the ordinary plaitpoint on the helium side; 



and further there are two heterogeneous plaitpoints, viz. a realisable 



one at the very small volumes, and a hidden one (see inter alia 



figs. 12 and 13 of the preceding communications). 



If now the first mentioned plaitpoint should coincide with the hidden 



one, as is assumed in the discussion of these figures, only one single 



plaitpoint would remain ; but another, more intricate case is possible. 



If — - = and — =0 are quite detached, as will happen with 

 dv* dx"* 



increasing temperature, the spinodal line may viz. either continue to 

 run round the two curves, as I have repeatedly drawn, or it may 

 split up between the two curves. For splitting it will be required 

 that they are so far apart that a point is found between them, in 



