( 737 ) 



branch. If this is the case the outmost q-\'mes on the two sides, both 

 that lying very low and that lying very high, have no points of 

 inflection. 



The spinodal curve and the plaitpoints. 



The spinodal curve is the locus of the points in which a p- and 



dv dv dxdv dx* 



a ^-line meet. In these points — = — and so 



dxp dxn d^xp d 7 xp 



dv* dxdv 



d*xpd*\p /d>V 



or = . In order to judge about the existence of such 



dv* dx' \dxdxj J ö 



points of contact, we shall have to trace the p and the q lines 



together. As appears from fig. 1 p. 630 the shape of the />-lines 



is very different according as a region is chosen lying on the 



left side, or in the middle or on the right side ; but the course of 



the ^-lines in the different regions is in so far independent of the 



choice of the regions that q— CJ > always represents the series of the 



possible volumes of the first component, and </-|-oo the series of the 



possible volumes of the second component, and also the line of the 



limiting volumes. As the shape of the /;-lines can be so very different 



we shall not be able to represent the shape of the spinodal line by 



a single figure. Besides the course of the jp-lines depends on the 



'/y rf 8 tf> 



existence or non-existence of the curve — = -— = 0, and the 



dv dv 



course of the ^-lines on the existence or non-existence of the curve 



72 t 



= 0, and besides, and this holds for both, on the existence of 



dx 2 



dhp 



the curve = 0. Hence if for all possible cases we would illustrate 



dxdv 



the course of the spinodal curve in details by figures, this examination 

 would become too lengthy. We shall, therefore, have to restrict 

 ourselves, and try to discuss a! least the main points. 



Let us for this purpose choose in the first place a region from 

 the left side of the general /^-figure, and let us think the temperature 

 so low, so below (7/.),, thai there arc still two isolated branches for 



(Id 

 the curve — = all oxer the width of the region. 

 dv 



