( 622 ) 



(/-line can be drawn. One single />-line, however, intersects an infinite 

 number of iines of the g-system, and every (/-line an infinite number 

 of lines of' the ^-system. One and the same p-Mne intersects a given 

 (/-line even in several points. However, it will, of course, be neces- 

 sary, that if two points indicate coexisting' phases, both the jp-line 

 and the (/-line which passes through the first point, passes also 

 through the second point. If we choose a p-line for two coexisting 

 phases, not every arbitrarily chosen value for a (/-line will satisfy the 

 condition of coexistence in its intersections with the />-line, because 

 a third condition must be satisfied, viz. that M, p, must have the 

 same value. The result comes to this: when all the p-lines and all 

 the (/-lines have been drawn and provided with their indices there 

 is one more rule required to determine the points which belong- 

 together as indicating coexisting points. So in the following pages 

 I shall have to show, when this method for the determination of 

 coexisting phases is followed: 1. What the shape of the /Mines is, 

 and how this shape depends on the choice of the components. 

 2. What the shape of the (/-lines is, and how this shape depends 

 on the choice of the components. 3. What ride exists to find the 

 pair or pairs of points representing coexisting phases from the infinite 

 number of pairs of points which have the same value of q, whenp 

 has been given — or when on the other hand the value of (/ is 

 chosen beforehand, to find the value of' p required for coexistence. 

 But for the determination of the shape of the spinodal curve the 

 application of the rule in question is not necessary. For this the 

 drawing of the p- and the (/-lines suffices. There is viz. a point of 

 the spinodal curve wherever a />-line touches a (/-line. We have viz. 



from — - — 4- -— = 0,and from — - — + -— = for — J 



dv \dxj p (I rdx dxdv \dxj q dx \dxj p 



d*tp d*tfj 



dxdv (d''\ llr ' 



the value ■ — and for — the value , and so we mav 



d 2 ip \dvjq d*tp J 



dv 1 dxdv 



write the equation of the spinodal curve : 



'dv \ /dv 



dx I p \dxy „ 



So if we are able to derive from the properties of the components 

 of a mixture what the course of the p- and of the (/-lines is, we 

 can derive much, if not everything, about the shape of the spinodal 

 curve. And even when the course of these lines can only be predicted 

 qualitatively, and the quantitatively accurate knowledge is wanting, 



