( 741 ) 



point lias also been drawn in (he figure. Also this r/-line may still 



be touched by two different /Mines, which, however, have not been 



represented in the drawing. For a still higher (/-line these points 



would coincide, and in consequence of the coincidence of two points 



f<Pv\ 

 of the spinodal curve a plaitpoint would then be formed. I — ) always 



fd*v\ 



being positive, I — I , which has been negative for a long time in 



the point lying on the left side, must first reverse its sign before it 



can coincide with the point lying on the right — a remark analogous 



to that which we made for the plaitpoint that we discussed above. 



If on the other hand the value of q is made to descend, the point 



of contact lying most to the left will move further and further from 



d*\p dp 



the curve = 0, and nearer and nearer to the curve — = 0, till 



dx* dv 



for (/-lines of very low degree, for which as we shall presently see, 



the number of points of contact has again descended to two, the 



whole bears the character of a point of contact lying on the liquid side. 



But something special may be remarked about the two inner 



points of contact of the four found on the above (/-line. When 



the (/-line descends in degree, these points will approach each 



other, and they will coincide on a certain </-line. Then we have 



fd*v\ f#v\ 



again a plaitpoint. In this case neither — I, nor — - need reverse 



its sign because these quantities have always the same sign for each 

 of the two points of contact which have not yet coincided, i. e. in 

 this case the positive sign. But in this case, too, there is again besides 

 contact, also intersection of the p- and y-lines. On the left of this 

 plaitpoint the (/-line lies at larger volumes, on the right on the other 

 hand at smaller volumes than the p-line, the latter changing its 

 course soon after again from one going to the right into one going 

 to the left. 



This plaitpoint, however, is not to be realised. With the two 

 plaitpoints discussed above all the />-line and all the (/-line, at least in 

 the neighbourhood of that point, lie outside the spinodal curve, and so 

 in the stable region. In this case they lie within the unstable region. 



Summarizing what has been said about tig. 8, we see that there is a 

 group of (/-lines which cut the spinodal curve in four points. The 

 outside lines of this group pass through plaitpoints. That with the 

 highest value of (/ passes through the plaitpoint that is to be realised ; 

 that with the lowest value of q passes through the plaitpoint that 

 is not to be realised. All the (/-lines lying outside this group intersect 



