( 440 ) 



tf *P — -o being able to exerl any influence on this. But the course 



dxdv 



d°\y 

 of the spinodal line is the result of properties of - - = as well 



as f _ ^ = and of* — — = 0; from this ii may already bo ex- 

 rfr' dxdv 



nected that when the curves — - m =0 and — =0 touch, the two 



1 ax il'\ 



heterogeneous plait-points will occur on the spinodal line, and will 



lie at some distance from each other. If this is so, this means that 



the limits for the existence and disappearance of the heterogeneous 



plaitpointfi are wider apart than the temperatures at which the two 



</'■& d*ib ! i • 



curves - = and =0 begin to intersect and stop doing SO; 



and a fortiori this is the case for the limits of the temperature 

 of their appearance and disappearance on the binodal line, and 

 so also for the limits of the temperature for the existence of 

 three-phase-pressure. And thai this is true may be seen when 

 we more closely examine the peculiarities which occur in the 

 course of the spinodal line in the case that the two curves still 

 intersect Lei us imagine the circumstances as in fig. 12, Vol. IX, 



dp 

 n 846 Contribution III, viz. the line - — at smaller volume 

 1 ' </.'•,• 



than the line — =0; bul preferably at somewhat lower temperature, 

 dv 



dp 

 so that at x = the two branches of =<> are still separated. 



dv 

 Then the isobars enter the figure at a? = l, have negative, and 



dx p 



iu the neighbourhood of — = they incline towards this curve which 



they intersect in a direction parallel to the axis of/-. So the quantity 



</'->' . d*v . ... 



is positive. For the r/-lines the quantity - - is negative m the 

 dx\ dx* q 



neighbourhood of — = 0. So in a point of contact of the p- and q- 



dv 



lines, a point of the spinodal line (see Vol. IX p. 747 Contr. II), 

 [ — ] is positive according to the formula: 



{A 



dv\ f<i'-\ \dx*Jq 



dxJspin \dicjp — q f d^V 



d? 



