

( 748 ) 



should have been indeed negative (here, as was accidentally 



represented in point 2 of the spinodal curve, the spinodal curve runs 



towards smaller volumes with increasing value of\x\ So if there occur 



points with maximum or minimum volume on the spinodal curve, 



/d 2 v\ fd v \ . 



[ — 1 = in those points. If on the other hand ( — J is infinitely 

 \da*J 9 \dxj spin 



large, which occurs in the case under consideration when the spinodal 



/d*v\ 

 curve is closed on the right side for 7 7 >(7V) 2 then I — J must be 



= 0, and so the p-line must have a point of inflection in such a 

 point, to which we had moreover already concluded before in anol her 

 way. A great number of other results may be derived from this 

 differential equation of the spinodal line. We shall, however, only 



fdv\ f^ v \ 



call attention to what follows. In a plaitpoint I — 1 = I y ) 



ydxjspin \dasj 



Sd'v 



For a plaitpoint it follows from this that I — 



If for a point of a spinodal curve ( — ) is indefinite, both 



d i v\ fd i v\ 



— I and — must be equal to 0. This takes place in two cases: 



1. in a case discussed above when the whole of the spinodal line is 

 reduced to one single point. 2. when a spinodal line splits up into 

 two branches, as is the case for mixtures for which also T/ c minimum 

 is found. In the former case the disappearing point has the properties 

 of an isolated point, in the second case of a double point. 



In the differential equation of the spinodal line the factor of dT 

 may be written : 



1 [f(PTi{\ d'ty (d*Tv}\ d*ty fd'Tr(\ d*ip\ 



d' 2 o\ (d*v 



p \LUb j q 



T (V dx* JoT dv* \dxdv J t dosdv \ </r 2 J i\, dx 



and by putting s — xp for T^\ it may be reduced to : 



1 id*yd*e d a ty d*s d'tpd^e 



T \dv* dx* dxdv dxdv dx* dv* 



or to 



1 d> J d*e fdvy d*e fdv\ dH j 



T dv* \dv*\dx) p — q dxdv\dxjp—q dx*\ 



ld*tp 

 The factor by which — ™tt ^ s *° ue multiplied, occurs for the 



