( 63? ) 



d*p 

 for which this value = 0. These are the points tor which — — = 0. 



dxdv 



d*p 



For smaller value of the volume — — - is therefore negative — on the 



dxdv 



other hand* positive for larger volumes. The approximate equation 



of state yields for the loci mentioned and for following loci these 



equations : 



db da 



dx dx C dp 



— - = — for 



v 



C J? dv = 



J dx 



db da 



dx dx f dp 



= — for — 



{v-by v* \dx y 



db da 



dx _ dx / d*p\ _ 



(v—b)' ~~ v* 01 \dxdv) ~ 

 And so forth. 



But let us now return after this digression to the description of 

 the shape of the 5-lines. Whenever a ^-line passes through the locus 



c 



ƒ 



)<it' = , the asymptote to which it will draw near at infinite 



volume is known by the value of x for that point of intersection. For 

 the present it does, indeed, pursue its course towards higher value of x, 



fdp\ 



but when its meets the locus — = 0, it has the highest value of 



\dacJo 



x, and a tangent // v-axis. From there it runs back to smaller value 



of x. 



And this would conclude the discussion of the complications in 



the shape of the ^-lines, if in many cases for values of T at which 



the solid state has not yet made its appearance, there did not exist 



another locus, which can strongly modify the shape of the g-lines, 



and as we shall see later on, so strongly that three-phase-pressure 



may be the consequence of it. 



The quantities and — - occur in the equation of the spinodal 



dv* dx' 2, 



curve in the same way. It may be already derived from this thai 



d*ip d'ip 



the existence of the loci = and = will have the same 



dv* dx* 



significance for the determination of the course of I he spinodal line. 



