( 747 ) 

 (Pui (dv\ (Pip 



and 



do 3 \dxjp dxdv 



cPtfj fd*v\ yPty fdv\* d'tp A/A d 5 w 



dv* \d,v*Jp {dv 3 \dasjp do i dm\dxJp das*dv) 

 from which appears that we can write the factor of dv in theform of: 



'd 2 ifj\ 2 (d?v 



(d*yj\* (d*v\ 

 \~dv~*J \dx~>) 



We might proceed in a similar way with regard to the factor of 

 das, but we can immediately find the shape of this factor by substi- 

 tuting the quantity x for v and q for p in the factor of dv. We find then : 



d*ip\* fd\v 



dx 1 J \dv' j q 



As long as we keep T constant, and this is necessary for the 

 course of a spinodal curve, the differential equation, therefore, may 

 be written : 



» dv — I — I — \d.v = 0. 



dv" 1 ) \dx* J p \dx* J \dv' 



fd\v\ fdx\Vd*v\ 



By taking into account that — — = — — ~r^ > w © obtain 

 J h \dv*J q \doJ q \dx*J q ' 



after some reductions which do not call for any explanation, the 



simple equation : 



d*v 



dv\ fdv\ Kdx* 



Ütö J spin \dX/ ^=7 



(d 2 v\ 

 [d?h 



As a first result we derive from this equation the thesis, that 



/dv\ (dv\ (d*v\ , fd*o\ 



— and — must have the same sign, if I — and — — 



\dxj spin \dxj p = q \dxy P \darj q 



have the same sign and vice versa. Thus on the vapour side in tig. 7 



Zd'iA , fd*v\ fdv\ 



I — I and I — 1 have always reversed sign, and I — I being 



\dx J p \dx Jq \dx/p = q 



fdo\ 

 negative, I — I is negative on the vapour branch of the spinodal 



\d® / sptn 



curve. Reversely the curvatures of the p and j-lines have the same 



f dv\ fdv\ 



sign on the liquid side, and I — 1 = I — 1 = positive. If, however, 



\dxjbin \daej p=q 



51 



Proceedings Royal Acad. Amsterdam. Vol. IX. 



