( 740 ) 



As 



and 



/dv\ 1 fd*v\ 1 Sd*v\ 



dv — ( — da H f — dx* -f — - — — dx z etc. 



' V^A 1 • 2 V** Vp ^1.2.3 \dm*) p 



/dv\ 1 APrA 1 fd s v\ 

 dv a = [ — ) d.s H rftf?* -f. f — dx* etc. 



we find for a plaitpoint : 



1 |/d 8 tA fd*v\ ) 



dv u — dv a = — - — } dx* etc. 



' q 1.2.3 (V^Vp V^'Al 



So the />- and the (/-lines meet and intersect in a plaitpoint, and 

 this is not always changed when a point should be a double plait- 

 point. We shall, namely, see later on that the criterion for a double 

 plaitpoint is sometimes as follows: 



'dv\ _ fdv 

 dmjp \dx /q 



and 



'd*v\ fd''v . 



0' 



dx*Jp \dx''yq 



Let us now proceed to the discussion of the case represented by 

 fig. 8. Here it is assumed that T lies below the temperature at 



which — = vanishes, so that tins locus exists, it being moreover 

 dx 1 



dp 

 supposed that it intersects the curve — = 0. It appears from the 

 1 dv 



drawing that for the (/-lines for which maximum and minimum 

 volume occurs, two new points of contact with the p-lines are 

 necessarily found in the neighbourhood of the points of largest and 

 smallest volumes at least for so tar as these points lie on the liquid 



dp 

 side of — = 0. 

 dv 



So there is a group of (/-lines on which 4 points of the spinodal 

 curve occur, and which will therefore intersect the spinodal curve 

 in 4 points. The two new points of contact lie on either side of 



— - == 0, and these two new points of contact do not move far away 



dx* 



from this curve, the two old points of contact not being far removed 



t dp n 

 from — = U. 



dv 



If we raise the value of q, the two new points of contact draw 



nearer to each other. Thus e. g. the (/-line which touches in its 



dx 



Alv\ /d 3 v\ 



highest point, and for which 1 — 1 = and also 1 — 1 = in that 



