( 745 ) 



ii cuiiiiiiueu ïiicjrcasc ui irinprraiure rue curves 

 (Pip 



with continued increase of temperature the curves — = and 



will no longer intersect, but will assume the toosition indicated 



by fig. 9. 



The spinodal line runs round the two curves, and so in conse- 



d*ip 

 quence of the presence of — - = it is forced to remain al an 



ax 



,. , , , d'tb 



exceedingly large distance from the curve — = 0. The question 



</r' 2 



may be raised whether the spiuodal curve cannot split up into two 



separated parts, one part enclosing the curve — = 0, the other part 



dv* 



passing round — — = 0. The answer must then he: probablv not. 

 dv i j 



d*l\> r/ 2 th 



In the points between the two curves and — are indeed, posi- 



'/'•'" d.c 2 



d**p 



tive, but still small, whereas does not at all occur in the figure, 



dx dv 



and will, therefore, in general, be large. Now if the temperature at which 



d 2 \p dhp 



— — = disappears, should lie above {T f: ) ly — - = shifts to the left, 



ax dv 



till it leaves the figure, and the spinodal curve is closed at x = 

 and T=(Tk\, and the new plaitpoint makes its appearance, which 

 we mentioned above. From this moment we have a spinodal curve 

 with two realisable plaitpoints. The graphical representation of the 

 curvature of the p- and the (/-lines is in this case very difficult, 

 because both groups of lines have only a slight curvature. If, howe- 

 ver, we keep to the rule, that the p- and the </-lines envelop the 

 spinodal curve at realisable plaitpoints, we conclude that the value of 



'd*v\ A/ 2 A . . _ 



— - and — is positive in 1\, and negative in the other plait- 



« J P \ da ' Jq 



point. When these points, called homogeneous plaitpoints by Kojrteweg, 



fd*v\ fd*v\ 

 coincide, | — - J = ( -— - ) = 0. Above the temperature at which this 

 \dx*J p \dx*J q 



takes place, thejj- and the ^-lines have no longer any point of contact. In 



,/> 

 consequence ot the disappearance of the locus — = 0, the course 



dv 3 



of the ^-lines has become chiefly from left to right, so in the direc- 

 tion of the .t-axis. On account of the disappearance of the locus 



