( 195 ) 



. . d'rp d*i|' 



which not only and are positive, but the product is equal to 



dx* dv* 



fd'tyX* fdp\ 



— which may the sooner take place when the line — = 



\dxdvj J F \dxJ vT 



is in the neighbourhood. In this case there originate two new realisable 

 plaitpoints. Then there are 5 plaitpoints at somewhat higher tempe- 

 rature, because 2 new ones have been added to the three above 

 mentioned ones. And now, as I demonstrated when I discussed such 

 a splitting up, at somewhat higher temperature the hidden plaitpoint 

 will coincide with one of the newly formed realisable ones, and 

 vanish as a couple of heterogeneous plaitpoints. So there are 3 realisable 

 plaitpoints left viz. one that is t lie plaitpoint of the half of the plait 

 (transverse plait) on the hydrogen side. And the two others, which 

 are the upper and lower plaitpoint of the half of the plait which 

 has got detached (longitudinal plait). In other words: one half is a 



plait that surrounds the curve = 0, and the other half runs round 



dv % 



— = 0. In this halt - — = performs in many respects the function 

 dx* dx 1 



d**P 

 which — — = perforins as a rule. The splitting up of the spinodal 



line, so that a closed longitudinal plait detached itself, can, therefore, 

 take place in such a way that this longitudinal plait is found at 



temperatures at which - — = still exists for the same value of x, 

 dv s 



but is then restricted to very small volumes (mixtures of water and 



ii-i "^V* 



phenol) ; or it may take place in such a way that = no longer 



dv % 



exists for the same value of x, but then the volumes need not be so 



very small. We might say : the detaching might take place in such 



a way that the two parts of the plait exist above or by the side of 



each other. 



Moreover the case may occur that - — has quite disappeared, and 



do 



«Ftp 



— alone exists. Then only a longitudinal plait is found. This can 

 dx"* 



only take place for temperatures above 7^, and Tk % , and if what 



I have called T n , is larger than T^ and T^. 



In fig. 27 I have drawn the 2^>y-pi'OJection of the plaitpoint line, 



which in the ivr-plane is again a line which proceeds continuously 



from the left to the right side. At Tk for i^ there are three points 



