( 130 ) 



Indeed. thi> was also to be derived from the p-figure (fig. 20) 

 where the branches ƒ and g must lie higher than the branches c 

 and '/. and therefore can never combine for the application of the 

 rule for coexistence: but then only for those 7-lines which are Of 

 higher degree than the loop-g-line ; whereas the rule for finding the 

 conditions for coexistence from the values of q when a p-line is 

 followed, holds for all p-values without exception. Let us consider 

 the case that this part of the plait has got quite detached from the 

 transverse plait as a closed longitudinal plait, and has the two 

 realisable plaitpoints, then a highest and a lowest />-line may be 

 drawn, along which the maximum and the minimum in the 5-line 

 have coincided, and in t lie point where they coincide they yield the 

 value of x for the two plaitpoints. 



We had already repeatedly occasion to call attention to the reci- 



d'ty , d*q> dip , dtp 



procity between — and — , and between and p or — and — . 

 1 ■ dx* dr' * l dx do 



Let us also do so in the case discussed. Here we have intersection 



d*tp , d*i|> 



in two points of — = and = 0, and it appeared that then 



dx 1 dxdv 



separate portions of g-lines occur, so that it was not always possible 



to pass without a leap from one part n\' a y-line to another part of 



such a line. Then it is desirable for the determination of the coexisting 



phases not to follow such a 7-line, but on the contrary to go along 



a /dine and to use the corresponding value of q. The reciprocal 



d'tp d*ip 



case is found in case of intersection of = and = 0, in 



»//•- dvdx 



which case the course of the p-lines is as is indicated in the middle 



region of the general p-figure. Then there are //-lines, namely those 



of higher degree than the loop-p-line, which have divided into two 



separate part.-: if we followed a //-line also then, in order to arrive 



at the coexisting phases by means of the values of q s we should be 



confronted by the same difficulties as we have met now when 



following the 7-line. If for a p-line of lower degree than the loop- 



//-line we draw the value of 7. then such a course for q follows from 



dx* Ts ~ [dxdvj 



(dq\ _ d 



as has been drawn in fig. 23, where 



d*ip 



J? 



the L' . 3 rd and 5 th branches lie in the stable region, and the 2 nd 

 and 4 th branches lie in the unstable region; if we take into account 

 that such a p-line passes 4 times through the spinodal line, in which 



