(137 ) 



region a point of inflection of the /v-lines and of the y-lines can lie. 



It appears from what has been observed about the loci of these 



points of inflection (These Proc. March 30, 1907 p. 736) thai this 



is possible for the (/-lines. Bui from what has been observed on 



the course of the locus of the points of inflection of the />-lines 



(These Proc. Febr. 23, 1907 p. 628) appears (hat in the stable part 



of that region no point of inflection can occur for these lines. 



Let us now take the other case, viz. thai the point with minimum 



dp 

 volume of — = exists, and is not found at very small value ofa. 

 dx 



If the spinodal line has split up into two parts, then there is a part 



dp 

 which we might consider as belonging to — = 0, and another part 



dv 



dhp 



that surrounds = 0. Now the splitting point lies again in the 



dx' 



dp 

 region where — is negative, but in a part of that region where as 

 dx 



well points of inflection of the /alines as of the «/-lines may occur, 



dp d'rp 



at least if — = still intersects the curve — = 0. Two branches 

 dx dx 1 



, . , d'v dp 



on which = 0, start from the point m which — = cuts the 



dx' q dx 



d'tp 

 curve — = 0. One ot these branches passes through the region 



dx' 

 d'\ 

 d^' 



d'xp 

 where — is negative, and leaves this region only at the point where 

 dv' 



= has the maximum volume. The second branch runs right 



dx' 



of the loop-g-line to larger volumes. But there is also a locus on 



d'u dp 



which = 0, which runs right of — =0, and passes through the 



dx'p dx 



dp 

 two following points. 1 st the point where — = has minimum 



'/.)■ 



dp dp 



volume, and 2 ntl the point where — = cuts the line — = 0. If 



dx dv 



the spinodal line splits up, this will have to take place in the point 



d'v 



ot intersection ot the line on which = with the second nien- 



dx' p 



d'v 



tioned branch on which = 0. It this case of splitting occurs 



dx'a 



