( 843 ) 



1 I 



By successively increasing x from — to — , and deriving the cor- 



Ó — 



responding values y q and — - — from the table of p. 829, we can 



a. -J- « 2 — 2a ]2 ii. 



calculate the value which must have at the least in 



1 . b x 



order to satisfy this inequality. If we put x = — , to which — = 



3 ^2 — ^1 



corresponds, we see that only a x = might be put. If x is made 



to increase, which implies that the ratio of the size of the molecules 



a x -j- a 2 — 2« 12 , . 



approaches 1, the value of required to satisfy the m- 



a x 



1 

 equality, decreases. For the limiting case x = — , b x =bz and y =0, 



a 



«1 + «S — 2 «1 2 , . ^ 16 . , , , . r r ^ rn 



— must be ^> — to enable us to put y 7 ^>7^. 



But this value must be larger for b x smaller than A 2 , and the 

 larger as the difference between 6 2 and ft, increases. If this equality 

 is not satisfied, so if T q <C Tk lt we have a plaitpoint line of a per- 

 fectly normal shape. This is inter alia the case when for a low ratio 

 between b x and b„ also a not very high ratio between the critical 

 temperatures is found. First, however, we should have to know how 

 rt 12 depends on a x and a S3 before for given ratio of b x and 6, we 



a i a 2 



could indicate how large the ratio of — and — would have to be to 



justify us in expecting either the complicated or the simple shape of 

 the plaitpoint line. Moreover, I repeat that it should be considered 

 in how far numerical values occurring in the given equations, would 

 have to be replaced by others on account of the only approximate 

 validity of the equation of state. 



From all this appears in how high a degree the properties of the 



function —-^ influence the shape of the plait, and so also the miscibility 



or non-miscibility in the liquid state, and that the influence of the 

 properties of this function may be put on a level with that of the 



function . We shall further demonstrate this bv also examining 



dv* 



d*ti> 

 the case that the curve = exists, and intersects the curve 



d.v* 



dxdv 



