( 38 ) 



R'l 



= - [,■ (!-.<■) (ar - p y a y -f a (t>-ft)'], 



(1) 



iüT= — *(1-* l_Ji^ + (1 



v [ \ v a J a \ v / J 



fti £ V a \ 



which with — = o> , — = n<a , — = <p passes into 



RT = — ?tü) 



• (1-*) l-« ü )( 9 ) + .r) + (? + *)' l-(l+^)tt) 



.(la) 



j/a (/a, -(-• «a ft ^\-\~ x ^ 



For — = = (f -f- * and — = — — = tu -f- #««> = (1 -\-nano). 



et a v v 



Now the spinodal curve must show a double point, in other words: 

 — - = and :r— = 0, 



0* OU) 



when ƒ represents the second member of (la). The first equation 

 gives : 



(i-2«) (i-zy - 2* (l-*) (i-z) wcü+2 (y+«) (i-y)* - 2 (*>+*)' (i-y)««> = °. 



when for the sake of brevity nia (<p-\-x) = z and (l+n*)o> = y is 

 put. Bearing in mind that «co = , we get for the last equation: 



(l-2*)(l- g )'- 2jr( ^ ) g(l- g ) + 2(y+*)(l-y) , -2(y + *)(l-y) g =0. (a) 

 y+* 



The second equation yields, when in (la) the factor a» is brought 

 within [ ] : 



*(1- 



.,) |"(1_«)» _ 2a> (1-,) n (9) + *1 + 



+ (<P+*r [(1 - yV - 2<o (1-y) (1 + ™) 1 = 0, 



or 



*(l-«) 



i. e. 



(!_*)._ 2* (l-*)+(<p+*) 



-] 



(l-y)'-2y(l-y) =0, 



] = * 



« (l-*)(l_«)(l-8*) + (y + .tf (1-2/) (l-3y) = 0. . . . (ft) 

 From (b) we solve : 



*(i— *) = — (»+*)• 



(1-*) (1-3*) 



Also from (a) : 

 1—2* = 



2(<p+*)(l-y) s + 2 fo>+*)'(l-y> + ^-^* (1-*) 



(l-*) s . 



