( 36 ) 



In this simple form the equation is very suitable for calculating 

 successive spinodal carves. It is of the second degree with respect 

 to X, of the third degree with respect to <o. For a given value of 

 r we have therefore only to put successively tt> :^ 1, 0,9, 0,8 etc. 

 down to 0, and then we find the corresponding values of x by 

 solution of ordinary quadratic equations. 



The equation {Id) becomes after division by ^(1 — x)a^v*: 



l/a 

 (1 - 2;r) + i— 



?(- 



9' 



3 + 



%^(i-V«)(i 



36 



1v) 



1. e. as — = \- ic ^ (p -\- a; 



a a 



(l-2^0 + (y + ^-)(l-^r 



X (1 — x) 



X {\ — x) 



(1 — to) (l — 3w) 



0, 



0. . (26) 



This equation of the plaitpoint curve is of the third degree with 

 respect to x^ of the fourth degree with respect to to. 



3. Before discussing the equations (16) and (26) more fully, we 



shall first derive a few relations between T^, T^ and T,. 



V «' 8 a^ 



As RTg =z — — (see above) and RT^ = — — , we find immediately : 

 6 27 6 



16 a. 



16 



r„ 27 ft' 27^' 



From this follows that for values of 9) <[ ^/^ [/3 {= 1,30) T^ will 

 be <i T^; i. e. the lower critical temperature of the two components 

 will then be lower than the critical temperature of mixing of the 

 two liquid phases at v =:b. 



so — 3::: 



As (fi = 



l/a,— l/a/ 



1 [/a 

 so — = — 1, and we have evidently : 



^(— :)■ 



For <p = isl\ = coX T,;for(p = o:>isT,= T,. For <p = 7, 1/3 

 (see above) ^^/t, = (1 + 7« ^3)" = 'U, (43 + 24 v/3) = 3,13. 



It will also prove important to know the amount of the pressure 

 for all points of the spinodal curves. For this purpose we reduce 

 the equation : 



_ RT 



to 



