( 43) 



It ma}' be easily demonstrated that in the neighbourhood of C^ 



such a minimum never appears in our case. For from (16) folloAvs 



Tj 16 

 with r =: —- = --<ƒ)*: 



T^ 27 

 16 



27 



r/^ =: 4a> 



.t-(i -.!■) + (.ƒ) + vy{i -o,y 



After substitution of x n= A, to = Ys (^ + ^)' ^^^ get, neglecting 

 A", which is justified by the result : 



a-f rf) 



9 A / 2A\ 

 7-7+1 + — (I - V.cf)^ 



or as 



l + cf 



= 1 — ff + (T^ 



yielding 



9 A 2A 



j-7+-"a 



4 y)^ «/) 



A = V,d'= 



9 2 



r-ï + - 



and so 



V,d)^ = 



= 3d^: 



1 



l + d 



9 8 



^+- 



1, 



-(l-V,cfr = V,rf«: 



The spinodal line 2'= Tj touches, therefore, the axis x = for 

 every value of (f, and, iit least on the assumptions made by us 

 concerning a and b, a minimum can therefore never appear in the 

 neighbourhood of 6\, in consequence of which the spinodal lines in 

 the immediate neighbourhood of Cj would enclose this point. 



Finally some corresponding values of x and a> are subjoined, which 

 determine the shape of the spinodal line t = 1 (7^= Tg). By solution 

 of the quadratic equation 



4tt> 



^ (1 — .v) + (1 + xY 1 — to) 



'] 



1 



follows immediately: 



ix) = l 0,8 0,7 0,6 0,5 0,4 0,33 0,3 0,2 0,1 



.v — 0,h 0,403 0,292 0,227 0,184 0,164 0,182 0,182 0,306 0,679 

 0,743 1,004 



So this line cuts the axis x = 1 for to = 0,7, and henceforth only 

 one solution satisfies, x becomes evidently 1 for to (1 — to)'' =: 7ia» 

 yielding about to = 0,07. 



From the above derived equation 4^(^-1- l)(^—<«)* + l — t(2— to)^0, 

 which was the condition for two equal values ofx, we find y = 1, t=: 1 : 



8to^ — 15to + 7 = 0, 

 from which, besides to=:l, m^ 1^ follows. To this belongs then 

 A' = ^Vii ^ 0,524. Between to = 1 and v) = 0,875 we find only 

 imaginaiy values for x in the above table. 



