{ m ) 



as ~ = — , while - and — are replaced bj their values (see ^ 2). 



Now : 



a 



a^<p^ 



lience : 



(O 



7?T =r ^== 



' 27 Z*, 27 Z> 



.^• (1 — .7) ( 1 — 7iio{(p -\- 0') H- (y + .^f ( 1 — co(l + na-) 



' if' 



If we now put T = Tj (1 + t), co = Vs (^ + ^)' ^'"^ becomes for 

 small values of x: 



1 -I- T = V. 



l + d 



y^ 



•^•(i-v,^^yr+^^(^i+2-J(i-a>r(^i-2— J 



in the second member of which only terms of finite value and those 

 of the order x remain. We draw attention to the fact that according 

 to (In!) Ö is of the order a\ Further substitution of to = 73(1+'^) 

 yields: 



1 + rf 



1+T:=74 



r L 



.^- (1 - V3 ^^wY + 



^''^1 + 2-^1 -ff)(l -nx)V 



as 1 - to r= V3 - 73 rf== V3(l-V,rf), so (l-tor=V«(l-rf) 

 The last expression becomes now : 



1 + T z=: (1 + tf) 



{"^-'Ump) 



v< 



;j^+(i+2i-.-„)]. 



or if we neglect terms of higher order than the first: 



1 + r 



(1-Va^^y)^ 





rf = net' I 



_|_ 1 4. 2 6—na^ + tf. 



And now it proves, that the terms with 6 vanish, so that we 

 do not lonnt the value of - from (la) for the calculation of the limiting 



value ot the relation -^). For the sake of completeness we have, 



however, calculated this value, as it may be of importance for some 

 problems to know in what way v varies with x in the neighbourhood 

 of the lower critical temperature (remaining on the plaitpoint curve). 



'^) This is, of course, in connection with the fact that at the critical temperature 

 of the first component the spinodal line touches the line a: = 0, and — as the 

 spinodal curve is rertical at that place (i.e. // to the v-axis) for very small values 

 of a; — a change of v will therefore only bring about a change of temperature 

 (and so also of the plaitpoint temperature) infinitely smaller than the change of 

 temperature, brought about by a change of x. 



