( 653 ) 



border curve of tlie mixture x in the p, r, T diagram. To the first 

 approximation its equation is : 



k- k 



P—P.ck= "^" (y — I'rA: )% (11) 



as for a simple substance ^). Hence to tlie lirst approximation the 

 border curve satisfies the law of cor responding states. 



That the border curve, apart from the deviations existing already 

 in pure substances does not altogether satisfy the law of correspon- 

 ding states, has a double cause. It is not only for mixtures which 

 differ little from the special mixture a^ that the experimental isother- 

 mal shows a slight slope, but this is even the case for the mixture 

 .Tk itself; only at the plaitpoint temperature it is perfectly horizontal 

 so that already for the mixture .% the border curve must deviate 

 from the law of corresponding states. If as before ^) we develop the 

 equation of the experimental isothermal : 



x—XTk — ^ 5 



we find : 



1 m., 7n,. 1 in" 

 p—pTk = m^, — h ^ {^v — WTkY 



-8m\, ^ ^--- '-^^ (v-VTk) {•v-.VTky + . (12) 



Q I 30 



m\^ H ■ 



.i?/,(l— .Pfc) 



and hence, for ,v = x/,, 



1 WijiWioi 1 m- 



m„„-- 



3 m,„ 5 ?n%„ J (T-TvY 



p=Pk+K. {T- T,)-8m%„ ^ ^Y^- ^^ i^-nt-^'i- + (13) 



771', H 



" (.tv^l-'-i-) 

 only for .Vk=:0 or 1, that is to say for the pure substances, the 

 third term is left out — and in the same way all the terms which 

 contain v — vk. 



If now by elimination of T—Ti between the equation of state 

 of the mixture x^ (equation (2), 1. c. p. 323) and the experimental 

 isothermal (10), we search for the border curve for that special 

 mixture, we see that the slope of the experimental isothermal only 

 influences the third term — viz. with {v — v^.)" — in the development 

 (11) of the border curve, so that this border curve only to a third 

 approximation shows a deviation from the law of corresponding 



1) These Proc. V, Oct. 25, 1902, p. 336. 



