( 168 ) 



of a\, from which -y- mav he derived: 



d. 



dp (/ "' -i)|i4--'-:(i-.t-,)f*%l. 



1 — 'ï-'i + 'ï?i e 



x\ 



So for .i\ ^ 1 



/^ r 

 dp _ ^ '- 1 



e 



If /> is a maxiiiuim for ./'j ^1, then fx'.,, = 0. 

 Van der Waals has also given an approximate vahie for ƒ«'.,, in 

 "Ternary Systems" ') : 



^ _ f dTcr dl0(ip,:r 



where T,, üh*' />-/■ represent the critical tempei-atiue and pressure 

 of the uiis|>lit mixlui-e and /' the known constant, aI)ont 7, which 

 inter alia also occurs in the formida, given much earlier hy van dkr 



Waals for a pure substance : ^^ep. io<j — =z — / — - — . 

 ' pk J 



This formuhi for ƒ/'.,, has been derived by van dkh Waals also 

 directly from the equation of state '^). 



If it only contained the first term, then a minimum critical tem- 

 perature wouhl be attended by a maximum pressure, the minimum 

 would therefore lie near the pure ether. Now however tiiis niiiiimum 

 will not be found there, as appears from the occurrence of the 

 second term. 



If we now assume that T,-,. depends linearly on ,/■ and that this is 



(IT dp, f 



also the case for /v,., then — ~ is about — 43 and —— about — 15, 



in consequence of which we find for {i.,-^ about 0,8, a value which 

 really lies between the values found. 



Also /t".i.,, the differential quotient of {i ,-, with respect to x^ may 

 be determined. The accurate relation derived by van dek Waals for 

 the dependence of the vapour pressure on the molecular concentra- 

 tion of the liquid mixture, where it is only assumed that the liquid 

 volume may be neglected by the side of that of the vapour, and that 

 the vapour phase may be considered as a rarefied one, is 

 1 dp I 1 , M 



1) VAN DER Waals, These Proc. V, p. 9. 

 2j VAN DER Waals, These Pioc. Yil p. 156. 



