( 157 ) 



than that of the [iressure of coincidence (pressure of (lie saturated 

 vapour for the unsplit mixture). 



Equation (2) however, can also be found directly from the ecpia- 

 tion of state. It was to be expected that this was possible, because 

 as I have shown in "The liquid state and equation of condition"^) 

 the formula for the vapour maj be derived from this equation. If 

 we want to find also for the factor /' the real value of about 7, 

 it is necessary to consider It as function of the volume. This not 

 only renders the derivation very complicate, l)ut it places us before 

 the unsolved question: in how far is the decrease of h wilh (he 

 volume to be ascribed to real or quasi diminution ? 



I have therefore confined myself for the moment to examining 

 what follows for the form of (2) from the equation of state, when 

 b is put independent of the volume. 



We have then to reduce : 



(lb da 



MRT — ^ 



dx diC 



V— h V 



We write for this successively : 



db da 

 MRT — — 



dx dtC / (t \ db 1 da 



V — b V \ ü'v t/tt'" V dx 



a 

 d- 

 _ db b fa a\db n l\da 



~~ ^' Jx~ ^ '^ [? ~ b^J dx ^Xj^bjdx' 



dbfl l\ f\ \\da 

 -Now tor a ~\ — — — we mav write 



b\c^ by V'* ^J'f' 



ax 



a{c—b) \ 1 (/,( c^b 1 db I a{c-b) \ 1 da 2 db / b\\ db 



be { a dx V b dx ] bv | a dx b dx y c J b dx 



a{v — b) 



and as according- to the equation of state — is equal to 



bv 



ail' — b) — b 



\--l = MRT + {MRT - cp)-j- 



be o 



we find after some reductions: 



db da a . a a 



MRT— — d- dl~~ dl- 



dx dx db b b^ c — b i' 



i' 



=/> T~l-+ ^1^^^^' -^ I -y^ {MRT-cp) --— 4- 

 ax dx dx (> ax 



v—b 1 db 



+ ^---iMRT-p{r-b)\ (3) 



h b ax 



1) These Proc. VI. p. 1:23. 



jLJL; 



