9i 



When we now write the vahie ol' ii.M^{l — ,f) -{- [j.^}f.i\ we tind 

 for it, at the height of A with density (j and concentration x 

 — MRTlog{v — K) 4- MRT[{1 - x)locj{l--x) -f xlo(jx\-^p^v — a^o — 



^ ''^ ^ die ' ''^ ^ dli" - '' die 



for 



d'^QX 



dlv 



1^2 a^a 



Q Q 



The pressnre p^ can be expelled from this relation when we 

 consider that p.^ -j- jyf^ (molecular pressure in the direction of tlie 

 capiUary layer) = /; -j- ajf)^, in which p represents the pressure 

 belonging to an homogeneous phase of the same density and con- 

 centration. In general jyf^=^ — o \sx — - C\ (1 — .2?) — C\iv\ holds, in 

 which g;i. = 6j (1 — x) -{- e^x, hence the energy for the quantity of the 

 mixture M^ (1 — x) -f- 3ij,i'. Now: 



d'Q{l—.v) 



8s — C, {\—^v) 4- 6\.^• — a^Q — I c,, {I -x) 



an 



d^QO,' d^(){l — .v) d'^QX 



hence : 



d^Q{l-x) d'^Qx d-Q{l-tv) d^^x 



^ '' ' ''^ ' dh' ^ - '"^ ^ Jh' ^2 '^ dh' ^- " dh' 

 If this value of jh ^^ introduced, the found relation passes into 

 — J//i T log (v - bj.) -\- MR T[{1 — x) log {I — x) -\- x log x\ -j- pu — axQ — 

 d"Q(l-x) d^Qx d'(}[l-x) d'^QX 



■,,{l-x) CiA^-^^)^J7V--<W^ 77^ c,,.^■ 



dh' ''' ' dh-' '' dir '' dh' 



= f*i^A (!—'<'■) + (J'^M^x. 

 This relation, which we have derived by means of kinetic consider- 

 ations only, is the first of the two conditions for the equilibrium 

 determined by van Eldik by a thermodynamic way. 



For the two homogeneous phases, which are in equilibrium with 

 each other, the following form holds : 



- M R Tlog{v-b, ) + MRT\{l-x)log{ 1 - x) + xlogx] + pv-asQ=nJI^ ( \-x) -|- iiJL^x 

 or 



If? -f- pv = ftiil/i (1— 'V) + [A^M^X. 



As the kinetic theory teaches that the pressure in the two phases 

 must be constant, it follows immediately from this that : 

 ip — fti^l/i (1—.^) — ii^M^x 



