( 54 ) 



to the solution, which would be equal to v only when i\ happened 

 to be equal to v^. 



2. In order to compare the results, found by Morse and Frazer, 

 more closely with those for the osmotic pressure alread}'^ given by 

 me in 1894, we shall return to its derivation for a moment, chiefly 

 in order to ascertain on what limiting suppositions this formula holds. 



With equilibrium between the pure solvent (concentration 0, 

 pressure p^) and the solvent in the solution (concentration c, pres- 

 sure p) [tlie dissolved substance is nowhere in equilibrium, for it 

 is supposed that there is a membrane impenetrable to it] the molecular 

 thermodynamic potentials must have the same value. Hence ^j : 



f*l ('^' P) = f^i (Ö' Po) • 



Now in general : 



dZ 



li,= — =C,-(9,-^RTlogc,, 



when C, = -k,T {log T - I) ^ {{e,\ -~ T{s,),), c, = ^ and 



do 

 6^ = ^ — ; being given by 



:= I fdv 



pv — RT 2 Wj . log 2 n^ . 



For binary mixtures of normal substances we may now introduce 

 the variable x and we obtain (^?z, is now := 1, so that the term 

 with log 2n^ vanishes), as may be supposed as known : 



li, = C,-Li-.x^-\-p(v-w~^^RTlog{l-x), . (1) 



when to is written for | pdv by way of abbreviation. 



This expression is perfectly accurate for the above mentioned 

 mixtures. For the further calculation we now introduce the idea 

 "ideal" mixtures. They are such as for which the influence of the 



two components inter se may be neglected. Then — — =: 0, and to 

 becomes a linear function of x. But also r — = 0, so that v becomes 



Ï) The following derivation is only different in form from the cited one in these 

 Proceedings. 



