the Theory of Solutions. G09 



(l)and(2) §1, we get 



O.'-' 0// d~ 



As both expressions for the total differential of it along the 

 membrane must be identical, we get as the necessary con- 

 dition for it : 



If we choose p instead of p as variable, we get in a 

 similar manner 



/cK\ d'' 1 Btt , 7 . 



Voc/jioO'i-K- o/A. 



By means of equations (4 a) and (4 6) there has been 

 developed a simple connexion between the concentration 

 gradient and the dependence of the Osmotic Pressure upon 

 the External Pressure, a connexion which makes it possible 

 to calculate one of these quantities when the other is known. 

 In the development of this formula nothing has been assumed 

 that restricts the general applicability of the solution found ; 

 the fluid may also even be compressible. The formula will 

 hold good, provided always that the fluid fulfils the equilibrium 

 condition (1) § 1, characteristic of an ideal fluid. 



TTe will now proceed to apply the formula for the calcu- 

 lation of ^— , as we have already found a value for ^— in 

 the first section. By the aid of equation (lie) § 1 we get 



d/> p jr^ K J)c v J 



The term that we in this way have found for the dependence 

 of Osmotic Pressure upon External Pressure, is now fully in 

 accordance with the equations found by Planck and Duhem 

 from another point of yiew. 



Phil Mag. S. 6. Vol. 13. No. 77. May 1907. 2 T 



