the Theory of Solutions. 611 



and with the help of equation (7) : 



'dp 



But (1 | is a very small quantity in comparison with 



the unit. We can therefore, when quantities of second and 

 higher order are left out of consideration, immediately 

 introduce one in the dominator and get the formula of 

 Planck. 



As already mentioned the formula (4«) holds good inde- 

 pendently of the compressibility as also of the molecular 

 volume's variation with the concentration. 



In Planck's formula the contraction is also taken into 

 consideration. From equations (4 a), (6), and (7), w r e can 

 now reversibly deduce the expression found in § 1 for the 

 concentration gradient. 



The dependence of Osmotic Pressure upon External Pres- 

 sure has also been theoretically treated by 0. E. Schiotz*. 

 He comes to the result, that the change of pressure on the 

 two sides of the membrane is connected by the following 

 equation : 



pdp = p dp Q , 

 and consequently 



"dp ' P 



This value for ^— - is obviously appreciably different from 



the one found above. The reason for the discrepancy must 

 be sought in the fact, that Schiotz in developing this formula, 

 has not taken under consideration the fact that the concen- 

 tration varies with the height. This, however, must be the 

 case, as w T e have seen. From our formula it appears that 



when the solution fulfils the condition — = 0, the formula 



developed by Schiotz will hold good for this special solution. 



We shall finally make a few comments concerning the 



variation of Osmotic Pressure with Concentration. In order 



to examine the influence of the concentration, we can suppose 



* O.E. Schiotz, "Ueber die Abhangigkeit des osniot. Bruckes undder 

 Dampfspannung- von dem Drucke" {Boltzmann-Festschrift, 1904, p. 618). 



2 T 2 



