Mr Vegard, On the Free Pressure in Osmosis. 



19 



The curve is determined hj two parameters A and X^. Of 

 these it is only the first one for which we have a physical inter- 

 pretation. As regards X^ we see from the equation that when \q 

 approaches X^,, ttq approaches iiifinity. Thus X^n is the upper limit 

 for the osmotic velocity in the stationary state. As to its physical 

 interpretation it will depend on A, further it must depend 

 on the coefficient of diffusion for cane sugar in water ; for it is 

 evident as the velocity is to be produced by the action of the 

 solution the velocity must be so small that the solution is able to 

 maintain a certain concentration in the layer next to the mem- 

 brane. 



Some values of X^ calculated for a series of velocities from the 

 curve directly observed are given in the following table. 



Mean value 461 mm./hour = 2-13. 10~®[cm. sec.~^]. 



7. From the very intimate relation between the friction line 

 and the velocity curve we can draw some important conclusions as 

 regards the mechanism of osmotic flow. 



The work (a) required in unit time for pressing the water 

 through the membrane with a velocity Xq is 



a = kQXq, 



where « is a constant dependent on the units. In the case of 

 osmosis we must be able to assume that in order to bring the 

 water through with a velocity Xq an amount of energy (a') is 

 required which cannot be less than the energy required for 

 pressing pure water through with the same velocity. Then we 

 must have 



a' 5 a. 

 But on the other hand the maximum of energy E which the 

 system can deliver in unit time is equal to the osmotic pressure 

 multiplied with the volume of solvent, which enters into the 

 solution in unit time, or 



JE ^ /cttoXq. 



Now the work (a') necessary to call forth the motion of solvent 

 through the membrane cannot be greater than £J, consequently 



kttqXq > a > kQXq. 



2—2 



