20 Mr Vegard, On the Free Pi'essure in Osmosis. 



This relation holds for all velocities. Letting \o converge towards 

 zero we get 



Regarding equation (2) 



,im(-^) = 



or Lim a' = ktto'X.o = kQ\o = a= E (4). 



Ao=0 



Thus we see that for small velocities the whole energy of the 

 system is made available for the motion through the membrane and 

 the work {a') required for the motion under osmosis is just the same 

 as the work (a) required for pressing the pure solvent through with 

 a velocity equal to the osmotic velocity. 



As the work is the same we must assume that also in the case 

 of osmosis we have a motion of pure water through by far the 

 greatest part of the membrane. But the motion of pure water 

 must have its cause in the fall of hydrostatic pressure in the 

 direction of the motion just sufficient to counteract the friction 

 corresponding to the osmotic velocity. 



8. From this we are led to consider the variation of hydro- 

 static pressure through the membrane. In those cases where 

 there is a layer next to the solvent where there is only pure 

 solvent we shall in this layer have a fall of pressure in the 

 direction of the motion, and when the pressure on the solution is 

 less than the corrected reversion pressure (tto')* we find that if we 

 pass through the membrane from the side of the solvent the 

 hydrostatic pressure will first fall to a minimum value and then 

 increase to the pressure of the solution. In the latter part the 

 motion takes place against the pressure fall and cannot be a 

 motion of the fluid in bulk, but is an intra-molecular motion 

 maintained by the energy made available when the two liquids 

 are brought into contact. 



The difference between the pressure on the solvent and the 

 minimum pressure we shall call the free pressure of osmosis. 

 The general features for the variation of hydrostatic pressure 

 through the membrane is indicated in Fig. 2. AF-^, AF^ etc. 

 represent the free pressure. 



If the distance from the minimum point to the surface next to 

 the solution is nl, where I is the average thickness of the mem- 

 brane, then an approximate value for the free pressure q is given 

 by the equation 



q = (n — l)A\. 



* See L. Vegard, loc. cit. p. 264. 



