18 Mr Vegard, On the Free Pressure in Osmosis. 



the sake of comparison the curve for experiment II* is put upon 

 Fig. 1 A as a dotted line. 



The power of giving a well-marked steady state after this first 

 sudden bend of the curve is a quality that does not belong to any 

 membrane showing osmotic activity. Even for the system here 

 under consideration it appears to be a matter of degree just as 

 the power of giving a reversion pressure near to the osmotic 

 pressure is a power only possessed by the very best membranes. 

 It will surely be of great interest to see how the different systems 

 behave in this respect. 



6. When the steady state is well defined the velocity correspond- 

 ing to this state can be considered as a function of concentration, 

 temperature, and further of some quantities dependent on the 

 membrane and the fluid. Instead of concentration we can 

 introduce the osmotic pressure ttq. As long as the properties of 

 the membrane and the temperature can be considered as con- 

 stants we are led to consider the variation of the velocity Xq with 

 the osmotic pressure of the solution. The relation between ttq 

 and Xfl is represented in Fig. 2 B, curve I. On the same figure is 

 also drawn the curve giving the relation between the velocity and 

 the friction pressure (curve II). 



We see that curves I and II stand in a very characteristic 

 relation to each other. The friction line is a tangent to the curve 

 at the zero point. 



A line parallel to the tto axis cuts the curves in two points 

 (ttq Xo) s^nd (QXo) which we shall call corresponding points, then 

 Q is the pressure necessary to force the pure solvent through the 

 membrane with a velocity equal to the osmotic velocity Xq called 

 forth by a solution of osmotic pressure ttq. In general we have 



for corresponding points -< 1, and - will decrease for increasing 



velocities ; but when the velocity decreases towards zero we get 



Lim 



-Q\ 



ini(^ =1 (2). 



=0 \^o/ 



Let Q, TTo, Xo be values belonging to corresponding points. 



TT — Q . 

 If we calculate the quantity " for different values of Xq 



we find that it gives a constant value. Remembering that Q = AXq 

 we get the following simple equation for the curve 



- ^^» =^X^-A^ (3). 



" "X "" "X —"X 



Xjn 



* L. Vegard, loc, cit. p. 404, 



