dm 



612 The Earl of Berkeley and Dr. C. V. Burton on 



osmotic contact with that in b at the level o£ the latter. 

 These two solutions are now in osmotic equilibrium through 

 the membranes q and g'. Push in the piston a' and simul- 

 taneously withdraw a until a mass dm of solvent has passed, 

 under osmotic equilibrium conditions, from V to b, the final 

 pressure in b being exactly p. 



The work done on the two pistons is 



(IV.) Reshutter the two membranes q and ^, separate the 

 cylinders, change the pressure in V back to its former value 

 p-h(g/w)xSh, restore the cylinders to their original places 

 and put their contents in osmotic communication with the 

 solution-column. The initial conditions are now restored. 



The balance of work done against gravity is g8h dm. 



Regarding stages (II.) and (IV.)? when the changes of 



pressure between p + (g/ic)8h and p + ( -— 1 ) ~ Bh are 



being made, the volume dealt with in (II.) is greater by sdm 

 than in the reverse operation (IV.) ; hence the change iiL 

 volume is greater by 



and the corresponding work-term is 



*l &-("£)} s """ 



Collecting the various terms, and remembering that 

 c 1 =:l — c 2 , we obtain, on division by hit dm, 



or 



Equation (26) gives the downward force acting on the- 

 solvent molecules per unit mass of the solvent, while- 



