VIII. 



SEMI-PERMEABLE FILMS AND OSMOTIC PRESSURE. 



[Nature, vol. LV, pp. 461, 462, Mar. 18, 1897.] 



LORD KELVIN'S very interesting problem concerning molecules 

 which differ only in their power of passing a diaphragm (see Nature 

 for January 21, p. 272), seems only to require for its solution the 

 relation between density and pressure for the fluid at the temperature 

 of the experiment, when this relation for small densities becomes that 

 of an ideal gas ; in other cases, a single numerical constant in addition 

 to the relation between density and pressure is sufficient. 



This will, perhaps, appear most readily if we imagine each of the 

 vessels A and B connected with a vertical column of the fluid which 

 it contains, these columns extending upwards until the state of an 

 ideal gas is reached. The equilibrium which we suppose to subsist 

 will not be disturbed by communications between the columns at as 

 many levels as we choose, if these communications are always made 

 through the same kind of semi-permeable diaphragm as that which 

 separates the vessels A and B. It will be observed tliat the difference 

 of level at which any same pressure is found in the two columns is 

 a constant quantity, easily determined in the upper parts (where the 

 fluids are in the ideal gaseous state) as a function of the composition 

 of the fluid in the A-column, and giving at once the height above the 

 vessel A, where in the A-column we find a pressure equal to that in 

 the vessel B. 



In fact, we have in either column 



dp= yydz, 



where the letters denote respectively pressure, force of gravity, density, 

 and vertical elevation. If we set 



wehave 



Integrating, with a different constant for each column, we get 



