SEMI-PERMEABLE FILMS AND OSMOTIC PRESSURE. 415 



quantities of the several kinds of molecules so regulated, that the 

 pressures at all the diaphragms shall have the same two values. 



It is evident that the vertical distance between successive con- 

 nections must be everywhere the same, say I ; also, that at all the 

 diaphragms, on the side of the greater pressure, the proportion of 

 molecules which can and which cannot pass the diaphragm must be 

 the same. Let the ratio be l:n. If we write y A , y B , etc., for the 

 densities of the several kinds of molecules, and y for the total 

 density, we have for the second cylinder 



For the third cylinder we have this equation, and also 



yA+y B +yo = 1 + 

 VA+ys 



which gives 



In this way, we have for the rth cylinder 



Now the vertical distance between equal pressures in the first and 

 rth cylinders, is 



(r-l)l. 



Now the equilibrium will not be destroyed if we connect all the 

 cylinders with the first through diaphragms impermeable to all except 

 A-molecules. And the last equation shows that as y/y A increases 

 geometrically, the vertical distance between any pressure in the 

 column when this ratio of densities is found, and the same pressure 

 in the first cylinder increases arithmetically. This distance, therefore, 

 may be represented by log(y/y A ) multiplied by a constant. This is 

 identical with our result for a volatile liquid, except that for that 

 case we found the value of the constant to be at/g. 



The following demonstration of van't Hoff's law, which is intended 

 to apply to existing substances, requires only that the solutum, i.e., 

 dissolved substance, should be capable of the ideal gaseous state, and 

 that its molecules, as they occur in the gas, should not be broken up 

 in the solution, nor united to one another in more complex molecules. 



It will be convenient to use certain quantities which may be called 

 the potentials of the solvent and of the solutum, the term being thus 

 defined : In any sensibly homogeneous mass, the potential of any 

 independently variable component substance is the differential co- 

 efficient of the thermodynamic energy of the mass taken with respect 



