414 SEMI-PERMEABLE FILMS AND OSMOTIC PRESSURE. 

 In the upper regions, 



r(p)-i-*; 



y P 



where t denotes temperature, and a the constant of the law of Boyle 

 and Charles. Hence, 



Moreover, if 1 : n represents the constant ratio in which the S- and 

 D-inolecules are mixed in the A-column, we shall have in the upper 

 regions, where the S-molecules have the same density in the two 

 columns, 



Therefore, at any height, 



This equation gives the required relation between the pressures in A 

 and B and the composition of the fluid in A. It agrees with vari't 

 Hoff's law, for when n is small the equation may be written 



or 



Pl-pB 



But we must not suppose, in any literal sense, that this difference 

 of pressure represents the part of the pressure in A which is everted 

 by the D-molecules, for that would make the total pressure calculable 

 by the law of Boyle and Charles. 



To show that the case is substantially the same, at least for any one 

 temperature, when the fluid is not volatile, we may suppose that we 

 have many kinds of molecules, A, B, C, etc., which are identical in all 

 properties except in regard to passing diaphragms. Let us imagine 

 a row of vertical cylinders or tubes closed at both ends. Let the first 

 contain A-molecules sufficient to give the pressure p f at a certain 

 level. Then let it be connected with the second cylinder through a 

 diaphragm impermeable to B-molecules, freely permeable to all others. 

 Let the second cylinder contain such quantities of A- and B-molecules 

 as to be in equilibrium with the first cylinder, and to have a certain 

 pressure p" at the level of p' in the first cylinder. At a higher level 

 this second cylinder will have the pressure which we have called p'. 

 There let it be connected with the third cylinder through a diaphragm 

 impermeable to C-molecules, and to them alone. Let this third 

 cylinder contain such quantities of A-, B-, and C-molecules as to be 

 in equilibrium with the second cylinder, and have the pressure p" at 

 the diaphragm ; and so on, the connections being so made, and the 



