the Osmotic Theory of Solutions. 609 1 



The numbers under the heading " oj Q CsCl (theoretical) " are 

 only approximate — they are calculated on the assumption that 

 equal molecular concentrations o£ CsCl and NaOl solutions 

 have the same osmotic pressures, and the value found for the 

 concentration of the middle sample is taken as a basis for 

 comparison. 



It will be noticed that considerably less difference was found 

 between the second and third samples than between the first 

 and second, while theory indicates that the inequality should 

 be markedly in the other direction ; the differences of con- 

 centration are, however, of the order of number indicated by 

 theory. 



General Investigation. 



Although the following argument can be readily applied 

 to the more general case of heterogeneous liquid or gaseous 

 mixtures, i. e. mixtures that differ in properties from point to 

 point of their mass in any manner, yet to enable a clearer 

 view to be obtained, we will limit the discussion to a column 

 of solution (subject to gravity) whose properties are uniform 

 at any given level. We shall not assume that equilibrium 

 has been attained, so that in general there will be relative 

 motion of solvent and solute throughout the liquid mass ; at 

 any given level one of the components will be moving down- 

 wards and the other upwards. This relative motion is 

 opposed by " internal viscosity/' and fixing our attention on 

 an infinitesimal volume element of the solution, we realize 

 that the solvent molecules in the aggregate must be acted 

 upon by a force in one direction (say downwards) and the 

 solute molecules by a force in the contrary direction. 



These two aggregate forces must be almost exactly equal 

 and opposite, for their resultant is measured by the accelera- 

 tion of the volume element as a whole multiplied by its mass; 

 and the acceleration in all practical cases will be excessively 

 minute. 



The same holds good for solutions contained in a uniformly 

 rotating centrifuge, provided we understand that the axes of 

 reference are rotating with the centrifuge, and avoid the 

 explicit appearance of accelerations by introducing the fiction 

 of centrifugal force ; so that here again we may always 

 consider the solvent and solute within any very small element 

 of volume to be acted on by sensibly equal and opposite 

 forces. 



Let dr be the volume of the element under consideration,. 

 Phil. Mag. S. 6. Vol. 17. No. 100. April 1909. 2 T 



