296 Prof. J. H. Pointing on Osmotic Pressure. 



we obtain Kirchhoff's result, 



. Lade 



Now let us consider the case of a dilute solution of a non- 

 evaporating salt. We know by direct observation that the 

 vapour-tension is reduced by the presence of the salt, and we 

 must suppose, on the hypothesis here advocated, that this 

 reduction is due to a decrease in the mobility of the liquid. 

 Let us follow out this idea by imagining that we have in the 

 same chamber maintained at a constant temperature two deep 

 vessels, one containing the pure solvent the other a dilute 

 solution. In this chamber we shall suppose that above the 

 liquids there is only the vapour of the solvent. To begin 

 with, we may suppose that each vessel is half full and at the 

 same level. Then the pure solvent will distill over into the 

 solution, and will continue to do so until the difference in 

 level in the two vessels is such that each surface is in equili- 

 brium with the vapour at its level. The hydrostatic pressure 

 in the solution at the level of the surface of the pure solvent 

 will then be the osmotic pressure. If we imagine a number 

 of non-wettable tubes inserted, as in fig. 1, in the sides of the 

 two vessels at various depths and turned upwards, the diame- 

 ters being so adjusted that the liquid does not flow out of any 

 of them, then in any pair at the same level we realize Fitz- 

 gerald's semi-permeable membrane ; and at each level the 

 two liquids must have equal vapour-tensions, which implies 

 that their mobilities are equal at each level. This also comes 

 out from our equations. Let tzr, -gt / be the flat surface vapour- 

 tensions of solvent and solution, p the density of the liquid — 

 practically the same for each — and H the final difference in 

 level between the two surfaces, so that the osmotic pressure 

 Y—gpH. If M, M' be the mobilities at the surface-levels, 



W ~ m'' 

 Now as we descend in the solution the mobility increases, and 



the rate of increase is —j- per unit pressure. For depth H 

 this increase is gp —j- —g — - n or the mobility 



M' 



•37 



But -us = -&' + glla , 



