420 UNPUBLISHED FRAGMENTS. 



water- vapor, y^, to be measured in a space containing only water- 

 vapor and separated from the liquid by a diaphragm permeable to 

 water and not to alcohol, then the above equation would probably 

 be applicable, since then the water-vapor might probably be treated 

 as an ideal gas. The same would be true (mutatis mutandis) of the 

 potential for alcohol in a mixture of alcohol and water containing 

 not more than T \j- of one per cent, of alcohol* 



This law, however, which makes the potential in a liquid depend 

 upon the density of the substance in some other phase is manifestly 

 not convenient for use. We may get over this difficulty most simply 

 by the law of Henry according to which the ratio of the densities of 

 a substance in coexistent liquid and gaseous phases is (in cases to 

 which the law applies) constant. If y be the density in the liquid 

 phase and y gas in the gas, we have 



y gas = cy, [3] 



and by substitution in equation [2] we have 



At 



u. = f unc (t) + -j-f log cy, 

 lu 



At 

 or u. = f unc m + -^ log y, [41 



' \ / ' I/I O / ' I. J 



At 

 where the function of the temperature has been increased by -^ log c. 



With this value of the potential, which is manifestly demonstrated 

 only to be used so far as the law of Henry applies, in connection with 

 the general equation (98), [" Equilib. Het. Subs."] viz., 



v v v v 



we may calculate the osmotic pressure, etc., etc., as we shall see more 

 particularly hereafter. 



I. Osmotic pressure. 

 II. Lowering freezing point. 

 III. Diminishing pressure of other gas. 

 Ilia. Effect on total pressure. 

 IIII. Raising boiling point with one pressure. 

 IHItt. Raising boiling point with two pressures. 



V. Interpolation formula for mixtures of liquids. 

 In fact, when y D t is small, we have approximately 



At 



*** 4 i T'^D rf\ 



, = Atd-?, [5] 



*Alao the potentials of water and alcohol in a mixture may be measured in a vertical 

 tube of sufficient height. [See p. 413.] 



t[In the following discussion, D indicates the dissolved substance, or solutum, and 8 

 the solvent.] 



