1909] on Osmotic Phenomena. 489 



volume of ice is greater than that of water). Consequently, some of 

 the ice must pass over into water, and the temperature must fall until 

 the vapour-pressures are again equal. The lowering of the freezing- 

 point by pressure, as observed by Lord Kelvin, and calculated by 

 James Thomson, agrees precisely with that deduced as above from 

 the condition of equality of vapour-pressure. 



'._'] Similar considerations apply to the equilibrium between a solution 

 and the pure solvent, or between solutions of different strengths. 

 To take a simple case, the vapour-pressure p" of a sugar solution is 

 always less than the vapour-pressure p of water at the same 

 temperature, and the ratio p" Ip' of the vapour-pressures depends 

 simply on the concentration of the solution, diminishing regularly 

 with increase of concentration and being independent of the 

 temperature. If separate vessels containing solution and water are 

 placed in communication at the same temperature by a tube through 

 which the vapour has free passage, vapour will immediately pass over 

 from the water to the solution in consequence of the pressure 

 difference, and will condense in the solution. The immediate effect 

 is to produce equality of vapour-pressure by change of temperature. 

 This takes only a few seconds. The vapour-pressure then remains 

 practically uniform throughout. As diffusion proceeds and the 

 temperature is slowly equalised, the water will gradually distil over 

 into the solution, but the process of diffusion is so infinitely slow 

 compared with the equalising of vapour-pressure that the final 

 attainment of equilibrium would take years unless the solution were 

 continually stirred. 



The reason why equality of vapour-pressure is so important as a 

 condition of physical equilibrium is that the vapour is so mobile and 

 so energetic as a carrier of energy in the form of latent heat. 

 The first effect is generally a change of temperature, but if the 

 temperature is kept constant there must then be a change of 

 concentration. Thus if two parts of the same solution are maintained 

 at different constant temperatures, the concentrations will change so 

 as to restore equality of vapour-pressure, if possible. Thus in a tube 

 of solution, the two ends of which are maintained at different 

 temperatures, the dissolved substance will appear to move towards 

 the hotter end. What really happens is that the vapour, which is 

 the mobile constituent, moves towards the colder end. If the tube 

 is horizontal, with a free space above the liquid for the vapour, this 

 transference will be effected with extreme rapidity. In fact, it will be 

 practically impossible to establish an appreciable difference of 

 temperature until the transfer is effected. If the vapour has to 

 diffuse through the solution in a vertical column heated at the top, 

 the process is greatly retarded, but the final effect is the same, and 

 can be readily calculated from the relation between the vapour- 

 pressure and the concentration. 



In explaining the production of osmotic pressure as a necessary 



2 K 2 



