1901)] on Osmotic Phenomena. 491 



tion is the product of the osmotic pressure P by the change of 

 volume U of the solution per gramme-molecule of solvent abstracted. 

 In the state of equilibrium of vapour-pressure, this osmotic work P U 

 must be equal to the work which the vapour could do by expanding 

 from the vapour-pressure 2^' of the pure solvent to the vapour- 

 pressure p" of the solution. Neglecting minor corrections, we thus 

 obtain the approximate relation — 



PU = R^ log (///').* 



From this point of view the osmotic pressure of a solution is not 

 a specific property of the solution in the same sense as the vapour- 

 pressure, or tlie density, or the concentration, but is merely the 

 mechanical pressure required under certain special conditions to 

 produce equilibrium of vapour-pressure when neither the temperature 

 nor the concentration are allowed to vary. One might with almost 

 equal propriety speak of the " osmotic temperature " of a solution, 

 meaning by that phrase the difference of temperature required to 

 make the vapour-pressure of the solution equal to that of the pure 

 solvent. The observation of the elevation of the boiling-point of a 

 solution above that of the pure solvent is a familiar instance of a 

 special case of such a temperature difference. It is just as much a 

 specific property of the solution as the osmotic pressure, and would 

 only require a perfectly non-conducting membrane for its production. 

 No one would regard the rise of boiling-point as being the 

 fundamental property of a solution in terms of which its other 

 properties should be expressed. By similar reasoning osmotic pres- 

 sure should not be regarded as existing loer se in the solution, and as 

 being the cause of the relative lowering of vapour-pressure and other 

 phenomena. This point of view does not detract in any way from 

 the reality and physical importance of the effects of osmotic pressure 

 when it comes into play, but it puts the phenomena in their true 

 light as consequences of the law of vapour-pressure. 



Regarded as a verification of the laws of vapour-pressure, direct 

 measurements of the osmotic pressure are of the highest value, but 

 there are comparatively few cases known at present in which such 

 direct measurements are possible. In other cases, the osmotic 

 pressure, if it exists, can always be calculated from a knowledge of 

 the vapour-pressure. For the elucidation of osmotic phenomena and 

 many other problems in the theory of solutions, we are compelled to 

 make a systematic study of the relations of vapour-pressure. Much 

 has been done in this direction in the past, but, owing to the 

 difficulty of the measurements, much remains yet to do. I may, 

 therefore, be pardoned if I allude briefly to some of the methods 



* Obtained by integrating U^P = vdp. Planck, Thermodynamik, also 

 Zeit. Phys. Chem., xli. 212, 1902, and xlii. 584, 1903. 



