490 Professor H. L. CalUndar [Feb. 26, 



consequence of the laws of vapour-pressure, there is one difficulty 

 which, though seldom expressed, has undoubtedly served very greatly 

 to retard progress. How can an insignificant difference of vapour- 

 pressure, which may not amount to so much as one-thousandth part 

 of an atmosphere in the case of a strong sugar solution at 0° C, be 

 regarded as the cause of an osmotic pressure exceeding 100 atmo- 

 spheres, or 100,000 times as great as itself ? The answer is that the 

 equilibrium does not depend at all on the absolute magnitude of the 

 vapour-pressure, but only on the work done for a given ratio of 

 expansion, which is the same in the limit for a gramme-molecule of 

 any vapour at the same temperature, however small the vapour- 

 pressure. Indirectly the smallness of the vapour-pressure may have 

 a great effect in retarding the attainment of equilibrium, especially if 

 obstructive influences, such as other vapours or liquids, are present. 

 Thus mercury at ordinary temperatures in the open air is regarded as 

 practically non-volatile. Its vapour-pressure is less than a millionth 

 of an atmosphere, and cannot be directly measured, though it may 

 easily be calculated. When, however, we take mercury in a perfect 

 vacuum, such as that of a Dewar vessel, the presence of the vapour 

 is readily manifested by its rapid condensation on the application of 

 liquid air in the form of a fine metallic mirror of frozen mercury. 

 The least trace of air or other gas in the vacuum will retard the 

 condensation excessively. 



Under the conditions of an osmotic-pressure experiment we have 

 solvent and solution in practical contact, separated only by a thin 

 porous membrane. It will facilitate our conception of the conditions 

 of equilibrium if we imagine the membrane to be a continuous 

 partition pierced by a large number of very fine holes, of the order 

 of a millionth of an inch in diameter. If the holes are not wetted by 

 the solution or the water, the liquid cannot get through unless the 

 pressure on it exceeds 100 atmospheres, but the vapour has free 

 passage. If the solvent and solution are under the same hydro- 

 static pressure, the vapour-pressure of the solvent will be the greater, 

 and the vapour will pass over into the solution. Since the surfaces 

 are practically in contact, no appreciable difference of temperature 

 can be maintained. If the solution is confined in a rigid envelope, 

 so that its volume cannot increase, the capillary sm'faces of the 

 solution will rapidly bulge out as the vapour condenses on them, 

 and the pressure on the solution will increase until condensation 

 finally ceases, when the vapour-pressure of the solution is raised to 

 equality with that of the pure solvent. The osmotic pressure is 

 simply the mechanical pressure -difference which must be applied to 

 the solution in order to increase its vapour-pressure to equality with 

 that of the pure solvent. If any pressure in excess of this value is 

 applied to the solution, the vapour will pass in the opposite direction, 

 and solvent will be forced out of solution. The osmotic work re- 

 quired to force a gramme-molecule of the solvent out of the solu- 



