4^6 Professor H. L. CaUendar [Feb. 2G, 



pressure developed in the state of equilibrium was found to be 

 proportional to the strength of the solution, and to increase with rise 

 of temperature at the same rate as the pressure of a gas at constant 

 volume. A few years later van 't Holf, reviewing these experiments 

 in the light of thermodynamics, showed that the osmotic pressure of 

 a dilute solution should be the same as the pressure exerted by a 

 number of molecules of gas equal to those of the dissolved substance 

 in a space equal to the volume of the solution, that it should be the 

 same for all solutions of equal molecular strength, and that osmotic 

 pressure followed the well-known laws of gas-pressure in a?l respects. 

 The most important generahsation was hailed as the first step to a 

 complete kinetic theory of solution, and the osmotic pressure itself 

 has generally been regarded as due to the bombardment of the sides 

 of the semipermeable membrane by the particles of solute, as though 

 they were able to move freely through the solution with velocities 

 comparable to those of the molecules of a gas. Such a view would 

 not now be seriously maintained. Imt the fascinating simplicity of the 

 gas-pressure analogy has frequently led to the attempt to express 

 everything in terms of the osmotic pressure, regarded simply, but 

 inaccurately, as obeying the gaseous laws, and has done much to 

 divert attention from other aspects of the phenomena, which, in reality, 

 are more important and have the advantage of being more easily 

 studied. It was very soon discovered that the gaseous laws for 

 osmotic pressure must be restricted to very dilute solutions, and that 

 the form of the laws was merely a consequence of the state of extreme 

 dilution, and did not necessarily involve any physical identity between 

 osmotic pressure and gas-pressure. Many different lines of argument 

 might be cited to illustrate this point, but it will be sufficient to take 

 some of the more recent experimental measurements of osmotic 

 pressure by the direct method of the semipermeal)le membrane. 



Morse and Frazer in 1905 succeeded in preparing ferrocyanide 

 membranes impermeable to sugar, and capable of withstanding 

 pressures of more than 20 atmospheres. They operated by Pfeffer's 

 original method, allowing water to diffuse into the solution in a 

 porous pot until the maximum pressure was developed. There are 

 many serious experimental and manipulative difficulties which the 

 authors carefully considered and discussed in applying this method, 

 but they succeeded in obtaining very consistent results. As a first 

 deduction from their investigations they considered that they had 

 established the relation that the osmotic pressure of cane-sugar was 

 the same as that exerted by the same number of molecules of gas at 

 the same temperature in the volume occupied by the solvent, and not 

 in the volume occupied by the solution. In other words, the osmotic 

 pressure of a strong solution was greater than that given by van 't 

 Hoff's formula for a dilute solution in proportion as the volume of 

 the whole solution exceeded the volume of the solvent contained in 

 it. It was a very natural extension of the gas-pressure analogy to 



