THERMODYNAMICS OF CHANGE OF STATE, ETC. 327 



conductivity of the solution, where the percentage dissociated comes out 

 to nearly the same value as that given by the depression of the freezing- 

 point. 



The theory of osmotic pressure which we have just given appears to 

 be the most satisfactory mode of treating the subject, in that it approaches 

 it through the phenomenon of vapour-pressure and the effects of change of 

 vapour-pressure, which are most easily subjected to direct measurement. 

 But historically the idea of osmotic pressure was arrived at through the 

 study of diffusion through membranes, and the difference of vapour- 

 pressure was regarded as a secondary phenomenon. We shall give a 

 brief account of the subject from this point of view, as it gives some 

 excellent examples of the application of thermodynamic reasoning. 



Semi-Permeable Membranes. It has long been known that if a 

 mixture or solution of spirit and water be separated by bladder from pure 

 water then the water passes into the solution more rapidly than the 

 spirit passes out, and will maintain an excess of pressure on the spirit 

 side. Dutrochet, who first carefully investigated this passage through 

 membranes, gave to it the name osmosis. Graham in 1854 {Phil. Trans., 

 1854, p. 177) showed that osmosis took place rapidly into alkaline solu- 

 tions ; and in 1861 he published his celebrated memoir on Dialysis (Phil. 

 Traits., 1861, p. 1183), in which he divided substances into two classes : 

 the crystalloids, which in solution will pass through membranes, and 

 which include bodies susceptible of crystallisation; and colloids, or glue-like 

 substances, such as gum, gelatine, albumen, which will not pass, or only 

 with great slowness. 



A new turn was given to the subject by Pfeffer's discovery in 1877 

 that membranes could be made through which a salt could not pass, 

 while water could pass freely. One such membrane he made by filling a 

 porous pot with a solution of potassium f errocyanide and immersing it in 

 a solution of copper-sulphate. Where the two solutions met in the pores 

 of the clay an insoluble gelatinous precipitate was formed, supported by 

 the clay and constituting the membrane. This membrane will allow 

 water to pass through it easily, but is impermeable to sugar. It is there- 

 fore termed a semi-permeable membrane. 



i Pfeffer working with sugar solution inside a semi-permeable mem- 

 brane and water without, found that the water passed in more rapidly 

 than it passed out, until a certain definite excess of pressure existed 

 within the vessel over that without. This excess of pressure, the osmotic 

 pressure we shall see later that it is identical with osmotic pressure as 

 defined above is found to be proportional to the amount of sugar in 

 solution and to rise with the temperature. Thus the osmotic pressure 

 was 53'1 cm. of mercury for 1 per cent, of sugar dissolved at 14'2 C., and 

 it rose from 50 '5 cm. at 6'8C. to 54 '8 cm. at 22. Pfeffer also worked with 

 some other solutions. In 1884 De Vries (Pringsheim's Jahrbucher, xiv. 

 p. 427, 1884) found that when certain vegetable cells, those of the epi- 

 dermis on the under side of the midrib of the leaves of Tradescantia 

 discolor being the best, are placed in concentrated salt solutions the 

 protoplasmic contents contract and shrink away from the cell walls, the 

 protoplasm being apparently covered with a semi-permeable membrane, 

 which allows the water to pass more freely from the dilute solution in the 

 protoplnsm than in the opposite direction. If the external solution is 



