464 



SCIENCE. 



[N. S. Vol. IV. No. 92. 



bombardment of its surface by particles of 

 discontinuous matter. The particles of the 

 liquid find ample opportunity, therefore, to 

 rise between the particles of the gas. 



Let us take a second case, which has, 

 however, as far as I am aware, never been 

 realized. Suppose a vessel having a wall 

 impervious to the molecules of one gas 

 but previous to those of a second. If 

 such a vessel containing the first gas is 

 placed in an atmosphere of the second the 

 molecules of the latter will pass the walls 

 and enter the space occupied by the first, 

 exactly as the molecules of the volatile 

 liquid rise among the molecules of the gas 

 above, and equilibrium will be established 

 only when the pressure exerted by the sec- 

 ond gas is equal within and without. The 

 pressure within the vessel will then exceed 

 that on the outside by exactly the pres- 

 sure exerted by the gas whose molecules 

 cannot pass the wall. 



The case with osmotic pressure is very 

 similar to that last mentioned. Here we 

 have a semi-permeable wall actually real- 

 ized. For instance, we may have a wall 

 which will allow water to pass freely but 

 which is impervious to the molecules of 

 sugar. If pure water be on one side of such 

 a wall, and a solution of sugar on the other, 

 equilibrium can exist only when the pres- 

 sure due to the water alone is equal on both 

 sides ; for the molecules of sugar, because 

 of their discontinuous character, can exert 

 no influence to cause the molecules of water 

 to pass one way or the other, exactly as a 

 gas can exert no permanent eflect to pre- 

 vent the vapor of a liquid from passing up- 

 ward into it. In the end, therefore, the 

 pressure on the side of the solution must 

 exceed that on the side of the pure solvent 

 by the amount of pressure due to the kinetic 

 energy of the molecules of the dissolved 

 substance. If we further suppose that this 

 energy is the same in the liquid as in the 

 gaseous state, and the laws of osmotic pres- 



sure give us every reason to believe that it 

 is, the explanation is complete. 



This explanation gives us a conception of 

 liquids as very closely related to gases in 

 many of their properties, the main differ- 

 ence being that in the liquid the molecule 

 does not possess enough kinetic energy to 

 separate it from the mass of neighboring 

 molecules, although its motion within the 

 confined space is very similar to that of the 

 molecule of a gas. 



But it is not only, nor indeed mainly, in 

 his study of the phenomena of osmose that 

 van't Hoff has rendered the greatest service. 

 Very few perfect semi-permeable walls are 

 known, and osmotic pressures are very 

 difficult to measure directly, so that, if we 

 were dependent on direct measurements, 

 the theory would be of scarcely more than 

 theoretical interest. Yan't Hofi" pointed 

 out, however, that the concentration of a 

 solution by the removal of the solvent, 

 whether efiected by a piston composed of a 

 semi-permeable wall, by the evaporation of 

 the solvent, or by the separation of crystals 

 of the pure solvent by freezing, is in each 

 case a reversible process analogous to the 

 compression of a gas, and that, as with all 

 other reversible processes, it is subject to 

 the second law of thermo-dynamics. This 

 made it possible to connect the lowering of 

 the vapor pressure and the depression of 

 the freezing point of solutions directly with 

 their osmotic pressure. This has given an 

 indirect determination of the osmotic pres- 

 sure in thousands of different cases. As a 

 practical result we have now at our disposal 

 a large number of methods for the deter- 

 mination of the molecular weights of solid 

 and liquid bodies. 



The work of Eaoult® in this field deserves 

 especial mention, because he developed 

 several methods of determining molecular 

 weights from an empirical standpoint, be- 

 fore the theoretical development of the sub- 

 ject had been given by van't Hoff". Ea- 



