380 SCIENCE PROGRESS. 



somewhat surprising result is opposed to the assumptions 

 made by Bredig (1890) and by Noyes (1890) in their theo- 

 retical treatment of strong solutions, and is arrived at in the 

 following way. Consider a molecule of dissolved substance 

 in a plane surface separating solvent from solution — such a 

 molecule as would be exerting osmotic pressure on a 

 semipermeable membrane separating the two. Of the 

 molecules attracting the molecule under consideration the 

 solvent molecules in the solution and those in the pure 

 solvent will pull it in opposite directions. Symmetrically 

 situated with respect to the plane there will be a molecule 

 in the pure solvent corresponding with every solvent mole- 

 cule in the solution, and the attractive effects of these two 

 sets of solvent molecules on the molecule in question will 

 balance each other. Consequently, the only solvent mole- 

 cules which affect the molecule in question are those in the 

 pure solvent which, as regards the plane, are placed sym- 

 metrically to those of the dissolved substance. The num- 

 ber of operative solvent molecules is proportional, therefore, 

 to the concentration of the dissolved substance, and, since the 

 total number of dissolved molecules in the plane at any in- 

 stant is also proportional to the concentration, the total 

 attractive effect between solvent and dissolved molecules is 

 proportional to the square of the concentration. It follows, 

 therefore, that setting aside polymerisation of dissolved 

 molecules, the osmotic pressure P of a solution of volume 

 V at the absolute temperature T is given by an equation 

 of the same form as that of van der Waals— 



P + » t ) ( V - i5 ) = R'T. 



Here, however, «, the attraction-constant, is a measure of 

 the difference between the attractions of the dissolved mole- 

 cules for one another and the attraction of solvent mole- 

 cules for dissolved molecules ; and /3 is a volume-correction 

 depending on the actual volume occupied by the molecules 

 of the solvent and the dissolved substance, since both of 

 these will diminish the space in which the dissolved mole- 

 cules can oscillate. 



