the Osmotic Theory of Solutions. 603 



the specific volumes of the pure solvent and the pure solute 

 respectively, when in osmotic equilibrium with the solution 

 at hydrostatic pressure p. If the pressure p is not great 

 (one atmosphere for example), and if, at the same time, the 

 concentration of (say) the solute is high, the correspon ding- 

 pressure on the solvent will have a high negative value, that 

 is to say there will be a considerable tension on the solvent ; 

 in many cases this tension will exceed the tension which the 

 solvent can support and will certainly not be experimentally 

 realizable. Moreover, when the solute is a solid substance, 

 our conception of osmotically equilibrating columns cannot 

 be realized for the pure solute. 



We can, however, put our differential equations in such a 

 form that they involve only the properties of the solution, 

 with their differential coefficients, at the point under con- 

 sideration ; it is evident, a priori, that all criteria of the 

 behaviour of the solution must be expressible in such 

 terms. 



The relations desired will first of all be deduced from (8), 

 (10), (11), and (12), by means of a simple transformation ; 

 a more general investigation will then be given, starting 

 from first principles, and without restriction to the case 

 where equilibrium is supposed to have been attained. 

 (See pp. 609-613.) 



In the first place we must adopt another mode of 

 differentiating the osmotic pressure with respect to concen- 

 tration. Instead of supposing solutions of concentrations e 2 , 

 and c 2 -\-dc 2 , and both at pressure^, to be separately put in 

 equilibrium with the pure solvent with resulting osmotic 

 pressures ~P 1 and P 2 -f d¥ x ; let us put the same two solutions 

 in direct osmotic communication with one another through a 

 membrane, permeable to the solvent only. The two solutions 

 will be in equilibrium when the pressures on them differ 

 by dp, where dp = a r F l and dY l is the (infinitesimal) osmotic 

 pressure of the solution c 2 + dc 2 Yelatively to solution c 2 . On 

 dividing this dPi by dc 2 we obtain a differential coefficient 



which we shall write ~ l . 

 tic. 



This coefficient refers to two infinitesimally different 

 solutions belonging to that (singly infinite) series, any 

 member of which is in osmotic equilibrium with the solution 

 of concentration c 2 and pressure p. 



Now, since the solution c 2 and the solution c 2 -\-dc 2 are in 

 direct osmotic equilibrium with one another, they will be 

 separately in equilibrium with the pure solvent at some one 



