34 Mr. S. A. Shorter : Application of the Theory 



It is interesting to note the connexion between such methods 

 of: proof and the more general method of Gibbs. In the 

 case of a system containing only one component, Gibbs's 

 general theorem gives a single equation which is the ordinary 

 equation of hydrostatic equilibrium. By the above device 

 we are able to deduce immediately the Gibbs equation for 

 the solvent in the solution by means of the coexisting column 

 of solvent vapour. The remaining Gibbs equation is de- 

 ducible in the manner stated above. We could have obtained 

 the same result by supposing the solution to be separated 

 from the pure liquid solvent by a membrane permeable to 

 the solvent only*. 



In order to obtain formulae for the practical calculation of 

 the concentration gradient we must express the quantity 

 So(s, p, 0) in terms of quantities which may be measured 

 experimentally. This may be done in three ways — in terms 

 of experimental data relating to CI) equilibrium between the 

 solution and solvent vapour, (2) osmotic equilibrium between 

 the solution and the liquid solvent, (3) equilibrium between 

 the solution and the solid solvent. The three expressions 

 thus obtained are of considerable importance in the general 

 theory of solutions. In the next section we will merely 

 obtain these expressions without actually performing the 

 substitution in equation (6). The expressions for the con- 

 centration gradient are hardly of such importance as to 

 justify writing them out in full. 



Expressions for the Practical Calculation of the 

 Concentration Derivative of the Solvent Potential. 



In Part II. of the present work three expressions were 

 deduced for the solvent potential lowering. Since 



S (s, p, 6) = — ^- A (s, p, 6), 



the three expressions for the concentration derivative of the 

 solvent potential may be obtained from the corresponding 

 expressions for the solvent potential lowering by differentiation 

 with respect to the concentration f. 



* This method is open to the objection that if the pressure in the 

 solution is low, equilibrium may not be possible unless the pure solvent 

 is capable of existing in a state of tension. 



t It will be noticed that none of the three expressions for the solvent 

 potential lowering is of the most general nature possible. Equations (15) 

 and (16) of Part II. give the value of A corresponding to the temperature 

 at which the experimental measurements are made, and any pressure, 

 while equation (17) gives the value corresponding to the experimental 

 pressure and any temperature. Expressions for the value of A at any 

 temperature and any pressure are easily obtained bv means of equations 

 <12) and (14) of Part II. 



