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L. Contributions to the Theory of Solutions. By 

 L, Vegard (Physical Institute, The University, Kristiania) *. 



§1. 



On the Change of Concentration in a Binary Solution, which is 

 in a field of force where the force is proportional to the 

 ponderable mass. 



1"N the thermodynamic treatment o£ mixtures of substances 

 dissolved in each other, it is always understood that the 

 effect of Gravity need not be considered. In other words, a 

 solution is supposed homogeneous, provided that equilibrium 

 has set in. It follows, then, that the functions become homo- 

 geneous with regard to the components of the mixture. 



If, however, the solution is submitted to the influence of a 

 force that is proportional to the ponderable mass of the in- 

 dividual components — exposed to the influence of Gravity for 

 instance — the homogeneity will be lost, since the pressure 

 varies from place to place in the fluid. Besides, it is a priori 

 probable that the proportions of mixture also change within 

 the solution;, when the latter is in equilibrium. For if there 

 were no inclination on the part of the substances to dissolve 

 in each other, Gravity would cause the components to accu- 

 mulate on the top of each other, each according to its own 

 specific density. This effect of Gravity is now counteracted 

 by the inclination towards solution ; an equilibrium must 

 ensue, in which the proportions of mixture change from place 

 to place, so that the Centre of Gravity of the whole lies lower 

 than if the system were homogeneous, but higher than if the 

 substances had not dissolved in each other. In a solution 

 exposed to the influence of Gravity, the thermodynamic 

 functions respecting the components will be homogeneous no 

 longer. In the neighbourhood of any point they can, how- 

 ever, be considered homogeneous. 



Let us suppose that we have, in the following, a binary 

 solution, that is to say, that we only have two components in 

 the fluid system. Let us further suppose that the field to 

 which the system is exposed is dependent on a potential U, 

 wmich may be given as a function of coordinates in a rect- 

 angular coordinate system. U as well as its first partial 

 derivatives are considered to be continuous in the space 

 occupied by the system. 



Let the two components have molecular masses Mi and M 2 . 



* Communicated by the Author. Placed before Kristiania Videnshabs- 

 selskab ou the 12th of October, 1906. 



