212 J. A. POLLOCK. 



For dilute solutions it is known that the value of the 

 foregoing expression for the surface energy becomes smaller 

 if the surface tension diminishes, so that for these solutions 

 it may be said that, provided the surface area is constant, 

 the surface energy decreases with any change which lowers 

 the value of the surface tension. In accordance with a 

 well known mechanical principle, such a change, if possible, 

 will spontaneously occur until the rate of variation of the 

 total energy of the liquid, with reference to the variable 

 involved, becomes zero. 



This application of the equilibrium principle of minimum 

 energy to dilute solutions discloses an important fact to 

 which attention was first directed by Willard Gibbs in the 

 essay already mentioned. For if the surface tension of a 

 dilute solution diminishes with increasing concentration, 

 the greater the concentration in the surface stratum the 

 less the surface energy; therefore, associated with the 

 creation of any new surface in such a solution, there will 

 be a movement of the molecules of the solute from the 

 mass of the liquid into the newly formed surface layer. 

 Such a movement, however, increases the chemical energy 

 in the surface stratum, and, under isothermal conditions, 

 equilibrium will be attained when the rate of decrease of 

 the surface excess of mechanical potential energy, with 

 respect to the increased amount of the solute in the surface 

 layer, is equal to the rate of increase of the surface excess 

 of chemical energy with reference to the same variable. 



If r is the surface excess of solute, per unit area of sur- 

 face, that is the amount of solute brought into the surface 

 stratum, per unit area, to establish equilibrium, o- the sur- 

 face excess of mechanical potential energy, per unit area 

 of surface, and p the chemical potential of the solute, then 

 the condition for equilibrium, under isothermal circum- 

 stances, is in symbols, 



