98 Walter Stiles 
between surface tension and concentration of a solution algebraic¬ 
ally. 
In the case of a solution of ethyl alcohol in water the surface 
tension will obviously be reduced if the concentration of alcohol in 
the surface is raised. According to the principle first enunciated by 
Gibbs (1878, 1906) and emphasized by J. J. Thomson (1888), there 
will thus be a tendency for the alcohol molecules to migrate to the 
surface, so that the concentration in the surface layer is greater than 
Concentration of alcohol in per cent. 
Fig. 2. Curves showing the relation between surface tension against air and 
composition of solutions of methyl ( M ), ethyl ( E), and isopropyl ( P) 
alcohols in water. 
in the rest of the liquid. Opposing this tendency is that of the 
dissolved substance to diffuse from a place of higher to one of lower 
concentration. An equilibrium condition will thus be reached where 
these two opposed tendencies balance one another. It has been 
shown by Gibbs that when equilibrium is attained 
p C da 
1 = -RT'dC 
where C is the concentration of the solute in the bulk of the solvent, 
F the excess of solute in the surface, the rate of change of surface 
tension with concentration of the solute, T the absolute temperature, 
and R the gas constant. 
