504 Mr. W. C. M. Lewis : Experimental Examination 
Now applying the gas law P = RTc, finally we obtain 
r - J- d(T 
1 2jl ~ RT dc 
This equation is of fundamental importance in that, if we 
assume its applicability to adsorption measurements, it con- 
tains the relationships between bulk-concentration, surface- 
tension, and quantity adsorbed in an experimentally 
determinable form. 
The same expression may be obtained more simply as 
follows : — * 
Consider the equilibrium at a surface (say of solid or 
liquid) in contact with a solution. 
Let a = surface-energy per unit of surface. 
s = area of surface exposed to the solution. 
m s = the mass of solute adsorbed at the surface of the 
solid in excess of that normally present. 
The temperature is supposed to be constant. 
U = total energy of the heterogeneous film per unit 
of surface. 
U can be increased : — 
(1) by increasing the surface area, in which case the work 
required = ads ; 
(2) by increasing the concentration of the solute in the 
interfacial layer. This is proportional to dm s namely 
[xdm% where /uu is the chemical potential of the solute. 
Then ^U = ads -f /judm s , 
d(TJ — fi-m 8 ') = ads — m s dfi. 
And since d(U — /u.m s ) is a complete differential, we have 
(da \ /dm s \ 
d/A/ s ~\ ds yy 
but-^— = mass adsorbed per unit area of surface, i. e. = V ; 
• r = - — . 
dfju 
dc 
Now since da = RT — , 
c 
where c =* the concentration of the solute in the 
bulk of the solution, 
*.I am indebted to Prof. W. B. Morton for this deduction. 
