256 
PHYSICS: I. LANGMUIR 
where 7 is the surface tension of the solution and 70 is that of water; 
a and b are constants. Szyszkowski found that b had the same value, 
namely 0.411, for all the fatty acids investigated, while the constant a 
had a different value for each substance. Over a large part of the 
range of concentrations investigated, a was negHgible compared to c so 
that the empirical equation 3 is equivalent to the relation found by 
Milner. That is, if we neglect a in (3) and differentiate, we obtain 
Since b was found to have the same value for all the fatty acids, this 
equation indicates that the same number of molecules of acid are ad- 
sorbed in the surface layer in each case. Placing 70 = 73 dynes per 
centimeter; b = 0.411, R = 83.2 X 10^ ergs, per degree and T = 29(fK 
we find ^ = 5.4 X 10 "^'^ gram mols. per square centimeter. This cor- 
responds to a value of a of 30.6 X 10"^^ sq. cm. per molecule. This 
agrees even better with our value of 24. X 10~^^ sq cm. per molecule 
for palmitic acid. 
Donnon and Barker^ have measured the amount of nonylic acid ad- 
sorbed in the surface of its water solutions and have compared the 
result with that calculated from surface tension measurements by Gibbs* 
equation. Both methods gave approximately the same results, averag- 
ing about 1.1 X 10~^ grams per square centimeter (independent of the 
concentration over a wide range). This corresponds to a value of a of 
23.7 X 10~^^ sq. cm. per molecule, practically identical with the values 
for the fatty acids given in table 1. 
We may therefore conclude that in moderately concentrated solu- 
tions of all substances which strongly depress the surface tension, the 
surface consists of a layer, one molecule deep, of the dissolved substance, 
and that there is never a transition layer in which the concentration 
varies progressively as we go further from the surface into the solution. 
The amount of solute required to form the monomolecular layer can 
be calculated from Gibbs' equation. The length and cross-sections of 
the molecules forming the surface layer may then be found. 
In the case of solutions of inorganic salts, such as NaCl, the surface 
tension is greater than that of pure water and increases linearly with 
the concentration. Milner^ pointed out, according to Gibbs' equation, 
that there is a deficiency of solute in the surface proportional to the 
dy 
dine 
Comparing this with (2), 
- 0.434 7o b. 
(4) 
0.434 7o b 
RT 
(5) 
