EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 275 



Impermeable Films. 



We have so far supposed, in treating of surfaces of discontinuity, 

 that they afford no obstacle to the passage of any of the component 

 substances from either of the homogeneous masses to the other. The 

 case, however, must be considered, in which there is a film of matter 

 at the surface of discontinuity which is impermeable to some or all of 

 the components of the contiguous masses. Such may be the case, 

 for example, when a film of oil is spread on a surface of water, even 

 when the film is too thin to exhibit the properties of the oil in mass. 

 In such cases, if there is communication between the contiguous 

 masses through other parts of the system to which they belong, such 

 that the components in question can pass freely from one mass to the 

 other, the impossibility of a direct passage through the film may be 

 regarded as an immaterial circumstance, so far as states of equilibrium 

 are concerned, and our formulas will require no change. But when 

 there is no such indirect communication, the potential for any 

 component for which the film is impermeable may have entirely 

 different values on opposite sides of the film, and the case evidently 

 requires a modification of our usual method. 



A single consideration will suggest the proper treatment of such 

 cases. If a certain component which is found on both sides of a film 

 cannot pass from either side to the other, the fact that the part of the 

 component which is on one side is the same kind of matter with the 

 part on the other side may be disregarded. All the general relations 

 must hold true, which would hold if they were really different 

 substances. We may therefore write fa for the potential of the 

 component on one side of the film, and /z 2 for the potential of the 

 same substance (to be treated as if it were a different substance) on 

 the other side; m\ for the excess of the quantity of the substance 

 on the first side of the film above the quantity which would be on 

 that side of the dividing surface (whether this is determined by the 

 surface of tension or otherwise) if the density of the substance were 

 the same near the dividing surface as at a distance, and mf for a 

 similar quantity relating to the other side of the film and dividing 



water, are made by the method of drops, the weight of the drops of different liquids 

 (from the same pipette) being regarded as proportional to their superficial tensions. 



M. Athanase Dupr4 has determined the superficial tensions of solutions of soap by 

 different methods. A statical method gives for one part of common soap in 5000 of 

 water a superficial tension about one-half as great as for pure water, but if the tension 

 be measured on a jet close to the orifice, the value (for the same solution) is sensibly 

 identical with that of pure water. He explains these different values of the superficial 

 tension of the same solution as well as the great effect on the superficial tension 

 which a very small quantity of soap or other trifling impurity may produce, by the 

 tendency of the soap or other substance to form a film on the surface of the liquid. 

 (See Annales de Chimie et de Physique, ser. 4, vol. vii, p. 409, and vol. ix, p. 379.) 



