440 tT. W. Gibbs — Equilibrium of Heterogeneous Substances. 



film. Each of these quantities is exceedingly small. The surface- 

 density when positive is of the same order of magnitude as the thick- 

 ness of the non-homogeneous film, but is not necessarily small com- 

 pared with other surface-densities because the volume-densities of 

 the same substance in the adjacent masses are small. Now the 

 potential of a substance which forms a very small part of a homo- 

 geneous mass certainly increases, and jjrobably very rapidly, as the 

 proportion of that component is increased. [See (171) and (217).] 

 The pressure, temperature, and the other potentials, will not be 

 sensibly affected. [See (98).] But the effect on the tension of this 

 increase of the potential will be proportional to the surface-density, 

 and will be to diminish the tension when the surface-density is 

 positive. [See (508).] It is therefore quite possible that a very 

 small trace of a substance in the homogeneous masses should greatly 

 diminish the tension, but not possible that such a trace should greatly 

 increase it.* 



Impermeable Eibns. 



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

 that they afford no obstacle to the passage of any of the comi)onent 

 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 



* From the experiments of M. E. Duclaux, (Annales de Chimie et de Physique, Ser. 4, 

 vol. xxi, p. 383,) it appears that one per cent, of alcohol in water will diminish the 

 superficial tension to .933, the value for pure water being- unity. The experiments do 

 not extend to pure alcohol, but the difEerence of the tensions for mixtures of alcohol 

 and water containing 1 and 20 per cent, water is comparatively small, the tensions 

 being .322 and .33G respectively. 



According to the same authority (page 427 of the volume cited), one 3200th part of 

 Castile soap will reduce the superficial tension of water by one-fourth ; one 800th part 

 of soap by one-half. These determinations, as well as those relating to alcohol and 

 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 Dupre 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 super- 

 ficial 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 Physiqw, Ser. 4, vol. vii, p. 409, and vol. ix, p. 379.) 



