274 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



present without our knowledge or desire, in the fluids which meet at 

 the surface investigated. 



When the establishment of equilibrium is rapid, the variation of 

 the tension from its normal value will be manifested especially during 

 the extension or contraction of the surface, the phenomenon resembling 

 that of viscosity, except that the variations of tension arising from 

 variations in the densities at and about the surface will be the same 

 in all directions, while the variations of tension due to any property 

 of the surface really analogous to viscosity would be greatest in 

 the direction of the most rapid extension. 



We may here notice the different action of traces in the homogeneous 

 masses of those substances which increase the tension and of those 

 which diminish it. When the volume-densities of a component are 

 very small, its surface-density may have a considerable positive value, 

 but can only have a very minute negative one.* For the value 

 when negative cannot exceed (numerically) the product of the 

 greater volume-density by the thickness of the non-homogeneous 

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

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

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

 compared 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 

 homogeneous mass certainly increases, and probably 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.t 



*It is here supposed that we have chosen for components such substances as are 

 incapable of resolution into other components which are independently variable in the 

 homogeneous masses. In a mixture of alcohol and water, for example, the components 

 must be pure alcohol and pure water. 



fFrom 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 difference of the tensions for mixtures of alcohol 

 and water containing 10 and 20 per cent, water is comparatively small, the tensions 

 being -322 and '336 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 



