EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 311 



existing in excess at the surface), is volatile, the effect of evaporation 

 and condensation may be considerable, even when the mean value of 

 the potential for that component is the same in the film as in the sur- 

 rounding atmosphere. To illustrate this, let us take the simple case 

 of two components 8 l and S 2 , as before. (See page 301.) It appears 

 from equation (508) that the potentials must vary in the film with 

 the height z, since the tension does, and from (98) that these varia- 

 tions must (very nearly) satisfy the relation 



* (658) 



/! and y 2 denoting the densities of 8^ and S 2 in the interior of the 

 film. The variation of the potential of S 2 as we pass from one level 

 to another is therefore as much more rapid than that of 8 lt as its 

 density in the interior of the film is less. If then the resistances 

 restraining the evaporation, transmission through the atmosphere, 

 and condensation of the two substances are the same, these processes 

 will go on much more rapidly with respect to S 2 . It will be observed 



that the values of ~- 1 and - will have opposite signs, the tendency 



of S 1 being to pass down through the atmosphere, and that of S 2 to 

 pass up. Moreover, it may easily be shown that the evaporation or 

 condensation of $ 2 will produce a very much greater effect than the 

 evaporation or condensation of the same quantity of 8 r These effects 

 are really of the same kind. For if condensation of $ 2 takes place at 

 the top of the film, it will cause a diminution of tension, and thus 

 occasion an extension of this part of the film, by which its thickness 

 will be reduced, as it would be by evaporation of 8 r We may infer 

 that it is a general condition of the persistence of liquid films, that the 

 substance which causes the diminution of tension in the lower parts of 

 the film must not be volatile. 



But apart from any action of the atmosphere, we have seen that a 

 film which is truly fluid in its interior is in general subject to a con- 

 tinual diminution of thickness by the internal currents due to gravity 

 and the suction at its edge. Sooner or later, the interior will some- 

 where cease to have the properties of matter in mass. The film will 

 then probably become unstable with respect to a flux of the interior 

 (see page 305), the thinnest parts tending to become still more thin 

 (apart from any external cause) very much as if there were an attrac- 

 tion between the surfaces of the film, insensible at greater distances, 

 but becoming sensible when the thickness of the film is sufficiently 

 reduced. We should expect this to determine the rupture of the film, 

 and such is doubtless the case with most liquids. In a film of soap- 

 water, however, the rupture does not take place, and the processes 



