482 J. ^V. Gihhs — Equilihriuni of Iteterogeneous Substances. 



masses of liquid. Tlie latter may be foi-med by gently depositing a 

 liquid drop upon the surface of a mass of the same or a different 

 liquid. This may be done (with suitable liquids) so that the con- 

 tiimity of the air separating the liquid di-op and mass is not broken, 

 but a film of air is formed, which, if the liquids are similar, is a 

 counterpart of the liquid film which is formed by a bubble of air ris- 

 ing to the top of a mass of the liquid. (If the bubble has the same 

 volume as the drop, the films will have precisely the same form, as 

 well as the rest of the surfaces which bound the bubble and the 

 drop.) Sometimes, when the weight and momentum of the drop 

 carry it through the surface of the mass on which it falls, it appears 

 surrounded by a com])lete spherical film of air, which is the counter- 

 part on a small scale of a soap-bubble hovering in air.* Since, how- 

 ever, the substance to which the necessary differences of tension in 

 the film are mainly due is a component of the liquid masses on each 

 side of the air film, the necessary differences of the potential of this 

 sixbstance cannot be permanently maintained, and these films have 

 little persistence compared with films of soap-water in air. In this 

 respect, the case of these air-films is analogous to that of liquid films 

 in an atmosphere containing substances by which their tension is 

 greatly reduced. Compare page 479. 



Surfaces of Discontinuity bettceen Solids a'lid Fluids. 



We have hitherto treated of surfaces of discontinuity on the sup- 

 position that the contiguous masses are fluid. This is by far the 

 most simple case for any rigorous treatment, since the masses are 

 necessarily isotropic both in nature and in their state of strain. In 

 this case, moreover, the mobility of the masses allows a satisfiictory 

 experimental verification of the mechanical conditions of equilibrium. 

 On the other hand, the rigidity of solids is in general so great, that 

 any tendency of the surfaces of discontinuity to vaiiation in area or 

 form may be neglected in comparison with the forces which are pro- 

 duced in the interior of the solids by any sensible strains, so that it 

 is not generally necessary to take account of the surfaces of discon- 

 tinuity in determining the state of strain of solid masses. But we 

 must take account of the nature of the surfaces of discontinuity 



* These spherical air-fihns are easily formed in soajj-water. They are distinguish- 

 able from ordinary air-bubbles by their general behavior and by their appearance. 

 The two concentric spherical surfaces are distinctly seen, the diameter of one appear- 

 ing to lie about three-quarters as large as that of the other. This is of course an 

 optical illusion, dejiendiug upon the index of refraction of the liquid. 



