258 EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 



sign, is always equal to two-thirds of the first, as appears from 

 equation (550) and the geometrical relation v' = Jm We may there- 

 fore write 



/>' (560) 



On the Possible Formation at the Surface where two different 

 Homogeneous Fluids meet of a Fluid of different Phase 

 from either. 



Let A, B, and C be three different fluid phases of matter, which 

 satisfy all the conditions necessary for equilibrium when they meet 

 at plane surfaces. The components of A and B may be the same or 

 different, but C must have no components except such as belong to 

 A or B. Let us suppose masses of the phases A and B to be separated 

 by a very thin sheet of the phase C. This sheet will not necessarily 

 be plane, but the sum of its principal curvatures must be zero. We 

 may treat such a system as consisting simply of masses of the phases 

 A and B with a certain surface of discontinuity, for in our previous 

 discussion there has been nothing to limit the thickness or the nature 

 of the film separating homogeneous masses, except that its thickness 

 has generally been supposed to be small in comparison with its radii 

 of curvature. The value of the superficial tension for such a film 

 will be CTAC + CTBCJ if we denote by these symbols the tensions of the 

 surfaces of contact of the phases A and C, and B and C, respectively. 

 This not only appears from evident mechanical considerations, but 

 may also be easily verified by equations (502) and (93), the first of 

 which may be regarded as defining the quantity or. This value will 

 not be affected by diminishing the thickness of the film, until the 

 limit is reached at which the interior of the film ceases to have the 

 properties of matter in mass. Now if c7 A o + o"BO i g greater than <T A B 

 the tension of the ordinary surface between A and B, such a film will 

 be at least practically unstable. (See page 240.) We cannot suppose 

 that (TAB > 0"Ac+<*"Bc> ^ or tins would make the ordinary surface between 

 A and B unstable and difficult to realize. If cr A B = 0"Ac + 0"Bc> we ma y 

 assume, in general, that this relation is not accidental, and that the 

 ordinary surface of contact for A and B is of the kind which we have 

 described. 



Let us now suppose the phases A and B to vary, so as still to 

 satisfy the conditions of equilibrium at plane contact, but so that the 

 pressure of the phase C determined by the temperature and potentials 



this work, the amount (p r p")v' will be expended in pressing the envelop inward, and 

 the rest in opening and closing the orifice. Both the opening and the closing will be 

 resisted by the capillary tension. If the orifice is circular, it must have, when widest 

 open, the radius determined by equation (550). 



