474 J. W. Gibhs — Eqidlihriuni of Seterogeneoxis Substances. 



surface of tension of the film will evidently divide the distance 

 betvv^een the surfaces of tension for the two surfaces of the film taken 

 separately, in the inverse ratio of their tensions. For practical pur- 

 poses, we may regard T simply as the mass of the film per unit of 

 area. It will be observed that the terms containing /'in (613) and 

 (614) are not to be neglected in our present application of these 

 equations. 



But the mechanical conditions of equilibrium for the film regarded 

 as an approximately homogeneous mass in the form of a thin sheet 

 bounded by two surfaces of discontinuity are not necessarily satisfied 

 when the film is in a state of apparent rest. In fact, these conditions 

 cannot be satisfied (in any place where the force of gravity has an 

 appreciable intensity) unless the film is horizontal. For the pressure 

 in the interior of the film cannot satisfy simultaneously condition 

 (612), which requires it to vary rapidly with the height z, and condi- 

 tion (613) applied separately to the different surfaces, which makes it 

 a certain mean between the pressui'es in the adjacent gas-masses. 

 Nor can these conditions be deduced from the general condition 

 of mechanical equilibrium (606) or (611), without supposing that the 

 interior of the film is free to move independently of the surfaces, 

 which is contrary to what we have supposed. 



Moreover, the potentials of the various components of the film will 

 not in general satisfy conditions (617), and cannot (when the tem- 

 perature is uniform) unless the film is hoi'izontal. For if these condi- 

 tions were satisfied, equation (612) would follow as a consequence. 

 (See page 449.) 



We may here remark that such a film as we are considering cannot 

 form any exception to the principle indicated on page 450, — that 

 when a surface of discontinuity which satisfies the conditions of 

 mechanical equilibrium has only one component which is not found 

 in the contigiious masses, and these masses satisfy all the conditions 

 of equilibrium, the potential for the component mentioned must satisfy 

 the law expressed in (617), as a consequence of the condition of 

 mechanical equilibrium (614). Therefore, as we have just seen that 

 it is impossible that all the potentials in a liquid film which is not hori- 

 zontal should conform to (617) when the temperature is uniform, it 

 follows that if a liquid film exhibits any persistence which is not due 

 to viscosity, or to a horizontal position, or to differences of tempera- 

 ture, it must have more than one component of which the potential 

 is not determined by the contiguous gas-masses in accordance with 

 (617). 



