306 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



cases in which the film exhibits a decided viscosity. That is, the 

 relation/* (618), (614), (615) will hold true, when by or we understand 

 the tension of the film regarded as a simple surface of discontinuity 

 (this is equivalent to the sum of the tensions of the two surfaces of 

 the film), and by I 1 its mass per unit of area diminished by the mass 

 of gas which would occupy the same space if the film should be 

 suppressed and the gases should meet at its surface of tension. This 

 Hwfitce of tension of the film will evidently divide the distance 

 between the surfaces of tension for the two surfaces of the film 

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

 purposes, we may regard F simply as the mass of the film per unit of 

 area. It will be observed that the terms containing F 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 

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

 Unmded 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 0, and 

 condition (613) applied separately to the different surfaces, which 

 makes it a certain mean between the pressures 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 

 temperature is uniform) unless the film is horizontal. For if these 

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

 (See page 283.) 



We may here remark that such a film as we are considering cam 

 form any exception to the principle indicated on page 284, thai 

 when a surface of discontinuity which satisfies the conditions 

 mechanical equilibrium has only one component which is not foun< 

 in the contiguous masses, and these masses satisfy all the conditioi 

 of equilibrium, the potential for the component mentioned must satisfy 

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

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

 it is impossible that all the potentials in a liquid film which is n< 

 horizontal should conform to (617) when the temperature is unifoi 

 it follows that if a liquid film exhibits any persistence which 



