370 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



within the films as well as without are the same, and the surfaces of 

 the films are also the same, there will be no difference of tension. 

 Nor will the tension of the same film be altered, if a part of the 

 interior drains away in the course of time, without affecting the 

 surfaces. If the thickness of the film is reduced by evaporation, its 

 tension may be either increased or diminished, according to the 

 relative volatility of its different components. 



Let us now suppose that the thickness of the film is reduced until 

 the limit is reached at which the interior ceases to have the properties 

 of matter in mass. The elasticity of the film, which determines its 

 stability with respect to extension and contraction, does not vanish 

 at this limit. But a certain kind of instability will generally arise, in 

 virtue of which inequalities in the thickness of the film will tend to 

 increase through currents in the interior of the film. This probably 

 leads to the destruction of the film, in the case of most liquids. In 

 a film of soap-water, the kind of instability described seems to be 

 manifested in the breaking out of the black spots. But the sudden 

 diminution in thickness which takes place in parts of the film is 

 arrested by some unknown cause, possibly by viscous or gelatinous 

 properties, so that the rupture of the film does not necessarily follow. 



Electromotive force. The conditions of equilibrium may be modified 

 by electromotive force. Of such cases a galvanic or electrolytic cell 

 may be regarded as the type. With respect to the potentials for the 

 ions and the electrical potential the following relation may be noticed: 

 When all the conditions of equilibrium are fulfilled in a galvanic 

 or electrolytic cell, the electromotive force is equal to the difference in 

 the values of the potential for any ion at the surfaces of the electrodes 

 multiplied by the electro-chemical equivalent of that ion, the greater 

 potential of an anion being at the same electrode as the greater elec- 

 trical potential, and the reverse being true of a cation. 



The relation which exists between the electromotive force of a 

 perfect electro-chemical apparatus (i.e., a galvanic or electrolytic cell 

 which satisfies the condition of reversibility), and the changes in the 

 cell which accompany the passage of electricity, may be expressed by 

 the equation 



d = (T-T f )de+tdri + dW G +dW P , (30) 



in which de denotes the increment of the intrinsic energy in the 

 apparatus, dq the increment of entropy, de the quantity of electricity 

 which passes through it, V and V" the electrical potentials in pieces 

 of the same kind of metal connected with the anode and cathode 

 respectively, dW Q the work done by gravity, and dW P the work done 

 by the pressures which act on the external surface of the apparatus. 

 The term dW Q may generally be neglected. The same is true of dW P , 

 when gases are not concerned. If no heat is supplied or withdrawn 



