J. AW. Gibbs—Equilibrium of Heterogeneous Substances. 457 
elations given above that, when a film has more than one com- 
ponent those components which diminish the tension will be 
found in greater proportion on the surfaces. When the film is 
extended, there will not be enough of these substances to keep 
up the same volume- and surface-densities as before, and the 
deficieney will cause a certain increase of tension. It does not 
follow that a thinner film has always a greater tension than a 
thicker formed of the same liquid. When the phases 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 ten- 
sion. 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 reaiaiaict 
evaporation, its tension may be either increased or diminish 
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 inequali- 
ties 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 sorta described seems to be 
manifested in the breaking out of the black spots. But the 
sudden diminution in thickness which takes place in parts o 
the film is arrested by some unknown cause, possibly by vis- 
cous or gelatinous properties, so that the rupture of the film 
does not necessarily follow. 
Hlectromotive force.—The conditions of equilibrium may be 
modified by electromotive force. Of such cases a galvanic or 
eectrolytic vell may be regarded as the type. With respect to 
€ potentials for the ae ene the electrical potential the fol- 
lowing relation may be n 
When all the conditions « e atheiais are fulfilled in a galvanic 
r electrolytic cell, the eectromotive force is equal to the difference in 
the values of the potential for any ton at the surfaces of the electrodes 
Multiplied by the depo Haack equivalent of that 10n, the greater 
potential of an anion bang at the same electrode as uh elec- 
trical potential, and the reverse being true of a 
The relation which exists between the decisis force of 
a perfect electro- chemical apparatus (i, €., & ga alvanic or electrolytic 
cell which satisfies the condition at reversibility,) and the 
changes in oe cell which accompany the passage of electricity, 
May be expressed by the equation 
dex (VV) de tay taWet BW (80) 
