304 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



extension increases the tension of a film and contraction diminishes 

 it. When a plane film is held vertically, the tension of the upper 

 portions must evidently be greater than that of the lower. The 

 tensions in every part of the film may be reduced to equality by 

 turning it into a horizontal position. By restoring the original 

 position we may restore the original tensions, or nearly so. It is 

 evident that the same element of the film is capable of supporting 

 very unequal tensions. Nor can this be always attributed to viscosity 

 of the film. For in many cases, if we hold the film nearly horizontal, 

 and elevate first one side and then another, the lighter portions of 

 the film will dart from one side to the other, so as to show a very 

 striking mobility in the film. The differences of tension which cause 

 these rapid movements are only a very small fraction of the difference 

 of tension in the upper and lower portions of the film when held 

 vertically. 



If we account for the power of an element of the film to support 

 an increase of tension by viscosity, it will be necessary to suppose 

 that the viscosity offers a resistance to a deformation of the film in 

 which its surface is enlarged and its thickness diminished, which is 

 enormously great in comparison with the resistance to a deformation 

 in which the film is extended in the direction of one tangent and 

 contracted in the direction of another, while its thickness and the 

 areas of its surfaces remain constant. This is not to be readily 

 admitted as a physical explanation, although to a certain extent the 

 phenomena resemble those which would be caused by such a singular 

 viscosity. (See page 274.) The only natural explanation of the 

 phenomena is that the extension of an element of the film, which 

 is the immediate result of an increase of external force applied to 

 its perimeter, causes an increase of its tension, by which it is brought 

 into true equilibrium with the external forces. 



The phenomena to which we have referred are such as are apparent 

 to a very cursory observation. In the following experiment, which 

 is described by M. Plateau,* an increased tension is manifested in a 

 film while contracting after a previous extension. The warmth of a 

 finger brought near to a bubble of soap-water with glycerine, which 

 is thin enough to show colors, causes a spot to appear indicating 

 a diminution of thickness. When the finger is removed, the spot 

 returns to its original color. This indicates a contraction, which 

 would be resisted by any viscosity of the film, and can only be due 

 to an excess of tension in the portion stretched, on the return of its 

 original temperature. 



We have so far supposed that the film is thick enough for its 



* Statique. expdrimentale et thdorique des liquides soumis aux seules forces moltculaires, 

 vol. i, p. 294. 



