J. W. Gibbs — Equilibrium of Heterogeneous Substances. 475 



The difficulties of the quantitative experimental verification of the 

 properties which have been described would be very great, even in 

 cases in which the conditions we have imagined were entirely ful- 

 filled. Yet the general effect of any divergence from these condi- 

 tions will be easily perceived, and when allowance is made for such 

 divergence, the general behavior of liquid films will be seen to agree 

 with the requirements of theory. 



The formation of a liquid film takes place most symmetrically 

 when a bubble of air rises to the top of a mass of the liquid. The 

 motion of the liquid, as it is displaced by the bubble, is evidently 

 such as to stretch the two sm-faces in which the liquid meets the air, 

 where these surfaces approach one another. This will cause an 

 increase of tension, which will tend to restrain the extension of the 

 surfaces. The extent to which this effect is produced will vary with 

 the nature of the liquid. Let us suppose that the case is one in 

 which the liquid contains one or more components which, although 

 constituting but a very small part of its mass, greatly reduce its ten- 

 sion. Such components will exist in excess on the surfaces of the 

 liquid. In this case the resti'aint upon the extension of the surfaces 

 will be considerable, and as the bubble of air rises above the general 

 level of the liquid, the motion of the latter will consist largely of a 

 running out from between the two surfaces. But this running out of 

 the liquid will be greatly retarded by its viscosity as soon as it is 

 reduced to the thickness of a film, and the effect of the extension of 

 the surfaces in increasing their tension will become greater and 

 more permanent as the quantity of liquid diminishes which is avail- 

 able for supplying the substances which go to form the increased sur- 

 faces. 



We may form a rough estimate of the amount of motion which is 

 possible for the interior of a liquid film, relatively to its exterior, by 

 calculating the descent of water between parallel vertical planes at 

 which the motion of the water is reduced to zero. If we use the 

 coefficient of viscosity as determined by Helmholtz and Piotrowski,* 

 we obtain 



V— 581 Z>2, (656) 



where V denotes the mean velocity of the water [i. e., that velocity 



* Sitzungsberichte der Wiener Akademie, (mathemat.-natnrwiss. Classe), B. xl, S. 

 607. The calculation of formula (656) and that of the factor (|) applied to the formula 

 of Poiseuille, to adapt it to a current between plane surfaces, have been made by 

 means of the general equations of the motion of a viscous liquid as given in the 

 memoir referred to. 



