EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 307 



not due to viscosity, or to a horizontal position, or to differences of 

 temperature, it must have more than one component of which the 

 potential is not determined by the contiguous gas- masses in accordance 

 with (617). 



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 

 fulfilled. Yet the general effect of any divergence from these 

 conditions 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 

 Huch as to stretch the two surfaces 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 

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

 liquid. In this case the restraint 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 

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

 reduced to tlm thickness of a film, arid Uio nH'w.t of Ui; ^xf^nsion of 

 tlm surfaces in increasing their tension will become greater and 

 more permanent as the quantity of liquid diminishes which is 

 available for supplying the substances which go to form the increased 

 surfaces. 



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 - 7=5811>!j (656) 



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



* Sitzunfftberichte der Wiener A kademie (mathemat.-naiurunwi. Clause), B. xl, H. 007. 

 Tli*! calculation of formula (65fi) and that of the factor (fl) applied to the formula of 

 PoiHOuille, to adapt it to a current between plane HurfaocH, have been made by meaiut 

 of the general equation!) of the motion of a VIBOOIUI liquid OH given in the memoir 

 referred to. 



