256 WITHDRAWN FROM THE ACTION OF GRAVITY. 



Henry,* that the cohesion of liquids is not of the same order with that of solids ; 

 it will be understood, therefore, that when the distance m n is so far reduced that 

 its further diminution cannot be effected with a rapidity nearly equal to that of 

 the ascension of the summit of the bubble, the liquid will still present m m n 

 much too great a resistance to the disunion of its molecules to be forced asunder, 

 and that hence it will be lifted up by the bubble under the shape of a film ; and 

 as this film, during its generation, is pressed from below upwards by the bubble 

 of air, and adheres by its circumference to the liquid of the vessel, it must be 

 convex towards the exterior. After the film has commenced forming, it must 

 become still more developed : for, incessantly pressed by the bubble of air, it 

 must continue to rise, while the liquid to which its circumference adheres cannot 

 follow it in mass on account of its weight ; this liquid must, therefore, remain 

 behind ; but, by virtue of the cohesion and viscosity, there can be no rupture 

 between the incipient film and the environing liquid, and the film will simply 

 increase until the action from below upAvard exerted on the lower part of the 

 bubble of air shall have had its whole effect. Mr. Hagen,t who has sought to 

 prove, contrary to the principle established by Poisson in his new theory oj 

 capillary action, that the density of the superficial stratum of liquids is greater 

 than that of their interior, cites, in support of his opinion, the fact of the forma- 

 tion of the films in question; but we see that is not at all necessary to resort to 

 such an hypothesis in order to account for this formation. 



In § 25 of the first series it was said that when a mass of oil a little less dense 

 than the alcoholic liquid in which it is immersed rises to the surface of the latter, 

 it is at first more or less flattened against that surface, as if encountering resist- 

 ance in traversing it; that after some time it makes its way through, and then 

 presents a portion of plane surface more or less extended on a level with that of 

 the alcoholic liquid. This phenomenon is now explicable in a natural manner 

 from the considerations which precede : it fares with the sphere of oil as with 

 the bubble of air ; it can only make its way to the exterior by disuniting the 

 molecules of the upper stratum of the ambient liquid, but this not growing thin 

 with sufficient rapidity on account of its viscosity, resists a rupture by virtue of 

 its cohesion; Only it is plain that, in this case, the pellicle cannot be elevated 

 above the level. 



§ 2. Let us recur to our convex film developed by the ascension of a bubble 

 of air. When it has attained its full development, and hence remains stationary, 

 it should assume (5 series, § 12) one of the figures of equilibrium which would 

 correspond to the surface of a liquid mass without gravity ; now this figure, 

 which is formed by an equal action in all azimuths around the vertical axis of 

 the air bubble, must evidently be one of revolution, and, as it is closed on the 

 axis, it can only constitute (IV, § 2) a portion of a sphere. What, now, does 

 theory teach tis on the extent of this portion relatively to the complete sphere ? 

 As regards molecular action, the superficial stratum of a full liquid mass may, ■ 

 as we know, be assimilated to a stretched membrane ; our liquid film, which is 

 obviously reduced to the superficial strata of its two faces, may therefore be 

 likened to a stretched membrane, and consequently has a tendency to occupy 

 the least possible extent. The question, then, if we neglect certain particulars 

 of which I shall presently speak, and which have no sensible influence when the 

 volume of air is somewhat large, is reduced to this : what, for a given volume, 

 is the segment of a sphere whose surface is smallest ? This problem is readily 

 solved by calculation, and we thus find that the segment in question is a hemis- 

 phere; but we reach the same result still more simply by the following reason- 

 ing, for the idea of which I am indebted to M. Lamar le. 



Let us conceive any two spherical segments, equal as regards one another, and 



* Philosophical Magazine, ]845, vol. xx, p. 541. 



t Vthcr die, Ob'-rfidchcn der FlussigkeAten (Ann. de M. Poggendorf, 1846, vol. LXVII, p. 1 .) 



