. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS WITHDRAWN FROM THE ACTION OF GRAVITY. BY J. [Continued from page 435, Report for 1865.] SIXTH SERIES. Theory of liquid jilms. Laics of films. Constitution of froth. Generation of films. Production of films hy frame-work. § 1. Let us prosecute the study of liquid films commenced in the second and continued in the fifth series. In § 2S of the second series I regarded the gene- ration of fi
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS WITHDRAWN FROM THE ACTION OF GRAVITY. BY J. [Continued from page 435, Report for 1865.] SIXTH SERIES. Theory of liquid jilms. Laics of films. Constitution of froth. Generation of films. Production of films hy frame-work. § 1. Let us prosecute the study of liquid films commenced in the second and continued in the fifth series. In § 2S of the second series I regarded the gene- ration of films as being due to a tendency towards a new figure of equilibrium. I now abandon that opinion, at least in part; though still believing that in the case where gravity does not intervene, the system, when the films are once produced, tends towards the new state of equilibrium which I have indicated. I consider the formation of the films itself as a result of the cohesion and viscosity of the liquid. Let us examine the matter somewhat more closely. We first take a very simple example, that of the film in shape of a spherical cap developed on the surface of a liquid by a bubble of air which has ascended from the interior of the liquid. Let U3 consider this bubble at the moment when it is within only a few milli- metres of the surface, (Fig. 10. *) In order that its summit shall traverse the distance m n which intervenes, the liquid molecules situated around this little right line must neces- sarily be driven toward every azimuth at once, in such man- ner that these molecules shall undergo relative displace- ments. Let us suppose, for simplification, that the ascen- sional movement of the bubble of air is uniform, so that, in equal intervals of time, the bubble shall propel, between itself and the upper surface of the liquid, equal quantities of this liquid. Let us further suppose that the liquid has no viscosity. Then, in proportion as the distance m n diminishes, the portions
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