EQUILIBRIUM IN LIQUID FILMS. 511 



The figures of equilibrium of liquid films are finely seen in the union of spheri- 

 cal bubbles and hollow lenses. When two spheres are brought into contact they 

 are united by a film common to both.* When the one is laid above the other, the 

 lower part of the upper one starts into union with the upper part of the lower one, 

 and forms a single circular film. If the upper sphere is retained by the pipe that 

 blows it, it may be rotate upon the other, as upon a joint, without any change in 

 the uniting film. If we now blow through this pipe we can enlarge the upper 

 sphere, and if we suck through it, we can diminish it ; so that we can at pleasure 

 make the two spheres equal or unequal. When the upper sphere is equal to the 

 lower, the uniting film is a circular plane. When it is greater than the lower, 

 the uniting film is convex, and when it is less, the uniting film is concave^ the con- 

 vex side being always turned to the larger sphere, f 



When two lenses are united by a film, the film is plane, convex, and concave, 

 according as the one lens is equal to, or greater and less than the other. A double 

 and equally convex lens may be formed at pleasure, as we shall presently see ; 

 but I have not been able to bring the lenses into union. They are, however, 

 frequently found in that position in experiments with the wire cube. 



The production of plane, convex, and concave films by the union of two 

 bubbles, and the protection of these films from aerial currents by the superincum- 

 bent bubble, I found of great use in studying the colours which they produced. 



The formation of films, by immersion, upon open and closed vessels of different 

 shapes, their deposition on the same vessels from bubbles, and their motion within 

 certain vessels, which I believe has never been observed, present many curious 

 phenomena. 



When a film is formed by immersion on the rim of a closed cylindrical vessel 

 it is generally plane, but sometimes concave, and rarely convex ; but in all cases 

 it may be made of any degree of convexity by the application of heat to the 

 vessel. When the vessel is open at both ends the film is always plane. 



When the film is formed on a closed cylindrical vessel by the deposition of a 

 bubble upon its rim, it is always plane. The bubble leaves the lower part of 

 itself upon the rim as a plane film, but quite separate from the rest of the bubble 

 which stands over it. 



If we use a thick metallic ring with a broad rim, which itself gives a plane 

 film by immersion, a bubble laid upon it deposits a concave film, which at first 

 appears to be the lower end of the bubble, but it is quite independent of it in 

 position, as the bubble rests upon the upper and outer side of the ring, while the 

 concave film adheres to the inner and lower end of the ring. They are, however, 

 so related to one another, that when the bubble bursts the concave films starts 



* See the preceding paper, p. 503. 



| The relation between the size of the spheres and the curvature of the uniting film was first 

 observed by M. Plateau. 



