Page:Popular Science Monthly Volume 36.djvu/640

 assume the form of Fig. 2. The twelve films from the edges of the cube meet a square unsupported plate of film in the center.

With No. 2 still on the frame, dip it again into the suds. You catch a bubble by doing this which goes at once to the center (Fig. 3), and forms such a cube as existed at the center of Fig. 1,



only large enough to show the curvature of the films necessary to make them meet at their fixed angle. The laws of films formulated are as follows: 1. From each wire edge of a frame proceeds a film. Generally, if care be taken, no air will be inclosed, then every film will be in contact with the surrounding air on both its faces. 2. Only three films can meet at any liquid edge. 3. When several liquid edges terminate in one point in the interior of the system, the edges are always four in number, and the angles included between them are equal. 4. Whenever the films can fulfill these conditions, and remain plain films, they are so; when they can not, they are curved, but so curved that their mean curvature is null—that is, if in one part of the film the law of its union requires an upward curvature, in some other portion there will be an equal downward curvature to compensate for it. In the films upon the cube frame, for instance, there is a slight curvature, just enough to enable them to meet each other on the angle of 120°. This is a very simple digression from the plane form, but in many other frames the divergence is very marked; for instance, in the triangular pyramid (Fig. 4) with wires dividing each side, after a bubble has been entrapped by a second dip, the curvature is very remarkable.

Plateau, the blind philosopher of Ghent, first studied this subject and formulated these laws. He began his studies with some experiments far removed from our films. In order to get some idea of the interaction of the molecular forces, he removed a mass of liquid matter he was observing, as far as he could, from the action of the physical forces. Using the well-known principle that a submerged body sinks till it has displaced its own weight of the fluid in which it is immersed, he made a