EQUILIBRIUM IX LIQUID FILMS. 507 



intended to produce it passes into the first cube and enlarges it, instead of taking 

 its place beside it. 



This method of inserting one or two hollow solids of any size in the figures of 

 equilibrium of liquid films, may be extended to the different figures discovered 

 and described by Professor Plateau. I have applied it successfully, as shown 

 in Figs. 7, 10, 11 ; Figs. 6, 8, 9, 12, being the figures given by Plateau ; and also, 

 as shown in Figs. 14, 15, to a remarkable system of wires, shown in Fig. 13, 

 &c. &c. which had not previously been the subject of experiment. 



In Fig. 6, where the wires form a tetrahedron, the bubble is introduced at the 

 centre where the four films meet, and the double three-sided hollow figure 

 which is thus produced is shown in Fig. 8. 



In Figs. 8 and 9, given by Plateau, where the wires form a quadrangular pyra- 

 mid, the bubble is introduced where the vertical line or film joins the other four, 

 and the single and double quadrangular figures thus produced are shown in Figs. 

 9, 10, and 11. 



In Fig. 12. given by Plateau, where the wires form two rectangles cut- 

 ting one another at right angles, a plane film, of nearly an elliptical shape, is 

 formed in the centre. It is inclined 45° to the planes of the rectangles, and is 

 attached by each of its sides to twocurvilineal films, which adhere to the four 

 vertical wires. The figure is thus composed of Jive films, one plane and/owr of a 

 singularly curvilineal form, as in Fig. 13. The hollow quadrangular figures pro- 

 duced by introducing one or more bubbles into the centre of this elliptical film, 

 or between the curvilineal films, in Fig. 13, is shown in Figs. 14 and 15. 



In all these systems of films, when two hollow figures are united, whether 

 they be spheres, lenses, cubes, or any other irregular figures, the film which 

 unites them is plane if the contents of the two hollow figures be equal, and con- 

 cave and convex if their contents are unequal — the convex side being always within 

 the largest figure. 



Professor Plateau does not appear to have studied the singular effects pro- 

 duced by constructing the system of wires, in Fig. 12, so as to vary the angle 

 formed by the two rectangular planes. With such a movable system we see at 

 once why the elliptical plane is formed between two of the pairs of right angles, 

 rather than between the other pair, for it must necessarily appear between the 

 pair whose angle is greater than 90°; and as it is impossible to join the rect- 

 angles with mathematical accuracy at right angles to each other, the oval 

 plane should appear only between the wires whose inclination is greater than 

 90°. This is true only when the rectangles are lifted perpendicularly out of 

 the soap solution ; for if they are lifted out obliquely, the oval film will be 

 formed in the angle which is uppermost, whether that angle is greater or less 

 than 90°, provided that the difference of the angles is not great. In the nor- 

 mal position of the rectangles perpendicular to each other, the major axis of the 



