TRANSACTIONS OF THE SECTIONS. 7 



ing- from the wires, and united to a plane quadrangular film in the centre. When 

 this vertical film was blown upon, M. Von Rees observed that it was reduced to 

 a line, and then reproduced in a horizontal position, from which it could be blown 

 again into a ^■ertical position. 



If wo suppose the quadrangular film removed, and all the twelve films radiating 

 from the centre of the cube. Professor Plateau found that such a system could not 

 be kept in equilibrium, unless there was something solid in the central point, such 

 as the end of a wire or a drop of fluid. 



In repeating these experiments the author found that, after converting the hori- 

 zontal into the vertical quadrangular film, and continuing the blowang, he produced 

 the radial sj-stem of films, which in an instant returned to the system with a ver- 

 tical film, and then into the system with the horizontal film. 



M. Von Kees had foimd that, by immersing the wire cube with the normal poly- 

 hedron a few millimetres in the soap -solution, the film formed on its lower face, 

 imprisoned the air in the quadrangidar pyramid above it, and that this air rose to 

 the centre of the cube, and replaced the quadrangular plane with a hollow cube 

 with curved faces. 



In this beautiful experiment the hollow cube is invariable in size, being neces- 

 sarily equal in its contents to one-fourth part of the -ss-ire cube. The author of the 

 present paper discovered a method of inserting a hollow cube of any magnitude in 

 the centre of the polyhedron. This was done by blowing a bubble of the requisite 

 .size, and introducing it within the wire cube. He succeeded also by this means in 

 inserting a second hollow cube beside the first, the side common to both being 

 plane wlien the two cubes were equal, convex when the one was less, and concave 

 when it was greater than the other. In such a system, which is in perfect equili- 

 brium, the number of films is niiiehvii. He found also that two hollow solid figures 

 could, Ijy the same means, be inserted in the other systems of films which Professor 

 Plateau had discovered in a wire tetrahedron, or a quadrangidar pj^amid, or a 

 regular octahedron, or a rectangular prism, or in a system obtained from two rectan- 

 gidar planes fixed at right angles to each other. 



This last and interesting system consists of four cm-ved films extending from each 

 vertical wire, and connected with an elliptical film in the common section of the 

 rectangles. The major axis of this film is four times greater than its minor axis, 

 and it is placed in the angle, which is a little greater than 90°, but sometimes also 

 in the other angle. 



By making this system of wires moveable, so that the rectangular planes can pass 

 froni'DO^to 180=, the author obtained some singular results. As the angle increased 

 from 90°, the minor axis of the elliptical film increased, till when it approached to 

 180° it was nearly circular, appropriating gradually the fluid of the four curved 

 films attached to the wires. 



By again diminishing this angle the almost circular film became more and more 

 elliptical, till it reached its normal state at 90°, giving back to the curved films the 

 fluid which formed them. If the angle of the rectangular plane which contains 

 the elliptical film is diminished, the film will grow more elliptical, and at 45° will 

 become a straigU line, giving up its fluid to the other four iilms. At this instant 

 the whole system changes, the oval film being reproduced in the angle of 135° ! 



Remarkable as this phenomenon is, there is one still more remarkable, which 

 requires the testimony of the eye to make it credible. If when tlie rectangles are 

 inclined 90° we blow upon the elliptical film a bubble of such a size as to replace 

 the system of films with a hollow curvilineal cube, and wait till it bursts, the si/4cm 

 of liquid Jilms u'hich it c.vpelled vill reappear, as if it had left its (/host behind it to 

 recorer the elements ichich the luhble had appropriated ! 



By uniting the upper and lower ends of all the wires in this system, and also by 

 uniting tlie wires at various points in their length, the author obtained a number 

 of beautiful and complex systems of films, which require numerous diagrams to 

 make them intelligible. 



After treating of the equilibrium of liquid films, as seen in the union of spherical 

 bubbles and other hollow solids, the author considers the formation of plaue,_ con- 

 vex, and conca^-e films upon the mouths of open and closed vessels of different 

 shapes, and their deposition on the same vessels from bubbles ; and he describes 



