506 SIR DAVID BREWSTER ON THE FIGURES OF 



and after continuing a very short time in that state, it returned into the system 

 of Fig. 1, and then into the original system of Fig. 2. In one experiment it became 

 permanent, as in fig. 1, and did not pass into Fig. 2. In several experiments the 

 system in Fig. 3 remained permanent, with a drop of fluid in the centre, as observed 

 by Plateau, but upon examining it with the microscope, it turned out to be a 

 hollow cube, which, as we shall presently see, forms with twelve tilms a system of 

 stable equilibrium. 



If we make these experiments with a wire rhomb, the same results will be 

 obtained with such differences as might be expected from the inclination of the 

 films to each other. 



When M. Van Rees had produced the normal polyhedron shown in Fig. 1, he 

 happened to dip the lower part of the wire cube into the solution to the depth of 

 some millimetres, and upon lifting it out again, he obtained the beautiful system 

 shown in Fig. 4, where the quadrangular film is replaced with a hollow cube, all 

 the faces of which are curved. When the wire cube is thus dipped into the fluid, 

 a film, as M. Plateau observes, is formed on its lower square. This film im- 

 prisons the air between itself and the oblique faces of the polyhedron imme- 

 diately above it, and rising, forms the hollow cube shown in the figure. 



As the new film which produces this effect is coincident with the lower face 

 of the wire cube, the hollow cube which it generates must be invariable in 

 size, containing the same quantity of air which is imprisoned in the lower por- 

 tion of the polyhedron ; that is, the contents of the hollow cube must always 

 be equal to one-fourth of the contents of the wire cube. 



In repeating this experiment, which does not always succeed, I discovered a 

 general method of introducing into the normal polyhedron hollow cubes of any size, 

 from the smallest to a size which nearly fills the whole interior of the wire cube. 

 This is done by blowing a bubble of the requisite size, and placing it in the central 

 quadrangle of the polyhedron. The bubble instantly starts into a hollow cube, 

 containing the same quantity of air as the bubble, obliterating the quadrangular 

 film, and forming a system of perfect equilibrium. If the cube is smaller than 

 we wish it to be, we can enlarge it by introducing another bubble. As hollow 

 cubes of every size form a system in perfect equilibrium, we see the reason why 

 the microscopic cube, already mentioned, kept the system shown in Fig. 3 in stable 

 equilibrium. 



By the same method we may introduce a second hollow cube beside the first, 

 displacing it from the centre of the polyhedron, and, along with it, taking up a 

 symmetrical position of equilibrium, as shown in Fig. 5. The two cubes are not 

 necessarily equal, but when they are so, the side common to both, and passing 

 through the centre of the polyhedron, is perfectly plane, while all the other sides 

 are curved. The second cube may be inserted on the right or left side of the 

 first, as well as above or below it ; but it sometimes happens that the bubble 



