510 SIR DAVID BREWSTER ON THE FIGURES OF 



5th. By uniting the middle and the upper ends of the wires. In this case the 

 system shown in Figs. 25, 26 consists of twenty-four films. 



6th. When the middle and the lower ends of the wires are united. In this case 

 the system shown in Figs. 27 and 28 consists of twenty-four films, and is the pre- 

 ceding one inverted. 



7th. When the wires are united at several points successively from their lower 

 ends, till they approach the position of the second system, in Figs. 19, 20, the fluid 

 never reaches the four triangles at the top. In this case the films are eight in 

 number in Figs. 29 and 30, and nine in Figs. 31 and 32. The curved films in Fig. 

 29 are changed into plane ones in Fig. 30 by raising the movable wire ; andby 

 raising it higher, a portion of a plane elliptical film is added beneath the quad- 

 rangular pyramid, and this film increases in altitude till the movable wire 

 reaches the top, when the whole figure is similar to that in Figs. 19 and 20. 



Professor Plateau has given the figure of equilibrium in an equilateral trian- 

 gular prism when its height is equal to one of its sides. It is very simple, con- 

 sisting only of eight films, as shown in Fig. 33. By dividing its height by means 

 of a movable equilateral triangle, I have obtained very curious figures. When 

 the movable wire bisected the height of the prism, I obtained two different 

 figures — the one as frequently as the other, and yet they had not the slightest 

 relation to each other. The most careful adjustment of the movable triangle 

 did not help me to determine which of the two belonged to the bisection. I 

 found, however, upon dividing the height of the prism unequally, that the one 

 figure belonged to the larger, and the other to the smaller half — the prism, in the 

 position of indifference, being guided in its choice of figure by some trifling cause 

 which I failed to ascertain. These figures are shown in Figs. 34, 35, 36, 37, 38, 

 39, 40, 41, and 42. 



Having obtained such curious systems of films by dividing the equilateral 

 prism into portions of different lengths, I was anxious to see the effects produced 

 in the triangular and quadrangular pyramids by wires passing from their apex to 

 the middle of the sides of their base. 



The systems of films produced in the triangular pyramid are shown in 

 Figs. 43, 44, 45, 46, 47, where the hexagonal figures are very beautiful. The 

 hexagonal faces are plane, convex, or concave, according as the contents of the 

 hollow figures which they separate are equal or unequal — the face being generally 

 concave. A view of the hexagons, as seen by looking down through the apex of 

 the system, is shown in Fig. 46, while Fig. 47 represents them as seen by looking 

 upwards through the base of the pyramid. The curves of contrary flexure, and 

 the convex ones joining the films adhering to the six vertical curves, and the 

 curved films which they bound, are not easily represented by simple lines. 



The systems of films produced in the quadragular pyramid are similar to those 

 in the triangular pyramid, the figures being octogonal in place of hexagonal, as 

 shown in Fig. 48. 



