1918] on Studies on Liquid Films 389 



The truncated trianii-ular films joining the vertical edges of the 

 cube to the central (hexagon) plane then become very short. In 

 Fig. 27 (a) they are shown by K a a! A' and ^ h h' B', while in 

 Fig 27 {h) the other two are shown by Q b h' C, and hj J} b h' D' 

 behind. All four are shown in profile in Fig. 27 {c) by the lines 

 A^^, D «, B ^ and C b. The kite-shaped planes from the apices and 

 0' of the divided octahedron are Fig. 27 {b) d e e and 0' d' c d, 

 which in Fig. 27 («) are only seen in profile — i.e. perpendicular to the 

 central irregular hexagon a c b V c' d . 



The edges of the two pvramids (half-ocfcahedrons) being A, 

 OB, C, D, 0' A', 0' B', 0' C, 0' D', then the triangular films 

 drawn in from four upper edges are in Fig. 27 («) and (Jj) Af/, 

 B r/, C e and D e behind C e. Similarly for the four lower 

 edges. These triangular films also seen foreshortened in Fig. 27 (c) 

 are indicated by the same letters. 



From the upper horizontal edges of the cube there also spring 

 four triangular films in two pairs, matched on opposite sides ; those 

 from the side edges A I), B 0, Fig. 27 (c), go down to the central 

 hexagon at a and b. Fig. 27 («), while those from the front and back 

 edges A B, DC, join up to the kite-shaped plane at d and e, 

 Fig. 27 (^). The four films are thus shown in Fig. 27 (c) by A D a, 

 B C &, and A B f/, DC e. The same is repeated from the four lower 

 edges of the cube. A' B', B' C, etc. There then remain two pairs of 

 quadrilateral films linking the kites and the hexagon to the triangular 

 films from the edges. These last are represented by Kdca, Bdcb, 

 in Fig. 27 (a), and Gecb in Fig. 27 (c) ; the other would be Deed 

 behind Cecb. The same is repeated on the lower edges. 



The whole complex thus numbers 81 films : 12 from the cube 

 edges, 8 from the pyramid edges, and 8 quadrilateral films, together 

 with the kite-shaped pair and the irregular hexagon forming the 

 backbone of the figure. 



EXTEXSIBILITY OF COLUMNS. 



When groups of l)ubbles are first formed the films of which they 

 are constituted are rather thick, because as a rule the segments 

 are not expanded to any great size. Owing, however, to the free 

 drainage down the intersecting channels, the excess liquid rapidly 

 accumulates in the lower segments, and the weight thus localised 

 distorts or breaks the group. 



Some measures were therefore made of the elongations produced 

 by added weights in various forms. In a single column it can be 

 seen that the upper segments are longer than those lower down ; 

 with additional loading the extension increases until parting takes 

 place. This is illustrated in Fig. 28 (which is drawn to scale). A 

 column of 13 bubbles is shown at (a) when freshly blown with air 

 containing 7 per cent, of hydrogen. After the hydrogen had diffused 



