1918] 



on Studies on Liquid Films 



;;si 



The groups of six, seven and eight nil luive the same type of 

 symmetry — namely, at the centre is a small plane polygon, from the 

 sides of which there radiates a ring of bubble segments, equally 

 spaced, with two others on an axis at right-angles to the central 

 plane. The six-group therefore has a ring of four segments round a 

 square central plane, the two others being on opposite sides of this 

 central plane. The two interlocked Ijubble segments thus take the 

 form of two truncated square pyramids in contact with each other 

 on the central square plane, having their bases bulged out on the 

 spherical contour, and the four other segments built in round the 



Fig. 22. 



faces of the truncated pyramids (Fig. '21a). The section of this is 

 shown in the central group of Fig. 20. The groups of seven and 

 eight are similarly formed, except that the square central plane is 

 replaced by a pentagon and hexagon respectively. In all cases the 

 polygon edges are slightly curved." Fig. '21d is a photograph of the 

 seven-group with pentagon centre. The wire frames for this group 

 and the eight-group with hexagon centre are shown in Fig. '2'^, 

 while sections through the two are given in Fig. 23. 



These " sections " are in reality photographs of the half groups 

 when formed on a horizontal glass plate (4 inches square). A 

 fountain-pen filler was used to make the equal half bubbles, by 



