IX] OF THE NASSELLARIAN SKELETON 713 



by the boundary-edges of a tetrahedral cluster of four co-equal 

 bubbles; and just as Plateau extended his experiment by blowing 

 a small bubble in the centre of his tetrahedral system, so we have 

 a central bubble also here. 



This bubble may be of any size*; but its situation (if it be 

 present at all) is always the same, and its shape is always such 

 as to give the Maraldi angles at its own four corners. The tensions 



A B 



Fig. 329. Diagrammatic construction of Callimitra. A, a bubble suspended within 

 a tetrahedral cage. B, another bubble within a skeleton of the former bubble. 



of its own walls, and those of the films by which it is supported Or 

 slung, all balance one another. Hence the bubble appears in plane 

 projection as a curvihnear equilateral triangle; and we have only 

 got to convert this plane diagram 

 into the corresponding sohd to obtain 

 the spherical tetrahedron we have 

 been seeking to explain (Fig. 329). 



We may make a simpHfied model 

 (omitting the central bubble) of the 

 tetrahedral skeleton of Callimitra, after 

 the fashion of that of the bee's cell 

 (p. 535). Take OC =^ CD = DB, and 

 draw a circle with radius OB and 

 diameter AB. Erect a perpendicular Fig. 330. Geometrical construction 



to AB at C, cutting the circle at E, F. °^ Callimitra-sl.eleton. 



AOE, ^Oi^ will be (as before) Maraldi angles of 109°; the arcs AE, 



* Plateau introduced the central bubble into his cube or tetrahedron by dipping 

 the cage a second time, and so adding an extra face-film; under these circum- 

 stances the bubble has a definite magnitude. 



